Subgroups — C₃×#34496 #10653103

Order 768.

2344 conjugacy classes of subgroups.

The subgroup lattice has 1052 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#548	C₂	1	1	yes	maximal, characteristic
2	C₃×#2378	C₂	1	2	yes	maximal, complemented
3	C₃×#2377	C₂	1	2	yes	maximal, complemented
4	C₃×#2372	C₂	1	2	yes	maximal, complemented
5	C₃×#2367	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#2363	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#2360	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2356	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#2353	C₂	1	2	yes	maximal, complemented
10	C₃×#2352	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×Q₈×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2339	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#2337	C₂	1	2	yes	maximal, complemented
14	C₃×#2333	C₂	1	2	yes	maximal, complemented
15	C₃×#2329	C₂	1	2	yes	maximal, complemented
16	C₃×#2324	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#2323	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#2319	C₂	1	2	yes	maximal, complemented
19	C₃×#2311	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×#2310	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×C₄×#124	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃×#2295	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×#2293	C₂	1	1	yes	maximal, characteristic, complemented
24	#34496	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
26	C₂³×C₃×Q₈	C₂²	1	1	yes	characteristic
27	C₃×#548	C₄	1	16	yes	complemented
28	C₂×C₃×#124	C₂²	1	1	yes	characteristic
29	C₂×C₃×#124	C₂²	1	2	yes	—
30	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
32	C₂×C₃×#121	C₂²	1	1	yes	characteristic
33	C₂×C₃×#121	C₂²	1	2	yes	—
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×D₄	C₂²	1	1	yes	characteristic
38	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
39	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
40	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
41	C₂×C₃×#117	C₂²	1	1	yes	characteristic
42	C₂×C₃×#117	C₂²	1	1	yes	characteristic
43	C₂×C₃×#117	C₂²	1	1	yes	characteristic
44	C₂²×C₃×C₄⋊C₄	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	2	yes	—
48	C₃×#391	C₂²	1	2	yes	—
49	C₃×#391	C₂²	1	1	yes	characteristic
50	C₃×#391	C₂²	1	1	yes	characteristic
51	C₃×#391	C₂²	1	1	yes	characteristic
52	C₃×#391	C₂²	1	2	yes	—
53	C₃×#391	C₂²	1	1	yes	characteristic
54	C₃×#391	C₂²	1	1	yes	characteristic
55	C₃×#390	C₂²	1	1	yes	characteristic
56	C₃×#390	C₂²	1	2	yes	—
57	C₃×#390	C₂²	1	1	yes	characteristic
58	C₃×#390	C₂²	1	1	yes	characteristic
59	C₃×#390	C₂²	1	1	yes	characteristic
60	C₃×#390	C₂²	1	2	yes	—
61	C₃×#389	C₂²	1	1	yes	characteristic
62	C₃×#389	C₂²	1	2	yes	—
63	C₃×#389	C₂²	1	1	yes	characteristic
64	C₃×#389	C₂²	1	1	yes	characteristic
65	C₃×#389	C₂²	1	1	yes	characteristic
66	C₃×#389	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	1	yes	characteristic
71	C₃×#388	C₂²	1	2	yes	—
72	C₃×#388	C₂²	1	2	yes	—
73	C₃×#388	C₂²	1	2	yes	—
74	C₃×#388	C₂²	1	1	yes	characteristic
75	C₃×#388	C₂²	1	1	yes	characteristic
76	C₃×#388	C₂²	1	1	yes	characteristic
77	C₃×#388	C₂²	1	2	yes	—
78	C₃×#388	C₂²	1	2	yes	—
79	C₃×#388	C₂²	1	2	yes	—
80	C₃×#387	C₂²	1	2	yes	—
81	C₃×#387	C₂²	1	2	yes	—
82	C₃×#387	C₂²	1	2	yes	—
83	C₃×#387	C₂²	1	2	yes	—
84	C₃×#387	C₂²	1	2	yes	—
85	C₃×#387	C₂²	1	2	yes	—
86	C₃×#387	C₂²	1	2	yes	—
87	C₃×#386	C₂²	1	2	yes	—
88	C₃×#386	C₂²	1	2	yes	—
89	C₃×#386	C₂²	1	2	yes	—
90	C₃×#386	C₂²	1	2	yes	—
91	C₃×#386	C₂²	1	2	yes	—
92	C₃×#386	C₂²	1	2	yes	—
93	C₃×#386	C₂²	1	2	yes	—
94	C₃×#385	C₂²	1	2	yes	—
95	C₃×#385	C₂²	1	2	yes	—
96	C₃×#385	C₂²	1	2	yes	—
97	C₃×#383	C₂²	1	2	yes	—
98	C₃×#382	C₂²	1	1	yes	characteristic
99	C₃×#381	C₂²	1	2	yes	—
100	C₃×#381	C₂²	1	2	yes	—
101	C₃×#381	C₂²	1	2	yes	—
102	C₃×#380	C₂²	1	2	yes	—
103	C₃×#380	C₂²	1	2	yes	—
104	C₃×#380	C₂²	1	2	yes	—
105	C₃×#380	C₂²	1	1	yes	characteristic
106	C₃×#380	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	2	yes	—
112	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
113	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
114	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
115	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
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×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
121	C₃×#376	C₂²	1	2	yes	—
122	C₃×#376	C₂²	1	2	yes	—
123	C₂×C₃×#95	C₂²	1	2	yes	—
124	C₃×C₄³	C₂²	1	1	yes	characteristic
125	C₂×#548	C₂×C₃	1	1	yes	characteristic
126	#2378	C₂×C₃	1	2	yes	complemented
127	#2377	C₂×C₃	1	2	yes	complemented
128	#2372	C₂×C₃	1	2	yes	complemented
129	#2367	C₂×C₃	1	1	yes	characteristic, complemented
130	#2363	C₂×C₃	1	1	yes	characteristic, complemented
