Subgroups — C₃×#36189 #10654796

Order 768.

1918 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2859	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2570	C₂	1	2	yes	maximal, complemented
5	C₃×#2511	C₂	1	2	yes	maximal, complemented
6	C₃×#2507	C₂	1	2	yes	maximal, complemented
7	C₃×#2497	C₂	1	2	yes	maximal, complemented
8	C₃×#2487	C₂	1	2	yes	maximal
9	C₃×#2442	C₂	1	2	yes	maximal, complemented
10	C₃×#2441	C₂	1	2	yes	maximal, complemented
11	C₃×#2423	C₂	1	2	yes	maximal, complemented
12	C₃×#2417	C₂	1	2	yes	maximal
13	C₃×#2360	C₂	1	2	yes	maximal, complemented
14	C₃×#2352	C₂	1	2	yes	maximal
15	C₃×#2345	C₂	1	2	yes	maximal, complemented
16	C₃×C₄×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#2285	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃×#384	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×C₄²×D₄	C₂	1	1	yes	maximal, characteristic
20	#36189	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₃×#125	C₂²	1	2	yes	—
23	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
24	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	—
26	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
29	C₂×C₃×#117	C₂²	1	2	yes	—
30	C₂²×C₃×C₄⋊C₄	C₂²	1	2	yes	—
31	C₂²×C₃×C₄⋊C₄	C₂²	1	2	yes	—
32	C₂²×C₃×C₄⋊C₄	C₂²	1	2	yes	—
33	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
34	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
35	C₃×#400	C₂²	1	4	yes	—
36	C₃×#400	C₂²	1	4	yes	—
37	C₃×#399	C₂²	1	4	yes	—
38	C₃×#398	C₂²	1	4	yes	—
39	C₃×#398	C₂²	1	4	yes	—
40	C₃×#396	C₂²	1	4	yes	—
41	C₃×#391	C₂²	1	2	yes	—
42	C₃×#391	C₂²	1	2	yes	—
43	C₃×#391	C₂²	1	2	yes	—
44	C₃×#389	C₂²	1	2	yes	—
45	C₃×#389	C₂²	1	4	yes	—
46	C₃×#389	C₂²	1	2	yes	—
47	C₃×#389	C₂²	1	2	yes	—
48	C₃×#389	C₂²	1	2	yes	—
49	C₃×#389	C₂²	1	2	yes	—
50	C₃×#389	C₂²	1	2	yes	—
51	C₃×#389	C₂²	1	2	yes	—
52	C₃×#389	C₂²	1	2	yes	—
53	C₃×#389	C₂²	1	2	yes	—
54	C₃×#389	C₂²	1	2	yes	—
55	C₃×#388	C₂²	1	4	yes	—
56	C₃×#387	C₂²	1	4	yes	—
57	C₃×#387	C₂²	1	4	yes	—
58	C₃×#387	C₂²	1	4	yes	—
59	C₃×#387	C₂²	1	4	yes	—
60	C₃×#386	C₂²	1	4	yes	—
61	C₃×#385	C₂²	1	4	yes	—
62	C₃×#384	C₂²	1	2	yes	—
63	C₃×#384	C₂²	1	2	yes	—
64	C₃×#384	C₂²	1	2	yes	—
65	C₃×#384	C₂²	1	1	yes	characteristic
66	C₃×#384	C₂²	1	1	yes	characteristic
67	C₃×#384	C₂²	1	1	yes	characteristic
68	C₃×#382	C₂²	1	2	yes	—
69	C₃×#382	C₂²	1	2	yes	—
70	C₃×#380	C₂²	1	2	yes	—
71	C₃×#380	C₂²	1	4	yes	—
72	C₃×#380	C₂²	1	2	yes	—
73	C₃×#380	C₂²	1	2	yes	—
74	C₃×#380	C₂²	1	2	yes	—
75	C₃×#380	C₂²	1	2	yes	—
76	C₃×#380	C₂²	1	2	yes	—
77	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
78	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
79	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
80	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
81	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
82	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
83	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
84	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
85	C₃×C₄×C₂²⋊C₄	C₂²	1	4	yes	—
86	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
87	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
88	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
89	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
90	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
91	C₃×C₄³	C₂²	1	1	yes	characteristic
92	#2859	C₂×C₃	1	1	yes	characteristic, complemented
93	#2857	C₂×C₃	1	1	yes	characteristic, complemented
94	#2857	C₂×C₃	1	1	yes	characteristic, complemented
95	#2570	C₂×C₃	1	2	yes	complemented
96	#2511	C₂×C₃	1	2	yes	complemented
