Subgroups — C₃×#40610 #10659217

Order 768.

1842 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2841	C₂	1	2	yes	maximal, complemented
2	C₃×#2788	C₂	1	2	yes	maximal, complemented
3	C₃×#2763	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2763	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2742	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#2729	C₂	1	2	yes	maximal, complemented
7	C₃×#2677	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2665	C₂	1	2	yes	maximal, complemented
9	C₃×#2628	C₂	1	2	yes	maximal, complemented
10	C₃×#2626	C₂	1	1	yes	maximal, characteristic
11	C₃×#2549	C₂	1	2	yes	maximal, complemented
12	C₃×#2505	C₂	1	2	yes	maximal, complemented
13	C₃×#2505	C₂	1	2	yes	maximal, complemented
14	C₃×#2439	C₂	1	2	yes	maximal, complemented
15	C₃×#2437	C₂	1	2	yes	maximal
16	C₃×#2434	C₂	1	2	yes	maximal, complemented
17	C₂×C₃×#393	C₂	1	1	yes	maximal, characteristic
18	C₃×#2342	C₂	1	2	yes	maximal
19	C₃×#2315	C₂	1	1	yes	maximal, characteristic
20	#40610	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂³×C₃×Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
23	C₂×C₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
24	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
26	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
27	C₂×C₃×#117	C₂²	1	2	yes	—
28	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₃×#400	C₂²	1	2	yes	complemented
33	C₃×#400	C₂²	1	2	yes	complemented
34	C₃×#400	C₂²	1	2	yes	complemented
35	C₃×#400	C₂²	1	2	yes	complemented
36	C₃×#400	C₂²	1	2	yes	complemented
37	C₃×#400	C₂²	1	2	yes	complemented
38	C₃×#399	C₂²	1	1	yes	characteristic
39	C₃×#399	C₂²	1	1	yes	characteristic
40	C₃×#399	C₂²	1	2	yes	—
41	C₃×#398	C₂²	1	2	yes	complemented
42	C₃×#398	C₂²	1	2	yes	complemented
43	C₃×#398	C₂²	1	2	yes	complemented
44	C₃×#398	C₂²	1	2	yes	complemented
45	C₃×#396	C₂²	1	2	yes	—
46	C₃×#396	C₂²	1	2	yes	—
47	C₃×#396	C₂²	1	2	yes	—
48	C₃×#396	C₂²	1	2	yes	—
49	C₃×#395	C₂²	1	2	yes	complemented
50	C₃×#395	C₂²	1	2	yes	complemented
51	C₃×#395	C₂²	1	2	yes	complemented
52	C₃×#395	C₂²	1	2	yes	complemented
53	C₃×#395	C₂²	1	2	yes	complemented
54	C₃×#395	C₂²	1	2	yes	complemented
55	C₃×#393	C₂²	1	1	yes	characteristic
56	C₃×#393	C₂²	1	1	yes	characteristic
57	C₃×#393	C₂²	1	2	yes	—
58	C₃×#393	C₂²	1	2	yes	—
59	C₃×#393	C₂²	1	1	yes	characteristic
60	C₃×#393	C₂²	1	1	yes	characteristic
61	C₃×#393	C₂²	1	2	yes	—
62	C₃×#393	C₂²	1	1	yes	characteristic
63	C₃×#393	C₂²	1	1	yes	characteristic
64	C₃×#391	C₂²	1	2	yes	complemented
65	C₃×#391	C₂²	1	2	yes	complemented
66	C₃×#391	C₂²	1	2	yes	complemented
67	C₃×#391	C₂²	1	2	yes	complemented
68	C₃×#389	C₂²	1	2	yes	complemented
69	C₃×#389	C₂²	1	2	yes	complemented
70	C₃×#389	C₂²	1	2	yes	complemented
71	C₃×#389	C₂²	1	2	yes	complemented
72	C₃×#388	C₂²	1	2	yes	—
73	C₃×#388	C₂²	1	2	yes	—
74	C₃×#388	C₂²	1	2	yes	—
75	C₃×#388	C₂²	1	2	yes	—
76	C₃×#387	C₂²	1	2	yes	complemented
77	C₃×#387	C₂²	1	2	yes	complemented
78	C₃×#387	C₂²	1	2	yes	complemented
79	C₃×#387	C₂²	1	2	yes	complemented
80	C₃×#385	C₂²	1	2	yes	—
81	C₃×#385	C₂²	1	1	yes	characteristic
82	C₃×#385	C₂²	1	2	yes	—
83	C₃×#385	C₂²	1	2	yes	—
84	C₃×#385	C₂²	1	2	yes	—
85	C₃×#385	C₂²	1	2	yes	—
86	C₃×#385	C₂²	1	2	yes	—
87	C₃×#385	C₂²	1	2	yes	—
88	C₃×#385	C₂²	1	1	yes	characteristic
89	C₃×#385	C₂²	1	1	yes	characteristic
90	C₃×#385	C₂²	1	2	yes	—
91	C₃×#385	C₂²	1	2	yes	—
92	C₃×#385	C₂²	1	1	yes	characteristic
93	C₃×#382	C₂²	1	2	yes	complemented
94	C₃×#382	C₂²	1	2	yes	complemented
95	C₃×#381	C₂²	1	2	yes	—
96	C₃×#380	C₂²	1	1	yes	characteristic
97	C₃×#380	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×#379	C₂²	1	2	yes	—
103	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
104	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
105	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
