Subgroups — C₃×#86420 #11910954

Order 1152.

2457 conjugacy classes of subgroups.

The subgroup lattice has 1355 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#538	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#5707	C₂	1	2	yes	maximal, complemented
3	C₃×#5704	C₂	1	2	yes	maximal, complemented
4	C₃×#5684	C₂	1	2	yes	maximal, complemented
5	C₃×#5676	C₂	1	2	yes	maximal, complemented
6	C₃×#5666	C₂	1	2	yes	maximal, complemented
7	C₃×#5658	C₂	1	2	yes	maximal, complemented
8	C₃×#5645	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#5627	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#5619	C₂	1	2	yes	maximal, complemented
11	C₃×#5605	C₂	1	2	yes	maximal, complemented
12	C₃×D₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#5597	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#5591	C₂	1	2	yes	maximal, complemented
15	C₃×#5590	C₂	1	2	yes	maximal, complemented
16	C₃×#5565	C₂	1	2	yes	maximal, complemented
17	C₃×#5554	C₂	1	2	yes	maximal, complemented
18	C₃×#5493	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₃×#883	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×#3534	—	3	1	no	maximal
21	#86420	C₃	1	1	yes	maximal, characteristic, direct product factor
22	C₂²×C₃×#67	C₂²	1	1	yes	characteristic
23	C₂²×C₃×#67	C₂²	1	2	yes	complemented
24	C₂×C₃×#239	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₃×#237	C₂²	1	2	yes	complemented
26	C₂×C₃×D₃×D₄	C₂²	1	2	yes	complemented
27	C₂×C₃×D₃×D₄	C₂²	1	2	yes	complemented
28	C₂×C₃×D₃×D₄	C₂²	1	1	yes	characteristic, complemented
29	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic, complemented
30	C₃²×#126	C₂²	1	2	yes	complemented
31	C₃²×#124	C₂²	1	2	yes	complemented
32	C₃²×#123	C₂²	1	2	yes	complemented
33	C₃²×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₃²×#121	C₂²	1	1	yes	characteristic, complemented
35	C₃²×#121	C₂²	1	2	yes	complemented
36	C₃²×#120	C₂²	1	2	yes	complemented
37	C₃²×C₄×D₄	C₂²	1	2	yes	complemented
38	C₂×C₃²×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₃×#217	C₂²	1	1	yes	characteristic, complemented
40	C₃×#946	C₂²	1	1	yes	characteristic, complemented
41	C₃×#946	C₂²	1	2	yes	complemented
42	C₃×#940	C₂²	1	2	yes	complemented
43	C₃×#939	C₂²	1	2	yes	complemented
44	C₃×#939	C₂²	1	2	yes	complemented
45	C₃×#939	C₂²	1	2	yes	complemented
46	C₃×#939	C₂²	1	2	yes	complemented
47	C₃×#939	C₂²	1	2	yes	complemented
48	C₃×#938	C₂²	1	2	yes	complemented
49	C₃×#938	C₂²	1	1	yes	characteristic, complemented
50	C₃×#937	C₂²	1	2	yes	—
51	C₃×#937	C₂²	1	2	yes	complemented
52	C₃×D₄×Dic₃	C₂²	1	2	yes	complemented
53	C₃×#930	C₂²	1	1	yes	characteristic
54	C₃×#930	C₂²	1	2	yes	complemented
55	C₃×#930	C₂²	1	1	yes	characteristic, complemented
56	C₃×#930	C₂²	1	2	yes	complemented
57	C₃×#930	C₂²	1	2	yes	complemented
58	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
60	C₃×#926	C₂²	1	2	yes	complemented
61	C₂×C₃×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₃×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
63	C₃×#898	C₂²	1	2	yes	complemented
64	C₃×#898	C₂²	1	2	yes	complemented
65	C₃×#898	C₂²	1	2	yes	complemented
66	C₃×#897	C₂²	1	2	yes	complemented
67	C₃×#896	C₂²	1	2	yes	complemented
68	C₃×#895	C₂²	1	2	yes	complemented
69	C₃×#895	C₂²	1	1	yes	characteristic, complemented
70	C₃×#895	C₂²	1	1	yes	characteristic, complemented
71	C₃×#894	C₂²	1	2	yes	complemented
72	C₃×#894	C₂²	1	2	yes	complemented
73	C₃×#893	C₂²	1	2	yes	complemented
74	C₃×#892	C₂²	1	1	yes	characteristic, complemented
75	C₃×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
76	C₃×#890	C₂²	1	2	yes	complemented
77	C₃×#886	C₂²	1	2	yes	complemented
78	C₃×#886	C₂²	1	2	yes	complemented
79	C₃×#886	C₂²	1	2	yes	complemented
80	C₃×#886	C₂²	1	2	yes	complemented
81	C₃×#885	C₂²	1	2	yes	complemented
82	C₃×#884	C₂²	1	2	yes	—
83	C₃×#884	C₂²	1	2	yes	complemented
84	C₃×#884	C₂²	1	2	yes	complemented
85	C₃×#884	C₂²	1	2	yes	complemented
86	C₃×#883	C₂²	1	2	yes	complemented
87	C₃×#883	C₂²	1	2	yes	complemented
88	C₃×#883	C₂²	1	2	yes	complemented
89	C₃×#883	C₂²	1	2	yes	complemented
90	C₃×#883	C₂²	1	2	yes	complemented
91	C₃×#883	C₂²	1	2	yes	complemented
92	C₃×#883	C₂²	1	2	yes	complemented
93	C₃×#882	C₂²	1	2	yes	complemented
94	C₃×#882	C₂²	1	2	yes	complemented
95	C₃×#882	C₂²	1	2	yes	complemented
96	C₃×#882	C₂²	1	2	yes	complemented
97	C₃×#882	C₂²	1	2	yes	complemented
98	C₃×#67⋊C₄	C₂²	1	2	yes	complemented
99	C₃×#67⋊C₄	C₂²	1	2	yes	complemented
100	C₃×#67⋊C₄	C₂²	1	2	yes	complemented
101	C₃×D₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
102	C₃×D₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
103	C₃×#878	C₂²	1	2	yes	complemented
104	C₃×#878	C₂²	1	2	yes	complemented
105	C₃×#875	C₂²	1	2	yes	complemented
106	C₃×C₄×D₁₂	C₂²	1	2	yes	complemented
107	C₃×C₄×D₁₂	C₂²	1	2	yes	complemented
108	C₃×#870	C₂²	1	2	yes	complemented
109	C₃×#562	—	3	2	no	—
110	C₃×#560	—	3	2	no	—
111	C₃×#553	—	3	2	no	—
112	C₃×#551	—	3	2	no	—
113	C₃×#546	—	3	2	no	—
114	C₃×#546	—	3	2	no	—
115	C₃×#546	—	3	2	no	—
116	C₃×D₄²	—	3	2	no	—
117	C₃×#540	—	3	2	no	—
118	C₃×#539	—	3	2	no	—
119	C₃×#539	—	3	1	no	—
120	C₃×#538	—	2	1	no	—
121	C₃×#538	—	3	2	no	—
122	C₃×#538	D₃	1	1	yes	characteristic, complemented
123	C₃×#538	C₂×C₃	1	1	yes	characteristic, complemented
124	C₃×#537	—	3	1	no	—
125	C₃×#534	—	3	2	no	—
126	C₃×#534	—	3	1	no	—
127	C₃×#525	—	3	1	no	—
128	C₂×C₃×#123	—	3	1	no	—
129	C₂×C₃×#121	—	3	1	no	—
130	#5707	C₂×C₃	1	2	yes	complemented
131	#5704	C₂×C₃	1	2	yes	complemented
132	#5684	C₂×C₃	1	2	yes	complemented
133	#5676	C₂×C₃	1	2	yes	complemented
134	#5666	C₂×C₃	1	2	yes	complemented
135	#5658	C₂×C₃	1	2	yes	complemented
136	#5645	C₂×C₃	1	1	yes	characteristic, complemented
137	#5627	C₂×C₃	1	1	yes	characteristic, complemented
138	#5619	C₂×C₃	1	2	yes	complemented
139	#5605	C₂×C₃	1	2	yes	complemented
140	D₃×#121	C₂×C₃	1	1	yes	characteristic, complemented
141	#5597	C₂×C₃	1	1	yes	characteristic, complemented
142	#5591	C₂×C₃	1	2	yes	complemented
143	#5590	C₂×C₃	1	2	yes	complemented
144	#5565	C₂×C₃	1	2	yes	complemented
145	#5554	C₂×C₃	1	2	yes	complemented
146	#5493	C₂×C₃	1	1	yes	characteristic, complemented
147	C₂×#883	C₂×C₃	1	1	yes	characteristic, complemented
148	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
149	C₂³×C₃×D₃	C₂³	1	1	yes	characteristic
150	C₂³×C₃×D₃	C₂³	1	2	yes	—
151	C₂³×C₃×D₃	C₂³	1	2	yes	—
152	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
153	C₂×C₃²×D₄	C₂³	1	2	yes	—
154	C₂×C₃²×D₄	C₂³	1	2	yes	—
155	C₂×C₃²×D₄	C₂³	1	2	yes	—
156	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
