Subgroups — C₃×#39879 #10658486

Order 768.

2128 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2850	C₂	1	1	yes	maximal, characteristic
4	C₃×#2725	C₂	1	2	yes	maximal, complemented
5	C₃×#2704	C₂	1	2	yes	maximal, complemented
6	C₃×#2702	C₂	1	2	yes	maximal, complemented
7	C₃×#2683	C₂	1	2	yes	maximal, complemented
8	C₃×#2637	C₂	1	2	yes	maximal, complemented
9	C₃×#2609	C₂	1	2	yes	maximal, complemented
10	C₃×#2601	C₂	1	2	yes	maximal, complemented
11	C₃×#2581	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2546	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#2545	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#2545	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#2452	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2451	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#2429	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#2429	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#2427	C₂	1	1	yes	maximal, characteristic
20	C₃×#2426	C₂	1	1	yes	maximal, characteristic
21	C₃×#2351	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃×#2323	C₂	1	2	yes	maximal, complemented
23	C₃×C₄×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
24	#39879	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₃×#556	—	2	8	no	—
26	C₃×#533	—	2	8	no	—
27	C₂×C₃×C₄⋊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×#126	C₂²	1	2	yes	—
32	C₂×C₃×#126	C₂²	1	2	yes	—
33	C₂×C₃×#125	C₂²	1	2	yes	—
34	C₂×C₃×#124	C₂²	1	1	yes	characteristic
35	C₂×C₃×#124	C₂²	1	1	yes	characteristic
36	C₂×C₃×#124	C₂²	1	1	yes	characteristic
37	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
38	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
39	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
40	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
41	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
42	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
43	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
44	C₂×C₃×#121	C₂²	1	1	yes	characteristic
45	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	—
46	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
47	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
48	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
49	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
50	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
51	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
52	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
53	C₂×C₃×#117	C₂²	1	2	yes	—
54	C₂×C₃×#117	C₂²	1	2	yes	—
55	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
56	C₃×#400	C₂²	1	2	yes	—
57	C₃×#398	C₂²	1	2	yes	—
58	C₃×#398	C₂²	1	2	yes	—
59	C₃×#398	C₂²	1	2	yes	—
60	C₃×#398	C₂²	1	2	yes	—
61	C₃×#398	C₂²	1	2	yes	—
62	C₃×#397	C₂²	1	2	yes	—
63	C₃×#396	C₂²	1	2	yes	—
64	C₃×#396	C₂²	1	2	yes	—
65	C₃×#396	C₂²	1	2	yes	—
66	C₃×#396	C₂²	1	2	yes	—
67	C₃×#396	C₂²	1	2	yes	—
68	C₃×#396	C₂²	1	2	yes	—
69	C₃×#396	C₂²	1	2	yes	—
70	C₃×#396	C₂²	1	2	yes	—
71	C₃×#395	C₂²	1	2	yes	—
72	C₃×#395	C₂²	1	2	yes	—
73	C₃×#394	C₂²	1	2	yes	—
74	C₃×#394	C₂²	1	2	yes	—
75	C₃×#393	C₂²	1	2	yes	—
76	C₃×#391	C₂²	1	1	yes	characteristic
77	C₃×#391	C₂²	1	1	yes	characteristic
78	C₃×#391	C₂²	1	1	yes	characteristic
79	C₃×#391	C₂²	1	2	yes	—
80	C₃×#391	C₂²	1	1	yes	characteristic
81	C₃×#391	C₂²	1	1	yes	characteristic
82	C₃×#390	C₂²	1	2	yes	—
83	C₃×#390	C₂²	1	1	yes	characteristic
84	C₃×#390	C₂²	1	1	yes	characteristic
85	C₃×#389	C₂²	1	1	yes	characteristic
86	C₃×#389	C₂²	1	1	yes	characteristic
87	C₃×#389	C₂²	1	2	yes	—
88	C₃×#389	C₂²	1	2	yes	—
89	C₃×#389	C₂²	1	2	yes	—
90	C₃×#389	C₂²	1	1	yes	characteristic
91	C₃×#389	C₂²	1	1	yes	characteristic
92	C₃×#389	C₂²	1	2	yes	—
93	C₃×#389	C₂²	1	2	yes	—
94	C₃×#389	C₂²	1	1	yes	characteristic
95	C₃×#389	C₂²	1	2	yes	—
96	C₃×#388	C₂²	1	2	yes	—
97	C₃×#388	C₂²	1	2	yes	—
98	C₃×#388	C₂²	1	2	yes	—
99	C₃×#388	C₂²	1	2	yes	—
100	C₃×#388	C₂²	1	2	yes	—
101	C₃×#388	C₂²	1	2	yes	—
102	C₃×#388	C₂²	1	2	yes	—
103	C₃×#388	C₂²	1	2	yes	—
104	C₃×#388	C₂²	1	2	yes	—
105	C₃×#387	C₂²	1	1	yes	characteristic
106	C₃×#387	C₂²	1	2	yes	—
107	C₃×#387	C₂²	1	2	yes	—
108	C₃×#387	C₂²	1	1	yes	characteristic
109	C₃×#387	C₂²	1	2	yes	—
110	C₃×#386	C₂²	1	2	yes	—
111	C₃×#386	C₂²	1	2	yes	—
112	C₃×#386	C₂²	1	2	yes	—
113	C₃×#385	C₂²	1	2	yes	—
114	C₃×#385	C₂²	1	1	yes	characteristic
115	C₃×#385	C₂²	1	1	yes	characteristic
116	C₃×#382	C₂²	1	2	yes	—
117	C₃×#382	C₂²	1	1	yes	characteristic
118	C₃×#380	C₂²	1	2	yes	—
119	C₃×#380	C₂²	1	1	yes	characteristic
120	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
121	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
