Subgroups — C₃×#36139 #10654746

Order 768.

2588 conjugacy classes of subgroups.

The subgroup lattice has 1106 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#532	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2855	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2854	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2850	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#2550	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#2544	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2521	C₂	1	2	yes	maximal, complemented
9	C₃×#2474	C₂	1	2	yes	maximal, complemented
10	C₃×#2468	C₂	1	2	yes	maximal, complemented
11	C₃×#2454	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2451	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#2447	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#2445	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#2443	C₂	1	2	yes	maximal, complemented
16	C₃×#2425	C₂	1	2	yes	maximal, complemented
17	C₃×#2406	C₂	1	2	yes	maximal, complemented
18	C₃×#2367	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#2359	C₂	1	2	yes	maximal, complemented
20	C₃×#2349	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×#2339	C₂	1	2	yes	maximal, complemented
22	C₃×C₄×#121	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₃×C₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
24	#36139	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂²×C₃×#41	C₂²	1	2	yes	—
26	C₃×#532	—	2	8	no	—
27	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₃×#127	C₂²	1	1	yes	characteristic
29	C₃×#529	—	2	8	no	—
30	C₂×C₃×#126	C₂²	1	2	yes	—
31	C₂×C₃×#125	C₂²	1	1	yes	characteristic
32	C₂×C₃×#124	C₂²	1	1	yes	characteristic
33	C₂×C₃×#124	C₂²	1	1	yes	characteristic
34	C₂×C₃×#124	C₂²	1	2	yes	—
35	C₂×C₃×#123	C₂²	1	2	yes	—
36	C₂×C₃×#123	C₂²	1	2	yes	—
37	C₂×C₃×#123	C₂²	1	2	yes	—
38	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
39	C₂×C₃×#121	C₂²	1	2	yes	—
40	C₂×C₃×#121	C₂²	1	1	yes	characteristic
41	C₂×C₃×#121	C₂²	1	1	yes	characteristic
42	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
43	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
44	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
45	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
46	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
47	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
48	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
49	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
50	C₂×C₃×#117	C₂²	1	2	yes	—
51	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
52	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
53	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
54	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
55	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
56	C₃×#399	C₂²	1	2	yes	—
57	C₃×#398	C₂²	1	2	yes	—
58	C₃×#398	C₂²	1	2	yes	—
59	C₃×#397	C₂²	1	2	yes	—
60	C₃×#397	C₂²	1	2	yes	—
61	C₃×#396	C₂²	1	2	yes	—
62	C₃×#395	C₂²	1	2	yes	—
63	C₃×#395	C₂²	1	2	yes	—
64	C₃×#394	C₂²	1	2	yes	—
65	C₃×#394	C₂²	1	2	yes	—
66	C₃×#394	C₂²	1	2	yes	—
67	C₃×#394	C₂²	1	2	yes	—
68	C₃×#391	C₂²	1	1	yes	characteristic
69	C₃×#391	C₂²	1	1	yes	characteristic
70	C₃×#391	C₂²	1	2	yes	—
71	C₃×#391	C₂²	1	1	yes	characteristic
72	C₃×#391	C₂²	1	2	yes	—
73	C₃×#390	C₂²	1	1	yes	characteristic
74	C₃×#390	C₂²	1	1	yes	characteristic
75	C₃×#390	C₂²	1	1	yes	characteristic
76	C₃×#390	C₂²	1	1	yes	characteristic
77	C₃×#389	C₂²	1	2	yes	—
78	C₃×#389	C₂²	1	1	yes	characteristic
79	C₃×#389	C₂²	1	1	yes	characteristic
80	C₃×#389	C₂²	1	1	yes	characteristic
81	C₃×#389	C₂²	1	1	yes	characteristic
82	C₃×#389	C₂²	1	1	yes	characteristic
83	C₃×#388	C₂²	1	2	yes	—
84	C₃×#388	C₂²	1	2	yes	—
85	C₃×#388	C₂²	1	2	yes	—
86	C₃×#388	C₂²	1	2	yes	—
87	C₃×#388	C₂²	1	2	yes	—
88	C₃×#388	C₂²	1	2	yes	—
89	C₃×#388	C₂²	1	2	yes	—
90	C₃×#387	C₂²	1	2	yes	—
91	C₃×#387	C₂²	1	2	yes	—
92	C₃×#387	C₂²	1	2	yes	—
93	C₃×#386	C₂²	1	2	yes	—
94	C₃×#386	C₂²	1	2	yes	—
95	C₃×#386	C₂²	1	2	yes	—
96	C₃×#386	C₂²	1	2	yes	—
97	C₃×#386	C₂²	1	2	yes	—
98	C₃×#386	C₂²	1	2	yes	—
99	C₃×#386	C₂²	1	2	yes	—
100	C₃×#385	C₂²	1	2	yes	—
101	C₃×#385	C₂²	1	2	yes	—
102	C₃×#385	C₂²	1	2	yes	—
103	C₃×#385	C₂²	1	2	yes	—
104	C₃×#385	C₂²	1	2	yes	—
105	C₃×#385	C₂²	1	2	yes	—
106	C₃×#382	C₂²	1	1	yes	characteristic
107	C₃×#381	C₂²	1	2	yes	—
108	C₃×#381	C₂²	1	2	yes	—
109	C₃×#380	C₂²	1	2	yes	—
110	C₃×#380	C₂²	1	2	yes	—
111	C₃×#380	C₂²	1	1	yes	characteristic
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×C₄⋊C₄	C₂²	1	1	yes	characteristic
119	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
