Subgroups — C₃×#34476 #10653083

Order 768.

2736 conjugacy classes of subgroups.

The subgroup lattice has 1144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#546	C₂	1	1	yes	maximal, characteristic
2	C₃×#2377	C₂	1	2	yes	maximal, complemented
3	C₃×#2376	C₂	1	2	yes	maximal, complemented
4	C₃×#2367	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2361	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#2360	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#2358	C₂	1	2	yes	maximal, complemented
8	C₃×#2354	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×D₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#2342	C₂	1	2	yes	maximal, complemented
11	C₃×#2341	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×D₄×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#2335	C₂	1	2	yes	maximal, complemented
14	C₃×#2326	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#2324	C₂	1	2	yes	maximal, complemented
16	C₃×#2324	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#2321	C₂	1	2	yes	maximal, complemented
18	C₃×#2319	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#2315	C₂	1	2	yes	maximal, complemented
20	C₃×#2311	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×C₄×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₃×#390	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×#2290	C₂	1	1	yes	maximal, characteristic, complemented
24	#34476	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
26	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic
27	C₃×#546	C₄	1	16	yes	complemented
28	C₂×C₃×#124	C₂²	1	1	yes	characteristic
29	C₂×C₃×#123	C₂²	1	2	yes	—
30	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₃×#121	C₂²	1	1	yes	characteristic
32	C₂×C₃×#121	C₂²	1	2	yes	—
33	C₂×C₃×#120	C₂²	1	2	yes	—
34	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
37	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
38	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
39	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
40	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
41	C₂×C₃×C₄×D₄	C₂²	1	2	yes	complemented
42	C₂×C₃×#117	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₃×#117	C₂²	1	2	yes	complemented
44	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
45	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
46	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
47	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
48	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
49	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
50	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
51	C₃×#391	C₂²	1	1	yes	characteristic, complemented
52	C₃×#391	C₂²	1	1	yes	characteristic, complemented
53	C₃×#390	C₂²	1	1	yes	characteristic
54	C₃×#390	C₂²	1	2	yes	—
55	C₃×#390	C₂²	1	1	yes	characteristic
56	C₃×#390	C₂²	1	1	yes	characteristic
57	C₃×#390	C₂²	1	2	yes	—
58	C₃×#390	C₂²	1	1	yes	characteristic
59	C₃×#390	C₂²	1	1	yes	characteristic
60	C₃×#390	C₂²	1	1	yes	characteristic
61	C₃×#390	C₂²	1	2	yes	complemented
62	C₃×#390	C₂²	1	2	yes	complemented
63	C₃×#390	C₂²	1	2	yes	complemented
64	C₃×#389	C₂²	1	1	yes	characteristic, complemented
65	C₃×#389	C₂²	1	2	yes	complemented
66	C₃×#389	C₂²	1	2	yes	complemented
67	C₃×#389	C₂²	1	1	yes	characteristic, complemented
68	C₃×#388	C₂²	1	2	yes	complemented
69	C₃×#388	C₂²	1	2	yes	complemented
70	C₃×#388	C₂²	1	2	yes	complemented
71	C₃×#388	C₂²	1	2	yes	complemented
72	C₃×#388	C₂²	1	2	yes	complemented
73	C₃×#388	C₂²	1	2	yes	complemented
74	C₃×#388	C₂²	1	1	yes	characteristic, complemented
75	C₃×#388	C₂²	1	2	yes	complemented
76	C₃×#388	C₂²	1	1	yes	characteristic, complemented
77	C₃×#388	C₂²	1	2	yes	complemented
78	C₃×#388	C₂²	1	2	yes	complemented
79	C₃×#388	C₂²	1	2	yes	complemented
80	C₃×#387	C₂²	1	2	yes	complemented
81	C₃×#387	C₂²	1	1	yes	characteristic, complemented
82	C₃×#387	C₂²	1	2	yes	complemented
83	C₃×#387	C₂²	1	1	yes	characteristic, complemented
84	C₃×#386	C₂²	1	2	yes	—
85	C₃×#386	C₂²	1	2	yes	—
86	C₃×#386	C₂²	1	1	yes	characteristic
87	C₃×#386	C₂²	1	1	yes	characteristic
88	C₃×#386	C₂²	1	2	yes	complemented
89	C₃×#386	C₂²	1	2	yes	complemented
90	C₃×#386	C₂²	1	2	yes	complemented
91	C₃×#386	C₂²	1	2	yes	complemented
92	C₃×#385	C₂²	1	2	yes	—
93	C₃×#385	C₂²	1	1	yes	characteristic
94	C₃×#385	C₂²	1	1	yes	characteristic
95	C₃×#385	C₂²	1	2	yes	—
96	C₃×#385	C₂²	1	2	yes	—
97	C₃×#385	C₂²	1	2	yes	complemented
98	C₃×#385	C₂²	1	2	yes	complemented
99	C₃×#385	C₂²	1	2	yes	complemented
100	C₃×#385	C₂²	1	2	yes	complemented
101	C₃×#385	C₂²	1	2	yes	complemented
102	C₃×#385	C₂²	1	2	yes	complemented
103	C₃×#384	C₂²	1	1	yes	characteristic, complemented
104	C₃×#381	C₂²	1	2	yes	complemented
105	C₃×#380	C₂²	1	1	yes	characteristic
106	C₃×#380	C₂²	1	2	yes	complemented
107	C₃×#380	C₂²	1	2	yes	complemented
108	C₃×#380	C₂²	1	2	yes	complemented
109	C₃×#380	C₂²	1	2	yes	complemented
110	C₃×#380	C₂²	1	2	yes	complemented
111	C₃×#380	C₂²	1	1	yes	characteristic, complemented
112	C₃×#379	C₂²	1	2	yes	—
113	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
114	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