131	#2360	C₂×C₃	1	1	yes	characteristic, complemented
132	#2356	C₂×C₃	1	1	yes	characteristic, complemented
133	#2353	C₂×C₃	1	2	yes	complemented
134	#2352	C₂×C₃	1	1	yes	characteristic, complemented
135	Q₈×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
136	#2339	C₂×C₃	1	1	yes	characteristic, complemented
137	#2337	C₂×C₃	1	2	yes	complemented
138	#2333	C₂×C₃	1	2	yes	complemented
139	#2329	C₂×C₃	1	2	yes	complemented
140	#2324	C₂×C₃	1	1	yes	characteristic, complemented
141	#2323	C₂×C₃	1	1	yes	characteristic, complemented
142	#2319	C₂×C₃	1	2	yes	complemented
143	#2311	C₂×C₃	1	1	yes	characteristic, complemented
144	#2310	C₂×C₃	1	1	yes	characteristic, complemented
145	C₄×#124	C₂×C₃	1	1	yes	characteristic, complemented
146	#2295	C₂×C₃	1	1	yes	characteristic, complemented
147	#2293	C₂×C₃	1	1	yes	characteristic, complemented
148	C₂×C₃×#41	—	4	2	no	—
149	C₂×C₃×#41	—	4	2	no	—
150	C₂×C₃×#41	C₂×C₄	1	8	yes	—
151	C₂²×C₃×Q₈	—	4	2	no	—
152	C₂²×C₃×Q₈	—	4	2	no	—
153	C₂²×C₃×Q₈	C₂×C₄	1	8	yes	complemented
154	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
155	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
156	C₂²×C₃×Q₈	C₂³	1	2	yes	—
157	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
158	C₂²×C₃×D₄	C₂³	1	2	yes	—
159	C₂²×C₃×D₄	C₂³	1	2	yes	—
160	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
161	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
162	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
163	C₂³×C₃×C₄	C₂³	1	2	yes	—
164	C₂³×C₃×C₄	C₂³	1	2	yes	—
165	C₂³×C₃×C₄	C₂³	1	2	yes	—
166	C₂³×C₃×C₄	C₂³	1	2	yes	—
167	C₂³×C₃×C₄	C₂³	1	2	yes	—
168	C₃×#124	C₂×C₄	1	8	yes	complemented
169	C₃×#124	C₂×C₄	1	16	yes	complemented
170	C₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
171	C₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
172	C₃×#121	C₂×C₄	1	8	yes	complemented
173	C₃×#121	C₂×C₄	1	16	yes	complemented
174	C₃×C₄×Q₈	—	4	2	no	—
175	C₃×C₄×Q₈	—	4	2	no	—
176	C₃×C₄×Q₈	C₂×C₄	1	8	yes	complemented
177	C₃×C₄×D₄	—	4	2	no	—
178	C₃×C₄×D₄	—	4	2	no	—
179	C₃×C₄×D₄	C₂×C₄	1	8	yes	complemented
180	C₃×C₄×D₄	C₂×C₄	1	16	yes	complemented
181	C₃×#117	—	4	2	no	—
182	C₃×#117	—	4	2	no	—
183	C₃×#117	—	4	2	no	—
184	C₂×C₃×C₄⋊C₄	—	4	2	no	—
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	1	yes	characteristic
189	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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×C₄⋊C₄	C₂³	1	1	yes	characteristic
201	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
202	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
203	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
204	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
205	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
206	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
207	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄	C₂³	1	2	yes	—
212	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
213	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
214	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
215	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
216	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
217	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
218	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
219	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
220	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
221	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
222	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
223	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
224	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
225	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
226	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
227	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
228	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
229	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
230	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
231	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
232	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
233	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
234	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
235	C₂×C₃×C₄²	C₂³	1	2	yes	—
236	C₂×C₃×C₄²	C₂³	1	2	yes	—
237	C₂×C₃×C₄²	C₂³	1	2	yes	—
238	C₂×C₃×C₄²	C₂³	1	2	yes	—
239	C₂×C₃×C₄²	C₂³	1	2	yes	—
240	C₂×C₃×C₄²	C₂³	1	2	yes	—
241	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
242	C₂×C₃×C₄²	C₂³	1	2	yes	—
243	C₃×#95	C₂³	1	1	yes	characteristic
244	C₃×#95	C₂³	1	2	yes	—
245	C₃×#95	C₂³	1	2	yes	—
246	C₃×#95	C₂³	1	2	yes	—
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	2	yes	—
254	C₃×#95	C₂³	1	1	yes	characteristic
255	C₃×#95	C₂³	1	1	yes	characteristic
