Subgroups — C₃×#35963 #10654570

Order 768.

1680 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2667	C₂	1	2	yes	maximal, complemented
2	C₃×#2647	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2589	C₂	1	2	yes	maximal, complemented
4	C₃×#2587	C₂	1	2	yes	maximal, complemented
5	C₃×#2569	C₂	1	2	yes	maximal, complemented
6	C₃×#2552	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#2550	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2497	C₂	1	2	yes	maximal, complemented
9	C₃×#2454	C₂	1	1	yes	maximal, characteristic
10	C₃×#2454	C₂	1	1	yes	maximal, characteristic
11	C₃×#2454	C₂	1	1	yes	maximal, characteristic
12	C₃×#2452	C₂	1	1	yes	maximal, characteristic
13	C₃×#2438	C₂	1	2	yes	maximal, complemented
14	C₃×#2423	C₂	1	2	yes	maximal, complemented
15	C₃×#2402	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2396	C₂	1	2	yes	maximal, complemented
17	C₃×#2370	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#2370	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#2370	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×#2365	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×#2357	C₂	1	1	yes	maximal, characteristic
22	C₃×#2354	C₂	1	1	yes	maximal, characteristic
23	C₃×#2275	C₂	1	1	yes	maximal, characteristic
24	#35963	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₃×#125	C₂²	1	1	yes	characteristic
27	C₂×C₃×#125	C₂²	1	1	yes	characteristic
28	C₂×C₃×#125	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
30	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	—
31	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
33	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
34	C₂×C₃×#117	C₂²	1	2	yes	—
35	C₃×#400	C₂²	1	2	yes	—
36	C₃×#400	C₂²	1	2	yes	—
37	C₃×#400	C₂²	1	1	yes	characteristic
38	C₃×#400	C₂²	1	1	yes	characteristic
39	C₃×#400	C₂²	1	1	yes	characteristic
40	C₃×#400	C₂²	1	1	yes	characteristic
41	C₃×#399	C₂²	1	2	yes	—
42	C₃×#399	C₂²	1	2	yes	—
43	C₃×#399	C₂²	1	2	yes	—
44	C₃×#398	C₂²	1	2	yes	—
45	C₃×#398	C₂²	1	2	yes	—
46	C₃×#398	C₂²	1	2	yes	—
47	C₃×#398	C₂²	1	1	yes	characteristic
48	C₃×#398	C₂²	1	1	yes	characteristic
49	C₃×#398	C₂²	1	1	yes	characteristic
50	C₃×#398	C₂²	1	1	yes	characteristic
51	C₃×#398	C₂²	1	2	yes	—
52	C₃×#398	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×#396	C₂²	1	2	yes	—
57	C₃×#395	C₂²	1	2	yes	—
58	C₃×#393	C₂²	1	2	yes	—
59	C₃×#391	C₂²	1	2	yes	—
60	C₃×#391	C₂²	1	2	yes	—
61	C₃×#390	C₂²	1	1	yes	characteristic
62	C₃×#390	C₂²	1	1	yes	characteristic
63	C₃×#390	C₂²	1	1	yes	characteristic
64	C₃×#390	C₂²	1	1	yes	characteristic
65	C₃×#389	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
70	C₃×#389	C₂²	1	2	yes	—
71	C₃×#389	C₂²	1	2	yes	—
72	C₃×#389	C₂²	1	2	yes	—
73	C₃×#389	C₂²	1	1	yes	characteristic
74	C₃×#389	C₂²	1	1	yes	characteristic
75	C₃×#389	C₂²	1	1	yes	characteristic
76	C₃×#389	C₂²	1	2	yes	—
77	C₃×#389	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×#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×#387	C₂²	1	2	yes	—
88	C₃×#387	C₂²	1	2	yes	—
89	C₃×#387	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×#384	C₂²	1	1	yes	characteristic
95	C₃×#384	C₂²	1	2	yes	—
96	C₃×#382	C₂²	1	1	yes	characteristic
97	C₃×#381	C₂²	1	2	yes	—
98	C₃×#380	C₂²	1	2	yes	—
99	C₃×#380	C₂²	1	2	yes	—