115	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
116	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
117	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
118	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
119	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
120	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
121	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
122	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
123	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
124	C₃×#376	C₂²	1	1	yes	characteristic, complemented
125	C₂×#546	C₂×C₃	1	1	yes	characteristic
126	#2377	C₂×C₃	1	2	yes	complemented
127	#2376	C₂×C₃	1	2	yes	complemented
128	#2367	C₂×C₃	1	1	yes	characteristic, complemented
129	#2361	C₂×C₃	1	1	yes	characteristic, complemented
130	#2360	C₂×C₃	1	1	yes	characteristic, complemented
131	#2358	C₂×C₃	1	2	yes	complemented
132	#2354	C₂×C₃	1	1	yes	characteristic, complemented
133	D₄×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
134	#2342	C₂×C₃	1	2	yes	complemented
135	#2341	C₂×C₃	1	1	yes	characteristic, complemented
136	D₄×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
137	#2335	C₂×C₃	1	2	yes	complemented
138	#2326	C₂×C₃	1	1	yes	characteristic, complemented
139	#2324	C₂×C₃	1	1	yes	characteristic, complemented
140	#2324	C₂×C₃	1	2	yes	complemented
141	#2321	C₂×C₃	1	2	yes	complemented
142	#2319	C₂×C₃	1	1	yes	characteristic, complemented
143	#2315	C₂×C₃	1	2	yes	complemented
144	#2311	C₂×C₃	1	1	yes	characteristic, complemented
145	C₄×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
146	C₂×#390	C₂×C₃	1	1	yes	characteristic, complemented
147	#2290	C₂×C₃	1	1	yes	characteristic, complemented
148	C₂⁵×C₃	C₂³	1	2	yes	—
149	C₂×C₃×#41	—	4	2	no	—
150	C₂×C₃×#41	—	4	2	no	—
151	C₂×C₃×#41	C₂×C₄	1	8	yes	complemented
152	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
153	C₂²×C₃×D₄	—	4	2	no	—
154	C₂²×C₃×D₄	—	4	2	no	—
155	C₂²×C₃×D₄	C₂×C₄	1	8	yes	complemented
156	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
157	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
158	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
159	C₂²×C₃×D₄	C₂³	1	2	yes	—
160	C₂²×C₃×D₄	C₂³	1	2	yes	—
161	C₂²×C₃×D₄	C₂³	1	2	yes	—
162	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
163	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
164	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
165	C₂³×C₃×C₄	C₂³	1	2	yes	—
166	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
167	C₂³×C₃×C₄	C₂³	1	2	yes	—
168	C₂³×C₃×C₄	C₂³	1	2	yes	—
169	C₂³×C₃×C₄	C₂³	1	2	yes	—
170	C₂³×C₃×C₄	C₂³	1	2	yes	—
171	C₂³×C₃×C₄	C₂³	1	2	yes	—
172	C₃×#124	C₂×C₄	1	8	yes	complemented
173	C₃×#123	C₂×C₄	1	16	yes	complemented
174	C₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
175	C₃×#121	C₂×C₄	1	8	yes	complemented
176	C₃×#121	C₂×C₄	1	16	yes	complemented
177	C₃×#120	C₂×C₄	1	16	yes	complemented
178	C₃×C₄×Q₈	—	4	2	no	—
179	C₃×C₄×Q₈	—	4	2	no	—
180	C₃×C₄×D₄	—	4	4	no	—
181	C₃×C₄×D₄	—	4	2	no	—
182	C₃×C₄×D₄	—	4	2	no	—
183	C₃×C₄×D₄	—	4	4	no	—
184	C₃×C₄×D₄	C₂×C₄	1	8	yes	complemented
185	C₃×C₄×D₄	C₂×C₄	1	8	yes	complemented
186	C₃×#117	—	4	2	no	—
187	C₃×#117	—	4	4	no	—
188	C₂×C₃×C₄⋊C₄	—	4	2	no	—
189	C₂×C₃×C₄⋊C₄	—	4	2	no	—
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	1	yes	characteristic
193	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
197	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
198	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
199	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
208	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
209	C₂×C₃×C₂²⋊C₄	—	4	4	no	—
210	C₂×C₃×C₂²⋊C₄	—	4	4	no	—
211	C₂×C₃×C₂²⋊C₄	—	4	4	no	—
212	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	16	yes	complemented
213	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
214	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
215	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
216	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
217	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
218	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
219	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
220	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
239	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
240	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
241	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
242	C₂×C₃×C₄²	—	4	2	no	—
243	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
244	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
245	C₂×C₃×C₄²	C₂³	1	2	yes	—
246	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
247	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
248	C₂×C₃×C₄²	C₂³	1	2	yes	—
249	C₂×C₃×C₄²	C₂³	1	2	yes	—
250	C₂×C₃×C₄²	C₂³	1	2	yes	—
251	C₂×C₃×C₄²	C₂³	1	2	yes	—
252	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
253	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
254	C₂×C₃×C₄²	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	2	yes	—
260	C₃×#95	C₂³	1	2	yes	—
261	C₃×#95	C₂³	1	2	yes	—
262	C₃×#95	C₂³	1	2	yes	—
