Subgroups — C₃×#35945 #10654552

Order 768.

1686 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2654	C₂	1	2	yes	maximal, complemented
2	C₃×#2647	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2590	C₂	1	2	yes	maximal, complemented
4	C₃×#2581	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2573	C₂	1	2	yes	maximal, complemented
6	C₃×#2538	C₂	1	1	yes	maximal, characteristic
7	C₃×#2533	C₂	1	2	yes	maximal, complemented
8	C₃×#2526	C₂	1	2	yes	maximal
9	C₃×#2497	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#2496	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#2479	C₂	1	2	yes	maximal
12	C₃×#2469	C₂	1	2	yes	maximal, complemented
13	C₃×#2423	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#2423	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#2398	C₂	1	1	yes	maximal, characteristic
16	C₃×#2396	C₂	1	2	yes	maximal, complemented
17	C₃×#2362	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#2360	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#2352	C₂	1	1	yes	maximal, characteristic
20	C₃×Q₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×#2347	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃×#2344	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×#2276	C₂	1	1	yes	maximal, characteristic, complemented
24	#35945	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂×C₃×#126	C₂²	1	2	yes	—
26	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	—
33	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
34	C₂×C₃×#117	C₂²	1	1	yes	characteristic
35	C₂×C₃×#117	C₂²	1	2	yes	—
36	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
37	C₃×#400	C₂²	1	2	yes	—
38	C₃×#400	C₂²	1	2	yes	—
39	C₃×#400	C₂²	1	2	yes	—
40	C₃×#400	C₂²	1	1	yes	characteristic
41	C₃×#400	C₂²	1	1	yes	characteristic
42	C₃×#400	C₂²	1	2	yes	—
43	C₃×#400	C₂²	1	2	yes	—
44	C₃×#399	C₂²	1	2	yes	—
45	C₃×#399	C₂²	1	2	yes	—
46	C₃×#398	C₂²	1	2	yes	—
47	C₃×#398	C₂²	1	2	yes	—
48	C₃×#398	C₂²	1	2	yes	—
49	C₃×#398	C₂²	1	2	yes	—
50	C₃×#397	C₂²	1	1	yes	characteristic
51	C₃×#397	C₂²	1	1	yes	characteristic
52	C₃×#397	C₂²	1	2	yes	—
53	C₃×#396	C₂²	1	2	yes	—
54	C₃×#396	C₂²	1	2	yes	—
55	C₃×#396	C₂²	1	2	yes	—
56	C₃×#395	C₂²	1	2	yes	—
57	C₃×#394	C₂²	1	1	yes	characteristic
58	C₃×#394	C₂²	1	1	yes	characteristic
59	C₃×#393	C₂²	1	1	yes	characteristic
60	C₃×#393	C₂²	1	1	yes	characteristic
61	C₃×#391	C₂²	1	1	yes	characteristic
62	C₃×#391	C₂²	1	1	yes	characteristic
63	C₃×#390	C₂²	1	2	yes	—
64	C₃×#389	C₂²	1	1	yes	characteristic
65	C₃×#389	C₂²	1	2	yes	—
66	C₃×#389	C₂²	1	1	yes	characteristic
67	C₃×#389	C₂²	1	1	yes	characteristic
68	C₃×#389	C₂²	1	1	yes	characteristic
69	C₃×#389	C₂²	1	2	yes	—
70	C₃×#389	C₂²	1	2	yes	—
71	C₃×#389	C₂²	1	1	yes	characteristic
72	C₃×#389	C₂²	1	1	yes	characteristic
73	C₃×#389	C₂²	1	2	yes	—
74	C₃×#389	C₂²	1	2	yes	—
75	C₃×#388	C₂²	1	2	yes	—
76	C₃×#388	C₂²	1	2	yes	—
77	C₃×#388	C₂²	1	2	yes	—
78	C₃×#388	C₂²	1	2	yes	—
79	C₃×#388	C₂²	1	2	yes	—
80	C₃×#388	C₂²	1	2	yes	—
81	C₃×#388	C₂²	1	2	yes	—
82	C₃×#388	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×#387	C₂²	1	2	yes	—
88	C₃×#387	C₂²	1	2	yes	—
89	C₃×#387	C₂²	1	2	yes	—
90	C₃×#387	C₂²	1	2	yes	—
91	C₃×#387	C₂²	1	2	yes	—
92	C₃×#387	C₂²	1	2	yes	—
93	C₃×#387	C₂²	1	2	yes	—
94	C₃×#386	C₂²	1	2	yes	—
95	C₃×#385	C₂²	1	2	yes	—
96	C₃×#384	C₂²	1	1	yes	characteristic
97	C₃×#384	C₂²	1	1	yes	characteristic
98	C₃×#384	C₂²	1	1	yes	characteristic
99	C₃×#383	C₂²	1	2	yes	—
100	C₃×#382	C₂²	1	1	yes	characteristic
101	C₃×#381	C₂²	1	2	yes	—
102	C₃×#380	C₂²	1	1	yes	characteristic
103	C₃×#380	C₂²	1	1	yes	characteristic
104	C₃×#380	C₂²	1	1	yes	characteristic
105	C₃×#380	C₂²	1	1	yes	characteristic
