Subgroups — C₃×#85840 #11903472

Order 1152.

2419 conjugacy classes of subgroups.

The subgroup lattice has 998 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×#5828	C₂	1	2	yes	maximal, complemented
3	C₃×#5584	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5581	C₂	1	2	yes	maximal, complemented
5	C₃×#5579	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#5563	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#5558	C₂	1	2	yes	maximal, complemented
8	C₃×#5556	C₂	1	4	yes	maximal, complemented
9	C₃×#5551	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#5550	C₂	1	2	yes	maximal, complemented
11	C₃×#5541	C₂	1	2	yes	maximal, complemented
12	C₃×#5528	C₂	1	4	yes	maximal, complemented
13	C₃×D₃×#117	C₂	1	2	yes	maximal, complemented
14	C₃×#5479	C₂	1	2	yes	maximal, complemented
15	C₃×C₄×#235	C₂	1	2	yes	maximal, complemented
16	C₂×C₃×C₄×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#5470	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#3475	—	3	1	no	maximal
19	#85840	C₃	1	1	yes	maximal, characteristic, direct product factor
20	C₂×C₃²×#41	C₂²	1	1	yes	characteristic
21	C₂×C₃×#235	C₂²	1	2	yes	—
22	C₂²×C₃×D₁₂	C₂²	1	1	yes	characteristic
23	C₂²×C₃×C₄×D₃	C₂²	1	2	yes	—
24	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
26	C₃²×C₄×D₄	C₂²	1	2	yes	—
27	C₃²×C₄×D₄	C₂²	1	2	yes	—
28	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
29	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
30	C₃²×#117	C₂²	1	1	yes	characteristic
31	C₃²×#117	C₂²	1	2	yes	complemented
32	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
33	C₂×C₃²×C₄²	C₂²	1	2	yes	complemented
34	C₃×#946	C₂²	1	2	yes	complemented
35	C₃×#946	C₂²	1	2	yes	complemented
36	C₃×#938	C₂²	1	2	yes	complemented
37	C₃×#938	C₂²	1	2	yes	complemented
38	C₃×#937	C₂²	1	4	yes	—
39	C₃×#935	C₂²	1	4	yes	—
40	C₃×#930	C₂²	1	2	yes	—
41	C₃×#929	C₂²	1	4	yes	complemented
42	C₃×C₄×#67	C₂²	1	4	yes	complemented
43	C₃×C₄×#67	C₂²	1	4	yes	complemented
44	C₃×C₄×#67	C₂²	1	4	yes	complemented
45	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
46	C₃×#926	C₂²	1	2	yes	—
47	C₃×#926	C₂²	1	2	yes	complemented
48	C₂×C₃×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
49	C₃×#924	C₂²	1	2	yes	—
50	C₃×#924	C₂²	1	2	yes	—
51	C₃×#924	C₂²	1	2	yes	complemented
52	C₃×#898	C₂²	1	4	yes	complemented
53	C₃×#896	C₂²	1	4	yes	complemented
54	C₃×#894	C₂²	1	4	yes	—
55	C₃×#892	C₂²	1	2	yes	complemented
56	C₃×#892	C₂²	1	2	yes	complemented
57	C₃×D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
58	C₃×D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
59	C₃×#889	C₂²	1	4	yes	complemented
60	C₃×#885	C₂²	1	4	yes	complemented
61	C₃×#884	C₂²	1	4	yes	—
62	C₃×#883	C₂²	1	4	yes	complemented
63	C₃×D₃×C₂²⋊C₄	C₂²	1	4	yes	—
64	C₃×#879	C₂²	1	4	yes	complemented
65	C₃×#877	C₂²	1	4	yes	—
66	C₃×#876	C₂²	1	4	yes	complemented
67	C₃×#875	C₂²	1	2	yes	—
68	C₃×C₄×D₁₂	C₂²	1	2	yes	—
69	C₃×C₄×D₁₂	C₂²	1	2	yes	—
70	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic
71	C₃×C₄×D₁₂	C₂²	1	2	yes	—
72	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic
73	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic
74	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic
75	C₃×#872	C₂²	1	4	yes	complemented
76	C₃×#872	C₂²	1	4	yes	complemented
77	C₃×C₄²×D₃	C₂²	1	4	yes	complemented
78	C₃×#870	C₂²	1	2	yes	complemented
79	C₃×#870	C₂²	1	2	yes	complemented
80	C₃×#869	C₂²	1	1	yes	characteristic, complemented
81	C₃×#869	C₂²	1	1	yes	characteristic, complemented
82	C₃×C₄×Dic₆	C₂²	1	2	yes	complemented
83	C₃×C₄×Dic₆	C₂²	1	2	yes	complemented
84	C₃×C₄×Dic₆	C₂²	1	2	yes	complemented
85	C₃×#556	—	3	1	no	—
86	C₃×#555	—	3	1	no	—
87	C₃×#554	—	3	1	no	—
88	C₃×#553	—	3	2	no	—
89	C₃×#552	—	3	2	no	—
90	C₃×#552	—	3	2	no	—
91	C₃×#551	—	3	4	no	—
92	C₃×#547	—	3	1	no	—
93	C₃×#546	—	3	2	no	—
94	C₃×#533	—	3	1	no	—
95	C₃×#529	—	3	4	no	—
96	C₃×#529	—	3	2	no	—
97	C₃×#525	—	3	2	no	—
98	C₃×C₄×#41	—	2	1	no	—
99	C₃×C₄×#41	—	3	2	no	—
100	C₃×C₄×#41	D₃	1	1	yes	characteristic, complemented
101	C₃×C₄×#41	C₂×C₃	1	1	yes	characteristic, complemented
102	C₂×C₃×C₄×D₄	—	3	1	no	—
103	C₂×C₃×#117	—	3	2	no	—
104	#5828	C₂×C₃	1	2	yes	complemented
105	#5584	C₂×C₃	1	1	yes	characteristic, complemented
106	#5581	C₂×C₃	1	2	yes	complemented
107	#5579	C₂×C₃	1	1	yes	characteristic, complemented
108	#5563	C₂×C₃	1	1	yes	characteristic, complemented
109	#5558	C₂×C₃	1	2	yes	complemented
110	#5556	C₂×C₃	1	4	yes	complemented
111	#5551	C₂×C₃	1	1	yes	characteristic, complemented
112	#5550	C₂×C₃	1	2	yes	complemented
113	#5541	C₂×C₃	1	2	yes	complemented
114	#5528	C₂×C₃	1	4	yes	complemented
115	D₃×#117	C₂×C₃	1	2	yes	complemented
116	#5479	C₂×C₃	1	2	yes	complemented
117	C₄×#235	C₂×C₃	1	2	yes	complemented
118	C₂×C₄×D₁₂	C₂×C₃	1	1	yes	characteristic, complemented
119	#5470	C₂×C₃	1	1	yes	characteristic, complemented
120	C₂³×C₃×D₃	C₂³	1	2	yes	—