120	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
121	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
122	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
123	C₂×C₃×#95	C₂²	1	1	yes	characteristic
124	C₂×C₃×#95	C₂²	1	1	yes	characteristic
125	C₂×C₃×#95	C₂²	1	2	yes	—
126	C₂×#532	C₂×C₃	1	1	yes	characteristic
127	C₂×#529	C₂×C₃	1	1	yes	characteristic, complemented
128	#2855	C₂×C₃	1	1	yes	characteristic, complemented
129	#2854	C₂×C₃	1	1	yes	characteristic, complemented
130	#2850	C₂×C₃	1	1	yes	characteristic, complemented
131	#2550	C₂×C₃	1	1	yes	characteristic, complemented
132	#2544	C₂×C₃	1	1	yes	characteristic, complemented
133	#2521	C₂×C₃	1	2	yes	complemented
134	#2474	C₂×C₃	1	2	yes	complemented
135	#2468	C₂×C₃	1	2	yes	complemented
136	#2454	C₂×C₃	1	1	yes	characteristic, complemented
137	#2451	C₂×C₃	1	1	yes	characteristic, complemented
138	#2447	C₂×C₃	1	1	yes	characteristic, complemented
139	#2445	C₂×C₃	1	1	yes	characteristic, complemented
140	#2443	C₂×C₃	1	2	yes	complemented
141	#2425	C₂×C₃	1	2	yes	complemented
142	#2406	C₂×C₃	1	2	yes	complemented
143	#2367	C₂×C₃	1	1	yes	characteristic, complemented
144	#2359	C₂×C₃	1	2	yes	complemented
145	#2349	C₂×C₃	1	1	yes	characteristic, complemented
146	#2339	C₂×C₃	1	2	yes	complemented
147	C₄×#121	C₂×C₃	1	1	yes	characteristic, complemented
148	C₂×C₄×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
149	C₂×C₃×#41	—	2	8	no	—
150	C₂×C₃×#41	—	2	8	no	—
151	C₂×C₃×#41	—	4	4	no	—
152	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
153	C₂²×C₃×Q₈	C₂³	1	2	yes	—
154	C₂²×C₃×D₄	C₂³	1	2	yes	—
155	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
156	C₂²×C₃×D₄	C₂³	1	2	yes	—
157	C₂²×C₃×D₄	C₂³	1	2	yes	—
158	C₂²×C₃×D₄	C₂³	1	2	yes	—
159	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
160	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
161	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
162	C₂³×C₃×C₄	C₂³	1	2	yes	—
163	C₂³×C₃×C₄	C₂³	1	2	yes	—
164	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
165	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
166	C₂³×C₃×C₄	C₂³	1	2	yes	—
167	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
168	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
169	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
170	C₂³×C₃×C₄	C₂³	1	2	yes	—
171	C₃×C₄⋊Q₈	—	2	4	no	—
172	C₃×#127	—	2	4	no	—
173	C₃×#126	—	2	8	no	—
174	C₃×#125	—	2	4	no	—
175	C₃×#124	—	2	4	no	—
176	C₃×#124	—	2	8	no	—
177	C₃×#124	—	2	4	no	—
178	C₃×#123	—	2	8	no	—
179	C₃×#123	—	2	8	no	—
180	C₃×#123	—	4	4	no	—
181	C₃×C₂²⋊Q₈	—	2	4	no	—
182	C₃×#121	—	2	8	no	—
183	C₃×#121	—	2	4	no	—
184	C₃×#121	D₄	1	8	yes	—
185	C₃×C₄×Q₈	—	2	4	no	—
186	C₃×C₄×D₄	—	2	4	no	—
187	C₃×C₄×D₄	—	2	8	no	—
188	C₃×C₄×D₄	—	2	4	no	—
189	C₃×C₄×D₄	—	2	4	no	—
190	C₃×C₄×D₄	—	2	8	no	—
191	C₃×C₄×D₄	—	2	4	no	—
192	C₃×C₄×D₄	—	4	4	no	—
193	C₃×#117	—	2	8	no	—
194	C₂×C₃×C₄⋊C₄	—	2	4	no	—
195	C₂×C₃×C₄⋊C₄	—	2	4	no	—
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	1	yes	characteristic
200	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
201	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
202	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
203	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
204	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
205	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
206	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
207	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
219	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
220	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
221	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
222	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
223	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
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	—	2	4	no	—
241	C₂×C₃×C₄²	—	2	4	no	—
242	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
243	C₂×C₃×C₄²	C₂³	1	2	yes	—
244	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
245	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
246	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
247	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
248	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
249	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
250	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
251	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
252	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
253	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
254	C₂×C₃×C₄²	C₂³	1	2	yes	—