157	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
158	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
159	C₂²×C₃²×C₄	C₂³	1	2	yes	—
160	C₂×C₃×#67	—	4	2	no	—
161	C₂×C₃×#67	—	4	4	no	—
162	C₂×C₃×#67	C₂³	1	2	yes	—
163	C₂×C₃×#67	C₂³	1	2	yes	—
164	C₂×C₃×#67	C₂³	1	2	yes	—
165	C₂×C₃×#67	C₂³	1	2	yes	—
166	C₂×C₃×#67	C₂³	1	2	yes	—
167	C₂×C₃×#67	C₂³	1	2	yes	—
168	C₂×C₃×#67	C₂³	1	2	yes	—
169	C₂×C₃×#67	C₂³	1	2	yes	—
170	C₂×C₃×#67	C₂³	1	2	yes	—
171	C₂×C₃×#67	C₂³	1	2	yes	—
172	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
173	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
174	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
175	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
176	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
177	C₃×#239	—	4	2	no	—
178	C₃×#237	—	4	4	no	—
179	C₃×D₃×D₄	—	4	2	no	—
180	C₃×D₃×D₄	—	4	4	no	—
181	C₃×D₃×D₄	—	4	4	no	—
182	C₂×C₃×D₁₂	C₂³	1	2	yes	—
183	C₂×C₃×D₁₂	C₂³	1	2	yes	—
184	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
185	C₂×C₃×D₁₂	C₂³	1	2	yes	—
186	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
187	C₂×C₃×D₁₂	C₂³	1	2	yes	—
188	C₂×C₃×C₄×D₃	—	4	2	no	—
189	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
190	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
191	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
192	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
193	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
194	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
195	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
196	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
197	C₂×C₃×Dic₆	C₂³	1	2	yes	—
198	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
199	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
200	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
201	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
202	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
203	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
204	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
205	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
206	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
207	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
208	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
209	C₃²×C₄²	C₂³	1	2	yes	—
210	C₃×#217	C₂³	1	2	yes	—
211	C₃×#217	C₂³	1	2	yes	—
212	C₃×#217	C₂³	1	2	yes	—
213	C₃×#217	C₂³	1	2	yes	—
214	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
215	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
216	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
217	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
218	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
219	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
220	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
221	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
222	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
223	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
227	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
228	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
229	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
230	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
231	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
232	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
233	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
234	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
235	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
236	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
237	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
238	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
239	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
240	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
241	C₃×C₄×Dic₃	C₂³	1	2	yes	—
242	C₃×C₄×Dic₃	C₂³	1	2	yes	—
243	#3534	—	3	1	no	Sylow
244	C₂×C₃×#41	—	3	1	no	—
245	C₂×C₃×#41	—	3	2	no	—
246	C₂²×C₃×D₄	—	3	1	no	—
247	C₂²×C₃×D₄	—	3	2	no	—
248	C₂²×C₃×D₄	—	3	1	no	—
249	C₂²×C₃×D₄	—	3	2	no	—
250	C₂²×C₃×D₄	—	3	2	no	—
251	C₂³×C₃×C₄	—	3	1	no	—
252	C₂²×#67	C₂²×C₃	1	1	yes	characteristic
253	C₂²×#67	C₂²×C₃	1	2	yes	complemented
254	C₂×#239	C₂²×C₃	1	1	yes	characteristic, complemented
255	C₂×#237	C₂²×C₃	1	2	yes	complemented
256	C₂×D₃×D₄	C₂²×C₃	1	2	yes	complemented
257	C₂×D₃×D₄	C₂²×C₃	1	2	yes	complemented
258	C₂×D₃×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
259	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic, complemented
260	C₃×#127	—	3	2	no	—
261	C₃×#126	—	2	2	no	—
262	C₃×#126	—	3	2	no	—
263	C₃×#126	—	3	2	no	—
264	C₃×#126	—	3	2	no	—
265	C₃×#126	C₂×D₃	1	2	yes	complemented
266	C₃×#126	C₂²×C₃	1	2	yes	complemented
267	C₃×#125	—	3	2	no	—
268	C₃×#125	—	3	2	no	—
269	C₃×#124	—	2	2	no	—
270	C₃×#124	—	3	2	no	—
271	C₃×#124	—	3	2	no	—
272	C₃×#124	C₂×D₃	1	2	yes	complemented
273	C₃×#124	C₂²×C₃	1	2	yes	complemented
274	C₃×#123	—	2	2	no	—
275	C₃×#123	—	3	2	no	—
276	C₃×#123	—	3	2	no	—
277	C₃×#123	—	3	2	no	—
278	C₃×#123	—	3	2	no	—
279	C₃×#123	—	3	2	no	—
280	C₃×#123	—	3	2	no	—
281	C₃×#123	—	3	2	no	—
282	C₃×#123	—	3	2	no	—
283	C₃×#123	—	3	2	no	—
284	C₃×#123	—	3	2	no	—
285	C₃×#123	—	3	2	no	—
286	C₃×#123	—	3	2	no	—
287	C₃×#123	—	3	2	no	—
288	C₃×#123	C₂×D₃	1	2	yes	complemented
289	C₃×#123	C₂²×C₃	1	2	yes	complemented
290	C₃×C₂²⋊Q₈	—	2	1	no	—
291	C₃×C₂²⋊Q₈	—	3	1	no	—
292	C₃×C₂²⋊Q₈	—	3	2	no	—
293	C₃×C₂²⋊Q₈	—	3	2	no	—
294	C₃×C₂²⋊Q₈	—	3	2	no	—
295	C₃×C₂²⋊Q₈	—	3	2	no	—
296	C₃×C₂²⋊Q₈	—	3	2	no	—
297	C₃×C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
298	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
299	C₃×#121	—	2	1	no	—
300	C₃×#121	—	2	2	no	—
301	C₃×#121	—	3	2	no	—
302	C₃×#121	—	3	2	no	—
303	C₃×#121	—	3	1	no	—
304	C₃×#121	—	3	2	no	—
305	C₃×#121	—	3	2	no	—
306	C₃×#121	—	3	2	no	—
307	C₃×#121	—	3	2	no	—
308	C₃×#121	—	3	2	no	—
309	C₃×#121	—	3	2	no	—
310	C₃×#121	—	3	1	no	—
311	C₃×#121	—	3	1	no	—
312	C₃×#121	—	3	2	no	—
313	C₃×#121	—	3	1	no	—
314	C₃×#121	—	3	2	no	—
315	C₃×#121	—	3	1	no	—
316	C₃×#121	—	3	2	no	—
317	C₃×#121	—	3	2	no	—
318	C₃×#121	—	3	2	no	—
319	C₃×#121	—	3	2	no	—
320	C₃×#121	C₂×D₃	1	1	yes	characteristic, complemented
321	C₃×#121	C₂×D₃	1	2	yes	complemented
322	C₃×#121	C₂²×C₃	1	1	yes	characteristic, complemented
323	C₃×#121	C₂²×C₃	1	2	yes	complemented
324	C₃×#120	—	2	2	no	—
325	C₃×#120	—	3	2	no	—
326	C₃×#120	—	3	2	no	—
327	C₃×#120	—	3	2	no	—
328	C₃×#120	—	3	2	no	—