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	1	yes	characteristic
267	C₃×#95	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
276	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
277	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic
278	#546	C₃×C₄	1	16	yes	complemented
279	C₂×#124	C₂²×C₃	1	1	yes	characteristic
280	C₂×#123	C₂²×C₃	1	2	yes	—
281	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
282	C₂×#121	C₂²×C₃	1	1	yes	characteristic
283	C₂×#121	C₂²×C₃	1	2	yes	—
284	C₂×#120	C₂²×C₃	1	2	yes	—
285	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
286	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
287	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
288	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
289	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
290	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
291	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
292	C₂×C₄×D₄	C₂²×C₃	1	2	yes	complemented
293	C₂×#117	C₂²×C₃	1	1	yes	characteristic, complemented
294	C₂×#117	C₂²×C₃	1	2	yes	complemented
295	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
296	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
297	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
298	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
299	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
300	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
301	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
302	#391	C₂²×C₃	1	1	yes	characteristic, complemented
303	#391	C₂²×C₃	1	1	yes	characteristic, complemented
304	#390	C₂²×C₃	1	1	yes	characteristic
305	#390	C₂²×C₃	1	1	yes	characteristic
306	#390	C₂²×C₃	1	1	yes	characteristic
307	#390	C₂²×C₃	1	1	yes	characteristic
308	#390	C₂²×C₃	1	2	yes	—
309	#390	C₂²×C₃	1	1	yes	characteristic
310	#390	C₂²×C₃	1	1	yes	characteristic
311	#390	C₂²×C₃	1	2	yes	—
312	#390	C₂²×C₃	1	2	yes	complemented
313	#390	C₂²×C₃	1	2	yes	complemented
314	#390	C₂²×C₃	1	2	yes	complemented
315	#389	C₂²×C₃	1	1	yes	characteristic, complemented
316	#389	C₂²×C₃	1	1	yes	characteristic, complemented
317	#389	C₂²×C₃	1	2	yes	complemented
318	#389	C₂²×C₃	1	2	yes	complemented
319	#388	C₂²×C₃	1	2	yes	complemented
320	#388	C₂²×C₃	1	2	yes	complemented
321	#388	C₂²×C₃	1	2	yes	complemented
322	#388	C₂²×C₃	1	2	yes	complemented
323	#388	C₂²×C₃	1	2	yes	complemented
324	#388	C₂²×C₃	1	1	yes	characteristic, complemented
325	#388	C₂²×C₃	1	2	yes	complemented
326	#388	C₂²×C₃	1	2	yes	complemented
327	#388	C₂²×C₃	1	2	yes	complemented
328	#388	C₂²×C₃	1	2	yes	complemented
329	#388	C₂²×C₃	1	2	yes	complemented
330	#388	C₂²×C₃	1	1	yes	characteristic, complemented
331	#387	C₂²×C₃	1	1	yes	characteristic, complemented
332	#387	C₂²×C₃	1	2	yes	complemented
333	#387	C₂²×C₃	1	1	yes	characteristic, complemented
334	#387	C₂²×C₃	1	2	yes	complemented
335	#386	C₂²×C₃	1	1	yes	characteristic
336	#386	C₂²×C₃	1	2	yes	—
337	#386	C₂²×C₃	1	2	yes	—
338	#386	C₂²×C₃	1	1	yes	characteristic
339	#386	C₂²×C₃	1	2	yes	complemented
340	#386	C₂²×C₃	1	2	yes	complemented
341	#386	C₂²×C₃	1	2	yes	complemented
342	#386	C₂²×C₃	1	2	yes	complemented
343	#385	C₂²×C₃	1	1	yes	characteristic
344	#385	C₂²×C₃	1	2	yes	—
345	#385	C₂²×C₃	1	2	yes	—
346	#385	C₂²×C₃	1	2	yes	—
347	#385	C₂²×C₃	1	1	yes	characteristic
348	#385	C₂²×C₃	1	2	yes	complemented
349	#385	C₂²×C₃	1	2	yes	complemented
350	#385	C₂²×C₃	1	2	yes	complemented
351	#385	C₂²×C₃	1	2	yes	complemented
352	#385	C₂²×C₃	1	2	yes	complemented
353	#385	C₂²×C₃	1	2	yes	complemented
354	#384	C₂²×C₃	1	1	yes	characteristic, complemented
355	#381	C₂²×C₃	1	2	yes	complemented
356	#380	C₂²×C₃	1	1	yes	characteristic
357	#380	C₂²×C₃	1	2	yes	complemented
358	#380	C₂²×C₃	1	2	yes	complemented
359	#380	C₂²×C₃	1	2	yes	complemented
360	#380	C₂²×C₃	1	2	yes	complemented
361	#380	C₂²×C₃	1	2	yes	complemented
362	#380	C₂²×C₃	1	1	yes	characteristic, complemented
363	#379	C₂²×C₃	1	2	yes	—
364	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
365	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
366	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
367	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
368	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
369	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
370	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
371	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
372	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
373	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
374	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
375	#376	C₂²×C₃	1	1	yes	characteristic, complemented
376	C₂⁴×C₃	—	2	4	no	—
377	C₂⁴×C₃	—	2	4	no	—
378	C₂⁴×C₃	—	4	2	no	—
379	C₂⁴×C₃	—	4	2	no	—
380	C₂⁴×C₃	—	4	2	no	—
381	C₂⁴×C₃	—	4	2	no	—
382	C₂⁴×C₃	C₂²×C₄	1	8	yes	—
383	C₂⁴×C₃	C₂⁴	1	2	yes	—
384	C₂⁴×C₃	C₂⁴	1	2	yes	—
385	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
386	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
387	C₃×#41	—	4	16	no	—
388	C₂×C₃×Q₈	—	2	2	no	—
389	C₂×C₃×Q₈	—	2	2	no	—
390	C₂×C₃×Q₈	C₂²×C₄	1	4	yes	—
391	C₂×C₃×D₄	—	2	2	no	—
392	C₂×C₃×D₄	—	2	2	no	—