256	C₃×#95	C₂³	1	2	yes	—
257	C₃×#95	C₂³	1	2	yes	—
258	C₃×#95	C₂³	1	1	yes	characteristic
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	2	yes	—
264	C₃×#95	C₂³	1	1	yes	characteristic
265	C₃×#95	C₂³	1	2	yes	—
266	C₃×#95	C₂³	1	2	yes	—
267	C₃×#95	C₂³	1	2	yes	—
268	C₃×#95	C₂³	1	2	yes	—
269	C₃×#95	C₂³	1	2	yes	—
270	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
271	C₂³×Q₈	C₂²×C₃	1	1	yes	characteristic
272	#548	C₃×C₄	1	16	yes	complemented
273	C₂×#124	C₂²×C₃	1	2	yes	—
274	C₂×#124	C₂²×C₃	1	1	yes	characteristic
275	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
276	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
277	C₂×#121	C₂²×C₃	1	1	yes	characteristic
278	C₂×#121	C₂²×C₃	1	2	yes	—
279	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
280	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
281	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
282	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
283	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
284	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
285	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
286	C₂×#117	C₂²×C₃	1	1	yes	characteristic
287	C₂×#117	C₂²×C₃	1	1	yes	characteristic
288	C₂×#117	C₂²×C₃	1	1	yes	characteristic
289	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
290	#391	C₂²×C₃	1	1	yes	characteristic
291	#391	C₂²×C₃	1	1	yes	characteristic
292	#391	C₂²×C₃	1	2	yes	—
293	#391	C₂²×C₃	1	1	yes	characteristic
294	#391	C₂²×C₃	1	1	yes	characteristic
295	#391	C₂²×C₃	1	2	yes	—
296	#391	C₂²×C₃	1	1	yes	characteristic
297	#391	C₂²×C₃	1	2	yes	—
298	#391	C₂²×C₃	1	2	yes	—
299	#391	C₂²×C₃	1	1	yes	characteristic
300	#390	C₂²×C₃	1	1	yes	characteristic
301	#390	C₂²×C₃	1	1	yes	characteristic
302	#390	C₂²×C₃	1	2	yes	—
303	#390	C₂²×C₃	1	2	yes	—
304	#390	C₂²×C₃	1	1	yes	characteristic
305	#390	C₂²×C₃	1	1	yes	characteristic
306	#389	C₂²×C₃	1	2	yes	—
307	#389	C₂²×C₃	1	2	yes	—
308	#389	C₂²×C₃	1	1	yes	characteristic
309	#389	C₂²×C₃	1	1	yes	characteristic
310	#389	C₂²×C₃	1	1	yes	characteristic
311	#389	C₂²×C₃	1	1	yes	characteristic
312	#388	C₂²×C₃	1	1	yes	characteristic
313	#388	C₂²×C₃	1	2	yes	—
314	#388	C₂²×C₃	1	2	yes	—
315	#388	C₂²×C₃	1	2	yes	—
316	#388	C₂²×C₃	1	2	yes	—
317	#388	C₂²×C₃	1	2	yes	—
318	#388	C₂²×C₃	1	2	yes	—
319	#388	C₂²×C₃	1	2	yes	—
320	#388	C₂²×C₃	1	1	yes	characteristic
321	#388	C₂²×C₃	1	2	yes	—
322	#388	C₂²×C₃	1	1	yes	characteristic
323	#388	C₂²×C₃	1	1	yes	characteristic
324	#388	C₂²×C₃	1	2	yes	—
325	#387	C₂²×C₃	1	2	yes	—
326	#387	C₂²×C₃	1	2	yes	—
327	#387	C₂²×C₃	1	2	yes	—
328	#387	C₂²×C₃	1	2	yes	—
329	#387	C₂²×C₃	1	2	yes	—
330	#387	C₂²×C₃	1	2	yes	—
331	#387	C₂²×C₃	1	2	yes	—
332	#386	C₂²×C₃	1	2	yes	—
333	#386	C₂²×C₃	1	2	yes	—
334	#386	C₂²×C₃	1	2	yes	—
335	#386	C₂²×C₃	1	2	yes	—
336	#386	C₂²×C₃	1	2	yes	—
337	#386	C₂²×C₃	1	2	yes	—
338	#386	C₂²×C₃	1	2	yes	—
339	#385	C₂²×C₃	1	2	yes	—
340	#385	C₂²×C₃	1	2	yes	—
341	#385	C₂²×C₃	1	2	yes	—
342	#383	C₂²×C₃	1	2	yes	—
343	#382	C₂²×C₃	1	1	yes	characteristic
344	#381	C₂²×C₃	1	2	yes	—
345	#381	C₂²×C₃	1	2	yes	—
346	#381	C₂²×C₃	1	2	yes	—
347	#380	C₂²×C₃	1	2	yes	—
348	#380	C₂²×C₃	1	2	yes	—
349	#380	C₂²×C₃	1	2	yes	—
350	#380	C₂²×C₃	1	1	yes	characteristic
351	#380	C₂²×C₃	1	1	yes	characteristic
352	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
353	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
354	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
355	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
356	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
357	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
358	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
359	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
360	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
361	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
362	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
363	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
364	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
365	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
366	#376	C₂²×C₃	1	2	yes	—
367	#376	C₂²×C₃	1	2	yes	—
368	C₂×#95	C₂²×C₃	1	2	yes	—
369	C₄³	C₂²×C₃	1	1	yes	characteristic
370	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
371	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
372	C₂⁴×C₃	C₂⁴	1	2	yes	—
373	C₃×#41	—	4	16	no	—
374	C₂×C₃×Q₈	—	2	2	no	—
375	C₂×C₃×Q₈	—	2	2	no	—
376	C₂×C₃×Q₈	—	2	2	no	—
377	C₂×C₃×Q₈	—	2	2	no	—
378	C₂×C₃×Q₈	—	4	2	no	—
379	C₂×C₃×Q₈	—	4	2	no	—
380	C₂×C₃×Q₈	—	4	16	no	—
381	C₂×C₃×Q₈	C₂²×C₄	1	4	yes	—
382	C₂×C₃×Q₈	C₂²×C₄	1	4	yes	—
383	C₂×C₃×Q₈	C₂²×C₄	1	8	yes	—
384	C₂×C₃×D₄	—	2	2	no	—
385	C₂×C₃×D₄	—	2	2	no	—
386	C₂×C₃×D₄	—	4	2	no	—