121	C₃²×#41	—	2	4	no	—
122	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
123	C₂×C₃²×D₄	C₂³	1	2	yes	—
124	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
125	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
126	C₂²×C₃²×C₄	C₂³	1	2	yes	—
127	C₂²×C₃²×C₄	C₂³	1	2	yes	—
128	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
129	C₂²×C₃²×C₄	C₂³	1	2	yes	—
130	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
131	C₂×C₃×#67	C₂³	1	4	yes	—
132	C₂×C₃×#67	C₂³	1	4	yes	—
133	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
134	C₃×#235	—	2	8	no	—
135	C₂×C₃×D₁₂	—	2	4	no	—
136	C₂×C₃×D₁₂	C₂³	1	2	yes	—
137	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
138	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
139	C₂×C₃×C₄×D₃	—	2	8	no	—
140	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
141	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
142	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
143	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
144	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
145	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
146	C₂×C₃×Dic₆	C₂³	1	2	yes	—
147	C₂×C₃×Dic₆	C₂³	1	2	yes	—
148	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
149	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
150	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
151	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
152	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
153	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
154	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
155	C₃²×C₄²	C₂³	1	1	yes	characteristic
156	C₃²×C₄²	C₂³	1	1	yes	characteristic
157	C₃²×C₄²	C₂³	1	1	yes	characteristic
158	C₃²×C₄²	C₂³	1	1	yes	characteristic
159	C₃²×C₄²	C₂³	1	2	yes	—
160	C₃²×C₄²	C₂³	1	2	yes	—
161	C₃²×C₄²	C₂³	1	2	yes	—
162	C₃×#217	C₂³	1	4	yes	—
163	C₃×#217	C₂³	1	4	yes	—
164	C₃×#217	C₂³	1	4	yes	—
165	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
166	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
167	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
168	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
169	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
170	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
171	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
172	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
173	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
174	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
175	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
176	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
177	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
178	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
179	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
180	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
181	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
182	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
183	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
184	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
185	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
186	C₃×C₄×Dic₃	C₂³	1	4	yes	—
187	C₃×C₄×Dic₃	C₂³	1	4	yes	—
188	C₃×C₄×Dic₃	C₂³	1	4	yes	—
189	#3475	—	3	1	no	Sylow
190	C₂×C₃×#41	—	2	1	no	—
191	C₂×C₃×#41	—	3	2	no	—
192	C₂×C₃×#41	C₂×D₃	1	1	yes	characteristic
193	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
194	C₂²×C₃×D₄	—	3	1	no	—
195	C₂³×C₃×C₄	—	3	2	no	—
196	C₂×#235	C₂²×C₃	1	2	yes	—
197	C₂²×D₁₂	C₂²×C₃	1	1	yes	characteristic
198	C₂²×C₄×D₃	C₂²×C₃	1	2	yes	—
199	C₃×C₄⋊Q₈	—	3	1	no	—
200	C₃×C₄⋊Q₈	—	3	1	no	—
201	C₃×#126	—	3	4	no	—
202	C₃×#126	—	3	4	no	—
203	C₃×#126	—	3	4	no	—
204	C₃×#125	—	3	4	no	—
205	C₃×#125	—	3	2	no	—
206	C₃×#125	—	3	2	no	—
207	C₃×#124	—	3	4	no	—
208	C₃×#124	—	3	2	no	—
209	C₃×#123	—	3	4	no	—
210	C₃×#123	—	3	4	no	—
211	C₃×#123	—	3	4	no	—
212	C₃×#123	—	3	4	no	—
213	C₃×C₂²⋊Q₈	—	3	2	no	—
214	C₃×C₂²⋊Q₈	—	3	2	no	—
215	C₃×C₂²⋊Q₈	—	3	2	no	—
216	C₃×C₂²⋊Q₈	—	3	2	no	—
217	C₃×C₂²⋊Q₈	—	3	2	no	—
218	C₃×C₂²⋊Q₈	—	3	4	no	—
219	C₃×#121	—	3	2	no	—
220	C₃×#121	—	3	2	no	—
221	C₃×#121	—	3	2	no	—
222	C₃×#121	—	3	4	no	—
223	C₃×#120	—	3	4	no	—
224	C₃×C₄×Q₈	—	2	1	no	—
225	C₃×C₄×Q₈	—	2	1	no	—
226	C₃×C₄×Q₈	—	3	2	no	—
227	C₃×C₄×Q₈	—	3	2	no	—
228	C₃×C₄×Q₈	—	3	2	no	—
229	C₃×C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
230	C₃×C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
231	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
232	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
233	C₃×C₄×D₄	—	2	2	no	—
234	C₃×C₄×D₄	—	2	2	no	—
235	C₃×C₄×D₄	—	2	1	no	—
236	C₃×C₄×D₄	—	2	1	no	—
237	C₃×C₄×D₄	—	3	4	no	—
238	C₃×C₄×D₄	—	3	4	no	—
239	C₃×C₄×D₄	—	3	4	no	—
240	C₃×C₄×D₄	—	3	1	no	—
241	C₃×C₄×D₄	—	3	1	no	—
242	C₃×C₄×D₄	—	3	2	no	—
243	C₃×C₄×D₄	—	3	1	no	—
244	C₃×C₄×D₄	—	3	2	no	—