106	C₂×C₃×#95	C₂²	1	1	yes	characteristic
107	C₂×C₃×#95	C₂²	1	2	yes	—
108	#2841	C₂×C₃	1	2	yes	complemented
109	#2788	C₂×C₃	1	2	yes	complemented
110	#2763	C₂×C₃	1	1	yes	characteristic, complemented
111	#2763	C₂×C₃	1	1	yes	characteristic, complemented
112	#2742	C₂×C₃	1	1	yes	characteristic, complemented
113	#2729	C₂×C₃	1	2	yes	complemented
114	#2677	C₂×C₃	1	1	yes	characteristic, complemented
115	#2665	C₂×C₃	1	2	yes	complemented
116	#2628	C₂×C₃	1	2	yes	complemented
117	#2626	C₂×C₃	1	1	yes	characteristic
118	#2549	C₂×C₃	1	2	yes	complemented
119	#2505	C₂×C₃	1	2	yes	complemented
120	#2505	C₂×C₃	1	2	yes	complemented
121	#2439	C₂×C₃	1	2	yes	complemented
122	#2437	C₂×C₃	1	2	yes	—
123	#2434	C₂×C₃	1	2	yes	complemented
124	C₂×#393	C₂×C₃	1	1	yes	characteristic
125	#2342	C₂×C₃	1	2	yes	—
126	#2315	C₂×C₃	1	1	yes	characteristic
127	C₂⁵×C₃	C₂³	1	1	yes	characteristic
128	C₂²×C₃×Q₈	—	4	2	no	—
129	C₂²×C₃×Q₈	—	4	4	no	—
130	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
131	C₂²×C₃×Q₈	C₂³	1	2	yes	—
132	C₂²×C₃×Q₈	C₂³	1	2	yes	—
133	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
134	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
135	C₂³×C₃×C₄	C₂³	1	2	yes	—
136	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
137	C₂³×C₃×C₄	C₂³	1	2	yes	—
138	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
139	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
140	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
141	C₂³×C₃×C₄	C₂³	1	2	yes	—
142	C₃×C₄⋊Q₈	—	4	4	no	—
143	C₃×C₄⋊Q₈	—	4	4	no	—
144	C₃×C₂²⋊Q₈	—	4	4	no	—
145	C₃×C₂²⋊Q₈	—	4	2	no	—
146	C₃×C₂²⋊Q₈	—	4	4	no	—
147	C₃×#117	—	4	4	no	—
148	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
149	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
150	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
151	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
152	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
153	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
154	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
155	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
156	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
157	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
158	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
159	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
160	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
161	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
162	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
163	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
164	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
165	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
166	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
167	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
168	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
169	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
170	C₂×C₃×C₂²⋊C₄	—	4	4	no	—
171	C₂×C₃×C₂²⋊C₄	—	4	2	no	—
172	C₂×C₃×C₂²⋊C₄	—	4	2	no	—
173	C₂×C₃×C₂²⋊C₄	Q₈	1	8	yes	complemented
174	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
183	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
184	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
185	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
188	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
189	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
190	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
191	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
192	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
193	C₂×C₃×C₄²	C₂³	1	2	yes	—
194	C₂×C₃×C₄²	C₂³	1	2	yes	—
195	C₂×C₃×C₄²	C₂³	1	2	yes	—
196	C₂×C₃×C₄²	C₂³	1	2	yes	—
197	C₃×#95	C₂³	1	1	yes	characteristic
198	C₃×#95	C₂³	1	2	yes	—
199	C₃×#95	C₂³	1	2	yes	—
