Subgroups — C₃×#85854 #11909409

Order 1152.

2239 conjugacy classes of subgroups.

The subgroup lattice has 1370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₄×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#5829	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#5824	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5583	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5582	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#5581	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#5568	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#5564	C₂	1	2	yes	maximal, complemented
9	C₃×#5560	C₂	1	2	yes	maximal, complemented
10	C₃×#5556	C₂	1	2	yes	maximal, complemented
11	C₃×#5554	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#5546	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#5545	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#5540	C₂	1	2	yes	maximal, complemented
15	C₃×#5539	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#5533	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#5531	C₂	1	2	yes	maximal, complemented
18	C₃×#5530	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#5527	C₂	1	2	yes	maximal, complemented
20	C₃×#5479	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×#5479	C₂	1	2	yes	maximal, complemented
22	C₃×#5479	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₃×#876	C₂	1	2	yes	maximal, complemented
24	C₃×#3521	—	3	1	no	maximal
25	#85854	C₃	1	1	yes	maximal, characteristic, direct product factor
26	C₂×C₃²×#41	C₂²	1	1	yes	characteristic
27	C₂×C₃×#237	C₂²	1	1	yes	characteristic
28	C₂×C₃×D₃×D₄	C₂²	1	1	yes	characteristic
29	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
30	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
32	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
33	C₃²×C₄×D₄	C₂²	1	2	yes	complemented
34	C₃²×C₄×D₄	C₂²	1	2	yes	complemented
35	C₃²×#117	C₂²	1	2	yes	complemented
36	C₃²×#117	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₃²×C₄²	C₂²	1	2	yes	complemented
38	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic, complemented
39	C₃×#947	C₂²	1	1	yes	characteristic
40	C₃×#946	C₂²	1	1	yes	characteristic
41	C₃×#946	C₂²	1	1	yes	characteristic, complemented
42	C₃×#944	C₂²	1	1	yes	characteristic, complemented
43	C₃×#939	C₂²	1	2	yes	—
44	C₃×#939	C₂²	1	2	yes	complemented
45	C₃×#937	C₂²	1	2	yes	—
46	C₃×#935	C₂²	1	2	yes	complemented
47	C₃×D₄×Dic₃	C₂²	1	1	yes	characteristic
48	C₃×D₄×Dic₃	C₂²	1	1	yes	characteristic
49	C₃×#930	C₂²	1	1	yes	characteristic
50	C₃×#930	C₂²	1	2	yes	—
51	C₃×#930	C₂²	1	1	yes	characteristic
52	C₃×#929	C₂²	1	2	yes	—
53	C₃×#929	C₂²	1	1	yes	characteristic
54	C₃×#929	C₂²	1	2	yes	complemented
55	C₃×#929	C₂²	1	1	yes	characteristic, complemented
56	C₃×#929	C₂²	1	2	yes	complemented
57	C₃×C₄×#67	C₂²	1	1	yes	characteristic
58	C₃×C₄×#67	C₂²	1	2	yes	—
59	C₃×C₄×#67	C₂²	1	1	yes	characteristic, complemented
60	C₃×C₄×#67	C₂²	1	2	yes	complemented
61	C₃×C₄×#67	C₂²	1	2	yes	complemented
62	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
63	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
64	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
65	C₃×#924	C₂²	1	1	yes	characteristic, complemented
66	C₃×#924	C₂²	1	2	yes	complemented
67	C₃×#924	C₂²	1	1	yes	characteristic, complemented
68	C₂×C₃×Dic₃⋊C₄	C₂²	1	2	yes	complemented
69	C₂×C₃×Dic₃⋊C₄	C₂²	1	2	yes	complemented
70	C₂×C₃×Dic₃⋊C₄	C₂²	1	2	yes	complemented
71	C₃×#898	C₂²	1	2	yes	—
72	C₃×#898	C₂²	1	2	yes	complemented
73	C₃×#897	C₂²	1	1	yes	characteristic
74	C₃×#896	C₂²	1	2	yes	complemented
75	C₃×#896	C₂²	1	2	yes	complemented
76	C₃×#895	C₂²	1	1	yes	characteristic
77	C₃×#894	C₂²	1	2	yes	—
78	C₃×#894	C₂²	1	2	yes	complemented
79	C₃×#893	C₂²	1	1	yes	characteristic
80	C₃×#892	C₂²	1	1	yes	characteristic
81	C₃×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
82	C₃×#890	C₂²	1	1	yes	characteristic, complemented
83	C₃×#889	C₂²	1	2	yes	complemented
84	C₃×#889	C₂²	1	2	yes	complemented
85	C₃×#888	C₂²	1	1	yes	characteristic, complemented
86	C₃×#887	C₂²	1	1	yes	characteristic, complemented
87	C₃×#886	C₂²	1	2	yes	—
88	C₃×#885	C₂²	1	2	yes	—
89	C₃×#884	C₂²	1	2	yes	complemented
90	C₃×#883	C₂²	1	2	yes	complemented
91	C₃×#882	C₂²	1	2	yes	—
92	C₃×#67⋊C₄	C₂²	1	2	yes	—
93	C₃×#67⋊C₄	C₂²	1	2	yes	complemented
94	C₃×D₃×C₂²⋊C₄	C₂²	1	2	yes	—
95	C₃×#879	C₂²	1	2	yes	complemented
96	C₃×#878	C₂²	1	2	yes	complemented
97	C₃×#878	C₂²	1	2	yes	complemented
98	C₃×#877	C₂²	1	2	yes	complemented
99	C₃×#876	C₂²	1	2	yes	—
100	C₃×#876	C₂²	1	2	yes	—
101	C₃×#876	C₂²	1	2	yes	—
102	C₃×#876	C₂²	1	1	yes	characteristic
103	C₃×#876	C₂²	1	2	yes	complemented
104	C₃×#876	C₂²	1	2	yes	complemented
105	C₃×#876	C₂²	1	2	yes	complemented
106	C₃×#876	C₂²	1	2	yes	complemented
107	C₃×#876	C₂²	1	1	yes	characteristic, complemented
108	C₃×#875	C₂²	1	1	yes	characteristic
109	C₃×#875	C₂²	1	1	yes	characteristic
110	C₃×#875	C₂²	1	2	yes	complemented
111	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic
112	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic
113	C₃×C₄×D₁₂	C₂²	1	2	yes	complemented
114	C₃×#872	C₂²	1	1	yes	characteristic
115	C₃×#872	C₂²	1	2	yes	complemented
116	C₃×#872	C₂²	1	2	yes	complemented
117	C₃×#872	C₂²	1	1	yes	characteristic, complemented
118	C₃×#872	C₂²	1	2	yes	complemented
119	C₃×#870	C₂²	1	1	yes	characteristic, complemented
120	C₃×#870	C₂²	1	1	yes	characteristic, complemented
121	C₃×#870	C₂²	1	2	yes	complemented
122	C₃×C₄×Dic₆	C₂²	1	2	yes	complemented
123	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
124	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
125	C₃×#556	—	3	1	no	—
126	C₃×#556	—	3	1	no	—
127	C₃×#554	—	3	1	no	—
128	C₃×#553	—	3	2	no	—
129	C₃×#553	—	3	1	no	—
130	C₃×#552	—	3	1	no	—
131	C₃×#552	—	3	2	no	—
132	C₃×#551	—	3	2	no	—
133	C₃×#551	—	3	2	no	—
134	C₃×#547	—	3	1	no	—
135	C₃×#546	—	3	1	no	—
136	C₃×#546	—	3	1	no	—
137	C₃×#542	—	3	1	no	—
138	C₃×#541	—	3	1	no	—
139	C₃×#539	—	3	2	no	—
140	C₃×#538	—	3	2	no	—
141	C₃×#529	—	3	2	no	—
142	C₃×#529	—	3	1	no	—
143	C₃×#529	—	3	1	no	—
144	C₂×C₃×#126	—	3	2	no	—
145	C₃×#520	—	3	1	no	—
146	C₃×#518	—	3	1	no	—
147	C₃×C₄×#41	—	2	1	no	—
148	C₃×C₄×#41	D₃	1	1	yes	characteristic, complemented
149	C₃×C₄×#41	C₂×C₃	1	1	yes	characteristic, complemented
150	#5829	C₂×C₃	1	1	yes	characteristic, complemented
151	#5824	C₂×C₃	1	1	yes	characteristic, complemented
152	#5583	C₂×C₃	1	1	yes	characteristic, complemented
153	#5582	C₂×C₃	1	1	yes	characteristic, complemented
154	#5581	C₂×C₃	1	1	yes	characteristic, complemented
155	#5568	C₂×C₃	1	1	yes	characteristic, complemented
156	#5564	C₂×C₃	1	2	yes	complemented
157	#5560	C₂×C₃	1	2	yes	complemented
158	#5556	C₂×C₃	1	2	yes	complemented