106	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
107	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
108	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
109	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
110	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
111	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
112	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
113	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
114	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
115	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
116	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
117	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
118	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
119	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
120	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
121	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
122	C₃×#376	C₂²	1	1	yes	characteristic
123	C₃×#376	C₂²	1	2	yes	—
124	#2654	C₂×C₃	1	2	yes	complemented
125	#2647	C₂×C₃	1	1	yes	characteristic, complemented
126	#2590	C₂×C₃	1	2	yes	complemented
127	#2581	C₂×C₃	1	1	yes	characteristic, complemented
128	#2573	C₂×C₃	1	2	yes	complemented
129	#2538	C₂×C₃	1	1	yes	characteristic
130	#2533	C₂×C₃	1	2	yes	complemented
131	#2526	C₂×C₃	1	2	yes	—
132	#2497	C₂×C₃	1	1	yes	characteristic, complemented
133	#2496	C₂×C₃	1	1	yes	characteristic, complemented
134	#2479	C₂×C₃	1	2	yes	—
135	#2469	C₂×C₃	1	2	yes	complemented
136	#2423	C₂×C₃	1	1	yes	characteristic, complemented
137	#2423	C₂×C₃	1	1	yes	characteristic, complemented
138	#2398	C₂×C₃	1	1	yes	characteristic
139	#2396	C₂×C₃	1	2	yes	complemented
140	#2362	C₂×C₃	1	1	yes	characteristic, complemented
141	#2360	C₂×C₃	1	1	yes	characteristic, complemented
142	#2352	C₂×C₃	1	1	yes	characteristic
143	Q₈×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
144	#2347	C₂×C₃	1	1	yes	characteristic, complemented
145	#2344	C₂×C₃	1	1	yes	characteristic, complemented
146	#2276	C₂×C₃	1	1	yes	characteristic, complemented
147	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
148	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
149	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
150	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
151	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
152	C₂³×C₃×C₄	C₂³	1	2	yes	—
153	C₃×#126	—	4	4	no	—
154	C₃×C₂²⋊Q₈	—	2	4	no	—
155	C₃×C₂²⋊Q₈	—	2	4	no	—
156	C₃×C₄×Q₈	—	2	4	no	—
157	C₃×C₄×Q₈	—	2	4	no	—
158	C₃×C₄×Q₈	—	2	4	no	—
159	C₃×C₄×Q₈	—	2	4	no	—
160	C₃×C₄×Q₈	—	4	4	no	—
161	C₃×C₄×D₄	—	2	4	no	—
162	C₃×#117	—	2	4	no	—
163	C₃×#117	—	4	4	no	—
164	C₂×C₃×C₄⋊C₄	—	2	4	no	—
165	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
166	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
167	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
168	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
169	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
170	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
172	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
173	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
177	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
178	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
179	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
181	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
186	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
187	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
193	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
194	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
195	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
