Subgroups — C₃×#34499 #10653106

Order 768.

2032 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#556	C₂	1	1	yes	maximal, characteristic
2	C₃×#2383	C₂	1	2	yes	maximal, complemented
3	C₃×#2378	C₂	1	2	yes	maximal, complemented
4	C₃×#2373	C₂	1	2	yes	maximal, complemented
5	C₃×#2367	C₂	1	1	yes	maximal, characteristic
6	C₃×#2367	C₂	1	1	yes	maximal, characteristic
7	C₃×#2365	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2355	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#2351	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×Q₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#2349	C₂	1	1	yes	maximal, characteristic
12	C₃×#2343	C₂	1	2	yes	maximal, complemented
13	C₃×#2334	C₂	1	2	yes	maximal, complemented
14	C₃×#2334	C₂	1	2	yes	maximal, complemented
15	C₃×#2329	C₂	1	2	yes	maximal, complemented
16	C₃×#2327	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#2326	C₂	1	1	yes	maximal, characteristic
18	C₃×#2320	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#2319	C₂	1	1	yes	maximal, characteristic
20	C₃×#2314	C₂	1	2	yes	maximal, complemented
21	C₃×C₄×#124	C₂	1	1	yes	maximal, characteristic
22	C₃×#2295	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×#2295	C₂	1	1	yes	maximal, characteristic, complemented
24	#34499	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₃×#556	C₄	1	16	yes	complemented
26	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₃×#126	C₂²	1	2	yes	—
28	C₂×C₃×#126	C₂²	1	2	yes	—
29	C₂×C₃×#124	C₂²	1	1	yes	characteristic
30	C₂×C₃×#124	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
32	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
34	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
35	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
36	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
37	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
38	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
39	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
40	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
41	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
42	C₂×C₃×#117	C₂²	1	2	yes	—
43	C₃×#391	C₂²	1	1	yes	characteristic
44	C₃×#391	C₂²	1	1	yes	characteristic
45	C₃×#391	C₂²	1	1	yes	characteristic
46	C₃×#391	C₂²	1	2	yes	—
47	C₃×#391	C₂²	1	1	yes	characteristic
48	C₃×#391	C₂²	1	1	yes	characteristic
49	C₃×#391	C₂²	1	1	yes	characteristic
50	C₃×#390	C₂²	1	1	yes	characteristic
51	C₃×#390	C₂²	1	1	yes	characteristic
52	C₃×#389	C₂²	1	2	yes	—
53	C₃×#389	C₂²	1	2	yes	—
54	C₃×#389	C₂²	1	2	yes	—
55	C₃×#389	C₂²	1	2	yes	—
56	C₃×#389	C₂²	1	1	yes	characteristic
57	C₃×#389	C₂²	1	2	yes	—
58	C₃×#389	C₂²	1	1	yes	characteristic
59	C₃×#389	C₂²	1	1	yes	characteristic
60	C₃×#389	C₂²	1	1	yes	characteristic
61	C₃×#389	C₂²	1	1	yes	characteristic
62	C₃×#389	C₂²	1	1	yes	characteristic
63	C₃×#388	C₂²	1	2	yes	—
64	C₃×#388	C₂²	1	2	yes	—
65	C₃×#388	C₂²	1	2	yes	—
66	C₃×#388	C₂²	1	2	yes	—
67	C₃×#388	C₂²	1	2	yes	—
68	C₃×#388	C₂²	1	2	yes	—
69	C₃×#388	C₂²	1	2	yes	—
70	C₃×#388	C₂²	1	2	yes	—
71	C₃×#388	C₂²	1	2	yes	—
72	C₃×#388	C₂²	1	2	yes	—
73	C₃×#387	C₂²	1	2	yes	—
74	C₃×#387	C₂²	1	2	yes	—
75	C₃×#387	C₂²	1	1	yes	characteristic
76	C₃×#387	C₂²	1	2	yes	—
77	C₃×#387	C₂²	1	2	yes	—
78	C₃×#387	C₂²	1	2	yes	—
79	C₃×#387	C₂²	1	2	yes	—
80	C₃×#387	C₂²	1	2	yes	—
81	C₃×#387	C₂²	1	1	yes	characteristic
82	C₃×#387	C₂²	1	2	yes	—
83	C₃×#387	C₂²	1	1	yes	characteristic
84	C₃×#387	C₂²	1	1	yes	characteristic
85	C₃×#387	C₂²	1	2	yes	—
86	C₃×#387	C₂²	1	2	yes	—
87	C₃×#387	C₂²	1	2	yes	—
88	C₃×#387	C₂²	1	2	yes	—
89	C₃×#385	C₂²	1	2	yes	—
90	C₃×#385	C₂²	1	2	yes	—
91	C₃×#385	C₂²	1	2	yes	—
92	C₃×#385	C₂²	1	2	yes	—
93	C₃×#385	C₂²	1	2	yes	—
94	C₃×#385	C₂²	1	2	yes	—
95	C₃×#384	C₂²	1	2	yes	—
96	C₃×#384	C₂²	1	1	yes	characteristic
97	C₃×#383	C₂²	1	2	yes	—
98	C₃×#382	C₂²	1	1	yes	characteristic
99	C₃×#382	C₂²	1	2	yes	—
100	C₃×#382	C₂²	1	1	yes	characteristic
101	C₃×#382	C₂²	1	2	yes	—
102	C₃×#381	C₂²	1	2	yes	—
103	C₃×#380	C₂²	1	2	yes	—
104	C₃×#380	C₂²	1	2	yes	—
105	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
106	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
107	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
108	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
109	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
110	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
111	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
