Subgroups — #34470

Order 256.

1318 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#546	C₂	1	1	yes	maximal, characteristic
2	#2379	C₂	1	1	yes	maximal, characteristic, complemented
3	#2378	C₂	1	1	yes	maximal, characteristic, complemented
4	#2377	C₂	1	1	yes	maximal, characteristic, complemented
5	#2375	C₂	1	1	yes	maximal, characteristic, complemented
6	#2374	C₂	1	1	yes	maximal, characteristic, complemented
7	#2364	C₂	1	1	yes	maximal, characteristic, complemented
8	#2361	C₂	1	1	yes	maximal, characteristic, complemented
9	#2359	C₂	1	1	yes	maximal, characteristic, complemented
10	#2358	C₂	1	1	yes	maximal, characteristic, complemented
11	#2357	C₂	1	1	yes	maximal, characteristic, complemented
12	#2352	C₂	1	1	yes	maximal, characteristic, complemented
13	#2342	C₂	1	1	yes	maximal, characteristic, complemented
14	#2342	C₂	1	1	yes	maximal, characteristic, complemented
15	#2339	C₂	1	1	yes	maximal, characteristic, complemented
16	D₄×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
17	#2337	C₂	1	1	yes	maximal, characteristic, complemented
18	#2335	C₂	1	1	yes	maximal, characteristic, complemented
19	#2333	C₂	1	1	yes	maximal, characteristic, complemented
20	#2332	C₂	1	1	yes	maximal, characteristic, complemented
21	#2325	C₂	1	1	yes	maximal, characteristic, complemented
22	#2324	C₂	1	1	yes	maximal, characteristic, complemented
23	#2321	C₂	1	1	yes	maximal, characteristic, complemented
24	#2321	C₂	1	1	yes	maximal, characteristic, complemented
25	#2318	C₂	1	1	yes	maximal, characteristic, complemented
26	#2318	C₂	1	1	yes	maximal, characteristic, complemented
27	#2312	C₂	1	1	yes	maximal, characteristic, complemented
28	#2308	C₂	1	1	yes	maximal, characteristic, complemented
29	C₄×#123	C₂	1	1	yes	maximal, characteristic, complemented
30	#2297	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂×#388	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂²×#41	C₂²	1	1	yes	characteristic
33	C₂³×D₄	C₂²	1	1	yes	characteristic
34	#546	C₄	1	16	yes	complemented
35	C₂×#124	C₂²	1	1	yes	characteristic
36	C₂×#123	C₂²	1	1	yes	characteristic
37	C₂×#123	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
39	C₂×#121	C₂²	1	1	yes	characteristic
40	C₂×#121	C₂²	1	1	yes	characteristic
41	C₂×#121	C₂²	1	1	yes	characteristic
42	C₂×#120	C₂²	1	1	yes	characteristic
43	C₂×#120	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
52	C₂×#117	C₂²	1	1	yes	characteristic, complemented
53	C₂×#117	C₂²	1	1	yes	characteristic, complemented
54	C₂²×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
55	C₂²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
56	C₂²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
57	C₂²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
58	C₂²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
59	C₂²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
60	C₂²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
61	C₂²×C₄²	C₂²	1	1	yes	characteristic, complemented
62	#391	C₂²	1	1	yes	characteristic, complemented
63	#391	C₂²	1	1	yes	characteristic, complemented
64	#391	C₂²	1	1	yes	characteristic, complemented
65	#391	C₂²	1	1	yes	characteristic, complemented
66	#390	C₂²	1	1	yes	characteristic
67	#390	C₂²	1	1	yes	characteristic
68	#390	C₂²	1	1	yes	characteristic
69	#390	C₂²	1	1	yes	characteristic
70	#390	C₂²	1	1	yes	characteristic, complemented
71	#390	C₂²	1	1	yes	characteristic, complemented
72	#390	C₂²	1	1	yes	characteristic, complemented
73	#390	C₂²	1	1	yes	characteristic, complemented
74	#389	C₂²	1	1	yes	characteristic, complemented
75	#389	C₂²	1	1	yes	characteristic, complemented
76	#388	C₂²	1	1	yes	characteristic
77	#388	C₂²	1	1	yes	characteristic
78	#388	C₂²	1	1	yes	characteristic
79	#388	C₂²	1	1	yes	characteristic
80	#388	C₂²	1	1	yes	characteristic
81	#388	C₂²	1	1	yes	characteristic
82	#388	C₂²	1	1	yes	characteristic
83	#388	C₂²	1	1	yes	characteristic
84	#388	C₂²	1	1	yes	characteristic
85	#388	C₂²	1	1	yes	characteristic
86	#388	C₂²	1	1	yes	characteristic
87	#388	C₂²	1	1	yes	characteristic
88	#388	C₂²	1	1	yes	characteristic, complemented
89	#388	C₂²	1	1	yes	characteristic, complemented
90	#388	C₂²	1	1	yes	characteristic, complemented
91	#388	C₂²	1	1	yes	characteristic, complemented
92	#388	C₂²	1	1	yes	characteristic, complemented
93	#388	C₂²	1	1	yes	characteristic, complemented
94	#388	C₂²	1	1	yes	characteristic, complemented
95	#388	C₂²	1	1	yes	characteristic, complemented