255	C₂×C₃×C₄²	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	1	yes	characteristic
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	C₃×#95	C₂³	1	2	yes	—
278	C₃×#95	C₂³	1	2	yes	—
279	C₂²×#41	C₂²×C₃	1	2	yes	—
280	#532	—	2	8	no	—
281	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
282	C₂×#127	C₂²×C₃	1	1	yes	characteristic
283	#529	—	2	8	no	—
284	C₂×#126	C₂²×C₃	1	2	yes	—
285	C₂×#125	C₂²×C₃	1	1	yes	characteristic
286	C₂×#124	C₂²×C₃	1	1	yes	characteristic
287	C₂×#124	C₂²×C₃	1	1	yes	characteristic
288	C₂×#124	C₂²×C₃	1	2	yes	—
289	C₂×#123	C₂²×C₃	1	2	yes	—
290	C₂×#123	C₂²×C₃	1	2	yes	—
291	C₂×#123	C₂²×C₃	1	2	yes	—
292	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
293	C₂×#121	C₂²×C₃	1	1	yes	characteristic
294	C₂×#121	C₂²×C₃	1	2	yes	—
295	C₂×#121	C₂²×C₃	1	1	yes	characteristic
296	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
297	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
298	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
299	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
300	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
301	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
302	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
303	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
304	C₂×#117	C₂²×C₃	1	2	yes	—
305	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
306	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
307	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
308	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
309	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
310	#399	C₂²×C₃	1	2	yes	—
311	#398	C₂²×C₃	1	2	yes	—
312	#398	C₂²×C₃	1	2	yes	—
313	#397	C₂²×C₃	1	2	yes	—
314	#397	C₂²×C₃	1	2	yes	—
315	#396	C₂²×C₃	1	2	yes	—
316	#395	C₂²×C₃	1	2	yes	—
317	#395	C₂²×C₃	1	2	yes	—
318	#394	C₂²×C₃	1	2	yes	—
319	#394	C₂²×C₃	1	2	yes	—
320	#394	C₂²×C₃	1	2	yes	—
321	#394	C₂²×C₃	1	2	yes	—
322	#391	C₂²×C₃	1	1	yes	characteristic
323	#391	C₂²×C₃	1	2	yes	—
324	#391	C₂²×C₃	1	2	yes	—
325	#391	C₂²×C₃	1	1	yes	characteristic
326	#391	C₂²×C₃	1	1	yes	characteristic
327	#390	C₂²×C₃	1	1	yes	characteristic
328	#390	C₂²×C₃	1	1	yes	characteristic
329	#390	C₂²×C₃	1	1	yes	characteristic
330	#390	C₂²×C₃	1	1	yes	characteristic
331	#389	C₂²×C₃	1	1	yes	characteristic
332	#389	C₂²×C₃	1	1	yes	characteristic
333	#389	C₂²×C₃	1	1	yes	characteristic
334	#389	C₂²×C₃	1	1	yes	characteristic
335	#389	C₂²×C₃	1	2	yes	—
336	#389	C₂²×C₃	1	1	yes	characteristic
337	#388	C₂²×C₃	1	2	yes	—
338	#388	C₂²×C₃	1	2	yes	—
339	#388	C₂²×C₃	1	2	yes	—
340	#388	C₂²×C₃	1	2	yes	—
341	#388	C₂²×C₃	1	2	yes	—
342	#388	C₂²×C₃	1	2	yes	—
343	#388	C₂²×C₃	1	2	yes	—
344	#387	C₂²×C₃	1	2	yes	—
345	#387	C₂²×C₃	1	2	yes	—
346	#387	C₂²×C₃	1	2	yes	—
347	#386	C₂²×C₃	1	2	yes	—
348	#386	C₂²×C₃	1	2	yes	—
349	#386	C₂²×C₃	1	2	yes	—
350	#386	C₂²×C₃	1	2	yes	—
351	#386	C₂²×C₃	1	2	yes	—
352	#386	C₂²×C₃	1	2	yes	—
353	#386	C₂²×C₃	1	2	yes	—
354	#385	C₂²×C₃	1	2	yes	—
355	#385	C₂²×C₃	1	2	yes	—
356	#385	C₂²×C₃	1	2	yes	—
357	#385	C₂²×C₃	1	2	yes	—
358	#385	C₂²×C₃	1	2	yes	—
359	#385	C₂²×C₃	1	2	yes	—
360	#382	C₂²×C₃	1	1	yes	characteristic
361	#381	C₂²×C₃	1	2	yes	—
362	#381	C₂²×C₃	1	2	yes	—
363	#380	C₂²×C₃	1	2	yes	—
364	#380	C₂²×C₃	1	1	yes	characteristic
365	#380	C₂²×C₃	1	2	yes	—
366	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
367	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
368	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
369	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
370	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
371	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
372	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
373	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
374	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
375	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
376	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
377	C₂×#95	C₂²×C₃	1	1	yes	characteristic
378	C₂×#95	C₂²×C₃	1	2	yes	—
379	C₂×#95	C₂²×C₃	1	1	yes	characteristic
380	C₂⁴×C₃	C₂⁴	1	2	yes	—
381	C₂⁴×C₃	C₂⁴	1	2	yes	—
382	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
383	C₃×#41	—	4	32	no	—
384	C₂×C₃×Q₈	—	2	2	no	—
385	C₂×C₃×Q₈	—	2	4	no	—
386	C₂×C₃×Q₈	—	2	2	no	—
387	C₂×C₃×Q₈	—	2	4	no	—
388	C₂×C₃×Q₈	—	2	2	no	—
389	C₂×C₃×Q₈	—	4	2	no	—
390	C₂×C₃×D₄	—	2	4	no	—
391	C₂×C₃×D₄	—	2	4	no	—
392	C₂×C₃×D₄	—	2	4	no	—
393	C₂×C₃×D₄	—	2	4	no	—
394	C₂×C₃×D₄	—	2	4	no	—
395	C₂×C₃×D₄	—	2	4	no	—
396	C₂×C₃×D₄	—	2	4	no	—
397	C₂×C₃×D₄	—	2	2	no	—
398	C₂×C₃×D₄	—	2	2	no	—
399	C₂×C₃×D₄	—	2	4	no	—
400	C₂×C₃×D₄	—	2	2	no	—