100	C₃×#380	C₂²	1	2	yes	—
101	C₃×#380	C₂²	1	2	yes	—
102	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
103	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
104	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
105	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
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	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	1	yes	characteristic
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×C₄⋊C₄	C₂²	1	1	yes	characteristic
117	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
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×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
122	C₃×#376	C₂²	1	1	yes	characteristic
123	C₂×C₃×#95	C₂²	1	2	yes	—
124	#2667	C₂×C₃	1	2	yes	complemented
125	#2647	C₂×C₃	1	1	yes	characteristic, complemented
126	#2589	C₂×C₃	1	2	yes	complemented
127	#2587	C₂×C₃	1	2	yes	complemented
128	#2569	C₂×C₃	1	2	yes	complemented
129	#2552	C₂×C₃	1	1	yes	characteristic, complemented
130	#2550	C₂×C₃	1	1	yes	characteristic, complemented
131	#2497	C₂×C₃	1	2	yes	complemented
132	#2454	C₂×C₃	1	1	yes	characteristic
133	#2454	C₂×C₃	1	1	yes	characteristic
134	#2454	C₂×C₃	1	1	yes	characteristic
135	#2452	C₂×C₃	1	1	yes	characteristic
136	#2438	C₂×C₃	1	2	yes	complemented
137	#2423	C₂×C₃	1	2	yes	complemented
138	#2402	C₂×C₃	1	1	yes	characteristic, complemented
139	#2396	C₂×C₃	1	2	yes	complemented
140	#2370	C₂×C₃	1	1	yes	characteristic, complemented
141	#2370	C₂×C₃	1	1	yes	characteristic, complemented
142	#2370	C₂×C₃	1	1	yes	characteristic, complemented
143	#2365	C₂×C₃	1	1	yes	characteristic, complemented
144	#2357	C₂×C₃	1	1	yes	characteristic
145	#2354	C₂×C₃	1	1	yes	characteristic
146	#2275	C₂×C₃	1	1	yes	characteristic
147	C₂²×C₃×Q₈	C₂³	1	2	yes	—
148	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
149	C₂³×C₃×C₄	C₂³	1	2	yes	—
150	C₂³×C₃×C₄	C₂³	1	2	yes	—
151	C₂³×C₃×C₄	C₂³	1	2	yes	—
152	C₃×C₄⋊Q₈	—	2	4	no	—
153	C₃×#125	—	2	4	no	—
154	C₃×#125	—	2	4	no	—
155	C₃×#125	—	2	4	no	—
156	C₃×C₂²⋊Q₈	—	4	4	no	—
157	C₃×C₄×Q₈	—	4	4	no	—
158	C₃×C₄×D₄	—	2	4	no	—
159	C₃×C₄×D₄	—	2	4	no	—
160	C₃×C₄×D₄	Q₈	1	8	yes	complemented
161	C₃×#117	—	4	4	no	—
162	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
163	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
164	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
175	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
176	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
181	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
182	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
183	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
184	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	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	2	yes	—
193	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
194	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
195	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
196	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
197	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
198	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
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×C₄²	C₂³	1	1	yes	characteristic
210	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