122	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
123	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
124	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
125	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
126	C₂×#556	C₂×C₃	1	1	yes	characteristic, complemented
127	C₂×#533	C₂×C₃	1	1	yes	characteristic, complemented
128	#2850	C₂×C₃	1	1	yes	characteristic
129	#2725	C₂×C₃	1	2	yes	complemented
130	#2704	C₂×C₃	1	2	yes	complemented
131	#2702	C₂×C₃	1	2	yes	complemented
132	#2683	C₂×C₃	1	2	yes	complemented
133	#2637	C₂×C₃	1	2	yes	complemented
134	#2609	C₂×C₃	1	2	yes	complemented
135	#2601	C₂×C₃	1	2	yes	complemented
136	#2581	C₂×C₃	1	1	yes	characteristic, complemented
137	#2546	C₂×C₃	1	1	yes	characteristic, complemented
138	#2545	C₂×C₃	1	1	yes	characteristic, complemented
139	#2545	C₂×C₃	1	1	yes	characteristic, complemented
140	#2452	C₂×C₃	1	1	yes	characteristic, complemented
141	#2451	C₂×C₃	1	1	yes	characteristic, complemented
142	#2429	C₂×C₃	1	1	yes	characteristic, complemented
143	#2429	C₂×C₃	1	1	yes	characteristic, complemented
144	#2427	C₂×C₃	1	1	yes	characteristic
145	#2426	C₂×C₃	1	1	yes	characteristic
146	#2351	C₂×C₃	1	1	yes	characteristic, complemented
147	#2323	C₂×C₃	1	2	yes	complemented
148	C₄×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
149	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
150	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
151	C₂²×C₃×Q₈	C₂³	1	2	yes	—
152	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
153	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
154	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
155	C₂²×C₃×D₄	C₂³	1	2	yes	—
156	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
157	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
158	C₂³×C₃×C₄	C₂³	1	2	yes	—
159	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
160	C₃×C₄⋊Q₈	—	2	4	no	—
161	C₃×C₄⋊Q₈	—	2	4	no	—
162	C₃×C₄⋊Q₈	—	2	4	no	—
163	C₃×C₄⋊Q₈	—	4	2	no	—
164	C₃×#126	—	2	8	no	—
165	C₃×#126	—	2	8	no	—
166	C₃×#125	—	2	8	no	—
167	C₃×#124	—	2	4	no	—
168	C₃×#124	—	2	4	no	—
169	C₃×#124	—	4	2	no	—
170	C₃×C₂²⋊Q₈	—	2	4	no	—
171	C₃×C₂²⋊Q₈	—	2	4	no	—
172	C₃×C₂²⋊Q₈	—	2	8	no	—
173	C₃×C₂²⋊Q₈	—	2	8	no	—
174	C₃×C₂²⋊Q₈	—	2	4	no	—
175	C₃×C₂²⋊Q₈	—	2	8	no	—
176	C₃×C₂²⋊Q₈	—	4	2	no	—
177	C₃×#121	—	4	2	no	—
178	C₃×C₄×Q₈	—	2	4	no	—
179	C₃×C₄×Q₈	—	2	8	no	—
180	C₃×C₄×Q₈	—	2	4	no	—
181	C₃×C₄×Q₈	—	2	4	no	—
182	C₃×C₄×Q₈	—	4	2	no	—
183	C₃×C₄×Q₈	—	4	2	no	—
184	C₃×C₄×Q₈	D₄	1	8	yes	complemented
185	C₃×C₄×D₄	—	2	4	no	—
186	C₃×#117	—	2	8	no	—
187	C₃×#117	—	2	8	no	—
188	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
189	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
190	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
191	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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×C₄⋊C₄	C₂³	1	1	yes	characteristic
199	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
200	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
201	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
202	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
203	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
204	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
205	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
206	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
207	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
208	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
209	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
210	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
211	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
212	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
213	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
214	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
215	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
216	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
217	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
218	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
219	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
220	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
221	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
222	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
223	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
224	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
225	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
226	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
227	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
