Subgroups — C₃×#42970 #10661577

Order 768.

2204 conjugacy classes of subgroups.

The subgroup lattice has 1110 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#552	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2820	C₂	1	2	yes	maximal, complemented
4	C₃×#2715	C₂	1	2	yes	maximal, complemented
5	C₃×#2691	C₂	1	2	yes	maximal, complemented
6	C₃×#2672	C₂	1	2	yes	maximal, complemented
7	C₃×#2671	C₂	1	2	yes	maximal, complemented
8	C₃×#2629	C₂	1	2	yes	maximal, complemented
9	C₃×#2620	C₂	1	2	yes	maximal, complemented
10	C₃×#2620	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#2609	C₂	1	2	yes	maximal, complemented
12	C₃×#2454	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#2451	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#2441	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#2440	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2427	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#2426	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#2417	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#2416	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×#2416	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×#2415	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃×#2392	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×#2317	C₂	1	1	yes	maximal, characteristic, complemented
24	#42970	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₃×#555	—	2	8	no	—
26	C₃×#552	—	2	8	no	—
27	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₃×#126	C₂²	1	2	yes	—
29	C₂×C₃×#125	C₂²	1	2	yes	—
30	C₂×C₃×#125	C₂²	1	1	yes	characteristic
31	C₂×C₃×#124	C₂²	1	2	yes	—
32	C₂×C₃×#124	C₂²	1	2	yes	—
33	C₂×C₃×#124	C₂²	1	1	yes	characteristic
34	C₂×C₃×#123	C₂²	1	2	yes	—
35	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
36	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
37	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
38	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
39	C₂×C₃×#121	C₂²	1	1	yes	characteristic
40	C₂×C₃×#121	C₂²	1	2	yes	—
41	C₂×C₃×#121	C₂²	1	1	yes	characteristic
42	C₂×C₃×#121	C₂²	1	2	yes	—
43	C₂×C₃×#121	C₂²	1	2	yes	—
44	C₂×C₃×#121	C₂²	1	1	yes	characteristic
45	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
46	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
47	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
48	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
49	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
50	C₂×C₃×#117	C₂²	1	2	yes	—
51	C₂×C₃×#117	C₂²	1	2	yes	—
52	C₂×C₃×#117	C₂²	1	1	yes	characteristic
53	C₂×C₃×#117	C₂²	1	1	yes	characteristic
54	C₂×C₃×#117	C₂²	1	1	yes	characteristic
55	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
56	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
57	C₃×#399	C₂²	1	2	yes	—
58	C₃×#399	C₂²	1	2	yes	—
59	C₃×#398	C₂²	1	1	yes	characteristic
60	C₃×#398	C₂²	1	2	yes	—
61	C₃×#398	C₂²	1	2	yes	—
62	C₃×#398	C₂²	1	2	yes	—
63	C₃×#397	C₂²	1	1	yes	characteristic
64	C₃×#397	C₂²	1	2	yes	—
65	C₃×#397	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×#396	C₂²	1	2	yes	—
72	C₃×#396	C₂²	1	2	yes	—
73	C₃×#396	C₂²	1	2	yes	—
74	C₃×#396	C₂²	1	1	yes	characteristic
75	C₃×#396	C₂²	1	1	yes	characteristic
76	C₃×#395	C₂²	1	2	yes	—
77	C₃×#395	C₂²	1	2	yes	—
78	C₃×#394	C₂²	1	1	yes	characteristic
79	C₃×#394	C₂²	1	2	yes	—
80	C₃×#394	C₂²	1	2	yes	—
81	C₃×#394	C₂²	1	2	yes	—
82	C₃×#394	C₂²	1	2	yes	—
83	C₃×#394	C₂²	1	2	yes	—
84	C₃×#394	C₂²	1	1	yes	characteristic
85	C₃×#394	C₂²	1	1	yes	characteristic
86	C₃×#394	C₂²	1	2	yes	—
87	C₃×#394	C₂²	1	2	yes	—
88	C₃×#392	C₂²	1	1	yes	characteristic
89	C₃×#391	C₂²	1	1	yes	characteristic
90	C₃×#391	C₂²	1	2	yes	—
91	C₃×#391	C₂²	1	1	yes	characteristic
92	C₃×#390	C₂²	1	1	yes	characteristic
93	C₃×#390	C₂²	1	2	yes	—
94	C₃×#390	C₂²	1	1	yes	characteristic
95	C₃×#389	C₂²	1	2	yes	—
96	C₃×#389	C₂²	1	2	yes	—
97	C₃×#389	C₂²	1	1	yes	characteristic
98	C₃×#389	C₂²	1	1	yes	characteristic
99	C₃×#389	C₂²	1	1	yes	characteristic
100	C₃×#389	C₂²	1	1	yes	characteristic
101	C₃×#389	C₂²	1	1	yes	characteristic
102	C₃×#389	C₂²	1	1	yes	characteristic
103	C₃×#388	C₂²	1	2	yes	—
104	C₃×#388	C₂²	1	2	yes	—
105	C₃×#387	C₂²	1	2	yes	—
106	C₃×#387	C₂²	1	2	yes	—
107	C₃×#386	C₂²	1	2	yes	—
108	C₃×#386	C₂²	1	2	yes	—
109	C₃×#386	C₂²	1	2	yes	—
110	C₃×#386	C₂²	1	2	yes	—
111	C₃×#385	C₂²	1	2	yes	—
112	C₃×#385	C₂²	1	2	yes	—
113	C₃×#385	C₂²	1	2	yes	—