97	#2507	C₂×C₃	1	2	yes	complemented
98	#2497	C₂×C₃	1	2	yes	complemented
99	#2487	C₂×C₃	1	2	yes	—
100	#2442	C₂×C₃	1	2	yes	complemented
101	#2441	C₂×C₃	1	2	yes	complemented
102	#2423	C₂×C₃	1	2	yes	complemented
103	#2417	C₂×C₃	1	2	yes	—
104	#2360	C₂×C₃	1	2	yes	complemented
105	#2352	C₂×C₃	1	2	yes	—
106	#2345	C₂×C₃	1	2	yes	complemented
107	C₄×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
108	#2285	C₂×C₃	1	1	yes	characteristic, complemented
109	C₂×#384	C₂×C₃	1	1	yes	characteristic, complemented
110	C₄²×D₄	C₂×C₃	1	1	yes	characteristic
111	C₂²×C₃×Q₈	C₂³	1	2	yes	—
112	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
113	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
114	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
115	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
116	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
117	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
118	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
119	C₂³×C₃×C₄	C₂³	1	4	yes	—
120	C₃×C₄⋊Q₈	—	2	4	no	—
121	C₃×#125	—	4	4	no	—
122	C₃×C₂²⋊Q₈	—	2	8	no	—
123	C₃×C₂²⋊Q₈	—	4	4	no	—
124	C₃×C₄×Q₈	—	4	4	no	—
125	C₃×C₄×D₄	—	2	4	no	—
126	C₃×C₄×D₄	—	2	4	no	—
127	C₃×C₄×D₄	Q₈	1	8	yes	complemented
128	C₃×#117	—	4	4	no	—
129	C₂×C₃×C₄⋊C₄	—	2	8	no	—
130	C₂×C₃×C₄⋊C₄	—	4	4	no	—
131	C₂×C₃×C₄⋊C₄	—	4	4	no	—
132	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
133	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
134	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
135	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
136	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
137	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
138	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
139	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
140	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
141	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
142	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
143	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
144	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
145	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
146	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
147	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
148	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
149	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
150	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
151	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
152	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
153	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
154	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
155	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
156	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
157	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
158	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
159	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
160	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
161	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
162	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
163	C₂×C₃×C₄²	—	2	4	no	—
164	C₂×C₃×C₄²	—	2	4	no	—
165	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
166	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
167	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
168	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
169	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
170	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