196	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
197	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
198	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
200	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
201	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
205	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
206	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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×C₄²	C₂³	1	1	yes	characteristic
212	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
213	C₂×C₃×C₄²	C₂³	1	2	yes	—
214	C₂×C₃×C₄²	C₂³	1	2	yes	—
215	C₂×C₃×C₄²	C₂³	1	2	yes	—
216	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
217	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
218	C₂×C₃×C₄²	C₂³	1	2	yes	—
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	1	yes	characteristic
225	C₃×#95	C₂³	1	1	yes	characteristic
226	C₃×#95	C₂³	1	2	yes	—
227	C₃×#95	C₂³	1	2	yes	—
228	C₃×#95	C₂³	1	1	yes	characteristic
229	C₃×#95	C₂³	1	1	yes	characteristic
230	C₃×#95	C₂³	1	1	yes	characteristic
231	C₃×#95	C₂³	1	2	yes	—
232	C₃×#95	C₂³	1	1	yes	characteristic
233	C₃×#95	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
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	2	yes	—
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	2	yes	—
255	C₃×#95	C₂³	1	2	yes	—
256	C₃×#95	C₂³	1	2	yes	—
257	C₃×#95	C₂³	1	2	yes	—
258	C₂×#126	C₂²×C₃	1	2	yes	—
259	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
260	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
261	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
262	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
263	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
264	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
265	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	—
266	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
267	C₂×#117	C₂²×C₃	1	1	yes	characteristic
268	C₂×#117	C₂²×C₃	1	2	yes	—
269	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
270	#400	C₂²×C₃	1	2	yes	—
271	#400	C₂²×C₃	1	2	yes	—
272	#400	C₂²×C₃	1	1	yes	characteristic
273	#400	C₂²×C₃	1	2	yes	—
274	#400	C₂²×C₃	1	2	yes	—
275	#400	C₂²×C₃	1	1	yes	characteristic
276	#400	C₂²×C₃	1	2	yes	—
277	#399	C₂²×C₃	1	2	yes	—
278	#399	C₂²×C₃	1	2	yes	—
279	#398	C₂²×C₃	1	2	yes	—
280	#398	C₂²×C₃	1	2	yes	—
281	#398	C₂²×C₃	1	2	yes	—
282	#398	C₂²×C₃	1	2	yes	—
283	#397	C₂²×C₃	1	1	yes	characteristic
284	#397	C₂²×C₃	1	1	yes	characteristic
285	#397	C₂²×C₃	1	2	yes	—
286	#396	C₂²×C₃	1	2	yes	—
287	#396	C₂²×C₃	1	2	yes	—
288	#396	C₂²×C₃	1	2	yes	—
289	#395	C₂²×C₃	1	2	yes	—
290	#394	C₂²×C₃	1	1	yes	characteristic
291	#394	C₂²×C₃	1	1	yes	characteristic
292	#393	C₂²×C₃	1	1	yes	characteristic
293	#393	C₂²×C₃	1	1	yes	characteristic
294	#391	C₂²×C₃	1	1	yes	characteristic
295	#391	C₂²×C₃	1	1	yes	characteristic
296	#390	C₂²×C₃	1	2	yes	—
297	#389	C₂²×C₃	1	2	yes	—
298	#389	C₂²×C₃	1	1	yes	characteristic
299	#389	C₂²×C₃	1	1	yes	characteristic
300	#389	C₂²×C₃	1	2	yes	—
301	#389	C₂²×C₃	1	2	yes	—
302	#389	C₂²×C₃	1	2	yes	—
303	#389	C₂²×C₃	1	1	yes	characteristic
304	#389	C₂²×C₃	1	1	yes	characteristic
305	#389	C₂²×C₃	1	2	yes	—
306	#389	C₂²×C₃	1	1	yes	characteristic
307	#389	C₂²×C₃	1	1	yes	characteristic
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	#388	C₂²×C₃	1	2	yes	—
313	#388	C₂²×C₃	1	2	yes	—
314	#388	C₂²×C₃	1	2	yes	—
315	#388	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	2	yes	—
324	#387	C₂²×C₃	1	2	yes	—
325	#387	C₂²×C₃	1	2	yes	—
326	#387	C₂²×C₃	1	2	yes	—
327	#386	C₂²×C₃	1	2	yes	—
328	#385	C₂²×C₃	1	2	yes	—
329	#384	C₂²×C₃	1	1	yes	characteristic
330	#384	C₂²×C₃	1	1	yes	characteristic