393	C₂×C₃×D₄	—	2	2	no	—
394	C₂×C₃×D₄	—	2	2	no	—
395	C₂×C₃×D₄	—	2	2	no	—
396	C₂×C₃×D₄	—	2	2	no	—
397	C₂×C₃×D₄	—	4	16	no	—
398	C₂×C₃×D₄	—	4	2	no	—
399	C₂×C₃×D₄	—	4	2	no	—
400	C₂×C₃×D₄	—	4	2	no	—
401	C₂×C₃×D₄	—	4	2	no	—
402	C₂×C₃×D₄	—	4	2	no	—
403	C₂×C₃×D₄	—	4	2	no	—
404	C₂×C₃×D₄	C₂²×C₄	1	4	yes	—
405	C₂×C₃×D₄	C₂²×C₄	1	4	yes	—
406	C₂×C₃×D₄	C₂²×C₄	1	4	yes	—
407	C₂×C₃×D₄	C₂²×C₄	1	8	yes	—
408	C₂×C₃×D₄	C₂²×C₄	1	8	yes	—
409	C₂×C₃×D₄	C₂²×C₄	1	8	yes	—
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	4	no	—
417	C₂²×C₃×C₄	—	2	2	no	—
418	C₂²×C₃×C₄	—	4	1	no	—
419	C₂²×C₃×C₄	—	4	1	no	—
420	C₂²×C₃×C₄	—	4	2	no	—
421	C₂²×C₃×C₄	—	4	2	no	—
422	C₂²×C₃×C₄	—	4	1	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	—	4	2	no	—
428	C₂²×C₃×C₄	—	4	2	no	—
429	C₂²×C₃×C₄	—	4	2	no	—
430	C₂²×C₃×C₄	—	4	2	no	—
431	C₂²×C₃×C₄	—	4	2	no	—
432	C₂²×C₃×C₄	—	4	2	no	—
433	C₂²×C₃×C₄	—	4	2	no	—
434	C₂²×C₃×C₄	—	4	2	no	—
435	C₂²×C₃×C₄	—	4	2	no	—
436	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
437	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
438	C₂²×C₃×C₄	C₂²×C₄	1	8	yes	—
439	C₂²×C₃×C₄	C₂²×C₄	1	8	yes	—
440	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
441	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
442	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
443	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
444	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
445	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
446	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
447	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
448	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
449	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
450	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
451	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
452	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
453	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
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	C₃×C₄⋊C₄	—	2	2	no	—
460	C₃×C₄⋊C₄	—	2	2	no	—
461	C₃×C₄⋊C₄	—	2	2	no	—
462	C₃×C₄⋊C₄	—	2	2	no	—
463	C₃×C₄⋊C₄	—	2	2	no	—
464	C₃×C₄⋊C₄	—	4	2	no	—
465	C₃×C₄⋊C₄	—	4	2	no	—
466	C₃×C₄⋊C₄	—	4	1	no	—
467	C₃×C₄⋊C₄	—	4	2	no	—
468	C₃×C₄⋊C₄	—	4	2	no	—
469	C₃×C₄⋊C₄	—	4	1	no	—
470	C₃×C₄⋊C₄	—	4	1	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	C₂²×C₄	1	4	yes	—
476	C₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
477	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
478	C₃×C₂²⋊C₄	—	2	2	no	—
479	C₃×C₂²⋊C₄	—	2	4	no	—
480	C₃×C₂²⋊C₄	—	2	2	no	—
481	C₃×C₂²⋊C₄	—	2	4	no	—
482	C₃×C₂²⋊C₄	—	2	4	no	—
483	C₃×C₂²⋊C₄	—	2	2	no	—
484	C₃×C₂²⋊C₄	—	4	2	no	—
485	C₃×C₂²⋊C₄	—	4	2	no	—
486	C₃×C₂²⋊C₄	—	4	2	no	—
487	C₃×C₂²⋊C₄	—	4	2	no	—
488	C₃×C₂²⋊C₄	—	4	2	no	—
489	C₃×C₂²⋊C₄	—	4	2	no	—
490	C₃×C₂²⋊C₄	—	4	2	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	2	no	—
497	C₃×C₂²⋊C₄	—	4	2	no	—
498	C₃×C₂²⋊C₄	—	4	2	no	—
499	C₃×C₂²⋊C₄	—	4	2	no	—
500	C₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
501	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
502	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
503	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
504	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
505	C₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
506	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
507	C₃×C₄²	—	2	2	no	—
508	C₃×C₄²	—	2	2	no	—
509	C₃×C₄²	—	2	4	no	—
510	C₃×C₄²	—	2	2	no	—
511	C₃×C₄²	—	2	2	no	—
512	C₃×C₄²	—	4	1	no	—
513	C₃×C₄²	—	4	1	no	—
514	C₃×C₄²	—	4	2	no	—
515	C₃×C₄²	—	4	2	no	—
516	C₃×C₄²	—	4	2	no	—
517	C₃×C₄²	—	4	2	no	—
518	C₃×C₄²	C₂²×C₄	1	4	yes	—
519	C₂⁵	C₂³×C₃	1	2	yes	—
520	C₂×#41	—	4	2	no	—
521	C₂×#41	—	4	2	no	—
522	C₂×#41	C₂×C₃×C₄	1	8	yes	complemented
523	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
524	C₂²×D₄	—	4	2	no	—
525	C₂²×D₄	—	4	2	no	—
526	C₂²×D₄	C₂×C₃×C₄	1	8	yes	complemented
527	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
528	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
529	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
530	C₂²×D₄	C₂³×C₃	1	2	yes	—
531	C₂²×D₄	C₂³×C₃	1	2	yes	—
532	C₂²×D₄	C₂³×C₃	1	2	yes	—
533	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
534	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
535	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
536	C₂³×C₄	C₂³×C₃	1	2	yes	—
537	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
538	C₂³×C₄	C₂³×C₃	1	2	yes	—
539	C₂³×C₄	C₂³×C₃	1	2	yes	—
540	C₂³×C₄	C₂³×C₃	1	2	yes	—
541	C₂³×C₄	C₂³×C₃	1	2	yes	—
542	C₂³×C₄	C₂³×C₃	1	2	yes	—
543	#124	C₂×C₃×C₄	1	8	yes	complemented
544	#123	C₂×C₃×C₄	1	16	yes	complemented
545	C₂²⋊Q₈	C₂×C₃×C₄	1	8	yes	complemented
546	#121	C₂×C₃×C₄	1	8	yes	complemented
547	#121	C₂×C₃×C₄	1	16	yes	complemented
548	#120	C₂×C₃×C₄	1	16	yes	complemented
549	C₄×Q₈	—	4	2	no	—
550	C₄×Q₈	—	4	2	no	—
551	C₄×D₄	—	4	4	no	—
552	C₄×D₄	—	4	2	no	—
553	C₄×D₄	—	4	2	no	—
554	C₄×D₄	—	4	4	no	—
555	C₄×D₄	C₂×C₃×C₄	1	8	yes	complemented
556	C₄×D₄	C₂×C₃×C₄	1	8	yes	complemented
557	#117	—	4	2	no	—
558	#117	—	4	4	no	—
559	C₂×C₄⋊C₄	—	4	2	no	—
560	C₂×C₄⋊C₄	—	4	2	no	—