171	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
172	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
173	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
174	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
175	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
176	C₂×C₃×C₄²	C₂³	1	4	yes	—
177	C₂×C₃×C₄²	C₂³	1	4	yes	—
178	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
179	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
180	C₃×#95	C₂³	1	1	yes	characteristic
181	C₃×#95	C₂³	1	1	yes	characteristic
182	C₃×#95	C₂³	1	1	yes	characteristic
183	C₃×#95	C₂³	1	1	yes	characteristic
184	C₃×#95	C₂³	1	1	yes	characteristic
185	C₃×#95	C₂³	1	1	yes	characteristic
186	C₃×#95	C₂³	1	4	yes	—
187	C₃×#95	C₂³	1	4	yes	—
188	C₃×#95	C₂³	1	4	yes	—
189	C₃×#95	C₂³	1	4	yes	—
190	C₃×#95	C₂³	1	4	yes	—
191	C₃×#95	C₂³	1	4	yes	—
192	C₃×#95	C₂³	1	4	yes	—
193	C₃×#95	C₂³	1	4	yes	—
194	C₃×#95	C₂³	1	4	yes	—
195	C₃×#95	C₂³	1	4	yes	—
196	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
197	C₂×#125	C₂²×C₃	1	2	yes	—
198	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
199	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
200	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	—
201	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
202	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
203	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
204	C₂×#117	C₂²×C₃	1	2	yes	—
205	C₂²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
206	C₂²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
207	C₂²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
208	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
209	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
210	#400	C₂²×C₃	1	4	yes	—
211	#400	C₂²×C₃	1	4	yes	—
212	#399	C₂²×C₃	1	4	yes	—
213	#398	C₂²×C₃	1	4	yes	—
214	#398	C₂²×C₃	1	4	yes	—
215	#396	C₂²×C₃	1	4	yes	—
216	#391	C₂²×C₃	1	2	yes	—
217	#391	C₂²×C₃	1	2	yes	—
218	#391	C₂²×C₃	1	2	yes	—
219	#389	C₂²×C₃	1	2	yes	—
220	#389	C₂²×C₃	1	2	yes	—
221	#389	C₂²×C₃	1	2	yes	—
222	#389	C₂²×C₃	1	2	yes	—
223	#389	C₂²×C₃	1	2	yes	—
224	#389	C₂²×C₃	1	2	yes	—
225	#389	C₂²×C₃	1	2	yes	—
226	#389	C₂²×C₃	1	2	yes	—
227	#389	C₂²×C₃	1	2	yes	—
228	#389	C₂²×C₃	1	2	yes	—
229	#389	C₂²×C₃	1	4	yes	—
230	#388	C₂²×C₃	1	4	yes	—
231	#387	C₂²×C₃	1	4	yes	—
232	#387	C₂²×C₃	1	4	yes	—
233	#387	C₂²×C₃	1	4	yes	—
234	#387	C₂²×C₃	1	4	yes	—
235	#386	C₂²×C₃	1	4	yes	—
236	#385	C₂²×C₃	1	4	yes	—
237	#384	C₂²×C₃	1	1	yes	characteristic
238	#384	C₂²×C₃	1	2	yes	—
239	#384	C₂²×C₃	1	1	yes	characteristic
240	#384	C₂²×C₃	1	1	yes	characteristic
241	#384	C₂²×C₃	1	2	yes	—
242	#384	C₂²×C₃	1	2	yes	—
243	#382	C₂²×C₃	1	2	yes	—
244	#382	C₂²×C₃	1	2	yes	—
245	#380	C₂²×C₃	1	2	yes	—
246	#380	C₂²×C₃	1	4	yes	—
247	#380	C₂²×C₃	1	2	yes	—
248	#380	C₂²×C₃	1	2	yes	—
249	#380	C₂²×C₃	1	2	yes	—
250	#380	C₂²×C₃	1	2	yes	—
251	#380	C₂²×C₃	1	2	yes	—
252	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
253	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
254	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
255	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
256	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
257	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
258	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
259	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
260	C₄×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
261	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
262	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
263	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