401	C₂×C₃×D₄	—	2	4	no	—
402	C₂×C₃×D₄	—	2	2	no	—
403	C₂×C₃×D₄	—	2	2	no	—
404	C₂×C₃×D₄	—	4	2	no	—
405	C₂×C₃×D₄	—	4	2	no	—
406	C₂×C₃×D₄	C₂×D₄	1	4	yes	—
407	C₂×C₃×D₄	C₂×D₄	1	8	yes	—
408	C₂²×C₃×C₄	—	2	2	no	—
409	C₂²×C₃×C₄	—	2	2	no	—
410	C₂²×C₃×C₄	—	2	2	no	—
411	C₂²×C₃×C₄	—	2	2	no	—
412	C₂²×C₃×C₄	—	2	2	no	—
413	C₂²×C₃×C₄	—	2	2	no	—
414	C₂²×C₃×C₄	—	2	2	no	—
415	C₂²×C₃×C₄	—	2	2	no	—
416	C₂²×C₃×C₄	—	2	2	no	—
417	C₂²×C₃×C₄	—	2	2	no	—
418	C₂²×C₃×C₄	—	2	4	no	—
419	C₂²×C₃×C₄	—	2	4	no	—
420	C₂²×C₃×C₄	—	2	2	no	—
421	C₂²×C₃×C₄	—	2	2	no	—
422	C₂²×C₃×C₄	—	2	2	no	—
423	C₂²×C₃×C₄	—	2	4	no	—
424	C₂²×C₃×C₄	—	2	2	no	—
425	C₂²×C₃×C₄	—	2	2	no	—
426	C₂²×C₃×C₄	—	2	2	no	—
427	C₂²×C₃×C₄	—	2	4	no	—
428	C₂²×C₃×C₄	—	2	4	no	—
429	C₂²×C₃×C₄	—	2	4	no	—
430	C₂²×C₃×C₄	—	2	4	no	—
431	C₂²×C₃×C₄	—	4	1	no	—
432	C₂²×C₃×C₄	—	4	1	no	—
433	C₂²×C₃×C₄	—	4	2	no	—
434	C₂²×C₃×C₄	—	4	1	no	—
435	C₂²×C₃×C₄	—	4	2	no	—
436	C₂²×C₃×C₄	—	4	2	no	—
437	C₂²×C₃×C₄	—	4	2	no	—
438	C₂²×C₃×C₄	—	4	2	no	—
439	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
440	C₂²×C₃×C₄	#41	1	4	yes	—
441	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
442	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
443	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
444	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
445	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
446	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
447	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
448	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
449	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
450	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
451	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
452	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
453	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
454	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
455	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
456	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
457	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
458	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
459	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
460	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
461	C₃×C₄⋊C₄	—	2	4	no	—
462	C₃×C₄⋊C₄	—	2	4	no	—
463	C₃×C₄⋊C₄	—	2	4	no	—
464	C₃×C₄⋊C₄	—	2	2	no	—
465	C₃×C₄⋊C₄	—	2	2	no	—
466	C₃×C₄⋊C₄	—	2	4	no	—
467	C₃×C₄⋊C₄	—	2	4	no	—
468	C₃×C₄⋊C₄	—	2	2	no	—
469	C₃×C₄⋊C₄	—	2	2	no	—
470	C₃×C₄⋊C₄	—	2	2	no	—
471	C₃×C₄⋊C₄	—	2	2	no	—
472	C₃×C₄⋊C₄	—	2	2	no	—
473	C₃×C₄⋊C₄	—	2	2	no	—
474	C₃×C₄⋊C₄	—	2	2	no	—
475	C₃×C₄⋊C₄	—	2	2	no	—
476	C₃×C₄⋊C₄	—	2	4	no	—
477	C₃×C₄⋊C₄	—	2	2	no	—
478	C₃×C₄⋊C₄	—	4	2	no	—
479	C₃×C₄⋊C₄	—	4	2	no	—
480	C₃×C₄⋊C₄	—	4	2	no	—
481	C₃×C₄⋊C₄	—	4	2	no	—
482	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
483	C₃×C₄⋊C₄	#41	1	4	yes	complemented
484	C₃×C₂²⋊C₄	—	2	4	no	—
485	C₃×C₂²⋊C₄	—	2	4	no	—
486	C₃×C₂²⋊C₄	—	2	4	no	—
487	C₃×C₂²⋊C₄	—	2	4	no	—
488	C₃×C₂²⋊C₄	—	2	4	no	—
489	C₃×C₂²⋊C₄	—	2	4	no	—
490	C₃×C₂²⋊C₄	—	2	4	no	—
491	C₃×C₂²⋊C₄	—	2	4	no	—
492	C₃×C₂²⋊C₄	—	2	4	no	—
493	C₃×C₂²⋊C₄	—	2	4	no	—
494	C₃×C₂²⋊C₄	—	2	4	no	—
495	C₃×C₂²⋊C₄	—	2	4	no	—
496	C₃×C₂²⋊C₄	—	2	4	no	—
497	C₃×C₂²⋊C₄	—	2	4	no	—
498	C₃×C₂²⋊C₄	—	4	2	no	—
499	C₃×C₂²⋊C₄	—	4	2	no	—
500	C₃×C₂²⋊C₄	—	4	2	no	—
501	C₃×C₂²⋊C₄	—	4	2	no	—
502	C₃×C₂²⋊C₄	—	4	2	no	—
503	C₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
504	C₃×C₄²	—	2	2	no	—
505	C₃×C₄²	—	2	2	no	—
506	C₃×C₄²	—	2	2	no	—
507	C₃×C₄²	—	2	2	no	—
508	C₃×C₄²	—	2	2	no	—
509	C₃×C₄²	—	2	2	no	—
510	C₃×C₄²	—	2	2	no	—
511	C₃×C₄²	—	2	2	no	—
512	C₃×C₄²	—	2	4	no	—
513	C₃×C₄²	—	2	2	no	—
514	C₃×C₄²	—	2	2	no	—
515	C₃×C₄²	—	2	2	no	—
516	C₃×C₄²	—	4	2	no	—
517	C₃×C₄²	#41	1	4	yes	complemented
518	C₂×#41	—	2	8	no	—
519	C₂×#41	—	2	8	no	—
520	C₂×#41	—	4	4	no	—
521	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
522	C₂²×Q₈	C₂³×C₃	1	2	yes	—
523	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
524	C₂²×D₄	C₂³×C₃	1	2	yes	—
525	C₂²×D₄	C₂³×C₃	1	2	yes	—
526	C₂²×D₄	C₂³×C₃	1	2	yes	—
527	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
528	C₂²×D₄	C₂³×C₃	1	2	yes	—
529	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
530	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
531	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
532	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
533	C₂³×C₄	C₂³×C₃	1	2	yes	—
534	C₂³×C₄	C₂³×C₃	1	2	yes	—
535	C₂³×C₄	C₂³×C₃	1	2	yes	—
536	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
537	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
538	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