114	C₃×#385	C₂²	1	2	yes	—
115	C₃×#384	C₂²	1	2	yes	—
116	C₃×#384	C₂²	1	1	yes	characteristic
117	C₃×#382	C₂²	1	2	yes	—
118	C₃×#380	C₂²	1	2	yes	—
119	C₃×#380	C₂²	1	2	yes	—
120	C₃×#380	C₂²	1	1	yes	characteristic
121	C₃×#380	C₂²	1	1	yes	characteristic
122	C₃×#380	C₂²	1	2	yes	—
123	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
124	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
125	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
126	C₂×#555	C₂×C₃	1	1	yes	characteristic, complemented
127	C₂×#552	C₂×C₃	1	1	yes	characteristic, complemented
128	#2820	C₂×C₃	1	2	yes	complemented
129	#2715	C₂×C₃	1	2	yes	complemented
130	#2691	C₂×C₃	1	2	yes	complemented
131	#2672	C₂×C₃	1	2	yes	complemented
132	#2671	C₂×C₃	1	2	yes	complemented
133	#2629	C₂×C₃	1	2	yes	complemented
134	#2620	C₂×C₃	1	2	yes	complemented
135	#2620	C₂×C₃	1	1	yes	characteristic, complemented
136	#2609	C₂×C₃	1	2	yes	complemented
137	#2454	C₂×C₃	1	1	yes	characteristic, complemented
138	#2451	C₂×C₃	1	1	yes	characteristic, complemented
139	#2441	C₂×C₃	1	1	yes	characteristic, complemented
140	#2440	C₂×C₃	1	1	yes	characteristic, complemented
141	#2427	C₂×C₃	1	1	yes	characteristic, complemented
142	#2426	C₂×C₃	1	1	yes	characteristic, complemented
143	#2417	C₂×C₃	1	1	yes	characteristic, complemented
144	#2416	C₂×C₃	1	1	yes	characteristic, complemented
145	#2416	C₂×C₃	1	1	yes	characteristic, complemented
146	#2415	C₂×C₃	1	1	yes	characteristic, complemented
147	#2392	C₂×C₃	1	1	yes	characteristic, complemented
148	#2317	C₂×C₃	1	1	yes	characteristic, complemented
149	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
150	C₂²×C₃×Q₈	C₂³	1	2	yes	—
151	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
152	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
153	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
154	C₂²×C₃×D₄	C₂³	1	2	yes	—
155	C₂²×C₃×D₄	C₂³	1	2	yes	—
156	C₂²×C₃×D₄	C₂³	1	2	yes	—
157	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
158	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
159	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
160	C₂³×C₃×C₄	C₂³	1	2	yes	—
161	C₂³×C₃×C₄	C₂³	1	2	yes	—
162	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
163	C₂³×C₃×C₄	C₂³	1	2	yes	—
164	C₃×C₄⋊Q₈	—	2	4	no	—
165	C₃×#126	—	2	8	no	—
166	C₃×#125	—	2	4	no	—
167	C₃×#125	—	2	8	no	—
168	C₃×#124	—	2	8	no	—
169	C₃×#124	—	2	8	no	—
170	C₃×#124	—	4	2	no	—
171	C₃×#123	—	2	8	no	—
172	C₃×C₂²⋊Q₈	—	2	4	no	—
173	C₃×C₂²⋊Q₈	—	2	4	no	—
174	C₃×C₂²⋊Q₈	—	4	4	no	—
175	C₃×C₂²⋊Q₈	—	4	2	no	—
176	C₃×#121	—	2	4	no	—
177	C₃×#121	—	2	4	no	—
178	C₃×#121	—	2	8	no	—
179	C₃×#121	—	4	4	no	—
180	C₃×#121	—	4	2	no	—
181	C₃×#121	—	4	4	no	—
182	C₃×C₄×Q₈	—	2	4	no	—
183	C₃×C₄×D₄	—	2	4	no	—
184	C₃×C₄×D₄	—	2	4	no	—
185	C₃×C₄×D₄	—	2	4	no	—
186	C₃×C₄×D₄	—	4	2	no	—
187	C₃×#117	—	2	4	no	—
188	C₃×#117	—	2	8	no	—
189	C₃×#117	—	2	8	no	—
190	C₃×#117	—	4	2	no	—
191	C₃×#117	D₄	1	8	yes	complemented
192	C₂×C₃×C₄⋊C₄	—	2	4	no	—
193	C₂×C₃×C₄⋊C₄	—	4	2	no	—
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	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	1	yes	characteristic
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	1	yes	characteristic
214	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
215	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
216	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
217	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
218	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
219	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
220	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
221	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
222	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
223	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
224	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
225	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
226	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
233	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
234	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
238	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
239	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
240	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
241	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
242	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