387	C₂×C₃×D₄	—	4	1	no	—
388	C₂×C₃×D₄	—	4	1	no	—
389	C₂×C₃×D₄	—	4	2	no	—
390	C₂×C₃×D₄	—	4	2	no	—
391	C₂×C₃×D₄	—	4	2	no	—
392	C₂×C₃×D₄	C₂²×C₄	1	4	yes	—
393	C₂×C₃×D₄	C₂²×C₄	1	4	yes	—
394	C₂×C₃×D₄	C₂²×C₄	1	8	yes	—
395	C₂×C₃×D₄	C₂²×C₄	1	8	yes	—
396	C₂²×C₃×C₄	—	2	2	no	—
397	C₂²×C₃×C₄	—	2	2	no	—
398	C₂²×C₃×C₄	—	2	2	no	—
399	C₂²×C₃×C₄	—	2	2	no	—
400	C₂²×C₃×C₄	—	2	4	no	—
401	C₂²×C₃×C₄	—	4	2	no	—
402	C₂²×C₃×C₄	—	4	2	no	—
403	C₂²×C₃×C₄	—	4	2	no	—
404	C₂²×C₃×C₄	—	4	2	no	—
405	C₂²×C₃×C₄	—	4	2	no	—
406	C₂²×C₃×C₄	—	4	2	no	—
407	C₂²×C₃×C₄	—	4	2	no	—
408	C₂²×C₃×C₄	—	4	2	no	—
409	C₂²×C₃×C₄	—	4	2	no	—
410	C₂²×C₃×C₄	—	4	2	no	—
411	C₂²×C₃×C₄	—	4	2	no	—
412	C₂²×C₃×C₄	—	4	2	no	—
413	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
414	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
415	C₂²×C₃×C₄	C₂²×C₄	1	8	yes	—
416	C₂²×C₃×C₄	C₂²×C₄	1	8	yes	—
417	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
418	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
419	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
420	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
421	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
422	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
423	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
424	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
425	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
426	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
427	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
428	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
429	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
430	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
431	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
432	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
433	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
434	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
435	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
436	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
437	C₃×C₄⋊C₄	—	2	2	no	—
438	C₃×C₄⋊C₄	—	2	2	no	—
439	C₃×C₄⋊C₄	—	2	2	no	—
440	C₃×C₄⋊C₄	—	2	2	no	—
441	C₃×C₄⋊C₄	—	4	2	no	—
442	C₃×C₄⋊C₄	—	4	1	no	—
443	C₃×C₄⋊C₄	—	4	1	no	—
444	C₃×C₄⋊C₄	—	4	2	no	—
445	C₃×C₄⋊C₄	—	4	2	no	—
446	C₃×C₄⋊C₄	—	4	1	no	—
447	C₃×C₄⋊C₄	—	4	1	no	—
448	C₃×C₄⋊C₄	—	4	1	no	—
449	C₃×C₄⋊C₄	—	4	1	no	—
450	C₃×C₄⋊C₄	—	4	2	no	—
451	C₃×C₄⋊C₄	—	4	2	no	—
452	C₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
453	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
454	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
455	C₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
456	C₃×C₂²⋊C₄	—	2	2	no	—
457	C₃×C₂²⋊C₄	—	2	2	no	—
458	C₃×C₂²⋊C₄	—	4	2	no	—
459	C₃×C₂²⋊C₄	—	4	1	no	—
460	C₃×C₂²⋊C₄	—	4	2	no	—
461	C₃×C₂²⋊C₄	—	4	1	no	—
462	C₃×C₂²⋊C₄	—	4	2	no	—
463	C₃×C₂²⋊C₄	—	4	2	no	—
464	C₃×C₂²⋊C₄	—	4	2	no	—
465	C₃×C₂²⋊C₄	—	4	2	no	—
466	C₃×C₂²⋊C₄	—	4	1	no	—
467	C₃×C₂²⋊C₄	—	4	1	no	—
468	C₃×C₂²⋊C₄	—	4	1	no	—
469	C₃×C₂²⋊C₄	—	4	1	no	—
470	C₃×C₂²⋊C₄	—	4	2	no	—
471	C₃×C₂²⋊C₄	—	4	2	no	—
472	C₃×C₂²⋊C₄	—	4	2	no	—
473	C₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
474	C₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
475	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
476	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
477	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
478	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
479	C₃×C₄²	—	2	2	no	—
480	C₃×C₄²	—	2	2	no	—
481	C₃×C₄²	—	2	2	no	—
482	C₃×C₄²	—	2	2	no	—
483	C₃×C₄²	—	2	2	no	—
484	C₃×C₄²	—	4	1	no	—
485	C₃×C₄²	—	4	2	no	—
486	C₃×C₄²	—	4	1	no	—
487	C₃×C₄²	—	4	2	no	—
488	C₃×C₄²	—	4	2	no	—
489	C₃×C₄²	—	4	1	no	—
490	C₃×C₄²	—	4	2	no	—
491	C₃×C₄²	—	4	2	no	—
492	C₃×C₄²	—	4	2	no	—
493	C₃×C₄²	C₂²×C₄	1	8	yes	—
494	C₃×C₄²	C₂²×C₄	1	4	yes	—
495	C₂×#41	—	4	2	no	—
496	C₂×#41	—	4	2	no	—
497	C₂×#41	C₂×C₃×C₄	1	8	yes	—
498	C₂²×Q₈	—	4	2	no	—
499	C₂²×Q₈	—	4	2	no	—
500	C₂²×Q₈	C₂×C₃×C₄	1	8	yes	complemented
501	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
502	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
503	C₂²×Q₈	C₂³×C₃	1	2	yes	—
504	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
505	C₂²×D₄	C₂³×C₃	1	2	yes	—
506	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
507	C₂²×D₄	C₂³×C₃	1	2	yes	—
508	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
509	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
510	C₂³×C₄	C₂³×C₃	1	2	yes	—
511	C₂³×C₄	C₂³×C₃	1	2	yes	—
512	C₂³×C₄	C₂³×C₃	1	2	yes	—
513	C₂³×C₄	C₂³×C₃	1	2	yes	—
514	C₂³×C₄	C₂³×C₃	1	2	yes	—
515	#124	C₂×C₃×C₄	1	8	yes	complemented
516	#124	C₂×C₃×C₄	1	16	yes	complemented
517	C₂²⋊Q₈	C₂×C₃×C₄	1	8	yes	complemented
518	C₂²⋊Q₈	C₂×C₃×C₄	1	16	yes	complemented