112	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
113	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
114	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
115	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
116	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
117	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
118	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
119	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
120	C₃×#376	C₂²	1	2	yes	—
121	C₃×#376	C₂²	1	1	yes	characteristic
122	C₃×#376	C₂²	1	1	yes	characteristic
123	C₂×C₃×#95	C₂²	1	2	yes	—
124	C₃×C₄³	C₂²	1	1	yes	characteristic
125	C₂×#556	C₂×C₃	1	1	yes	characteristic
126	#2383	C₂×C₃	1	2	yes	complemented
127	#2378	C₂×C₃	1	2	yes	complemented
128	#2373	C₂×C₃	1	2	yes	complemented
129	#2367	C₂×C₃	1	1	yes	characteristic
130	#2367	C₂×C₃	1	1	yes	characteristic
131	#2365	C₂×C₃	1	1	yes	characteristic, complemented
132	#2355	C₂×C₃	1	1	yes	characteristic, complemented
133	#2351	C₂×C₃	1	1	yes	characteristic, complemented
134	Q₈×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
135	#2349	C₂×C₃	1	1	yes	characteristic
136	#2343	C₂×C₃	1	2	yes	complemented
137	#2334	C₂×C₃	1	2	yes	complemented
138	#2334	C₂×C₃	1	2	yes	complemented
139	#2329	C₂×C₃	1	2	yes	complemented
140	#2327	C₂×C₃	1	1	yes	characteristic, complemented
141	#2326	C₂×C₃	1	1	yes	characteristic
142	#2320	C₂×C₃	1	1	yes	characteristic, complemented
143	#2319	C₂×C₃	1	1	yes	characteristic
144	#2314	C₂×C₃	1	2	yes	complemented
145	C₄×#124	C₂×C₃	1	1	yes	characteristic
146	#2295	C₂×C₃	1	1	yes	characteristic, complemented
147	#2295	C₂×C₃	1	1	yes	characteristic, complemented
148	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
149	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
150	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
151	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
152	C₂³×C₃×C₄	C₂³	1	2	yes	—
153	C₂³×C₃×C₄	C₂³	1	2	yes	—
154	C₂³×C₃×C₄	C₂³	1	2	yes	—
155	C₃×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
156	C₃×#126	C₂×C₄	1	16	yes	complemented
157	C₃×#126	C₂×C₄	1	16	yes	complemented
158	C₃×#124	C₂×C₄	1	8	yes	—
159	C₃×#124	C₂×C₄	1	8	yes	—
160	C₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
161	C₃×C₄×Q₈	—	4	2	no	—
162	C₃×C₄×Q₈	—	4	2	no	—
163	C₃×C₄×Q₈	—	4	2	no	—
164	C₃×C₄×Q₈	—	4	2	no	—
165	C₃×C₄×Q₈	C₂×C₄	1	8	yes	complemented
166	C₃×C₄×Q₈	C₂×C₄	1	8	yes	complemented
167	C₃×C₄×Q₈	C₂×C₄	1	8	yes	complemented
168	C₃×C₄×D₄	—	4	2	no	—
169	C₃×C₄×D₄	—	4	2	no	—
170	C₃×C₄×D₄	C₂×C₄	1	8	yes	—
171	C₃×#117	C₂×C₄	1	16	yes	complemented
172	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
173	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
174	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
175	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
177	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
178	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
179	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
180	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
181	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
182	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
183	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
184	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
185	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
186	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
187	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
188	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
189	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
190	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
191	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
192	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
193	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
194	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
195	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
196	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
197	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
198	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
199	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
200	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
201	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
203	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