159	#5554	C₂×C₃	1	1	yes	characteristic, complemented
160	#5546	C₂×C₃	1	1	yes	characteristic, complemented
161	#5545	C₂×C₃	1	1	yes	characteristic, complemented
162	#5540	C₂×C₃	1	2	yes	complemented
163	#5539	C₂×C₃	1	1	yes	characteristic, complemented
164	#5533	C₂×C₃	1	1	yes	characteristic, complemented
165	#5531	C₂×C₃	1	2	yes	complemented
166	#5530	C₂×C₃	1	1	yes	characteristic, complemented
167	#5527	C₂×C₃	1	2	yes	complemented
168	#5479	C₂×C₃	1	1	yes	characteristic, complemented
169	#5479	C₂×C₃	1	1	yes	characteristic, complemented
170	#5479	C₂×C₃	1	2	yes	complemented
171	C₂×#876	C₂×C₃	1	2	yes	complemented
172	C₂³×C₃×D₃	C₂³	1	2	yes	—
173	C₃²×#41	—	2	4	no	—
174	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
175	C₂×C₃²×D₄	C₂³	1	2	yes	—
176	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
177	C₂²×C₃²×C₄	C₂³	1	2	yes	—
178	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
179	C₂²×C₃²×C₄	C₂³	1	2	yes	—
180	C₂²×C₃²×C₄	C₂³	1	2	yes	—
181	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
182	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
183	C₂×C₃×#67	C₂³	1	2	yes	—
184	C₂×C₃×#67	C₂³	1	2	yes	—
185	C₂×C₃×#67	C₂³	1	2	yes	—
186	C₂×C₃×#67	C₂³	1	1	yes	characteristic
187	C₂×C₃×#67	C₂³	1	1	yes	characteristic
188	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
189	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
190	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
191	C₃×#237	—	2	4	no	—
192	C₃×D₃×D₄	—	2	4	no	—
193	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
194	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
195	C₂×C₃×D₁₂	C₂³	1	2	yes	—
196	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
197	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
198	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
199	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
200	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
201	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
202	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
203	C₂×C₃×Dic₆	C₂³	1	2	yes	—
204	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
205	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
206	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
207	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
208	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
209	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
210	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
211	C₃²×C₄²	C₂³	1	1	yes	characteristic
212	C₃²×C₄²	C₂³	1	2	yes	—
213	C₃²×C₄²	C₂³	1	1	yes	characteristic
214	C₃²×C₄²	C₂³	1	1	yes	characteristic
215	C₃²×C₄²	C₂³	1	1	yes	characteristic
216	C₃²×C₄²	C₂³	1	2	yes	—
217	C₃²×C₄²	C₂³	1	2	yes	—
218	C₃×#217	C₂³	1	2	yes	—
219	C₃×#217	C₂³	1	2	yes	—
220	C₃×#217	C₂³	1	1	yes	characteristic
221	C₃×#217	C₂³	1	2	yes	—
222	C₃×#217	C₂³	1	1	yes	characteristic
223	C₃×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
224	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
225	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
226	C₃×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
227	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
228	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
229	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
230	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
231	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
232	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
233	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
234	C₃×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
235	C₃×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
236	C₃×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
237	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
238	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
239	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
240	C₃×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
241	C₃×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
242	C₃×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
243	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
244	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
245	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
246	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
247	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
248	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
249	C₃×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
250	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
251	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
252	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
253	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
254	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
255	C₃×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
256	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
257	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
258	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
259	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
260	C₃×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
261	C₃×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
262	C₃×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
263	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
264	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
265	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
266	C₃×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
267	C₃×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
268	C₃×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
269	C₃×C₄×Dic₃	C₂³	1	2	yes	—
270	C₃×C₄×Dic₃	C₂³	1	2	yes	—
271	C₃×C₄×Dic₃	C₂³	1	2	yes	—
272	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
273	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
274	#3521	—	3	1	no	Sylow
275	C₂×C₃×#41	—	2	1	no	—
276	C₂×C₃×#41	—	3	1	no	—
277	C₂×C₃×#41	C₂×D₃	1	1	yes	characteristic
278	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
279	C₂²×C₃×D₄	—	3	1	no	—
280	C₂×#237	C₂²×C₃	1	1	yes	characteristic
281	C₂×D₃×D₄	C₂²×C₃	1	1	yes	characteristic
282	C₃×C₄⋊Q₈	—	3	1	no	—
283	C₃×C₄⋊Q₈	—	3	1	no	—
284	C₃×#126	—	3	2	no	—
285	C₃×#126	—	3	2	no	—
286	C₃×#126	—	3	2	no	—
287	C₃×#126	—	3	1	no	—
288	C₃×#126	—	3	2	no	—
289	C₃×#126	—	3	2	no	—
290	C₃×#126	—	3	2	no	—
291	C₃×#126	—	3	2	no	—
292	C₃×#126	—	3	2	no	—
293	C₃×#126	—	3	2	no	—
294	C₃×#126	—	3	2	no	—
295	C₃×#126	—	3	1	no	—
296	C₃×#125	—	3	2	no	—
297	C₃×#125	—	3	2	no	—
298	C₃×#125	—	3	1	no	—
299	C₃×#125	—	3	2	no	—
300	C₃×#125	—	3	1	no	—
301	C₃×#125	—	3	1	no	—
302	C₃×#124	—	3	1	no	—
303	C₃×#124	—	3	2	no	—
304	C₃×#124	—	3	2	no	—
305	C₃×#124	—	3	1	no	—
306	C₃×#124	—	3	1	no	—