200	C₃×#95	C₂³	1	2	yes	—
201	C₃×#95	C₂³	1	2	yes	—
202	C₃×#95	C₂³	1	2	yes	—
203	C₃×#95	C₂³	1	1	yes	characteristic
204	C₃×#95	C₂³	1	2	yes	—
205	C₃×#95	C₂³	1	2	yes	—
206	C₃×#95	C₂³	1	2	yes	—
207	C₃×#95	C₂³	1	2	yes	—
208	C₃×#95	C₂³	1	2	yes	—
209	C₃×#95	C₂³	1	2	yes	—
210	C₃×#95	C₂³	1	2	yes	—
211	C₃×#95	C₂³	1	1	yes	characteristic
212	C₃×#95	C₂³	1	2	yes	—
213	C₃×#95	C₂³	1	2	yes	—
214	C₃×#95	C₂³	1	2	yes	—
215	C₃×#95	C₂³	1	2	yes	—
216	C₃×#95	C₂³	1	2	yes	—
217	C₃×#95	C₂³	1	2	yes	—
218	C₃×#95	C₂³	1	1	yes	characteristic
219	C₃×#95	C₂³	1	2	yes	—
220	C₃×#95	C₂³	1	2	yes	—
221	C₃×#95	C₂³	1	2	yes	—
222	C₃×#95	C₂³	1	2	yes	—
223	C₃×#95	C₂³	1	2	yes	—
224	C₃×#95	C₂³	1	2	yes	—
225	C₃×#95	C₂³	1	2	yes	—
226	C₂³×Q₈	C₂²×C₃	1	1	yes	characteristic
227	C₂×C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
228	C₂×C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
229	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
230	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
231	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
232	C₂×#117	C₂²×C₃	1	2	yes	—
233	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
234	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
235	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
236	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
237	#400	C₂²×C₃	1	2	yes	complemented
238	#400	C₂²×C₃	1	2	yes	complemented
239	#400	C₂²×C₃	1	2	yes	complemented
240	#400	C₂²×C₃	1	2	yes	complemented
241	#400	C₂²×C₃	1	2	yes	complemented
242	#400	C₂²×C₃	1	2	yes	complemented
243	#399	C₂²×C₃	1	2	yes	—
244	#399	C₂²×C₃	1	1	yes	characteristic
245	#399	C₂²×C₃	1	1	yes	characteristic
246	#398	C₂²×C₃	1	2	yes	complemented
247	#398	C₂²×C₃	1	2	yes	complemented
248	#398	C₂²×C₃	1	2	yes	complemented
249	#398	C₂²×C₃	1	2	yes	complemented
250	#396	C₂²×C₃	1	2	yes	—
251	#396	C₂²×C₃	1	2	yes	—
252	#396	C₂²×C₃	1	2	yes	—
253	#396	C₂²×C₃	1	2	yes	—
254	#395	C₂²×C₃	1	2	yes	complemented
255	#395	C₂²×C₃	1	2	yes	complemented
256	#395	C₂²×C₃	1	2	yes	complemented
257	#395	C₂²×C₃	1	2	yes	complemented
258	#395	C₂²×C₃	1	2	yes	complemented
259	#395	C₂²×C₃	1	2	yes	complemented
260	#393	C₂²×C₃	1	1	yes	characteristic
261	#393	C₂²×C₃	1	1	yes	characteristic
262	#393	C₂²×C₃	1	1	yes	characteristic
263	#393	C₂²×C₃	1	2	yes	—
264	#393	C₂²×C₃	1	2	yes	—
265	#393	C₂²×C₃	1	1	yes	characteristic
266	#393	C₂²×C₃	1	1	yes	characteristic
267	#393	C₂²×C₃	1	2	yes	—
268	#393	C₂²×C₃	1	1	yes	characteristic
269	#391	C₂²×C₃	1	2	yes	complemented
270	#391	C₂²×C₃	1	2	yes	complemented
271	#391	C₂²×C₃	1	2	yes	complemented
272	#391	C₂²×C₃	1	2	yes	complemented
273	#389	C₂²×C₃	1	2	yes	complemented
274	#389	C₂²×C₃	1	2	yes	complemented
275	#389	C₂²×C₃	1	2	yes	complemented
276	#389	C₂²×C₃	1	2	yes	complemented
277	#388	C₂²×C₃	1	2	yes	—
278	#388	C₂²×C₃	1	2	yes	—
279	#388	C₂²×C₃	1	2	yes	—
280	#388	C₂²×C₃	1	2	yes	—
281	#387	C₂²×C₃	1	2	yes	complemented
282	#387	C₂²×C₃	1	2	yes	complemented
283	#387	C₂²×C₃	1	2	yes	complemented
284	#387	C₂²×C₃	1	2	yes	complemented
285	#385	C₂²×C₃	1	1	yes	characteristic
286	#385	C₂²×C₃	1	2	yes	—
287	#385	C₂²×C₃	1	1	yes	characteristic
288	#385	C₂²×C₃	1	1	yes	characteristic
289	#385	C₂²×C₃	1	2	yes	—
290	#385	C₂²×C₃	1	1	yes	characteristic
291	#385	C₂²×C₃	1	2	yes	—
292	#385	C₂²×C₃	1	2	yes	—
293	#385	C₂²×C₃	1	2	yes	—
294	#385	C₂²×C₃	1	2	yes	—
295	#385	C₂²×C₃	1	2	yes	—
296	#385	C₂²×C₃	1	2	yes	—
297	#385	C₂²×C₃	1	2	yes	—
298	#382	C₂²×C₃	1	2	yes	complemented
299	#382	C₂²×C₃	1	2	yes	complemented
300	#381	C₂²×C₃	1	2	yes	—
301	#380	C₂²×C₃	1	2	yes	—
302	#380	C₂²×C₃	1	2	yes	—
303	#380	C₂²×C₃	1	2	yes	—
304	#380	C₂²×C₃	1	1	yes	characteristic
305	#380	C₂²×C₃	1	2	yes	—
306	#380	C₂²×C₃	1	2	yes	—
307	#379	C₂²×C₃	1	2	yes	—
308	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
309	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