264	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
265	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
266	C₄³	C₂²×C₃	1	1	yes	characteristic
267	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
268	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
269	C₂×C₃×Q₈	—	2	4	no	—
270	C₂×C₃×Q₈	—	2	4	no	—
271	C₂×C₃×Q₈	—	2	4	no	—
272	C₂×C₃×D₄	—	2	2	no	—
273	C₂×C₃×D₄	—	2	2	no	—
274	C₂×C₃×D₄	C₂×Q₈	1	4	yes	—
275	C₂²×C₃×C₄	—	2	2	no	—
276	C₂²×C₃×C₄	—	2	2	no	—
277	C₂²×C₃×C₄	—	2	2	no	—
278	C₂²×C₃×C₄	—	2	2	no	—
279	C₂²×C₃×C₄	—	2	2	no	—
280	C₂²×C₃×C₄	—	2	2	no	—
281	C₂²×C₃×C₄	—	2	2	no	—
282	C₂²×C₃×C₄	—	2	2	no	—
283	C₂²×C₃×C₄	—	2	8	no	—
284	C₂²×C₃×C₄	—	2	2	no	—
285	C₂²×C₃×C₄	—	2	2	no	—
286	C₂²×C₃×C₄	—	2	2	no	—
287	C₂²×C₃×C₄	—	2	2	no	—
288	C₂²×C₃×C₄	—	2	2	no	—
289	C₂²×C₃×C₄	—	2	2	no	—
290	C₂²×C₃×C₄	—	4	4	no	—
291	C₂²×C₃×C₄	—	4	4	no	—
292	C₂²×C₃×C₄	C₂×Q₈	1	4	yes	—
293	C₂²×C₃×C₄	C₂×Q₈	1	4	yes	—
294	C₂²×C₃×C₄	#41	1	4	yes	—
295	C₂²×C₃×C₄	#41	1	4	yes	—
296	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
297	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
298	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
299	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
300	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
301	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
302	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
303	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
304	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
305	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
306	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
307	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
308	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
309	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
310	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
311	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
312	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
313	C₃×C₄⋊C₄	—	2	8	no	—
314	C₃×C₄⋊C₄	—	2	4	no	—
315	C₃×C₄⋊C₄	—	2	4	no	—
316	C₃×C₄⋊C₄	—	2	2	no	—
317	C₃×C₄⋊C₄	—	2	2	no	—
318	C₃×C₄⋊C₄	—	2	4	no	—
319	C₃×C₄⋊C₄	—	2	8	no	—
320	C₃×C₄⋊C₄	—	2	4	no	—
321	C₃×C₄⋊C₄	—	2	4	no	—
322	C₃×C₄⋊C₄	—	2	4	no	—
323	C₃×C₄⋊C₄	—	2	4	no	—
324	C₃×C₄⋊C₄	—	2	4	no	—
325	C₃×C₄⋊C₄	—	2	4	no	—
326	C₃×C₄⋊C₄	—	2	4	no	—
327	C₃×C₄⋊C₄	—	2	4	no	—
328	C₃×C₄⋊C₄	—	4	4	no	—
329	C₃×C₄⋊C₄	—	4	4	no	—
330	C₃×C₄⋊C₄	—	4	4	no	—
331	C₃×C₄⋊C₄	—	4	4	no	—
332	C₃×C₄⋊C₄	—	4	4	no	—
333	C₃×C₄⋊C₄	—	4	4	no	—
334	C₃×C₄⋊C₄	C₂×Q₈	1	4	yes	—
335	C₃×C₂²⋊C₄	—	2	2	no	—
336	C₃×C₂²⋊C₄	—	2	2	no	—
337	C₃×C₂²⋊C₄	—	2	8	no	—
338	C₃×C₂²⋊C₄	—	2	2	no	—
339	C₃×C₂²⋊C₄	—	2	2	no	—
340	C₃×C₂²⋊C₄	—	4	4	no	—
341	C₃×C₂²⋊C₄	—	4	4	no	—
342	C₃×C₂²⋊C₄	C₂×Q₈	1	4	yes	—
343	C₃×C₂²⋊C₄	C₂×Q₈	1	4	yes	—
344	C₃×C₄²	—	2	2	no	—
345	C₃×C₄²	—	2	2	no	—
346	C₃×C₄²	—	2	2	no	—
347	C₃×C₄²	—	2	2	no	—
348	C₃×C₄²	—	2	2	no	—
349	C₃×C₄²	—	2	2	no	—
350	C₃×C₄²	—	2	2	no	—
351	C₃×C₄²	—	2	2	no	—
352	C₃×C₄²	—	2	2	no	—
353	C₃×C₄²	—	2	2	no	—
354	C₃×C₄²	—	2	2	no	—
355	C₃×C₄²	—	4	4	no	—
356	C₃×C₄²	—	4	4	no	—
357	C₃×C₄²	C₂×Q₈	1	4	yes	—
358	C₃×C₄²	#41	1	4	yes	—
359	C₂²×Q₈	C₂³×C₃	1	2	yes	—
360	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
361	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
362	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
363	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
364	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
365	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
366	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