539	C₂³×C₄	C₂³×C₃	1	2	yes	—
540	C₄⋊Q₈	—	2	4	no	—
541	#127	—	2	4	no	—
542	#126	—	2	8	no	—
543	#125	—	2	4	no	—
544	#124	—	2	4	no	—
545	#124	—	2	8	no	—
546	#124	—	2	4	no	—
547	#123	—	2	8	no	—
548	#123	—	2	8	no	—
549	#123	—	4	4	no	—
550	C₂²⋊Q₈	—	2	4	no	—
551	#121	—	2	8	no	—
552	#121	—	2	4	no	—
553	#121	C₃×D₄	1	8	yes	—
554	C₄×Q₈	—	2	4	no	—
555	C₄×D₄	—	2	4	no	—
556	C₄×D₄	—	2	8	no	—
557	C₄×D₄	—	2	4	no	—
558	C₄×D₄	—	2	4	no	—
559	C₄×D₄	—	2	8	no	—
560	C₄×D₄	—	2	4	no	—
561	C₄×D₄	—	4	4	no	—
562	#117	—	2	8	no	—
563	C₂×C₄⋊C₄	—	2	4	no	—
564	C₂×C₄⋊C₄	—	2	4	no	—
565	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
566	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
567	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
568	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
569	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
570	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
571	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
572	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
573	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
574	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
575	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
576	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
577	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
579	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
580	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
581	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
582	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
583	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
584	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
585	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
586	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
587	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
588	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
589	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
590	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
594	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
597	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
598	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
599	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
600	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
601	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
602	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
603	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
605	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
606	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
607	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
608	C₂×C₄²	—	2	4	no	—
609	C₂×C₄²	—	2	4	no	—
610	C₂×C₄²	—	2	4	no	—
611	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
612	C₂×C₄²	C₂³×C₃	1	2	yes	—
613	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
614	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
615	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
616	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
617	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
618	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
619	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
620	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
621	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
622	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
623	C₂×C₄²	C₂³×C₃	1	2	yes	—
624	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
625	#95	C₂³×C₃	1	1	yes	characteristic
626	#95	C₂³×C₃	1	1	yes	characteristic
627	#95	C₂³×C₃	1	1	yes	characteristic
628	#95	C₂³×C₃	1	1	yes	characteristic
629	#95	C₂³×C₃	1	1	yes	characteristic
630	#95	C₂³×C₃	1	1	yes	characteristic
631	#95	C₂³×C₃	1	1	yes	characteristic
632	#95	C₂³×C₃	1	1	yes	characteristic
633	#95	C₂³×C₃	1	2	yes	—
634	#95	C₂³×C₃	1	2	yes	—
635	#95	C₂³×C₃	1	2	yes	—
636	#95	C₂³×C₃	1	2	yes	—
637	#95	C₂³×C₃	1	2	yes	—
638	#95	C₂³×C₃	1	2	yes	—
639	#95	C₂³×C₃	1	2	yes	—
640	#95	C₂³×C₃	1	2	yes	—
641	#95	C₂³×C₃	1	2	yes	—
642	#95	C₂³×C₃	1	2	yes	—
643	#95	C₂³×C₃	1	2	yes	—
644	#95	C₂³×C₃	1	2	yes	—
645	#95	C₂³×C₃	1	2	yes	—
646	#95	C₂³×C₃	1	2	yes	—
647	#95	C₂³×C₃	1	2	yes	—
648	C₂³×C₃	—	2	1	no	—
649	C₂³×C₃	—	2	1	no	—
650	C₂³×C₃	—	2	1	no	—
651	C₂³×C₃	—	2	1	no	—
652	C₂³×C₃	—	2	2	no	—
653	C₂³×C₃	—	2	2	no	—
654	C₂³×C₃	—	2	2	no	—
655	C₂³×C₃	—	2	2	no	—
656	C₂³×C₃	—	2	2	no	—
657	C₂³×C₃	—	2	2	no	—
658	C₂³×C₃	—	2	2	no	—
659	C₂³×C₃	—	2	2	no	—
660	C₂³×C₃	—	2	2	no	—
661	C₂³×C₃	—	2	2	no	—
662	C₂³×C₃	—	2	2	no	—
663	C₂³×C₃	—	2	2	no	—