310	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
311	C₂×#95	C₂²×C₃	1	1	yes	characteristic
312	C₂×#95	C₂²×C₃	1	2	yes	—
313	C₂⁴×C₃	—	2	2	no	—
314	C₂⁴×C₃	—	2	2	no	—
315	C₂⁴×C₃	—	4	2	no	—
316	C₂⁴×C₃	—	4	2	no	—
317	C₂⁴×C₃	C₂×Q₈	1	4	yes	—
318	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
319	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
320	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
321	C₂×C₃×Q₈	—	2	4	no	—
322	C₂×C₃×Q₈	—	2	4	no	—
323	C₂×C₃×Q₈	—	2	4	no	—
324	C₂×C₃×Q₈	—	4	2	no	—
325	C₂×C₃×Q₈	—	4	1	no	—
326	C₂×C₃×Q₈	—	4	2	no	—
327	C₂×C₃×Q₈	—	4	1	no	—
328	C₂×C₃×Q₈	—	4	2	no	—
329	C₂×C₃×Q₈	—	4	2	no	—
330	C₂×C₃×Q₈	—	4	1	no	—
331	C₂×C₃×Q₈	—	4	2	no	—
332	C₂×C₃×Q₈	—	4	2	no	—
333	C₂×C₃×Q₈	—	4	16	no	—
334	C₂²×C₃×C₄	—	2	2	no	—
335	C₂²×C₃×C₄	—	2	4	no	—
336	C₂²×C₃×C₄	—	2	2	no	—
337	C₂²×C₃×C₄	—	2	4	no	—
338	C₂²×C₃×C₄	—	2	4	no	—
339	C₂²×C₃×C₄	—	4	2	no	—
340	C₂²×C₃×C₄	—	4	2	no	—
341	C₂²×C₃×C₄	—	4	2	no	—
342	C₂²×C₃×C₄	—	4	2	no	—
343	C₂²×C₃×C₄	—	4	2	no	—
344	C₂²×C₃×C₄	—	4	1	no	—
345	C₂²×C₃×C₄	—	4	1	no	—
346	C₂²×C₃×C₄	—	4	2	no	—
347	C₂²×C₃×C₄	—	4	2	no	—
348	C₂²×C₃×C₄	—	4	2	no	—
349	C₂²×C₃×C₄	—	4	2	no	—
350	C₂²×C₃×C₄	C₂×Q₈	1	8	yes	complemented
351	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
352	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
353	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
354	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
355	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
356	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
357	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
358	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
359	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
360	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
361	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
362	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
363	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
364	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
365	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
366	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
367	C₃×C₄⋊C₄	—	2	4	no	—
368	C₃×C₄⋊C₄	—	2	4	no	—
369	C₃×C₄⋊C₄	—	4	2	no	—
370	C₃×C₄⋊C₄	—	4	2	no	—
371	C₃×C₄⋊C₄	—	4	2	no	—
372	C₃×C₄⋊C₄	—	4	2	no	—
373	C₃×C₄⋊C₄	—	4	2	no	—
374	C₃×C₄⋊C₄	—	4	2	no	—
375	C₃×C₄⋊C₄	—	4	2	no	—
376	C₃×C₄⋊C₄	—	4	2	no	—
377	C₃×C₄⋊C₄	—	4	2	no	—
378	C₃×C₄⋊C₄	—	4	2	no	—
379	C₃×C₄⋊C₄	—	4	2	no	—
380	C₃×C₄⋊C₄	—	4	2	no	—
381	C₃×C₄⋊C₄	—	4	2	no	—
382	C₃×C₄⋊C₄	—	4	1	no	—
383	C₃×C₄⋊C₄	—	4	2	no	—
384	C₃×C₄⋊C₄	—	4	2	no	—
385	C₃×C₄⋊C₄	—	4	2	no	—
386	C₃×C₄⋊C₄	—	4	2	no	—
387	C₃×C₄⋊C₄	—	4	2	no	—
388	C₃×C₄⋊C₄	—	4	2	no	—
389	C₃×C₂²⋊C₄	—	2	4	no	—
390	C₃×C₂²⋊C₄	—	2	4	no	—
391	C₃×C₂²⋊C₄	—	2	4	no	—
392	C₃×C₂²⋊C₄	—	2	4	no	—
393	C₃×C₂²⋊C₄	—	2	4	no	—
394	C₃×C₂²⋊C₄	—	4	2	no	—
395	C₃×C₂²⋊C₄	—	4	2	no	—
396	C₃×C₂²⋊C₄	—	4	2	no	—
397	C₃×C₂²⋊C₄	—	4	1	no	—
398	C₃×C₂²⋊C₄	—	4	1	no	—
399	C₃×C₂²⋊C₄	—	4	1	no	—
400	C₃×C₂²⋊C₄	—	4	1	no	—
401	C₃×C₂²⋊C₄	—	4	2	no	—
402	C₃×C₂²⋊C₄	—	4	2	no	—
403	C₃×C₂²⋊C₄	—	4	2	no	—
404	C₃×C₂²⋊C₄	—	4	2	no	—
405	C₃×C₂²⋊C₄	C₂×Q₈	1	8	yes	—
406	C₃×C₂²⋊C₄	C₂×Q₈	1	4	yes	complemented
407	C₃×C₂²⋊C₄	C₂×Q₈	1	4	yes	complemented
408	C₃×C₄²	—	2	4	no	—
409	C₃×C₄²	—	4	2	no	—
410	C₃×C₄²	—	4	2	no	—
411	C₃×C₄²	—	4	2	no	—
412	C₂⁵	C₂³×C₃	1	1	yes	characteristic
413	C₂²×Q₈	—	4	2	no	—
414	C₂²×Q₈	—	4	4	no	—
415	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
416	C₂²×Q₈	C₂³×C₃	1	2	yes	—
417	C₂²×Q₈	C₂³×C₃	1	2	yes	—
418	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
419	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
420	C₂³×C₄	C₂³×C₃	1	2	yes	—
421	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
422	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
423	C₂³×C₄	C₂³×C₃	1	2	yes	—