245	C₃×C₄×D₄	—	3	1	no	—
246	C₃×C₄×D₄	—	3	2	no	—
247	C₃×C₄×D₄	C₂×D₃	1	2	yes	—
248	C₃×C₄×D₄	C₂×D₃	1	2	yes	—
249	C₃×C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
250	C₃×C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
251	C₃×C₄×D₄	C₂²×C₃	1	2	yes	—
252	C₃×C₄×D₄	C₂²×C₃	1	2	yes	—
253	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
254	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
255	C₃×#117	—	2	1	no	—
256	C₃×#117	—	2	2	no	—
257	C₃×#117	—	3	2	no	—
258	C₃×#117	—	3	2	no	—
259	C₃×#117	—	3	2	no	—
260	C₃×#117	—	3	2	no	—
261	C₃×#117	—	3	4	no	—
262	C₃×#117	—	3	4	no	—
263	C₃×#117	—	3	4	no	—
264	C₃×#117	C₂×D₃	1	1	yes	characteristic
265	C₃×#117	C₂×D₃	1	2	yes	complemented
266	C₃×#117	C₂²×C₃	1	1	yes	characteristic
267	C₃×#117	C₂²×C₃	1	2	yes	complemented
268	C₂×C₃×C₄⋊C₄	—	3	1	no	—
269	C₂×C₃×C₄⋊C₄	—	3	2	no	—
270	C₂×C₃×C₄⋊C₄	—	3	2	no	—
271	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
272	C₂×C₃×C₂²⋊C₄	—	3	4	no	—
273	C₂×C₃×C₄²	—	2	1	no	—
274	C₂×C₃×C₄²	—	2	2	no	—
275	C₂×C₃×C₄²	—	3	4	no	—
276	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
277	C₂×C₃×C₄²	C₂×D₃	1	2	yes	complemented
278	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
279	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	complemented
280	#946	C₂²×C₃	1	2	yes	complemented
281	#946	C₂²×C₃	1	2	yes	complemented
282	#938	C₂²×C₃	1	2	yes	complemented
283	#938	C₂²×C₃	1	2	yes	complemented
284	#937	C₂²×C₃	1	4	yes	—
285	#935	C₂²×C₃	1	4	yes	—
286	#930	C₂²×C₃	1	2	yes	—
287	#929	C₂²×C₃	1	4	yes	complemented
288	C₄×#67	C₂²×C₃	1	4	yes	complemented
289	C₄×#67	C₂²×C₃	1	4	yes	complemented
290	C₄×#67	C₂²×C₃	1	4	yes	complemented
291	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
292	#926	C₂²×C₃	1	2	yes	—
293	#926	C₂²×C₃	1	2	yes	complemented
294	C₂×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
295	#924	C₂²×C₃	1	2	yes	—
296	#924	C₂²×C₃	1	2	yes	—
297	#924	C₂²×C₃	1	2	yes	complemented
298	#898	C₂²×C₃	1	4	yes	complemented
299	#896	C₂²×C₃	1	4	yes	complemented
300	#894	C₂²×C₃	1	4	yes	—
301	#892	C₂²×C₃	1	2	yes	complemented
302	#892	C₂²×C₃	1	2	yes	complemented
303	D₃×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
304	D₃×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
305	#889	C₂²×C₃	1	4	yes	complemented
306	#885	C₂²×C₃	1	4	yes	complemented
307	#884	C₂²×C₃	1	4	yes	—
308	#883	C₂²×C₃	1	4	yes	complemented
309	D₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
310	#879	C₂²×C₃	1	4	yes	complemented
311	#877	C₂²×C₃	1	4	yes	—
312	#876	C₂²×C₃	1	4	yes	complemented
313	#875	C₂²×C₃	1	2	yes	—
314	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic
315	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic
316	C₄×D₁₂	C₂²×C₃	1	2	yes	—
317	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic
318	C₄×D₁₂	C₂²×C₃	1	2	yes	—
319	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic
320	C₄×D₁₂	C₂²×C₃	1	2	yes	—
321	#872	C₂²×C₃	1	4	yes	complemented
322	#872	C₂²×C₃	1	4	yes	complemented
323	C₄²×D₃	C₂²×C₃	1	4	yes	complemented
324	#870	C₂²×C₃	1	2	yes	complemented
325	#870	C₂²×C₃	1	2	yes	complemented
326	#869	C₂²×C₃	1	1	yes	characteristic, complemented
327	#869	C₂²×C₃	1	1	yes	characteristic, complemented
328	C₄×Dic₆	C₂²×C₃	1	2	yes	complemented
329	C₄×Dic₆	C₂²×C₃	1	2	yes	complemented
330	C₄×Dic₆	C₂²×C₃	1	2	yes	complemented
331	C₂³×C₃²	C₂⁴	1	2	yes	—
332	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
333	C₂²×C₃×D₃	—	2	4	no	—
334	C₂²×C₃×D₃	—	2	4	no	—
335	C₂²×C₃×D₃	—	4	2	no	—
336	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
337	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
338	C₃²×Q₈	—	2	2	no	—
339	C₃²×D₄	—	2	4	no	—
340	C₃²×D₄	—	2	2	no	—
341	C₂×C₃²×C₄	—	2	4	no	—
342	C₂×C₃²×C₄	—	2	2	no	—
343	C₂×C₃²×C₄	—	2	4	no	—
344	C₂×C₃²×C₄	—	4	1	no	—
345	C₂×C₃²×C₄	—	4	2	no	—
346	C₂×C₃²×C₄	#41	1	4	yes	complemented
347	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
348	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
349	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
350	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
351	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
352	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
353	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
354	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
355	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
356	C₃×#67	—	2	8	no	—
357	C₃×#67	—	4	4	no	—
358	C₂×C₃×Dic₃	—	2	4	no	—
359	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
360	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
361	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
362	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
363	C₃×D₁₂	—	2	4	no	—
364	C₃×D₁₂	—	2	2	no	—
365	C₃×D₁₂	#41	1	4	yes	complemented
366	C₃×C₄×D₃	—	2	8	no	—
367	C₃×C₄×D₃	—	2	4	no	—
368	C₃×C₄×D₃	—	2	4	no	—
369	C₃×C₄×D₃	—	2	4	no	—