329	C₃×#120	—	3	2	no	—
330	C₃×#120	—	3	2	no	—
331	C₃×#120	—	3	2	no	—
332	C₃×#120	C₂×D₃	1	2	yes	complemented
333	C₃×#120	C₂²×C₃	1	2	yes	complemented
334	C₃×C₄×D₄	—	2	2	no	—
335	C₃×C₄×D₄	—	3	2	no	—
336	C₃×C₄×D₄	—	3	2	no	—
337	C₃×C₄×D₄	—	3	2	no	—
338	C₃×C₄×D₄	—	3	2	no	—
339	C₃×C₄×D₄	—	3	2	no	—
340	C₃×C₄×D₄	—	3	2	no	—
341	C₃×C₄×D₄	—	3	2	no	—
342	C₃×C₄×D₄	C₂×D₃	1	2	yes	complemented
343	C₃×C₄×D₄	C₂²×C₃	1	2	yes	complemented
344	C₃×#117	—	3	2	no	—
345	C₃×#117	—	3	1	no	—
346	C₂×C₃×C₄⋊C₄	—	3	1	no	—
347	C₂×C₃×C₄⋊C₄	—	3	1	no	—
348	C₂×C₃×C₄⋊C₄	—	3	1	no	—
349	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
350	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
351	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
352	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
353	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
354	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
355	C₂×C₃×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
356	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
357	C₂×#217	C₂²×C₃	1	1	yes	characteristic, complemented
358	#946	C₂²×C₃	1	2	yes	complemented
359	#946	C₂²×C₃	1	1	yes	characteristic, complemented
360	#940	C₂²×C₃	1	2	yes	complemented
361	#939	C₂²×C₃	1	2	yes	complemented
362	#939	C₂²×C₃	1	2	yes	complemented
363	#939	C₂²×C₃	1	2	yes	complemented
364	#939	C₂²×C₃	1	2	yes	complemented
365	#939	C₂²×C₃	1	2	yes	complemented
366	#938	C₂²×C₃	1	2	yes	complemented
367	#938	C₂²×C₃	1	1	yes	characteristic, complemented
368	#937	C₂²×C₃	1	2	yes	—
369	#937	C₂²×C₃	1	2	yes	complemented
370	D₄×Dic₃	C₂²×C₃	1	2	yes	complemented
371	#930	C₂²×C₃	1	1	yes	characteristic
372	#930	C₂²×C₃	1	2	yes	complemented
373	#930	C₂²×C₃	1	2	yes	complemented
374	#930	C₂²×C₃	1	2	yes	complemented
375	#930	C₂²×C₃	1	1	yes	characteristic, complemented
376	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	complemented
377	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
378	#926	C₂²×C₃	1	2	yes	complemented
379	C₂×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
380	C₂×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
381	#898	C₂²×C₃	1	2	yes	complemented
382	#898	C₂²×C₃	1	2	yes	complemented
383	#898	C₂²×C₃	1	2	yes	complemented
384	#897	C₂²×C₃	1	2	yes	complemented
385	#896	C₂²×C₃	1	2	yes	complemented
386	#895	C₂²×C₃	1	1	yes	characteristic, complemented
387	#895	C₂²×C₃	1	2	yes	complemented
388	#895	C₂²×C₃	1	1	yes	characteristic, complemented
389	#894	C₂²×C₃	1	2	yes	complemented
390	#894	C₂²×C₃	1	2	yes	complemented
391	#893	C₂²×C₃	1	2	yes	complemented
392	#892	C₂²×C₃	1	1	yes	characteristic, complemented
393	D₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
394	#890	C₂²×C₃	1	2	yes	complemented
395	#886	C₂²×C₃	1	2	yes	complemented
396	#886	C₂²×C₃	1	2	yes	complemented
397	#886	C₂²×C₃	1	2	yes	complemented
398	#886	C₂²×C₃	1	2	yes	complemented
399	#885	C₂²×C₃	1	2	yes	complemented
400	#884	C₂²×C₃	1	2	yes	—
401	#884	C₂²×C₃	1	2	yes	complemented
402	#884	C₂²×C₃	1	2	yes	complemented
403	#884	C₂²×C₃	1	2	yes	complemented
404	#883	C₂²×C₃	1	2	yes	complemented
405	#883	C₂²×C₃	1	2	yes	complemented
406	#883	C₂²×C₃	1	2	yes	complemented
407	#883	C₂²×C₃	1	2	yes	complemented
408	#883	C₂²×C₃	1	2	yes	complemented
409	#883	C₂²×C₃	1	2	yes	complemented
410	#883	C₂²×C₃	1	2	yes	complemented
411	#882	C₂²×C₃	1	2	yes	complemented
412	#882	C₂²×C₃	1	2	yes	complemented
413	#882	C₂²×C₃	1	2	yes	complemented
414	#882	C₂²×C₃	1	2	yes	complemented
415	#882	C₂²×C₃	1	2	yes	complemented
416	#67⋊C₄	C₂²×C₃	1	2	yes	complemented
417	#67⋊C₄	C₂²×C₃	1	2	yes	complemented
418	#67⋊C₄	C₂²×C₃	1	2	yes	complemented
419	D₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
420	D₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
421	#878	C₂²×C₃	1	2	yes	complemented
422	#878	C₂²×C₃	1	2	yes	complemented
423	#875	C₂²×C₃	1	2	yes	complemented
424	C₄×D₁₂	C₂²×C₃	1	2	yes	complemented
425	C₄×D₁₂	C₂²×C₃	1	2	yes	complemented
426	#870	C₂²×C₃	1	2	yes	complemented
427	C₂³×C₃²	—	2	2	no	—
428	C₂³×C₃²	—	4	1	no	—
429	C₂³×C₃²	—	4	1	no	—
430	C₂³×C₃²	C₂⁴	1	2	yes	—
431	C₂³×C₃²	C₂⁴	1	2	yes	—
432	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
433	C₂²×C₃×D₃	—	2	2	no	—
434	C₂²×C₃×D₃	—	2	2	no	—
435	C₂²×C₃×D₃	—	2	4	no	—
436	C₂²×C₃×D₃	—	4	1	no	—
437	C₂²×C₃×D₃	—	4	2	no	—
438	C₂²×C₃×D₃	—	4	2	no	—
439	C₂²×C₃×D₃	—	4	2	no	—
440	C₂²×C₃×D₃	—	4	2	no	—
441	C₂²×C₃×D₃	—	4	2	no	—
442	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
443	C₂²×C₃×D₃	C₂⁴	1	1	yes	characteristic
444	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
445	C₂²×C₃×D₃	C₂⁴	1	1	yes	characteristic
446	C₃²×Q₈	—	4	1	no	—
447	C₃²×D₄	—	2	4	no	—
448	C₃²×D₄	—	4	1	no	—
449	C₃²×D₄	—	4	2	no	—
450	C₃²×D₄	—	4	2	no	—
451	C₂×C₃²×C₄	—	4	1	no	—
452	C₂×C₃²×C₄	—	4	1	no	—
453	C₂×C₃²×C₄	—	4	2	no	—
454	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
455	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
456	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
457	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
458	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
459	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
460	C₃×#67	—	2	4	no	—
461	C₃×#67	—	2	4	no	—
462	C₃×#67	—	2	4	no	—
463	C₃×#67	—	4	2	no	—
464	C₃×#67	—	4	2	no	—
465	C₃×#67	—	4	2	no	—
466	C₃×#67	—	4	2	no	—
467	C₃×#67	—	4	2	no	—
468	C₃×#67	—	4	2	no	—
469	C₃×#67	—	4	2	no	—
470	C₂×C₃×Dic₃	—	2	2	no	—
471	C₂×C₃×Dic₃	—	4	1	no	—
472	C₂×C₃×Dic₃	—	4	2	no	—
473	C₂×C₃×Dic₃	—	4	2	no	—
474	C₂×C₃×Dic₃	—	4	1	no	—
475	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
476	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
477	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
478	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
479	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
480	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
481	C₃×D₁₂	—	2	4	no	—
482	C₃×D₁₂	—	4	2	no	—
483	C₃×D₁₂	—	4	2	no	—
484	C₃×D₁₂	—	4	2	no	—
485	C₃×D₁₂	—	4	1	no	—
486	C₃×D₁₂	—	4	1	no	—
487	C₃×C₄×D₃	—	2	2	no	—
488	C₃×C₄×D₃	—	2	2	no	—
489	C₃×C₄×D₃	—	4	1	no	—
490	C₃×C₄×D₃	—	4	1	no	—
491	C₃×C₄×D₃	—	4	2	no	—
492	C₃×C₄×D₃	—	4	2	no	—
493	C₃×C₄×D₃	—	4	2	no	—
494	C₃×C₄×D₃	—	4	2	no	—
495	C₃×Dic₆	—	4	2	no	—
496	#562	—	3	2	no	—
497	#560	—	3	2	no	—
498	#553	—	3	2	no	—
499	#551	—	3	2	no	—
500	#546	—	3	2	no	—
501	#546	—	3	2	no	—
502	#546	—	3	2	no	—
503	D₄²	—	3	2	no	—
504	#540	—	3	2	no	—
505	#539	—	3	2	no	—
506	#539	—	3	1	no	—
507	#538	—	3	2	no	—
508	#538	C₃×D₃	1	1	yes	characteristic, complemented
509	#537	—	3	1	no	—