664	C₂³×C₃	—	2	2	no	—
665	C₂³×C₃	C₂²×D₄	1	4	yes	—
666	C₂³×C₃	C₂²×D₄	1	2	yes	—
667	C₂³×C₃	C₂×#41	1	2	yes	—
668	C₂³×C₃	H(5,𝔽₂)	1	2	yes	—
669	C₂³×C₃	C₂⁵	1	1	yes	characteristic
670	C₃×Q₈	—	4	8	no	—
671	C₃×Q₈	—	4	4	no	—
672	C₃×D₄	—	2	16	no	—
673	C₃×D₄	—	2	8	no	—
674	C₃×D₄	—	4	8	no	—
675	C₃×D₄	—	4	8	no	—
676	C₃×D₄	—	4	8	no	—
677	C₃×D₄	—	4	4	no	—
678	C₂×C₃×C₄	—	2	8	no	—
679	C₂×C₃×C₄	—	2	8	no	—
680	C₂×C₃×C₄	—	2	1	no	—
681	C₂×C₃×C₄	—	2	1	no	—
682	C₂×C₃×C₄	—	2	1	no	—
683	C₂×C₃×C₄	—	2	1	no	—
684	C₂×C₃×C₄	—	2	1	no	—
685	C₂×C₃×C₄	—	2	1	no	—
686	C₂×C₃×C₄	—	2	1	no	—
687	C₂×C₃×C₄	—	2	1	no	—
688	C₂×C₃×C₄	—	2	1	no	—
689	C₂×C₃×C₄	—	2	2	no	—
690	C₂×C₃×C₄	—	2	1	no	—
691	C₂×C₃×C₄	—	2	2	no	—
692	C₂×C₃×C₄	—	2	1	no	—
693	C₂×C₃×C₄	—	2	1	no	—
694	C₂×C₃×C₄	—	2	1	no	—
695	C₂×C₃×C₄	—	2	1	no	—
696	C₂×C₃×C₄	—	2	1	no	—
697	C₂×C₃×C₄	—	2	1	no	—
698	C₂×C₃×C₄	—	2	8	no	—
699	C₂×C₃×C₄	—	2	1	no	—
700	C₂×C₃×C₄	—	2	1	no	—
701	C₂×C₃×C₄	—	2	1	no	—
702	C₂×C₃×C₄	—	2	1	no	—
703	C₂×C₃×C₄	—	2	2	no	—
704	C₂×C₃×C₄	—	2	2	no	—
705	C₂×C₃×C₄	—	2	2	no	—
706	C₂×C₃×C₄	—	2	1	no	—
707	C₂×C₃×C₄	—	2	2	no	—
708	C₂×C₃×C₄	—	2	2	no	—
709	C₂×C₃×C₄	—	2	2	no	—
710	C₂×C₃×C₄	—	2	2	no	—
711	C₂×C₃×C₄	—	2	1	no	—
712	C₂×C₃×C₄	—	2	1	no	—
713	C₂×C₃×C₄	—	2	1	no	—
714	C₂×C₃×C₄	—	2	1	no	—
715	C₂×C₃×C₄	—	2	2	no	—
716	C₂×C₃×C₄	—	2	2	no	—
717	C₂×C₃×C₄	—	2	2	no	—
718	C₂×C₃×C₄	—	2	1	no	—
719	C₂×C₃×C₄	—	2	1	no	—
720	C₂×C₃×C₄	—	2	1	no	—
721	C₂×C₃×C₄	—	2	2	no	—
722	C₂×C₃×C₄	—	2	2	no	—
723	C₂×C₃×C₄	—	2	2	no	—
724	C₂×C₃×C₄	—	2	1	no	—
725	C₂×C₃×C₄	—	2	1	no	—
726	C₂×C₃×C₄	—	2	2	no	—
727	C₂×C₃×C₄	—	2	2	no	—
728	C₂×C₃×C₄	—	2	1	no	—
729	C₂×C₃×C₄	—	4	8	no	—
730	C₂×C₃×C₄	—	4	4	no	—
731	C₂×C₃×C₄	—	4	8	no	—
732	C₂×C₃×C₄	—	4	4	no	—
733	C₂×C₃×C₄	—	4	4	no	—
734	C₂×C₃×C₄	—	4	8	no	—
735	C₂×C₃×C₄	—	4	4	no	—
736	C₂×C₃×C₄	—	8	4	no	—
737	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
738	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
739	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
740	C₂×C₃×C₄	C₂×#41	1	2	yes	—
741	C₂×C₃×C₄	C₂×#41	1	2	yes	—
742	C₂×C₃×C₄	C₂×#41	1	2	yes	—
743	C₂×C₃×C₄	C₂×#41	1	2	yes	—
744	C₂×C₃×C₄	C₂×#41	1	2	yes	—
745	C₂×C₃×C₄	C₂×#41	1	2	yes	—
746	C₂×C₃×C₄	C₂×#41	1	2	yes	—
747	C₂×C₃×C₄	C₂×#41	1	2	yes	—
748	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
749	C₂⁴	C₂⁴×C₃	1	2	yes	—
750	C₂⁴	C₂⁴×C₃	1	2	yes	—
751	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
752	#41	—	4	32	no	—
753	C₂×Q₈	—	2	2	no	—
754	C₂×Q₈	—	2	4	no	—
755	C₂×Q₈	—	2	2	no	—
756	C₂×Q₈	—	2	4	no	—
757	C₂×Q₈	—	2	2	no	—
758	C₂×Q₈	—	4	2	no	—
759	C₂×D₄	—	2	4	no	—
760	C₂×D₄	—	2	4	no	—
761	C₂×D₄	—	2	4	no	—
762	C₂×D₄	—	2	4	no	—
763	C₂×D₄	—	2	4	no	—
764	C₂×D₄	—	2	4	no	—
765	C₂×D₄	—	2	4	no	—
766	C₂×D₄	—	2	2	no	—
767	C₂×D₄	—	2	2	no	—
768	C₂×D₄	—	2	4	no	—
769	C₂×D₄	—	2	2	no	—
770	C₂×D₄	—	2	4	no	—
771	C₂×D₄	—	2	2	no	—
772	C₂×D₄	—	2	2	no	—
773	C₂×D₄	—	4	2	no	—
774	C₂×D₄	—	4	2	no	—
775	C₂×D₄	C₂×C₃×D₄	1	4	yes	—
776	C₂×D₄	C₂×C₃×D₄	1	8	yes	—
777	C₂²×C₄	—	2	2	no	—
778	C₂²×C₄	—	2	2	no	—
779	C₂²×C₄	—	2	2	no	—
780	C₂²×C₄	—	2	2	no	—
781	C₂²×C₄	—	2	2	no	—
782	C₂²×C₄	—	2	2	no	—
783	C₂²×C₄	—	2	2	no	—
784	C₂²×C₄	—	2	2	no	—
785	C₂²×C₄	—	2	2	no	—
786	C₂²×C₄	—	2	2	no	—
787	C₂²×C₄	—	2	4	no	—
788	C₂²×C₄	—	2	4	no	—
789	C₂²×C₄	—	2	2	no	—
790	C₂²×C₄	—	2	2	no	—
791	C₂²×C₄	—	2	2	no	—
792	C₂²×C₄	—	2	4	no	—
793	C₂²×C₄	—	2	2	no	—
794	C₂²×C₄	—	2	2	no	—
795	C₂²×C₄	—	2	2	no	—
796	C₂²×C₄	—	2	4	no	—
797	C₂²×C₄	—	2	4	no	—
798	C₂²×C₄	—	2	4	no	—
799	C₂²×C₄	—	2	4	no	—
800	C₂²×C₄	—	4	2	no	—
801	C₂²×C₄	—	4	2	no	—
802	C₂²×C₄	—	4	1	no	—
803	C₂²×C₄	—	4	1	no	—
804	C₂²×C₄	—	4	2	no	—
805	C₂²×C₄	—	4	1	no	—
806	C₂²×C₄	—	4	2	no	—
807	C₂²×C₄	—	4	2	no	—
808	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
809	C₂²×C₄	C₃×#41	1	4	yes	—
810	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
811	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
812	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
813	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
814	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
815	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
816	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
817	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
818	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
819	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
820	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
821	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
822	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
823	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
824	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