243	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
244	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
245	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
246	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
247	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
248	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
249	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
250	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
251	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
252	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
253	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
254	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
255	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
256	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
257	C₂×C₃×C₄²	C₂³	1	2	yes	—
258	C₂×C₃×C₄²	C₂³	1	2	yes	—
259	C₂×C₃×C₄²	C₂³	1	2	yes	—
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	1	yes	characteristic
265	C₃×#95	C₂³	1	1	yes	characteristic
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	#555	—	2	8	no	—
279	#552	—	2	8	no	—
280	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
281	C₂×#126	C₂²×C₃	1	2	yes	—
282	C₂×#125	C₂²×C₃	1	2	yes	—
283	C₂×#125	C₂²×C₃	1	1	yes	characteristic
284	C₂×#124	C₂²×C₃	1	2	yes	—
285	C₂×#124	C₂²×C₃	1	2	yes	—
286	C₂×#124	C₂²×C₃	1	1	yes	characteristic
287	C₂×#123	C₂²×C₃	1	2	yes	—
288	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
289	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
290	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
291	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
292	C₂×#121	C₂²×C₃	1	1	yes	characteristic
293	C₂×#121	C₂²×C₃	1	2	yes	—
294	C₂×#121	C₂²×C₃	1	1	yes	characteristic
295	C₂×#121	C₂²×C₃	1	2	yes	—
296	C₂×#121	C₂²×C₃	1	2	yes	—
297	C₂×#121	C₂²×C₃	1	1	yes	characteristic
298	C₂×C₄×Q₈	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	1	yes	characteristic
302	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
303	C₂×#117	C₂²×C₃	1	2	yes	—
304	C₂×#117	C₂²×C₃	1	2	yes	—
305	C₂×#117	C₂²×C₃	1	1	yes	characteristic
306	C₂×#117	C₂²×C₃	1	1	yes	characteristic
307	C₂×#117	C₂²×C₃	1	1	yes	characteristic
308	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
309	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
310	#399	C₂²×C₃	1	2	yes	—
311	#399	C₂²×C₃	1	2	yes	—
312	#398	C₂²×C₃	1	2	yes	—
313	#398	C₂²×C₃	1	1	yes	characteristic
314	#398	C₂²×C₃	1	2	yes	—
315	#398	C₂²×C₃	1	2	yes	—
316	#397	C₂²×C₃	1	2	yes	—
317	#397	C₂²×C₃	1	2	yes	—
318	#397	C₂²×C₃	1	1	yes	characteristic
319	#396	C₂²×C₃	1	1	yes	characteristic
320	#396	C₂²×C₃	1	2	yes	—
321	#396	C₂²×C₃	1	2	yes	—
322	#396	C₂²×C₃	1	2	yes	—
323	#396	C₂²×C₃	1	1	yes	characteristic
324	#396	C₂²×C₃	1	2	yes	—
325	#396	C₂²×C₃	1	2	yes	—
326	#396	C₂²×C₃	1	2	yes	—
327	#396	C₂²×C₃	1	2	yes	—
328	#396	C₂²×C₃	1	2	yes	—
329	#395	C₂²×C₃	1	2	yes	—
330	#395	C₂²×C₃	1	2	yes	—
331	#394	C₂²×C₃	1	2	yes	—
332	#394	C₂²×C₃	1	2	yes	—
333	#394	C₂²×C₃	1	2	yes	—
334	#394	C₂²×C₃	1	1	yes	characteristic
335	#394	C₂²×C₃	1	2	yes	—
336	#394	C₂²×C₃	1	2	yes	—
337	#394	C₂²×C₃	1	2	yes	—
338	#394	C₂²×C₃	1	2	yes	—
339	#394	C₂²×C₃	1	1	yes	characteristic
340	#394	C₂²×C₃	1	1	yes	characteristic
341	#392	C₂²×C₃	1	1	yes	characteristic
342	#391	C₂²×C₃	1	1	yes	characteristic
343	#391	C₂²×C₃	1	2	yes	—
344	#391	C₂²×C₃	1	1	yes	characteristic
345	#390	C₂²×C₃	1	1	yes	characteristic
346	#390	C₂²×C₃	1	2	yes	—
347	#390	C₂²×C₃	1	1	yes	characteristic
348	#389	C₂²×C₃	1	1	yes	characteristic
349	#389	C₂²×C₃	1	1	yes	characteristic
350	#389	C₂²×C₃	1	1	yes	characteristic
351	#389	C₂²×C₃	1	1	yes	characteristic
352	#389	C₂²×C₃	1	2	yes	—
353	#389	C₂²×C₃	1	2	yes	—
354	#389	C₂²×C₃	1	1	yes	characteristic
355	#389	C₂²×C₃	1	1	yes	characteristic
356	#388	C₂²×C₃	1	2	yes	—
357	#388	C₂²×C₃	1	2	yes	—
358	#387	C₂²×C₃	1	2	yes	—
359	#387	C₂²×C₃	1	2	yes	—
360	#386	C₂²×C₃	1	2	yes	—
361	#386	C₂²×C₃	1	2	yes	—
362	#386	C₂²×C₃	1	2	yes	—
363	#386	C₂²×C₃	1	2	yes	—
364	#385	C₂²×C₃	1	2	yes	—
365	#385	C₂²×C₃	1	2	yes	—
366	#385	C₂²×C₃	1	2	yes	—
367	#385	C₂²×C₃	1	2	yes	—
368	#384	C₂²×C₃	1	2	yes	—
369	#384	C₂²×C₃	1	1	yes	characteristic
370	#382	C₂²×C₃	1	2	yes	—
371	#380	C₂²×C₃	1	2	yes	—
372	#380	C₂²×C₃	1	2	yes	—
373	#380	C₂²×C₃	1	1	yes	characteristic
374	#380	C₂²×C₃	1	1	yes	characteristic
375	#380	C₂²×C₃	1	2	yes	—
376	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