307	C₃×#123	—	3	2	no	—
308	C₃×#123	—	3	2	no	—
309	C₃×#123	—	3	1	no	—
310	C₃×#123	—	3	2	no	—
311	C₃×#123	—	3	2	no	—
312	C₃×#123	—	3	1	no	—
313	C₃×#123	—	3	2	no	—
314	C₃×#123	—	3	2	no	—
315	C₃×#123	—	3	2	no	—
316	C₃×#123	—	3	2	no	—
317	C₃×C₂²⋊Q₈	—	3	1	no	—
318	C₃×C₂²⋊Q₈	—	3	1	no	—
319	C₃×C₂²⋊Q₈	—	3	1	no	—
320	C₃×C₂²⋊Q₈	—	3	1	no	—
321	C₃×C₂²⋊Q₈	—	3	2	no	—
322	C₃×C₂²⋊Q₈	—	3	2	no	—
323	C₃×C₂²⋊Q₈	—	3	2	no	—
324	C₃×C₂²⋊Q₈	—	3	1	no	—
325	C₃×C₂²⋊Q₈	—	3	2	no	—
326	C₃×C₂²⋊Q₈	—	3	2	no	—
327	C₃×#121	—	3	2	no	—
328	C₃×#121	—	3	2	no	—
329	C₃×#121	—	3	1	no	—
330	C₃×#121	—	3	1	no	—
331	C₃×#121	—	3	2	no	—
332	C₃×#121	—	3	1	no	—
333	C₃×#121	—	3	2	no	—
334	C₃×#120	—	3	2	no	—
335	C₃×#120	—	3	2	no	—
336	C₃×C₄×Q₈	—	2	1	no	—
337	C₃×C₄×Q₈	—	2	1	no	—
338	C₃×C₄×Q₈	—	3	1	no	—
339	C₃×C₄×Q₈	—	3	1	no	—
340	C₃×C₄×Q₈	—	3	2	no	—
341	C₃×C₄×Q₈	—	3	1	no	—
342	C₃×C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
343	C₃×C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
344	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
345	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
346	C₃×C₄×D₄	—	2	1	no	—
347	C₃×C₄×D₄	—	2	1	no	—
348	C₃×C₄×D₄	—	2	2	no	—
349	C₃×C₄×D₄	—	2	2	no	—
350	C₃×C₄×D₄	—	3	1	no	—
351	C₃×C₄×D₄	—	3	1	no	—
352	C₃×C₄×D₄	—	3	2	no	—
353	C₃×C₄×D₄	—	3	1	no	—
354	C₃×C₄×D₄	—	3	2	no	—
355	C₃×C₄×D₄	—	3	1	no	—
356	C₃×C₄×D₄	—	3	2	no	—
357	C₃×C₄×D₄	—	3	1	no	—
358	C₃×C₄×D₄	—	3	2	no	—
359	C₃×C₄×D₄	—	3	2	no	—
360	C₃×C₄×D₄	—	3	1	no	—
361	C₃×C₄×D₄	—	3	1	no	—
362	C₃×C₄×D₄	—	3	2	no	—
363	C₃×C₄×D₄	C₂×D₃	1	1	yes	characteristic
364	C₃×C₄×D₄	C₂×D₃	1	1	yes	characteristic
365	C₃×C₄×D₄	C₂×D₃	1	2	yes	complemented
366	C₃×C₄×D₄	C₂×D₃	1	2	yes	complemented
367	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
368	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
369	C₃×C₄×D₄	C₂²×C₃	1	2	yes	complemented
370	C₃×C₄×D₄	C₂²×C₃	1	2	yes	complemented
371	C₃×#117	—	2	2	no	—
372	C₃×#117	—	2	1	no	—
373	C₃×#117	—	3	1	no	—
374	C₃×#117	—	3	2	no	—
375	C₃×#117	—	3	1	no	—
376	C₃×#117	—	3	1	no	—
377	C₃×#117	—	3	2	no	—
378	C₃×#117	—	3	2	no	—
379	C₃×#117	—	3	2	no	—
380	C₃×#117	C₂×D₃	1	2	yes	complemented
381	C₃×#117	C₂×D₃	1	1	yes	characteristic, complemented
382	C₃×#117	C₂²×C₃	1	2	yes	complemented
383	C₃×#117	C₂²×C₃	1	1	yes	characteristic, complemented
384	C₂×C₃×C₄⋊C₄	—	3	2	no	—
385	C₂×C₃×C₄⋊C₄	—	3	2	no	—
386	C₂×C₃×C₄⋊C₄	—	3	2	no	—
387	C₂×C₃×C₄⋊C₄	—	3	1	no	—
388	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
389	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
390	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
391	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
392	C₂×C₃×C₄²	—	2	2	no	—
393	C₂×C₃×C₄²	—	2	1	no	—
394	C₂×C₃×C₄²	C₂×D₃	1	2	yes	complemented
395	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic, complemented
396	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	complemented
397	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic, complemented
398	#947	C₂²×C₃	1	1	yes	characteristic
399	#946	C₂²×C₃	1	1	yes	characteristic
400	#946	C₂²×C₃	1	1	yes	characteristic, complemented
401	#944	C₂²×C₃	1	1	yes	characteristic, complemented
402	#939	C₂²×C₃	1	2	yes	—
403	#939	C₂²×C₃	1	2	yes	complemented
404	#937	C₂²×C₃	1	2	yes	—
405	#935	C₂²×C₃	1	2	yes	complemented
406	D₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
407	D₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
408	#930	C₂²×C₃	1	1	yes	characteristic
409	#930	C₂²×C₃	1	2	yes	—
410	#930	C₂²×C₃	1	1	yes	characteristic
411	#929	C₂²×C₃	1	2	yes	—
412	#929	C₂²×C₃	1	1	yes	characteristic
413	#929	C₂²×C₃	1	2	yes	complemented
414	#929	C₂²×C₃	1	1	yes	characteristic, complemented
415	#929	C₂²×C₃	1	2	yes	complemented
416	C₄×#67	C₂²×C₃	1	1	yes	characteristic
417	C₄×#67	C₂²×C₃	1	2	yes	—
418	C₄×#67	C₂²×C₃	1	1	yes	characteristic, complemented
419	C₄×#67	C₂²×C₃	1	2	yes	complemented
420	C₄×#67	C₂²×C₃	1	2	yes	complemented
421	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
422	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
423	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
424	#924	C₂²×C₃	1	1	yes	characteristic, complemented
425	#924	C₂²×C₃	1	2	yes	complemented
426	#924	C₂²×C₃	1	1	yes	characteristic, complemented
427	C₂×Dic₃⋊C₄	C₂²×C₃	1	2	yes	complemented
428	C₂×Dic₃⋊C₄	C₂²×C₃	1	2	yes	complemented
429	C₂×Dic₃⋊C₄	C₂²×C₃	1	2	yes	complemented
430	#898	C₂²×C₃	1	2	yes	—
431	#898	C₂²×C₃	1	2	yes	complemented
432	#897	C₂²×C₃	1	1	yes	characteristic
433	#896	C₂²×C₃	1	2	yes	complemented
434	#896	C₂²×C₃	1	2	yes	complemented
435	#895	C₂²×C₃	1	1	yes	characteristic
436	#894	C₂²×C₃	1	2	yes	—
437	#894	C₂²×C₃	1	2	yes	complemented
438	#893	C₂²×C₃	1	1	yes	characteristic
439	#892	C₂²×C₃	1	1	yes	characteristic
440	D₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
441	#890	C₂²×C₃	1	1	yes	characteristic, complemented
442	#889	C₂²×C₃	1	2	yes	complemented
443	#889	C₂²×C₃	1	2	yes	complemented
444	#888	C₂²×C₃	1	1	yes	characteristic, complemented
445	#887	C₂²×C₃	1	1	yes	characteristic, complemented
446	#886	C₂²×C₃	1	2	yes	—
447	#885	C₂²×C₃	1	2	yes	—
448	#884	C₂²×C₃	1	2	yes	complemented
449	#883	C₂²×C₃	1	2	yes	complemented
450	#882	C₂²×C₃	1	2	yes	—
451	#67⋊C₄	C₂²×C₃	1	2	yes	—
452	#67⋊C₄	C₂²×C₃	1	2	yes	complemented
453	D₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
454	#879	C₂²×C₃	1	2	yes	complemented
455	#878	C₂²×C₃	1	2	yes	complemented
456	#878	C₂²×C₃	1	2	yes	complemented
457	#877	C₂²×C₃	1	2	yes	complemented
458	#876	C₂²×C₃	1	1	yes	characteristic
459	#876	C₂²×C₃	1	2	yes	—
460	#876	C₂²×C₃	1	2	yes	—
461	#876	C₂²×C₃	1	2	yes	—
462	#876	C₂²×C₃	1	2	yes	complemented
463	#876	C₂²×C₃	1	2	yes	complemented
464	#876	C₂²×C₃	1	2	yes	complemented
465	#876	C₂²×C₃	1	2	yes	complemented
466	#876	C₂²×C₃	1	1	yes	characteristic, complemented
467	#875	C₂²×C₃	1	1	yes	characteristic
468	#875	C₂²×C₃	1	1	yes	characteristic
469	#875	C₂²×C₃	1	2	yes	complemented
470	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic
471	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic
472	C₄×D₁₂	C₂²×C₃	1	2	yes	complemented
473	#872	C₂²×C₃	1	1	yes	characteristic
474	#872	C₂²×C₃	1	2	yes	complemented
475	#872	C₂²×C₃	1	2	yes	complemented
476	#872	C₂²×C₃	1	1	yes	characteristic, complemented
477	#872	C₂²×C₃	1	2	yes	complemented
478	#870	C₂²×C₃	1	1	yes	characteristic, complemented
479	#870	C₂²×C₃	1	1	yes	characteristic, complemented
480	#870	C₂²×C₃	1	2	yes	complemented
481	C₄×Dic₆	C₂²×C₃	1	2	yes	complemented
482	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic, complemented
483	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic, complemented
484	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
485	C₂³×C₃²	C₂⁴	1	2	yes	—
486	C₂²×C₃×D₃	—	2	4	no	—
487	C₂²×C₃×D₃	—	4	2	no	—