424	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
425	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
426	C₂³×C₄	C₂³×C₃	1	2	yes	—
427	C₄⋊Q₈	—	4	4	no	—
428	C₄⋊Q₈	—	4	4	no	—
429	C₂²⋊Q₈	—	4	4	no	—
430	C₂²⋊Q₈	—	4	2	no	—
431	C₂²⋊Q₈	—	4	4	no	—
432	#117	—	4	4	no	—
433	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
434	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
435	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
436	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
437	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
438	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
439	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
440	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
441	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
442	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
443	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
444	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
445	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
446	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
447	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
448	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
449	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
450	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
451	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
452	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
453	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
454	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
455	C₂×C₂²⋊C₄	—	4	4	no	—
456	C₂×C₂²⋊C₄	—	4	2	no	—
457	C₂×C₂²⋊C₄	—	4	2	no	—
458	C₂×C₂²⋊C₄	C₃×Q₈	1	8	yes	complemented
459	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
460	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
461	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
462	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
463	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
464	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
465	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
466	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
467	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
468	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
469	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
470	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
471	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
472	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
473	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
474	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
475	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
476	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
477	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
478	C₂×C₄²	C₂³×C₃	1	2	yes	—
479	C₂×C₄²	C₂³×C₃	1	2	yes	—
480	C₂×C₄²	C₂³×C₃	1	2	yes	—
481	C₂×C₄²	C₂³×C₃	1	2	yes	—
482	#95	C₂³×C₃	1	1	yes	characteristic
483	#95	C₂³×C₃	1	2	yes	—
484	#95	C₂³×C₃	1	2	yes	—
485	#95	C₂³×C₃	1	2	yes	—
486	#95	C₂³×C₃	1	2	yes	—
487	#95	C₂³×C₃	1	2	yes	—
488	#95	C₂³×C₃	1	1	yes	characteristic
489	#95	C₂³×C₃	1	2	yes	—
490	#95	C₂³×C₃	1	2	yes	—
491	#95	C₂³×C₃	1	2	yes	—
492	#95	C₂³×C₃	1	2	yes	—
493	#95	C₂³×C₃	1	2	yes	—
494	#95	C₂³×C₃	1	2	yes	—
495	#95	C₂³×C₃	1	2	yes	—
496	#95	C₂³×C₃	1	1	yes	characteristic
497	#95	C₂³×C₃	1	2	yes	—
498	#95	C₂³×C₃	1	2	yes	—
499	#95	C₂³×C₃	1	2	yes	—
500	#95	C₂³×C₃	1	2	yes	—
501	#95	C₂³×C₃	1	2	yes	—
502	#95	C₂³×C₃	1	2	yes	—
503	#95	C₂³×C₃	1	1	yes	characteristic
504	#95	C₂³×C₃	1	2	yes	—
505	#95	C₂³×C₃	1	2	yes	—
506	#95	C₂³×C₃	1	2	yes	—
507	#95	C₂³×C₃	1	2	yes	—
508	#95	C₂³×C₃	1	2	yes	—
509	#95	C₂³×C₃	1	2	yes	—
510	#95	C₂³×C₃	1	2	yes	—
511	C₂³×C₃	—	2	2	no	—
512	C₂³×C₃	—	2	2	no	—
513	C₂³×C₃	—	2	2	no	—
514	C₂³×C₃	—	2	2	no	—