204	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
205	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
206	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
207	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
208	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
209	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
210	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
211	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
212	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
213	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
214	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
215	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
216	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
217	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
218	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
219	C₂×C₃×C₄²	C₂³	1	2	yes	—
220	C₂×C₃×C₄²	C₂³	1	2	yes	—
221	C₂×C₃×C₄²	C₂³	1	2	yes	—
222	C₂×C₃×C₄²	C₂³	1	2	yes	—
223	C₂×C₃×C₄²	C₂³	1	2	yes	—
224	C₂×C₃×C₄²	C₂³	1	2	yes	—
225	C₂×C₃×C₄²	C₂³	1	2	yes	—
226	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
227	C₂×C₃×C₄²	C₂³	1	2	yes	—
228	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
229	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
230	C₂×C₃×C₄²	C₂³	1	2	yes	—
231	C₃×#95	C₂³	1	1	yes	characteristic
232	C₃×#95	C₂³	1	2	yes	—
233	C₃×#95	C₂³	1	2	yes	—
234	C₃×#95	C₂³	1	2	yes	—
235	C₃×#95	C₂³	1	2	yes	—
236	C₃×#95	C₂³	1	1	yes	characteristic
237	C₃×#95	C₂³	1	1	yes	characteristic
238	C₃×#95	C₂³	1	2	yes	—
239	C₃×#95	C₂³	1	1	yes	characteristic
240	C₃×#95	C₂³	1	1	yes	characteristic
241	C₃×#95	C₂³	1	1	yes	characteristic
242	C₃×#95	C₂³	1	2	yes	—
243	C₃×#95	C₂³	1	1	yes	characteristic
244	C₃×#95	C₂³	1	1	yes	characteristic
245	C₃×#95	C₂³	1	1	yes	characteristic
246	C₃×#95	C₂³	1	1	yes	characteristic
247	C₃×#95	C₂³	1	1	yes	characteristic
248	C₃×#95	C₂³	1	2	yes	—
249	C₃×#95	C₂³	1	2	yes	—
250	C₃×#95	C₂³	1	2	yes	—
251	C₃×#95	C₂³	1	2	yes	—
252	C₃×#95	C₂³	1	2	yes	—
253	C₃×#95	C₂³	1	1	yes	characteristic
254	C₃×#95	C₂³	1	1	yes	characteristic
255	C₃×#95	C₂³	1	2	yes	—
256	C₃×#95	C₂³	1	2	yes	—
257	C₃×#95	C₂³	1	2	yes	—
258	C₃×#95	C₂³	1	2	yes	—
259	C₃×#95	C₂³	1	2	yes	—
260	C₃×#95	C₂³	1	2	yes	—
261	C₃×#95	C₂³	1	2	yes	—
262	C₃×#95	C₂³	1	2	yes	—
263	C₃×#95	C₂³	1	1	yes	characteristic
264	#556	C₃×C₄	1	16	yes	complemented
265	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
266	C₂×#126	C₂²×C₃	1	2	yes	—
267	C₂×#126	C₂²×C₃	1	2	yes	—
268	C₂×#124	C₂²×C₃	1	1	yes	characteristic
269	C₂×#124	C₂²×C₃	1	1	yes	characteristic
270	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
271	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
272	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
273	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
274	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
275	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
276	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
277	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
278	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
279	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
280	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
281	C₂×#117	C₂²×C₃	1	2	yes	—
282	#391	C₂²×C₃	1	1	yes	characteristic
283	#391	C₂²×C₃	1	1	yes	characteristic
284	#391	C₂²×C₃	1	1	yes	characteristic
285	#391	C₂²×C₃	1	1	yes	characteristic
286	#391	C₂²×C₃	1	2	yes	—
287	#391	C₂²×C₃	1	1	yes	characteristic
288	#391	C₂²×C₃	1	1	yes	characteristic
289	#390	C₂²×C₃	1	1	yes	characteristic
290	#390	C₂²×C₃	1	1	yes	characteristic
291	#389	C₂²×C₃	1	1	yes	characteristic
292	#389	C₂²×C₃	1	1	yes	characteristic
293	#389	C₂²×C₃	1	1	yes	characteristic
294	#389	C₂²×C₃	1	2	yes	—
295	#389	C₂²×C₃	1	2	yes	—
296	#389	C₂²×C₃	1	1	yes	characteristic
297	#389	C₂²×C₃	1	2	yes	—
298	#389	C₂²×C₃	1	2	yes	—
299	#389	C₂²×C₃	1	2	yes	—
300	#389	C₂²×C₃	1	1	yes	characteristic
301	#389	C₂²×C₃	1	1	yes	characteristic
302	#388	C₂²×C₃	1	2	yes	—
303	#388	C₂²×C₃	1	2	yes	—
304	#388	C₂²×C₃	1	2	yes	—
305	#388	C₂²×C₃	1	2	yes	—
306	#388	C₂²×C₃	1	2	yes	—
307	#388	C₂²×C₃	1	2	yes	—
308	#388	C₂²×C₃	1	2	yes	—
309	#388	C₂²×C₃	1	2	yes	—
310	#388	C₂²×C₃	1	2	yes	—
311	#388	C₂²×C₃	1	2	yes	—
312	#387	C₂²×C₃	1	1	yes	characteristic
313	#387	C₂²×C₃	1	2	yes	—
314	#387	C₂²×C₃	1	2	yes	—
315	#387	C₂²×C₃	1	2	yes	—
316	#387	C₂²×C₃	1	2	yes	—