228	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
229	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
230	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
231	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
232	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
233	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
234	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
235	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
236	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
237	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
238	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
239	C₂×C₃×C₄²	—	2	4	no	—
240	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
241	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
242	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
243	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
244	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
245	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
246	C₂×C₃×C₄²	C₂³	1	2	yes	—
247	C₂×C₃×C₄²	C₂³	1	2	yes	—
248	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
249	C₂×C₃×C₄²	C₂³	1	2	yes	—
250	C₂×C₃×C₄²	C₂³	1	2	yes	—
251	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
252	C₂×C₃×C₄²	C₂³	1	2	yes	—
253	C₃×#95	C₂³	1	1	yes	characteristic
254	C₃×#95	C₂³	1	1	yes	characteristic
255	C₃×#95	C₂³	1	1	yes	characteristic
256	C₃×#95	C₂³	1	1	yes	characteristic
257	C₃×#95	C₂³	1	1	yes	characteristic
258	C₃×#95	C₂³	1	1	yes	characteristic
259	C₃×#95	C₂³	1	1	yes	characteristic
260	C₃×#95	C₂³	1	1	yes	characteristic
261	C₃×#95	C₂³	1	2	yes	—
262	C₃×#95	C₂³	1	1	yes	characteristic
263	C₃×#95	C₂³	1	1	yes	characteristic
264	C₃×#95	C₂³	1	2	yes	—
265	C₃×#95	C₂³	1	2	yes	—
266	C₃×#95	C₂³	1	2	yes	—
267	C₃×#95	C₂³	1	2	yes	—
268	C₃×#95	C₂³	1	2	yes	—
269	C₃×#95	C₂³	1	2	yes	—
270	C₃×#95	C₂³	1	2	yes	—
271	C₃×#95	C₂³	1	2	yes	—
272	C₃×#95	C₂³	1	2	yes	—
273	C₃×#95	C₂³	1	2	yes	—
274	C₃×#95	C₂³	1	2	yes	—
275	C₃×#95	C₂³	1	2	yes	—
276	C₃×#95	C₂³	1	2	yes	—
277	#556	—	2	8	no	—
278	#533	—	2	8	no	—
279	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
280	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
281	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
282	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
283	C₂×#126	C₂²×C₃	1	2	yes	—
284	C₂×#126	C₂²×C₃	1	2	yes	—
285	C₂×#125	C₂²×C₃	1	2	yes	—
286	C₂×#124	C₂²×C₃	1	1	yes	characteristic
287	C₂×#124	C₂²×C₃	1	1	yes	characteristic
288	C₂×#124	C₂²×C₃	1	1	yes	characteristic
289	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
290	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
291	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
292	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
293	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
294	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
295	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
296	C₂×#121	C₂²×C₃	1	1	yes	characteristic
297	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	—
298	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
299	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
300	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
301	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
302	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
303	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
304	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
305	C₂×#117	C₂²×C₃	1	2	yes	—
306	C₂×#117	C₂²×C₃	1	2	yes	—
307	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
308	#400	C₂²×C₃	1	2	yes	—
309	#398	C₂²×C₃	1	2	yes	—
310	#398	C₂²×C₃	1	2	yes	—
311	#398	C₂²×C₃	1	2	yes	—
312	#398	C₂²×C₃	1	2	yes	—
313	#398	C₂²×C₃	1	2	yes	—
314	#397	C₂²×C₃	1	2	yes	—
315	#396	C₂²×C₃	1	2	yes	—
316	#396	C₂²×C₃	1	2	yes	—
317	#396	C₂²×C₃	1	2	yes	—
318	#396	C₂²×C₃	1	2	yes	—
319	#396	C₂²×C₃	1	2	yes	—
320	#396	C₂²×C₃	1	2	yes	—
321	#396	C₂²×C₃	1	2	yes	—
322	#396	C₂²×C₃	1	2	yes	—
323	#395	C₂²×C₃	1	2	yes	—
324	#395	C₂²×C₃	1	2	yes	—
325	#394	C₂²×C₃	1	2	yes	—
326	#394	C₂²×C₃	1	2	yes	—
327	#393	C₂²×C₃	1	2	yes	—
328	#391	C₂²×C₃	1	2	yes	—
329	#391	C₂²×C₃	1	1	yes	characteristic
330	#391	C₂²×C₃	1	1	yes	characteristic
331	#391	C₂²×C₃	1	1	yes	characteristic
332	#391	C₂²×C₃	1	1	yes	characteristic
333	#391	C₂²×C₃	1	1	yes	characteristic
334	#390	C₂²×C₃	1	1	yes	characteristic
335	#390	C₂²×C₃	1	2	yes	—
336	#390	C₂²×C₃	1	1	yes	characteristic
337	#389	C₂²×C₃	1	2	yes	—
338	#389	C₂²×C₃	1	2	yes	—
339	#389	C₂²×C₃	1	2	yes	—
340	#389	C₂²×C₃	1	1	yes	characteristic
341	#389	C₂²×C₃	1	1	yes	characteristic