370	C₃×C₄×D₃	—	2	4	no	—
371	C₃×C₄×D₃	—	4	4	no	—
372	C₃×Dic₆	—	2	4	no	—
373	C₃×Dic₆	—	4	2	no	—
374	#556	—	3	1	no	—
375	#555	—	3	1	no	—
376	#554	—	3	1	no	—
377	#553	—	3	2	no	—
378	#552	—	3	2	no	—
379	#552	—	3	2	no	—
380	#551	—	3	4	no	—
381	#547	—	3	1	no	—
382	#546	—	3	2	no	—
383	#533	—	3	1	no	—
384	#529	—	3	4	no	—
385	#529	—	3	2	no	—
386	#525	—	3	2	no	—
387	C₄×#41	—	3	2	no	—
388	C₄×#41	C₃×D₃	1	1	yes	characteristic, complemented
389	C₂×C₄×D₄	—	3	1	no	—
390	C₂×#117	—	3	2	no	—
391	C₂⁴×C₃	—	3	2	no	—
392	C₂³×D₃	C₂³×C₃	1	2	yes	—
393	C₃×#41	—	2	8	no	—
394	C₃×#41	—	2	4	no	—
395	C₃×#41	—	2	4	no	—
396	C₃×#41	—	6	8	no	—
397	C₂×C₃×Q₈	—	2	1	no	—
398	C₂×C₃×Q₈	—	3	2	no	—
399	C₂×C₃×Q₈	—	3	2	no	—
400	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
401	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
402	C₂×C₃×D₄	—	2	2	no	—
403	C₂×C₃×D₄	—	2	1	no	—
404	C₂×C₃×D₄	—	3	4	no	—
405	C₂×C₃×D₄	—	3	4	no	—
406	C₂×C₃×D₄	—	3	1	no	—
407	C₂×C₃×D₄	—	3	2	no	—
408	C₂×C₃×D₄	—	3	1	no	—
409	C₂×C₃×D₄	—	6	4	no	—
410	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
411	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic
412	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
413	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
414	C₂²×C₃×C₄	—	2	2	no	—
415	C₂²×C₃×C₄	—	2	1	no	—
416	C₂²×C₃×C₄	—	2	1	no	—
417	C₂²×C₃×C₄	—	2	2	no	—
418	C₂²×C₃×C₄	—	2	1	no	—
419	C₂²×C₃×C₄	—	2	2	no	—
420	C₂²×C₃×C₄	—	3	2	no	—
421	C₂²×C₃×C₄	—	3	4	no	—
422	C₂²×C₃×C₄	—	3	2	no	—
423	C₂²×C₃×C₄	—	3	2	no	—
424	C₂²×C₃×C₄	—	3	2	no	—
425	C₂²×C₃×C₄	—	3	2	no	—
426	C₂²×C₃×C₄	—	3	4	no	—
427	C₂²×C₃×C₄	—	6	8	no	—
428	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
429	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
430	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
431	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
432	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
433	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
434	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
435	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
436	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
437	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
438	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
439	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
440	C₂×#67	C₂³×C₃	1	4	yes	—
441	C₂×#67	C₂³×C₃	1	4	yes	—
442	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
443	#235	—	2	8	no	—
444	C₂×D₁₂	—	2	4	no	—
445	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
446	C₂×D₁₂	C₂³×C₃	1	2	yes	—
447	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
448	C₂×C₄×D₃	—	2	8	no	—
449	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
450	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
451	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
452	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
453	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
454	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
455	C₂×Dic₆	C₂³×C₃	1	2	yes	—
456	C₂×Dic₆	C₂³×C₃	1	2	yes	—
457	C₃×C₄⋊C₄	—	2	1	no	—
458	C₃×C₄⋊C₄	—	2	1	no	—
459	C₃×C₄⋊C₄	—	2	2	no	—
460	C₃×C₄⋊C₄	—	2	2	no	—
461	C₃×C₄⋊C₄	—	3	4	no	—
462	C₃×C₄⋊C₄	—	3	4	no	—
463	C₃×C₄⋊C₄	—	3	4	no	—
464	C₃×C₄⋊C₄	—	3	4	no	—
465	C₃×C₄⋊C₄	—	3	4	no	—
466	C₃×C₄⋊C₄	—	3	4	no	—
467	C₃×C₄⋊C₄	—	3	1	no	—
468	C₃×C₄⋊C₄	—	3	2	no	—
469	C₃×C₄⋊C₄	—	3	2	no	—
470	C₃×C₄⋊C₄	—	3	1	no	—
471	C₃×C₄⋊C₄	—	3	2	no	—
472	C₃×C₄⋊C₄	—	3	2	no	—
473	C₃×C₄⋊C₄	—	3	2	no	—
474	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
475	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
476	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
477	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
478	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
479	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
480	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
481	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
482	C₃×C₂²⋊C₄	—	2	2	no	—
483	C₃×C₂²⋊C₄	—	2	2	no	—
484	C₃×C₂²⋊C₄	—	2	2	no	—
485	C₃×C₂²⋊C₄	—	3	4	no	—
486	C₃×C₂²⋊C₄	—	3	4	no	—
487	C₃×C₂²⋊C₄	—	3	4	no	—
488	C₃×C₂²⋊C₄	—	3	2	no	—
489	C₃×C₂²⋊C₄	—	3	4	no	—
490	C₃×C₂²⋊C₄	—	3	4	no	—
491	C₃×C₂²⋊C₄	—	3	2	no	—
492	C₃×C₂²⋊C₄	—	3	2	no	—
493	C₃×C₂²⋊C₄	—	3	2	no	—
494	C₃×C₂²⋊C₄	—	3	4	no	—
495	C₃×C₂²⋊C₄	—	3	4	no	—
496	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
497	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
498	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
499	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
500	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
501	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
502	C₃×C₄²	—	2	1	no	—
503	C₃×C₄²	—	2	2	no	—
504	C₃×C₄²	—	2	1	no	—
505	C₃×C₄²	—	2	1	no	—
506	C₃×C₄²	—	2	1	no	—
507	C₃×C₄²	—	2	2	no	—
508	C₃×C₄²	—	2	2	no	—
509	C₃×C₄²	—	3	4	no	—