561	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	1	yes	characteristic
565	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
566	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
567	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
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	2	yes	—
571	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
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	2	yes	—
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	1	yes	characteristic
578	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
579	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
580	C₂×C₂²⋊C₄	—	4	4	no	—
581	C₂×C₂²⋊C₄	—	4	4	no	—
582	C₂×C₂²⋊C₄	—	4	4	no	—
583	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	16	yes	complemented
584	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
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×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
589	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	1	yes	characteristic
600	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	1	yes	characteristic
606	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	1	yes	characteristic
612	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
613	C₂×C₄²	—	4	2	no	—
614	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
615	C₂×C₄²	C₂³×C₃	1	2	yes	—
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	2	yes	—
620	C₂×C₄²	C₂³×C₃	1	2	yes	—
621	C₂×C₄²	C₂³×C₃	1	2	yes	—
622	C₂×C₄²	C₂³×C₃	1	2	yes	—
623	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
624	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
625	C₂×C₄²	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	1	yes	characteristic
635	#95	C₂³×C₃	1	1	yes	characteristic
636	#95	C₂³×C₃	1	1	yes	characteristic
637	#95	C₂³×C₃	1	1	yes	characteristic
638	#95	C₂³×C₃	1	1	yes	characteristic
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	1	yes	characteristic
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	2	no	—
652	C₂³×C₃	—	2	2	no	—
653	C₂³×C₃	—	2	1	no	—
654	C₂³×C₃	—	2	2	no	—
655	C₂³×C₃	—	2	1	no	—
656	C₂³×C₃	—	2	1	no	—
657	C₂³×C₃	—	2	2	no	—
658	C₂³×C₃	—	2	2	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	2	no	—
666	C₂³×C₃	—	2	2	no	—
667	C₂³×C₃	—	2	1	no	—
668	C₂³×C₃	—	2	2	no	—
669	C₂³×C₃	—	2	16	no	—
670	C₂³×C₃	—	4	8	no	—
671	C₂³×C₃	—	4	8	no	—
672	C₂³×C₃	—	8	4	no	—
673	C₂³×C₃	—	8	4	no	—
674	C₂³×C₃	—	8	4	no	—
675	C₂³×C₃	—	8	4	no	—
676	C₂³×C₃	C₂³×C₄	1	4	yes	—
677	C₂³×C₃	C₂³×C₄	1	4	yes	—
678	C₂³×C₃	C₂³×C₄	1	2	yes	—
679	C₂³×C₃	C₂³×C₄	1	2	yes	—
680	C₂³×C₃	H(5,𝔽₂)	1	2	yes	—
681	C₂³×C₃	2₋¹⁺⁴	1	2	yes	—
682	C₂³×C₃	C₂⁵	1	1	yes	characteristic
683	C₃×Q₈	—	2	8	no	—
684	C₃×D₄	—	2	8	no	—
685	C₃×D₄	—	2	8	no	—
686	C₃×D₄	—	2	8	no	—
687	C₃×D₄	—	4	8	no	—
688	C₃×D₄	—	4	8	no	—
689	C₃×D₄	—	4	8	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	2	no	—
695	C₂×C₃×C₄	—	2	2	no	—
696	C₂×C₃×C₄	—	2	1	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	1	no	—
702	C₂×C₃×C₄	—	2	1	no	—
703	C₂×C₃×C₄	—	2	2	no	—
704	C₂×C₃×C₄	—	2	8	no	—
705	C₂×C₃×C₄	—	2	8	no	—
706	C₂×C₃×C₄	—	2	1	no	—
707	C₂×C₃×C₄	—	2	1	no	—
708	C₂×C₃×C₄	—	2	1	no	—
709	C₂×C₃×C₄	—	2	1	no	—
710	C₂×C₃×C₄	—	2	1	no	—
711	C₂×C₃×C₄	—	2	1	no	—
712	C₂×C₃×C₄	—	2	2	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	2	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	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	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	2	no	—
731	C₂×C₃×C₄	—	2	1	no	—
732	C₂×C₃×C₄	—	2	1	no	—
733	C₂×C₃×C₄	—	2	1	no	—
734	C₂×C₃×C₄	—	2	1	no	—
735	C₂×C₃×C₄	—	2	1	no	—
736	C₂×C₃×C₄	—	2	2	no	—
737	C₂×C₃×C₄	—	2	1	no	—
738	C₂×C₃×C₄	—	2	1	no	—
739	C₂×C₃×C₄	—	4	8	no	—
740	C₂×C₃×C₄	—	4	8	no	—
741	C₂×C₃×C₄	—	4	4	no	—
742	C₂×C₃×C₄	—	4	4	no	—
743	C₂×C₃×C₄	—	8	4	no	—
744	C₂×C₃×C₄	—	8	4	no	—
745	C₂×C₃×C₄	—	8	4	no	—
746	C₂×C₃×C₄	—	8	4	no	—
747	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
748	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
749	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
750	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
751	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
752	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
753	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
754	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
755	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
756	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
757	C₂⁴	—	2	4	no	—
758	C₂⁴	—	2	4	no	—
759	C₂⁴	—	4	2	no	—
760	C₂⁴	—	4	2	no	—
761	C₂⁴	—	4	2	no	—
762	C₂⁴	—	4	2	no	—
763	C₂⁴	C₂²×C₃×C₄	1	8	yes	—
764	C₂⁴	C₂⁴×C₃	1	2	yes	—
765	C₂⁴	C₂⁴×C₃	1	2	yes	—
766	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
767	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
768	#41	—	4	16	no	—
769	C₂×Q₈	—	2	2	no	—
770	C₂×Q₈	—	2	2	no	—
771	C₂×Q₈	C₂²×C₃×C₄	1	4	yes	—
772	C₂×D₄	—	2	2	no	—
773	C₂×D₄	—	2	2	no	—
774	C₂×D₄	—	2	2	no	—
775	C₂×D₄	—	2	2	no	—
776	C₂×D₄	—	2	2	no	—
777	C₂×D₄	—	2	2	no	—
778	C₂×D₄	—	4	16	no	—
779	C₂×D₄	—	4	2	no	—
780	C₂×D₄	—	4	2	no	—
781	C₂×D₄	—	4	2	no	—
782	C₂×D₄	—	4	2	no	—
783	C₂×D₄	—	4	2	no	—
784	C₂×D₄	—	4	2	no	—