331	#384	C₂²×C₃	1	1	yes	characteristic
332	#383	C₂²×C₃	1	2	yes	—
333	#382	C₂²×C₃	1	1	yes	characteristic
334	#381	C₂²×C₃	1	2	yes	—
335	#380	C₂²×C₃	1	1	yes	characteristic
336	#380	C₂²×C₃	1	1	yes	characteristic
337	#380	C₂²×C₃	1	1	yes	characteristic
338	#380	C₂²×C₃	1	1	yes	characteristic
339	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
340	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
341	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
342	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
343	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
344	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
345	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
346	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
347	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
348	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
349	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
350	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
351	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
352	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
353	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
354	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
355	#376	C₂²×C₃	1	1	yes	characteristic
356	#376	C₂²×C₃	1	2	yes	—
357	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
358	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
359	C₂×C₃×Q₈	—	2	2	no	—
360	C₂×C₃×Q₈	—	2	2	no	—
361	C₂×C₃×Q₈	—	2	2	no	—
362	C₂×C₃×Q₈	—	2	2	no	—
363	C₂×C₃×Q₈	—	2	2	no	—
364	C₂×C₃×Q₈	#41	1	4	yes	—
365	C₂×C₃×D₄	—	2	2	no	—
366	C₂×C₃×D₄	—	2	2	no	—
367	C₂×C₃×D₄	—	4	1	no	—
368	C₂²×C₃×C₄	—	2	4	no	—
369	C₂²×C₃×C₄	—	2	4	no	—
370	C₂²×C₃×C₄	—	2	2	no	—
371	C₂²×C₃×C₄	—	2	2	no	—
372	C₂²×C₃×C₄	—	2	2	no	—
373	C₂²×C₃×C₄	—	2	2	no	—
374	C₂²×C₃×C₄	—	2	2	no	—
375	C₂²×C₃×C₄	—	2	2	no	—
376	C₂²×C₃×C₄	—	4	2	no	—
377	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
378	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
379	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
380	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
381	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
382	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
383	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
384	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
385	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
386	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
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	2	yes	—
391	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
392	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
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	1	yes	characteristic
397	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
398	C₃×C₄⋊C₄	—	2	4	no	—
399	C₃×C₄⋊C₄	—	2	2	no	—
400	C₃×C₄⋊C₄	—	2	2	no	—
401	C₃×C₄⋊C₄	—	2	2	no	—
402	C₃×C₄⋊C₄	—	2	2	no	—
403	C₃×C₄⋊C₄	—	2	2	no	—
404	C₃×C₄⋊C₄	—	2	4	no	—
405	C₃×C₄⋊C₄	—	2	4	no	—
406	C₃×C₄⋊C₄	—	2	4	no	—
407	C₃×C₄⋊C₄	—	2	2	no	—
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	4	no	—
413	C₃×C₄⋊C₄	—	2	4	no	—
414	C₃×C₄⋊C₄	—	2	4	no	—
415	C₃×C₄⋊C₄	—	2	4	no	—
416	C₃×C₄⋊C₄	—	2	4	no	—
417	C₃×C₄⋊C₄	—	4	2	no	—
418	C₃×C₄⋊C₄	—	4	2	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	#41	1	4	yes	—
427	C₃×C₂²⋊C₄	—	2	2	no	—
428	C₃×C₂²⋊C₄	—	2	2	no	—
429	C₃×C₂²⋊C₄	—	2	4	no	—
430	C₃×C₂²⋊C₄	—	2	2	no	—
431	C₃×C₂²⋊C₄	—	2	2	no	—
432	C₃×C₂²⋊C₄	—	2	4	no	—
433	C₃×C₂²⋊C₄	—	2	4	no	—
434	C₃×C₂²⋊C₄	—	2	2	no	—
435	C₃×C₂²⋊C₄	—	2	2	no	—
436	C₃×C₂²⋊C₄	—	2	2	no	—
437	C₃×C₂²⋊C₄	—	2	2	no	—
438	C₃×C₂²⋊C₄	—	4	2	no	—
439	C₃×C₂²⋊C₄	—	4	1	no	—
440	C₃×C₂²⋊C₄	—	4	1	no	—