519	#121	C₂×C₃×C₄	1	8	yes	complemented
520	#121	C₂×C₃×C₄	1	16	yes	complemented
521	C₄×Q₈	—	4	2	no	—
522	C₄×Q₈	—	4	2	no	—
523	C₄×Q₈	C₂×C₃×C₄	1	8	yes	complemented
524	C₄×D₄	—	4	2	no	—
525	C₄×D₄	—	4	2	no	—
526	C₄×D₄	C₂×C₃×C₄	1	8	yes	complemented
527	C₄×D₄	C₂×C₃×C₄	1	16	yes	complemented
528	#117	—	4	2	no	—
529	#117	—	4	2	no	—
530	#117	—	4	2	no	—
531	C₂×C₄⋊C₄	—	4	2	no	—
532	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
533	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
534	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
535	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
536	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
537	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
538	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
539	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
540	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
541	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
542	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
543	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
544	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
545	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
546	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
547	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
548	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
549	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
550	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
552	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
553	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
555	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
556	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
557	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
558	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
559	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
560	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
561	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
562	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
563	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
564	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
565	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
566	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
567	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
568	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
569	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
570	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
571	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
574	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
575	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
576	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
577	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
578	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
579	C₂×C₄²	C₂³×C₃	1	2	yes	—
580	C₂×C₄²	C₂³×C₃	1	2	yes	—
581	C₂×C₄²	C₂³×C₃	1	2	yes	—
582	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
583	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
584	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
585	C₂×C₄²	C₂³×C₃	1	2	yes	—
586	C₂×C₄²	C₂³×C₃	1	2	yes	—
587	C₂×C₄²	C₂³×C₃	1	2	yes	—
588	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
589	C₂×C₄²	C₂³×C₃	1	2	yes	—
590	#95	C₂³×C₃	1	1	yes	characteristic
591	#95	C₂³×C₃	1	2	yes	—
592	#95	C₂³×C₃	1	2	yes	—
593	#95	C₂³×C₃	1	2	yes	—
594	#95	C₂³×C₃	1	1	yes	characteristic
595	#95	C₂³×C₃	1	2	yes	—
596	#95	C₂³×C₃	1	2	yes	—
597	#95	C₂³×C₃	1	2	yes	—
598	#95	C₂³×C₃	1	2	yes	—
599	#95	C₂³×C₃	1	2	yes	—
600	#95	C₂³×C₃	1	2	yes	—
601	#95	C₂³×C₃	1	1	yes	characteristic
602	#95	C₂³×C₃	1	1	yes	characteristic
603	#95	C₂³×C₃	1	2	yes	—
604	#95	C₂³×C₃	1	2	yes	—
605	#95	C₂³×C₃	1	1	yes	characteristic
606	#95	C₂³×C₃	1	2	yes	—
607	#95	C₂³×C₃	1	2	yes	—
608	#95	C₂³×C₃	1	2	yes	—
609	#95	C₂³×C₃	1	2	yes	—
610	#95	C₂³×C₃	1	2	yes	—
611	#95	C₂³×C₃	1	1	yes	characteristic
612	#95	C₂³×C₃	1	2	yes	—
613	#95	C₂³×C₃	1	2	yes	—
614	#95	C₂³×C₃	1	2	yes	—
615	#95	C₂³×C₃	1	2	yes	—
616	#95	C₂³×C₃	1	2	yes	—
617	C₂³×C₃	—	2	1	no	—
618	C₂³×C₃	—	2	1	no	—
619	C₂³×C₃	—	2	1	no	—
620	C₂³×C₃	—	2	2	no	—
621	C₂³×C₃	—	2	2	no	—
622	C₂³×C₃	—	2	1	no	—
623	C₂³×C₃	—	2	1	no	—
624	C₂³×C₃	—	2	1	no	—
625	C₂³×C₃	—	2	2	no	—
626	C₂³×C₃	—	2	1	no	—
627	C₂³×C₃	—	2	2	no	—
628	C₂³×C₃	—	2	2	no	—
629	C₂³×C₃	—	2	1	no	—
630	C₂³×C₃	—	2	1	no	—
631	C₂³×C₃	—	2	1	no	—
632	C₂³×C₃	—	2	2	no	—
633	C₂³×C₃	—	2	1	no	—
634	C₂³×C₃	—	2	1	no	—
635	C₂³×C₃	C₂³×C₄	1	2	yes	—
636	C₂³×C₃	C₂³×C₄	1	4	yes	—
637	C₂³×C₃	C₂³×C₄	1	2	yes	—
638	C₂³×C₃	C₂⁵	1	1	yes	characteristic
639	C₃×Q₈	—	2	8	no	—
640	C₃×Q₈	—	2	8	no	—
641	C₃×Q₈	—	4	8	no	—