515	C₂³×C₃	—	2	1	no	—
516	C₂³×C₃	—	2	1	no	—
517	C₂³×C₃	—	2	1	no	—
518	C₂³×C₃	—	2	1	no	—
519	C₂³×C₃	—	2	2	no	—
520	C₂³×C₃	—	2	2	no	—
521	C₂³×C₃	—	2	8	no	—
522	C₂³×C₃	—	4	8	no	—
523	C₂³×C₃	—	8	2	no	—
524	C₂³×C₃	—	8	2	no	—
525	C₂³×C₃	—	8	4	no	—
526	C₂³×C₃	C₂²×Q₈	1	2	yes	—
527	C₂³×C₃	C₂²×Q₈	1	2	yes	—
528	C₂³×C₃	C₂²×Q₈	1	2	yes	—
529	C₂³×C₃	H(5,𝔽₂)	1	2	yes	—
530	C₂³×C₃	2₋¹⁺⁴	1	2	yes	—
531	C₂³×C₃	C₂⁵	1	1	yes	characteristic
532	C₃×Q₈	—	4	4	no	—
533	C₃×Q₈	—	4	8	no	—
534	C₃×Q₈	—	4	4	no	—
535	C₃×Q₈	—	8	4	no	—
536	C₃×Q₈	—	8	2	no	—
537	C₂×C₃×C₄	—	2	2	no	—
538	C₂×C₃×C₄	—	2	2	no	—
539	C₂×C₃×C₄	—	2	2	no	—
540	C₂×C₃×C₄	—	2	2	no	—
541	C₂×C₃×C₄	—	2	2	no	—
542	C₂×C₃×C₄	—	2	2	no	—
543	C₂×C₃×C₄	—	2	2	no	—
544	C₂×C₃×C₄	—	2	2	no	—
545	C₂×C₃×C₄	—	2	2	no	—
546	C₂×C₃×C₄	—	2	2	no	—
547	C₂×C₃×C₄	—	2	2	no	—
548	C₂×C₃×C₄	—	2	2	no	—
549	C₂×C₃×C₄	—	2	2	no	—
550	C₂×C₃×C₄	—	2	2	no	—
551	C₂×C₃×C₄	—	2	2	no	—
552	C₂×C₃×C₄	—	2	1	no	—
553	C₂×C₃×C₄	—	2	1	no	—
554	C₂×C₃×C₄	—	2	1	no	—
555	C₂×C₃×C₄	—	2	1	no	—
556	C₂×C₃×C₄	—	2	2	no	—
557	C₂×C₃×C₄	—	2	2	no	—
558	C₂×C₃×C₄	—	2	2	no	—
559	C₂×C₃×C₄	—	2	2	no	—
560	C₂×C₃×C₄	—	2	2	no	—
561	C₂×C₃×C₄	—	2	2	no	—
562	C₂×C₃×C₄	—	2	2	no	—
563	C₂×C₃×C₄	—	2	2	no	—
564	C₂×C₃×C₄	—	2	2	no	—
565	C₂×C₃×C₄	—	2	2	no	—
566	C₂×C₃×C₄	—	2	2	no	—
567	C₂×C₃×C₄	—	2	2	no	—
568	C₂×C₃×C₄	—	2	2	no	—
569	C₂×C₃×C₄	—	2	2	no	—
570	C₂×C₃×C₄	—	2	2	no	—
571	C₂×C₃×C₄	—	2	2	no	—
572	C₂×C₃×C₄	—	2	2	no	—
573	C₂×C₃×C₄	—	2	2	no	—
574	C₂×C₃×C₄	—	2	2	no	—
575	C₂×C₃×C₄	—	2	2	no	—
576	C₂×C₃×C₄	—	2	2	no	—
577	C₂×C₃×C₄	—	2	2	no	—
578	C₂×C₃×C₄	—	4	8	no	—
579	C₂×C₃×C₄	—	4	8	no	—
580	C₂×C₃×C₄	—	4	4	no	—
581	C₂×C₃×C₄	—	8	2	no	—
582	C₂×C₃×C₄	—	8	4	no	—
583	C₂×C₃×C₄	—	8	2	no	—
584	C₂×C₃×C₄	—	8	2	no	—
585	C₂×C₃×C₄	C₂²×Q₈	1	4	yes	—
586	C₂×C₃×C₄	C₂²×Q₈	1	4	yes	—
587	C₂×C₃×C₄	H(5,𝔽₂)	1	4	yes	—
588	C₂⁴	—	2	2	no	—
589	C₂⁴	—	2	2	no	—
590	C₂⁴	—	4	2	no	—
591	C₂⁴	—	4	2	no	—
592	C₂⁴	C₂×C₃×Q₈	1	4	yes	—
593	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
594	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
595	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
596	C₂×Q₈	—	2	4	no	—
597	C₂×Q₈	—	2	4	no	—
598	C₂×Q₈	—	2	4	no	—
599	C₂×Q₈	—	4	2	no	—
600	C₂×Q₈	—	4	1	no	—
601	C₂×Q₈	—	4	2	no	—
602	C₂×Q₈	—	4	1	no	—
603	C₂×Q₈	—	4	2	no	—
604	C₂×Q₈	—	4	2	no	—
605	C₂×Q₈	—	4	1	no	—
606	C₂×Q₈	—	4	2	no	—
607	C₂×Q₈	—	4	2	no	—
608	C₂×Q₈	—	4	16	no	—
609	C₂²×C₄	—	2	2	no	—
610	C₂²×C₄	—	2	4	no	—
611	C₂²×C₄	—	2	2	no	—
612	C₂²×C₄	—	2	4	no	—
613	C₂²×C₄	—	2	4	no	—
614	C₂²×C₄	—	4	2	no	—
615	C₂²×C₄	—	4	2	no	—
616	C₂²×C₄	—	4	2	no	—
617	C₂²×C₄	—	4	2	no	—
618	C₂²×C₄	—	4	2	no	—
619	C₂²×C₄	—	4	1	no	—
620	C₂²×C₄	—	4	1	no	—
621	C₂²×C₄	—	4	2	no	—
622	C₂²×C₄	—	4	2	no	—
623	C₂²×C₄	—	4	2	no	—
624	C₂²×C₄	—	4	2	no	—
625	C₂²×C₄	C₂×C₃×Q₈	1	8	yes	complemented
626	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
627	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
628	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
629	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
630	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
631	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
632	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
633	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
634	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
635	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
636	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
637	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
638	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
639	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
640	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
641	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
642	C₄⋊C₄	—	2	4	no	—
643	C₄⋊C₄	—	2	4	no	—
644	C₄⋊C₄	—	4	2	no	—
645	C₄⋊C₄	—	4	2	no	—
646	C₄⋊C₄	—	4	2	no	—