342	#389	C₂²×C₃	1	2	yes	—
343	#389	C₂²×C₃	1	1	yes	characteristic
344	#389	C₂²×C₃	1	2	yes	—
345	#389	C₂²×C₃	1	1	yes	characteristic
346	#389	C₂²×C₃	1	2	yes	—
347	#389	C₂²×C₃	1	1	yes	characteristic
348	#388	C₂²×C₃	1	2	yes	—
349	#388	C₂²×C₃	1	2	yes	—
350	#388	C₂²×C₃	1	2	yes	—
351	#388	C₂²×C₃	1	2	yes	—
352	#388	C₂²×C₃	1	2	yes	—
353	#388	C₂²×C₃	1	2	yes	—
354	#388	C₂²×C₃	1	2	yes	—
355	#388	C₂²×C₃	1	2	yes	—
356	#388	C₂²×C₃	1	2	yes	—
357	#387	C₂²×C₃	1	1	yes	characteristic
358	#387	C₂²×C₃	1	2	yes	—
359	#387	C₂²×C₃	1	2	yes	—
360	#387	C₂²×C₃	1	2	yes	—
361	#387	C₂²×C₃	1	1	yes	characteristic
362	#386	C₂²×C₃	1	2	yes	—
363	#386	C₂²×C₃	1	2	yes	—
364	#386	C₂²×C₃	1	2	yes	—
365	#385	C₂²×C₃	1	1	yes	characteristic
366	#385	C₂²×C₃	1	1	yes	characteristic
367	#385	C₂²×C₃	1	2	yes	—
368	#382	C₂²×C₃	1	1	yes	characteristic
369	#382	C₂²×C₃	1	2	yes	—
370	#380	C₂²×C₃	1	2	yes	—
371	#380	C₂²×C₃	1	1	yes	characteristic
372	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
373	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
374	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
375	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
376	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
377	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
378	C₂⁴×C₃	C₂⁴	1	2	yes	—
379	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
380	C₂×C₃×Q₈	—	2	2	no	—
381	C₂×C₃×Q₈	—	2	4	no	—
382	C₂×C₃×Q₈	—	2	2	no	—
383	C₂×C₃×Q₈	—	2	2	no	—
384	C₂×C₃×Q₈	—	2	4	no	—
385	C₂×C₃×Q₈	—	2	2	no	—
386	C₂×C₃×Q₈	—	2	2	no	—
387	C₂×C₃×Q₈	—	2	2	no	—
388	C₂×C₃×Q₈	—	2	2	no	—
389	C₂×C₃×Q₈	—	2	2	no	—
390	C₂×C₃×Q₈	—	2	2	no	—
391	C₂×C₃×Q₈	—	2	2	no	—
392	C₂×C₃×Q₈	—	4	1	no	—
393	C₂×C₃×Q₈	—	4	2	no	—
394	C₂×C₃×Q₈	C₂×D₄	1	4	yes	—
395	C₂×C₃×D₄	—	2	4	no	—
396	C₂×C₃×D₄	—	2	2	no	—
397	C₂×C₃×D₄	—	2	2	no	—
398	C₂×C₃×D₄	—	2	2	no	—
399	C₂×C₃×D₄	—	4	2	no	—
400	C₂×C₃×D₄	—	4	2	no	—
401	C₂²×C₃×C₄	—	2	2	no	—
402	C₂²×C₃×C₄	—	2	2	no	—
403	C₂²×C₃×C₄	—	2	2	no	—
404	C₂²×C₃×C₄	—	2	2	no	—
405	C₂²×C₃×C₄	—	2	2	no	—
406	C₂²×C₃×C₄	—	2	4	no	—
407	C₂²×C₃×C₄	—	2	2	no	—
408	C₂²×C₃×C₄	—	2	4	no	—
409	C₂²×C₃×C₄	—	2	2	no	—
410	C₂²×C₃×C₄	—	2	2	no	—
411	C₂²×C₃×C₄	—	4	2	no	—
412	C₂²×C₃×C₄	—	4	1	no	—
413	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
414	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
415	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
416	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
417	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
418	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
419	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
420	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
421	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
422	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
423	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
424	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
425	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
426	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
427	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
428	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
429	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
430	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
431	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
432	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
433	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
434	C₃×C₄⋊C₄	—	2	2	no	—
435	C₃×C₄⋊C₄	—	2	4	no	—
436	C₃×C₄⋊C₄	—	2	4	no	—
437	C₃×C₄⋊C₄	—	2	4	no	—
438	C₃×C₄⋊C₄	—	2	4	no	—
439	C₃×C₄⋊C₄	—	2	4	no	—
440	C₃×C₄⋊C₄	—	2	4	no	—
441	C₃×C₄⋊C₄	—	2	4	no	—
442	C₃×C₄⋊C₄	—	2	4	no	—
443	C₃×C₄⋊C₄	—	2	2	no	—
444	C₃×C₄⋊C₄	—	2	2	no	—
445	C₃×C₄⋊C₄	—	2	2	no	—
446	C₃×C₄⋊C₄	—	2	4	no	—
447	C₃×C₄⋊C₄	—	2	2	no	—
448	C₃×C₄⋊C₄	—	2	4	no	—
449	C₃×C₄⋊C₄	—	2	2	no	—
450	C₃×C₄⋊C₄	—	2	4	no	—
451	C₃×C₄⋊C₄	—	2	2	no	—
452	C₃×C₄⋊C₄	—	2	2	no	—
453	C₃×C₄⋊C₄	—	2	2	no	—
454	C₃×C₄⋊C₄	—	2	2	no	—
455	C₃×C₄⋊C₄	—	4	1	no	—
456	C₃×C₄⋊C₄	—	4	2	no	—
457	C₃×C₄⋊C₄	—	4	2	no	—
458	C₃×C₄⋊C₄	—	4	2	no	—
459	C₃×C₄⋊C₄	—	4	2	no	—
460	C₃×C₄⋊C₄	—	4	2	no	—
461	C₃×C₄⋊C₄	—	4	2	no	—
462	C₃×C₄⋊C₄	—	4	2	no	—
463	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
464	C₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
465	C₃×C₄⋊C₄	#41	1	4	yes	—
466	C₃×C₂²⋊C₄	—	2	2	no	—
467	C₃×C₂²⋊C₄	—	2	2	no	—
468	C₃×C₂²⋊C₄	—	2	4	no	—
469	C₃×C₂²⋊C₄	—	2	4	no	—
470	C₃×C₂²⋊C₄	—	2	4	no	—
471	C₃×C₂²⋊C₄	—	2	4	no	—
472	C₃×C₂²⋊C₄	—	2	4	no	—
473	C₃×C₂²⋊C₄	—	2	4	no	—
474	C₃×C₂²⋊C₄	—	2	4	no	—
475	C₃×C₂²⋊C₄	—	2	4	no	—
476	C₃×C₂²⋊C₄	—	2	2	no	—
477	C₃×C₂²⋊C₄	—	2	2	no	—
478	C₃×C₂²⋊C₄	—	2	4	no	—
479	C₃×C₂²⋊C₄	—	2	4	no	—