317	#387	C₂²×C₃	1	2	yes	—
318	#387	C₂²×C₃	1	2	yes	—
319	#387	C₂²×C₃	1	2	yes	—
320	#387	C₂²×C₃	1	2	yes	—
321	#387	C₂²×C₃	1	2	yes	—
322	#387	C₂²×C₃	1	2	yes	—
323	#387	C₂²×C₃	1	1	yes	characteristic
324	#387	C₂²×C₃	1	2	yes	—
325	#387	C₂²×C₃	1	1	yes	characteristic
326	#387	C₂²×C₃	1	1	yes	characteristic
327	#387	C₂²×C₃	1	2	yes	—
328	#385	C₂²×C₃	1	2	yes	—
329	#385	C₂²×C₃	1	2	yes	—
330	#385	C₂²×C₃	1	2	yes	—
331	#385	C₂²×C₃	1	2	yes	—
332	#385	C₂²×C₃	1	2	yes	—
333	#385	C₂²×C₃	1	2	yes	—
334	#384	C₂²×C₃	1	2	yes	—
335	#384	C₂²×C₃	1	1	yes	characteristic
336	#383	C₂²×C₃	1	2	yes	—
337	#382	C₂²×C₃	1	2	yes	—
338	#382	C₂²×C₃	1	1	yes	characteristic
339	#382	C₂²×C₃	1	2	yes	—
340	#382	C₂²×C₃	1	1	yes	characteristic
341	#381	C₂²×C₃	1	2	yes	—
342	#380	C₂²×C₃	1	2	yes	—
343	#380	C₂²×C₃	1	2	yes	—
344	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
345	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
346	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
347	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
348	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
349	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
350	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
351	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
352	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
353	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
354	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
355	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
356	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
357	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
358	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
359	#376	C₂²×C₃	1	1	yes	characteristic
360	#376	C₂²×C₃	1	1	yes	characteristic
361	#376	C₂²×C₃	1	2	yes	—
362	C₂×#95	C₂²×C₃	1	2	yes	—
363	C₄³	C₂²×C₃	1	1	yes	characteristic
364	C₂⁴×C₃	C₂⁴	1	2	yes	—
365	C₂×C₃×Q₈	—	2	2	no	—
366	C₂×C₃×Q₈	—	2	2	no	—
367	C₂×C₃×Q₈	—	2	2	no	—
368	C₂×C₃×Q₈	—	2	2	no	—
369	C₂×C₃×Q₈	—	4	1	no	—
370	C₂×C₃×Q₈	—	4	1	no	—
371	C₂×C₃×Q₈	C₂²×C₄	1	4	yes	—
372	C₂×C₃×Q₈	C₂²×C₄	1	4	yes	—
373	C₂×C₃×Q₈	C₂²×C₄	1	4	yes	—
374	C₂×C₃×D₄	—	2	2	no	—
375	C₂×C₃×D₄	—	2	2	no	—
376	C₂×C₃×D₄	C₂²×C₄	1	4	yes	—
377	C₂²×C₃×C₄	—	2	4	no	—
378	C₂²×C₃×C₄	—	4	2	no	—
379	C₂²×C₃×C₄	—	4	2	no	—
380	C₂²×C₃×C₄	—	4	2	no	—
381	C₂²×C₃×C₄	—	4	2	no	—
382	C₂²×C₃×C₄	—	4	2	no	—
383	C₂²×C₃×C₄	—	4	2	no	—
384	C₂²×C₃×C₄	—	4	2	no	—
385	C₂²×C₃×C₄	C₂²×C₄	1	8	yes	—
386	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
387	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
388	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
389	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
390	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
391	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
392	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
393	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
394	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
395	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
396	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
397	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
398	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
399	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
400	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
401	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
402	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
403	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
404	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
405	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
406	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
407	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
408	C₃×C₄⋊C₄	—	2	2	no	—
409	C₃×C₄⋊C₄	—	2	2	no	—
410	C₃×C₄⋊C₄	—	2	2	no	—
411	C₃×C₄⋊C₄	—	2	2	no	—
412	C₃×C₄⋊C₄	—	2	2	no	—
413	C₃×C₄⋊C₄	—	2	2	no	—
414	C₃×C₄⋊C₄	—	4	1	no	—
415	C₃×C₄⋊C₄	—	4	1	no	—
416	C₃×C₄⋊C₄	—	4	1	no	—
417	C₃×C₄⋊C₄	—	4	2	no	—
418	C₃×C₄⋊C₄	—	4	1	no	—
419	C₃×C₄⋊C₄	—	4	2	no	—
420	C₃×C₄⋊C₄	—	4	2	no	—
421	C₃×C₄⋊C₄	—	4	2	no	—
422	C₃×C₄⋊C₄	—	4	2	no	—
423	C₃×C₄⋊C₄	—	4	2	no	—
424	C₃×C₄⋊C₄	—	4	2	no	—
425	C₃×C₄⋊C₄	—	4	2	no	—
426	C₃×C₄⋊C₄	—	4	2	no	—
427	C₃×C₄⋊C₄	—	4	2	no	—
428	C₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
429	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
430	C₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