367	C₂³×C₄	C₂³×C₃	1	4	yes	—
368	C₄⋊Q₈	—	2	4	no	—
369	#125	—	4	4	no	—
370	C₂²⋊Q₈	—	2	8	no	—
371	C₂²⋊Q₈	—	4	4	no	—
372	C₄×Q₈	—	4	4	no	—
373	C₄×D₄	—	2	4	no	—
374	C₄×D₄	—	2	4	no	—
375	C₄×D₄	C₃×Q₈	1	8	yes	complemented
376	#117	—	4	4	no	—
377	C₂×C₄⋊C₄	—	2	8	no	—
378	C₂×C₄⋊C₄	—	4	4	no	—
379	C₂×C₄⋊C₄	—	4	4	no	—
380	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
381	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
382	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
383	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
384	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
385	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
386	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
387	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
388	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
389	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
390	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
391	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
392	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
393	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
394	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
395	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
396	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
397	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
398	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
399	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
400	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
401	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
402	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
403	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
404	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
405	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
406	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
407	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
408	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
409	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
410	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
411	C₂×C₄²	—	2	4	no	—
412	C₂×C₄²	—	2	4	no	—
413	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
414	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
415	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
416	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
417	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
418	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
419	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
420	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
421	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
422	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
423	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
424	C₂×C₄²	C₂³×C₃	1	4	yes	—
425	C₂×C₄²	C₂³×C₃	1	4	yes	—
426	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
427	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
428	#95	C₂³×C₃	1	1	yes	characteristic
429	#95	C₂³×C₃	1	1	yes	characteristic
430	#95	C₂³×C₃	1	1	yes	characteristic
431	#95	C₂³×C₃	1	1	yes	characteristic
432	#95	C₂³×C₃	1	1	yes	characteristic
433	#95	C₂³×C₃	1	1	yes	characteristic
434	#95	C₂³×C₃	1	4	yes	—
435	#95	C₂³×C₃	1	4	yes	—
436	#95	C₂³×C₃	1	4	yes	—
437	#95	C₂³×C₃	1	4	yes	—
438	#95	C₂³×C₃	1	4	yes	—
439	#95	C₂³×C₃	1	4	yes	—
440	#95	C₂³×C₃	1	4	yes	—
441	#95	C₂³×C₃	1	4	yes	—
442	#95	C₂³×C₃	1	4	yes	—
443	#95	C₂³×C₃	1	4	yes	—
444	C₂³×C₃	—	2	1	no	—
445	C₂³×C₃	—	2	1	no	—
446	C₂³×C₃	—	2	1	no	—