785	C₂×D₄	C₂²×C₃×C₄	1	4	yes	—
786	C₂×D₄	C₂²×C₃×C₄	1	4	yes	—
787	C₂×D₄	C₂²×C₃×C₄	1	4	yes	—
788	C₂×D₄	C₂²×C₃×C₄	1	8	yes	—
789	C₂×D₄	C₂²×C₃×C₄	1	8	yes	—
790	C₂×D₄	C₂²×C₃×C₄	1	8	yes	—
791	C₂²×C₄	—	2	2	no	—
792	C₂²×C₄	—	2	2	no	—
793	C₂²×C₄	—	2	2	no	—
794	C₂²×C₄	—	2	2	no	—
795	C₂²×C₄	—	2	2	no	—
796	C₂²×C₄	—	2	2	no	—
797	C₂²×C₄	—	2	4	no	—
798	C₂²×C₄	—	2	2	no	—
799	C₂²×C₄	—	4	1	no	—
800	C₂²×C₄	—	4	1	no	—
801	C₂²×C₄	—	4	2	no	—
802	C₂²×C₄	—	4	2	no	—
803	C₂²×C₄	—	4	2	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	—	4	2	no	—
809	C₂²×C₄	—	4	2	no	—
810	C₂²×C₄	—	4	2	no	—
811	C₂²×C₄	—	4	2	no	—
812	C₂²×C₄	—	4	2	no	—
813	C₂²×C₄	—	4	2	no	—
814	C₂²×C₄	—	4	2	no	—
815	C₂²×C₄	—	4	2	no	—
816	C₂²×C₄	—	4	2	no	—
817	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
818	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
819	C₂²×C₄	C₂²×C₃×C₄	1	8	yes	—
820	C₂²×C₄	C₂²×C₃×C₄	1	8	yes	—
821	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
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	2	yes	—
828	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
829	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
830	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
831	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
832	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
833	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
834	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
835	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
836	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
837	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
838	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
839	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
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	—	4	2	no	—
846	C₄⋊C₄	—	4	2	no	—
847	C₄⋊C₄	—	4	2	no	—
848	C₄⋊C₄	—	4	1	no	—
849	C₄⋊C₄	—	4	1	no	—
850	C₄⋊C₄	—	4	2	no	—
851	C₄⋊C₄	—	4	2	no	—
852	C₄⋊C₄	—	4	2	no	—
853	C₄⋊C₄	—	4	2	no	—
854	C₄⋊C₄	—	4	1	no	—
855	C₄⋊C₄	—	4	2	no	—
856	C₄⋊C₄	C₂²×C₃×C₄	1	4	yes	—
857	C₄⋊C₄	C₂²×C₃×C₄	1	4	yes	—
858	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
859	C₂²⋊C₄	—	2	2	no	—
860	C₂²⋊C₄	—	2	4	no	—
861	C₂²⋊C₄	—	2	2	no	—
862	C₂²⋊C₄	—	2	4	no	—
863	C₂²⋊C₄	—	2	4	no	—
864	C₂²⋊C₄	—	2	2	no	—
865	C₂²⋊C₄	—	4	2	no	—
866	C₂²⋊C₄	—	4	2	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	—	4	2	no	—
873	C₂²⋊C₄	—	4	1	no	—
874	C₂²⋊C₄	—	4	1	no	—
875	C₂²⋊C₄	—	4	2	no	—
876	C₂²⋊C₄	—	4	2	no	—
877	C₂²⋊C₄	—	4	2	no	—
878	C₂²⋊C₄	—	4	2	no	—
879	C₂²⋊C₄	—	4	2	no	—
880	C₂²⋊C₄	—	4	1	no	—
881	C₂²⋊C₄	C₂²×C₃×C₄	1	4	yes	—
882	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
883	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
884	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
885	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
886	C₂²⋊C₄	C₂²×C₃×C₄	1	4	yes	—
887	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
888	C₄²	—	2	2	no	—
889	C₄²	—	2	2	no	—
890	C₄²	—	2	4	no	—
891	C₄²	—	2	2	no	—
892	C₄²	—	2	2	no	—
893	C₄²	—	4	1	no	—
894	C₄²	—	4	1	no	—
895	C₄²	—	4	2	no	—
896	C₄²	—	4	2	no	—
897	C₄²	—	4	2	no	—
898	C₄²	—	4	2	no	—
899	C₄²	C₂²×C₃×C₄	1	4	yes	—
900	C₂²×C₃	—	2	2	no	—
901	C₂²×C₃	—	2	2	no	—
902	C₂²×C₃	—	2	2	no	—
903	C₂²×C₃	—	2	2	no	—
904	C₂²×C₃	—	2	2	no	—
905	C₂²×C₃	—	2	2	no	—
906	C₂²×C₃	—	2	2	no	—
907	C₂²×C₃	—	2	4	no	—
908	C₂²×C₃	—	2	4	no	—
909	C₂²×C₃	—	2	2	no	—
910	C₂²×C₃	—	2	4	no	—
911	C₂²×C₃	—	2	4	no	—
912	C₂²×C₃	—	2	4	no	—
913	C₂²×C₃	—	2	2	no	—
914	C₂²×C₃	—	2	4	no	—
915	C₂²×C₃	—	4	1	no	—
916	C₂²×C₃	—	4	2	no	—
917	C₂²×C₃	—	4	2	no	—
918	C₂²×C₃	—	4	2	no	—
919	C₂²×C₃	—	4	1	no	—
920	C₂²×C₃	—	4	2	no	—
921	C₂²×C₃	—	4	1	no	—
922	C₂²×C₃	—	4	2	no	—
923	C₂²×C₃	—	4	2	no	—
924	C₂²×C₃	—	4	1	no	—
925	C₂²×C₃	—	4	2	no	—
926	C₂²×C₃	—	4	2	no	—
927	C₂²×C₃	—	8	16	no	—
928	C₂²×C₃	#520	1	4	yes	—
929	C₂²×C₃	C₂⁴×C₄	1	1	yes	characteristic
930	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
931	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
932	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
933	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
934	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
935	C₂²×C₃	#585	1	1	yes	characteristic
936	C₃×C₄	—	2	2	no	—
937	C₃×C₄	—	2	2	no	—
938	C₃×C₄	—	2	4	no	—
939	C₃×C₄	—	2	2	no	—
940	C₃×C₄	—	2	2	no	—
941	C₃×C₄	—	2	4	no	—
942	C₃×C₄	—	2	2	no	—
943	C₃×C₄	—	4	1	no	—
944	C₃×C₄	—	4	1	no	—
945	C₃×C₄	—	4	1	no	—
946	C₃×C₄	—	4	1	no	—
947	C₃×C₄	—	4	2	no	—
948	C₃×C₄	—	4	1	no	—
949	C₃×C₄	—	4	2	no	—
950	C₃×C₄	—	4	2	no	—
951	C₃×C₄	—	4	1	no	—
952	C₃×C₄	—	4	2	no	—
953	C₃×C₄	—	4	1	no	—
954	C₃×C₄	#518	1	4	yes	—
955	C₂³	—	2	1	no	—
956	C₂³	—	2	1	no	—
957	C₂³	—	2	1	no	—
958	C₂³	—	2	1	no	—
959	C₂³	—	2	2	no	—
960	C₂³	—	2	2	no	—
961	C₂³	—	2	1	no	—
962	C₂³	—	2	2	no	—
963	C₂³	—	2	1	no	—
964	C₂³	—	2	1	no	—
965	C₂³	—	2	2	no	—
966	C₂³	—	2	2	no	—
967	C₂³	—	2	2	no	—
968	C₂³	—	2	1	no	—
969	C₂³	—	2	2	no	—
970	C₂³	—	2	2	no	—
971	C₂³	—	2	1	no	—
972	C₂³	—	2	2	no	—
973	C₂³	—	2	2	no	—
974	C₂³	—	2	2	no	—
975	C₂³	—	2	1	no	—
976	C₂³	—	2	2	no	—
977	C₂³	—	2	16	no	—
978	C₂³	—	4	8	no	—
979	C₂³	—	4	8	no	—
980	C₂³	—	8	4	no	—
981	C₂³	—	8	4	no	—
982	C₂³	—	8	4	no	—