510	C₃×C₄²	—	3	4	no	—
511	C₃×C₄²	—	3	4	no	—
512	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
513	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
514	C₃×C₄²	C₂²×D₃	1	2	yes	—
515	C₃×C₄²	C₂²×D₃	1	2	yes	—
516	C₃×C₄²	C₂²×D₃	1	2	yes	—
517	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
518	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
519	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
520	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
521	C₃×C₄²	C₂³×C₃	1	2	yes	—
522	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
523	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
524	C₃×C₄²	C₂³×C₃	1	2	yes	—
525	C₃×C₄²	C₂³×C₃	1	2	yes	—
526	#217	C₂³×C₃	1	4	yes	—
527	#217	C₂³×C₃	1	4	yes	—
528	#217	C₂³×C₃	1	4	yes	—
529	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
530	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
531	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
532	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
533	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
534	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
535	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
536	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
537	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
538	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
539	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
540	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
541	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
542	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
543	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
544	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
545	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
546	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
547	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
548	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
549	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
550	C₄×Dic₃	C₂³×C₃	1	4	yes	—
551	C₄×Dic₃	C₂³×C₃	1	4	yes	—
552	C₄×Dic₃	C₂³×C₃	1	4	yes	—
553	C₂²×C₃²	—	2	2	no	—
554	C₂²×C₃²	—	2	1	no	—
555	C₂²×C₃²	—	2	1	no	—
556	C₂²×C₃²	—	2	2	no	—
557	C₂²×C₃²	—	2	2	no	—
558	C₂²×C₃²	C₂×#41	1	2	yes	—
559	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
560	C₂×C₃×D₃	—	2	2	no	—
561	C₂×C₃×D₃	—	2	2	no	—
562	C₂×C₃×D₃	—	2	2	no	—
563	C₂×C₃×D₃	—	2	2	no	—
564	C₂×C₃×D₃	—	2	2	no	—
565	C₂×C₃×D₃	—	4	8	no	—
566	C₂×C₃×D₃	C₂×#41	1	4	yes	—
567	C₃²×C₄	—	2	2	no	—
568	C₃²×C₄	—	2	1	no	—
569	C₃²×C₄	—	2	2	no	—
570	C₃²×C₄	—	2	1	no	—
571	C₃²×C₄	—	2	1	no	—
572	C₃²×C₄	—	2	2	no	—
573	C₃²×C₄	C₂×#41	1	2	yes	—
574	C₃²×C₄	C₂×#41	1	2	yes	—
575	C₃²×C₄	C₂×#41	1	2	yes	—
576	C₃×Dic₃	—	2	4	no	—
577	C₃×Dic₃	—	2	2	no	—
578	C₃×Dic₃	—	2	2	no	—
579	C₃×Dic₃	—	2	4	no	—
580	C₂×#41	—	3	2	no	—
581	C₂×#41	C₂×C₃×D₃	1	1	yes	characteristic
582	C₂²×D₄	—	3	1	no	—
583	C₂³×C₄	—	3	2	no	—
584	C₄⋊Q₈	—	3	1	no	—
585	C₄⋊Q₈	—	3	1	no	—
586	#126	—	3	4	no	—
587	#126	—	3	4	no	—
588	#126	—	3	4	no	—
589	#125	—	3	4	no	—
590	#125	—	3	2	no	—
591	#125	—	3	2	no	—
592	#124	—	3	4	no	—
593	#124	—	3	2	no	—
594	#123	—	3	4	no	—
595	#123	—	3	4	no	—
596	#123	—	3	4	no	—
597	#123	—	3	4	no	—
598	C₂²⋊Q₈	—	3	2	no	—
599	C₂²⋊Q₈	—	3	2	no	—
600	C₂²⋊Q₈	—	3	2	no	—
601	C₂²⋊Q₈	—	3	2	no	—
602	C₂²⋊Q₈	—	3	2	no	—
603	C₂²⋊Q₈	—	3	4	no	—
604	#121	—	3	2	no	—
605	#121	—	3	2	no	—
606	#121	—	3	2	no	—
607	#121	—	3	4	no	—
608	#120	—	3	4	no	—
609	C₄×Q₈	—	3	2	no	—
610	C₄×Q₈	—	3	2	no	—
611	C₄×Q₈	—	3	2	no	—
612	C₄×Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
613	C₄×Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
614	C₄×D₄	—	3	4	no	—
615	C₄×D₄	—	3	4	no	—
616	C₄×D₄	—	3	4	no	—
617	C₄×D₄	—	3	1	no	—
618	C₄×D₄	—	3	1	no	—
619	C₄×D₄	—	3	2	no	—
620	C₄×D₄	—	3	1	no	—
621	C₄×D₄	—	3	2	no	—
622	C₄×D₄	—	3	1	no	—
623	C₄×D₄	—	3	2	no	—
624	C₄×D₄	C₂×C₃×D₃	1	2	yes	—
625	C₄×D₄	C₂×C₃×D₃	1	2	yes	—
626	C₄×D₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
627	C₄×D₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
628	#117	—	3	2	no	—
629	#117	—	3	2	no	—
630	#117	—	3	2	no	—
631	#117	—	3	2	no	—
632	#117	—	3	4	no	—
633	#117	—	3	4	no	—
634	#117	—	3	4	no	—
635	#117	C₂×C₃×D₃	1	1	yes	characteristic
636	#117	C₂×C₃×D₃	1	2	yes	complemented
637	C₂×C₄⋊C₄	—	3	1	no	—
638	C₂×C₄⋊C₄	—	3	2	no	—
639	C₂×C₄⋊C₄	—	3	2	no	—
640	C₂×C₂²⋊C₄	—	3	2	no	—
641	C₂×C₂²⋊C₄	—	3	4	no	—
642	C₂×C₄²	—	3	4	no	—
643	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
644	C₂×C₄²	C₂×C₃×D₃	1	2	yes	complemented
645	C₂³×C₃	—	2	2	no	—
646	C₂³×C₃	—	2	1	no	—
647	C₂³×C₃	—	3	2	no	—
648	C₂³×C₃	—	3	2	no	—
649	C₂³×C₃	—	6	4	no	—
650	C₂³×C₃	—	6	4	no	—
651	C₂³×C₃	—	12	2	no	—
652	C₂³×C₃	C₂³×D₃	1	2	yes	—
653	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
654	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
655	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