825	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
826	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
827	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
828	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
829	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
830	C₄⋊C₄	—	2	4	no	—
831	C₄⋊C₄	—	2	4	no	—
832	C₄⋊C₄	—	2	4	no	—
833	C₄⋊C₄	—	2	2	no	—
834	C₄⋊C₄	—	2	2	no	—
835	C₄⋊C₄	—	2	4	no	—
836	C₄⋊C₄	—	2	4	no	—
837	C₄⋊C₄	—	2	2	no	—
838	C₄⋊C₄	—	2	2	no	—
839	C₄⋊C₄	—	2	2	no	—
840	C₄⋊C₄	—	2	2	no	—
841	C₄⋊C₄	—	2	2	no	—
842	C₄⋊C₄	—	2	2	no	—
843	C₄⋊C₄	—	2	2	no	—
844	C₄⋊C₄	—	2	2	no	—
845	C₄⋊C₄	—	2	4	no	—
846	C₄⋊C₄	—	2	2	no	—
847	C₄⋊C₄	—	4	2	no	—
848	C₄⋊C₄	—	4	2	no	—
849	C₄⋊C₄	—	4	2	no	—
850	C₄⋊C₄	—	4	2	no	—
851	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
852	C₄⋊C₄	C₃×#41	1	4	yes	complemented
853	C₂²⋊C₄	—	2	4	no	—
854	C₂²⋊C₄	—	2	4	no	—
855	C₂²⋊C₄	—	2	4	no	—
856	C₂²⋊C₄	—	2	4	no	—
857	C₂²⋊C₄	—	2	4	no	—
858	C₂²⋊C₄	—	2	4	no	—
859	C₂²⋊C₄	—	2	4	no	—
860	C₂²⋊C₄	—	2	4	no	—
861	C₂²⋊C₄	—	2	4	no	—
862	C₂²⋊C₄	—	2	4	no	—
863	C₂²⋊C₄	—	2	4	no	—
864	C₂²⋊C₄	—	2	4	no	—
865	C₂²⋊C₄	—	2	4	no	—
866	C₂²⋊C₄	—	2	4	no	—
867	C₂²⋊C₄	—	4	2	no	—
868	C₂²⋊C₄	—	4	2	no	—
869	C₂²⋊C₄	—	4	2	no	—
870	C₂²⋊C₄	—	4	2	no	—
871	C₂²⋊C₄	—	4	2	no	—
872	C₂²⋊C₄	C₂×C₃×D₄	1	8	yes	—
873	C₄²	—	2	2	no	—
874	C₄²	—	2	2	no	—
875	C₄²	—	2	2	no	—
876	C₄²	—	2	2	no	—
877	C₄²	—	2	2	no	—
878	C₄²	—	2	2	no	—
879	C₄²	—	2	2	no	—
880	C₄²	—	2	2	no	—
881	C₄²	—	2	4	no	—
882	C₄²	—	2	2	no	—
883	C₄²	—	2	2	no	—
884	C₄²	—	2	2	no	—
885	C₄²	—	4	2	no	—
886	C₄²	C₃×#41	1	4	yes	complemented
887	C₂²×C₃	—	2	2	no	—
888	C₂²×C₃	—	2	2	no	—
889	C₂²×C₃	—	2	2	no	—
890	C₂²×C₃	—	2	2	no	—
891	C₂²×C₃	—	2	2	no	—
892	C₂²×C₃	—	2	2	no	—
893	C₂²×C₃	—	2	4	no	—
894	C₂²×C₃	—	2	4	no	—
895	C₂²×C₃	—	2	4	no	—
896	C₂²×C₃	—	4	2	no	—
897	C₂²×C₃	—	4	2	no	—
898	C₂²×C₃	—	4	2	no	—
899	C₂²×C₃	—	4	2	no	—
900	C₂²×C₃	—	4	2	no	—
901	C₂²×C₃	—	4	2	no	—
902	C₂²×C₃	—	4	2	no	—
903	C₂²×C₃	—	4	2	no	—
904	C₂²×C₃	—	4	2	no	—
905	C₂²×C₃	—	4	2	no	—
906	C₂²×C₃	—	4	2	no	—
907	C₂²×C₃	#546	1	4	yes	—
908	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
909	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
910	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
911	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
912	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
913	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
914	C₂²×C₃	#585	1	1	yes	characteristic
915	C₃×C₄	—	2	2	no	—
916	C₃×C₄	—	2	2	no	—
917	C₃×C₄	—	2	2	no	—
918	C₃×C₄	—	2	2	no	—
919	C₃×C₄	—	2	4	no	—
920	C₃×C₄	—	2	2	no	—
921	C₃×C₄	—	2	2	no	—
922	C₃×C₄	—	2	2	no	—
923	C₃×C₄	—	2	2	no	—
924	C₃×C₄	—	4	1	no	—
925	C₃×C₄	—	4	1	no	—
926	C₃×C₄	—	4	2	no	—
927	C₃×C₄	—	4	2	no	—
928	C₃×C₄	—	4	1	no	—
929	C₃×C₄	—	4	1	no	—
930	C₃×C₄	—	4	2	no	—
931	C₃×C₄	—	4	1	no	—
932	C₃×C₄	—	4	2	no	—
933	C₃×C₄	—	4	2	no	—
934	C₃×C₄	#547	1	4	yes	—
935	C₂³	—	2	1	no	—
936	C₂³	—	2	1	no	—
937	C₂³	—	2	1	no	—
938	C₂³	—	2	1	no	—
939	C₂³	—	2	2	no	—
940	C₂³	—	2	2	no	—
941	C₂³	—	2	2	no	—
942	C₂³	—	2	2	no	—
943	C₂³	—	2	2	no	—
944	C₂³	—	2	2	no	—
945	C₂³	—	2	2	no	—
946	C₂³	—	2	2	no	—
947	C₂³	—	2	2	no	—
948	C₂³	—	2	2	no	—
949	C₂³	—	2	2	no	—
950	C₂³	—	2	2	no	—
951	C₂³	—	2	2	no	—
952	C₂³	C₂²×C₃×D₄	1	4	yes	—
953	C₂³	C₂²×C₃×D₄	1	2	yes	—
954	C₂³	C₂×C₃×#41	1	2	yes	—
955	C₂³	C₃×H(5,𝔽₂)	1	2	yes	—
956	C₂³	C₂⁵×C₃	1	1	yes	characteristic
957	Q₈	—	4	8	no	—
958	Q₈	—	4	4	no	—
959	D₄	—	2	16	no	—
960	D₄	—	2	8	no	—
961	D₄	—	4	8	no	—
962	D₄	—	4	8	no	—
963	D₄	—	4	8	no	—
964	D₄	—	4	4	no	—
965	C₂×C₄	—	2	8	no	—
966	C₂×C₄	—	2	1	no	—
967	C₂×C₄	—	2	1	no	—
968	C₂×C₄	—	2	1	no	—
969	C₂×C₄	—	2	1	no	—
970	C₂×C₄	—	2	1	no	—
971	C₂×C₄	—	2	1	no	—
972	C₂×C₄	—	2	1	no	—
973	C₂×C₄	—	2	1	no	—
974	C₂×C₄	—	2	1	no	—
975	C₂×C₄	—	2	2	no	—
976	C₂×C₄	—	2	1	no	—
977	C₂×C₄	—	2	2	no	—
978	C₂×C₄	—	2	1	no	—
979	C₂×C₄	—	2	1	no	—
980	C₂×C₄	—	2	1	no	—
981	C₂×C₄	—	2	1	no	—
982	C₂×C₄	—	2	1	no	—
983	C₂×C₄	—	2	1	no	—
984	C₂×C₄	—	2	8	no	—
985	C₂×C₄	—	2	8	no	—
986	C₂×C₄	—	2	1	no	—
987	C₂×C₄	—	2	1	no	—
988	C₂×C₄	—	2	1	no	—
989	C₂×C₄	—	2	1	no	—
990	C₂×C₄	—	2	2	no	—
991	C₂×C₄	—	2	2	no	—
992	C₂×C₄	—	2	2	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	2	no	—
995	C₂×C₄	—	2	2	no	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	2	2	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	2	1	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	2	no	—
1004	C₂×C₄	—	2	2	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	2	no	—
1009	C₂×C₄	—	2	2	no	—
1010	C₂×C₄	—	2	2	no	—
1011	C₂×C₄	—	2	1	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	4	8	no	—