447	C₂³×C₃	—	2	1	no	—
448	C₂³×C₃	—	2	1	no	—
449	C₂³×C₃	—	2	1	no	—
450	C₂³×C₃	—	2	1	no	—
451	C₂³×C₃	—	2	1	no	—
452	C₂³×C₃	—	2	1	no	—
453	C₂³×C₃	—	2	1	no	—
454	C₂³×C₃	C₂²×Q₈	1	2	yes	—
455	C₂³×C₃	C₂²×Q₈	1	2	yes	—
456	C₂³×C₃	C₂×#41	1	2	yes	—
457	C₂³×C₃	C₂×#41	1	2	yes	—
458	C₂³×C₃	C₂⁵	1	1	yes	characteristic
459	C₃×Q₈	—	4	8	no	—
460	C₃×D₄	—	2	8	no	—
461	C₂×C₃×C₄	—	2	1	no	—
462	C₂×C₃×C₄	—	2	1	no	—
463	C₂×C₃×C₄	—	2	1	no	—
464	C₂×C₃×C₄	—	2	1	no	—
465	C₂×C₃×C₄	—	2	1	no	—
466	C₂×C₃×C₄	—	2	1	no	—
467	C₂×C₃×C₄	—	2	1	no	—
468	C₂×C₃×C₄	—	2	1	no	—
469	C₂×C₃×C₄	—	2	1	no	—
470	C₂×C₃×C₄	—	2	1	no	—
471	C₂×C₃×C₄	—	2	1	no	—
472	C₂×C₃×C₄	—	2	1	no	—
473	C₂×C₃×C₄	—	2	8	no	—
474	C₂×C₃×C₄	—	2	8	no	—
475	C₂×C₃×C₄	—	2	8	no	—
476	C₂×C₃×C₄	—	2	8	no	—
477	C₂×C₃×C₄	—	2	1	no	—
478	C₂×C₃×C₄	—	2	1	no	—
479	C₂×C₃×C₄	—	2	1	no	—
480	C₂×C₃×C₄	—	2	1	no	—
481	C₂×C₃×C₄	—	2	4	no	—
482	C₂×C₃×C₄	—	2	1	no	—
483	C₂×C₃×C₄	—	2	1	no	—
484	C₂×C₃×C₄	—	2	4	no	—
485	C₂×C₃×C₄	—	2	4	no	—
486	C₂×C₃×C₄	—	2	4	no	—
487	C₂×C₃×C₄	—	2	4	no	—
488	C₂×C₃×C₄	—	2	1	no	—
489	C₂×C₃×C₄	—	2	1	no	—
490	C₂×C₃×C₄	—	2	1	no	—
491	C₂×C₃×C₄	—	2	4	no	—
492	C₂×C₃×C₄	—	2	4	no	—
493	C₂×C₃×C₄	—	2	4	no	—
494	C₂×C₃×C₄	—	2	4	no	—
495	C₂×C₃×C₄	—	2	4	no	—
496	C₂×C₃×C₄	—	2	4	no	—
497	C₂×C₃×C₄	—	2	1	no	—
498	C₂×C₃×C₄	—	2	1	no	—
499	C₂×C₃×C₄	—	2	4	no	—
500	C₂×C₃×C₄	—	2	1	no	—
501	C₂×C₃×C₄	—	4	4	no	—
502	C₂×C₃×C₄	—	4	4	no	—
503	C₂×C₃×C₄	—	8	8	no	—
504	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
505	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
506	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
507	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
508	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
509	C₂×C₃×C₄	C₂×#41	1	2	yes	—
510	C₂×C₃×C₄	C₂×#41	1	2	yes	—
511	C₂×C₃×C₄	C₂×#41	1	2	yes	—
512	C₂×C₃×C₄	C₂×#41	1	2	yes	—
513	C₂×C₃×C₄	C₂×#41	1	2	yes	—
514	C₂×C₃×C₄	C₂×#41	1	2	yes	—
515	C₂×C₃×C₄	C₂×#41	1	2	yes	—
516	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
517	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
518	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
519	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
520	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
521	C₂×Q₈	—	2	4	no	—
522	C₂×Q₈	—	2	4	no	—
523	C₂×Q₈	—	2	4	no	—
524	C₂×D₄	—	2	2	no	—
525	C₂×D₄	—	2	2	no	—
526	C₂×D₄	C₂×C₃×Q₈	1	4	yes	—
527	C₂²×C₄	—	2	2	no	—
528	C₂²×C₄	—	2	2	no	—
529	C₂²×C₄	—	2	2	no	—
530	C₂²×C₄	—	2	2	no	—
531	C₂²×C₄	—	2	2	no	—
532	C₂²×C₄	—	2	2	no	—
533	C₂²×C₄	—	2	2	no	—
534	C₂²×C₄	—	2	2	no	—
535	C₂²×C₄	—	2	8	no	—
536	C₂²×C₄	—	2	2	no	—
537	C₂²×C₄	—	2	2	no	—
538	C₂²×C₄	—	2	2	no	—
539	C₂²×C₄	—	2	2	no	—
540	C₂²×C₄	—	2	2	no	—
541	C₂²×C₄	—	2	2	no	—
542	C₂²×C₄	—	4	4	no	—
543	C₂²×C₄	—	4	4	no	—
544	C₂²×C₄	C₂×C₃×Q₈	1	4	yes	—
545	C₂²×C₄	C₂×C₃×Q₈	1	4	yes	—
546	C₂²×C₄	C₃×#41	1	4	yes	—
547	C₂²×C₄	C₃×#41	1	4	yes	—
548	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
549	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
550	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
551	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
552	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
553	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
554	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
555	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
556	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
557	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
558	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
559	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