377	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
378	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
379	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
380	C₂⁴×C₃	C₂⁴	1	2	yes	—
381	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
382	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
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	—	4	2	no	—
388	C₂×C₃×Q₈	—	4	2	no	—
389	C₂×C₃×D₄	—	2	2	no	—
390	C₂×C₃×D₄	—	2	2	no	—
391	C₂×C₃×D₄	—	2	2	no	—
392	C₂×C₃×D₄	—	2	2	no	—
393	C₂×C₃×D₄	—	2	4	no	—
394	C₂×C₃×D₄	—	2	4	no	—
395	C₂×C₃×D₄	—	2	2	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	2	no	—
400	C₂×C₃×D₄	—	4	1	no	—
401	C₂×C₃×D₄	—	4	1	no	—
402	C₂×C₃×D₄	—	4	1	no	—
403	C₂×C₃×D₄	—	4	1	no	—
404	C₂×C₃×D₄	—	4	2	no	—
405	C₂×C₃×D₄	—	4	2	no	—
406	C₂×C₃×D₄	—	4	2	no	—
407	C₂×C₃×D₄	—	4	2	no	—
408	C₂×C₃×D₄	—	4	2	no	—
409	C₂×C₃×D₄	—	4	2	no	—
410	C₂²×C₃×C₄	—	2	2	no	—
411	C₂²×C₃×C₄	—	2	2	no	—
412	C₂²×C₃×C₄	—	2	4	no	—
413	C₂²×C₃×C₄	—	2	4	no	—
414	C₂²×C₃×C₄	—	2	2	no	—
415	C₂²×C₃×C₄	—	2	4	no	—
416	C₂²×C₃×C₄	—	2	2	no	—
417	C₂²×C₃×C₄	—	2	2	no	—
418	C₂²×C₃×C₄	—	2	2	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	—	4	2	no	—
423	C₂²×C₃×C₄	—	4	2	no	—
424	C₂²×C₃×C₄	—	4	2	no	—
425	C₂²×C₃×C₄	—	4	2	no	—
426	C₂²×C₃×C₄	—	4	2	no	—
427	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
428	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
429	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
430	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
431	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
432	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
433	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
434	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
435	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
436	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
437	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
438	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
439	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
440	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
441	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
442	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
443	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
444	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
445	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
446	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
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	4	no	—
453	C₃×C₄⋊C₄	—	2	4	no	—
454	C₃×C₄⋊C₄	—	2	2	no	—
455	C₃×C₄⋊C₄	—	2	4	no	—
456	C₃×C₄⋊C₄	—	2	4	no	—
457	C₃×C₄⋊C₄	—	2	4	no	—
458	C₃×C₄⋊C₄	—	2	2	no	—
459	C₃×C₄⋊C₄	—	2	2	no	—
460	C₃×C₄⋊C₄	—	2	2	no	—
461	C₃×C₄⋊C₄	—	4	2	no	—
462	C₃×C₄⋊C₄	—	4	2	no	—
463	C₃×C₄⋊C₄	—	4	2	no	—
464	C₃×C₄⋊C₄	—	4	1	no	—
465	C₃×C₄⋊C₄	—	4	2	no	—
466	C₃×C₄⋊C₄	—	4	1	no	—
467	C₃×C₄⋊C₄	—	4	1	no	—
468	C₃×C₄⋊C₄	—	4	1	no	—
469	C₃×C₄⋊C₄	—	4	2	no	—
470	C₃×C₄⋊C₄	—	4	2	no	—
471	C₃×C₄⋊C₄	—	4	2	no	—
472	C₃×C₄⋊C₄	—	4	2	no	—
473	C₃×C₄⋊C₄	—	4	2	no	—
474	C₃×C₄⋊C₄	—	4	2	no	—
475	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
476	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
477	C₃×C₂²⋊C₄	—	2	2	no	—
478	C₃×C₂²⋊C₄	—	2	2	no	—
479	C₃×C₂²⋊C₄	—	2	4	no	—
480	C₃×C₂²⋊C₄	—	2	4	no	—
481	C₃×C₂²⋊C₄	—	2	2	no	—
482	C₃×C₂²⋊C₄	—	2	2	no	—
483	C₃×C₂²⋊C₄	—	2	4	no	—
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	2	no	—
489	C₃×C₂²⋊C₄	—	2	2	no	—
490	C₃×C₂²⋊C₄	—	4	1	no	—
491	C₃×C₂²⋊C₄	—	4	2	no	—
492	C₃×C₂²⋊C₄	—	4	2	no	—
493	C₃×C₂²⋊C₄	—	4	1	no	—
494	C₃×C₂²⋊C₄	—	4	1	no	—
495	C₃×C₂²⋊C₄	—	4	1	no	—
496	C₃×C₂²⋊C₄	—	4	1	no	—
497	C₃×C₂²⋊C₄	—	4	1	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	—	4	2	no	—
504	C₃×C₂²⋊C₄	—	4	2	no	—
505	C₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
506	C₃×C₄²	—	2	4	no	—
507	C₃×C₄²	—	2	4	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	C₂×D₄	1	8	yes	—
513	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
514	C₂²×Q₈	C₂³×C₃	1	2	yes	—
515	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
516	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
517	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
518	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
519	C₂²×D₄	C₂³×C₃	1	2	yes	—
520	C₂²×D₄	C₂³×C₃	1	2	yes	—
521	C₂²×D₄	C₂³×C₃	1	2	yes	—
522	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