1017	C₂×C₄	—	4	8	no	—
1018	C₂×C₄	—	4	4	no	—
1019	C₂×C₄	—	4	8	no	—
1020	C₂×C₄	—	4	4	no	—
1021	C₂×C₄	—	4	4	no	—
1022	C₂×C₄	—	4	4	no	—
1023	C₂×C₄	—	8	4	no	—
1024	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1025	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
1026	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1027	C₂×C₄	C₂×C₃×#41	1	2	yes	—
1028	C₂×C₄	C₂×C₃×#41	1	2	yes	—
1029	C₂×C₄	C₂×C₃×#41	1	2	yes	—
1030	C₂×C₄	C₂×C₃×#41	1	2	yes	—
1031	C₂×C₄	C₂×C₃×#41	1	2	yes	—
1032	C₂×C₄	C₂×C₃×#41	1	2	yes	—
1033	C₂×C₄	C₂×C₃×#41	1	2	yes	—
1034	C₂×C₄	C₂×C₃×#41	1	2	yes	—
1035	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
1036	C₂×C₃	—	2	4	no	—
1037	C₂×C₃	—	4	4	no	—
1038	C₂×C₃	—	8	2	no	—
1039	C₂×C₃	#3444	1	1	yes	characteristic
1040	C₂×C₃	C₂×#546	1	1	yes	characteristic
1041	C₂×C₃	C₂×#547	1	1	yes	characteristic
1042	C₂×C₃	D₄×#41	1	1	yes	characteristic
1043	C₂×C₃	#3494	1	1	yes	characteristic
1044	C₂×C₃	#3507	1	1	yes	characteristic
1045	C₂×C₃	#3522	1	1	yes	characteristic
1046	C₂²	—	2	2	no	—
1047	C₂²	—	2	2	no	—
1048	C₂²	—	2	2	no	—
1049	C₂²	—	2	2	no	—
1050	C₂²	—	2	2	no	—
1051	C₂²	—	2	2	no	—
1052	C₂²	—	2	4	no	—
1053	C₂²	—	2	4	no	—
1054	C₂²	—	2	4	no	—
1055	C₂²	—	4	2	no	—
1056	C₂²	—	4	2	no	—
1057	C₂²	—	4	2	no	—
1058	C₂²	—	4	2	no	—
1059	C₂²	—	4	2	no	—
1060	C₂²	—	4	2	no	—
1061	C₂²	—	4	2	no	—
1062	C₂²	—	4	2	no	—
1063	C₂²	—	4	2	no	—
1064	C₂²	—	4	2	no	—
1065	C₂²	—	4	2	no	—
1066	C₂²	C₃×#546	1	4	yes	—
1067	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
1068	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
1069	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
1070	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
1071	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1072	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
1073	C₂²	C₃×#585	1	1	yes	characteristic
1074	C₄	—	2	2	no	—
1075	C₄	—	2	2	no	—
1076	C₄	—	2	2	no	—
1077	C₄	—	2	2	no	—
1078	C₄	—	2	4	no	—
1079	C₄	—	2	2	no	—
1080	C₄	—	2	2	no	—
1081	C₄	—	2	2	no	—
1082	C₄	—	2	2	no	—
1083	C₄	—	4	2	no	—
1084	C₄	—	4	1	no	—
1085	C₄	—	4	1	no	—
1086	C₄	—	4	2	no	—
1087	C₄	—	4	1	no	—
1088	C₄	—	4	1	no	—
1089	C₄	—	4	2	no	—
1090	C₄	—	4	1	no	—
1091	C₄	—	4	2	no	—
1092	C₄	—	4	2	no	—
1093	C₄	C₃×#547	1	4	yes	—
1094	C₃	#36139	1	1	yes	characteristic, direct product factor, Sylow
1095	C₂	—	2	4	no	—
1096	C₂	—	4	4	no	—
1097	C₂	—	8	2	no	—
1098	C₂	C₃×#3444	1	1	yes	characteristic
1099	C₂	C₂×C₃×#546	1	1	yes	characteristic
1100	C₂	C₂×C₃×#547	1	1	yes	characteristic
1101	C₂	C₃×D₄×#41	1	1	yes	characteristic
1102	C₂	C₃×#3494	1	1	yes	characteristic
1103	C₂	C₃×#3507	1	1	yes	characteristic
1104	C₂	C₃×#3522	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂×C₃×#532	C₂
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
2. C₂×C₃×#529	C₂	semidirect
3. C₃×#2855	C₂	semidirect
4. C₃×#2854	C₂	semidirect
5. C₃×#2850	C₂	semidirect
6. C₃×#2550	C₂	semidirect
7. C₃×#2544	C₂	semidirect
8. C₃×#2521	C₂	semidirect
9. C₃×#2474	C₂	semidirect
10. C₃×#2468	C₂	semidirect
11. C₃×#2454	C₂	semidirect
12. C₃×#2451	C₂	semidirect
13. C₃×#2447	C₂	semidirect
14. C₃×#2445	C₂	semidirect
15. C₃×#2443	C₂	semidirect
16. C₃×#2425	C₂	semidirect
17. C₃×#2406	C₂	semidirect
18. C₃×#2367	C₂	semidirect
19. C₃×#2359	C₂	semidirect
20. C₃×#2349	C₂	semidirect
21. C₃×#2339	C₂	semidirect
22. C₃×C₄×#121	C₂	semidirect
23. C₂×C₃×C₄×C₄⋊C₄	C₂	semidirect
24. #36139	C₃	direct (N × H)
127. C₂×#529	C₂×C₃	semidirect
128. #2855	C₂×C₃	semidirect
129. #2854	C₂×C₃	semidirect
130. #2850	C₂×C₃	semidirect
131. #2550	C₂×C₃	semidirect
132. #2544	C₂×C₃	semidirect
133. #2521	C₂×C₃	semidirect
134. #2474	C₂×C₃	semidirect
135. #2468	C₂×C₃	semidirect
136. #2454	C₂×C₃	semidirect
137. #2451	C₂×C₃	semidirect
138. #2447	C₂×C₃	semidirect
139. #2445	C₂×C₃	semidirect
140. #2443	C₂×C₃	semidirect
141. #2425	C₂×C₃	semidirect
142. #2406	C₂×C₃	semidirect
143. #2367	C₂×C₃	semidirect
144. #2359	C₂×C₃	semidirect
145. #2349	C₂×C₃	semidirect
146. #2339	C₂×C₃	semidirect
147. C₄×#121	C₂×C₃	semidirect
148. C₂×C₄×C₄⋊C₄	C₂×C₃	semidirect
483. C₃×C₄⋊C₄	#41	semidirect
517. C₃×C₄²	#41	semidirect
852. C₄⋊C₄	C₃×#41	semidirect
886. C₄²	C₃×#41	semidirect
1094. C₃	#36139	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×#532	2
C₂×C₃×#529	2
C₃×#2855	2
C₃×#2854	2
C₃×#2850	2
C₃×#2550	2
C₃×#2544	2
C₃×#2521	2
C₃×#2474	2
C₃×#2468	2
C₃×#2454	2
C₃×#2451	2
C₃×#2447	2
C₃×#2445	2
C₃×#2443	2
C₃×#2425	2
C₃×#2406	2
C₃×#2367	2
C₃×#2359	2
C₃×#2349	2
C₃×#2339	2
C₃×C₄×#121	2
C₂×C₃×C₄×C₄⋊C₄	2
#36139	3

Subgroups — C3×#36139 #10654746

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#36139 #10654746