642	C₃×D₄	—	2	8	no	—
643	C₃×D₄	—	4	4	no	—
644	C₃×D₄	—	4	8	no	—
645	C₃×D₄	—	4	8	no	—
646	C₂×C₃×C₄	—	2	1	no	—
647	C₂×C₃×C₄	—	2	1	no	—
648	C₂×C₃×C₄	—	2	2	no	—
649	C₂×C₃×C₄	—	2	2	no	—
650	C₂×C₃×C₄	—	2	1	no	—
651	C₂×C₃×C₄	—	2	1	no	—
652	C₂×C₃×C₄	—	2	1	no	—
653	C₂×C₃×C₄	—	2	2	no	—
654	C₂×C₃×C₄	—	2	2	no	—
655	C₂×C₃×C₄	—	2	1	no	—
656	C₂×C₃×C₄	—	2	1	no	—
657	C₂×C₃×C₄	—	2	2	no	—
658	C₂×C₃×C₄	—	2	1	no	—
659	C₂×C₃×C₄	—	2	1	no	—
660	C₂×C₃×C₄	—	2	2	no	—
661	C₂×C₃×C₄	—	2	1	no	—
662	C₂×C₃×C₄	—	2	8	no	—
663	C₂×C₃×C₄	—	2	8	no	—
664	C₂×C₃×C₄	—	2	1	no	—
665	C₂×C₃×C₄	—	2	1	no	—
666	C₂×C₃×C₄	—	2	1	no	—
667	C₂×C₃×C₄	—	2	1	no	—
668	C₂×C₃×C₄	—	2	1	no	—
669	C₂×C₃×C₄	—	2	1	no	—
670	C₂×C₃×C₄	—	2	1	no	—
671	C₂×C₃×C₄	—	2	2	no	—
672	C₂×C₃×C₄	—	2	2	no	—
673	C₂×C₃×C₄	—	2	2	no	—
674	C₂×C₃×C₄	—	2	2	no	—
675	C₂×C₃×C₄	—	2	1	no	—
676	C₂×C₃×C₄	—	2	1	no	—
677	C₂×C₃×C₄	—	2	1	no	—
678	C₂×C₃×C₄	—	2	2	no	—
679	C₂×C₃×C₄	—	2	1	no	—
680	C₂×C₃×C₄	—	2	1	no	—
681	C₂×C₃×C₄	—	2	1	no	—
682	C₂×C₃×C₄	—	2	1	no	—
683	C₂×C₃×C₄	—	2	1	no	—
684	C₂×C₃×C₄	—	2	2	no	—
685	C₂×C₃×C₄	—	2	2	no	—
686	C₂×C₃×C₄	—	2	2	no	—
687	C₂×C₃×C₄	—	2	2	no	—
688	C₂×C₃×C₄	—	2	1	no	—
689	C₂×C₃×C₄	—	2	1	no	—
690	C₂×C₃×C₄	—	2	1	no	—
691	C₂×C₃×C₄	—	2	1	no	—
692	C₂×C₃×C₄	—	2	2	no	—
693	C₂×C₃×C₄	—	2	2	no	—
694	C₂×C₃×C₄	—	2	2	no	—
695	C₂×C₃×C₄	—	2	1	no	—
696	C₂×C₃×C₄	—	2	1	no	—
697	C₂×C₃×C₄	—	4	8	no	—
698	C₂×C₃×C₄	—	4	8	no	—
699	C₂×C₃×C₄	—	8	4	no	—
700	C₂×C₃×C₄	—	8	4	no	—
701	C₂×C₃×C₄	—	8	4	no	—
702	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
703	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
704	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
705	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
706	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
707	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
708	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
709	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
710	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
711	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
712	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
713	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
714	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
715	C₂⁴	C₂⁴×C₃	1	2	yes	—
716	#41	—	4	16	no	—
717	C₂×Q₈	—	2	2	no	—
718	C₂×Q₈	—	2	2	no	—
719	C₂×Q₈	—	2	2	no	—
720	C₂×Q₈	—	2	2	no	—
721	C₂×Q₈	—	4	2	no	—
722	C₂×Q₈	—	4	2	no	—
723	C₂×Q₈	—	4	16	no	—
724	C₂×Q₈	C₂²×C₃×C₄	1	4	yes	—
725	C₂×Q₈	C₂²×C₃×C₄	1	4	yes	—
726	C₂×Q₈	C₂²×C₃×C₄	1	8	yes	—
727	C₂×D₄	—	2	2	no	—
728	C₂×D₄	—	2	2	no	—
729	C₂×D₄	—	4	2	no	—
730	C₂×D₄	—	4	2	no	—
731	C₂×D₄	—	4	2	no	—
732	C₂×D₄	—	4	1	no	—
733	C₂×D₄	—	4	1	no	—
734	C₂×D₄	—	4	2	no	—
735	C₂×D₄	C₂²×C₃×C₄	1	4	yes	—
736	C₂×D₄	C₂²×C₃×C₄	1	4	yes	—
737	C₂×D₄	C₂²×C₃×C₄	1	8	yes	—
738	C₂×D₄	C₂²×C₃×C₄	1	8	yes	—
739	C₂²×C₄	—	2	2	no	—
740	C₂²×C₄	—	2	2	no	—
741	C₂²×C₄	—	2	2	no	—
742	C₂²×C₄	—	2	2	no	—
743	C₂²×C₄	—	2	4	no	—
744	C₂²×C₄	—	4	2	no	—
745	C₂²×C₄	—	4	2	no	—
746	C₂²×C₄	—	4	2	no	—
747	C₂²×C₄	—	4	2	no	—
748	C₂²×C₄	—	4	2	no	—
749	C₂²×C₄	—	4	2	no	—
750	C₂²×C₄	—	4	2	no	—
751	C₂²×C₄	—	4	2	no	—
752	C₂²×C₄	—	4	2	no	—
753	C₂²×C₄	—	4	2	no	—
754	C₂²×C₄	—	4	2	no	—
755	C₂²×C₄	—	4	2	no	—
756	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
757	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
758	C₂²×C₄	C₂²×C₃×C₄	1	8	yes	—
759	C₂²×C₄	C₂²×C₃×C₄	1	8	yes	—
760	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
761	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
762	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
763	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
764	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
765	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
766	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
767	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
768	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
769	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
770	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
771	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
772	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
773	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
774	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
775	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
776	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
777	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
778	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
779	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
780	C₄⋊C₄	—	2	2	no	—
781	C₄⋊C₄	—	2	2	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	2	no	—
784	C₄⋊C₄	—	4	2	no	—
785	C₄⋊C₄	—	4	1	no	—
786	C₄⋊C₄	—	4	1	no	—