441	C₃×C₂²⋊C₄	—	4	2	no	—
442	C₃×C₂²⋊C₄	—	4	2	no	—
443	C₃×C₂²⋊C₄	—	4	2	no	—
444	C₃×C₄²	—	2	4	no	—
445	C₃×C₄²	—	2	4	no	—
446	C₃×C₄²	—	2	4	no	—
447	C₃×C₄²	—	2	2	no	—
448	C₃×C₄²	—	2	2	no	—
449	C₃×C₄²	—	2	4	no	—
450	C₃×C₄²	—	2	2	no	—
451	C₃×C₄²	—	2	2	no	—
452	C₃×C₄²	—	2	4	no	—
453	C₃×C₄²	—	4	2	no	—
454	C₃×C₄²	—	4	2	no	—
455	C₃×C₄²	—	4	2	no	—
456	C₃×C₄²	—	4	2	no	—
457	C₃×C₄²	#41	1	4	yes	—
458	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
459	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
460	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
461	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
462	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
463	C₂³×C₄	C₂³×C₃	1	2	yes	—
464	#126	—	4	4	no	—
465	C₂²⋊Q₈	—	2	4	no	—
466	C₂²⋊Q₈	—	2	4	no	—
467	C₄×Q₈	—	2	4	no	—
468	C₄×Q₈	—	2	4	no	—
469	C₄×Q₈	—	2	4	no	—
470	C₄×Q₈	—	2	4	no	—
471	C₄×Q₈	—	4	4	no	—
472	C₄×D₄	—	2	4	no	—
473	#117	—	2	4	no	—
474	#117	—	4	4	no	—
475	C₂×C₄⋊C₄	—	2	4	no	—
476	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
477	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
478	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
479	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
480	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
481	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
482	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
483	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
484	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
485	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
486	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
487	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
488	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
489	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
490	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
491	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
492	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
493	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
494	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
495	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
496	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
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	1	yes	characteristic
505	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
506	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
507	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
508	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
509	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
510	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
511	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
512	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
513	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
514	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
515	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
516	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
521	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
522	C₂×C₄²	C₂³×C₃	1	2	yes	—
523	C₂×C₄²	C₂³×C₃	1	2	yes	—
524	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
525	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
526	C₂×C₄²	C₂³×C₃	1	2	yes	—
527	C₂×C₄²	C₂³×C₃	1	2	yes	—
528	C₂×C₄²	C₂³×C₃	1	2	yes	—
529	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
530	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
531	C₂×C₄²	C₂³×C₃	1	2	yes	—
532	C₂×C₄²	C₂³×C₃	1	2	yes	—
533	C₂×C₄²	C₂³×C₃	1	2	yes	—
534	C₂×C₄²	C₂³×C₃	1	2	yes	—
535	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
536	#95	C₂³×C₃	1	1	yes	characteristic
537	#95	C₂³×C₃	1	2	yes	—