523	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
524	C₂³×C₄	C₂³×C₃	1	2	yes	—
525	C₂³×C₄	C₂³×C₃	1	2	yes	—
526	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
527	C₂³×C₄	C₂³×C₃	1	2	yes	—
528	C₄⋊Q₈	—	2	4	no	—
529	#126	—	2	8	no	—
530	#125	—	2	4	no	—
531	#125	—	2	8	no	—
532	#124	—	2	8	no	—
533	#124	—	2	8	no	—
534	#124	—	4	2	no	—
535	#123	—	2	8	no	—
536	C₂²⋊Q₈	—	2	4	no	—
537	C₂²⋊Q₈	—	2	4	no	—
538	C₂²⋊Q₈	—	4	4	no	—
539	C₂²⋊Q₈	—	4	2	no	—
540	#121	—	2	4	no	—
541	#121	—	2	4	no	—
542	#121	—	2	8	no	—
543	#121	—	4	4	no	—
544	#121	—	4	2	no	—
545	#121	—	4	4	no	—
546	C₄×Q₈	—	2	4	no	—
547	C₄×D₄	—	2	4	no	—
548	C₄×D₄	—	2	4	no	—
549	C₄×D₄	—	2	4	no	—
550	C₄×D₄	—	4	2	no	—
551	#117	—	2	4	no	—
552	#117	—	2	8	no	—
553	#117	—	2	8	no	—
554	#117	—	4	2	no	—
555	#117	C₃×D₄	1	8	yes	complemented
556	C₂×C₄⋊C₄	—	2	4	no	—
557	C₂×C₄⋊C₄	—	4	2	no	—
558	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
559	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
560	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
561	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
562	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
563	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
564	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
565	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
566	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
567	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
568	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
569	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
570	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
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	1	yes	characteristic
574	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
575	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
576	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
577	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
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	2	yes	—
582	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
594	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
595	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
597	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
598	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
599	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
600	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
601	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
602	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
603	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
604	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
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×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
611	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
612	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
613	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
614	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
615	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
616	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
617	C₂×C₄²	C₂³×C₃	1	2	yes	—
618	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
619	C₂×C₄²	C₂³×C₃	1	2	yes	—
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	#95	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	2	yes	—
631	#95	C₂³×C₃	1	2	yes	—
632	#95	C₂³×C₃	1	2	yes	—
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	C₂³×C₃	—	2	1	no	—
643	C₂³×C₃	—	2	1	no	—
644	C₂³×C₃	—	2	1	no	—
645	C₂³×C₃	—	2	1	no	—
646	C₂³×C₃	—	2	1	no	—
647	C₂³×C₃	—	2	1	no	—
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	1	no	—
653	C₂³×C₃	—	2	1	no	—
654	C₂³×C₃	—	2	1	no	—
655	C₂³×C₃	—	2	2	no	—
656	C₂³×C₃	—	2	1	no	—
657	C₂³×C₃	—	2	2	no	—
658	C₂³×C₃	—	2	1	no	—
659	C₂³×C₃	—	2	2	no	—
660	C₂³×C₃	—	2	1	no	—
661	C₂³×C₃	—	2	2	no	—
662	C₂³×C₃	—	2	2	no	—
663	C₂³×C₃	—	2	1	no	—
664	C₂³×C₃	—	2	2	no	—
665	C₂³×C₃	—	2	1	no	—
666	C₂³×C₃	—	2	2	no	—
667	C₂³×C₃	—	2	1	no	—
668	C₂³×C₃	C₂²×D₄	1	2	yes	—
669	C₂³×C₃	H(5,𝔽₂)	1	2	yes	—
670	C₂³×C₃	C₂⁵	1	1	yes	characteristic
671	C₃×Q₈	—	4	4	no	—
672	C₃×Q₈	—	8	4	no	—
673	C₃×D₄	—	4	4	no	—
674	C₃×D₄	—	4	4	no	—
675	C₃×D₄	—	4	4	no	—
676	C₃×D₄	—	4	4	no	—
677	C₃×D₄	—	8	4	no	—
678	C₃×D₄	—	8	4	no	—
679	C₃×D₄	—	8	4	no	—
680	C₂×C₃×C₄	—	2	1	no	—
681	C₂×C₃×C₄	—	2	1	no	—
682	C₂×C₃×C₄	—	2	2	no	—
683	C₂×C₃×C₄	—	2	1	no	—