983	C₂³	—	8	4	no	—
984	C₂³	C₂³×C₃×C₄	1	4	yes	—
985	C₂³	C₂³×C₃×C₄	1	4	yes	—
986	C₂³	C₂³×C₃×C₄	1	2	yes	—
987	C₂³	C₂³×C₃×C₄	1	2	yes	—
988	C₂³	C₃×H(5,𝔽₂)	1	2	yes	—
989	C₂³	C₃×2₋¹⁺⁴	1	2	yes	—
990	C₂³	C₂⁵×C₃	1	1	yes	characteristic
991	Q₈	—	2	8	no	—
992	D₄	—	2	8	no	—
993	D₄	—	2	8	no	—
994	D₄	—	2	8	no	—
995	D₄	—	4	8	no	—
996	D₄	—	4	8	no	—
997	D₄	—	4	8	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	2	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	1	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	2	no	—
1012	C₂×C₄	—	2	8	no	—
1013	C₂×C₄	—	2	8	no	—
1014	C₂×C₄	—	2	1	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	2	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	2	no	—
1024	C₂×C₄	—	2	2	no	—
1025	C₂×C₄	—	2	2	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	2	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	2	no	—
1031	C₂×C₄	—	2	2	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	2	no	—
1037	C₂×C₄	—	2	2	no	—
1038	C₂×C₄	—	2	2	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	2	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	4	8	no	—
1048	C₂×C₄	—	4	8	no	—
1049	C₂×C₄	—	4	4	no	—
1050	C₂×C₄	—	4	4	no	—
1051	C₂×C₄	—	8	4	no	—
1052	C₂×C₄	—	8	4	no	—
1053	C₂×C₄	—	8	4	no	—
1054	C₂×C₄	—	8	4	no	—
1055	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
1056	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
1057	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
1058	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
1059	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
1060	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
1061	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
1062	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
1063	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
1064	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
1065	C₂×C₃	—	2	4	no	—
1066	C₂×C₃	—	4	2	no	—
1067	C₂×C₃	—	4	4	no	—
1068	C₂×C₃	—	4	4	no	—
1069	C₂×C₃	C₂×#518	1	1	yes	characteristic
1070	C₂×C₃	C₂×#520	1	1	yes	characteristic
1071	C₂×C₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
1072	C₂×C₃	#3536	1	1	yes	characteristic
1073	C₂×C₃	#3542	1	1	yes	characteristic
1074	C₂×C₃	#3543	1	1	yes	characteristic
1075	C₂×C₃	#3561	1	1	yes	characteristic
1076	C₂²	—	2	2	no	—
1077	C₂²	—	2	2	no	—
1078	C₂²	—	2	2	no	—
1079	C₂²	—	2	2	no	—
1080	C₂²	—	2	2	no	—
1081	C₂²	—	2	2	no	—
1082	C₂²	—	2	2	no	—
1083	C₂²	—	2	4	no	—
1084	C₂²	—	2	4	no	—
1085	C₂²	—	2	2	no	—
1086	C₂²	—	2	4	no	—
1087	C₂²	—	2	4	no	—
1088	C₂²	—	2	4	no	—
1089	C₂²	—	2	2	no	—
1090	C₂²	—	2	4	no	—
1091	C₂²	—	4	2	no	—
1092	C₂²	—	4	2	no	—
1093	C₂²	—	4	1	no	—
1094	C₂²	—	4	2	no	—
1095	C₂²	—	4	2	no	—
1096	C₂²	—	4	1	no	—
1097	C₂²	—	4	1	no	—
1098	C₂²	—	4	2	no	—
1099	C₂²	—	4	2	no	—
1100	C₂²	—	4	2	no	—
1101	C₂²	—	4	2	no	—
1102	C₂²	—	4	1	no	—
1103	C₂²	—	8	16	no	—
1104	C₂²	C₃×#520	1	4	yes	—
1105	C₂²	C₂⁴×C₃×C₄	1	1	yes	characteristic
1106	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1107	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1108	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1109	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1110	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
1111	C₂²	C₃×#585	1	1	yes	characteristic
1112	C₄	—	2	2	no	—
1113	C₄	—	2	2	no	—
1114	C₄	—	2	4	no	—
1115	C₄	—	2	2	no	—
1116	C₄	—	2	2	no	—
1117	C₄	—	2	4	no	—
1118	C₄	—	2	2	no	—
1119	C₄	—	4	1	no	—
1120	C₄	—	4	1	no	—
1121	C₄	—	4	1	no	—
1122	C₄	—	4	1	no	—
1123	C₄	—	4	1	no	—
1124	C₄	—	4	2	no	—
1125	C₄	—	4	2	no	—
1126	C₄	—	4	1	no	—
1127	C₄	—	4	2	no	—
1128	C₄	—	4	2	no	—
1129	C₄	—	4	1	no	—
1130	C₄	C₃×#518	1	4	yes	—
1131	C₃	#34476	1	1	yes	characteristic, direct product factor, Sylow
1132	C₂	—	2	4	no	—
1133	C₂	—	4	4	no	—
1134	C₂	—	4	4	no	—
1135	C₂	—	4	2	no	—
1136	C₂	C₂×C₃×#518	1	1	yes	characteristic
1137	C₂	C₂×C₃×#520	1	1	yes	characteristic
1138	C₂	C₃×C₄×H(5,𝔽₂)	1	1	yes	characteristic
1139	C₂	C₃×#3536	1	1	yes	characteristic
1140	C₂	C₃×#3542	1	1	yes	characteristic
1141	C₂	C₃×#3543	1	1	yes	characteristic
1142	C₂	C₃×#3561	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator	C₂²	C₂⁴×C₃×C₄
Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂×C₃×#546	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₃×#2377	C₂	semidirect
3. C₃×#2376	C₂	semidirect
4. C₃×#2367	C₂	semidirect
5. C₃×#2361	C₂	semidirect
6. C₃×#2360	C₂	semidirect
7. C₃×#2358	C₂	semidirect
8. C₃×#2354	C₂	semidirect
9. C₃×D₄×C₄⋊C₄	C₂	semidirect
10. C₃×#2342	C₂	semidirect
11. C₃×#2341	C₂	semidirect
12. C₃×D₄×C₂²⋊C₄	C₂	semidirect
13. C₃×#2335	C₂	semidirect
14. C₃×#2326	C₂	semidirect
15. C₃×#2324	C₂	semidirect
16. C₃×#2324	C₂	semidirect
17. C₃×#2321	C₂	semidirect
18. C₃×#2319	C₂	semidirect
19. C₃×#2315	C₂	semidirect
20. C₃×#2311	C₂	semidirect
21. C₃×C₄×C₂²⋊Q₈	C₂	semidirect
22. C₂×C₃×#390	C₂	semidirect
23. C₃×#2290	C₂	semidirect
24. #34476	C₃	direct (N × H)
27. C₃×#546	C₄	semidirect
34. C₂×C₃×C₄×Q₈	C₂²	semidirect
35. C₂×C₃×C₄×Q₈	C₂²	semidirect
41. C₂×C₃×C₄×D₄	C₂²	semidirect
42. C₂×C₃×#117	C₂²	semidirect
43. C₂×C₃×#117	C₂²	semidirect
45. C₂²×C₃×C₄⋊C₄	C₂²	semidirect
51. C₃×#391	C₂²	semidirect