787	C₄⋊C₄	—	4	1	no	—
788	C₄⋊C₄	—	4	1	no	—
789	C₄⋊C₄	—	4	2	no	—
790	C₄⋊C₄	—	4	2	no	—
791	C₄⋊C₄	—	4	1	no	—
792	C₄⋊C₄	—	4	1	no	—
793	C₄⋊C₄	—	4	2	no	—
794	C₄⋊C₄	—	4	2	no	—
795	C₄⋊C₄	C₂²×C₃×C₄	1	4	yes	—
796	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
797	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
798	C₄⋊C₄	C₂²×C₃×C₄	1	4	yes	—
799	C₂²⋊C₄	—	2	2	no	—
800	C₂²⋊C₄	—	2	2	no	—
801	C₂²⋊C₄	—	4	1	no	—
802	C₂²⋊C₄	—	4	1	no	—
803	C₂²⋊C₄	—	4	1	no	—
804	C₂²⋊C₄	—	4	1	no	—
805	C₂²⋊C₄	—	4	2	no	—
806	C₂²⋊C₄	—	4	2	no	—
807	C₂²⋊C₄	—	4	2	no	—
808	C₂²⋊C₄	—	4	2	no	—
809	C₂²⋊C₄	—	4	1	no	—
810	C₂²⋊C₄	—	4	2	no	—
811	C₂²⋊C₄	—	4	1	no	—
812	C₂²⋊C₄	—	4	2	no	—
813	C₂²⋊C₄	—	4	2	no	—
814	C₂²⋊C₄	—	4	2	no	—
815	C₂²⋊C₄	—	4	2	no	—
816	C₂²⋊C₄	C₂²×C₃×C₄	1	4	yes	—
817	C₂²⋊C₄	C₂²×C₃×C₄	1	4	yes	—
818	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
819	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
820	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
821	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
822	C₄²	—	2	2	no	—
823	C₄²	—	2	2	no	—
824	C₄²	—	2	2	no	—
825	C₄²	—	2	2	no	—
826	C₄²	—	2	2	no	—
827	C₄²	—	4	2	no	—
828	C₄²	—	4	2	no	—
829	C₄²	—	4	2	no	—
830	C₄²	—	4	1	no	—
831	C₄²	—	4	2	no	—
832	C₄²	—	4	1	no	—
833	C₄²	—	4	2	no	—
834	C₄²	—	4	2	no	—
835	C₄²	—	4	1	no	—
836	C₄²	C₂²×C₃×C₄	1	8	yes	—
837	C₄²	C₂²×C₃×C₄	1	4	yes	—
838	C₂²×C₃	—	2	2	no	—
839	C₂²×C₃	—	2	2	no	—
840	C₂²×C₃	—	2	4	no	—
841	C₂²×C₃	—	2	2	no	—
842	C₂²×C₃	—	2	2	no	—
843	C₂²×C₃	—	2	4	no	—
844	C₂²×C₃	—	2	2	no	—
845	C₂²×C₃	—	2	2	no	—
846	C₂²×C₃	—	2	4	no	—
847	C₂²×C₃	—	4	1	no	—
848	C₂²×C₃	—	4	1	no	—
849	C₂²×C₃	—	4	2	no	—
850	C₂²×C₃	—	4	2	no	—
851	C₂²×C₃	—	4	1	no	—
852	C₂²×C₃	—	4	1	no	—
853	C₂²×C₃	—	4	2	no	—
854	C₂²×C₃	—	4	1	no	—
855	C₂²×C₃	—	4	1	no	—
856	C₂²×C₃	—	4	1	no	—
857	C₂²×C₃	—	4	1	no	—
858	C₂²×C₃	—	4	2	no	—
859	C₂²×C₃	C₂⁴×C₄	1	1	yes	characteristic
860	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
861	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
862	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
863	C₂²×C₃	#585	1	1	yes	characteristic
864	C₂²×C₃	#585	1	1	yes	characteristic
865	C₂²×C₃	#585	1	1	yes	characteristic
866	C₃×C₄	—	2	2	no	—
867	C₃×C₄	—	2	2	no	—
868	C₃×C₄	—	2	4	no	—
869	C₃×C₄	—	2	4	no	—
870	C₃×C₄	—	2	4	no	—
871	C₃×C₄	—	2	2	no	—
872	C₃×C₄	—	2	2	no	—
873	C₃×C₄	—	2	2	no	—
874	C₃×C₄	—	4	1	no	—
875	C₃×C₄	—	4	1	no	—
876	C₃×C₄	—	4	1	no	—
877	C₃×C₄	—	4	1	no	—
878	C₃×C₄	—	4	1	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	—	4	2	no	—
884	C₃×C₄	—	4	2	no	—
885	C₃×C₄	#518	1	4	yes	—
886	C₂³	—	2	1	no	—
887	C₂³	—	2	1	no	—
888	C₂³	—	2	1	no	—
889	C₂³	—	2	2	no	—
890	C₂³	—	2	2	no	—
891	C₂³	—	2	1	no	—
892	C₂³	—	2	1	no	—
893	C₂³	—	2	1	no	—
894	C₂³	—	2	2	no	—
895	C₂³	—	2	1	no	—
896	C₂³	—	2	2	no	—
897	C₂³	—	2	2	no	—
898	C₂³	—	2	1	no	—
899	C₂³	—	2	1	no	—
900	C₂³	—	2	1	no	—
901	C₂³	—	2	2	no	—
902	C₂³	—	2	1	no	—
903	C₂³	—	2	1	no	—
904	C₂³	C₂³×C₃×C₄	1	2	yes	—
905	C₂³	C₂³×C₃×C₄	1	4	yes	—
906	C₂³	C₂³×C₃×C₄	1	2	yes	—
907	C₂³	C₂⁵×C₃	1	1	yes	characteristic
908	Q₈	—	2	8	no	—
909	Q₈	—	2	8	no	—
910	Q₈	—	4	8	no	—
911	D₄	—	2	8	no	—
912	D₄	—	4	8	no	—
913	D₄	—	4	4	no	—
914	D₄	—	4	8	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	1	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	1	no	—
920	C₂×C₄	—	2	1	no	—
921	C₂×C₄	—	2	1	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	2	no	—
924	C₂×C₄	—	2	1	no	—
925	C₂×C₄	—	2	1	no	—
926	C₂×C₄	—	2	2	no	—
927	C₂×C₄	—	2	1	no	—
928	C₂×C₄	—	2	1	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	2	1	no	—
931	C₂×C₄	—	2	8	no	—
932	C₂×C₄	—	2	8	no	—
933	C₂×C₄	—	2	1	no	—
934	C₂×C₄	—	2	1	no	—
935	C₂×C₄	—	2	1	no	—
936	C₂×C₄	—	2	1	no	—
937	C₂×C₄	—	2	1	no	—
938	C₂×C₄	—	2	1	no	—
939	C₂×C₄	—	2	1	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	2	2	no	—
943	C₂×C₄	—	2	2	no	—
944	C₂×C₄	—	2	1	no	—
945	C₂×C₄	—	2	1	no	—
946	C₂×C₄	—	2	1	no	—
947	C₂×C₄	—	2	2	no	—
948	C₂×C₄	—	2	1	no	—
949	C₂×C₄	—	2	1	no	—
950	C₂×C₄	—	2	1	no	—
951	C₂×C₄	—	2	1	no	—
952	C₂×C₄	—	2	1	no	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	1	no	—
958	C₂×C₄	—	2	1	no	—
959	C₂×C₄	—	2	1	no	—
960	C₂×C₄	—	2	1	no	—
961	C₂×C₄	—	2	2	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	2	no	—
964	C₂×C₄	—	2	1	no	—
965	C₂×C₄	—	2	1	no	—
966	C₂×C₄	—	4	8	no	—
967	C₂×C₄	—	4	8	no	—
968	C₂×C₄	—	8	4	no	—
969	C₂×C₄	—	8	4	no	—
970	C₂×C₄	—	8	4	no	—
971	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
972	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
973	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
974	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
975	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
976	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