488	C₂²×C₃×D₃	—	4	2	no	—
489	C₂²×C₃×D₃	C₂⁴	1	1	yes	characteristic
490	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
491	C₂²×C₃×D₃	C₂⁴	1	1	yes	characteristic
492	C₃²×Q₈	—	2	2	no	—
493	C₃²×D₄	—	2	4	no	—
494	C₃²×D₄	#41	1	4	yes	—
495	C₂×C₃²×C₄	—	2	4	no	—
496	C₂×C₃²×C₄	—	2	2	no	—
497	C₂×C₃²×C₄	—	4	2	no	—
498	C₂×C₃²×C₄	—	4	1	no	—
499	C₂×C₃²×C₄	—	4	2	no	—
500	C₂×C₃²×C₄	—	4	1	no	—
501	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
502	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
503	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
504	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
505	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
506	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
507	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
508	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
509	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
510	C₃×#67	—	2	4	no	—
511	C₃×#67	—	2	4	no	—
512	C₃×#67	—	4	1	no	—
513	C₃×#67	—	4	2	no	—
514	C₃×#67	—	4	1	no	—
515	C₂×C₃×Dic₃	—	2	4	no	—
516	C₂×C₃×Dic₃	—	4	2	no	—
517	C₂×C₃×Dic₃	—	4	2	no	—
518	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
519	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
520	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
521	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
522	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
523	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
524	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
525	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
526	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
527	C₃×D₁₂	—	2	2	no	—
528	C₃×D₁₂	—	4	1	no	—
529	C₃×D₁₂	—	4	2	no	—
530	C₃×C₄×D₃	—	2	2	no	—
531	C₃×C₄×D₃	—	2	2	no	—
532	C₃×C₄×D₃	—	4	2	no	—
533	C₃×C₄×D₃	—	4	2	no	—
534	C₃×C₄×D₃	—	4	2	no	—
535	C₃×Dic₆	—	2	2	no	—
536	C₃×Dic₆	—	4	2	no	—
537	C₃×Dic₆	—	4	1	no	—
538	#556	—	3	1	no	—
539	#556	—	3	1	no	—
540	#554	—	3	1	no	—
541	#553	—	3	2	no	—
542	#553	—	3	1	no	—
543	#552	—	3	1	no	—
544	#552	—	3	2	no	—
545	#551	—	3	2	no	—
546	#551	—	3	2	no	—
547	#547	—	3	1	no	—
548	#546	—	3	1	no	—
549	#546	—	3	1	no	—
550	#542	—	3	1	no	—
551	#541	—	3	1	no	—
552	#539	—	3	2	no	—
553	#538	—	3	2	no	—
554	#529	—	3	2	no	—
555	#529	—	3	1	no	—
556	#529	—	3	1	no	—
557	C₂×#126	—	3	2	no	—
558	#520	—	3	1	no	—
559	#518	—	3	1	no	—
560	C₄×#41	C₃×D₃	1	1	yes	characteristic, complemented
561	C₂⁴×C₃	—	3	2	no	—
562	C₂³×D₃	C₂³×C₃	1	2	yes	—
563	C₃×#41	—	2	8	no	—
564	C₃×#41	—	2	4	no	—
565	C₃×#41	—	2	4	no	—
566	C₃×#41	—	6	4	no	—
567	C₂×C₃×Q₈	—	2	1	no	—
568	C₂×C₃×Q₈	—	3	1	no	—
569	C₂×C₃×Q₈	—	3	1	no	—
570	C₂×C₃×Q₈	—	3	2	no	—
571	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
572	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
573	C₂×C₃×D₄	—	2	2	no	—
574	C₂×C₃×D₄	—	2	1	no	—
575	C₂×C₃×D₄	—	3	2	no	—
576	C₂×C₃×D₄	—	3	2	no	—
577	C₂×C₃×D₄	—	3	1	no	—
578	C₂×C₃×D₄	—	3	2	no	—
579	C₂×C₃×D₄	—	3	1	no	—
580	C₂×C₃×D₄	—	3	1	no	—
581	C₂×C₃×D₄	—	3	1	no	—
582	C₂×C₃×D₄	—	3	2	no	—
583	C₂×C₃×D₄	—	6	4	no	—
584	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
585	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic
586	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
587	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
588	C₂²×C₃×C₄	—	2	2	no	—
589	C₂²×C₃×C₄	—	2	1	no	—
590	C₂²×C₃×C₄	—	2	2	no	—
591	C₂²×C₃×C₄	—	2	2	no	—
592	C₂²×C₃×C₄	—	2	1	no	—
593	C₂²×C₃×C₄	—	2	1	no	—
594	C₂²×C₃×C₄	—	3	2	no	—
595	C₂²×C₃×C₄	—	3	2	no	—
596	C₂²×C₃×C₄	—	3	2	no	—
597	C₂²×C₃×C₄	—	3	1	no	—
598	C₂²×C₃×C₄	—	3	1	no	—
599	C₂²×C₃×C₄	—	3	2	no	—
600	C₂²×C₃×C₄	—	3	2	no	—
601	C₂²×C₃×C₄	—	3	2	no	—
602	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
603	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
604	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
605	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
606	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
607	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
608	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
609	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
610	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
611	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
612	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
613	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
614	C₂×#67	C₂³×C₃	1	2	yes	—
615	C₂×#67	C₂³×C₃	1	2	yes	—
616	C₂×#67	C₂³×C₃	1	2	yes	—
617	C₂×#67	C₂³×C₃	1	1	yes	characteristic
618	C₂×#67	C₂³×C₃	1	1	yes	characteristic
619	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
620	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
621	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
622	#237	—	2	4	no	—
623	D₃×D₄	—	2	4	no	—
624	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
625	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
626	C₂×D₁₂	C₂³×C₃	1	2	yes	—
627	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
628	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
629	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
630	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
631	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
632	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
633	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
634	C₂×Dic₆	C₂³×C₃	1	2	yes	—
635	C₃×C₄⋊C₄	—	2	1	no	—
636	C₃×C₄⋊C₄	—	2	1	no	—
637	C₃×C₄⋊C₄	—	2	2	no	—
638	C₃×C₄⋊C₄	—	2	2	no	—
639	C₃×C₄⋊C₄	—	3	1	no	—
640	C₃×C₄⋊C₄	—	3	2	no	—
641	C₃×C₄⋊C₄	—	3	1	no	—
642	C₃×C₄⋊C₄	—	3	1	no	—
643	C₃×C₄⋊C₄	—	3	2	no	—
644	C₃×C₄⋊C₄	—	3	2	no	—
645	C₃×C₄⋊C₄	—	3	2	no	—
646	C₃×C₄⋊C₄	—	3	2	no	—
647	C₃×C₄⋊C₄	—	3	2	no	—
648	C₃×C₄⋊C₄	—	3	2	no	—
649	C₃×C₄⋊C₄	—	3	2	no	—
650	C₃×C₄⋊C₄	—	3	2	no	—
651	C₃×C₄⋊C₄	—	3	1	no	—
652	C₃×C₄⋊C₄	—	3	1	no	—
653	C₃×C₄⋊C₄	—	3	1	no	—
654	C₃×C₄⋊C₄	—	3	1	no	—
655	C₃×C₄⋊C₄	—	3	2	no	—
656	C₃×C₄⋊C₄	—	3	2	no	—
657	C₃×C₄⋊C₄	—	3	2	no	—
658	C₃×C₄⋊C₄	—	3	1	no	—
659	C₃×C₄⋊C₄	—	3	1	no	—
660	C₃×C₄⋊C₄	—	3	1	no	—
661	C₃×C₄⋊C₄	—	3	2	no	—
662	C₃×C₄⋊C₄	—	3	1	no	—
663	C₃×C₄⋊C₄	—	3	1	no	—
664	C₃×C₄⋊C₄	—	3	2	no	—
665	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
666	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
667	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
668	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
669	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
670	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
671	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
672	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
673	C₃×C₂²⋊C₄	—	2	2	no	—
674	C₃×C₂²⋊C₄	—	2	2	no	—
675	C₃×C₂²⋊C₄	—	2	2	no	—
676	C₃×C₂²⋊C₄	—	3	2	no	—
677	C₃×C₂²⋊C₄	—	3	2	no	—
678	C₃×C₂²⋊C₄	—	3	1	no	—
679	C₃×C₂²⋊C₄	—	3	2	no	—