510	#534	—	3	2	no	—
511	#534	—	3	1	no	—
512	#525	—	3	1	no	—
513	C₂×#123	—	3	1	no	—
514	C₂×#121	—	3	1	no	—
515	C₂⁴×C₃	—	2	1	no	—
516	C₂⁴×C₃	—	3	1	no	—
517	C₂⁴×C₃	—	3	2	no	—
518	C₂⁴×C₃	—	3	2	no	—
519	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
520	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
521	C₂³×D₃	C₂³×C₃	1	1	yes	characteristic
522	C₂³×D₃	C₂³×C₃	1	2	yes	—
523	C₂³×D₃	C₂³×C₃	1	2	yes	—
524	C₃×#41	—	12	4	no	—
525	C₃×#41	—	12	2	no	—
526	C₂×C₃×Q₈	—	2	1	no	—
527	C₂×C₃×Q₈	—	3	2	no	—
528	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
529	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
530	C₂×C₃×D₄	—	2	2	no	—
531	C₂×C₃×D₄	—	2	2	no	—
532	C₂×C₃×D₄	—	2	2	no	—
533	C₂×C₃×D₄	—	2	1	no	—
534	C₂×C₃×D₄	—	3	2	no	—
535	C₂×C₃×D₄	—	3	2	no	—
536	C₂×C₃×D₄	—	3	2	no	—
537	C₂×C₃×D₄	—	3	2	no	—
538	C₂×C₃×D₄	—	3	2	no	—
539	C₂×C₃×D₄	—	3	2	no	—
540	C₂×C₃×D₄	—	3	2	no	—
541	C₂×C₃×D₄	—	3	2	no	—
542	C₂×C₃×D₄	—	3	2	no	—
543	C₂×C₃×D₄	—	3	2	no	—
544	C₂×C₃×D₄	—	3	2	no	—
545	C₂×C₃×D₄	—	3	2	no	—
546	C₂×C₃×D₄	—	3	2	no	—
547	C₂×C₃×D₄	—	3	1	no	—
548	C₂×C₃×D₄	—	3	1	no	—
549	C₂×C₃×D₄	—	3	2	no	—
550	C₂×C₃×D₄	—	12	2	no	—
551	C₂×C₃×D₄	—	12	4	no	—
552	C₂×C₃×D₄	—	12	4	no	—
553	C₂×C₃×D₄	—	12	4	no	—
554	C₂×C₃×D₄	—	12	2	no	—
555	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
556	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
557	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
558	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic
559	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
560	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
561	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
562	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
563	C₂²×C₃×C₄	—	2	1	no	—
564	C₂²×C₃×C₄	—	2	1	no	—
565	C₂²×C₃×C₄	—	2	2	no	—
566	C₂²×C₃×C₄	—	3	1	no	—
567	C₂²×C₃×C₄	—	3	1	no	—
568	C₂²×C₃×C₄	—	3	2	no	—
569	C₂²×C₃×C₄	—	3	1	no	—
570	C₂²×C₃×C₄	—	3	2	no	—
571	C₂²×C₃×C₄	—	3	1	no	—
572	C₂²×C₃×C₄	—	3	1	no	—
573	C₂²×C₃×C₄	—	3	2	no	—
574	C₂²×C₃×C₄	—	3	2	no	—
575	C₂²×C₃×C₄	—	3	2	no	—
576	C₂²×C₃×C₄	—	3	1	no	—
577	C₂²×C₃×C₄	—	3	2	no	—
578	C₂²×C₃×C₄	—	3	1	no	—
579	C₂²×C₃×C₄	—	12	2	no	—
580	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
581	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
582	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
583	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
584	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
585	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
586	C₂×#67	—	4	2	no	—
587	C₂×#67	—	4	4	no	—
588	C₂×#67	C₂³×C₃	1	2	yes	—
589	C₂×#67	C₂³×C₃	1	2	yes	—
590	C₂×#67	C₂³×C₃	1	2	yes	—
591	C₂×#67	C₂³×C₃	1	2	yes	—
592	C₂×#67	C₂³×C₃	1	2	yes	—
593	C₂×#67	C₂³×C₃	1	2	yes	—
594	C₂×#67	C₂³×C₃	1	2	yes	—
595	C₂×#67	C₂³×C₃	1	2	yes	—
596	C₂×#67	C₂³×C₃	1	2	yes	—
597	C₂×#67	C₂³×C₃	1	2	yes	—
598	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
599	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
600	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
601	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
602	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
603	#239	—	4	2	no	—
604	#237	—	4	4	no	—
605	D₃×D₄	—	4	2	no	—
606	D₃×D₄	—	4	4	no	—
607	D₃×D₄	—	4	4	no	—
608	C₂×D₁₂	C₂³×C₃	1	2	yes	—
609	C₂×D₁₂	C₂³×C₃	1	2	yes	—
610	C₂×D₁₂	C₂³×C₃	1	2	yes	—
611	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
612	C₂×D₁₂	C₂³×C₃	1	2	yes	—
613	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
614	C₂×C₄×D₃	—	4	2	no	—
615	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
616	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
617	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
618	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
619	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
620	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
621	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
622	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
623	C₂×Dic₆	C₂³×C₃	1	2	yes	—
624	C₃×C₄⋊C₄	—	2	2	no	—
625	C₃×C₄⋊C₄	—	2	2	no	—
626	C₃×C₄⋊C₄	—	2	1	no	—
627	C₃×C₄⋊C₄	—	2	1	no	—
628	C₃×C₄⋊C₄	—	3	2	no	—
629	C₃×C₄⋊C₄	—	3	2	no	—
630	C₃×C₄⋊C₄	—	3	2	no	—
631	C₃×C₄⋊C₄	—	3	2	no	—
632	C₃×C₄⋊C₄	—	3	2	no	—
633	C₃×C₄⋊C₄	—	3	2	no	—
634	C₃×C₄⋊C₄	—	3	2	no	—
635	C₃×C₄⋊C₄	—	3	1	no	—
636	C₃×C₄⋊C₄	—	3	2	no	—
637	C₃×C₄⋊C₄	—	3	1	no	—
638	C₃×C₄⋊C₄	—	3	2	no	—
639	C₃×C₄⋊C₄	—	3	2	no	—
640	C₃×C₄⋊C₄	—	3	2	no	—
641	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
642	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
643	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
644	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
645	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
646	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
647	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
648	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
649	C₃×C₂²⋊C₄	—	2	2	no	—
650	C₃×C₂²⋊C₄	—	2	2	no	—
651	C₃×C₂²⋊C₄	—	2	2	no	—
652	C₃×C₂²⋊C₄	—	2	2	no	—
653	C₃×C₂²⋊C₄	—	2	2	no	—
654	C₃×C₂²⋊C₄	—	2	2	no	—
655	C₃×C₂²⋊C₄	—	2	2	no	—
656	C₃×C₂²⋊C₄	—	3	2	no	—
657	C₃×C₂²⋊C₄	—	3	2	no	—
658	C₃×C₂²⋊C₄	—	3	2	no	—
659	C₃×C₂²⋊C₄	—	3	2	no	—
660	C₃×C₂²⋊C₄	—	3	2	no	—
661	C₃×C₂²⋊C₄	—	3	2	no	—
662	C₃×C₂²⋊C₄	—	3	2	no	—
663	C₃×C₂²⋊C₄	—	3	2	no	—
664	C₃×C₂²⋊C₄	—	3	2	no	—
665	C₃×C₂²⋊C₄	—	3	2	no	—
666	C₃×C₂²⋊C₄	—	3	2	no	—
667	C₃×C₂²⋊C₄	—	3	2	no	—
668	C₃×C₂²⋊C₄	—	3	2	no	—
669	C₃×C₂²⋊C₄	—	3	2	no	—
670	C₃×C₂²⋊C₄	—	3	2	no	—
671	C₃×C₂²⋊C₄	—	3	2	no	—
672	C₃×C₂²⋊C₄	—	3	2	no	—
673	C₃×C₂²⋊C₄	—	3	2	no	—
674	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
675	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
676	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
677	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
678	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
679	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
680	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
681	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
682	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
683	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
684	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
685	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
686	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
687	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
688	C₃×C₄²	—	2	2	no	—
689	C₃×C₄²	—	3	2	no	—
690	C₃×C₄²	—	3	2	no	—
691	C₃×C₄²	C₂²×D₃	1	2	yes	—
692	C₃×C₄²	C₂³×C₃	1	2	yes	—