977	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
978	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
979	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
980	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
981	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
982	C₂×C₃	—	4	2	no	—
983	C₂×C₃	—	4	2	no	—
984	C₂×C₃	—	4	4	no	—
985	C₂×C₃	C₂×#518	1	1	yes	characteristic
986	C₂×C₃	#3428	1	1	yes	characteristic
987	C₂×C₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
988	C₂×C₃	#3547	1	1	yes	characteristic
989	C₂×C₃	#3551	1	1	yes	characteristic
990	C₂×C₃	#3561	1	1	yes	characteristic
991	C₂×C₃	#3562	1	1	yes	characteristic
992	C₂²	—	2	2	no	—
993	C₂²	—	2	2	no	—
994	C₂²	—	2	4	no	—
995	C₂²	—	2	2	no	—
996	C₂²	—	2	2	no	—
997	C₂²	—	2	4	no	—
998	C₂²	—	2	2	no	—
999	C₂²	—	2	2	no	—
1000	C₂²	—	2	4	no	—
1001	C₂²	—	4	1	no	—
1002	C₂²	—	4	1	no	—
1003	C₂²	—	4	2	no	—
1004	C₂²	—	4	2	no	—
1005	C₂²	—	4	1	no	—
1006	C₂²	—	4	1	no	—
1007	C₂²	—	4	2	no	—
1008	C₂²	—	4	1	no	—
1009	C₂²	—	4	1	no	—
1010	C₂²	—	4	1	no	—
1011	C₂²	—	4	1	no	—
1012	C₂²	—	4	2	no	—
1013	C₂²	C₂⁴×C₃×C₄	1	1	yes	characteristic
1014	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1015	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1016	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
1017	C₂²	C₃×#585	1	1	yes	characteristic
1018	C₂²	C₃×#585	1	1	yes	characteristic
1019	C₂²	C₃×#585	1	1	yes	characteristic
1020	C₄	—	2	2	no	—
1021	C₄	—	2	2	no	—
1022	C₄	—	2	4	no	—
1023	C₄	—	2	4	no	—
1024	C₄	—	2	4	no	—
1025	C₄	—	2	2	no	—
1026	C₄	—	2	2	no	—
1027	C₄	—	2	2	no	—
1028	C₄	—	4	1	no	—
1029	C₄	—	4	1	no	—
1030	C₄	—	4	1	no	—
1031	C₄	—	4	1	no	—
1032	C₄	—	4	2	no	—
1033	C₄	—	4	1	no	—
1034	C₄	—	4	1	no	—
1035	C₄	—	4	2	no	—
1036	C₄	—	4	2	no	—
1037	C₄	—	4	2	no	—
1038	C₄	—	4	1	no	—
1039	C₄	C₃×#518	1	4	yes	—
1040	C₃	#34496	1	1	yes	characteristic, direct product factor, Sylow
1041	C₂	—	4	2	no	—
1042	C₂	—	4	2	no	—
1043	C₂	—	4	4	no	—
1044	C₂	C₂×C₃×#518	1	1	yes	characteristic
1045	C₂	C₃×#3428	1	1	yes	characteristic
1046	C₂	C₃×C₄×2₋¹⁺⁴	1	1	yes	characteristic
1047	C₂	C₃×#3547	1	1	yes	characteristic
1048	C₂	C₃×#3551	1	1	yes	characteristic
1049	C₂	C₃×#3561	1	1	yes	characteristic
1050	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	C₂×C₃×#548	C₂
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×#2378	C₂	semidirect
3. C₃×#2377	C₂	semidirect
4. C₃×#2372	C₂	semidirect
5. C₃×#2367	C₂	semidirect
6. C₃×#2363	C₂	semidirect
7. C₃×#2360	C₂	semidirect
8. C₃×#2356	C₂	semidirect
9. C₃×#2353	C₂	semidirect
10. C₃×#2352	C₂	semidirect
11. C₃×Q₈×C₂²⋊C₄	C₂	semidirect
12. C₃×#2339	C₂	semidirect
13. C₃×#2337	C₂	semidirect
14. C₃×#2333	C₂	semidirect
15. C₃×#2329	C₂	semidirect
16. C₃×#2324	C₂	semidirect
17. C₃×#2323	C₂	semidirect
18. C₃×#2319	C₂	semidirect
19. C₃×#2311	C₂	semidirect
20. C₃×#2310	C₂	semidirect
21. C₃×C₄×#124	C₂	semidirect
22. C₃×#2295	C₂	semidirect
23. C₃×#2293	C₂	semidirect
24. #34496	C₃	direct (N × H)
27. C₃×#548	C₄	semidirect
126. #2378	C₂×C₃	semidirect
127. #2377	C₂×C₃	semidirect
128. #2372	C₂×C₃	semidirect
129. #2367	C₂×C₃	semidirect
130. #2363	C₂×C₃	semidirect
131. #2360	C₂×C₃	semidirect
132. #2356	C₂×C₃	semidirect
133. #2353	C₂×C₃	semidirect
134. #2352	C₂×C₃	semidirect
135. Q₈×C₂²⋊C₄	C₂×C₃	semidirect
136. #2339	C₂×C₃	semidirect
137. #2337	C₂×C₃	semidirect
138. #2333	C₂×C₃	semidirect
139. #2329	C₂×C₃	semidirect
140. #2324	C₂×C₃	semidirect
141. #2323	C₂×C₃	semidirect
142. #2319	C₂×C₃	semidirect
143. #2311	C₂×C₃	semidirect
144. #2310	C₂×C₃	semidirect
145. C₄×#124	C₂×C₃	semidirect
146. #2295	C₂×C₃	semidirect
147. #2293	C₂×C₃	semidirect
153. C₂²×C₃×Q₈	C₂×C₄	semidirect
168. C₃×#124	C₂×C₄	semidirect
169. C₃×#124	C₂×C₄	semidirect
170. C₃×C₂²⋊Q₈	C₂×C₄	semidirect
171. C₃×C₂²⋊Q₈	C₂×C₄	semidirect
172. C₃×#121	C₂×C₄	semidirect
173. C₃×#121	C₂×C₄	semidirect
176. C₃×C₄×Q₈	C₂×C₄	semidirect
179. C₃×C₄×D₄	C₂×C₄	semidirect
180. C₃×C₄×D₄	C₂×C₄	semidirect
272. #548	C₃×C₄	semidirect
500. C₂²×Q₈	C₂×C₃×C₄	semidirect
515. #124	C₂×C₃×C₄	semidirect
516. #124	C₂×C₃×C₄	semidirect
517. C₂²⋊Q₈	C₂×C₃×C₄	semidirect
518. C₂²⋊Q₈	C₂×C₃×C₄	semidirect
519. #121	C₂×C₃×C₄	semidirect
520. #121	C₂×C₃×C₄	semidirect
523. C₄×Q₈	C₂×C₃×C₄	semidirect
526. C₄×D₄	C₂×C₃×C₄	semidirect
527. C₄×D₄	C₂×C₃×C₄	semidirect
1040. C₃	#34496	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×#548	2
C₃×#2378	2
C₃×#2377	2
C₃×#2372	2
C₃×#2367	2
C₃×#2363	2
C₃×#2360	2
C₃×#2356	2
C₃×#2353	2
C₃×#2352	2
C₃×Q₈×C₂²⋊C₄	2
C₃×#2339	2
C₃×#2337	2
C₃×#2333	2
C₃×#2329	2
C₃×#2324	2
C₃×#2323	2
C₃×#2319	2
C₃×#2311	2
C₃×#2310	2
C₃×C₄×#124	2
C₃×#2295	2
C₃×#2293	2
#34496	3

Subgroups — C3×#34496 #10653103

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#34496 #10653103