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	2	yes	—
216	C₂×C₃×C₄²	C₂³	1	2	yes	—
217	C₂×C₃×C₄²	C₂³	1	2	yes	—
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	1	yes	characteristic
223	C₃×#95	C₂³	1	1	yes	characteristic
224	C₃×#95	C₂³	1	2	yes	—
225	C₃×#95	C₂³	1	2	yes	—
226	C₃×#95	C₂³	1	2	yes	—
227	C₃×#95	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
235	C₃×#95	C₂³	1	1	yes	characteristic
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	2	yes	—
240	C₃×#95	C₂³	1	1	yes	characteristic
241	C₃×#95	C₂³	1	2	yes	—
242	C₃×#95	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	1	yes	characteristic
247	C₃×#95	C₂³	1	2	yes	—
248	C₃×#95	C₂³	1	1	yes	characteristic
249	C₃×#95	C₂³	1	1	yes	characteristic
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	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
257	C₂×#125	C₂²×C₃	1	1	yes	characteristic
258	C₂×#125	C₂²×C₃	1	1	yes	characteristic
259	C₂×#125	C₂²×C₃	1	1	yes	characteristic
260	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
261	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	—
262	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
263	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
264	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
265	C₂×#117	C₂²×C₃	1	2	yes	—
266	#400	C₂²×C₃	1	1	yes	characteristic
267	#400	C₂²×C₃	1	2	yes	—
268	#400	C₂²×C₃	1	1	yes	characteristic
269	#400	C₂²×C₃	1	2	yes	—
270	#400	C₂²×C₃	1	1	yes	characteristic
271	#400	C₂²×C₃	1	1	yes	characteristic
272	#399	C₂²×C₃	1	2	yes	—
273	#399	C₂²×C₃	1	2	yes	—
274	#399	C₂²×C₃	1	2	yes	—
275	#398	C₂²×C₃	1	2	yes	—
276	#398	C₂²×C₃	1	2	yes	—
277	#398	C₂²×C₃	1	2	yes	—
278	#398	C₂²×C₃	1	1	yes	characteristic
279	#398	C₂²×C₃	1	2	yes	—
280	#398	C₂²×C₃	1	1	yes	characteristic
281	#398	C₂²×C₃	1	1	yes	characteristic
282	#398	C₂²×C₃	1	1	yes	characteristic
283	#398	C₂²×C₃	1	2	yes	—
284	#396	C₂²×C₃	1	2	yes	—
285	#396	C₂²×C₃	1	2	yes	—
286	#396	C₂²×C₃	1	2	yes	—
287	#396	C₂²×C₃	1	2	yes	—
288	#395	C₂²×C₃	1	2	yes	—
289	#393	C₂²×C₃	1	2	yes	—
290	#391	C₂²×C₃	1	2	yes	—
291	#391	C₂²×C₃	1	2	yes	—
292	#390	C₂²×C₃	1	1	yes	characteristic
293	#390	C₂²×C₃	1	1	yes	characteristic
294	#390	C₂²×C₃	1	1	yes	characteristic
295	#390	C₂²×C₃	1	1	yes	characteristic
296	#389	C₂²×C₃	1	2	yes	—
297	#389	C₂²×C₃	1	2	yes	—
298	#389	C₂²×C₃	1	2	yes	—
299	#389	C₂²×C₃	1	1	yes	characteristic
300	#389	C₂²×C₃	1	1	yes	characteristic
301	#389	C₂²×C₃	1	1	yes	characteristic
302	#389	C₂²×C₃	1	1	yes	characteristic
303	#389	C₂²×C₃	1	1	yes	characteristic
304	#389	C₂²×C₃	1	2	yes	—
305	#389	C₂²×C₃	1	2	yes	—
306	#389	C₂²×C₃	1	1	yes	characteristic
307	#389	C₂²×C₃	1	1	yes	characteristic
308	#389	C₂²×C₃	1	1	yes	characteristic
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	#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	#385	C₂²×C₃	1	2	yes	—
322	#385	C₂²×C₃	1	2	yes	—
323	#385	C₂²×C₃	1	2	yes	—
324	#385	C₂²×C₃	1	2	yes	—
325	#384	C₂²×C₃	1	1	yes	characteristic
326	#384	C₂²×C₃	1	2	yes	—
327	#382	C₂²×C₃	1	1	yes	characteristic
328	#381	C₂²×C₃	1	2	yes	—
329	#380	C₂²×C₃	1	2	yes	—
330	#380	C₂²×C₃	1	2	yes	—
331	#380	C₂²×C₃	1	2	yes	—
332	#380	C₂²×C₃	1	2	yes	—
333	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