656	C₂²×D₃	—	2	4	no	—
657	C₂²×D₃	—	2	4	no	—
658	C₂²×D₃	—	4	2	no	—
659	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
660	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
661	C₃×Q₈	—	2	4	no	—
662	C₃×Q₈	—	2	2	no	—
663	C₃×Q₈	—	2	2	no	—
664	C₃×Q₈	—	6	4	no	—
665	C₃×Q₈	—	12	2	no	—
666	C₃×D₄	—	2	8	no	—
667	C₃×D₄	—	2	4	no	—
668	C₃×D₄	—	2	4	no	—
669	C₃×D₄	—	2	4	no	—
670	C₃×D₄	—	2	2	no	—
671	C₃×D₄	—	2	2	no	—
672	C₃×D₄	—	3	4	no	—
673	C₃×D₄	—	6	4	no	—
674	C₃×D₄	—	6	8	no	—
675	C₃×D₄	—	6	2	no	—
676	C₃×D₄	—	12	4	no	—
677	C₂×C₃×C₄	—	2	8	no	—
678	C₂×C₃×C₄	—	2	4	no	—
679	C₂×C₃×C₄	—	2	2	no	—
680	C₂×C₃×C₄	—	2	4	no	—
681	C₂×C₃×C₄	—	2	2	no	—
682	C₂×C₃×C₄	—	2	4	no	—
683	C₂×C₃×C₄	—	2	4	no	—
684	C₂×C₃×C₄	—	2	1	no	—
685	C₂×C₃×C₄	—	2	1	no	—
686	C₂×C₃×C₄	—	2	1	no	—
687	C₂×C₃×C₄	—	2	2	no	—
688	C₂×C₃×C₄	—	2	1	no	—
689	C₂×C₃×C₄	—	2	2	no	—
690	C₂×C₃×C₄	—	2	2	no	—
691	C₂×C₃×C₄	—	2	1	no	—
692	C₂×C₃×C₄	—	2	1	no	—
693	C₂×C₃×C₄	—	2	4	no	—
694	C₂×C₃×C₄	—	3	2	no	—
695	C₂×C₃×C₄	—	3	4	no	—
696	C₂×C₃×C₄	—	3	4	no	—
697	C₂×C₃×C₄	—	3	2	no	—
698	C₂×C₃×C₄	—	4	2	no	—
699	C₂×C₃×C₄	—	4	4	no	—
700	C₂×C₃×C₄	—	4	2	no	—
701	C₂×C₃×C₄	—	4	1	no	—
702	C₂×C₃×C₄	—	4	1	no	—
703	C₂×C₃×C₄	—	4	2	no	—
704	C₂×C₃×C₄	—	4	4	no	—
705	C₂×C₃×C₄	—	4	2	no	—
706	C₂×C₃×C₄	—	6	8	no	—
707	C₂×C₃×C₄	—	6	4	no	—
708	C₂×C₃×C₄	—	6	4	no	—
709	C₂×C₃×C₄	—	6	4	no	—
710	C₂×C₃×C₄	—	6	4	no	—
711	C₂×C₃×C₄	—	6	4	no	—
712	C₂×C₃×C₄	—	12	4	no	—
713	C₂×C₃×C₄	#235	1	4	yes	complemented
714	C₂×C₃×C₄	C₃×#41	1	4	yes	complemented
715	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
716	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
717	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
718	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
719	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
720	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
721	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
722	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
723	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
724	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
725	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
726	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
727	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
728	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
729	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
730	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
731	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
732	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
733	#67	—	2	8	no	—
734	#67	—	4	4	no	—
735	C₂×Dic₃	—	2	4	no	—
736	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
737	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
738	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
739	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
740	D₁₂	—	2	4	no	—
741	D₁₂	—	2	2	no	—
742	D₁₂	C₃×#41	1	4	yes	complemented
743	C₄×D₃	—	2	8	no	—
744	C₄×D₃	—	2	4	no	—
745	C₄×D₃	—	2	4	no	—
746	C₄×D₃	—	2	4	no	—
747	C₄×D₃	—	2	4	no	—
748	C₄×D₃	—	4	4	no	—
749	Dic₆	—	2	4	no	—
750	Dic₆	—	4	2	no	—
751	C₂×C₃²	—	2	2	no	—
752	C₂×C₃²	—	4	2	no	—
753	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
754	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
755	C₂×C₃²	#585	1	1	yes	characteristic
756	C₃×D₃	—	2	4	no	—
757	C₃×D₃	—	4	2	no	—
758	C₂⁴	—	3	2	no	—
759	#41	—	2	4	no	—
760	#41	—	6	8	no	—
761	C₂×Q₈	—	3	2	no	—
762	C₂×Q₈	—	3	2	no	—
763	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
764	C₂×D₄	—	3	4	no	—
765	C₂×D₄	—	3	4	no	—
766	C₂×D₄	—	3	1	no	—
767	C₂×D₄	—	3	2	no	—
768	C₂×D₄	—	3	1	no	—
769	C₂×D₄	—	6	4	no	—
770	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
771	C₂×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
772	C₂²×C₄	—	3	2	no	—
773	C₂²×C₄	—	3	2	no	—
774	C₂²×C₄	—	3	4	no	—
775	C₂²×C₄	—	3	2	no	—
776	C₂²×C₄	—	3	2	no	—
777	C₂²×C₄	—	3	2	no	—
778	C₂²×C₄	—	3	4	no	—
779	C₂²×C₄	—	6	8	no	—
780	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
781	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
782	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
783	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
784	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
785	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
786	C₄⋊C₄	—	3	1	no	—
787	C₄⋊C₄	—	3	2	no	—
788	C₄⋊C₄	—	3	2	no	—
789	C₄⋊C₄	—	3	4	no	—
790	C₄⋊C₄	—	3	4	no	—
791	C₄⋊C₄	—	3	1	no	—
792	C₄⋊C₄	—	3	2	no	—
793	C₄⋊C₄	—	3	2	no	—
794	C₄⋊C₄	—	3	4	no	—
795	C₄⋊C₄	—	3	4	no	—
796	C₄⋊C₄	—	3	4	no	—
797	C₄⋊C₄	—	3	4	no	—
798	C₄⋊C₄	—	3	2	no	—
799	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
800	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
801	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
802	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
803	C₂²⋊C₄	—	3	4	no	—
804	C₂²⋊C₄	—	3	4	no	—