52. C₃×#391	C₂²	semidirect
61. C₃×#390	C₂²	semidirect
62. C₃×#390	C₂²	semidirect
63. C₃×#390	C₂²	semidirect
64. C₃×#389	C₂²	semidirect
65. C₃×#389	C₂²	semidirect
66. C₃×#389	C₂²	semidirect
67. C₃×#389	C₂²	semidirect
68. C₃×#388	C₂²	semidirect
69. C₃×#388	C₂²	semidirect
70. C₃×#388	C₂²	semidirect
71. C₃×#388	C₂²	semidirect
72. C₃×#388	C₂²	semidirect
73. C₃×#388	C₂²	semidirect
74. C₃×#388	C₂²	semidirect
75. C₃×#388	C₂²	semidirect
76. C₃×#388	C₂²	semidirect
77. C₃×#388	C₂²	semidirect
78. C₃×#388	C₂²	semidirect
79. C₃×#388	C₂²	semidirect
80. C₃×#387	C₂²	semidirect
81. C₃×#387	C₂²	semidirect
82. C₃×#387	C₂²	semidirect
83. C₃×#387	C₂²	semidirect
88. C₃×#386	C₂²	semidirect
89. C₃×#386	C₂²	semidirect
90. C₃×#386	C₂²	semidirect
91. C₃×#386	C₂²	semidirect
97. C₃×#385	C₂²	semidirect
98. C₃×#385	C₂²	semidirect
99. C₃×#385	C₂²	semidirect
100. C₃×#385	C₂²	semidirect
101. C₃×#385	C₂²	semidirect
102. C₃×#385	C₂²	semidirect
103. C₃×#384	C₂²	semidirect
104. C₃×#381	C₂²	semidirect
106. C₃×#380	C₂²	semidirect
107. C₃×#380	C₂²	semidirect
108. C₃×#380	C₂²	semidirect
109. C₃×#380	C₂²	semidirect
110. C₃×#380	C₂²	semidirect
111. C₃×#380	C₂²	semidirect
113. C₃×C₄×C₄⋊C₄	C₂²	semidirect
114. C₃×C₄×C₄⋊C₄	C₂²	semidirect
115. C₃×C₄×C₄⋊C₄	C₂²	semidirect
116. C₃×C₄×C₄⋊C₄	C₂²	semidirect
117. C₃×C₄×C₄⋊C₄	C₂²	semidirect
121. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
122. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
123. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
124. C₃×#376	C₂²	semidirect
126. #2377	C₂×C₃	semidirect
127. #2376	C₂×C₃	semidirect
128. #2367	C₂×C₃	semidirect
129. #2361	C₂×C₃	semidirect
130. #2360	C₂×C₃	semidirect
131. #2358	C₂×C₃	semidirect
132. #2354	C₂×C₃	semidirect
133. D₄×C₄⋊C₄	C₂×C₃	semidirect
134. #2342	C₂×C₃	semidirect
135. #2341	C₂×C₃	semidirect
136. D₄×C₂²⋊C₄	C₂×C₃	semidirect
137. #2335	C₂×C₃	semidirect
138. #2326	C₂×C₃	semidirect
139. #2324	C₂×C₃	semidirect
140. #2324	C₂×C₃	semidirect
141. #2321	C₂×C₃	semidirect
142. #2319	C₂×C₃	semidirect
143. #2315	C₂×C₃	semidirect
144. #2311	C₂×C₃	semidirect
145. C₄×C₂²⋊Q₈	C₂×C₃	semidirect
146. C₂×#390	C₂×C₃	semidirect
147. #2290	C₂×C₃	semidirect
151. C₂×C₃×#41	C₂×C₄	semidirect
155. C₂²×C₃×D₄	C₂×C₄	semidirect
172. C₃×#124	C₂×C₄	semidirect
173. C₃×#123	C₂×C₄	semidirect
174. C₃×C₂²⋊Q₈	C₂×C₄	semidirect
175. C₃×#121	C₂×C₄	semidirect
176. C₃×#121	C₂×C₄	semidirect
177. C₃×#120	C₂×C₄	semidirect
184. C₃×C₄×D₄	C₂×C₄	semidirect
185. C₃×C₄×D₄	C₂×C₄	semidirect
212. C₂×C₃×C₂²⋊C₄	C₂×C₄	semidirect
278. #546	C₃×C₄	semidirect
285. C₂×C₄×Q₈	C₂²×C₃	semidirect
286. C₂×C₄×Q₈	C₂²×C₃	semidirect
292. C₂×C₄×D₄	C₂²×C₃	semidirect
293. C₂×#117	C₂²×C₃	semidirect
294. C₂×#117	C₂²×C₃	semidirect
296. C₂²×C₄⋊C₄	C₂²×C₃	semidirect
302. #391	C₂²×C₃	semidirect
303. #391	C₂²×C₃	semidirect
312. #390	C₂²×C₃	semidirect
313. #390	C₂²×C₃	semidirect
314. #390	C₂²×C₃	semidirect
315. #389	C₂²×C₃	semidirect
316. #389	C₂²×C₃	semidirect
317. #389	C₂²×C₃	semidirect
318. #389	C₂²×C₃	semidirect
319. #388	C₂²×C₃	semidirect
320. #388	C₂²×C₃	semidirect
321. #388	C₂²×C₃	semidirect
322. #388	C₂²×C₃	semidirect
323. #388	C₂²×C₃	semidirect
324. #388	C₂²×C₃	semidirect
325. #388	C₂²×C₃	semidirect
326. #388	C₂²×C₃	semidirect
327. #388	C₂²×C₃	semidirect
328. #388	C₂²×C₃	semidirect
329. #388	C₂²×C₃	semidirect
330. #388	C₂²×C₃	semidirect
331. #387	C₂²×C₃	semidirect
332. #387	C₂²×C₃	semidirect
333. #387	C₂²×C₃	semidirect
334. #387	C₂²×C₃	semidirect
339. #386	C₂²×C₃	semidirect
340. #386	C₂²×C₃	semidirect
341. #386	C₂²×C₃	semidirect
342. #386	C₂²×C₃	semidirect
348. #385	C₂²×C₃	semidirect
349. #385	C₂²×C₃	semidirect
350. #385	C₂²×C₃	semidirect
351. #385	C₂²×C₃	semidirect
352. #385	C₂²×C₃	semidirect
353. #385	C₂²×C₃	semidirect
354. #384	C₂²×C₃	semidirect
355. #381	C₂²×C₃	semidirect
357. #380	C₂²×C₃	semidirect
358. #380	C₂²×C₃	semidirect
359. #380	C₂²×C₃	semidirect
360. #380	C₂²×C₃	semidirect
361. #380	C₂²×C₃	semidirect
362. #380	C₂²×C₃	semidirect
364. C₄×C₄⋊C₄	C₂²×C₃	semidirect
365. C₄×C₄⋊C₄	C₂²×C₃	semidirect
366. C₄×C₄⋊C₄	C₂²×C₃	semidirect
367. C₄×C₄⋊C₄	C₂²×C₃	semidirect
368. C₄×C₄⋊C₄	C₂²×C₃	semidirect
372. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
373. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
374. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
375. #376	C₂²×C₃	semidirect
522. C₂×#41	C₂×C₃×C₄	semidirect
526. C₂²×D₄	C₂×C₃×C₄	semidirect
543. #124	C₂×C₃×C₄	semidirect
544. #123	C₂×C₃×C₄	semidirect
545. C₂²⋊Q₈	C₂×C₃×C₄	semidirect
546. #121	C₂×C₃×C₄	semidirect
547. #121	C₂×C₃×C₄	semidirect
548. #120	C₂×C₃×C₄	semidirect
555. C₄×D₄	C₂×C₃×C₄	semidirect
556. C₄×D₄	C₂×C₃×C₄	semidirect
583. C₂×C₂²⋊C₄	C₂×C₃×C₄	semidirect
1131. C₃	#34476	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×#546	2
C₃×#2377	2
C₃×#2376	2
C₃×#2367	2
C₃×#2361	2
C₃×#2360	2
C₃×#2358	2
C₃×#2354	2
C₃×D₄×C₄⋊C₄	2
C₃×#2342	2
C₃×#2341	2
C₃×D₄×C₂²⋊C₄	2
C₃×#2335	2
C₃×#2326	2
C₃×#2324	2
C₃×#2321	2
C₃×#2319	2
C₃×#2315	2
C₃×#2311	2
C₃×C₄×C₂²⋊Q₈	2
C₂×C₃×#390	2
C₃×#2290	2
#34476	3

Subgroups — C3×#34476 #10653083

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#34476 #10653083