560	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
561	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
562	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
563	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
564	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
565	C₄⋊C₄	—	2	8	no	—
566	C₄⋊C₄	—	2	4	no	—
567	C₄⋊C₄	—	2	4	no	—
568	C₄⋊C₄	—	2	2	no	—
569	C₄⋊C₄	—	2	2	no	—
570	C₄⋊C₄	—	2	4	no	—
571	C₄⋊C₄	—	2	8	no	—
572	C₄⋊C₄	—	2	4	no	—
573	C₄⋊C₄	—	2	4	no	—
574	C₄⋊C₄	—	2	4	no	—
575	C₄⋊C₄	—	2	4	no	—
576	C₄⋊C₄	—	2	4	no	—
577	C₄⋊C₄	—	2	4	no	—
578	C₄⋊C₄	—	2	4	no	—
579	C₄⋊C₄	—	2	4	no	—
580	C₄⋊C₄	—	4	4	no	—
581	C₄⋊C₄	—	4	4	no	—
582	C₄⋊C₄	—	4	4	no	—
583	C₄⋊C₄	—	4	4	no	—
584	C₄⋊C₄	—	4	4	no	—
585	C₄⋊C₄	—	4	4	no	—
586	C₄⋊C₄	C₂×C₃×Q₈	1	4	yes	—
587	C₂²⋊C₄	—	2	2	no	—
588	C₂²⋊C₄	—	2	2	no	—
589	C₂²⋊C₄	—	2	8	no	—
590	C₂²⋊C₄	—	2	2	no	—
591	C₂²⋊C₄	—	2	2	no	—
592	C₂²⋊C₄	—	4	4	no	—
593	C₂²⋊C₄	—	4	4	no	—
594	C₂²⋊C₄	C₂×C₃×Q₈	1	4	yes	—
595	C₂²⋊C₄	C₂×C₃×Q₈	1	4	yes	—
596	C₄²	—	2	2	no	—
597	C₄²	—	2	2	no	—
598	C₄²	—	2	2	no	—
599	C₄²	—	2	2	no	—
600	C₄²	—	2	2	no	—
601	C₄²	—	2	2	no	—
602	C₄²	—	2	2	no	—
603	C₄²	—	2	2	no	—
604	C₄²	—	2	2	no	—
605	C₄²	—	2	2	no	—
606	C₄²	—	2	2	no	—
607	C₄²	—	4	4	no	—
608	C₄²	—	4	4	no	—
609	C₄²	C₂×C₃×Q₈	1	4	yes	—
610	C₄²	C₃×#41	1	4	yes	—
611	C₂²×C₃	—	2	2	no	—
612	C₂²×C₃	—	2	2	no	—
613	C₂²×C₃	—	2	2	no	—
614	C₂²×C₃	—	2	2	no	—
615	C₂²×C₃	—	2	2	no	—
616	C₂²×C₃	—	2	2	no	—
617	C₂²×C₃	—	2	2	no	—
618	C₂²×C₃	—	2	2	no	—
619	C₂²×C₃	—	2	2	no	—
620	C₂²×C₃	—	4	1	no	—
621	C₂²×C₃	—	4	1	no	—
622	C₂²×C₃	—	4	1	no	—
623	C₂²×C₃	—	4	1	no	—
624	C₂²×C₃	#533	1	4	yes	—
625	C₂²×C₃	C₂³×Q₈	1	1	yes	characteristic
626	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
627	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
628	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
629	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
630	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
631	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
632	C₃×C₄	—	2	2	no	—
633	C₃×C₄	—	2	2	no	—
634	C₃×C₄	—	2	2	no	—
635	C₃×C₄	—	2	2	no	—
636	C₃×C₄	—	2	2	no	—
637	C₃×C₄	—	2	2	no	—
638	C₃×C₄	—	4	1	no	—
639	C₃×C₄	—	4	1	no	—
640	C₃×C₄	—	4	4	no	—
641	C₃×C₄	—	4	1	no	—
642	C₃×C₄	—	4	4	no	—
643	C₃×C₄	—	4	4	no	—
644	C₃×C₄	—	4	1	no	—
645	C₃×C₄	—	4	4	no	—
646	C₃×C₄	#552	1	4	yes	—
647	C₃×C₄	#553	1	4	yes	—
648	C₃×C₄	#554	1	4	yes	—
649	C₂³	—	2	1	no	—
650	C₂³	—	2	1	no	—
651	C₂³	—	2	1	no	—
652	C₂³	—	2	1	no	—
653	C₂³	—	2	1	no	—
654	C₂³	—	2	1	no	—
655	C₂³	—	2	1	no	—
656	C₂³	—	2	1	no	—
657	C₂³	—	2	1	no	—
658	C₂³	—	2	1	no	—
659	C₂³	C₂²×C₃×Q₈	1	2	yes	—
660	C₂³	C₂²×C₃×Q₈	1	2	yes	—
661	C₂³	C₂×C₃×#41	1	2	yes	—
662	C₂³	C₂×C₃×#41	1	2	yes	—
663	C₂³	C₂⁵×C₃	1	1	yes	characteristic
664	Q₈	—	4	8	no	—
665	D₄	—	2	8	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	8	no	—
679	C₂×C₄	—	2	8	no	—
680	C₂×C₄	—	2	8	no	—
681	C₂×C₄	—	2	8	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	4	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	4	no	—
690	C₂×C₄	—	2	4	no	—
691	C₂×C₄	—	2	4	no	—
692	C₂×C₄	—	2	4	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	4	no	—
697	C₂×C₄	—	2	4	no	—
698	C₂×C₄	—	2	4	no	—
699	C₂×C₄	—	2	4	no	—
700	C₂×C₄	—	2	4	no	—
701	C₂×C₄	—	2	4	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	4	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	4	4	no	—
707	C₂×C₄	—	4	4	no	—
708	C₂×C₄	—	8	8	no	—
709	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
710	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
711	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