334	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
335	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
336	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
337	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
338	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
339	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
340	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
341	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
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	2	yes	—
345	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
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	1	yes	characteristic
349	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
350	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
351	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
352	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
353	#376	C₂²×C₃	1	1	yes	characteristic
354	C₂×#95	C₂²×C₃	1	2	yes	—
355	C₂⁴×C₃	C₂⁴	1	2	yes	—
356	C₂×C₃×Q₈	—	2	4	no	—
357	C₂×C₃×Q₈	—	2	4	no	—
358	C₂×C₃×Q₈	—	4	2	no	—
359	C₂×C₃×D₄	—	2	2	no	—
360	C₂×C₃×D₄	—	2	2	no	—
361	C₂×C₃×D₄	C₂×Q₈	1	4	yes	—
362	C₂²×C₃×C₄	—	2	4	no	—
363	C₂²×C₃×C₄	—	2	4	no	—
364	C₂²×C₃×C₄	—	4	2	no	—
365	C₂²×C₃×C₄	—	4	2	no	—
366	C₂²×C₃×C₄	—	4	2	no	—
367	C₂²×C₃×C₄	—	4	2	no	—
368	C₂²×C₃×C₄	—	4	2	no	—
369	C₂²×C₃×C₄	—	4	2	no	—
370	C₂²×C₃×C₄	C₂×Q₈	1	8	yes	—
371	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
372	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
373	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
374	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
375	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
376	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
377	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
378	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
379	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
380	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
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	2	yes	—
386	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
387	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
388	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
393	C₃×C₄⋊C₄	—	2	4	no	—
394	C₃×C₄⋊C₄	—	2	4	no	—
395	C₃×C₄⋊C₄	—	2	4	no	—
396	C₃×C₄⋊C₄	—	2	4	no	—
397	C₃×C₄⋊C₄	—	2	4	no	—
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	4	no	—
403	C₃×C₄⋊C₄	—	2	2	no	—
404	C₃×C₄⋊C₄	—	2	2	no	—
405	C₃×C₄⋊C₄	—	2	2	no	—
406	C₃×C₄⋊C₄	—	2	2	no	—
407	C₃×C₄⋊C₄	—	4	1	no	—
408	C₃×C₄⋊C₄	—	4	2	no	—
409	C₃×C₄⋊C₄	—	4	2	no	—
410	C₃×C₄⋊C₄	—	4	1	no	—
411	C₃×C₄⋊C₄	—	4	2	no	—
412	C₃×C₄⋊C₄	—	4	1	no	—
413	C₃×C₄⋊C₄	—	4	1	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	1	no	—
418	C₃×C₄⋊C₄	—	4	2	no	—
419	C₃×C₄⋊C₄	—	4	2	no	—
420	C₃×C₄⋊C₄	—	4	1	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	C₂×Q₈	1	4	yes	—
427	C₃×C₄⋊C₄	#41	1	4	yes	—
428	C₃×C₄⋊C₄	#41	1	4	yes	—
429	C₃×C₂²⋊C₄	—	2	4	no	—
430	C₃×C₂²⋊C₄	—	2	4	no	—
431	C₃×C₂²⋊C₄	—	2	4	no	—
432	C₃×C₂²⋊C₄	—	4	2	no	—
433	C₃×C₂²⋊C₄	—	4	2	no	—
434	C₃×C₂²⋊C₄	—	4	2	no	—
435	C₃×C₂²⋊C₄	—	4	2	no	—
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	C₂×Q₈	1	8	yes	—
440	C₃×C₄²	—	2	2	no	—
441	C₃×C₄²	—	2	2	no	—
442	C₃×C₄²	—	2	2	no	—
443	C₃×C₄²	—	2	2	no	—
444	C₃×C₄²	—	2	2	no	—