647	C₄⋊C₄	—	4	2	no	—
648	C₄⋊C₄	—	4	2	no	—
649	C₄⋊C₄	—	4	2	no	—
650	C₄⋊C₄	—	4	2	no	—
651	C₄⋊C₄	—	4	1	no	—
652	C₄⋊C₄	—	4	2	no	—
653	C₄⋊C₄	—	4	2	no	—
654	C₄⋊C₄	—	4	2	no	—
655	C₄⋊C₄	—	4	2	no	—
656	C₄⋊C₄	—	4	2	no	—
657	C₄⋊C₄	—	4	2	no	—
658	C₄⋊C₄	—	4	2	no	—
659	C₄⋊C₄	—	4	2	no	—
660	C₄⋊C₄	—	4	2	no	—
661	C₄⋊C₄	—	4	2	no	—
662	C₄⋊C₄	—	4	2	no	—
663	C₄⋊C₄	—	4	2	no	—
664	C₂²⋊C₄	—	2	4	no	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	4	no	—
668	C₂²⋊C₄	—	2	4	no	—
669	C₂²⋊C₄	—	4	2	no	—
670	C₂²⋊C₄	—	4	2	no	—
671	C₂²⋊C₄	—	4	2	no	—
672	C₂²⋊C₄	—	4	1	no	—
673	C₂²⋊C₄	—	4	1	no	—
674	C₂²⋊C₄	—	4	1	no	—
675	C₂²⋊C₄	—	4	1	no	—
676	C₂²⋊C₄	—	4	2	no	—
677	C₂²⋊C₄	—	4	2	no	—
678	C₂²⋊C₄	—	4	2	no	—
679	C₂²⋊C₄	—	4	2	no	—
680	C₂²⋊C₄	C₂×C₃×Q₈	1	8	yes	—
681	C₂²⋊C₄	C₂×C₃×Q₈	1	4	yes	complemented
682	C₂²⋊C₄	C₂×C₃×Q₈	1	4	yes	complemented
683	C₄²	—	2	4	no	—
684	C₄²	—	4	2	no	—
685	C₄²	—	4	2	no	—
686	C₄²	—	4	2	no	—
687	C₂²×C₃	—	2	4	no	—
688	C₂²×C₃	—	2	2	no	—
689	C₂²×C₃	—	2	2	no	—
690	C₂²×C₃	—	2	4	no	—
691	C₂²×C₃	—	2	2	no	—
692	C₂²×C₃	—	2	2	no	—
693	C₂²×C₃	—	2	4	no	—
694	C₂²×C₃	—	2	4	no	—
695	C₂²×C₃	—	4	1	no	—
696	C₂²×C₃	—	4	1	no	—
697	C₂²×C₃	—	4	1	no	—
698	C₂²×C₃	—	4	1	no	—
699	C₂²×C₃	—	4	2	no	—
700	C₂²×C₃	—	4	2	no	—
701	C₂²×C₃	—	8	8	no	—
702	C₂²×C₃	#544	1	4	yes	—
703	C₂²×C₃	C₂³×Q₈	1	1	yes	characteristic
704	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
705	C₂²×C₃	C₂×H(5,𝔽₂)	1	2	yes	—
706	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
707	C₂²×C₃	#585	1	2	yes	—
708	C₃×C₄	—	2	4	no	—
709	C₃×C₄	—	2	4	no	—
710	C₃×C₄	—	2	4	no	—
711	C₃×C₄	—	4	2	no	—
712	C₃×C₄	—	4	1	no	—
713	C₃×C₄	—	4	1	no	—
714	C₃×C₄	—	4	2	no	—
715	C₃×C₄	—	4	2	no	—
716	C₃×C₄	—	4	2	no	—
717	C₃×C₄	—	4	1	no	—
718	C₃×C₄	—	4	1	no	—
719	C₃×C₄	—	4	2	no	—
720	C₃×C₄	—	4	2	no	—
721	C₃×C₄	—	4	2	no	—
722	C₃×C₄	—	4	2	no	—
723	C₃×C₄	—	4	2	no	—
724	C₂³	—	2	2	no	—
725	C₂³	—	2	2	no	—
726	C₂³	—	2	2	no	—
727	C₂³	—	2	2	no	—
728	C₂³	—	2	1	no	—
729	C₂³	—	2	1	no	—
730	C₂³	—	2	1	no	—
731	C₂³	—	2	1	no	—
732	C₂³	—	2	2	no	—
733	C₂³	—	2	2	no	—
734	C₂³	—	2	8	no	—
735	C₂³	—	4	8	no	—
736	C₂³	—	8	2	no	—
737	C₂³	—	8	2	no	—
738	C₂³	—	8	4	no	—
739	C₂³	C₂²×C₃×Q₈	1	2	yes	—
740	C₂³	C₂²×C₃×Q₈	1	2	yes	—
741	C₂³	C₂²×C₃×Q₈	1	2	yes	—
742	C₂³	C₃×H(5,𝔽₂)	1	2	yes	—
743	C₂³	C₃×2₋¹⁺⁴	1	2	yes	—
744	C₂³	C₂⁵×C₃	1	1	yes	characteristic
745	Q₈	—	4	4	no	—
746	Q₈	—	4	8	no	—
747	Q₈	—	4	4	no	—
748	Q₈	—	8	4	no	—
749	Q₈	—	8	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	1	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	4	8	no	—
792	C₂×C₄	—	4	8	no	—
793	C₂×C₄	—	4	4	no	—
794	C₂×C₄	—	8	2	no	—
795	C₂×C₄	—	8	4	no	—
796	C₂×C₄	—	8	2	no	—
797	C₂×C₄	—	8	2	no	—
798	C₂×C₄	C₂²×C₃×Q₈	1	4	yes	—
799	C₂×C₄	C₂²×C₃×Q₈	1	4	yes	—
800	C₂×C₄	C₃×H(5,𝔽₂)	1	4	yes	—
801	C₂×C₃	—	2	4	no	—
802	C₂×C₃	—	4	2	no	—
803	C₂×C₃	—	4	2	no	—
804	C₂×C₃	C₂×#544	1	1	yes	characteristic
805	C₂×C₃	#3501	1	2	yes	—
806	C₂×C₃	#3532	1	1	yes	characteristic
807	C₂×C₃	#3545	1	1	yes	characteristic
808	C₂×C₃	#3561	1	2	yes	—
809	C₂²	—	2	4	no	—
810	C₂²	—	2	2	no	—
811	C₂²	—	2	2	no	—
812	C₂²	—	2	4	no	—
813	C₂²	—	2	2	no	—
814	C₂²	—	2	2	no	—
815	C₂²	—	2	4	no	—
816	C₂²	—	2	4	no	—
817	C₂²	—	4	1	no	—
818	C₂²	—	4	1	no	—
819	C₂²	—	4	1	no	—
820	C₂²	—	4	1	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	4	2	no	—
823	C₂²	—	8	8	no	—
824	C₂²	C₃×#544	1	4	yes	—
825	C₂²	C₂³×C₃×Q₈	1	1	yes	characteristic
826	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
827	C₂²	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
828	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
829	C₂²	C₃×#585	1	2	yes	—
830	C₄	—	2	4	no	—
831	C₄	—	2	4	no	—
832	C₄	—	2	4	no	—
833	C₄	—	4	2	no	—
834	C₄	—	4	1	no	—
835	C₄	—	4	1	no	—
836	C₄	—	4	2	no	—
837	C₄	—	4	2	no	—
838	C₄	—	4	1	no	—
839	C₄	—	4	2	no	—
840	C₄	—	4	1	no	—
841	C₄	—	4	2	no	—
842	C₄	—	4	2	no	—