538	#95	C₂³×C₃	1	2	yes	—
539	#95	C₂³×C₃	1	1	yes	characteristic
540	#95	C₂³×C₃	1	1	yes	characteristic
541	#95	C₂³×C₃	1	1	yes	characteristic
542	#95	C₂³×C₃	1	2	yes	—
543	#95	C₂³×C₃	1	1	yes	characteristic
544	#95	C₂³×C₃	1	1	yes	characteristic
545	#95	C₂³×C₃	1	2	yes	—
546	#95	C₂³×C₃	1	2	yes	—
547	#95	C₂³×C₃	1	1	yes	characteristic
548	#95	C₂³×C₃	1	1	yes	characteristic
549	#95	C₂³×C₃	1	1	yes	characteristic
550	#95	C₂³×C₃	1	1	yes	characteristic
551	#95	C₂³×C₃	1	1	yes	characteristic
552	#95	C₂³×C₃	1	1	yes	characteristic
553	#95	C₂³×C₃	1	2	yes	—
554	#95	C₂³×C₃	1	2	yes	—
555	#95	C₂³×C₃	1	2	yes	—
556	#95	C₂³×C₃	1	2	yes	—
557	#95	C₂³×C₃	1	2	yes	—
558	#95	C₂³×C₃	1	2	yes	—
559	#95	C₂³×C₃	1	2	yes	—
560	#95	C₂³×C₃	1	2	yes	—
561	#95	C₂³×C₃	1	2	yes	—
562	#95	C₂³×C₃	1	2	yes	—
563	#95	C₂³×C₃	1	2	yes	—
564	#95	C₂³×C₃	1	2	yes	—
565	#95	C₂³×C₃	1	2	yes	—
566	#95	C₂³×C₃	1	2	yes	—
567	#95	C₂³×C₃	1	2	yes	—
568	#95	C₂³×C₃	1	2	yes	—
569	C₂³×C₃	—	2	1	no	—
570	C₂³×C₃	—	2	1	no	—
571	C₂³×C₃	—	2	1	no	—
572	C₂³×C₃	—	2	1	no	—
573	C₂³×C₃	—	2	1	no	—
574	C₂³×C₃	—	2	1	no	—
575	C₂³×C₃	—	2	1	no	—
576	C₂³×C₃	—	2	1	no	—
577	C₂³×C₃	—	2	1	no	—
578	C₂³×C₃	—	2	1	no	—
579	C₂³×C₃	—	2	1	no	—
580	C₂³×C₃	—	2	1	no	—
581	C₂³×C₃	—	2	1	no	—
582	C₂³×C₃	2₋¹⁺⁴	1	2	yes	—
583	C₂³×C₃	C₂⁵	1	1	yes	characteristic
584	C₃×Q₈	—	2	8	no	—
585	C₃×Q₈	—	2	8	no	—
586	C₃×D₄	—	4	4	no	—
587	C₂×C₃×C₄	—	2	2	no	—
588	C₂×C₃×C₄	—	2	2	no	—
589	C₂×C₃×C₄	—	2	1	no	—
590	C₂×C₃×C₄	—	2	1	no	—
591	C₂×C₃×C₄	—	2	2	no	—
592	C₂×C₃×C₄	—	2	1	no	—
593	C₂×C₃×C₄	—	2	1	no	—
594	C₂×C₃×C₄	—	2	2	no	—
595	C₂×C₃×C₄	—	2	1	no	—
596	C₂×C₃×C₄	—	2	1	no	—
597	C₂×C₃×C₄	—	2	1	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	1	no	—
602	C₂×C₃×C₄	—	2	2	no	—
603	C₂×C₃×C₄	—	2	2	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	2	no	—
608	C₂×C₃×C₄	—	2	1	no	—
609	C₂×C₃×C₄	—	2	2	no	—
610	C₂×C₃×C₄	—	2	2	no	—
611	C₂×C₃×C₄	—	2	1	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	2	no	—
617	C₂×C₃×C₄	—	2	2	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	2	no	—
624	C₂×C₃×C₄	—	2	1	no	—
625	C₂×C₃×C₄	—	2	1	no	—
626	C₂×C₃×C₄	—	2	1	no	—
627	C₂×C₃×C₄	—	2	1	no	—
628	C₂×C₃×C₄	—	2	1	no	—
629	C₂×C₃×C₄	—	2	1	no	—
630	C₂×C₃×C₄	—	2	2	no	—
631	C₂×C₃×C₄	—	2	2	no	—
632	C₂×C₃×C₄	—	2	2	no	—
633	C₂×C₃×C₄	—	2	1	no	—
634	C₂×C₃×C₄	—	2	1	no	—
635	C₂×C₃×C₄	—	2	1	no	—
636	C₂×C₃×C₄	—	2	2	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	2	no	—
641	C₂×C₃×C₄	—	4	8	no	—
642	C₂×C₃×C₄	—	4	4	no	—
643	C₂×C₃×C₄	—	4	4	no	—
644	C₂×C₃×C₄	C₂×#41	1	2	yes	—
645	C₂×C₃×C₄	C₂×#41	1	4	yes	—
646	C₂×C₃×C₄	C₂×#41	1	4	yes	—
647	C₂×C₃×C₄	C₂×#41	1	2	yes	—
648	C₂×C₃×C₄	C₂×#41	1	2	yes	—
649	C₂×C₃×C₄	C₂×#41	1	2	yes	—
650	C₂×C₃×C₄	C₂×#41	1	2	yes	—
651	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
652	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
653	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
654	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
655	C₂×Q₈	—	2	2	no	—
656	C₂×Q₈	—	2	2	no	—
657	C₂×Q₈	—	2	2	no	—
658	C₂×Q₈	—	2	2	no	—
659	C₂×Q₈	—	2	2	no	—
660	C₂×Q₈	C₃×#41	1	4	yes	—
661	C₂×D₄	—	2	2	no	—
662	C₂×D₄	—	2	2	no	—
663	C₂×D₄	—	4	1	no	—
664	C₂²×C₄	—	2	4	no	—
665	C₂²×C₄	—	2	4	no	—
666	C₂²×C₄	—	2	2	no	—
667	C₂²×C₄	—	2	2	no	—
668	C₂²×C₄	—	2	2	no	—
669	C₂²×C₄	—	2	2	no	—
670	C₂²×C₄	—	2	2	no	—
671	C₂²×C₄	—	2	2	no	—
672	C₂²×C₄	—	4	2	no	—
673	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
674	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
675	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
676	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
677	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
678	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