431	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
432	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
433	C₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
434	C₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
435	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
436	C₃×C₂²⋊C₄	—	4	2	no	—
437	C₃×C₂²⋊C₄	—	4	2	no	—
438	C₃×C₂²⋊C₄	—	4	2	no	—
439	C₃×C₂²⋊C₄	—	4	2	no	—
440	C₃×C₂²⋊C₄	—	4	2	no	—
441	C₃×C₂²⋊C₄	—	4	2	no	—
442	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
443	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
444	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
445	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
446	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
447	C₃×C₄²	—	2	2	no	—
448	C₃×C₄²	—	2	2	no	—
449	C₃×C₄²	—	2	2	no	—
450	C₃×C₄²	—	2	2	no	—
451	C₃×C₄²	—	2	2	no	—
452	C₃×C₄²	—	4	2	no	—
453	C₃×C₄²	—	4	1	no	—
454	C₃×C₄²	—	4	2	no	—
455	C₃×C₄²	—	4	2	no	—
456	C₃×C₄²	—	4	1	no	—
457	C₃×C₄²	—	4	1	no	—
458	C₃×C₄²	—	4	2	no	—
459	C₃×C₄²	—	4	2	no	—
460	C₃×C₄²	—	4	2	no	—
461	C₃×C₄²	—	4	2	no	—
462	C₃×C₄²	C₂²×C₄	1	8	yes	—
463	C₃×C₄²	C₂²×C₄	1	8	yes	—
464	C₃×C₄²	C₂²×C₄	1	4	yes	—
465	C₃×C₄²	C₂²×C₄	1	4	yes	—
466	C₃×C₄²	C₂²×C₄	1	4	yes	—
467	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
468	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
469	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
470	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
471	C₂³×C₄	C₂³×C₃	1	2	yes	—
472	C₂³×C₄	C₂³×C₃	1	2	yes	—
473	C₂³×C₄	C₂³×C₃	1	2	yes	—
474	C₄⋊Q₈	C₂×C₃×C₄	1	8	yes	complemented
475	#126	C₂×C₃×C₄	1	16	yes	complemented
476	#126	C₂×C₃×C₄	1	16	yes	complemented
477	#124	C₂×C₃×C₄	1	8	yes	—
478	#124	C₂×C₃×C₄	1	8	yes	—
479	C₂²⋊Q₈	C₂×C₃×C₄	1	16	yes	complemented
480	C₄×Q₈	—	4	2	no	—
481	C₄×Q₈	—	4	2	no	—
482	C₄×Q₈	—	4	2	no	—
483	C₄×Q₈	—	4	2	no	—
484	C₄×Q₈	C₂×C₃×C₄	1	8	yes	complemented
485	C₄×Q₈	C₂×C₃×C₄	1	8	yes	complemented
486	C₄×Q₈	C₂×C₃×C₄	1	8	yes	complemented
487	C₄×D₄	—	4	2	no	—
488	C₄×D₄	—	4	2	no	—
489	C₄×D₄	C₂×C₃×C₄	1	8	yes	—
490	#117	C₂×C₃×C₄	1	16	yes	complemented
491	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
492	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
493	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
494	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
495	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
496	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
497	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
498	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
499	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
500	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
501	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
502	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
503	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
504	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
505	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
506	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
507	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
508	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
509	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
510	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
511	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
512	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
513	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
514	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
515	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
516	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
517	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
518	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
525	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
526	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
527	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
528	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
529	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
530	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
531	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
532	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
533	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
534	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
535	C₂×C₄²	C₂³×C₃	1	2	yes	—
536	C₂×C₄²	C₂³×C₃	1	2	yes	—