680	C₃×C₂²⋊C₄	—	3	1	no	—
681	C₃×C₂²⋊C₄	—	3	1	no	—
682	C₃×C₂²⋊C₄	—	3	1	no	—
683	C₃×C₂²⋊C₄	—	3	2	no	—
684	C₃×C₂²⋊C₄	—	3	1	no	—
685	C₃×C₂²⋊C₄	—	3	1	no	—
686	C₃×C₂²⋊C₄	—	3	2	no	—
687	C₃×C₂²⋊C₄	—	3	2	no	—
688	C₃×C₂²⋊C₄	—	3	2	no	—
689	C₃×C₂²⋊C₄	—	3	2	no	—
690	C₃×C₂²⋊C₄	—	3	2	no	—
691	C₃×C₂²⋊C₄	—	3	2	no	—
692	C₃×C₂²⋊C₄	—	3	2	no	—
693	C₃×C₂²⋊C₄	—	3	2	no	—
694	C₃×C₂²⋊C₄	—	3	1	no	—
695	C₃×C₂²⋊C₄	—	3	1	no	—
696	C₃×C₂²⋊C₄	—	3	1	no	—
697	C₃×C₂²⋊C₄	—	3	2	no	—
698	C₃×C₂²⋊C₄	—	3	2	no	—
699	C₃×C₂²⋊C₄	—	3	2	no	—
700	C₃×C₂²⋊C₄	—	3	1	no	—
701	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
702	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
703	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
704	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
705	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
706	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
707	C₃×C₄²	—	2	1	no	—
708	C₃×C₄²	—	2	1	no	—
709	C₃×C₄²	—	2	2	no	—
710	C₃×C₄²	—	2	1	no	—
711	C₃×C₄²	—	2	2	no	—
712	C₃×C₄²	—	2	1	no	—
713	C₃×C₄²	—	2	2	no	—
714	C₃×C₄²	—	3	2	no	—
715	C₃×C₄²	—	3	2	no	—
716	C₃×C₄²	—	3	2	no	—
717	C₃×C₄²	—	3	1	no	—
718	C₃×C₄²	—	3	1	no	—
719	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
720	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
721	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
722	C₃×C₄²	C₂²×D₃	1	2	yes	—
723	C₃×C₄²	C₂²×D₃	1	2	yes	—
724	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
725	C₃×C₄²	C₂²×D₃	1	2	yes	—
726	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
727	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
728	C₃×C₄²	C₂³×C₃	1	2	yes	—
729	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
730	C₃×C₄²	C₂³×C₃	1	2	yes	—
731	C₃×C₄²	C₂³×C₃	1	2	yes	—
732	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
733	#217	C₂³×C₃	1	2	yes	—
734	#217	C₂³×C₃	1	2	yes	—
735	#217	C₂³×C₃	1	1	yes	characteristic
736	#217	C₂³×C₃	1	2	yes	—
737	#217	C₂³×C₃	1	1	yes	characteristic
738	(C₂×D₃)⋊C₄	C₂³×C₃	1	1	yes	characteristic
739	(C₂×D₃)⋊C₄	C₂³×C₃	1	1	yes	characteristic
740	(C₂×D₃)⋊C₄	C₂³×C₃	1	1	yes	characteristic
741	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
742	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
743	(C₂×D₃)⋊C₄	C₂³×C₃	1	1	yes	characteristic
744	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
745	(C₂×D₃)⋊C₄	C₂³×C₃	1	1	yes	characteristic
746	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
747	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
748	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
749	(C₂×D₃)⋊C₄	C₂³×C₃	1	1	yes	characteristic
750	(C₂×D₃)⋊C₄	C₂³×C₃	1	1	yes	characteristic
751	(C₂×D₃)⋊C₄	C₂³×C₃	1	1	yes	characteristic
752	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
753	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
754	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
755	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
756	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
757	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
758	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
759	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
760	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
761	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
762	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
763	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
764	Dic₃⋊C₄	C₂³×C₃	1	1	yes	characteristic
765	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
766	Dic₃⋊C₄	C₂³×C₃	1	1	yes	characteristic
767	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
768	Dic₃⋊C₄	C₂³×C₃	1	1	yes	characteristic
769	Dic₃⋊C₄	C₂³×C₃	1	1	yes	characteristic
770	Dic₃⋊C₄	C₂³×C₃	1	1	yes	characteristic
771	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
772	Dic₃⋊C₄	C₂³×C₃	1	1	yes	characteristic
773	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
774	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
775	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
776	Dic₃⋊C₄	C₂³×C₃	1	1	yes	characteristic
777	Dic₃⋊C₄	C₂³×C₃	1	1	yes	characteristic
778	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
779	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
780	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
781	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
782	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
783	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
784	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
785	C₄×Dic₃	C₂³×C₃	1	2	yes	—
786	C₄×Dic₃	C₂³×C₃	1	2	yes	—
787	C₄×Dic₃	C₂³×C₃	1	2	yes	—
788	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
789	C₂²×C₃²	—	2	1	no	—
790	C₂²×C₃²	—	2	2	no	—
791	C₂²×C₃²	—	2	2	no	—
792	C₂²×C₃²	—	2	1	no	—
793	C₂²×C₃²	—	2	1	no	—
794	C₂²×C₃²	C₂×#41	1	4	yes	—
795	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
796	C₂×C₃×D₃	—	2	1	no	—
797	C₂×C₃×D₃	—	2	1	no	—
798	C₂×C₃×D₃	—	2	2	no	—
799	C₂×C₃×D₃	—	2	1	no	—
800	C₂×C₃×D₃	—	2	2	no	—
801	C₂×C₃×D₃	—	2	2	no	—
802	C₂×C₃×D₃	—	2	1	no	—
803	C₂×C₃×D₃	—	2	1	no	—
804	C₂×C₃×D₃	—	2	1	no	—
805	C₂×C₃×D₃	—	8	4	no	—
806	C₃²×C₄	—	2	1	no	—
807	C₃²×C₄	—	2	2	no	—
808	C₃²×C₄	—	2	1	no	—
809	C₃²×C₄	—	2	1	no	—
810	C₃²×C₄	—	2	2	no	—
811	C₃²×C₄	—	2	1	no	—
812	C₃²×C₄	—	2	1	no	—
813	C₃²×C₄	—	2	2	no	—
814	C₃²×C₄	C₂×#41	1	2	yes	—
815	C₃×Dic₃	—	2	2	no	—
816	C₃×Dic₃	—	2	1	no	—
817	C₃×Dic₃	—	2	1	no	—
818	C₃×Dic₃	—	2	1	no	—
819	C₃×Dic₃	—	2	1	no	—
820	C₃×Dic₃	—	2	2	no	—
821	C₃×Dic₃	—	2	1	no	—
822	C₃×Dic₃	—	2	2	no	—
823	C₃×Dic₃	—	2	1	no	—
824	C₂×#41	—	3	1	no	—
825	C₂×#41	C₂×C₃×D₃	1	1	yes	characteristic
826	C₂²×D₄	—	3	1	no	—
827	C₄⋊Q₈	—	3	1	no	—
828	C₄⋊Q₈	—	3	1	no	—
829	#126	—	3	2	no	—
830	#126	—	3	2	no	—
831	#126	—	3	2	no	—
832	#126	—	3	1	no	—
833	#126	—	3	2	no	—
834	#126	—	3	2	no	—
835	#126	—	3	2	no	—
836	#126	—	3	2	no	—
837	#126	—	3	2	no	—
838	#126	—	3	2	no	—
839	#126	—	3	2	no	—
840	#126	—	3	1	no	—
841	#125	—	3	2	no	—
842	#125	—	3	2	no	—
843	#125	—	3	1	no	—
844	#125	—	3	2	no	—
845	#125	—	3	1	no	—
846	#125	—	3	1	no	—
847	#124	—	3	1	no	—
848	#124	—	3	2	no	—
849	#124	—	3	2	no	—
850	#124	—	3	1	no	—
851	#124	—	3	1	no	—
852	#123	—	3	2	no	—
853	#123	—	3	2	no	—
854	#123	—	3	2	no	—
855	#123	—	3	2	no	—
856	#123	—	3	1	no	—
857	#123	—	3	1	no	—
858	#123	—	3	2	no	—
859	#123	—	3	2	no	—
860	#123	—	3	2	no	—
861	#123	—	3	2	no	—
862	C₂²⋊Q₈	—	3	1	no	—
863	C₂²⋊Q₈	—	3	1	no	—
864	C₂²⋊Q₈	—	3	1	no	—
865	C₂²⋊Q₈	—	3	1	no	—
866	C₂²⋊Q₈	—	3	2	no	—
867	C₂²⋊Q₈	—	3	2	no	—
868	C₂²⋊Q₈	—	3	1	no	—
869	C₂²⋊Q₈	—	3	2	no	—
870	C₂²⋊Q₈	—	3	2	no	—
871	C₂²⋊Q₈	—	3	2	no	—
872	#121	—	3	2	no	—
873	#121	—	3	2	no	—
874	#121	—	3	1	no	—
875	#121	—	3	1	no	—
876	#121	—	3	2	no	—
877	#121	—	3	1	no	—
878	#121	—	3	2	no	—
879	#120	—	3	2	no	—
880	#120	—	3	2	no	—