712	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
713	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
714	C₂×C₄	C₂×C₃×#41	1	2	yes	—
715	C₂×C₄	C₂×C₃×#41	1	2	yes	—
716	C₂×C₄	C₂×C₃×#41	1	2	yes	—
717	C₂×C₄	C₂×C₃×#41	1	2	yes	—
718	C₂×C₄	C₂×C₃×#41	1	2	yes	—
719	C₂×C₄	C₂×C₃×#41	1	2	yes	—
720	C₂×C₄	C₂×C₃×#41	1	2	yes	—
721	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
722	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
723	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
724	C₂×C₃	—	2	4	no	—
725	C₂×C₃	—	4	2	no	—
726	C₂×C₃	C₂×#533	1	1	yes	characteristic
727	C₂×C₃	C₂×#552	1	1	yes	characteristic
728	C₂×C₃	C₂×#553	1	1	yes	characteristic
729	C₂×C₃	C₂×#554	1	1	yes	characteristic
730	C₂×C₃	#3503	1	1	yes	characteristic
731	C₂×C₃	#3508	1	1	yes	characteristic
732	C₂×C₃	#3511	1	1	yes	characteristic
733	C₂²	—	2	2	no	—
734	C₂²	—	2	2	no	—
735	C₂²	—	2	2	no	—
736	C₂²	—	2	2	no	—
737	C₂²	—	2	2	no	—
738	C₂²	—	2	2	no	—
739	C₂²	—	2	2	no	—
740	C₂²	—	2	2	no	—
741	C₂²	—	2	2	no	—
742	C₂²	—	4	1	no	—
743	C₂²	—	4	1	no	—
744	C₂²	—	4	1	no	—
745	C₂²	—	4	1	no	—
746	C₂²	C₃×#533	1	4	yes	—
747	C₂²	C₂³×C₃×Q₈	1	1	yes	characteristic
748	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
749	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
750	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
751	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
752	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
753	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
754	C₄	—	2	2	no	—
755	C₄	—	2	2	no	—
756	C₄	—	2	2	no	—
757	C₄	—	2	2	no	—
758	C₄	—	2	2	no	—
759	C₄	—	2	2	no	—
760	C₄	—	4	1	no	—
761	C₄	—	4	1	no	—
762	C₄	—	4	4	no	—
763	C₄	—	4	4	no	—
764	C₄	—	4	4	no	—
765	C₄	—	4	1	no	—
766	C₄	—	4	1	no	—
767	C₄	—	4	4	no	—
768	C₄	C₃×#552	1	4	yes	—
769	C₄	C₃×#553	1	4	yes	—
770	C₄	C₃×#554	1	4	yes	—
771	C₃	#36189	1	1	yes	characteristic, direct product factor, Sylow
772	C₂	—	2	4	no	—
773	C₂	—	4	2	no	—
774	C₂	C₂×C₃×#533	1	1	yes	characteristic
775	C₂	C₂×C₃×#552	1	1	yes	characteristic
776	C₂	C₂×C₃×#553	1	1	yes	characteristic
777	C₂	C₂×C₃×#554	1	1	yes	characteristic
778	C₂	C₃×#3503	1	1	yes	characteristic
779	C₂	C₃×#3508	1	1	yes	characteristic
780	C₂	C₃×#3511	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×#2859	C₂	semidirect
2. C₃×#2857	C₂	semidirect
3. C₃×#2857	C₂	semidirect
4. C₃×#2570	C₂	semidirect
5. C₃×#2511	C₂	semidirect
6. C₃×#2507	C₂	semidirect
7. C₃×#2497	C₂	semidirect
9. C₃×#2442	C₂	semidirect
10. C₃×#2441	C₂	semidirect
11. C₃×#2423	C₂	semidirect
13. C₃×#2360	C₂	semidirect
15. C₃×#2345	C₂	semidirect
16. C₃×C₄×C₄⋊Q₈	C₂	semidirect
17. C₃×#2285	C₂	semidirect
18. C₂×C₃×#384	C₂	semidirect
20. #36189	C₃	direct (N × H)
92. #2859	C₂×C₃	semidirect
93. #2857	C₂×C₃	semidirect
94. #2857	C₂×C₃	semidirect
95. #2570	C₂×C₃	semidirect
96. #2511	C₂×C₃	semidirect
97. #2507	C₂×C₃	semidirect
98. #2497	C₂×C₃	semidirect
100. #2442	C₂×C₃	semidirect
101. #2441	C₂×C₃	semidirect
102. #2423	C₂×C₃	semidirect
104. #2360	C₂×C₃	semidirect
106. #2345	C₂×C₃	semidirect
107. C₄×C₄⋊Q₈	C₂×C₃	semidirect
108. #2285	C₂×C₃	semidirect
109. C₂×#384	C₂×C₃	semidirect
127. C₃×C₄×D₄	Q₈	semidirect
375. C₄×D₄	C₃×Q₈	semidirect
771. C₃	#36189	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×#2859	2
C₃×#2857	2
C₃×#2570	2
C₃×#2511	2
C₃×#2507	2
C₃×#2497	2
C₃×#2487	2
C₃×#2442	2
C₃×#2441	2
C₃×#2423	2
C₃×#2417	2
C₃×#2360	2
C₃×#2352	2
C₃×#2345	2
C₃×C₄×C₄⋊Q₈	2
C₃×#2285	2
C₂×C₃×#384	2
C₃×C₄²×D₄	2
#36189	3

Subgroups — C3×#36189 #10654796

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#36189 #10654796