445	C₃×C₄²	—	2	2	no	—
446	C₃×C₄²	—	2	4	no	—
447	C₃×C₄²	—	4	2	no	—
448	C₃×C₄²	—	4	2	no	—
449	C₃×C₄²	—	4	2	no	—
450	C₃×C₄²	—	4	2	no	—
451	C₃×C₄²	—	4	2	no	—
452	C₃×C₄²	—	4	2	no	—
453	C₃×C₄²	C₂×Q₈	1	4	yes	—
454	C₂²×Q₈	C₂³×C₃	1	2	yes	—
455	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
456	C₂³×C₄	C₂³×C₃	1	2	yes	—
457	C₂³×C₄	C₂³×C₃	1	2	yes	—
458	C₂³×C₄	C₂³×C₃	1	2	yes	—
459	C₄⋊Q₈	—	2	4	no	—
460	#125	—	2	4	no	—
461	#125	—	2	4	no	—
462	#125	—	2	4	no	—
463	C₂²⋊Q₈	—	4	4	no	—
464	C₄×Q₈	—	4	4	no	—
465	C₄×D₄	—	2	4	no	—
466	C₄×D₄	—	2	4	no	—
467	C₄×D₄	C₃×Q₈	1	8	yes	complemented
468	#117	—	4	4	no	—
469	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
470	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
471	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
472	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
473	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
474	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
475	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
476	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
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	2	yes	—
480	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
481	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
482	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
483	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
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	2	yes	—
488	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
489	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
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	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	1	yes	characteristic
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	1	yes	characteristic
503	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
504	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
505	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
506	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
507	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
508	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
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	2	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
513	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
514	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
515	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
516	C₂×C₄²	C₂³×C₃	1	2	yes	—
517	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
518	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
519	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
520	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
521	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
522	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
523	C₂×C₄²	C₂³×C₃	1	2	yes	—
524	C₂×C₄²	C₂³×C₃	1	2	yes	—
525	C₂×C₄²	C₂³×C₃	1	2	yes	—
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	#95	C₂³×C₃	1	1	yes	characteristic
531	#95	C₂³×C₃	1	2	yes	—
532	#95	C₂³×C₃	1	2	yes	—
533	#95	C₂³×C₃	1	2	yes	—
534	#95	C₂³×C₃	1	1	yes	characteristic
535	#95	C₂³×C₃	1	1	yes	characteristic
536	#95	C₂³×C₃	1	1	yes	characteristic
537	#95	C₂³×C₃	1	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
549	#95	C₂³×C₃	1	2	yes	—