805	C₂²⋊C₄	—	3	4	no	—
806	C₂²⋊C₄	—	3	2	no	—
807	C₂²⋊C₄	—	3	4	no	—
808	C₂²⋊C₄	—	3	4	no	—
809	C₂²⋊C₄	—	3	2	no	—
810	C₂²⋊C₄	—	3	2	no	—
811	C₂²⋊C₄	—	3	2	no	—
812	C₂²⋊C₄	—	3	4	no	—
813	C₂²⋊C₄	—	3	4	no	—
814	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
815	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
816	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
817	C₄²	—	3	4	no	—
818	C₄²	—	3	4	no	—
819	C₄²	—	3	4	no	—
820	C₄²	C₂²×C₃×D₃	1	2	yes	—
821	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
822	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
823	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
824	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
825	C₄²	C₂²×C₃×D₃	1	2	yes	—
826	C₄²	C₂²×C₃×D₃	1	2	yes	—
827	C₂²×C₃	—	2	1	no	—
828	C₂²×C₃	—	2	1	no	—
829	C₂²×C₃	—	2	1	no	—
830	C₂²×C₃	—	2	1	no	—
831	C₂²×C₃	—	2	4	no	—
832	C₂²×C₃	—	2	2	no	—
833	C₂²×C₃	—	2	2	no	—
834	C₂²×C₃	—	2	2	no	—
835	C₂²×C₃	—	2	2	no	—
836	C₂²×C₃	—	2	2	no	—
837	C₂²×C₃	—	2	2	no	—
838	C₂²×C₃	—	2	2	no	—
839	C₂²×C₃	—	2	1	no	—
840	C₂²×C₃	—	3	4	no	—
841	C₂²×C₃	—	4	1	no	—
842	C₂²×C₃	—	4	1	no	—
843	C₂²×C₃	—	4	2	no	—
844	C₂²×C₃	—	4	2	no	—
845	C₂²×C₃	—	6	2	no	—
846	C₂²×C₃	—	6	2	no	—
847	C₂²×C₃	—	6	2	no	—
848	C₂²×C₃	—	6	2	no	—
849	C₂²×C₃	—	6	2	no	—
850	C₂²×C₃	—	12	8	no	—
851	C₂²×C₃	C₂×#235	1	2	yes	—
852	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
853	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
854	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
855	C₂×D₃	—	2	2	no	—
856	C₂×D₃	—	2	2	no	—
857	C₂×D₃	—	2	2	no	—
858	C₂×D₃	—	2	2	no	—
859	C₂×D₃	—	2	2	no	—
860	C₂×D₃	—	4	8	no	—
861	C₂×D₃	C₂×C₃×#41	1	4	yes	—
862	C₃×C₄	—	2	4	no	—
863	C₃×C₄	—	2	2	no	—
864	C₃×C₄	—	2	2	no	—
865	C₃×C₄	—	2	2	no	—
866	C₃×C₄	—	2	1	no	—
867	C₃×C₄	—	2	1	no	—
868	C₃×C₄	—	2	2	no	—
869	C₃×C₄	—	2	1	no	—
870	C₃×C₄	—	2	2	no	—
871	C₃×C₄	—	2	1	no	—
872	C₃×C₄	—	2	2	no	—
873	C₃×C₄	—	2	1	no	—
874	C₃×C₄	—	2	2	no	—
875	C₃×C₄	—	2	1	no	—
876	C₃×C₄	—	2	2	no	—
877	C₃×C₄	—	2	2	no	—
878	C₃×C₄	—	2	2	no	—
879	C₃×C₄	—	4	2	no	—
880	C₃×C₄	—	4	1	no	—
881	C₃×C₄	—	4	2	no	—
882	C₃×C₄	—	4	1	no	—
883	C₃×C₄	—	6	2	no	—
884	C₃×C₄	—	6	2	no	—
885	C₃×C₄	—	6	4	no	—
886	C₃×C₄	—	6	4	no	—
887	C₃×C₄	C₂×#235	1	2	yes	—
888	C₃×C₄	C₂×#235	1	2	yes	—
889	C₃×C₄	D₃×#41	1	2	yes	—
890	C₃×C₄	C₂×C₃×#41	1	2	yes	—
891	C₃×C₄	C₂×C₃×#41	1	2	yes	—
892	C₃×C₄	C₂×C₃×#41	1	2	yes	—
893	Dic₃	—	2	4	no	—
894	Dic₃	—	2	2	no	—
895	Dic₃	—	2	2	no	—
896	Dic₃	—	2	4	no	—
897	C₃²	#3475	1	1	yes	characteristic, complemented, Sylow
898	C₂³	—	3	2	no	—
899	C₂³	—	3	2	no	—
900	C₂³	—	6	4	no	—
901	C₂³	—	6	4	no	—
902	C₂³	—	12	2	no	—
903	C₂³	C₂³×C₃×D₃	1	2	yes	—
904	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
905	Q₈	—	2	2	no	—
906	Q₈	—	6	4	no	—
907	Q₈	—	12	2	no	—
908	D₄	—	2	4	no	—
909	D₄	—	2	2	no	—
910	D₄	—	3	4	no	—
911	D₄	—	6	4	no	—
912	D₄	—	6	8	no	—
913	D₄	—	6	2	no	—
914	D₄	—	12	4	no	—
915	C₂×C₄	—	2	4	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	4	no	—
918	C₂×C₄	—	3	2	no	—
919	C₂×C₄	—	3	4	no	—
920	C₂×C₄	—	3	4	no	—
921	C₂×C₄	—	3	2	no	—
922	C₂×C₄	—	4	2	no	—
923	C₂×C₄	—	4	1	no	—
924	C₂×C₄	—	6	8	no	—
925	C₂×C₄	—	6	4	no	—
926	C₂×C₄	—	6	4	no	—
927	C₂×C₄	—	6	4	no	—
928	C₂×C₄	—	6	4	no	—
929	C₂×C₄	—	6	4	no	—
930	C₂×C₄	—	12	4	no	—
931	C₂×C₄	C₃×#235	1	4	yes	complemented
932	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
933	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
934	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
935	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
936	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
937	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
938	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
939	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
940	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
941	C₂×C₃	—	2	2	no	—
942	C₂×C₃	—	2	2	no	—
943	C₂×C₃	—	2	1	no	—
944	C₂×C₃	—	2	1	no	—
945	C₂×C₃	—	2	1	no	—
946	C₂×C₃	—	4	2	no	—
947	C₂×C₃	—	4	4	no	—
948	C₂×C₃	—	4	2	no	—
949	C₂×C₃	—	4	2	no	—
950	C₂×C₃	—	6	4	no	—
951	C₂×C₃	—	12	2	no	—
952	C₂×C₃	C₂²×#235	1	1	yes	characteristic
953	C₂×C₃	C₂×D₃×#41	1	1	yes	characteristic
954	C₂×C₃	#5964	1	1	yes	characteristic
955	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
956	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
957	C₂×C₃	C₃×#585	1	1	yes	characteristic
958	D₃	—	2	4	no	—
959	D₃	—	4	2	no	—
960	C₂²	—	2	1	no	—
961	C₂²	—	2	1	no	—
962	C₂²	—	2	2	no	—
963	C₂²	—	2	2	no	—
964	C₂²	—	2	2	no	—
965	C₂²	—	3	4	no	—
966	C₂²	—	6	2	no	—
967	C₂²	—	6	2	no	—
968	C₂²	—	6	2	no	—
969	C₂²	—	6	2	no	—
970	C₂²	—	6	2	no	—
971	C₂²	—	12	8	no	—
972	C₂²	C₂×C₃×#235	1	2	yes	—
973	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
974	C₄	—	2	2	no	—
975	C₄	—	2	2	no	—
976	C₄	—	2	1	no	—
977	C₄	—	2	1	no	—
978	C₄	—	2	2	no	—
979	C₄	—	2	1	no	—
980	C₄	—	6	2	no	—
981	C₄	—	6	2	no	—