881	C₄×Q₈	—	3	1	no	—
882	C₄×Q₈	—	3	1	no	—
883	C₄×Q₈	—	3	2	no	—
884	C₄×Q₈	—	3	1	no	—
885	C₄×Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
886	C₄×Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
887	C₄×D₄	—	3	1	no	—
888	C₄×D₄	—	3	1	no	—
889	C₄×D₄	—	3	2	no	—
890	C₄×D₄	—	3	2	no	—
891	C₄×D₄	—	3	1	no	—
892	C₄×D₄	—	3	1	no	—
893	C₄×D₄	—	3	2	no	—
894	C₄×D₄	—	3	1	no	—
895	C₄×D₄	—	3	2	no	—
896	C₄×D₄	—	3	2	no	—
897	C₄×D₄	—	3	1	no	—
898	C₄×D₄	—	3	1	no	—
899	C₄×D₄	—	3	2	no	—
900	C₄×D₄	C₂×C₃×D₃	1	1	yes	characteristic
901	C₄×D₄	C₂×C₃×D₃	1	1	yes	characteristic
902	C₄×D₄	C₂×C₃×D₃	1	2	yes	complemented
903	C₄×D₄	C₂×C₃×D₃	1	2	yes	complemented
904	#117	—	3	1	no	—
905	#117	—	3	2	no	—
906	#117	—	3	1	no	—
907	#117	—	3	1	no	—
908	#117	—	3	2	no	—
909	#117	—	3	2	no	—
910	#117	—	3	2	no	—
911	#117	C₂×C₃×D₃	1	2	yes	complemented
912	#117	C₂×C₃×D₃	1	1	yes	characteristic, complemented
913	C₂×C₄⋊C₄	—	3	2	no	—
914	C₂×C₄⋊C₄	—	3	2	no	—
915	C₂×C₄⋊C₄	—	3	2	no	—
916	C₂×C₄⋊C₄	—	3	1	no	—
917	C₂×C₂²⋊C₄	—	3	2	no	—
918	C₂×C₂²⋊C₄	—	3	2	no	—
919	C₂×C₂²⋊C₄	—	3	2	no	—
920	C₂×C₂²⋊C₄	—	3	2	no	—
921	C₂×C₄²	C₂×C₃×D₃	1	2	yes	complemented
922	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic, complemented
923	C₂³×C₃	—	2	1	no	—
924	C₂³×C₃	—	2	2	no	—
925	C₂³×C₃	—	3	1	no	—
926	C₂³×C₃	—	3	2	no	—
927	C₂³×C₃	—	3	1	no	—
928	C₂³×C₃	—	6	4	no	—
929	C₂³×C₃	—	12	2	no	—
930	C₂³×C₃	—	12	2	no	—
931	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
932	C₂³×C₃	C₂³×D₃	1	2	yes	—
933	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
934	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
935	C₂²×D₃	—	2	4	no	—
936	C₂²×D₃	—	4	2	no	—
937	C₂²×D₃	—	4	2	no	—
938	C₂²×D₃	C₂⁴×C₃	1	1	yes	characteristic
939	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
940	C₂²×D₃	C₂⁴×C₃	1	1	yes	characteristic
941	C₃×Q₈	—	2	4	no	—
942	C₃×Q₈	—	2	2	no	—
943	C₃×Q₈	—	2	2	no	—
944	C₃×Q₈	—	6	2	no	—
945	C₃×Q₈	—	12	1	no	—
946	C₃×Q₈	—	12	2	no	—
947	C₃×D₄	—	2	8	no	—
948	C₃×D₄	—	2	4	no	—
949	C₃×D₄	—	2	4	no	—
950	C₃×D₄	—	2	4	no	—
951	C₃×D₄	—	6	4	no	—
952	C₃×D₄	—	6	4	no	—
953	C₃×D₄	—	6	2	no	—
954	C₃×D₄	—	12	1	no	—
955	C₃×D₄	—	12	2	no	—
956	C₃×D₄	—	12	2	no	—
957	C₃×D₄	—	12	1	no	—
958	C₃×D₄	—	12	1	no	—
959	C₃×D₄	#235	1	4	yes	—
960	C₃×D₄	C₃×#41	1	4	yes	—
961	C₂×C₃×C₄	—	2	8	no	—
962	C₂×C₃×C₄	—	2	4	no	—
963	C₂×C₃×C₄	—	2	4	no	—
964	C₂×C₃×C₄	—	2	4	no	—
965	C₂×C₃×C₄	—	2	2	no	—
966	C₂×C₃×C₄	—	2	2	no	—
967	C₂×C₃×C₄	—	2	1	no	—
968	C₂×C₃×C₄	—	2	1	no	—
969	C₂×C₃×C₄	—	2	1	no	—
970	C₂×C₃×C₄	—	2	2	no	—
971	C₂×C₃×C₄	—	2	1	no	—
972	C₂×C₃×C₄	—	2	1	no	—
973	C₂×C₃×C₄	—	2	2	no	—
974	C₂×C₃×C₄	—	2	1	no	—
975	C₂×C₃×C₄	—	2	2	no	—
976	C₂×C₃×C₄	—	3	1	no	—
977	C₂×C₃×C₄	—	3	2	no	—
978	C₂×C₃×C₄	—	3	1	no	—
979	C₂×C₃×C₄	—	3	1	no	—
980	C₂×C₃×C₄	—	3	2	no	—
981	C₂×C₃×C₄	—	3	1	no	—
982	C₂×C₃×C₄	—	3	1	no	—
983	C₂×C₃×C₄	—	3	2	no	—
984	C₂×C₃×C₄	—	3	1	no	—
985	C₂×C₃×C₄	—	4	2	no	—
986	C₂×C₃×C₄	—	4	1	no	—
987	C₂×C₃×C₄	—	4	2	no	—
988	C₂×C₃×C₄	—	4	1	no	—
989	C₂×C₃×C₄	—	4	2	no	—
990	C₂×C₃×C₄	—	4	1	no	—
991	C₂×C₃×C₄	—	4	2	no	—
992	C₂×C₃×C₄	—	4	1	no	—
993	C₂×C₃×C₄	—	4	4	no	—
994	C₂×C₃×C₄	—	4	2	no	—
995	C₂×C₃×C₄	—	4	4	no	—
996	C₂×C₃×C₄	—	4	2	no	—
997	C₂×C₃×C₄	—	6	4	no	—
998	C₂×C₃×C₄	—	6	2	no	—
999	C₂×C₃×C₄	—	6	2	no	—
1000	C₂×C₃×C₄	—	12	2	no	—
1001	C₂×C₃×C₄	—	12	2	no	—
1002	C₂×C₃×C₄	—	12	2	no	—
1003	C₂×C₃×C₄	—	12	2	no	—
1004	C₂×C₃×C₄	—	12	2	no	—
1005	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
1006	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
1007	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
1008	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
1009	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
1010	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
1011	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
1012	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
1013	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
1014	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
1015	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
1016	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
1017	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
1018	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
1019	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
1020	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
1021	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
1022	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
1023	#67	—	2	4	no	—
1024	#67	—	2	4	no	—
1025	#67	—	4	1	no	—
1026	#67	—	4	2	no	—
1027	#67	—	4	1	no	—
1028	C₂×Dic₃	—	2	4	no	—
1029	C₂×Dic₃	—	4	2	no	—
1030	C₂×Dic₃	—	4	2	no	—
1031	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1032	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1033	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
1034	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1035	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
1036	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1037	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
1038	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1039	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
1040	D₁₂	—	2	2	no	—
1041	D₁₂	—	4	1	no	—
1042	D₁₂	—	4	2	no	—
1043	C₄×D₃	—	2	2	no	—
1044	C₄×D₃	—	2	2	no	—
1045	C₄×D₃	—	4	2	no	—
1046	C₄×D₃	—	4	2	no	—
1047	C₄×D₃	—	4	2	no	—
1048	Dic₆	—	2	2	no	—
1049	Dic₆	—	4	2	no	—
1050	Dic₆	—	4	1	no	—
1051	C₂×C₃²	—	2	4	no	—
1052	C₂×C₃²	—	4	1	no	—
1053	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
1054	C₂×C₃²	#585	1	1	yes	characteristic
1055	C₂×C₃²	#585	1	1	yes	characteristic
1056	C₃×D₃	—	4	1	no	—
1057	C₃×D₃	—	4	2	no	—
1058	C₃×D₃	—	4	1	no	—
1059	C₂⁴	—	3	2	no	—
1060	#41	—	2	4	no	—
1061	#41	—	6	4	no	—
1062	C₂×Q₈	—	3	1	no	—
1063	C₂×Q₈	—	3	1	no	—
1064	C₂×Q₈	—	3	2	no	—
1065	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
1066	C₂×D₄	—	3	2	no	—
1067	C₂×D₄	—	3	2	no	—
1068	C₂×D₄	—	3	1	no	—
1069	C₂×D₄	—	3	2	no	—
1070	C₂×D₄	—	3	1	no	—
1071	C₂×D₄	—	3	1	no	—
1072	C₂×D₄	—	3	1	no	—
1073	C₂×D₄	—	3	2	no	—
1074	C₂×D₄	—	6	4	no	—
1075	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
1076	C₂×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
1077	C₂²×C₄	—	3	2	no	—
1078	C₂²×C₄	—	3	2	no	—
1079	C₂²×C₄	—	3	2	no	—
1080	C₂²×C₄	—	3	1	no	—
1081	C₂²×C₄	—	3	1	no	—
1082	C₂²×C₄	—	3	2	no	—
1083	C₂²×C₄	—	3	2	no	—
1084	C₂²×C₄	—	3	2	no	—
1085	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
1086	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1087	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
1088	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
1089	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1090	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1091	C₄⋊C₄	—	3	1	no	—