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	1	yes	characteristic
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	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	C₂³×C₃	—	2	2	no	—
564	C₂³×C₃	—	2	2	no	—
565	C₂³×C₃	—	2	2	no	—
566	C₂³×C₃	—	2	2	no	—
567	C₂³×C₃	—	2	2	no	—
568	C₂³×C₃	—	2	2	no	—
569	C₂³×C₃	C₂²×Q₈	1	4	yes	—
570	C₂³×C₃	C₂⁵	1	1	yes	characteristic
571	C₃×Q₈	—	4	8	no	—
572	C₃×D₄	—	2	8	no	—
573	C₂×C₃×C₄	—	2	1	no	—
574	C₂×C₃×C₄	—	2	2	no	—
575	C₂×C₃×C₄	—	2	2	no	—
576	C₂×C₃×C₄	—	2	1	no	—
577	C₂×C₃×C₄	—	2	1	no	—
578	C₂×C₃×C₄	—	2	2	no	—
579	C₂×C₃×C₄	—	2	2	no	—
580	C₂×C₃×C₄	—	2	2	no	—
581	C₂×C₃×C₄	—	2	2	no	—
582	C₂×C₃×C₄	—	2	1	no	—
583	C₂×C₃×C₄	—	2	1	no	—
584	C₂×C₃×C₄	—	2	1	no	—
585	C₂×C₃×C₄	—	2	1	no	—
586	C₂×C₃×C₄	—	2	1	no	—
587	C₂×C₃×C₄	—	2	1	no	—
588	C₂×C₃×C₄	—	2	1	no	—
589	C₂×C₃×C₄	—	2	1	no	—
590	C₂×C₃×C₄	—	2	1	no	—
591	C₂×C₃×C₄	—	2	1	no	—
592	C₂×C₃×C₄	—	2	1	no	—
593	C₂×C₃×C₄	—	2	1	no	—
594	C₂×C₃×C₄	—	2	1	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	2	no	—
599	C₂×C₃×C₄	—	2	2	no	—
600	C₂×C₃×C₄	—	2	2	no	—
601	C₂×C₃×C₄	—	2	1	no	—
602	C₂×C₃×C₄	—	2	1	no	—
603	C₂×C₃×C₄	—	2	1	no	—
604	C₂×C₃×C₄	—	2	2	no	—
605	C₂×C₃×C₄	—	2	2	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	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	2	no	—
619	C₂×C₃×C₄	—	2	2	no	—
620	C₂×C₃×C₄	—	2	1	no	—
621	C₂×C₃×C₄	—	2	1	no	—
622	C₂×C₃×C₄	—	2	1	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	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	—	4	8	no	—
631	C₂×C₃×C₄	—	8	4	no	—
632	C₂×C₃×C₄	—	8	4	no	—
633	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
634	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
635	C₂×C₃×C₄	C₂²×Q₈	1	4	yes	—
636	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
637	C₂×C₃×C₄	C₂×#41	1	4	yes	—
638	C₂×C₃×C₄	C₂×#41	1	4	yes	—
639	C₂×C₃×C₄	C₂×#41	1	2	yes	—
640	C₂×C₃×C₄	C₂×#41	1	2	yes	—
641	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
642	C₂⁴	C₂⁴×C₃	1	2	yes	—
643	C₂×Q₈	—	2	4	no	—
644	C₂×Q₈	—	2	4	no	—
645	C₂×Q₈	—	4	2	no	—
646	C₂×D₄	—	2	2	no	—
647	C₂×D₄	—	2	2	no	—
648	C₂×D₄	C₂×C₃×Q₈	1	4	yes	—
649	C₂²×C₄	—	2	4	no	—
650	C₂²×C₄	—	2	4	no	—
651	C₂²×C₄	—	4	2	no	—
652	C₂²×C₄	—	4	2	no	—
653	C₂²×C₄	—	4	2	no	—
654	C₂²×C₄	—	4	2	no	—
655	C₂²×C₄	—	4	2	no	—
656	C₂²×C₄	—	4	2	no	—
657	C₂²×C₄	C₂×C₃×Q₈	1	8	yes	—
658	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
659	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
660	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
661	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
662	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
663	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
664	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
665	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
666	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
667	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
668	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
669	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
670	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
671	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
672	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
673	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