679	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
680	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
681	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
682	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
683	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
684	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
685	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
686	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
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	1	yes	characteristic
694	C₄⋊C₄	—	2	4	no	—
695	C₄⋊C₄	—	2	2	no	—
696	C₄⋊C₄	—	2	2	no	—
697	C₄⋊C₄	—	2	2	no	—
698	C₄⋊C₄	—	2	2	no	—
699	C₄⋊C₄	—	2	2	no	—
700	C₄⋊C₄	—	2	4	no	—
701	C₄⋊C₄	—	2	4	no	—
702	C₄⋊C₄	—	2	4	no	—
703	C₄⋊C₄	—	2	2	no	—
704	C₄⋊C₄	—	2	2	no	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	4	no	—
709	C₄⋊C₄	—	2	4	no	—
710	C₄⋊C₄	—	2	4	no	—
711	C₄⋊C₄	—	2	4	no	—
712	C₄⋊C₄	—	2	4	no	—
713	C₄⋊C₄	—	4	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	2	no	—
719	C₄⋊C₄	—	4	2	no	—
720	C₄⋊C₄	—	4	2	no	—
721	C₄⋊C₄	—	4	2	no	—
722	C₄⋊C₄	C₃×#41	1	4	yes	—
723	C₂²⋊C₄	—	2	2	no	—
724	C₂²⋊C₄	—	2	2	no	—
725	C₂²⋊C₄	—	2	4	no	—
726	C₂²⋊C₄	—	2	2	no	—
727	C₂²⋊C₄	—	2	2	no	—
728	C₂²⋊C₄	—	2	4	no	—
729	C₂²⋊C₄	—	2	4	no	—
730	C₂²⋊C₄	—	2	2	no	—
731	C₂²⋊C₄	—	2	2	no	—
732	C₂²⋊C₄	—	2	2	no	—
733	C₂²⋊C₄	—	2	2	no	—
734	C₂²⋊C₄	—	4	2	no	—
735	C₂²⋊C₄	—	4	2	no	—
736	C₂²⋊C₄	—	4	2	no	—
737	C₂²⋊C₄	—	4	2	no	—
738	C₂²⋊C₄	—	4	1	no	—
739	C₂²⋊C₄	—	4	1	no	—
740	C₄²	—	2	4	no	—
741	C₄²	—	2	4	no	—
742	C₄²	—	2	4	no	—
743	C₄²	—	2	2	no	—
744	C₄²	—	2	2	no	—
745	C₄²	—	2	4	no	—
746	C₄²	—	2	2	no	—
747	C₄²	—	2	2	no	—
748	C₄²	—	2	4	no	—
749	C₄²	—	4	2	no	—
750	C₄²	—	4	2	no	—
751	C₄²	—	4	2	no	—
752	C₄²	—	4	2	no	—
753	C₄²	C₃×#41	1	4	yes	—
754	C₂²×C₃	—	2	2	no	—
755	C₂²×C₃	—	2	2	no	—
756	C₂²×C₃	—	2	2	no	—
757	C₂²×C₃	—	4	1	no	—
758	C₂²×C₃	—	4	1	no	—
759	C₂²×C₃	—	4	1	no	—
760	C₂²×C₃	—	4	1	no	—
761	C₂²×C₃	—	4	1	no	—
762	C₂²×C₃	—	4	1	no	—
763	C₂²×C₃	—	4	1	no	—
764	C₂²×C₃	—	4	1	no	—
765	C₂²×C₃	—	4	1	no	—
766	C₂²×C₃	—	4	1	no	—
767	C₂²×C₃	—	4	1	no	—
768	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
769	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
770	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
771	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
772	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
773	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
774	C₂²×C₃	#585	1	1	yes	characteristic
775	C₃×C₄	—	2	4	no	—
776	C₃×C₄	—	2	2	no	—
777	C₃×C₄	—	2	2	no	—
778	C₃×C₄	—	2	2	no	—
779	C₃×C₄	—	2	2	no	—
780	C₃×C₄	—	2	4	no	—
781	C₃×C₄	—	4	1	no	—
782	C₃×C₄	—	4	1	no	—
783	C₃×C₄	—	4	2	no	—
784	C₃×C₄	—	4	1	no	—
785	C₃×C₄	—	4	1	no	—
786	C₃×C₄	—	4	1	no	—
787	C₃×C₄	—	4	2	no	—
788	C₃×C₄	—	4	2	no	—
789	C₃×C₄	—	4	2	no	—
790	C₃×C₄	—	4	1	no	—
791	C₃×C₄	—	4	2	no	—
792	C₃×C₄	—	4	1	no	—
793	C₃×C₄	—	4	2	no	—
794	C₃×C₄	—	4	1	no	—
795	C₃×C₄	#529	1	4	yes	—
796	C₂³	—	2	1	no	—
797	C₂³	—	2	1	no	—
798	C₂³	—	2	1	no	—
799	C₂³	—	2	1	no	—
800	C₂³	—	2	1	no	—
801	C₂³	—	2	1	no	—
802	C₂³	—	2	1	no	—
803	C₂³	—	2	1	no	—
804	C₂³	—	2	1	no	—
805	C₂³	—	2	1	no	—
806	C₂³	—	2	1	no	—
807	C₂³	—	2	1	no	—
808	C₂³	—	2	1	no	—
809	C₂³	C₃×2₋¹⁺⁴	1	2	yes	—
810	C₂³	C₂⁵×C₃	1	1	yes	characteristic
811	Q₈	—	2	8	no	—
812	Q₈	—	2	8	no	—
813	D₄	—	4	4	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	1	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	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	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	1	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	2	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	1	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	4	8	no	—