1092	C₄⋊C₄	—	3	2	no	—
1093	C₄⋊C₄	—	3	1	no	—
1094	C₄⋊C₄	—	3	1	no	—
1095	C₄⋊C₄	—	3	2	no	—
1096	C₄⋊C₄	—	3	2	no	—
1097	C₄⋊C₄	—	3	1	no	—
1098	C₄⋊C₄	—	3	2	no	—
1099	C₄⋊C₄	—	3	2	no	—
1100	C₄⋊C₄	—	3	2	no	—
1101	C₄⋊C₄	—	3	2	no	—
1102	C₄⋊C₄	—	3	2	no	—
1103	C₄⋊C₄	—	3	2	no	—
1104	C₄⋊C₄	—	3	1	no	—
1105	C₄⋊C₄	—	3	1	no	—
1106	C₄⋊C₄	—	3	1	no	—
1107	C₄⋊C₄	—	3	1	no	—
1108	C₄⋊C₄	—	3	1	no	—
1109	C₄⋊C₄	—	3	2	no	—
1110	C₄⋊C₄	—	3	2	no	—
1111	C₄⋊C₄	—	3	2	no	—
1112	C₄⋊C₄	—	3	1	no	—
1113	C₄⋊C₄	—	3	2	no	—
1114	C₄⋊C₄	—	3	1	no	—
1115	C₄⋊C₄	—	3	1	no	—
1116	C₄⋊C₄	—	3	2	no	—
1117	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1118	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1119	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1120	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1121	C₂²⋊C₄	—	3	2	no	—
1122	C₂²⋊C₄	—	3	2	no	—
1123	C₂²⋊C₄	—	3	1	no	—
1124	C₂²⋊C₄	—	3	2	no	—
1125	C₂²⋊C₄	—	3	1	no	—
1126	C₂²⋊C₄	—	3	1	no	—
1127	C₂²⋊C₄	—	3	2	no	—
1128	C₂²⋊C₄	—	3	1	no	—
1129	C₂²⋊C₄	—	3	1	no	—
1130	C₂²⋊C₄	—	3	1	no	—
1131	C₂²⋊C₄	—	3	2	no	—
1132	C₂²⋊C₄	—	3	2	no	—
1133	C₂²⋊C₄	—	3	2	no	—
1134	C₂²⋊C₄	—	3	2	no	—
1135	C₂²⋊C₄	—	3	2	no	—
1136	C₂²⋊C₄	—	3	2	no	—
1137	C₂²⋊C₄	—	3	2	no	—
1138	C₂²⋊C₄	—	3	2	no	—
1139	C₂²⋊C₄	—	3	1	no	—
1140	C₂²⋊C₄	—	3	1	no	—
1141	C₂²⋊C₄	—	3	1	no	—
1142	C₂²⋊C₄	—	3	2	no	—
1143	C₂²⋊C₄	—	3	2	no	—
1144	C₂²⋊C₄	—	3	2	no	—
1145	C₂²⋊C₄	—	3	1	no	—
1146	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1147	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1148	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1149	C₄²	—	3	2	no	—
1150	C₄²	—	3	2	no	—
1151	C₄²	—	3	2	no	—
1152	C₄²	—	3	1	no	—
1153	C₄²	—	3	1	no	—
1154	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
1155	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
1156	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
1157	C₄²	C₂²×C₃×D₃	1	2	yes	—
1158	C₄²	C₂²×C₃×D₃	1	2	yes	—
1159	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
1160	C₄²	C₂²×C₃×D₃	1	2	yes	—
1161	C₂²×C₃	—	2	2	no	—
1162	C₂²×C₃	—	2	2	no	—
1163	C₂²×C₃	—	2	2	no	—
1164	C₂²×C₃	—	2	2	no	—
1165	C₂²×C₃	—	2	2	no	—
1166	C₂²×C₃	—	2	1	no	—
1167	C₂²×C₃	—	2	1	no	—
1168	C₂²×C₃	—	2	1	no	—
1169	C₂²×C₃	—	2	1	no	—
1170	C₂²×C₃	—	2	1	no	—
1171	C₂²×C₃	—	2	1	no	—
1172	C₂²×C₃	—	2	4	no	—
1173	C₂²×C₃	—	2	1	no	—
1174	C₂²×C₃	—	4	2	no	—
1175	C₂²×C₃	—	4	2	no	—
1176	C₂²×C₃	—	4	1	no	—
1177	C₂²×C₃	—	4	1	no	—
1178	C₂²×C₃	—	6	1	no	—
1179	C₂²×C₃	—	6	1	no	—
1180	C₂²×C₃	—	6	2	no	—
1181	C₂²×C₃	—	6	1	no	—
1182	C₂²×C₃	—	6	2	no	—
1183	C₂²×C₃	—	6	2	no	—
1184	C₂²×C₃	—	6	1	no	—
1185	C₂²×C₃	—	6	1	no	—
1186	C₂²×C₃	—	6	1	no	—
1187	C₂²×C₃	—	24	4	no	—
1188	C₂²×C₃	C₂×#235	1	4	yes	—
1189	C₂²×C₃	C₂×C₃×#41	1	4	yes	—
1190	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
1191	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
1192	C₂×D₃	—	2	1	no	—
1193	C₂×D₃	—	2	1	no	—
1194	C₂×D₃	—	2	2	no	—
1195	C₂×D₃	—	2	1	no	—
1196	C₂×D₃	—	2	2	no	—
1197	C₂×D₃	—	2	2	no	—
1198	C₂×D₃	—	2	1	no	—
1199	C₂×D₃	—	2	1	no	—
1200	C₂×D₃	—	2	1	no	—
1201	C₂×D₃	—	8	4	no	—
1202	C₃×C₄	—	2	2	no	—
1203	C₃×C₄	—	2	4	no	—
1204	C₃×C₄	—	2	2	no	—
1205	C₃×C₄	—	2	2	no	—
1206	C₃×C₄	—	2	1	no	—
1207	C₃×C₄	—	2	2	no	—
1208	C₃×C₄	—	2	1	no	—
1209	C₃×C₄	—	2	1	no	—
1210	C₃×C₄	—	2	2	no	—
1211	C₃×C₄	—	2	1	no	—
1212	C₃×C₄	—	2	1	no	—
1213	C₃×C₄	—	2	2	no	—
1214	C₃×C₄	—	2	1	no	—
1215	C₃×C₄	—	2	2	no	—
1216	C₃×C₄	—	2	2	no	—
1217	C₃×C₄	—	2	1	no	—
1218	C₃×C₄	—	2	1	no	—
1219	C₃×C₄	—	2	2	no	—
1220	C₃×C₄	—	2	1	no	—
1221	C₃×C₄	—	2	1	no	—
1222	C₃×C₄	—	2	2	no	—
1223	C₃×C₄	—	4	2	no	—
1224	C₃×C₄	—	4	1	no	—
1225	C₃×C₄	—	4	1	no	—
1226	C₃×C₄	—	4	2	no	—
1227	C₃×C₄	—	6	1	no	—
1228	C₃×C₄	—	6	1	no	—
1229	C₃×C₄	—	6	2	no	—
1230	C₃×C₄	—	6	2	no	—
1231	C₃×C₄	—	6	1	no	—
1232	C₃×C₄	—	6	1	no	—
1233	C₃×C₄	—	6	2	no	—
1234	C₃×C₄	—	6	1	no	—
1235	C₃×C₄	—	6	1	no	—
1236	C₃×C₄	C₂×#235	1	2	yes	—
1237	C₃×C₄	C₂×C₃×#41	1	2	yes	—
1238	Dic₃	—	2	2	no	—
1239	Dic₃	—	2	1	no	—
1240	Dic₃	—	2	1	no	—
1241	Dic₃	—	2	1	no	—
1242	Dic₃	—	2	1	no	—
1243	Dic₃	—	2	2	no	—
1244	Dic₃	—	2	1	no	—
1245	Dic₃	—	2	2	no	—
1246	Dic₃	—	2	1	no	—
1247	C₃²	#3521	1	1	yes	characteristic, complemented, Sylow
1248	C₂³	—	3	1	no	—
1249	C₂³	—	3	2	no	—
1250	C₂³	—	3	1	no	—
1251	C₂³	—	6	4	no	—
1252	C₂³	—	12	2	no	—
1253	C₂³	—	12	2	no	—
1254	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
1255	C₂³	C₂³×C₃×D₃	1	2	yes	—
1256	Q₈	—	2	2	no	—
1257	Q₈	—	6	2	no	—
1258	Q₈	—	12	1	no	—
1259	Q₈	—	12	2	no	—
1260	D₄	—	2	4	no	—
1261	D₄	—	6	4	no	—
1262	D₄	—	6	4	no	—
1263	D₄	—	6	2	no	—
1264	D₄	—	12	1	no	—
1265	D₄	—	12	2	no	—
1266	D₄	—	12	2	no	—
1267	D₄	—	12	1	no	—
1268	D₄	—	12	1	no	—
1269	D₄	C₃×#235	1	4	yes	—
1270	C₂×C₄	—	2	4	no	—
1271	C₂×C₄	—	2	2	no	—
1272	C₂×C₄	—	3	1	no	—
1273	C₂×C₄	—	3	2	no	—
1274	C₂×C₄	—	3	1	no	—
1275	C₂×C₄	—	3	2	no	—
1276	C₂×C₄	—	3	1	no	—
1277	C₂×C₄	—	3	1	no	—
1278	C₂×C₄	—	3	2	no	—
1279	C₂×C₄	—	3	1	no	—
1280	C₂×C₄	—	3	1	no	—
1281	C₂×C₄	—	4	2	no	—
1282	C₂×C₄	—	4	1	no	—
1283	C₂×C₄	—	4	2	no	—
1284	C₂×C₄	—	4	1	no	—
1285	C₂×C₄	—	6	4	no	—
1286	C₂×C₄	—	6	2	no	—
1287	C₂×C₄	—	6	2	no	—
1288	C₂×C₄	—	12	2	no	—
1289	C₂×C₄	—	12	2	no	—
1290	C₂×C₄	—	12	2	no	—
1291	C₂×C₄	—	12	2	no	—
1292	C₂×C₄	—	12	2	no	—
1293	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1294	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1295	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1296	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1297	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1298	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1299	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1300	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1301	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1302	C₂×C₃	—	2	4	no	—
1303	C₂×C₃	—	2	4	no	—
1304	C₂×C₃	—	2	1	no	—
1305	C₂×C₃	—	2	1	no	—
1306	C₂×C₃	—	2	1	no	—
1307	C₂×C₃	—	4	4	no	—
1308	C₂×C₃	—	4	2	no	—
1309	C₂×C₃	—	4	1	no	—
1310	C₂×C₃	—	4	1	no	—
1311	C₂×C₃	—	12	1	no	—
1312	C₂×C₃	—	12	2	no	—
1313	C₂×C₃	—	12	1	no	—
1314	C₂×C₃	C₂²×#235	1	1	yes	characteristic
1315	C₂×C₃	#5964	1	1	yes	characteristic
1316	C₂×C₃	#5964	1	1	yes	characteristic
1317	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
1318	C₂×C₃	C₃×#585	1	1	yes	characteristic
1319	C₂×C₃	C₃×#585	1	1	yes	characteristic
1320	D₃	—	4	1	no	—
1321	D₃	—	4	2	no	—
1322	D₃	—	4	1	no	—
1323	C₂²	—	2	2	no	—
1324	C₂²	—	2	2	no	—
1325	C₂²	—	2	1	no	—
1326	C₂²	—	2	1	no	—
1327	C₂²	—	2	1	no	—
1328	C₂²	—	6	1	no	—
1329	C₂²	—	6	1	no	—
1330	C₂²	—	6	2	no	—
1331	C₂²	—	6	1	no	—
1332	C₂²	—	6	2	no	—
1333	C₂²	—	6	2	no	—
1334	C₂²	—	6	1	no	—
1335	C₂²	—	6	1	no	—
1336	C₂²	—	6	1	no	—
1337	C₂²	—	24	4	no	—
1338	C₂²	C₂×C₃×#235	1	4	yes	—
1339	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
1340	C₄	—	2	1	no	—
1341	C₄	—	2	2	no	—
1342	C₄	—	2	1	no	—