537	C₂×C₄²	C₂³×C₃	1	2	yes	—
538	C₂×C₄²	C₂³×C₃	1	2	yes	—
539	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
540	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
541	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
542	C₂×C₄²	C₂³×C₃	1	2	yes	—
543	C₂×C₄²	C₂³×C₃	1	2	yes	—
544	C₂×C₄²	C₂³×C₃	1	2	yes	—
545	C₂×C₄²	C₂³×C₃	1	2	yes	—
546	C₂×C₄²	C₂³×C₃	1	2	yes	—
547	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
548	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
549	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
550	#95	C₂³×C₃	1	1	yes	characteristic
551	#95	C₂³×C₃	1	2	yes	—
552	#95	C₂³×C₃	1	2	yes	—
553	#95	C₂³×C₃	1	2	yes	—
554	#95	C₂³×C₃	1	2	yes	—
555	#95	C₂³×C₃	1	1	yes	characteristic
556	#95	C₂³×C₃	1	1	yes	characteristic
557	#95	C₂³×C₃	1	2	yes	—
558	#95	C₂³×C₃	1	1	yes	characteristic
559	#95	C₂³×C₃	1	1	yes	characteristic
560	#95	C₂³×C₃	1	1	yes	characteristic
561	#95	C₂³×C₃	1	2	yes	—
562	#95	C₂³×C₃	1	1	yes	characteristic
563	#95	C₂³×C₃	1	1	yes	characteristic
564	#95	C₂³×C₃	1	1	yes	characteristic
565	#95	C₂³×C₃	1	1	yes	characteristic
566	#95	C₂³×C₃	1	1	yes	characteristic
567	#95	C₂³×C₃	1	2	yes	—
568	#95	C₂³×C₃	1	2	yes	—
569	#95	C₂³×C₃	1	2	yes	—
570	#95	C₂³×C₃	1	2	yes	—
571	#95	C₂³×C₃	1	2	yes	—
572	#95	C₂³×C₃	1	1	yes	characteristic
573	#95	C₂³×C₃	1	1	yes	characteristic
574	#95	C₂³×C₃	1	2	yes	—
575	#95	C₂³×C₃	1	2	yes	—
576	#95	C₂³×C₃	1	2	yes	—
577	#95	C₂³×C₃	1	2	yes	—
578	#95	C₂³×C₃	1	2	yes	—
579	#95	C₂³×C₃	1	2	yes	—
580	#95	C₂³×C₃	1	2	yes	—
581	#95	C₂³×C₃	1	2	yes	—
582	#95	C₂³×C₃	1	1	yes	characteristic
583	C₂³×C₃	—	2	2	no	—
584	C₂³×C₃	—	2	2	no	—
585	C₂³×C₃	—	2	2	no	—
586	C₂³×C₃	—	2	2	no	—
587	C₂³×C₃	—	2	2	no	—
588	C₂³×C₃	—	2	2	no	—
589	C₂³×C₃	C₂³×C₄	1	4	yes	—
590	C₂³×C₃	C₂⁵	1	1	yes	characteristic
591	C₃×Q₈	—	2	8	no	—
592	C₃×Q₈	—	2	8	no	—
593	C₃×Q₈	—	4	4	no	—
594	C₃×D₄	—	2	8	no	—
595	C₂×C₃×C₄	—	2	1	no	—
596	C₂×C₃×C₄	—	2	2	no	—
597	C₂×C₃×C₄	—	2	2	no	—
598	C₂×C₃×C₄	—	2	1	no	—
599	C₂×C₃×C₄	—	2	1	no	—
600	C₂×C₃×C₄	—	2	1	no	—
601	C₂×C₃×C₄	—	2	2	no	—
602	C₂×C₃×C₄	—	2	2	no	—
603	C₂×C₃×C₄	—	2	1	no	—
604	C₂×C₃×C₄	—	2	1	no	—
605	C₂×C₃×C₄	—	2	1	no	—
606	C₂×C₃×C₄	—	2	1	no	—
607	C₂×C₃×C₄	—	2	1	no	—
608	C₂×C₃×C₄	—	2	1	no	—
609	C₂×C₃×C₄	—	2	1	no	—
610	C₂×C₃×C₄	—	2	2	no	—
611	C₂×C₃×C₄	—	2	2	no	—
612	C₂×C₃×C₄	—	2	1	no	—
613	C₂×C₃×C₄	—	2	1	no	—
614	C₂×C₃×C₄	—	2	1	no	—
615	C₂×C₃×C₄	—	2	1	no	—
616	C₂×C₃×C₄	—	2	1	no	—
617	C₂×C₃×C₄	—	2	1	no	—
618	C₂×C₃×C₄	—	2	1	no	—
619	C₂×C₃×C₄	—	2	1	no	—
620	C₂×C₃×C₄	—	2	2	no	—
621	C₂×C₃×C₄	—	2	2	no	—
622	C₂×C₃×C₄	—	2	2	no	—
623	C₂×C₃×C₄	—	2	1	no	—
624	C₂×C₃×C₄	—	2	1	no	—
625	C₂×C₃×C₄	—	2	1	no	—
626	C₂×C₃×C₄	—	2	2	no	—
627	C₂×C₃×C₄	—	2	1	no	—
628	C₂×C₃×C₄	—	2	1	no	—
629	C₂×C₃×C₄	—	2	2	no	—
630	C₂×C₃×C₄	—	2	2	no	—
631	C₂×C₃×C₄	—	2	1	no	—
632	C₂×C₃×C₄	—	2	1	no	—
633	C₂×C₃×C₄	—	2	2	no	—
634	C₂×C₃×C₄	—	2	2	no	—
635	C₂×C₃×C₄	—	2	1	no	—
636	C₂×C₃×C₄	—	2	1	no	—
637	C₂×C₃×C₄	—	2	1	no	—
638	C₂×C₃×C₄	—	2	2	no	—
639	C₂×C₃×C₄	—	2	2	no	—
640	C₂×C₃×C₄	—	2	1	no	—
641	C₂×C₃×C₄	—	2	1	no	—
642	C₂×C₃×C₄	—	2	2	no	—
643	C₂×C₃×C₄	—	2	1	no	—
644	C₂×C₃×C₄	—	2	1	no	—
645	C₂×C₃×C₄	—	2	2	no	—
646	C₂×C₃×C₄	—	2	1	no	—
647	C₂×C₃×C₄	—	2	1	no	—
648	C₂×C₃×C₄	—	4	8	no	—
649	C₂×C₃×C₄	—	8	4	no	—
650	C₂×C₃×C₄	—	8	4	no	—
651	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
652	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
653	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
654	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
655	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
656	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
657	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
658	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
659	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
660	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
661	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
662	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
663	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
664	C₂⁴	C₂⁴×C₃	1	2	yes	—
665	C₂×Q₈	—	2	2	no	—
666	C₂×Q₈	—	2	2	no	—
667	C₂×Q₈	—	2	2	no	—
668	C₂×Q₈	—	2	2	no	—
669	C₂×Q₈	—	4	1	no	—
670	C₂×Q₈	—	4	1	no	—
671	C₂×Q₈	C₂²×C₃×C₄	1	4	yes	—
672	C₂×Q₈	C₂²×C₃×C₄	1	4	yes	—
673	C₂×Q₈	C₂²×C₃×C₄	1	4	yes	—
674	C₂×D₄	—	2	2	no	—
675	C₂×D₄	—	2	2	no	—
676	C₂×D₄	C₂²×C₃×C₄	1	4	yes	—
677	C₂²×C₄	—	2	4	no	—
678	C₂²×C₄	—	4	2	no	—
679	C₂²×C₄	—	4	2	no	—