693	#217	C₂³×C₃	1	2	yes	—
694	#217	C₂³×C₃	1	2	yes	—
695	#217	C₂³×C₃	1	2	yes	—
696	#217	C₂³×C₃	1	2	yes	—
697	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
698	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
699	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
700	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
701	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
702	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
703	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
704	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
705	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
706	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
707	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
708	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
709	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
710	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
711	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
712	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
713	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
714	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
715	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
716	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
717	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
718	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
719	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
720	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
721	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
722	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
723	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
724	C₄×Dic₃	C₂³×C₃	1	2	yes	—
725	C₄×Dic₃	C₂³×C₃	1	2	yes	—
726	C₂²×C₃²	—	2	1	no	—
727	C₂²×C₃²	—	2	1	no	—
728	C₂²×C₃²	—	2	2	no	—
729	C₂²×C₃²	—	2	2	no	—
730	C₂²×C₃²	—	2	2	no	—
731	C₂²×C₃²	—	2	2	no	—
732	C₂²×C₃²	—	2	2	no	—
733	C₂²×C₃²	—	2	2	no	—
734	C₂²×C₃²	—	8	2	no	—
735	C₂²×C₃²	H(5,𝔽₂)	1	2	yes	—
736	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
737	C₂×C₃×D₃	—	2	1	no	—
738	C₂×C₃×D₃	—	2	1	no	—
739	C₂×C₃×D₃	—	2	1	no	—
740	C₂×C₃×D₃	—	2	2	no	—
741	C₂×C₃×D₃	—	2	2	no	—
742	C₂×C₃×D₃	—	2	2	no	—
743	C₂×C₃×D₃	—	2	1	no	—
744	C₂×C₃×D₃	—	2	2	no	—
745	C₂×C₃×D₃	—	2	1	no	—
746	C₂×C₃×D₃	—	2	2	no	—
747	C₂×C₃×D₃	—	2	2	no	—
748	C₂×C₃×D₃	—	4	4	no	—
749	C₂×C₃×D₃	—	8	4	no	—
750	C₂×C₃×D₃	—	8	4	no	—
751	C₂×C₃×D₃	H(5,𝔽₂)	1	2	yes	—
752	C₃²×C₄	—	2	2	no	—
753	C₃²×C₄	—	2	1	no	—
754	C₃²×C₄	—	2	1	no	—
755	C₃²×C₄	—	2	2	no	—
756	C₃²×C₄	—	2	2	no	—
757	C₃²×C₄	—	2	2	no	—
758	C₃×Dic₃	—	2	2	no	—
759	C₃×Dic₃	—	2	2	no	—
760	C₃×Dic₃	—	2	1	no	—
761	C₃×Dic₃	—	2	1	no	—
762	C₃×Dic₃	—	2	2	no	—
763	C₃×Dic₃	—	2	2	no	—
764	C₂×#41	—	3	1	no	—
765	C₂×#41	—	3	2	no	—
766	C₂²×D₄	—	3	1	no	—
767	C₂²×D₄	—	3	2	no	—
768	C₂²×D₄	—	3	1	no	—
769	C₂²×D₄	—	3	2	no	—
770	C₂²×D₄	—	3	2	no	—
771	C₂³×C₄	—	3	1	no	—
772	#127	—	3	2	no	—
773	#126	—	3	2	no	—
774	#126	—	3	2	no	—
775	#126	—	3	2	no	—
776	#126	C₂×C₃×D₃	1	2	yes	complemented
777	#125	—	3	2	no	—
778	#125	—	3	2	no	—
779	#124	—	3	2	no	—
780	#124	—	3	2	no	—
781	#124	C₂×C₃×D₃	1	2	yes	complemented
782	#123	—	3	2	no	—
783	#123	—	3	2	no	—
784	#123	—	3	2	no	—
785	#123	—	3	2	no	—
786	#123	—	3	2	no	—
787	#123	—	3	2	no	—
788	#123	—	3	2	no	—
789	#123	—	3	2	no	—
790	#123	—	3	2	no	—
791	#123	—	3	2	no	—
792	#123	—	3	2	no	—
793	#123	—	3	2	no	—
794	#123	—	3	2	no	—
795	#123	C₂×C₃×D₃	1	2	yes	complemented
796	C₂²⋊Q₈	—	3	1	no	—
797	C₂²⋊Q₈	—	3	2	no	—
798	C₂²⋊Q₈	—	3	2	no	—
799	C₂²⋊Q₈	—	3	2	no	—
800	C₂²⋊Q₈	—	3	2	no	—
801	C₂²⋊Q₈	—	3	2	no	—
802	C₂²⋊Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
803	#121	—	3	1	no	—
804	#121	—	3	2	no	—
805	#121	—	3	2	no	—
806	#121	—	3	2	no	—
807	#121	—	3	2	no	—
808	#121	—	3	2	no	—
809	#121	—	3	2	no	—
810	#121	—	3	1	no	—
811	#121	—	3	1	no	—
812	#121	—	3	2	no	—
813	#121	—	3	2	no	—
814	#121	—	3	2	no	—
815	#121	—	3	1	no	—
816	#121	—	3	1	no	—
817	#121	—	3	2	no	—
818	#121	—	3	2	no	—
819	#121	—	3	2	no	—
820	#121	—	3	2	no	—
821	#121	—	3	2	no	—
822	#121	C₂×C₃×D₃	1	1	yes	characteristic, complemented
823	#121	C₂×C₃×D₃	1	2	yes	complemented
824	#120	—	3	2	no	—
825	#120	—	3	2	no	—
826	#120	—	3	2	no	—
827	#120	—	3	2	no	—
828	#120	—	3	2	no	—
829	#120	—	3	2	no	—
830	#120	—	3	2	no	—
831	#120	C₂×C₃×D₃	1	2	yes	complemented
832	C₄×D₄	—	3	2	no	—
833	C₄×D₄	—	3	2	no	—
834	C₄×D₄	—	3	2	no	—
835	C₄×D₄	—	3	2	no	—
836	C₄×D₄	—	3	2	no	—
837	C₄×D₄	—	3	2	no	—
838	C₄×D₄	—	3	2	no	—
839	C₄×D₄	C₂×C₃×D₃	1	2	yes	complemented
840	#117	—	3	2	no	—
841	#117	—	3	1	no	—
842	C₂×C₄⋊C₄	—	3	1	no	—
843	C₂×C₄⋊C₄	—	3	1	no	—
844	C₂×C₄⋊C₄	—	3	1	no	—
845	C₂×C₂²⋊C₄	—	3	1	no	—
846	C₂×C₂²⋊C₄	—	3	1	no	—
847	C₂×C₂²⋊C₄	—	3	2	no	—
848	C₂×C₂²⋊C₄	—	3	2	no	—
849	C₂×C₂²⋊C₄	—	3	2	no	—
850	C₂×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
851	C₂³×C₃	—	2	2	no	—
852	C₂³×C₃	—	2	2	no	—
853	C₂³×C₃	—	2	1	no	—
854	C₂³×C₃	—	2	2	no	—
855	C₂³×C₃	—	2	2	no	—
856	C₂³×C₃	—	3	1	no	—
857	C₂³×C₃	—	3	2	no	—
858	C₂³×C₃	—	3	2	no	—
859	C₂³×C₃	—	3	1	no	—
860	C₂³×C₃	—	4	2	no	—
861	C₂³×C₃	—	4	1	no	—
862	C₂³×C₃	—	4	1	no	—
863	C₂³×C₃	—	4	1	no	—
864	C₂³×C₃	—	4	1	no	—
865	C₂³×C₃	—	6	2	no	—
866	C₂³×C₃	—	6	4	no	—
867	C₂³×C₃	—	6	2	no	—
868	C₂³×C₃	—	8	1	no	—
869	C₂³×C₃	—	8	1	no	—
870	C₂³×C₃	—	12	1	no	—
871	C₂³×C₃	—	12	2	no	—
872	C₂³×C₃	—	12	2	no	—
873	C₂³×C₃	—	12	2	no	—
874	C₂³×C₃	—	12	2	no	—
875	C₂³×C₃	—	12	2	no	—
876	C₂³×C₃	C₂³×D₃	1	2	yes	—
877	C₂³×C₃	C₂³×D₃	1	2	yes	—
878	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
879	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
880	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
881	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
882	C₂²×D₃	—	2	2	no	—
883	C₂²×D₃	—	2	2	no	—
884	C₂²×D₃	—	2	4	no	—
885	C₂²×D₃	—	4	1	no	—
886	C₂²×D₃	—	4	2	no	—
887	C₂²×D₃	—	4	2	no	—
888	C₂²×D₃	—	4	2	no	—
889	C₂²×D₃	—	4	2	no	—
890	C₂²×D₃	—	4	2	no	—
891	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
892	C₂²×D₃	C₂⁴×C₃	1	1	yes	characteristic
893	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
894	C₂²×D₃	C₂⁴×C₃	1	1	yes	characteristic
895	C₃×Q₈	—	4	1	no	—
896	C₃×Q₈	—	4	1	no	—
897	C₃×Q₈	—	8	1	no	—
898	C₃×Q₈	—	12	2	no	—
899	C₃×D₄	—	2	4	no	—
900	C₃×D₄	—	2	4	no	—
901	C₃×D₄	—	4	4	no	—
902	C₃×D₄	—	4	1	no	—
903	C₃×D₄	—	4	2	no	—
904	C₃×D₄	—	4	1	no	—
905	C₃×D₄	—	4	2	no	—
906	C₃×D₄	—	4	2	no	—
907	C₃×D₄	—	4	2	no	—
908	C₃×D₄	—	6	4	no	—
909	C₃×D₄	—	6	4	no	—
910	C₃×D₄	—	6	4	no	—
911	C₃×D₄	—	6	4	no	—
912	C₃×D₄	—	8	1	no	—
913	C₃×D₄	—	8	2	no	—
914	C₃×D₄	—	8	2	no	—
915	C₃×D₄	—	12	2	no	—