480	C₃×C₂²⋊C₄	—	4	2	no	—
481	C₃×C₂²⋊C₄	—	4	2	no	—
482	C₃×C₂²⋊C₄	—	4	2	no	—
483	C₃×C₂²⋊C₄	—	4	2	no	—
484	C₃×C₂²⋊C₄	—	4	2	no	—
485	C₃×C₄²	—	2	2	no	—
486	C₃×C₄²	—	2	2	no	—
487	C₃×C₄²	—	2	2	no	—
488	C₃×C₄²	—	2	4	no	—
489	C₃×C₄²	—	2	4	no	—
490	C₃×C₄²	—	2	2	no	—
491	C₃×C₄²	—	2	2	no	—
492	C₃×C₄²	—	2	2	no	—
493	C₃×C₄²	—	2	2	no	—
494	C₃×C₄²	—	4	2	no	—
495	C₃×C₄²	—	4	2	no	—
496	C₃×C₄²	C₂×D₄	1	4	yes	—
497	C₃×C₄²	C₂×D₄	1	8	yes	—
498	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
499	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
500	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
501	C₂²×Q₈	C₂³×C₃	1	2	yes	—
502	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
503	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
504	C₂²×D₄	C₂³×C₃	1	2	yes	—
505	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
506	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
507	C₂³×C₄	C₂³×C₃	1	2	yes	—
508	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
509	C₄⋊Q₈	—	2	4	no	—
510	C₄⋊Q₈	—	2	4	no	—
511	C₄⋊Q₈	—	2	4	no	—
512	C₄⋊Q₈	—	4	2	no	—
513	#126	—	2	8	no	—
514	#126	—	2	8	no	—
515	#125	—	2	8	no	—
516	#124	—	2	4	no	—
517	#124	—	2	4	no	—
518	#124	—	4	2	no	—
519	C₂²⋊Q₈	—	2	4	no	—
520	C₂²⋊Q₈	—	2	4	no	—
521	C₂²⋊Q₈	—	2	8	no	—
522	C₂²⋊Q₈	—	2	8	no	—
523	C₂²⋊Q₈	—	2	8	no	—
524	C₂²⋊Q₈	—	2	4	no	—
525	C₂²⋊Q₈	—	4	2	no	—
526	#121	—	4	2	no	—
527	C₄×Q₈	—	2	4	no	—
528	C₄×Q₈	—	2	8	no	—
529	C₄×Q₈	—	2	4	no	—
530	C₄×Q₈	—	2	4	no	—
531	C₄×Q₈	—	4	2	no	—
532	C₄×Q₈	—	4	2	no	—
533	C₄×Q₈	C₃×D₄	1	8	yes	complemented
534	C₄×D₄	—	2	4	no	—
535	#117	—	2	8	no	—
536	#117	—	2	8	no	—
537	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
538	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
539	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
540	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
541	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
542	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
543	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
544	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
545	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
546	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
547	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
548	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
549	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
550	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
551	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
552	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
553	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
554	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
555	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
556	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
557	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
558	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
559	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
560	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
561	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
562	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
563	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
564	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
565	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
566	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
567	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
568	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
569	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
570	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
571	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
574	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
576	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
577	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
578	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
579	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
580	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
581	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
582	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
583	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
584	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
586	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
588	C₂×C₄²	—	2	4	no	—
589	C₂×C₄²	C₂³×C₃	1	2	yes	—
590	C₂×C₄²	C₂³×C₃	1	2	yes	—
591	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
592	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
593	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