674	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
675	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
676	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
677	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
678	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
679	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
680	C₄⋊C₄	—	2	4	no	—
681	C₄⋊C₄	—	2	4	no	—
682	C₄⋊C₄	—	2	4	no	—
683	C₄⋊C₄	—	2	4	no	—
684	C₄⋊C₄	—	2	4	no	—
685	C₄⋊C₄	—	2	4	no	—
686	C₄⋊C₄	—	2	2	no	—
687	C₄⋊C₄	—	2	2	no	—
688	C₄⋊C₄	—	2	2	no	—
689	C₄⋊C₄	—	2	4	no	—
690	C₄⋊C₄	—	2	2	no	—
691	C₄⋊C₄	—	2	2	no	—
692	C₄⋊C₄	—	2	2	no	—
693	C₄⋊C₄	—	2	2	no	—
694	C₄⋊C₄	—	4	2	no	—
695	C₄⋊C₄	—	4	2	no	—
696	C₄⋊C₄	—	4	2	no	—
697	C₄⋊C₄	—	4	2	no	—
698	C₄⋊C₄	—	4	2	no	—
699	C₄⋊C₄	—	4	1	no	—
700	C₄⋊C₄	—	4	2	no	—
701	C₄⋊C₄	—	4	2	no	—
702	C₄⋊C₄	—	4	1	no	—
703	C₄⋊C₄	—	4	2	no	—
704	C₄⋊C₄	—	4	1	no	—
705	C₄⋊C₄	—	4	1	no	—
706	C₄⋊C₄	—	4	1	no	—
707	C₄⋊C₄	—	4	1	no	—
708	C₄⋊C₄	—	4	1	no	—
709	C₄⋊C₄	—	4	1	no	—
710	C₄⋊C₄	—	4	2	no	—
711	C₄⋊C₄	—	4	2	no	—
712	C₄⋊C₄	—	4	1	no	—
713	C₄⋊C₄	C₂×C₃×Q₈	1	4	yes	—
714	C₄⋊C₄	C₃×#41	1	4	yes	—
715	C₄⋊C₄	C₃×#41	1	4	yes	—
716	C₂²⋊C₄	—	2	4	no	—
717	C₂²⋊C₄	—	2	4	no	—
718	C₂²⋊C₄	—	2	4	no	—
719	C₂²⋊C₄	—	4	2	no	—
720	C₂²⋊C₄	—	4	2	no	—
721	C₂²⋊C₄	—	4	2	no	—
722	C₂²⋊C₄	—	4	2	no	—
723	C₂²⋊C₄	—	4	2	no	—
724	C₂²⋊C₄	—	4	2	no	—
725	C₂²⋊C₄	—	4	2	no	—
726	C₂²⋊C₄	C₂×C₃×Q₈	1	8	yes	—
727	C₄²	—	2	2	no	—
728	C₄²	—	2	2	no	—
729	C₄²	—	2	2	no	—
730	C₄²	—	2	2	no	—
731	C₄²	—	2	2	no	—
732	C₄²	—	2	2	no	—
733	C₄²	—	2	4	no	—
734	C₄²	—	4	2	no	—
735	C₄²	—	4	2	no	—
736	C₄²	—	4	2	no	—
737	C₄²	—	4	2	no	—
738	C₄²	—	4	2	no	—
739	C₄²	—	4	2	no	—
740	C₄²	C₂×C₃×Q₈	1	4	yes	—
741	C₂²×C₃	—	2	4	no	—
742	C₂²×C₃	—	2	4	no	—
743	C₂²×C₃	—	2	4	no	—
744	C₂²×C₃	—	4	2	no	—
745	C₂²×C₃	—	4	2	no	—
746	C₂²×C₃	—	4	2	no	—
747	C₂²×C₃	—	4	2	no	—
748	C₂²×C₃	C₂³×Q₈	1	1	yes	characteristic
749	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
750	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
751	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
752	C₂²×C₃	#585	1	1	yes	characteristic
753	C₂²×C₃	#585	1	1	yes	characteristic
754	C₂²×C₃	#585	1	1	yes	characteristic
755	C₃×C₄	—	2	2	no	—
756	C₃×C₄	—	2	4	no	—
757	C₃×C₄	—	2	2	no	—
758	C₃×C₄	—	2	4	no	—
759	C₃×C₄	—	2	2	no	—
760	C₃×C₄	—	2	4	no	—
761	C₃×C₄	—	4	1	no	—
762	C₃×C₄	—	4	1	no	—
763	C₃×C₄	—	4	2	no	—
764	C₃×C₄	—	4	1	no	—
765	C₃×C₄	—	4	1	no	—
766	C₃×C₄	—	4	1	no	—
767	C₃×C₄	—	4	2	no	—
768	C₃×C₄	—	4	2	no	—
769	C₃×C₄	—	4	1	no	—
770	C₃×C₄	—	4	1	no	—
771	C₃×C₄	—	4	1	no	—
772	C₃×C₄	—	4	1	no	—
773	C₃×C₄	—	4	1	no	—
774	C₃×C₄	—	4	1	no	—
775	C₃×C₄	—	4	2	no	—
776	C₃×C₄	#533	1	4	yes	—
777	C₂³	—	2	2	no	—
778	C₂³	—	2	2	no	—
779	C₂³	—	2	2	no	—
780	C₂³	—	2	2	no	—
781	C₂³	—	2	2	no	—
782	C₂³	—	2	2	no	—
783	C₂³	C₂²×C₃×Q₈	1	4	yes	—
784	C₂³	C₂⁵×C₃	1	1	yes	characteristic
785	Q₈	—	4	8	no	—
786	D₄	—	2	8	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	2	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	2	no	—
833	C₂×C₄	—	2	2	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	1	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	4	8	no	—
845	C₂×C₄	—	8	4	no	—
846	C₂×C₄	—	8	4	no	—
847	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