916	C₃×D₄	—	12	2	no	—
917	C₃×D₄	—	12	2	no	—
918	C₃×D₄	—	12	1	no	—
919	C₃×D₄	—	12	1	no	—
920	C₃×D₄	—	12	2	no	—
921	C₃×D₄	—	12	2	no	—
922	C₃×D₄	—	12	2	no	—
923	C₃×D₄	—	12	2	no	—
924	C₃×D₄	—	12	2	no	—
925	C₃×D₄	—	12	2	no	—
926	C₃×D₄	—	12	2	no	—
927	C₂×C₃×C₄	—	2	2	no	—
928	C₂×C₃×C₄	—	2	2	no	—
929	C₂×C₃×C₄	—	2	2	no	—
930	C₂×C₃×C₄	—	2	1	no	—
931	C₂×C₃×C₄	—	2	2	no	—
932	C₂×C₃×C₄	—	2	1	no	—
933	C₂×C₃×C₄	—	3	1	no	—
934	C₂×C₃×C₄	—	3	2	no	—
935	C₂×C₃×C₄	—	3	2	no	—
936	C₂×C₃×C₄	—	3	2	no	—
937	C₂×C₃×C₄	—	3	2	no	—
938	C₂×C₃×C₄	—	3	1	no	—
939	C₂×C₃×C₄	—	4	1	no	—
940	C₂×C₃×C₄	—	4	1	no	—
941	C₂×C₃×C₄	—	4	1	no	—
942	C₂×C₃×C₄	—	4	2	no	—
943	C₂×C₃×C₄	—	4	1	no	—
944	C₂×C₃×C₄	—	4	2	no	—
945	C₂×C₃×C₄	—	6	2	no	—
946	C₂×C₃×C₄	—	6	2	no	—
947	C₂×C₃×C₄	—	6	2	no	—
948	C₂×C₃×C₄	—	8	1	no	—
949	C₂×C₃×C₄	—	8	1	no	—
950	C₂×C₃×C₄	—	8	2	no	—
951	C₂×C₃×C₄	—	12	1	no	—
952	C₂×C₃×C₄	—	12	1	no	—
953	C₂×C₃×C₄	—	12	2	no	—
954	C₂×C₃×C₄	—	12	2	no	—
955	C₂×C₃×C₄	—	12	2	no	—
956	C₂×C₃×C₄	—	12	2	no	—
957	C₂×C₃×C₄	—	12	1	no	—
958	C₂×C₃×C₄	—	12	2	no	—
959	C₂×C₃×C₄	—	12	1	no	—
960	C₂×C₃×C₄	—	12	2	no	—
961	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
962	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
963	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
964	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
965	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
966	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
967	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
968	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
969	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
970	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
971	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
972	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
973	#67	—	2	4	no	—
974	#67	—	2	4	no	—
975	#67	—	2	4	no	—
976	#67	—	4	2	no	—
977	#67	—	4	2	no	—
978	#67	—	4	2	no	—
979	#67	—	4	2	no	—
980	#67	—	4	2	no	—
981	#67	—	4	2	no	—
982	#67	—	4	2	no	—
983	C₂×Dic₃	—	2	2	no	—
984	C₂×Dic₃	—	4	1	no	—
985	C₂×Dic₃	—	4	2	no	—
986	C₂×Dic₃	—	4	2	no	—
987	C₂×Dic₃	—	4	1	no	—
988	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
989	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
990	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
991	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
992	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
993	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
994	D₁₂	—	2	4	no	—
995	D₁₂	—	4	2	no	—
996	D₁₂	—	4	2	no	—
997	D₁₂	—	4	2	no	—
998	D₁₂	—	4	1	no	—
999	D₁₂	—	4	1	no	—
1000	C₄×D₃	—	2	2	no	—
1001	C₄×D₃	—	2	2	no	—
1002	C₄×D₃	—	4	1	no	—
1003	C₄×D₃	—	4	1	no	—
1004	C₄×D₃	—	4	2	no	—
1005	C₄×D₃	—	4	2	no	—
1006	C₄×D₃	—	4	2	no	—
1007	C₄×D₃	—	4	2	no	—
1008	Dic₆	—	4	2	no	—
1009	C₂×C₃²	—	2	2	no	—
1010	C₂×C₃²	—	4	2	no	—
1011	C₂×C₃²	—	4	2	no	—
1012	C₂×C₃²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1013	C₂×C₃²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1014	C₂×C₃²	#585	1	1	yes	characteristic
1015	C₃×D₃	—	2	2	no	—
1016	C₃×D₃	—	4	1	no	—
1017	C₃×D₃	—	4	2	no	—
1018	C₃×D₃	—	4	2	no	—
1019	C₂⁴	—	3	1	no	—
1020	C₂⁴	—	3	2	no	—
1021	C₂⁴	—	3	2	no	—
1022	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
1023	#41	—	12	4	no	—
1024	#41	—	12	2	no	—
1025	C₂×Q₈	—	3	2	no	—
1026	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
1027	C₂×D₄	—	3	2	no	—
1028	C₂×D₄	—	3	2	no	—
1029	C₂×D₄	—	3	2	no	—
1030	C₂×D₄	—	3	2	no	—
1031	C₂×D₄	—	3	2	no	—
1032	C₂×D₄	—	3	2	no	—
1033	C₂×D₄	—	3	2	no	—
1034	C₂×D₄	—	3	2	no	—
1035	C₂×D₄	—	3	2	no	—
1036	C₂×D₄	—	3	2	no	—
1037	C₂×D₄	—	3	2	no	—
1038	C₂×D₄	—	3	2	no	—
1039	C₂×D₄	—	3	2	no	—
1040	C₂×D₄	—	3	1	no	—
1041	C₂×D₄	—	3	1	no	—
1042	C₂×D₄	—	3	2	no	—
1043	C₂×D₄	—	12	2	no	—
1044	C₂×D₄	—	12	4	no	—
1045	C₂×D₄	—	12	4	no	—
1046	C₂×D₄	—	12	4	no	—
1047	C₂×D₄	—	12	2	no	—
1048	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
1049	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
1050	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
1051	C₂×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
1052	C₂²×C₄	—	3	1	no	—
1053	C₂²×C₄	—	3	1	no	—
1054	C₂²×C₄	—	3	2	no	—
1055	C₂²×C₄	—	3	1	no	—
1056	C₂²×C₄	—	3	2	no	—
1057	C₂²×C₄	—	3	1	no	—
1058	C₂²×C₄	—	3	1	no	—
1059	C₂²×C₄	—	3	2	no	—
1060	C₂²×C₄	—	3	2	no	—
1061	C₂²×C₄	—	3	2	no	—
1062	C₂²×C₄	—	3	1	no	—
1063	C₂²×C₄	—	3	2	no	—
1064	C₂²×C₄	—	3	1	no	—
1065	C₂²×C₄	—	12	2	no	—
1066	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1067	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
1068	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1069	C₄⋊C₄	—	3	2	no	—
1070	C₄⋊C₄	—	3	2	no	—
1071	C₄⋊C₄	—	3	1	no	—
1072	C₄⋊C₄	—	3	2	no	—
1073	C₄⋊C₄	—	3	2	no	—
1074	C₄⋊C₄	—	3	2	no	—
1075	C₄⋊C₄	—	3	1	no	—
1076	C₄⋊C₄	—	3	2	no	—
1077	C₄⋊C₄	—	3	2	no	—
1078	C₄⋊C₄	—	3	2	no	—
1079	C₄⋊C₄	—	3	2	no	—
1080	C₄⋊C₄	—	3	2	no	—
1081	C₄⋊C₄	—	3	2	no	—
1082	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1083	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
1084	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1085	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1086	C₂²⋊C₄	—	3	2	no	—
1087	C₂²⋊C₄	—	3	2	no	—
1088	C₂²⋊C₄	—	3	2	no	—
1089	C₂²⋊C₄	—	3	2	no	—
1090	C₂²⋊C₄	—	3	2	no	—
1091	C₂²⋊C₄	—	3	2	no	—
1092	C₂²⋊C₄	—	3	2	no	—
1093	C₂²⋊C₄	—	3	2	no	—
1094	C₂²⋊C₄	—	3	2	no	—
1095	C₂²⋊C₄	—	3	2	no	—
1096	C₂²⋊C₄	—	3	2	no	—
1097	C₂²⋊C₄	—	3	2	no	—
1098	C₂²⋊C₄	—	3	2	no	—
1099	C₂²⋊C₄	—	3	2	no	—
1100	C₂²⋊C₄	—	3	2	no	—
1101	C₂²⋊C₄	—	3	2	no	—
1102	C₂²⋊C₄	—	3	2	no	—
1103	C₂²⋊C₄	—	3	2	no	—
1104	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1105	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1106	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1107	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1108	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1109	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1110	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
1111	C₄²	—	3	2	no	—
1112	C₄²	—	3	2	no	—
1113	C₄²	C₂²×C₃×D₃	1	2	yes	—
1114	C₂²×C₃	—	2	1	no	—
1115	C₂²×C₃	—	2	1	no	—
1116	C₂²×C₃	—	2	1	no	—
1117	C₂²×C₃	—	2	1	no	—
1118	C₂²×C₃	—	2	2	no	—
1119	C₂²×C₃	—	2	2	no	—
1120	C₂²×C₃	—	2	2	no	—
1121	C₂²×C₃	—	2	2	no	—
1122	C₂²×C₃	—	2	2	no	—
1123	C₂²×C₃	—	2	2	no	—
1124	C₂²×C₃	—	2	2	no	—
1125	C₂²×C₃	—	2	2	no	—
1126	C₂²×C₃	—	2	2	no	—
1127	C₂²×C₃	—	2	2	no	—
1128	C₂²×C₃	—	2	2	no	—
1129	C₂²×C₃	—	2	2	no	—
1130	C₂²×C₃	—	2	2	no	—
1131	C₂²×C₃	—	2	1	no	—
1132	C₂²×C₃	—	3	2	no	—
1133	C₂²×C₃	—	4	1	no	—