594	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
595	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
596	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
597	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
598	C₂×C₄²	C₂³×C₃	1	2	yes	—
599	C₂×C₄²	C₂³×C₃	1	2	yes	—
600	C₂×C₄²	C₂³×C₃	1	2	yes	—
601	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
602	#95	C₂³×C₃	1	1	yes	characteristic
603	#95	C₂³×C₃	1	1	yes	characteristic
604	#95	C₂³×C₃	1	1	yes	characteristic
605	#95	C₂³×C₃	1	1	yes	characteristic
606	#95	C₂³×C₃	1	1	yes	characteristic
607	#95	C₂³×C₃	1	1	yes	characteristic
608	#95	C₂³×C₃	1	1	yes	characteristic
609	#95	C₂³×C₃	1	1	yes	characteristic
610	#95	C₂³×C₃	1	2	yes	—
611	#95	C₂³×C₃	1	1	yes	characteristic
612	#95	C₂³×C₃	1	1	yes	characteristic
613	#95	C₂³×C₃	1	2	yes	—
614	#95	C₂³×C₃	1	2	yes	—
615	#95	C₂³×C₃	1	2	yes	—
616	#95	C₂³×C₃	1	2	yes	—
617	#95	C₂³×C₃	1	2	yes	—
618	#95	C₂³×C₃	1	2	yes	—
619	#95	C₂³×C₃	1	2	yes	—
620	#95	C₂³×C₃	1	2	yes	—
621	#95	C₂³×C₃	1	2	yes	—
622	#95	C₂³×C₃	1	2	yes	—
623	#95	C₂³×C₃	1	2	yes	—
624	#95	C₂³×C₃	1	2	yes	—
625	#95	C₂³×C₃	1	2	yes	—
626	C₂³×C₃	—	2	1	no	—
627	C₂³×C₃	—	2	1	no	—
628	C₂³×C₃	—	2	1	no	—
629	C₂³×C₃	—	2	1	no	—
630	C₂³×C₃	—	2	1	no	—
631	C₂³×C₃	—	2	1	no	—
632	C₂³×C₃	—	2	2	no	—
633	C₂³×C₃	—	2	2	no	—
634	C₂³×C₃	—	2	2	no	—
635	C₂³×C₃	—	2	2	no	—
636	C₂³×C₃	—	2	2	no	—
637	C₂³×C₃	—	2	2	no	—
638	C₂³×C₃	—	2	2	no	—
639	C₂³×C₃	2₋¹⁺⁴	1	2	yes	—
640	C₂³×C₃	C₂⁵	1	1	yes	characteristic
641	C₃×Q₈	—	2	8	no	—
642	C₃×Q₈	—	4	4	no	—
643	C₃×Q₈	—	4	8	no	—
644	C₃×Q₈	—	4	4	no	—
645	C₃×Q₈	—	4	4	no	—
646	C₃×D₄	—	4	4	no	—
647	C₃×D₄	—	8	4	no	—
648	C₂×C₃×C₄	—	2	8	no	—
649	C₂×C₃×C₄	—	2	1	no	—
650	C₂×C₃×C₄	—	2	1	no	—
651	C₂×C₃×C₄	—	2	1	no	—
652	C₂×C₃×C₄	—	2	1	no	—
653	C₂×C₃×C₄	—	2	2	no	—
654	C₂×C₃×C₄	—	2	1	no	—
655	C₂×C₃×C₄	—	2	2	no	—
656	C₂×C₃×C₄	—	2	1	no	—
657	C₂×C₃×C₄	—	2	1	no	—
658	C₂×C₃×C₄	—	2	1	no	—
659	C₂×C₃×C₄	—	2	1	no	—
660	C₂×C₃×C₄	—	2	2	no	—
661	C₂×C₃×C₄	—	2	1	no	—
662	C₂×C₃×C₄	—	2	2	no	—
663	C₂×C₃×C₄	—	2	1	no	—
664	C₂×C₃×C₄	—	2	1	no	—
665	C₂×C₃×C₄	—	2	1	no	—
666	C₂×C₃×C₄	—	2	1	no	—
667	C₂×C₃×C₄	—	2	1	no	—
668	C₂×C₃×C₄	—	2	2	no	—
669	C₂×C₃×C₄	—	2	1	no	—
670	C₂×C₃×C₄	—	2	2	no	—
671	C₂×C₃×C₄	—	2	2	no	—
672	C₂×C₃×C₄	—	2	1	no	—
673	C₂×C₃×C₄	—	2	2	no	—
674	C₂×C₃×C₄	—	2	1	no	—
675	C₂×C₃×C₄	—	2	2	no	—
676	C₂×C₃×C₄	—	2	1	no	—
677	C₂×C₃×C₄	—	2	1	no	—
678	C₂×C₃×C₄	—	2	1	no	—
679	C₂×C₃×C₄	—	2	2	no	—
680	C₂×C₃×C₄	—	2	2	no	—
681	C₂×C₃×C₄	—	2	1	no	—
682	C₂×C₃×C₄	—	2	2	no	—
683	C₂×C₃×C₄	—	2	2	no	—
684	C₂×C₃×C₄	—	2	1	no	—
685	C₂×C₃×C₄	—	2	1	no	—
686	C₂×C₃×C₄	—	2	2	no	—
687	C₂×C₃×C₄	—	2	1	no	—
688	C₂×C₃×C₄	—	2	1	no	—
689	C₂×C₃×C₄	—	2	1	no	—
690	C₂×C₃×C₄	—	2	1	no	—
691	C₂×C₃×C₄	—	2	1	no	—
692	C₂×C₃×C₄	—	2	1	no	—
693	C₂×C₃×C₄	—	2	2	no	—
694	C₂×C₃×C₄	—	2	2	no	—
695	C₂×C₃×C₄	—	2	2	no	—
696	C₂×C₃×C₄	—	2	1	no	—
697	C₂×C₃×C₄	—	2	2	no	—
698	C₂×C₃×C₄	—	2	1	no	—
699	C₂×C₃×C₄	—	2	2	no	—
700	C₂×C₃×C₄	—	2	1	no	—
701	C₂×C₃×C₄	—	4	8	no	—
702	C₂×C₃×C₄	—	4	4	no	—
703	C₂×C₃×C₄	—	4	4	no	—
704	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
705	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
706	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
707	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
708	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
709	C₂×C₃×C₄	C₂×#41	1	2	yes	—
710	C₂×C₃×C₄	C₂×#41	1	2	yes	—
711	C₂×C₃×C₄	C₂×#41	1	2	yes	—
712	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
713	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
714	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
715	C₂⁴	C₂⁴×C₃	1	2	yes	—
716	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
717	C₂×Q₈	—	2	2	no	—
718	C₂×Q₈	—	2	4	no	—
719	C₂×Q₈	—	2	2	no	—
720	C₂×Q₈	—	2	2	no	—
721	C₂×Q₈	—	2	4	no	—
722	C₂×Q₈	—	2	2	no	—
723	C₂×Q₈	—	2	2	no	—
724	C₂×Q₈	—	2	2	no	—
725	C₂×Q₈	—	2	2	no	—
726	C₂×Q₈	—	2	2	no	—
727	C₂×Q₈	—	2	2	no	—
728	C₂×Q₈	—	2	2	no	—
729	C₂×Q₈	—	4	1	no	—
730	C₂×Q₈	—	4	2	no	—
731	C₂×Q₈	C₂×C₃×D₄	1	4	yes	—
732	C₂×D₄	—	2	4	no	—
733	C₂×D₄	—	2	2	no	—
734	C₂×D₄	—	2	2	no	—
735	C₂×D₄	—	2	2	no	—
736	C₂×D₄	—	4	2	no	—
737	C₂×D₄	—	4	2	no	—
738	C₂²×C₄	—	2	2	no	—
739	C₂²×C₄	—	2	2	no	—
740	C₂²×C₄	—	2	2	no	—
741	C₂²×C₄	—	2	2	no	—
742	C₂²×C₄	—	2	2	no	—
743	C₂²×C₄	—	2	4	no	—
744	C₂²×C₄	—	2	2	no	—
745	C₂²×C₄	—	2	4	no	—
746	C₂²×C₄	—	2	2	no	—
747	C₂²×C₄	—	2	2	no	—
748	C₂²×C₄	—	4	2	no	—
749	C₂²×C₄	—	4	1	no	—
750	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
751	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
752	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
753	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