1343	C₄	—	2	1	no	—
1344	C₄	—	2	2	no	—
1345	C₄	—	2	1	no	—
1346	C₄	—	2	1	no	—
1347	C₄	—	2	2	no	—
1348	C₄	—	6	1	no	—
1349	C₄	—	6	1	no	—
1350	C₄	—	6	2	no	—
1351	C₄	—	6	2	no	—
1352	C₄	—	6	1	no	—
1353	C₄	—	6	1	no	—
1354	C₄	—	6	2	no	—
1355	C₄	—	6	1	no	—
1356	C₄	—	6	1	no	—
1357	C₄	C₂×C₃×#235	1	2	yes	—
1358	C₃	—	2	1	no	—
1359	C₃	#85854	1	1	yes	characteristic, direct product factor
1360	C₃	C₃×#3521	1	1	yes	characteristic, complemented
1361	C₂	—	2	4	no	—
1362	C₂	—	4	1	no	—
1363	C₂	—	12	1	no	—
1364	C₂	—	12	2	no	—
1365	C₂	—	12	1	no	—
1366	C₂	C₂²×C₃×#235	1	1	yes	characteristic
1367	C₂	C₃×#5964	1	1	yes	characteristic
1368	C₂	C₃×#5964	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂⁴×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₃²×C₄×#41	C₂
socle	C₂²×C₃²	C₂⁵
hypercenter	C₃×C₄×#41	D₃
hypocenter	C₃	C₃×#3521
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄×#41

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃²×C₄×#41	C₂	semidirect
2. C₃×#5829	C₂	semidirect
3. C₃×#5824	C₂	semidirect
4. C₃×#5583	C₂	semidirect
5. C₃×#5582	C₂	semidirect
6. C₃×#5581	C₂	semidirect
7. C₃×#5568	C₂	semidirect
8. C₃×#5564	C₂	semidirect
9. C₃×#5560	C₂	semidirect
10. C₃×#5556	C₂	semidirect
11. C₃×#5554	C₂	semidirect
12. C₃×#5546	C₂	semidirect
13. C₃×#5545	C₂	semidirect
14. C₃×#5540	C₂	semidirect
15. C₃×#5539	C₂	semidirect
16. C₃×#5533	C₂	semidirect
17. C₃×#5531	C₂	semidirect
18. C₃×#5530	C₂	semidirect
19. C₃×#5527	C₂	semidirect
20. C₃×#5479	C₂	semidirect
21. C₃×#5479	C₂	semidirect
22. C₃×#5479	C₂	semidirect
23. C₂×C₃×#876	C₂	semidirect
25. #85854	C₃	direct (N × H)
29. C₃²×C₄×Q₈	C₂²	semidirect
30. C₃²×C₄×Q₈	C₂²	semidirect
33. C₃²×C₄×D₄	C₂²	semidirect
34. C₃²×C₄×D₄	C₂²	semidirect
35. C₃²×#117	C₂²	semidirect
36. C₃²×#117	C₂²	semidirect
37. C₂×C₃²×C₄²	C₂²	semidirect
38. C₂×C₃²×C₄²	C₂²	semidirect
41. C₃×#946	C₂²	semidirect
42. C₃×#944	C₂²	semidirect
44. C₃×#939	C₂²	semidirect
46. C₃×#935	C₂²	semidirect
54. C₃×#929	C₂²	semidirect
55. C₃×#929	C₂²	semidirect
56. C₃×#929	C₂²	semidirect
59. C₃×C₄×#67	C₂²	semidirect
60. C₃×C₄×#67	C₂²	semidirect
61. C₃×C₄×#67	C₂²	semidirect
65. C₃×#924	C₂²	semidirect
66. C₃×#924	C₂²	semidirect
67. C₃×#924	C₂²	semidirect
68. C₂×C₃×Dic₃⋊C₄	C₂²	semidirect
69. C₂×C₃×Dic₃⋊C₄	C₂²	semidirect
70. C₂×C₃×Dic₃⋊C₄	C₂²	semidirect
72. C₃×#898	C₂²	semidirect
74. C₃×#896	C₂²	semidirect
75. C₃×#896	C₂²	semidirect
78. C₃×#894	C₂²	semidirect
81. C₃×D₃×C₄⋊C₄	C₂²	semidirect
82. C₃×#890	C₂²	semidirect
83. C₃×#889	C₂²	semidirect
84. C₃×#889	C₂²	semidirect
85. C₃×#888	C₂²	semidirect
86. C₃×#887	C₂²	semidirect
89. C₃×#884	C₂²	semidirect
90. C₃×#883	C₂²	semidirect
93. C₃×#67⋊C₄	C₂²	semidirect
95. C₃×#879	C₂²	semidirect
96. C₃×#878	C₂²	semidirect
97. C₃×#878	C₂²	semidirect
98. C₃×#877	C₂²	semidirect
103. C₃×#876	C₂²	semidirect
104. C₃×#876	C₂²	semidirect
105. C₃×#876	C₂²	semidirect
106. C₃×#876	C₂²	semidirect
107. C₃×#876	C₂²	semidirect
110. C₃×#875	C₂²	semidirect
113. C₃×C₄×D₁₂	C₂²	semidirect
115. C₃×#872	C₂²	semidirect
116. C₃×#872	C₂²	semidirect
117. C₃×#872	C₂²	semidirect
118. C₃×#872	C₂²	semidirect
119. C₃×#870	C₂²	semidirect
120. C₃×#870	C₂²	semidirect
121. C₃×#870	C₂²	semidirect
122. C₃×C₄×Dic₆	C₂²	semidirect
123. C₃×C₄×Dic₆	C₂²	semidirect
124. C₃×C₄×Dic₆	C₂²	semidirect
148. C₃×C₄×#41	D₃	semidirect
149. C₃×C₄×#41	C₂×C₃	semidirect
150. #5829	C₂×C₃	semidirect
151. #5824	C₂×C₃	semidirect
152. #5583	C₂×C₃	semidirect
153. #5582	C₂×C₃	semidirect
154. #5581	C₂×C₃	semidirect
155. #5568	C₂×C₃	semidirect
156. #5564	C₂×C₃	semidirect
157. #5560	C₂×C₃	semidirect
158. #5556	C₂×C₃	semidirect
159. #5554	C₂×C₃	semidirect
160. #5546	C₂×C₃	semidirect
161. #5545	C₂×C₃	semidirect
162. #5540	C₂×C₃	semidirect
163. #5539	C₂×C₃	semidirect
164. #5533	C₂×C₃	semidirect
165. #5531	C₂×C₃	semidirect
166. #5530	C₂×C₃	semidirect
167. #5527	C₂×C₃	semidirect
168. #5479	C₂×C₃	semidirect
169. #5479	C₂×C₃	semidirect
170. #5479	C₂×C₃	semidirect
171. C₂×#876	C₂×C₃	semidirect
342. C₃×C₄×Q₈	C₂×D₃	semidirect
343. C₃×C₄×Q₈	C₂×D₃	semidirect
344. C₃×C₄×Q₈	C₂²×C₃	semidirect
345. C₃×C₄×Q₈	C₂²×C₃	semidirect
365. C₃×C₄×D₄	C₂×D₃	semidirect
366. C₃×C₄×D₄	C₂×D₃	semidirect
369. C₃×C₄×D₄	C₂²×C₃	semidirect
370. C₃×C₄×D₄	C₂²×C₃	semidirect
380. C₃×#117	C₂×D₃	semidirect
381. C₃×#117	C₂×D₃	semidirect
382. C₃×#117	C₂²×C₃	semidirect
383. C₃×#117	C₂²×C₃	semidirect
394. C₂×C₃×C₄²	C₂×D₃	semidirect
395. C₂×C₃×C₄²	C₂×D₃	semidirect
396. C₂×C₃×C₄²	C₂²×C₃	semidirect
397. C₂×C₃×C₄²	C₂²×C₃	semidirect
400. #946	C₂²×C₃	semidirect
401. #944	C₂²×C₃	semidirect
403. #939	C₂²×C₃	semidirect
405. #935	C₂²×C₃	semidirect
413. #929	C₂²×C₃	semidirect
414. #929	C₂²×C₃	semidirect
415. #929	C₂²×C₃	semidirect
418. C₄×#67	C₂²×C₃	semidirect
419. C₄×#67	C₂²×C₃	semidirect
420. C₄×#67	C₂²×C₃	semidirect
424. #924	C₂²×C₃	semidirect
425. #924	C₂²×C₃	semidirect
426. #924	C₂²×C₃	semidirect
427. C₂×Dic₃⋊C₄	C₂²×C₃	semidirect
428. C₂×Dic₃⋊C₄	C₂²×C₃	semidirect
429. C₂×Dic₃⋊C₄	C₂²×C₃	semidirect
431. #898	C₂²×C₃	semidirect
433. #896	C₂²×C₃	semidirect
434. #896	C₂²×C₃	semidirect
437. #894	C₂²×C₃	semidirect
440. D₃×C₄⋊C₄	C₂²×C₃	semidirect
441. #890	C₂²×C₃	semidirect
442. #889	C₂²×C₃	semidirect
443. #889	C₂²×C₃	semidirect
444. #888	C₂²×C₃	semidirect
445. #887	C₂²×C₃	semidirect
448. #884	C₂²×C₃	semidirect
449. #883	C₂²×C₃	semidirect
452. #67⋊C₄	C₂²×C₃	semidirect
454. #879	C₂²×C₃	semidirect
455. #878	C₂²×C₃	semidirect
456. #878	C₂²×C₃	semidirect
457. #877	C₂²×C₃	semidirect
462. #876	C₂²×C₃	semidirect
463. #876	C₂²×C₃	semidirect
464. #876	C₂²×C₃	semidirect
465. #876	C₂²×C₃	semidirect
466. #876	C₂²×C₃	semidirect
469. #875	C₂²×C₃	semidirect
472. C₄×D₁₂	C₂²×C₃	semidirect
474. #872	C₂²×C₃	semidirect
475. #872	C₂²×C₃	semidirect
476. #872	C₂²×C₃	semidirect
477. #872	C₂²×C₃	semidirect
478. #870	C₂²×C₃	semidirect
479. #870	C₂²×C₃	semidirect
480. #870	C₂²×C₃	semidirect
481. C₄×Dic₆	C₂²×C₃	semidirect
482. C₄×Dic₆	C₂²×C₃	semidirect
483. C₄×Dic₆	C₂²×C₃	semidirect
560. C₄×#41	C₃×D₃	semidirect
885. C₄×Q₈	C₂×C₃×D₃	semidirect
886. C₄×Q₈	C₂×C₃×D₃	semidirect
902. C₄×D₄	C₂×C₃×D₃	semidirect
903. C₄×D₄	C₂×C₃×D₃	semidirect
911. #117	C₂×C₃×D₃	semidirect
912. #117	C₂×C₃×D₃	semidirect
921. C₂×C₄²	C₂×C₃×D₃	semidirect
922. C₂×C₄²	C₂×C₃×D₃	semidirect
1247. C₃²	#3521	semidirect
1359. C₃	#85854	direct (N × H)
1360. C₃	C₃×#3521	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃²×C₄×#41	2
C₃×#5829	2
C₃×#5824	2
C₃×#5583	2
C₃×#5582	2
C₃×#5581	2
C₃×#5568	2
C₃×#5564	2
C₃×#5560	2
C₃×#5556	2
C₃×#5554	2
C₃×#5546	2
C₃×#5545	2
C₃×#5540	2
C₃×#5539	2
C₃×#5533	2
C₃×#5531	2
C₃×#5530	2
C₃×#5527	2
C₃×#5479	2
C₂×C₃×#876	2
C₃×#3521	3
#85854	3

Subgroups — C3×#85854 #11909409

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#85854 #11909409