843	C₄	—	4	2	no	—
844	C₄	—	4	2	no	—
845	C₄	—	4	2	no	—
846	C₃	#40610	1	1	yes	characteristic, direct product factor, Sylow
847	C₂	—	2	4	no	—
848	C₂	—	4	2	no	—
849	C₂	—	4	2	no	—
850	C₂	C₂×C₃×#544	1	1	yes	characteristic
851	C₂	C₃×#3501	1	2	yes	—
852	C₂	C₃×#3532	1	1	yes	characteristic
853	C₂	C₃×#3545	1	1	yes	characteristic
854	C₂	C₃×#3561	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂⁵×C₃	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×#2841	C₂	semidirect
2. C₃×#2788	C₂	semidirect
3. C₃×#2763	C₂	semidirect
4. C₃×#2763	C₂	semidirect
5. C₃×#2742	C₂	semidirect
6. C₃×#2729	C₂	semidirect
7. C₃×#2677	C₂	semidirect
8. C₃×#2665	C₂	semidirect
9. C₃×#2628	C₂	semidirect
11. C₃×#2549	C₂	semidirect
12. C₃×#2505	C₂	semidirect
13. C₃×#2505	C₂	semidirect
14. C₃×#2439	C₂	semidirect
16. C₃×#2434	C₂	semidirect
20. #40610	C₃	direct (N × H)
22. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
23. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
32. C₃×#400	C₂²	semidirect
33. C₃×#400	C₂²	semidirect
34. C₃×#400	C₂²	semidirect
35. C₃×#400	C₂²	semidirect
36. C₃×#400	C₂²	semidirect
37. C₃×#400	C₂²	semidirect
41. C₃×#398	C₂²	semidirect
42. C₃×#398	C₂²	semidirect
43. C₃×#398	C₂²	semidirect
44. C₃×#398	C₂²	semidirect
49. C₃×#395	C₂²	semidirect
50. C₃×#395	C₂²	semidirect
51. C₃×#395	C₂²	semidirect
52. C₃×#395	C₂²	semidirect
53. C₃×#395	C₂²	semidirect
54. C₃×#395	C₂²	semidirect
64. C₃×#391	C₂²	semidirect
65. C₃×#391	C₂²	semidirect
66. C₃×#391	C₂²	semidirect
67. C₃×#391	C₂²	semidirect
68. C₃×#389	C₂²	semidirect
69. C₃×#389	C₂²	semidirect
70. C₃×#389	C₂²	semidirect
71. C₃×#389	C₂²	semidirect
76. C₃×#387	C₂²	semidirect
77. C₃×#387	C₂²	semidirect
78. C₃×#387	C₂²	semidirect
79. C₃×#387	C₂²	semidirect
93. C₃×#382	C₂²	semidirect
94. C₃×#382	C₂²	semidirect
108. #2841	C₂×C₃	semidirect
109. #2788	C₂×C₃	semidirect
110. #2763	C₂×C₃	semidirect
111. #2763	C₂×C₃	semidirect
112. #2742	C₂×C₃	semidirect
113. #2729	C₂×C₃	semidirect
114. #2677	C₂×C₃	semidirect
115. #2665	C₂×C₃	semidirect
116. #2628	C₂×C₃	semidirect
118. #2549	C₂×C₃	semidirect
119. #2505	C₂×C₃	semidirect
120. #2505	C₂×C₃	semidirect
121. #2439	C₂×C₃	semidirect
123. #2434	C₂×C₃	semidirect
173. C₂×C₃×C₂²⋊C₄	Q₈	semidirect
227. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
228. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
237. #400	C₂²×C₃	semidirect
238. #400	C₂²×C₃	semidirect
239. #400	C₂²×C₃	semidirect
240. #400	C₂²×C₃	semidirect
241. #400	C₂²×C₃	semidirect
242. #400	C₂²×C₃	semidirect
246. #398	C₂²×C₃	semidirect
247. #398	C₂²×C₃	semidirect
248. #398	C₂²×C₃	semidirect
249. #398	C₂²×C₃	semidirect
254. #395	C₂²×C₃	semidirect
255. #395	C₂²×C₃	semidirect
256. #395	C₂²×C₃	semidirect
257. #395	C₂²×C₃	semidirect
258. #395	C₂²×C₃	semidirect
259. #395	C₂²×C₃	semidirect
269. #391	C₂²×C₃	semidirect
270. #391	C₂²×C₃	semidirect
271. #391	C₂²×C₃	semidirect
272. #391	C₂²×C₃	semidirect
273. #389	C₂²×C₃	semidirect
274. #389	C₂²×C₃	semidirect
275. #389	C₂²×C₃	semidirect
276. #389	C₂²×C₃	semidirect
281. #387	C₂²×C₃	semidirect
282. #387	C₂²×C₃	semidirect
283. #387	C₂²×C₃	semidirect
284. #387	C₂²×C₃	semidirect
298. #382	C₂²×C₃	semidirect
299. #382	C₂²×C₃	semidirect
350. C₂²×C₃×C₄	C₂×Q₈	semidirect
406. C₃×C₂²⋊C₄	C₂×Q₈	semidirect
407. C₃×C₂²⋊C₄	C₂×Q₈	semidirect
458. C₂×C₂²⋊C₄	C₃×Q₈	semidirect
625. C₂²×C₄	C₂×C₃×Q₈	semidirect
681. C₂²⋊C₄	C₂×C₃×Q₈	semidirect
682. C₂²⋊C₄	C₂×C₃×Q₈	semidirect
846. C₃	#40610	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×#2841	2
C₃×#2788	2
C₃×#2763	2
C₃×#2742	2
C₃×#2729	2
C₃×#2677	2
C₃×#2665	2
C₃×#2628	2
C₃×#2626	2
C₃×#2549	2
C₃×#2505	2
C₃×#2439	2
C₃×#2437	2
C₃×#2434	2
C₂×C₃×#393	2
C₃×#2342	2
C₃×#2315	2
#40610	3

Subgroups — C3×#40610 #10659217

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#40610 #10659217