680	C₂²×C₄	—	4	2	no	—
681	C₂²×C₄	—	4	2	no	—
682	C₂²×C₄	—	4	2	no	—
683	C₂²×C₄	—	4	2	no	—
684	C₂²×C₄	—	4	2	no	—
685	C₂²×C₄	C₂²×C₃×C₄	1	8	yes	—
686	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
687	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
688	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
689	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
690	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
691	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
692	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
693	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
694	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
695	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
696	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
697	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
698	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
699	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
700	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
701	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
702	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
703	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
704	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
705	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
706	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
707	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	2	no	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	2	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	4	2	no	—
715	C₄⋊C₄	—	4	2	no	—
716	C₄⋊C₄	—	4	2	no	—
717	C₄⋊C₄	—	4	2	no	—
718	C₄⋊C₄	—	4	1	no	—
719	C₄⋊C₄	—	4	1	no	—
720	C₄⋊C₄	—	4	1	no	—
721	C₄⋊C₄	—	4	2	no	—
722	C₄⋊C₄	—	4	1	no	—
723	C₄⋊C₄	—	4	2	no	—
724	C₄⋊C₄	—	4	2	no	—
725	C₄⋊C₄	—	4	2	no	—
726	C₄⋊C₄	—	4	2	no	—
727	C₄⋊C₄	—	4	2	no	—
728	C₄⋊C₄	C₂²×C₃×C₄	1	4	yes	—
729	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
730	C₄⋊C₄	C₂²×C₃×C₄	1	4	yes	—
731	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
732	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
733	C₄⋊C₄	C₂²×C₃×C₄	1	4	yes	—
734	C₄⋊C₄	C₂²×C₃×C₄	1	4	yes	—
735	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
736	C₂²⋊C₄	—	4	2	no	—
737	C₂²⋊C₄	—	4	2	no	—
738	C₂²⋊C₄	—	4	2	no	—
739	C₂²⋊C₄	—	4	2	no	—
740	C₂²⋊C₄	—	4	2	no	—
741	C₂²⋊C₄	—	4	2	no	—
742	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
743	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
744	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
745	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
746	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
747	C₄²	—	2	2	no	—
748	C₄²	—	2	2	no	—
749	C₄²	—	2	2	no	—
750	C₄²	—	2	2	no	—
751	C₄²	—	2	2	no	—
752	C₄²	—	4	2	no	—
753	C₄²	—	4	2	no	—
754	C₄²	—	4	2	no	—
755	C₄²	—	4	2	no	—
756	C₄²	—	4	2	no	—
757	C₄²	—	4	1	no	—
758	C₄²	—	4	2	no	—
759	C₄²	—	4	2	no	—
760	C₄²	—	4	1	no	—
761	C₄²	—	4	1	no	—
762	C₄²	C₂²×C₃×C₄	1	8	yes	—
763	C₄²	C₂²×C₃×C₄	1	8	yes	—
764	C₄²	C₂²×C₃×C₄	1	4	yes	—
765	C₄²	C₂²×C₃×C₄	1	4	yes	—
766	C₄²	C₂²×C₃×C₄	1	4	yes	—
767	C₂²×C₃	—	2	4	no	—
768	C₂²×C₃	—	2	4	no	—
769	C₂²×C₃	—	2	4	no	—
770	C₂²×C₃	—	4	2	no	—
771	C₂²×C₃	—	4	2	no	—
772	C₂²×C₃	—	4	2	no	—
773	C₂²×C₃	—	4	2	no	—
774	C₂²×C₃	C₂⁴×C₄	1	1	yes	characteristic
775	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
776	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
777	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
778	C₂²×C₃	#585	1	1	yes	characteristic
779	C₂²×C₃	#585	1	1	yes	characteristic
780	C₂²×C₃	#585	1	1	yes	characteristic
781	C₃×C₄	—	2	4	no	—
782	C₃×C₄	—	2	4	no	—
783	C₃×C₄	—	2	2	no	—
784	C₃×C₄	—	2	4	no	—
785	C₃×C₄	—	2	2	no	—
786	C₃×C₄	—	2	2	no	—
787	C₃×C₄	—	2	2	no	—
788	C₃×C₄	—	2	2	no	—
789	C₃×C₄	—	2	2	no	—
790	C₃×C₄	—	2	2	no	—
791	C₃×C₄	—	4	1	no	—
792	C₃×C₄	—	4	1	no	—
793	C₃×C₄	—	4	2	no	—
794	C₃×C₄	—	4	1	no	—
795	C₃×C₄	—	4	1	no	—
796	C₃×C₄	—	4	2	no	—
797	C₃×C₄	—	4	1	no	—
798	C₃×C₄	—	4	1	no	—
799	C₃×C₄	—	4	2	no	—
800	C₃×C₄	—	4	2	no	—
801	C₃×C₄	—	4	1	no	—
802	C₃×C₄	#520	1	4	yes	—
803	C₂³	—	2	2	no	—
804	C₂³	—	2	2	no	—
805	C₂³	—	2	2	no	—
806	C₂³	—	2	2	no	—
807	C₂³	—	2	2	no	—
808	C₂³	—	2	2	no	—
809	C₂³	C₂³×C₃×C₄	1	4	yes	—
810	C₂³	C₂⁵×C₃	1	1	yes	characteristic
811	Q₈	—	2	8	no	—
812	Q₈	—	2	8	no	—
813	Q₈	—	4	4	no	—
814	D₄	—	2	8	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	4	8	no	—
869	C₂×C₄	—	8	4	no	—
870	C₂×C₄	—	8	4	no	—