684	C₂×C₃×C₄	—	2	2	no	—
685	C₂×C₃×C₄	—	2	2	no	—
686	C₂×C₃×C₄	—	2	1	no	—
687	C₂×C₃×C₄	—	2	2	no	—
688	C₂×C₃×C₄	—	2	8	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	2	no	—
693	C₂×C₃×C₄	—	2	2	no	—
694	C₂×C₃×C₄	—	2	1	no	—
695	C₂×C₃×C₄	—	2	1	no	—
696	C₂×C₃×C₄	—	2	2	no	—
697	C₂×C₃×C₄	—	2	1	no	—
698	C₂×C₃×C₄	—	2	1	no	—
699	C₂×C₃×C₄	—	2	1	no	—
700	C₂×C₃×C₄	—	2	1	no	—
701	C₂×C₃×C₄	—	2	2	no	—
702	C₂×C₃×C₄	—	2	1	no	—
703	C₂×C₃×C₄	—	2	2	no	—
704	C₂×C₃×C₄	—	2	1	no	—
705	C₂×C₃×C₄	—	2	1	no	—
706	C₂×C₃×C₄	—	2	2	no	—
707	C₂×C₃×C₄	—	2	2	no	—
708	C₂×C₃×C₄	—	2	1	no	—
709	C₂×C₃×C₄	—	2	1	no	—
710	C₂×C₃×C₄	—	2	2	no	—
711	C₂×C₃×C₄	—	2	2	no	—
712	C₂×C₃×C₄	—	2	1	no	—
713	C₂×C₃×C₄	—	2	2	no	—
714	C₂×C₃×C₄	—	2	1	no	—
715	C₂×C₃×C₄	—	2	1	no	—
716	C₂×C₃×C₄	—	2	1	no	—
717	C₂×C₃×C₄	—	2	1	no	—
718	C₂×C₃×C₄	—	2	1	no	—
719	C₂×C₃×C₄	—	2	2	no	—
720	C₂×C₃×C₄	—	2	1	no	—
721	C₂×C₃×C₄	—	2	1	no	—
722	C₂×C₃×C₄	—	2	1	no	—
723	C₂×C₃×C₄	—	2	1	no	—
724	C₂×C₃×C₄	—	2	2	no	—
725	C₂×C₃×C₄	—	2	2	no	—
726	C₂×C₃×C₄	—	2	1	no	—
727	C₂×C₃×C₄	—	2	1	no	—
728	C₂×C₃×C₄	—	2	2	no	—
729	C₂×C₃×C₄	—	2	2	no	—
730	C₂×C₃×C₄	—	2	1	no	—
731	C₂×C₃×C₄	—	4	8	no	—
732	C₂×C₃×C₄	—	4	8	no	—
733	C₂×C₃×C₄	—	4	4	no	—
734	C₂×C₃×C₄	—	4	4	no	—
735	C₂×C₃×C₄	—	8	4	no	—
736	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
737	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
738	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
739	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
740	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
741	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
742	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
743	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
744	C₂⁴	C₂⁴×C₃	1	2	yes	—
745	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
746	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
747	C₂×Q₈	—	2	2	no	—
748	C₂×Q₈	—	2	4	no	—
749	C₂×Q₈	—	2	2	no	—
750	C₂×Q₈	—	2	2	no	—
751	C₂×Q₈	—	4	2	no	—
752	C₂×Q₈	—	4	2	no	—
753	C₂×D₄	—	2	2	no	—
754	C₂×D₄	—	2	2	no	—
755	C₂×D₄	—	2	2	no	—
756	C₂×D₄	—	2	2	no	—
757	C₂×D₄	—	2	4	no	—
758	C₂×D₄	—	2	4	no	—
759	C₂×D₄	—	2	2	no	—
760	C₂×D₄	—	2	4	no	—
761	C₂×D₄	—	2	2	no	—
762	C₂×D₄	—	2	2	no	—
763	C₂×D₄	—	2	2	no	—
764	C₂×D₄	—	4	1	no	—
765	C₂×D₄	—	4	1	no	—
766	C₂×D₄	—	4	1	no	—
767	C₂×D₄	—	4	1	no	—
768	C₂×D₄	—	4	2	no	—
769	C₂×D₄	—	4	2	no	—
770	C₂×D₄	—	4	2	no	—
771	C₂×D₄	—	4	2	no	—
772	C₂×D₄	—	4	2	no	—
773	C₂×D₄	—	4	2	no	—
774	C₂²×C₄	—	2	2	no	—
775	C₂²×C₄	—	2	2	no	—
776	C₂²×C₄	—	2	4	no	—
777	C₂²×C₄	—	2	4	no	—
778	C₂²×C₄	—	2	2	no	—
779	C₂²×C₄	—	2	4	no	—
780	C₂²×C₄	—	2	2	no	—
781	C₂²×C₄	—	2	2	no	—
782	C₂²×C₄	—	2	2	no	—
783	C₂²×C₄	—	2	4	no	—
784	C₂²×C₄	—	2	2	no	—
785	C₂²×C₄	—	2	2	no	—
786	C₂²×C₄	—	4	2	no	—
787	C₂²×C₄	—	4	2	no	—
788	C₂²×C₄	—	4	2	no	—
789	C₂²×C₄	—	4	2	no	—
790	C₂²×C₄	—	4	2	no	—
791	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
792	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
793	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
794	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
795	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
796	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
797	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
798	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
799	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
800	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
801	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
802	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
803	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
804	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
805	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
806	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
807	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
808	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
809	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
810	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
811	C₄⋊C₄	—	2	2	no	—
812	C₄⋊C₄	—	2	4	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	2	4	no	—
815	C₄⋊C₄	—	2	2	no	—
816	C₄⋊C₄	—	2	4	no	—
817	C₄⋊C₄	—	2	4	no	—
818	C₄⋊C₄	—	2	2	no	—
819	C₄⋊C₄	—	2	4	no	—
820	C₄⋊C₄	—	2	4	no	—
821	C₄⋊C₄	—	2	4	no	—
822	C₄⋊C₄	—	2	2	no	—
823	C₄⋊C₄	—	2	2	no	—
824	C₄⋊C₄	—	2	2	no	—
825	C₄⋊C₄	—	4	2	no	—
826	C₄⋊C₄	—	4	1	no	—
827	C₄⋊C₄	—	4	1	no	—