982	C₄	—	6	4	no	—
983	C₄	—	6	4	no	—
984	C₄	C₂×C₃×#235	1	2	yes	—
985	C₄	C₂×C₃×#235	1	2	yes	—
986	C₄	C₃×D₃×#41	1	2	yes	—
987	C₃	—	2	1	no	—
988	C₃	#85840	1	1	yes	characteristic, direct product factor
989	C₃	C₃×#3475	1	1	yes	characteristic, complemented
990	C₂	—	2	2	no	—
991	C₂	—	4	2	no	—
992	C₂	—	6	4	no	—
993	C₂	—	12	2	no	—
994	C₂	C₂²×C₃×#235	1	1	yes	characteristic
995	C₂	C₂×C₃×D₃×#41	1	1	yes	characteristic
996	C₂	C₃×#5964	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×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×#3475
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ 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×#5828	C₂	semidirect
3. C₃×#5584	C₂	semidirect
4. C₃×#5581	C₂	semidirect
5. C₃×#5579	C₂	semidirect
6. C₃×#5563	C₂	semidirect
7. C₃×#5558	C₂	semidirect
8. C₃×#5556	C₂	semidirect
9. C₃×#5551	C₂	semidirect
10. C₃×#5550	C₂	semidirect
11. C₃×#5541	C₂	semidirect
12. C₃×#5528	C₂	semidirect
13. C₃×D₃×#117	C₂	semidirect
14. C₃×#5479	C₂	semidirect
15. C₃×C₄×#235	C₂	semidirect
16. C₂×C₃×C₄×D₁₂	C₂	semidirect
17. C₃×#5470	C₂	semidirect
19. #85840	C₃	direct (N × H)
24. C₃²×C₄×Q₈	C₂²	semidirect
25. C₃²×C₄×Q₈	C₂²	semidirect
28. C₃²×C₄×D₄	C₂²	semidirect
29. C₃²×C₄×D₄	C₂²	semidirect
31. C₃²×#117	C₂²	semidirect
33. C₂×C₃²×C₄²	C₂²	semidirect
34. C₃×#946	C₂²	semidirect
35. C₃×#946	C₂²	semidirect
36. C₃×#938	C₂²	semidirect
37. C₃×#938	C₂²	semidirect
41. C₃×#929	C₂²	semidirect
42. C₃×C₄×#67	C₂²	semidirect
43. C₃×C₄×#67	C₂²	semidirect
44. C₃×C₄×#67	C₂²	semidirect
47. C₃×#926	C₂²	semidirect
51. C₃×#924	C₂²	semidirect
52. C₃×#898	C₂²	semidirect
53. C₃×#896	C₂²	semidirect
55. C₃×#892	C₂²	semidirect
56. C₃×#892	C₂²	semidirect
57. C₃×D₃×C₄⋊C₄	C₂²	semidirect
58. C₃×D₃×C₄⋊C₄	C₂²	semidirect
59. C₃×#889	C₂²	semidirect
60. C₃×#885	C₂²	semidirect
62. C₃×#883	C₂²	semidirect
64. C₃×#879	C₂²	semidirect
66. C₃×#876	C₂²	semidirect
75. C₃×#872	C₂²	semidirect
76. C₃×#872	C₂²	semidirect
77. C₃×C₄²×D₃	C₂²	semidirect
78. C₃×#870	C₂²	semidirect
79. C₃×#870	C₂²	semidirect
80. C₃×#869	C₂²	semidirect
81. C₃×#869	C₂²	semidirect
82. C₃×C₄×Dic₆	C₂²	semidirect
83. C₃×C₄×Dic₆	C₂²	semidirect
84. C₃×C₄×Dic₆	C₂²	semidirect
100. C₃×C₄×#41	D₃	semidirect
101. C₃×C₄×#41	C₂×C₃	semidirect
104. #5828	C₂×C₃	semidirect
105. #5584	C₂×C₃	semidirect
106. #5581	C₂×C₃	semidirect
107. #5579	C₂×C₃	semidirect
108. #5563	C₂×C₃	semidirect
109. #5558	C₂×C₃	semidirect
110. #5556	C₂×C₃	semidirect
111. #5551	C₂×C₃	semidirect
112. #5550	C₂×C₃	semidirect
113. #5541	C₂×C₃	semidirect
114. #5528	C₂×C₃	semidirect
115. D₃×#117	C₂×C₃	semidirect
116. #5479	C₂×C₃	semidirect
117. C₄×#235	C₂×C₃	semidirect
118. C₂×C₄×D₁₂	C₂×C₃	semidirect
119. #5470	C₂×C₃	semidirect
229. C₃×C₄×Q₈	C₂×D₃	semidirect
230. C₃×C₄×Q₈	C₂×D₃	semidirect
231. C₃×C₄×Q₈	C₂²×C₃	semidirect
232. C₃×C₄×Q₈	C₂²×C₃	semidirect
249. C₃×C₄×D₄	C₂×D₃	semidirect
250. C₃×C₄×D₄	C₂×D₃	semidirect
253. C₃×C₄×D₄	C₂²×C₃	semidirect
254. C₃×C₄×D₄	C₂²×C₃	semidirect
265. C₃×#117	C₂×D₃	semidirect
267. C₃×#117	C₂²×C₃	semidirect
277. C₂×C₃×C₄²	C₂×D₃	semidirect
279. C₂×C₃×C₄²	C₂²×C₃	semidirect
280. #946	C₂²×C₃	semidirect
281. #946	C₂²×C₃	semidirect
282. #938	C₂²×C₃	semidirect
283. #938	C₂²×C₃	semidirect
287. #929	C₂²×C₃	semidirect
288. C₄×#67	C₂²×C₃	semidirect
289. C₄×#67	C₂²×C₃	semidirect
290. C₄×#67	C₂²×C₃	semidirect
293. #926	C₂²×C₃	semidirect
297. #924	C₂²×C₃	semidirect
298. #898	C₂²×C₃	semidirect
299. #896	C₂²×C₃	semidirect
301. #892	C₂²×C₃	semidirect
302. #892	C₂²×C₃	semidirect
303. D₃×C₄⋊C₄	C₂²×C₃	semidirect
304. D₃×C₄⋊C₄	C₂²×C₃	semidirect
305. #889	C₂²×C₃	semidirect
306. #885	C₂²×C₃	semidirect
308. #883	C₂²×C₃	semidirect
310. #879	C₂²×C₃	semidirect
312. #876	C₂²×C₃	semidirect
321. #872	C₂²×C₃	semidirect
322. #872	C₂²×C₃	semidirect
323. C₄²×D₃	C₂²×C₃	semidirect
324. #870	C₂²×C₃	semidirect
325. #870	C₂²×C₃	semidirect
326. #869	C₂²×C₃	semidirect
327. #869	C₂²×C₃	semidirect
328. C₄×Dic₆	C₂²×C₃	semidirect
329. C₄×Dic₆	C₂²×C₃	semidirect
330. C₄×Dic₆	C₂²×C₃	semidirect
346. C₂×C₃²×C₄	#41	semidirect
365. C₃×D₁₂	#41	semidirect
388. C₄×#41	C₃×D₃	semidirect
612. C₄×Q₈	C₂×C₃×D₃	semidirect
613. C₄×Q₈	C₂×C₃×D₃	semidirect
626. C₄×D₄	C₂×C₃×D₃	semidirect
627. C₄×D₄	C₂×C₃×D₃	semidirect
636. #117	C₂×C₃×D₃	semidirect
644. C₂×C₄²	C₂×C₃×D₃	semidirect
713. C₂×C₃×C₄	#235	semidirect
714. C₂×C₃×C₄	C₃×#41	semidirect
742. D₁₂	C₃×#41	semidirect
897. C₃²	#3475	semidirect
931. C₂×C₄	C₃×#235	semidirect
988. C₃	#85840	direct (N × H)
989. C₃	C₃×#3475	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×#5828	2
C₃×#5584	2
C₃×#5581	2
C₃×#5579	2
C₃×#5563	2
C₃×#5558	2
C₃×#5556	2
C₃×#5551	2
C₃×#5550	2
C₃×#5541	2
C₃×#5528	2
C₃×D₃×#117	2
C₃×#5479	2
C₃×C₄×#235	2
C₂×C₃×C₄×D₁₂	2
C₃×#5470	2
C₃×#3475	3
#85840	3

Subgroups — C3×#85840 #11903472

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#85840 #11903472