871	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
872	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
873	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
874	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
875	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
876	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
877	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
878	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
879	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
880	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
881	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
882	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
883	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
884	C₂×C₃	—	4	4	no	—
885	C₂×C₃	C₂×#520	1	1	yes	characteristic
886	C₂×C₃	#3428	1	1	yes	characteristic
887	C₂×C₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
888	C₂×C₃	#3555	1	1	yes	characteristic
889	C₂×C₃	#3557	1	1	yes	characteristic
890	C₂×C₃	#3561	1	1	yes	characteristic
891	C₂×C₃	#3562	1	1	yes	characteristic
892	C₂²	—	2	4	no	—
893	C₂²	—	2	4	no	—
894	C₂²	—	2	4	no	—
895	C₂²	—	4	2	no	—
896	C₂²	—	4	2	no	—
897	C₂²	—	4	2	no	—
898	C₂²	—	4	2	no	—
899	C₂²	C₂⁴×C₃×C₄	1	1	yes	characteristic
900	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
901	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
902	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
903	C₂²	C₃×#585	1	1	yes	characteristic
904	C₂²	C₃×#585	1	1	yes	characteristic
905	C₂²	C₃×#585	1	1	yes	characteristic
906	C₄	—	2	4	no	—
907	C₄	—	2	4	no	—
908	C₄	—	2	2	no	—
909	C₄	—	2	4	no	—
910	C₄	—	2	2	no	—
911	C₄	—	2	2	no	—
912	C₄	—	2	2	no	—
913	C₄	—	2	2	no	—
914	C₄	—	2	2	no	—
915	C₄	—	2	2	no	—
916	C₄	—	4	1	no	—
917	C₄	—	4	1	no	—
918	C₄	—	4	2	no	—
919	C₄	—	4	2	no	—
920	C₄	—	4	1	no	—
921	C₄	—	4	1	no	—
922	C₄	—	4	1	no	—
923	C₄	—	4	2	no	—
924	C₄	—	4	1	no	—
925	C₄	—	4	1	no	—
926	C₄	—	4	2	no	—
927	C₄	C₃×#520	1	4	yes	—
928	C₃	#34499	1	1	yes	characteristic, direct product factor, Sylow
929	C₂	—	4	4	no	—
930	C₂	C₂×C₃×#520	1	1	yes	characteristic
931	C₂	C₃×#3428	1	1	yes	characteristic
932	C₂	C₃×C₄×2₋¹⁺⁴	1	1	yes	characteristic
933	C₂	C₃×#3555	1	1	yes	characteristic
934	C₂	C₃×#3557	1	1	yes	characteristic
935	C₂	C₃×#3561	1	1	yes	characteristic
936	C₂	C₃×#3562	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator	C₂²	C₂⁴×C₃×C₄
Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂²×C₃×D₄	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×#2383	C₂	semidirect
3. C₃×#2378	C₂	semidirect
4. C₃×#2373	C₂	semidirect
7. C₃×#2365	C₂	semidirect
8. C₃×#2355	C₂	semidirect
9. C₃×#2351	C₂	semidirect
10. C₃×Q₈×C₄⋊C₄	C₂	semidirect
12. C₃×#2343	C₂	semidirect
13. C₃×#2334	C₂	semidirect
14. C₃×#2334	C₂	semidirect
15. C₃×#2329	C₂	semidirect
16. C₃×#2327	C₂	semidirect
18. C₃×#2320	C₂	semidirect
20. C₃×#2314	C₂	semidirect
22. C₃×#2295	C₂	semidirect
23. C₃×#2295	C₂	semidirect
24. #34499	C₃	direct (N × H)
25. C₃×#556	C₄	semidirect
126. #2383	C₂×C₃	semidirect
127. #2378	C₂×C₃	semidirect
128. #2373	C₂×C₃	semidirect
131. #2365	C₂×C₃	semidirect
132. #2355	C₂×C₃	semidirect
133. #2351	C₂×C₃	semidirect
134. Q₈×C₄⋊C₄	C₂×C₃	semidirect
136. #2343	C₂×C₃	semidirect
137. #2334	C₂×C₃	semidirect
138. #2334	C₂×C₃	semidirect
139. #2329	C₂×C₃	semidirect
140. #2327	C₂×C₃	semidirect
142. #2320	C₂×C₃	semidirect
144. #2314	C₂×C₃	semidirect
146. #2295	C₂×C₃	semidirect
147. #2295	C₂×C₃	semidirect
155. C₃×C₄⋊Q₈	C₂×C₄	semidirect
156. C₃×#126	C₂×C₄	semidirect
157. C₃×#126	C₂×C₄	semidirect
160. C₃×C₂²⋊Q₈	C₂×C₄	semidirect
165. C₃×C₄×Q₈	C₂×C₄	semidirect
166. C₃×C₄×Q₈	C₂×C₄	semidirect
167. C₃×C₄×Q₈	C₂×C₄	semidirect
171. C₃×#117	C₂×C₄	semidirect
264. #556	C₃×C₄	semidirect
474. C₄⋊Q₈	C₂×C₃×C₄	semidirect
475. #126	C₂×C₃×C₄	semidirect
476. #126	C₂×C₃×C₄	semidirect
479. C₂²⋊Q₈	C₂×C₃×C₄	semidirect
484. C₄×Q₈	C₂×C₃×C₄	semidirect
485. C₄×Q₈	C₂×C₃×C₄	semidirect
486. C₄×Q₈	C₂×C₃×C₄	semidirect
490. #117	C₂×C₃×C₄	semidirect
928. C₃	#34499	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#556	2
C₃×#2383	2
C₃×#2378	2
C₃×#2373	2
C₃×#2367	2
C₃×#2365	2
C₃×#2355	2
C₃×#2351	2
C₃×Q₈×C₄⋊C₄	2
C₃×#2349	2
C₃×#2343	2
C₃×#2334	2
C₃×#2329	2
C₃×#2327	2
C₃×#2326	2
C₃×#2320	2
C₃×#2319	2
C₃×#2314	2
C₃×C₄×#124	2
C₃×#2295	2
#34499	3

Subgroups — C3×#34499 #10653106

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#34499 #10653106