828	C₄⋊C₄	—	4	1	no	—
829	C₄⋊C₄	—	4	2	no	—
830	C₄⋊C₄	—	4	2	no	—
831	C₄⋊C₄	—	4	2	no	—
832	C₄⋊C₄	—	4	2	no	—
833	C₄⋊C₄	—	4	2	no	—
834	C₄⋊C₄	—	4	2	no	—
835	C₄⋊C₄	—	4	2	no	—
836	C₄⋊C₄	—	4	2	no	—
837	C₄⋊C₄	—	4	1	no	—
838	C₄⋊C₄	—	4	2	no	—
839	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
840	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
841	C₂²⋊C₄	—	2	2	no	—
842	C₂²⋊C₄	—	2	2	no	—
843	C₂²⋊C₄	—	2	4	no	—
844	C₂²⋊C₄	—	2	4	no	—
845	C₂²⋊C₄	—	2	2	no	—
846	C₂²⋊C₄	—	2	2	no	—
847	C₂²⋊C₄	—	2	4	no	—
848	C₂²⋊C₄	—	2	4	no	—
849	C₂²⋊C₄	—	2	4	no	—
850	C₂²⋊C₄	—	2	4	no	—
851	C₂²⋊C₄	—	2	4	no	—
852	C₂²⋊C₄	—	2	2	no	—
853	C₂²⋊C₄	—	2	2	no	—
854	C₂²⋊C₄	—	4	1	no	—
855	C₂²⋊C₄	—	4	1	no	—
856	C₂²⋊C₄	—	4	1	no	—
857	C₂²⋊C₄	—	4	1	no	—
858	C₂²⋊C₄	—	4	2	no	—
859	C₂²⋊C₄	—	4	2	no	—
860	C₂²⋊C₄	—	4	2	no	—
861	C₂²⋊C₄	—	4	2	no	—
862	C₂²⋊C₄	—	4	2	no	—
863	C₂²⋊C₄	—	4	2	no	—
864	C₂²⋊C₄	—	4	2	no	—
865	C₂²⋊C₄	—	4	1	no	—
866	C₂²⋊C₄	—	4	2	no	—
867	C₂²⋊C₄	—	4	2	no	—
868	C₂²⋊C₄	—	4	1	no	—
869	C₂²⋊C₄	C₂×C₃×D₄	1	8	yes	—
870	C₄²	—	2	4	no	—
871	C₄²	—	2	4	no	—
872	C₄²	—	2	2	no	—
873	C₄²	—	2	2	no	—
874	C₄²	—	2	2	no	—
875	C₄²	—	2	2	no	—
876	C₄²	C₂×C₃×D₄	1	8	yes	—
877	C₂²×C₃	—	2	2	no	—
878	C₂²×C₃	—	2	2	no	—
879	C₂²×C₃	—	2	2	no	—
880	C₂²×C₃	—	2	2	no	—
881	C₂²×C₃	—	2	2	no	—
882	C₂²×C₃	—	2	2	no	—
883	C₂²×C₃	—	4	1	no	—
884	C₂²×C₃	—	4	1	no	—
885	C₂²×C₃	—	4	1	no	—
886	C₂²×C₃	—	4	1	no	—
887	C₂²×C₃	—	4	1	no	—
888	C₂²×C₃	—	4	1	no	—
889	C₂²×C₃	—	4	1	no	—
890	C₂²×C₃	—	4	1	no	—
891	C₂²×C₃	—	4	1	no	—
892	C₂²×C₃	—	4	2	no	—
893	C₂²×C₃	—	4	1	no	—
894	C₂²×C₃	—	4	2	no	—
895	C₂²×C₃	—	4	2	no	—
896	C₂²×C₃	—	4	1	no	—
897	C₂²×C₃	—	4	1	no	—
898	C₂²×C₃	—	4	2	no	—
899	C₂²×C₃	—	4	1	no	—
900	C₂²×C₃	—	4	2	no	—
901	C₂²×C₃	—	4	1	no	—
902	C₂²×C₃	—	4	2	no	—
903	C₂²×C₃	—	4	1	no	—
904	C₂²×C₃	—	4	2	no	—
905	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
906	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
907	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
908	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
909	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
910	C₂²×C₃	#585	1	1	yes	characteristic
911	C₂²×C₃	#585	1	1	yes	characteristic
912	C₃×C₄	—	2	2	no	—
913	C₃×C₄	—	2	4	no	—
914	C₃×C₄	—	2	2	no	—
915	C₃×C₄	—	2	4	no	—
916	C₃×C₄	—	4	1	no	—
917	C₃×C₄	—	4	1	no	—
918	C₃×C₄	—	4	2	no	—
919	C₃×C₄	—	4	2	no	—
920	C₃×C₄	—	4	1	no	—
921	C₃×C₄	—	4	2	no	—
922	C₃×C₄	—	4	1	no	—
923	C₃×C₄	—	4	1	no	—
924	C₃×C₄	—	4	1	no	—
925	C₃×C₄	—	4	2	no	—
926	C₃×C₄	—	4	2	no	—
927	C₃×C₄	—	4	1	no	—
928	C₃×C₄	—	4	1	no	—
929	C₃×C₄	—	4	1	no	—
930	C₃×C₄	#537	1	4	yes	—
931	C₂³	—	2	1	no	—
932	C₂³	—	2	1	no	—
933	C₂³	—	2	1	no	—
934	C₂³	—	2	1	no	—
935	C₂³	—	2	1	no	—
936	C₂³	—	2	1	no	—
937	C₂³	—	2	1	no	—
938	C₂³	—	2	1	no	—
939	C₂³	—	2	1	no	—
940	C₂³	—	2	1	no	—
941	C₂³	—	2	1	no	—
942	C₂³	—	2	1	no	—
943	C₂³	—	2	1	no	—
944	C₂³	—	2	2	no	—
945	C₂³	—	2	1	no	—
946	C₂³	—	2	2	no	—
947	C₂³	—	2	1	no	—
948	C₂³	—	2	2	no	—
949	C₂³	—	2	1	no	—
950	C₂³	—	2	2	no	—
951	C₂³	—	2	2	no	—
952	C₂³	—	2	1	no	—
953	C₂³	—	2	2	no	—
954	C₂³	—	2	1	no	—
955	C₂³	—	2	2	no	—
956	C₂³	—	2	1	no	—
957	C₂³	C₂²×C₃×D₄	1	2	yes	—
958	C₂³	C₃×H(5,𝔽₂)	1	2	yes	—
959	C₂³	C₂⁵×C₃	1	1	yes	characteristic
960	Q₈	—	4	4	no	—
961	Q₈	—	8	4	no	—
962	D₄	—	4	4	no	—
963	D₄	—	4	4	no	—
964	D₄	—	4	4	no	—
965	D₄	—	4	4	no	—
966	D₄	—	8	4	no	—
967	D₄	—	8	4	no	—
968	D₄	—	8	4	no	—
969	C₂×C₄	—	2	1	no	—
970	C₂×C₄	—	2	1	no	—
971	C₂×C₄	—	2	2	no	—
972	C₂×C₄	—	2	1	no	—
973	C₂×C₄	—	2	2	no	—
974	C₂×C₄	—	2	2	no	—
975	C₂×C₄	—	2	1	no	—
976	C₂×C₄	—	2	2	no	—
977	C₂×C₄	—	2	8	no	—
978	C₂×C₄	—	2	1	no	—
979	C₂×C₄	—	2	1	no	—
980	C₂×C₄	—	2	1	no	—
981	C₂×C₄	—	2	2	no	—
982	C₂×C₄	—	2	2	no	—
983	C₂×C₄	—	2	1	no	—
984	C₂×C₄	—	2	1	no	—
985	C₂×C₄	—	2	2	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	1	no	—
992	C₂×C₄	—	2	2	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	2	no	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	2	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	2	1	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	1	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	1	no	—
1010	C₂×C₄	—	2	1	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	—	2	1	no	—
1017	C₂×C₄	—	2	2	no	—
1018	C₂×C₄	—	2	2	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	4	8	no	—
1021	C₂×C₄	—	4	8	no	—
1022	C₂×C₄	—	4	4	no	—
1023	C₂×C₄	—	4	4	no	—
1024	C₂×C₄	—	8	4	no	—
1025	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