1134	C₂²×C₃	—	4	1	no	—
1135	C₂²×C₃	—	4	2	no	—
1136	C₂²×C₃	—	4	2	no	—
1137	C₂²×C₃	—	4	2	no	—
1138	C₂²×C₃	—	4	2	no	—
1139	C₂²×C₃	—	4	2	no	—
1140	C₂²×C₃	—	4	2	no	—
1141	C₂²×C₃	—	6	1	no	—
1142	C₂²×C₃	—	6	1	no	—
1143	C₂²×C₃	—	6	2	no	—
1144	C₂²×C₃	—	6	2	no	—
1145	C₂²×C₃	—	6	1	no	—
1146	C₂²×C₃	—	6	1	no	—
1147	C₂²×C₃	—	6	2	no	—
1148	C₂²×C₃	—	6	2	no	—
1149	C₂²×C₃	—	6	1	no	—
1150	C₂²×C₃	—	6	2	no	—
1151	C₂²×C₃	—	6	2	no	—
1152	C₂²×C₃	—	8	2	no	—
1153	C₂²×C₃	—	8	2	no	—
1154	C₂²×C₃	—	8	4	no	—
1155	C₂²×C₃	—	12	4	no	—
1156	C₂²×C₃	—	24	4	no	—
1157	C₂²×C₃	—	24	4	no	—
1158	C₂²×C₃	#1009	1	2	yes	—
1159	C₂²×C₃	C₃×H(5,𝔽₂)	1	2	yes	—
1160	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
1161	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
1162	C₂×D₃	—	2	1	no	—
1163	C₂×D₃	—	2	1	no	—
1164	C₂×D₃	—	2	1	no	—
1165	C₂×D₃	—	2	2	no	—
1166	C₂×D₃	—	2	2	no	—
1167	C₂×D₃	—	2	2	no	—
1168	C₂×D₃	—	2	1	no	—
1169	C₂×D₃	—	2	2	no	—
1170	C₂×D₃	—	2	1	no	—
1171	C₂×D₃	—	2	2	no	—
1172	C₂×D₃	—	2	2	no	—
1173	C₂×D₃	—	4	4	no	—
1174	C₂×D₃	—	8	4	no	—
1175	C₂×D₃	—	8	4	no	—
1176	C₂×D₃	C₃×H(5,𝔽₂)	1	2	yes	—
1177	C₃×C₄	—	2	2	no	—
1178	C₃×C₄	—	2	1	no	—
1179	C₃×C₄	—	2	1	no	—
1180	C₃×C₄	—	2	2	no	—
1181	C₃×C₄	—	2	2	no	—
1182	C₃×C₄	—	2	2	no	—
1183	C₃×C₄	—	2	2	no	—
1184	C₃×C₄	—	2	1	no	—
1185	C₃×C₄	—	2	1	no	—
1186	C₃×C₄	—	2	2	no	—
1187	C₃×C₄	—	2	2	no	—
1188	C₃×C₄	—	2	2	no	—
1189	C₃×C₄	—	4	2	no	—
1190	C₃×C₄	—	4	1	no	—
1191	C₃×C₄	—	4	2	no	—
1192	C₃×C₄	—	4	1	no	—
1193	C₃×C₄	—	4	2	no	—
1194	C₃×C₄	—	4	2	no	—
1195	C₃×C₄	—	6	2	no	—
1196	C₃×C₄	—	6	2	no	—
1197	C₃×C₄	—	6	2	no	—
1198	C₃×C₄	—	6	1	no	—
1199	C₃×C₄	—	6	1	no	—
1200	C₃×C₄	—	6	2	no	—
1201	Dic₃	—	2	2	no	—
1202	Dic₃	—	2	2	no	—
1203	Dic₃	—	2	1	no	—
1204	Dic₃	—	2	1	no	—
1205	Dic₃	—	2	2	no	—
1206	Dic₃	—	2	2	no	—
1207	C₃²	#3534	1	1	yes	characteristic, complemented, Sylow
1208	C₂³	—	2	2	no	—
1209	C₂³	—	3	1	no	—
1210	C₂³	—	3	2	no	—
1211	C₂³	—	3	2	no	—
1212	C₂³	—	3	1	no	—
1213	C₂³	—	4	1	no	—
1214	C₂³	—	4	1	no	—
1215	C₂³	—	6	2	no	—
1216	C₂³	—	6	4	no	—
1217	C₂³	—	6	2	no	—
1218	C₂³	—	12	1	no	—
1219	C₂³	—	12	2	no	—
1220	C₂³	—	12	2	no	—
1221	C₂³	—	12	2	no	—
1222	C₂³	—	12	2	no	—
1223	C₂³	—	12	2	no	—
1224	C₂³	C₂³×C₃×D₃	1	2	yes	—
1225	C₂³	C₂³×C₃×D₃	1	2	yes	—
1226	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
1227	Q₈	—	4	1	no	—
1228	Q₈	—	12	2	no	—
1229	D₄	—	2	4	no	—
1230	D₄	—	4	1	no	—
1231	D₄	—	4	2	no	—
1232	D₄	—	4	2	no	—
1233	D₄	—	6	4	no	—
1234	D₄	—	6	4	no	—
1235	D₄	—	6	4	no	—
1236	D₄	—	6	4	no	—
1237	D₄	—	12	2	no	—
1238	D₄	—	12	1	no	—
1239	D₄	—	12	1	no	—
1240	D₄	—	12	2	no	—
1241	D₄	—	12	2	no	—
1242	D₄	—	12	2	no	—
1243	D₄	—	12	2	no	—
1244	D₄	—	12	2	no	—
1245	D₄	—	12	2	no	—
1246	D₄	—	12	2	no	—
1247	D₄	—	12	2	no	—
1248	D₄	—	12	2	no	—
1249	C₂×C₄	—	3	1	no	—
1250	C₂×C₄	—	3	2	no	—
1251	C₂×C₄	—	3	2	no	—
1252	C₂×C₄	—	3	2	no	—
1253	C₂×C₄	—	3	2	no	—
1254	C₂×C₄	—	3	1	no	—
1255	C₂×C₄	—	4	1	no	—
1256	C₂×C₄	—	4	1	no	—
1257	C₂×C₄	—	4	2	no	—
1258	C₂×C₄	—	6	2	no	—
1259	C₂×C₄	—	6	2	no	—
1260	C₂×C₄	—	6	2	no	—
1261	C₂×C₄	—	12	1	no	—
1262	C₂×C₄	—	12	1	no	—
1263	C₂×C₄	—	12	2	no	—
1264	C₂×C₄	—	12	2	no	—
1265	C₂×C₄	—	12	2	no	—
1266	C₂×C₄	—	12	2	no	—
1267	C₂×C₄	—	12	1	no	—
1268	C₂×C₄	—	12	2	no	—
1269	C₂×C₄	—	12	1	no	—
1270	C₂×C₄	—	12	2	no	—
1271	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1272	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1273	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1274	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
1275	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1276	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
1277	C₂×C₃	—	2	2	no	—
1278	C₂×C₃	—	2	2	no	—
1279	C₂×C₃	—	2	1	no	—
1280	C₂×C₃	—	2	1	no	—
1281	C₂×C₃	—	2	1	no	—
1282	C₂×C₃	—	4	2	no	—
1283	C₂×C₃	—	4	2	no	—
1284	C₂×C₃	—	4	2	no	—
1285	C₂×C₃	—	4	2	no	—
1286	C₂×C₃	—	4	2	no	—
1287	C₂×C₃	—	6	2	no	—
1288	C₂×C₃	—	8	2	no	—
1289	C₂×C₃	—	8	2	no	—
1290	C₂×C₃	—	12	1	no	—
1291	C₂×C₃	—	12	2	no	—
1292	C₂×C₃	—	12	2	no	—
1293	C₂×C₃	C₂×#1009	1	1	yes	characteristic
1294	C₂×C₃	D₃×H(5,𝔽₂)	1	1	yes	characteristic
1295	C₂×C₃	#5966	1	1	yes	characteristic
1296	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1297	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1298	C₂×C₃	C₃×#585	1	1	yes	characteristic
1299	D₃	—	2	2	no	—
1300	D₃	—	4	1	no	—
1301	D₃	—	4	2	no	—
1302	D₃	—	4	2	no	—
1303	C₂²	—	2	1	no	—
1304	C₂²	—	2	1	no	—
1305	C₂²	—	2	2	no	—
1306	C₂²	—	2	2	no	—
1307	C₂²	—	2	2	no	—
1308	C₂²	—	2	2	no	—
1309	C₂²	—	2	2	no	—
1310	C₂²	—	2	2	no	—
1311	C₂²	—	3	2	no	—
1312	C₂²	—	6	1	no	—
1313	C₂²	—	6	1	no	—
1314	C₂²	—	6	2	no	—
1315	C₂²	—	6	2	no	—
1316	C₂²	—	6	1	no	—
1317	C₂²	—	6	1	no	—
1318	C₂²	—	6	2	no	—
1319	C₂²	—	6	2	no	—
1320	C₂²	—	6	1	no	—
1321	C₂²	—	6	2	no	—
1322	C₂²	—	6	2	no	—
1323	C₂²	—	8	2	no	—
1324	C₂²	—	12	4	no	—
1325	C₂²	—	24	4	no	—
1326	C₂²	—	24	4	no	—
1327	C₂²	C₃×#1009	1	2	yes	—
1328	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
1329	C₄	—	2	2	no	—
1330	C₄	—	2	1	no	—
1331	C₄	—	2	1	no	—
1332	C₄	—	2	2	no	—
1333	C₄	—	2	2	no	—
1334	C₄	—	2	2	no	—
1335	C₄	—	6	2	no	—
1336	C₄	—	6	2	no	—
1337	C₄	—	6	2	no	—
1338	C₄	—	6	1	no	—
1339	C₄	—	6	1	no	—
1340	C₄	—	6	2	no	—
1341	C₃	—	2	1	no	—
1342	C₃	#86420	1	1	yes	characteristic, direct product factor
1343	C₃	C₃×#3534	1	1	yes	characteristic, complemented
1344	C₂	—	2	2	no	—
1345	C₂	—	4	2	no	—
1346	C₂	—	4	2	no	—
1347	C₂	—	6	2	no	—
1348	C₂	—	12	1	no	—
1349	C₂	—	12	2	no	—
1350	C₂	—	12	2	no	—
1351	C₂	C₂×C₃×#1009	1	1	yes	characteristic
1352	C₂	C₃×D₃×H(5,𝔽₂)	1	1	yes	characteristic
1353	C₂	C₃×#5966	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×#538	C₂
socle	C₂²×C₃²	C₂⁵
hypercenter	C₃×#538	D₃
hypocenter	C₃	C₃×#3534
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#538

Complements

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

N	H ≅ G/N	type
1. C₃²×#538	C₂	semidirect
2. C₃×#5707	C₂	semidirect
3. C₃×#5704	C₂	semidirect
4. C₃×#5684	C₂	semidirect
5. C₃×#5676	C₂	semidirect
6. C₃×#5666	C₂	semidirect
7. C₃×#5658	C₂	semidirect
8. C₃×#5645	C₂	semidirect
9. C₃×#5627	C₂	semidirect
10. C₃×#5619	C₂	semidirect
11. C₃×#5605	C₂	semidirect
12. C₃×D₃×#121	C₂	semidirect
13. C₃×#5597	C₂	semidirect
14. C₃×#5591	C₂	semidirect
15. C₃×#5590	C₂	semidirect
16. C₃×#5565	C₂	semidirect
17. C₃×#5554	C₂	semidirect
18. C₃×#5493	C₂	semidirect
19. C₂×C₃×#883	C₂	semidirect
21. #86420	C₃	direct (N × H)
23. C₂²×C₃×#67	C₂²	semidirect
24. C₂×C₃×#239	C₂²	semidirect
25. C₂×C₃×#237	C₂²	semidirect
26. C₂×C₃×D₃×D₄	C₂²	semidirect
27. C₂×C₃×D₃×D₄	C₂²	semidirect