848	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
849	C₂×C₄	C₂²×C₃×Q₈	1	4	yes	—
850	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
851	C₂×C₄	C₂×C₃×#41	1	4	yes	—
852	C₂×C₄	C₂×C₃×#41	1	4	yes	—
853	C₂×C₄	C₂×C₃×#41	1	2	yes	—
854	C₂×C₄	C₂×C₃×#41	1	2	yes	—
855	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
856	C₂×C₃	—	4	4	no	—
857	C₂×C₃	C₂×#533	1	1	yes	characteristic
858	C₂×C₃	#3501	1	1	yes	characteristic
859	C₂×C₃	#3504	1	1	yes	characteristic
860	C₂×C₃	#3513	1	1	yes	characteristic
861	C₂×C₃	#3517	1	1	yes	characteristic
862	C₂×C₃	#3521	1	1	yes	characteristic
863	C₂×C₃	#3524	1	1	yes	characteristic
864	C₂²	—	2	4	no	—
865	C₂²	—	2	4	no	—
866	C₂²	—	2	4	no	—
867	C₂²	—	4	2	no	—
868	C₂²	—	4	2	no	—
869	C₂²	—	4	2	no	—
870	C₂²	—	4	2	no	—
871	C₂²	C₂³×C₃×Q₈	1	1	yes	characteristic
872	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
873	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
874	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
875	C₂²	C₃×#585	1	1	yes	characteristic
876	C₂²	C₃×#585	1	1	yes	characteristic
877	C₂²	C₃×#585	1	1	yes	characteristic
878	C₄	—	2	2	no	—
879	C₄	—	2	4	no	—
880	C₄	—	2	2	no	—
881	C₄	—	2	4	no	—
882	C₄	—	2	2	no	—
883	C₄	—	2	4	no	—
884	C₄	—	4	1	no	—
885	C₄	—	4	2	no	—
886	C₄	—	4	1	no	—
887	C₄	—	4	1	no	—
888	C₄	—	4	1	no	—
889	C₄	—	4	1	no	—
890	C₄	—	4	2	no	—
891	C₄	—	4	2	no	—
892	C₄	—	4	1	no	—
893	C₄	—	4	1	no	—
894	C₄	—	4	1	no	—
895	C₄	—	4	1	no	—
896	C₄	—	4	1	no	—
897	C₄	—	4	1	no	—
898	C₄	—	4	2	no	—
899	C₄	C₃×#533	1	4	yes	—
900	C₃	#35963	1	1	yes	characteristic, direct product factor, Sylow
901	C₂	—	4	4	no	—
902	C₂	C₂×C₃×#533	1	1	yes	characteristic
903	C₂	C₃×#3501	1	1	yes	characteristic
904	C₂	C₃×#3504	1	1	yes	characteristic
905	C₂	C₃×#3513	1	1	yes	characteristic
906	C₂	C₃×#3517	1	1	yes	characteristic
907	C₂	C₃×#3521	1	1	yes	characteristic
908	C₂	C₃×#3524	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×#2667	C₂	semidirect
2. C₃×#2647	C₂	semidirect
3. C₃×#2589	C₂	semidirect
4. C₃×#2587	C₂	semidirect
5. C₃×#2569	C₂	semidirect
6. C₃×#2552	C₂	semidirect
7. C₃×#2550	C₂	semidirect
8. C₃×#2497	C₂	semidirect
13. C₃×#2438	C₂	semidirect
14. C₃×#2423	C₂	semidirect
15. C₃×#2402	C₂	semidirect
16. C₃×#2396	C₂	semidirect
17. C₃×#2370	C₂	semidirect
18. C₃×#2370	C₂	semidirect
19. C₃×#2370	C₂	semidirect
20. C₃×#2365	C₂	semidirect
24. #35963	C₃	direct (N × H)
124. #2667	C₂×C₃	semidirect
125. #2647	C₂×C₃	semidirect
126. #2589	C₂×C₃	semidirect
127. #2587	C₂×C₃	semidirect
128. #2569	C₂×C₃	semidirect
129. #2552	C₂×C₃	semidirect
130. #2550	C₂×C₃	semidirect
131. #2497	C₂×C₃	semidirect
136. #2438	C₂×C₃	semidirect
137. #2423	C₂×C₃	semidirect
138. #2402	C₂×C₃	semidirect
139. #2396	C₂×C₃	semidirect
140. #2370	C₂×C₃	semidirect
141. #2370	C₂×C₃	semidirect
142. #2370	C₂×C₃	semidirect
143. #2365	C₂×C₃	semidirect
160. C₃×C₄×D₄	Q₈	semidirect
467. C₄×D₄	C₃×Q₈	semidirect
900. C₃	#35963	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×#2667	2
C₃×#2647	2
C₃×#2589	2
C₃×#2587	2
C₃×#2569	2
C₃×#2552	2
C₃×#2550	2
C₃×#2497	2
C₃×#2454	2
C₃×#2452	2
C₃×#2438	2
C₃×#2423	2
C₃×#2402	2
C₃×#2396	2
C₃×#2370	2
C₃×#2365	2
C₃×#2357	2
C₃×#2354	2
C₃×#2275	2
#35963	3

Subgroups — C3×#35963 #10654570

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#35963 #10654570