1026	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
1027	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1028	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1029	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
1030	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
1031	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
1032	C₂×C₃	—	4	2	no	—
1033	C₂×C₃	—	4	2	no	—
1034	C₂×C₃	—	8	1	no	—
1035	C₂×C₃	—	8	2	no	—
1036	C₂×C₃	C₂×#537	1	1	yes	characteristic
1037	C₂×C₃	#3488	1	1	yes	characteristic
1038	C₂×C₃	#3489	1	1	yes	characteristic
1039	C₂×C₃	#3542	1	1	yes	characteristic
1040	C₂×C₃	#3544	1	1	yes	characteristic
1041	C₂×C₃	#3547	1	1	yes	characteristic
1042	C₂×C₃	#3565	1	1	yes	characteristic
1043	C₂²	—	2	2	no	—
1044	C₂²	—	2	2	no	—
1045	C₂²	—	2	2	no	—
1046	C₂²	—	2	2	no	—
1047	C₂²	—	2	2	no	—
1048	C₂²	—	2	2	no	—
1049	C₂²	—	4	1	no	—
1050	C₂²	—	4	1	no	—
1051	C₂²	—	4	1	no	—
1052	C₂²	—	4	1	no	—
1053	C₂²	—	4	1	no	—
1054	C₂²	—	4	1	no	—
1055	C₂²	—	4	1	no	—
1056	C₂²	—	4	1	no	—
1057	C₂²	—	4	1	no	—
1058	C₂²	—	4	2	no	—
1059	C₂²	—	4	1	no	—
1060	C₂²	—	4	2	no	—
1061	C₂²	—	4	2	no	—
1062	C₂²	—	4	1	no	—
1063	C₂²	—	4	1	no	—
1064	C₂²	—	4	2	no	—
1065	C₂²	—	4	1	no	—
1066	C₂²	—	4	2	no	—
1067	C₂²	—	4	1	no	—
1068	C₂²	—	4	2	no	—
1069	C₂²	—	4	1	no	—
1070	C₂²	—	4	2	no	—
1071	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
1072	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1073	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1074	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
1075	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
1076	C₂²	C₃×#585	1	1	yes	characteristic
1077	C₂²	C₃×#585	1	1	yes	characteristic
1078	C₄	—	2	2	no	—
1079	C₄	—	2	4	no	—
1080	C₄	—	2	2	no	—
1081	C₄	—	2	4	no	—
1082	C₄	—	4	1	no	—
1083	C₄	—	4	1	no	—
1084	C₄	—	4	2	no	—
1085	C₄	—	4	2	no	—
1086	C₄	—	4	1	no	—
1087	C₄	—	4	2	no	—
1088	C₄	—	4	1	no	—
1089	C₄	—	4	1	no	—
1090	C₄	—	4	2	no	—
1091	C₄	—	4	2	no	—
1092	C₄	—	4	1	no	—
1093	C₄	—	4	1	no	—
1094	C₄	—	4	1	no	—
1095	C₄	—	4	1	no	—
1096	C₄	C₃×#537	1	4	yes	—
1097	C₃	#42970	1	1	yes	characteristic, direct product factor, Sylow
1098	C₂	—	4	2	no	—
1099	C₂	—	4	2	no	—
1100	C₂	—	8	1	no	—
1101	C₂	—	8	2	no	—
1102	C₂	C₂×C₃×#537	1	1	yes	characteristic
1103	C₂	C₃×#3488	1	1	yes	characteristic
1104	C₂	C₃×#3489	1	1	yes	characteristic
1105	C₂	C₃×#3542	1	1	yes	characteristic
1106	C₂	C₃×#3544	1	1	yes	characteristic
1107	C₂	C₃×#3547	1	1	yes	characteristic
1108	C₂	C₃×#3565	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
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×#555	C₂	semidirect
2. C₂×C₃×#552	C₂	semidirect
3. C₃×#2820	C₂	semidirect
4. C₃×#2715	C₂	semidirect
5. C₃×#2691	C₂	semidirect
6. C₃×#2672	C₂	semidirect
7. C₃×#2671	C₂	semidirect
8. C₃×#2629	C₂	semidirect
9. C₃×#2620	C₂	semidirect
10. C₃×#2620	C₂	semidirect
11. C₃×#2609	C₂	semidirect
12. C₃×#2454	C₂	semidirect
13. C₃×#2451	C₂	semidirect
14. C₃×#2441	C₂	semidirect
15. C₃×#2440	C₂	semidirect
16. C₃×#2427	C₂	semidirect
17. C₃×#2426	C₂	semidirect
18. C₃×#2417	C₂	semidirect
19. C₃×#2416	C₂	semidirect
20. C₃×#2416	C₂	semidirect
21. C₃×#2415	C₂	semidirect
22. C₃×#2392	C₂	semidirect
23. C₃×#2317	C₂	semidirect
24. #42970	C₃	direct (N × H)
126. C₂×#555	C₂×C₃	semidirect
127. C₂×#552	C₂×C₃	semidirect
128. #2820	C₂×C₃	semidirect
129. #2715	C₂×C₃	semidirect
130. #2691	C₂×C₃	semidirect
131. #2672	C₂×C₃	semidirect
132. #2671	C₂×C₃	semidirect
133. #2629	C₂×C₃	semidirect
134. #2620	C₂×C₃	semidirect
135. #2620	C₂×C₃	semidirect
136. #2609	C₂×C₃	semidirect
137. #2454	C₂×C₃	semidirect
138. #2451	C₂×C₃	semidirect
139. #2441	C₂×C₃	semidirect
140. #2440	C₂×C₃	semidirect
141. #2427	C₂×C₃	semidirect
142. #2426	C₂×C₃	semidirect
143. #2417	C₂×C₃	semidirect
144. #2416	C₂×C₃	semidirect
145. #2416	C₂×C₃	semidirect
146. #2415	C₂×C₃	semidirect
147. #2392	C₂×C₃	semidirect
148. #2317	C₂×C₃	semidirect
191. C₃×#117	D₄	semidirect
555. #117	C₃×D₄	semidirect
1097. C₃	#42970	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×#555	2
C₂×C₃×#552	2
C₃×#2820	2
C₃×#2715	2
C₃×#2691	2
C₃×#2672	2
C₃×#2671	2
C₃×#2629	2
C₃×#2620	2
C₃×#2609	2
C₃×#2454	2
C₃×#2451	2
C₃×#2441	2
C₃×#2440	2
C₃×#2427	2
C₃×#2426	2
C₃×#2417	2
C₃×#2416	2
C₃×#2415	2
C₃×#2392	2
C₃×#2317	2
#42970	3

Subgroups — C3×#42970 #10661577

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#42970 #10661577