28. C₂×C₃×D₃×D₄	C₂²	semidirect
29. C₂²×C₃×C₄×D₃	C₂²	semidirect
30. C₃²×#126	C₂²	semidirect
31. C₃²×#124	C₂²	semidirect
32. C₃²×#123	C₂²	semidirect
33. C₃²×C₂²⋊Q₈	C₂²	semidirect
34. C₃²×#121	C₂²	semidirect
35. C₃²×#121	C₂²	semidirect
36. C₃²×#120	C₂²	semidirect
37. C₃²×C₄×D₄	C₂²	semidirect
38. C₂×C₃²×C₂²⋊C₄	C₂²	semidirect
39. C₂×C₃×#217	C₂²	semidirect
40. C₃×#946	C₂²	semidirect
41. C₃×#946	C₂²	semidirect
42. C₃×#940	C₂²	semidirect
43. C₃×#939	C₂²	semidirect
44. C₃×#939	C₂²	semidirect
45. C₃×#939	C₂²	semidirect
46. C₃×#939	C₂²	semidirect
47. C₃×#939	C₂²	semidirect
48. C₃×#938	C₂²	semidirect
49. C₃×#938	C₂²	semidirect
51. C₃×#937	C₂²	semidirect
52. C₃×D₄×Dic₃	C₂²	semidirect
54. C₃×#930	C₂²	semidirect
55. C₃×#930	C₂²	semidirect
56. C₃×#930	C₂²	semidirect
57. C₃×#930	C₂²	semidirect
58. C₂×C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
59. C₂×C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
60. C₃×#926	C₂²	semidirect
61. C₂×C₃×C₄⋊Dic₃	C₂²	semidirect
62. C₂×C₃×Dic₃⋊C₄	C₂²	semidirect
63. C₃×#898	C₂²	semidirect
64. C₃×#898	C₂²	semidirect
65. C₃×#898	C₂²	semidirect
66. C₃×#897	C₂²	semidirect
67. C₃×#896	C₂²	semidirect
68. C₃×#895	C₂²	semidirect
69. C₃×#895	C₂²	semidirect
70. C₃×#895	C₂²	semidirect
71. C₃×#894	C₂²	semidirect
72. C₃×#894	C₂²	semidirect
73. C₃×#893	C₂²	semidirect
74. C₃×#892	C₂²	semidirect
75. C₃×D₃×C₄⋊C₄	C₂²	semidirect
76. C₃×#890	C₂²	semidirect
77. C₃×#886	C₂²	semidirect
78. C₃×#886	C₂²	semidirect
79. C₃×#886	C₂²	semidirect
80. C₃×#886	C₂²	semidirect
81. C₃×#885	C₂²	semidirect
83. C₃×#884	C₂²	semidirect
84. C₃×#884	C₂²	semidirect
85. C₃×#884	C₂²	semidirect
86. C₃×#883	C₂²	semidirect
87. C₃×#883	C₂²	semidirect
88. C₃×#883	C₂²	semidirect
89. C₃×#883	C₂²	semidirect
90. C₃×#883	C₂²	semidirect
91. C₃×#883	C₂²	semidirect
92. C₃×#883	C₂²	semidirect
93. C₃×#882	C₂²	semidirect
94. C₃×#882	C₂²	semidirect
95. C₃×#882	C₂²	semidirect
96. C₃×#882	C₂²	semidirect
97. C₃×#882	C₂²	semidirect
98. C₃×#67⋊C₄	C₂²	semidirect
99. C₃×#67⋊C₄	C₂²	semidirect
100. C₃×#67⋊C₄	C₂²	semidirect
101. C₃×D₃×C₂²⋊C₄	C₂²	semidirect
102. C₃×D₃×C₂²⋊C₄	C₂²	semidirect
103. C₃×#878	C₂²	semidirect
104. C₃×#878	C₂²	semidirect
105. C₃×#875	C₂²	semidirect
106. C₃×C₄×D₁₂	C₂²	semidirect
107. C₃×C₄×D₁₂	C₂²	semidirect
108. C₃×#870	C₂²	semidirect
122. C₃×#538	D₃	semidirect
123. C₃×#538	C₂×C₃	semidirect
130. #5707	C₂×C₃	semidirect
131. #5704	C₂×C₃	semidirect
132. #5684	C₂×C₃	semidirect
133. #5676	C₂×C₃	semidirect
134. #5666	C₂×C₃	semidirect
135. #5658	C₂×C₃	semidirect
136. #5645	C₂×C₃	semidirect
137. #5627	C₂×C₃	semidirect
138. #5619	C₂×C₃	semidirect
139. #5605	C₂×C₃	semidirect
140. D₃×#121	C₂×C₃	semidirect
141. #5597	C₂×C₃	semidirect
142. #5591	C₂×C₃	semidirect
143. #5590	C₂×C₃	semidirect
144. #5565	C₂×C₃	semidirect
145. #5554	C₂×C₃	semidirect
146. #5493	C₂×C₃	semidirect
147. C₂×#883	C₂×C₃	semidirect
253. C₂²×#67	C₂²×C₃	semidirect
254. C₂×#239	C₂²×C₃	semidirect
255. C₂×#237	C₂²×C₃	semidirect
256. C₂×D₃×D₄	C₂²×C₃	semidirect
257. C₂×D₃×D₄	C₂²×C₃	semidirect
258. C₂×D₃×D₄	C₂²×C₃	semidirect
259. C₂²×C₄×D₃	C₂²×C₃	semidirect
265. C₃×#126	C₂×D₃	semidirect
266. C₃×#126	C₂²×C₃	semidirect
272. C₃×#124	C₂×D₃	semidirect
273. C₃×#124	C₂²×C₃	semidirect
288. C₃×#123	C₂×D₃	semidirect
289. C₃×#123	C₂²×C₃	semidirect
297. C₃×C₂²⋊Q₈	C₂×D₃	semidirect
298. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
320. C₃×#121	C₂×D₃	semidirect
321. C₃×#121	C₂×D₃	semidirect
322. C₃×#121	C₂²×C₃	semidirect
323. C₃×#121	C₂²×C₃	semidirect
332. C₃×#120	C₂×D₃	semidirect
333. C₃×#120	C₂²×C₃	semidirect
342. C₃×C₄×D₄	C₂×D₃	semidirect
343. C₃×C₄×D₄	C₂²×C₃	semidirect
355. C₂×C₃×C₂²⋊C₄	C₂×D₃	semidirect
356. C₂×C₃×C₂²⋊C₄	C₂²×C₃	semidirect
357. C₂×#217	C₂²×C₃	semidirect
358. #946	C₂²×C₃	semidirect
359. #946	C₂²×C₃	semidirect
360. #940	C₂²×C₃	semidirect
361. #939	C₂²×C₃	semidirect
362. #939	C₂²×C₃	semidirect
363. #939	C₂²×C₃	semidirect
364. #939	C₂²×C₃	semidirect
365. #939	C₂²×C₃	semidirect
366. #938	C₂²×C₃	semidirect
367. #938	C₂²×C₃	semidirect
369. #937	C₂²×C₃	semidirect
370. D₄×Dic₃	C₂²×C₃	semidirect
372. #930	C₂²×C₃	semidirect
373. #930	C₂²×C₃	semidirect
374. #930	C₂²×C₃	semidirect
375. #930	C₂²×C₃	semidirect
376. C₂×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
377. C₂×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
378. #926	C₂²×C₃	semidirect
379. C₂×C₄⋊Dic₃	C₂²×C₃	semidirect
380. C₂×Dic₃⋊C₄	C₂²×C₃	semidirect
381. #898	C₂²×C₃	semidirect
382. #898	C₂²×C₃	semidirect
383. #898	C₂²×C₃	semidirect
384. #897	C₂²×C₃	semidirect
385. #896	C₂²×C₃	semidirect
386. #895	C₂²×C₃	semidirect
387. #895	C₂²×C₃	semidirect
388. #895	C₂²×C₃	semidirect
389. #894	C₂²×C₃	semidirect
390. #894	C₂²×C₃	semidirect
391. #893	C₂²×C₃	semidirect
392. #892	C₂²×C₃	semidirect
393. D₃×C₄⋊C₄	C₂²×C₃	semidirect
394. #890	C₂²×C₃	semidirect
395. #886	C₂²×C₃	semidirect
396. #886	C₂²×C₃	semidirect
397. #886	C₂²×C₃	semidirect
398. #886	C₂²×C₃	semidirect
399. #885	C₂²×C₃	semidirect
401. #884	C₂²×C₃	semidirect
402. #884	C₂²×C₃	semidirect
403. #884	C₂²×C₃	semidirect
404. #883	C₂²×C₃	semidirect
405. #883	C₂²×C₃	semidirect
406. #883	C₂²×C₃	semidirect
407. #883	C₂²×C₃	semidirect
408. #883	C₂²×C₃	semidirect
409. #883	C₂²×C₃	semidirect
410. #883	C₂²×C₃	semidirect
411. #882	C₂²×C₃	semidirect
412. #882	C₂²×C₃	semidirect
413. #882	C₂²×C₃	semidirect
414. #882	C₂²×C₃	semidirect
415. #882	C₂²×C₃	semidirect
416. #67⋊C₄	C₂²×C₃	semidirect
417. #67⋊C₄	C₂²×C₃	semidirect
418. #67⋊C₄	C₂²×C₃	semidirect
419. D₃×C₂²⋊C₄	C₂²×C₃	semidirect
420. D₃×C₂²⋊C₄	C₂²×C₃	semidirect
421. #878	C₂²×C₃	semidirect
422. #878	C₂²×C₃	semidirect
423. #875	C₂²×C₃	semidirect
424. C₄×D₁₂	C₂²×C₃	semidirect
425. C₄×D₁₂	C₂²×C₃	semidirect
426. #870	C₂²×C₃	semidirect
508. #538	C₃×D₃	semidirect
776. #126	C₂×C₃×D₃	semidirect
781. #124	C₂×C₃×D₃	semidirect
795. #123	C₂×C₃×D₃	semidirect
802. C₂²⋊Q₈	C₂×C₃×D₃	semidirect
822. #121	C₂×C₃×D₃	semidirect
823. #121	C₂×C₃×D₃	semidirect
831. #120	C₂×C₃×D₃	semidirect
839. C₄×D₄	C₂×C₃×D₃	semidirect
850. C₂×C₂²⋊C₄	C₂×C₃×D₃	semidirect
1207. C₃²	#3534	semidirect
1342. C₃	#86420	direct (N × H)
1343. C₃	C₃×#3534	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#538	2
C₃×#5707	2
C₃×#5704	2
C₃×#5684	2
C₃×#5676	2
C₃×#5666	2
C₃×#5658	2
C₃×#5645	2
C₃×#5627	2
C₃×#5619	2
C₃×#5605	2
C₃×D₃×#121	2
C₃×#5597	2
C₃×#5591	2
C₃×#5590	2
C₃×#5565	2
C₃×#5554	2
C₃×#5493	2
C₂×C₃×#883	2
C₃×#3534	3
#86420	3

Subgroups — C3×#86420 #11910954

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#86420 #11910954