754	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
755	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
756	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
757	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
758	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
759	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
760	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
761	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
762	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
763	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
764	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
765	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
766	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
767	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
768	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
769	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
770	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
771	C₄⋊C₄	—	2	2	no	—
772	C₄⋊C₄	—	2	4	no	—
773	C₄⋊C₄	—	2	4	no	—
774	C₄⋊C₄	—	2	4	no	—
775	C₄⋊C₄	—	2	4	no	—
776	C₄⋊C₄	—	2	4	no	—
777	C₄⋊C₄	—	2	4	no	—
778	C₄⋊C₄	—	2	4	no	—
779	C₄⋊C₄	—	2	4	no	—
780	C₄⋊C₄	—	2	2	no	—
781	C₄⋊C₄	—	2	2	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	4	no	—
784	C₄⋊C₄	—	2	4	no	—
785	C₄⋊C₄	—	2	2	no	—
786	C₄⋊C₄	—	2	2	no	—
787	C₄⋊C₄	—	2	4	no	—
788	C₄⋊C₄	—	2	2	no	—
789	C₄⋊C₄	—	2	2	no	—
790	C₄⋊C₄	—	2	2	no	—
791	C₄⋊C₄	—	2	2	no	—
792	C₄⋊C₄	—	4	2	no	—
793	C₄⋊C₄	—	4	2	no	—
794	C₄⋊C₄	—	4	2	no	—
795	C₄⋊C₄	—	4	2	no	—
796	C₄⋊C₄	—	4	2	no	—
797	C₄⋊C₄	—	4	1	no	—
798	C₄⋊C₄	—	4	2	no	—
799	C₄⋊C₄	—	4	2	no	—
800	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
801	C₄⋊C₄	C₂×C₃×D₄	1	8	yes	—
802	C₄⋊C₄	C₃×#41	1	4	yes	—
803	C₂²⋊C₄	—	2	2	no	—
804	C₂²⋊C₄	—	2	2	no	—
805	C₂²⋊C₄	—	2	4	no	—
806	C₂²⋊C₄	—	2	4	no	—
807	C₂²⋊C₄	—	2	4	no	—
808	C₂²⋊C₄	—	2	4	no	—
809	C₂²⋊C₄	—	2	4	no	—
810	C₂²⋊C₄	—	2	4	no	—
811	C₂²⋊C₄	—	2	4	no	—
812	C₂²⋊C₄	—	2	4	no	—
813	C₂²⋊C₄	—	2	2	no	—
814	C₂²⋊C₄	—	2	2	no	—
815	C₂²⋊C₄	—	2	4	no	—
816	C₂²⋊C₄	—	2	4	no	—
817	C₂²⋊C₄	—	4	2	no	—
818	C₂²⋊C₄	—	4	2	no	—
819	C₂²⋊C₄	—	4	2	no	—
820	C₂²⋊C₄	—	4	2	no	—
821	C₂²⋊C₄	—	4	2	no	—
822	C₄²	—	2	2	no	—
823	C₄²	—	2	2	no	—
824	C₄²	—	2	2	no	—
825	C₄²	—	2	4	no	—
826	C₄²	—	2	4	no	—
827	C₄²	—	2	2	no	—
828	C₄²	—	2	2	no	—
829	C₄²	—	2	2	no	—
830	C₄²	—	2	2	no	—
831	C₄²	—	4	2	no	—
832	C₄²	—	4	2	no	—
833	C₄²	C₂×C₃×D₄	1	4	yes	—
834	C₄²	C₂×C₃×D₄	1	8	yes	—
835	C₂²×C₃	—	2	2	no	—
836	C₂²×C₃	—	2	2	no	—
837	C₂²×C₃	—	2	2	no	—
838	C₂²×C₃	—	4	1	no	—
839	C₂²×C₃	—	4	1	no	—
840	C₂²×C₃	—	4	1	no	—
841	C₂²×C₃	—	4	1	no	—
842	C₂²×C₃	—	4	2	no	—
843	C₂²×C₃	—	4	2	no	—
844	C₂²×C₃	—	4	2	no	—
845	C₂²×C₃	—	4	2	no	—
846	C₂²×C₃	—	4	2	no	—
847	C₂²×C₃	—	4	2	no	—
848	C₂²×C₃	—	4	2	no	—
849	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
850	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
851	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
852	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
853	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
854	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
855	C₂²×C₃	#585	1	1	yes	characteristic
856	C₃×C₄	—	2	4	no	—
857	C₃×C₄	—	2	2	no	—
858	C₃×C₄	—	2	4	no	—
859	C₃×C₄	—	2	2	no	—
860	C₃×C₄	—	2	2	no	—
861	C₃×C₄	—	2	2	no	—
862	C₃×C₄	—	2	2	no	—
863	C₃×C₄	—	2	2	no	—
864	C₃×C₄	—	4	1	no	—
865	C₃×C₄	—	4	2	no	—
866	C₃×C₄	—	4	2	no	—
867	C₃×C₄	—	4	1	no	—
868	C₃×C₄	—	4	2	no	—
869	C₃×C₄	—	4	1	no	—
870	C₃×C₄	—	4	1	no	—
871	C₃×C₄	—	4	1	no	—
872	C₃×C₄	—	4	2	no	—
873	C₃×C₄	—	4	1	no	—
874	C₃×C₄	—	4	1	no	—
875	C₃×C₄	—	4	2	no	—
876	C₃×C₄	#537	1	4	yes	—
877	C₂³	—	2	1	no	—
878	C₂³	—	2	1	no	—
879	C₂³	—	2	1	no	—
880	C₂³	—	2	1	no	—
881	C₂³	—	2	1	no	—
882	C₂³	—	2	1	no	—
883	C₂³	—	2	2	no	—
884	C₂³	—	2	2	no	—
885	C₂³	—	2	2	no	—
886	C₂³	—	2	2	no	—
887	C₂³	—	2	2	no	—
888	C₂³	—	2	2	no	—
889	C₂³	—	2	2	no	—
890	C₂³	C₃×2₋¹⁺⁴	1	2	yes	—
891	C₂³	C₂⁵×C₃	1	1	yes	characteristic
892	Q₈	—	2	8	no	—
893	Q₈	—	4	4	no	—
894	Q₈	—	4	8	no	—
895	Q₈	—	4	4	no	—
896	Q₈	—	4	4	no	—
897	D₄	—	4	4	no	—
898	D₄	—	8	4	no	—
899	C₂×C₄	—	2	8	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	2	1	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	1	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	1	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	1	no	—
917	C₂×C₄	—	2	1	no	—
918	C₂×C₄	—	2	1	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	1	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	1	no	—
924	C₂×C₄	—	2	2	no	—
925	C₂×C₄	—	2	1	no	—
926	C₂×C₄	—	2	2	no	—
927	C₂×C₄	—	2	1	no	—
928	C₂×C₄	—	2	1	no	—
929	C₂×C₄	—	2	1	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	2	1	no	—