869	C₂×C₄	—	4	4	no	—
870	C₂×C₄	—	4	4	no	—
871	C₂×C₄	C₂×C₃×#41	1	2	yes	—
872	C₂×C₄	C₂×C₃×#41	1	4	yes	—
873	C₂×C₄	C₂×C₃×#41	1	4	yes	—
874	C₂×C₄	C₂×C₃×#41	1	2	yes	—
875	C₂×C₄	C₂×C₃×#41	1	2	yes	—
876	C₂×C₄	C₂×C₃×#41	1	2	yes	—
877	C₂×C₄	C₂×C₃×#41	1	2	yes	—
878	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
879	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
880	C₂×C₃	—	4	2	no	—
881	C₂×C₃	—	8	1	no	—
882	C₂×C₃	C₂×#529	1	1	yes	characteristic
883	C₂×C₃	#3492	1	1	yes	characteristic
884	C₂×C₃	#3495	1	1	yes	characteristic
885	C₂×C₃	#3517	1	1	yes	characteristic
886	C₂×C₃	#3518	1	1	yes	characteristic
887	C₂×C₃	#3520	1	1	yes	characteristic
888	C₂×C₃	#3523	1	1	yes	characteristic
889	C₂²	—	2	2	no	—
890	C₂²	—	2	2	no	—
891	C₂²	—	2	2	no	—
892	C₂²	—	4	1	no	—
893	C₂²	—	4	1	no	—
894	C₂²	—	4	1	no	—
895	C₂²	—	4	1	no	—
896	C₂²	—	4	1	no	—
897	C₂²	—	4	1	no	—
898	C₂²	—	4	1	no	—
899	C₂²	—	4	1	no	—
900	C₂²	—	4	1	no	—
901	C₂²	—	4	1	no	—
902	C₂²	—	4	1	no	—
903	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
904	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
905	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
906	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
907	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
908	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
909	C₂²	C₃×#585	1	1	yes	characteristic
910	C₄	—	2	4	no	—
911	C₄	—	2	2	no	—
912	C₄	—	2	2	no	—
913	C₄	—	2	2	no	—
914	C₄	—	2	2	no	—
915	C₄	—	2	4	no	—
916	C₄	—	4	1	no	—
917	C₄	—	4	1	no	—
918	C₄	—	4	2	no	—
919	C₄	—	4	1	no	—
920	C₄	—	4	1	no	—
921	C₄	—	4	1	no	—
922	C₄	—	4	2	no	—
923	C₄	—	4	2	no	—
924	C₄	—	4	2	no	—
925	C₄	—	4	1	no	—
926	C₄	—	4	2	no	—
927	C₄	—	4	2	no	—
928	C₄	—	4	1	no	—
929	C₄	—	4	1	no	—
930	C₄	C₃×#529	1	4	yes	—
931	C₃	#35945	1	1	yes	characteristic, direct product factor, Sylow
932	C₂	—	4	2	no	—
933	C₂	—	8	1	no	—
934	C₂	C₂×C₃×#529	1	1	yes	characteristic
935	C₂	C₃×#3492	1	1	yes	characteristic
936	C₂	C₃×#3495	1	1	yes	characteristic
937	C₂	C₃×#3517	1	1	yes	characteristic
938	C₂	C₃×#3518	1	1	yes	characteristic
939	C₂	C₃×#3520	1	1	yes	characteristic
940	C₂	C₃×#3523	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₃×#2654	C₂	semidirect
2. C₃×#2647	C₂	semidirect
3. C₃×#2590	C₂	semidirect
4. C₃×#2581	C₂	semidirect
5. C₃×#2573	C₂	semidirect
7. C₃×#2533	C₂	semidirect
9. C₃×#2497	C₂	semidirect
10. C₃×#2496	C₂	semidirect
12. C₃×#2469	C₂	semidirect
13. C₃×#2423	C₂	semidirect
14. C₃×#2423	C₂	semidirect
16. C₃×#2396	C₂	semidirect
17. C₃×#2362	C₂	semidirect
18. C₃×#2360	C₂	semidirect
20. C₃×Q₈×C₄⋊C₄	C₂	semidirect
21. C₃×#2347	C₂	semidirect
22. C₃×#2344	C₂	semidirect
23. C₃×#2276	C₂	semidirect
24. #35945	C₃	direct (N × H)
124. #2654	C₂×C₃	semidirect
125. #2647	C₂×C₃	semidirect
126. #2590	C₂×C₃	semidirect
127. #2581	C₂×C₃	semidirect
128. #2573	C₂×C₃	semidirect
130. #2533	C₂×C₃	semidirect
132. #2497	C₂×C₃	semidirect
133. #2496	C₂×C₃	semidirect
135. #2469	C₂×C₃	semidirect
136. #2423	C₂×C₃	semidirect
137. #2423	C₂×C₃	semidirect
139. #2396	C₂×C₃	semidirect
140. #2362	C₂×C₃	semidirect
141. #2360	C₂×C₃	semidirect
143. Q₈×C₄⋊C₄	C₂×C₃	semidirect
144. #2347	C₂×C₃	semidirect
145. #2344	C₂×C₃	semidirect
146. #2276	C₂×C₃	semidirect
931. C₃	#35945	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#2654	2
C₃×#2647	2
C₃×#2590	2
C₃×#2581	2
C₃×#2573	2
C₃×#2538	2
C₃×#2533	2
C₃×#2526	2
C₃×#2497	2
C₃×#2496	2
C₃×#2479	2
C₃×#2469	2
C₃×#2423	2
C₃×#2398	2
C₃×#2396	2
C₃×#2362	2
C₃×#2360	2
C₃×#2352	2
C₃×Q₈×C₄⋊C₄	2
C₃×#2347	2
C₃×#2344	2
C₃×#2276	2
#35945	3

Subgroups — C3×#35945 #10654552

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#35945 #10654552