933	C₂×C₄	—	2	2	no	—
934	C₂×C₄	—	2	2	no	—
935	C₂×C₄	—	2	1	no	—
936	C₂×C₄	—	2	1	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	2	1	no	—
939	C₂×C₄	—	2	1	no	—
940	C₂×C₄	—	2	1	no	—
941	C₂×C₄	—	2	1	no	—
942	C₂×C₄	—	2	1	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	2	2	no	—
945	C₂×C₄	—	2	2	no	—
946	C₂×C₄	—	2	2	no	—
947	C₂×C₄	—	2	1	no	—
948	C₂×C₄	—	2	2	no	—
949	C₂×C₄	—	2	1	no	—
950	C₂×C₄	—	2	2	no	—
951	C₂×C₄	—	2	1	no	—
952	C₂×C₄	—	4	8	no	—
953	C₂×C₄	—	4	4	no	—
954	C₂×C₄	—	4	4	no	—
955	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
956	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
957	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
958	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
959	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
960	C₂×C₄	C₂×C₃×#41	1	2	yes	—
961	C₂×C₄	C₂×C₃×#41	1	2	yes	—
962	C₂×C₄	C₂×C₃×#41	1	2	yes	—
963	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
964	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
965	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
966	C₂×C₃	—	4	2	no	—
967	C₂×C₃	—	8	2	no	—
968	C₂×C₃	C₂×#537	1	1	yes	characteristic
969	C₂×C₃	D₄×#41	1	1	yes	characteristic
970	C₂×C₃	#3486	1	1	yes	characteristic
971	C₂×C₃	#3511	1	1	yes	characteristic
972	C₂×C₃	#3523	1	1	yes	characteristic
973	C₂×C₃	#3555	1	1	yes	characteristic
974	C₂×C₃	#3561	1	1	yes	characteristic
975	C₂²	—	2	2	no	—
976	C₂²	—	2	2	no	—
977	C₂²	—	2	2	no	—
978	C₂²	—	4	1	no	—
979	C₂²	—	4	1	no	—
980	C₂²	—	4	1	no	—
981	C₂²	—	4	1	no	—
982	C₂²	—	4	2	no	—
983	C₂²	—	4	2	no	—
984	C₂²	—	4	2	no	—
985	C₂²	—	4	2	no	—
986	C₂²	—	4	2	no	—
987	C₂²	—	4	2	no	—
988	C₂²	—	4	2	no	—
989	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
990	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
991	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
992	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
993	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
994	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
995	C₂²	C₃×#585	1	1	yes	characteristic
996	C₄	—	2	4	no	—
997	C₄	—	2	2	no	—
998	C₄	—	2	4	no	—
999	C₄	—	2	2	no	—
1000	C₄	—	2	2	no	—
1001	C₄	—	2	2	no	—
1002	C₄	—	2	2	no	—
1003	C₄	—	2	2	no	—
1004	C₄	—	4	1	no	—
1005	C₄	—	4	2	no	—
1006	C₄	—	4	2	no	—
1007	C₄	—	4	1	no	—
1008	C₄	—	4	2	no	—
1009	C₄	—	4	1	no	—
1010	C₄	—	4	1	no	—
1011	C₄	—	4	1	no	—
1012	C₄	—	4	2	no	—
1013	C₄	—	4	2	no	—
1014	C₄	—	4	1	no	—
1015	C₄	—	4	1	no	—
1016	C₄	C₃×#537	1	4	yes	—
1017	C₃	#39879	1	1	yes	characteristic, direct product factor, Sylow
1018	C₂	—	4	2	no	—
1019	C₂	—	8	2	no	—
1020	C₂	C₂×C₃×#537	1	1	yes	characteristic
1021	C₂	C₃×D₄×#41	1	1	yes	characteristic
1022	C₂	C₃×#3486	1	1	yes	characteristic
1023	C₂	C₃×#3511	1	1	yes	characteristic
1024	C₂	C₃×#3523	1	1	yes	characteristic
1025	C₂	C₃×#3555	1	1	yes	characteristic
1026	C₂	C₃×#3561	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂×C₃×#121	C₂²
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. C₂×C₃×#556	C₂	semidirect
2. C₂×C₃×#533	C₂	semidirect
4. C₃×#2725	C₂	semidirect
5. C₃×#2704	C₂	semidirect
6. C₃×#2702	C₂	semidirect
7. C₃×#2683	C₂	semidirect
8. C₃×#2637	C₂	semidirect
9. C₃×#2609	C₂	semidirect
10. C₃×#2601	C₂	semidirect
11. C₃×#2581	C₂	semidirect
12. C₃×#2546	C₂	semidirect
13. C₃×#2545	C₂	semidirect
14. C₃×#2545	C₂	semidirect
15. C₃×#2452	C₂	semidirect
16. C₃×#2451	C₂	semidirect
17. C₃×#2429	C₂	semidirect
18. C₃×#2429	C₂	semidirect
21. C₃×#2351	C₂	semidirect
22. C₃×#2323	C₂	semidirect
23. C₃×C₄×C₂²⋊Q₈	C₂	semidirect
24. #39879	C₃	direct (N × H)
126. C₂×#556	C₂×C₃	semidirect
127. C₂×#533	C₂×C₃	semidirect
129. #2725	C₂×C₃	semidirect
130. #2704	C₂×C₃	semidirect
131. #2702	C₂×C₃	semidirect
132. #2683	C₂×C₃	semidirect
133. #2637	C₂×C₃	semidirect
134. #2609	C₂×C₃	semidirect
135. #2601	C₂×C₃	semidirect
136. #2581	C₂×C₃	semidirect
137. #2546	C₂×C₃	semidirect
138. #2545	C₂×C₃	semidirect
139. #2545	C₂×C₃	semidirect
140. #2452	C₂×C₃	semidirect
141. #2451	C₂×C₃	semidirect
142. #2429	C₂×C₃	semidirect
143. #2429	C₂×C₃	semidirect
146. #2351	C₂×C₃	semidirect
147. #2323	C₂×C₃	semidirect
148. C₄×C₂²⋊Q₈	C₂×C₃	semidirect
184. C₃×C₄×Q₈	D₄	semidirect
533. C₄×Q₈	C₃×D₄	semidirect
1017. C₃	#39879	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#556	2
C₂×C₃×#533	2
C₃×#2850	2
C₃×#2725	2
C₃×#2704	2
C₃×#2702	2
C₃×#2683	2
C₃×#2637	2
C₃×#2609	2
C₃×#2601	2
C₃×#2581	2
C₃×#2546	2
C₃×#2545	2
C₃×#2452	2
C₃×#2451	2
C₃×#2429	2
C₃×#2427	2
C₃×#2426	2
C₃×#2351	2
C₃×#2323	2
C₃×C₄×C₂²⋊Q₈	2
#39879	3

Subgroups — C3×#39879 #10658486

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#39879 #10658486