96	#388	C₂²	1	1	yes	characteristic, complemented
97	#388	C₂²	1	1	yes	characteristic, complemented
98	#388	C₂²	1	1	yes	characteristic, complemented
99	#388	C₂²	1	1	yes	characteristic, complemented
100	#388	C₂²	1	1	yes	characteristic, complemented
101	#388	C₂²	1	1	yes	characteristic, complemented
102	#388	C₂²	1	1	yes	characteristic, complemented
103	#388	C₂²	1	1	yes	characteristic, complemented
104	#388	C₂²	1	1	yes	characteristic, complemented
105	#388	C₂²	1	1	yes	characteristic, complemented
106	#387	C₂²	1	1	yes	characteristic, complemented
107	#387	C₂²	1	1	yes	characteristic, complemented
108	#387	C₂²	1	1	yes	characteristic, complemented
109	#387	C₂²	1	1	yes	characteristic, complemented
110	#387	C₂²	1	1	yes	characteristic, complemented
111	#387	C₂²	1	1	yes	characteristic, complemented
112	#387	C₂²	1	1	yes	characteristic, complemented
113	#387	C₂²	1	1	yes	characteristic, complemented
114	#387	C₂²	1	1	yes	characteristic, complemented
115	#387	C₂²	1	1	yes	characteristic, complemented
116	#386	C₂²	1	1	yes	characteristic
117	#386	C₂²	1	1	yes	characteristic
118	#386	C₂²	1	1	yes	characteristic
119	#386	C₂²	1	1	yes	characteristic
120	#386	C₂²	1	1	yes	characteristic
121	#386	C₂²	1	1	yes	characteristic
122	#386	C₂²	1	1	yes	characteristic
123	#386	C₂²	1	1	yes	characteristic
124	#386	C₂²	1	1	yes	characteristic
125	#386	C₂²	1	1	yes	characteristic
126	#386	C₂²	1	1	yes	characteristic
127	#386	C₂²	1	1	yes	characteristic
128	#386	C₂²	1	1	yes	characteristic
129	#386	C₂²	1	1	yes	characteristic
130	#386	C₂²	1	1	yes	characteristic, complemented
131	#386	C₂²	1	1	yes	characteristic, complemented
132	#386	C₂²	1	1	yes	characteristic, complemented
133	#386	C₂²	1	1	yes	characteristic, complemented
134	#386	C₂²	1	1	yes	characteristic, complemented
135	#386	C₂²	1	1	yes	characteristic, complemented
136	#386	C₂²	1	1	yes	characteristic, complemented
137	#386	C₂²	1	1	yes	characteristic, complemented
138	#385	C₂²	1	1	yes	characteristic, complemented
139	#385	C₂²	1	1	yes	characteristic, complemented
140	#385	C₂²	1	1	yes	characteristic, complemented
141	#385	C₂²	1	1	yes	characteristic, complemented
142	#385	C₂²	1	1	yes	characteristic, complemented
143	#385	C₂²	1	1	yes	characteristic, complemented
144	#385	C₂²	1	1	yes	characteristic, complemented
145	#385	C₂²	1	1	yes	characteristic, complemented
146	#385	C₂²	1	1	yes	characteristic, complemented
147	#385	C₂²	1	1	yes	characteristic, complemented
148	#383	C₂²	1	1	yes	characteristic, complemented
149	#382	C₂²	1	1	yes	characteristic, complemented
150	#382	C₂²	1	1	yes	characteristic, complemented
151	#381	C₂²	1	1	yes	characteristic
152	#381	C₂²	1	1	yes	characteristic
153	#381	C₂²	1	1	yes	characteristic, complemented
154	#381	C₂²	1	1	yes	characteristic, complemented
155	#381	C₂²	1	1	yes	characteristic, complemented
156	#380	C₂²	1	1	yes	characteristic
157	#380	C₂²	1	1	yes	characteristic, complemented
158	#380	C₂²	1	1	yes	characteristic, complemented
159	#380	C₂²	1	1	yes	characteristic, complemented
160	#380	C₂²	1	1	yes	characteristic, complemented
161	#379	C₂²	1	1	yes	characteristic
162	#379	C₂²	1	1	yes	characteristic
163	#379	C₂²	1	1	yes	characteristic
164	#379	C₂²	1	1	yes	characteristic
165	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
166	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
167	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
168	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
169	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
170	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
171	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
172	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
173	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
174	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
175	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
176	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
177	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
178	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
179	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
180	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
181	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
182	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
183	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
184	C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
185	C₂×#95	C₂²	1	1	yes	characteristic, complemented
186	C₂×#95	C₂²	1	1	yes	characteristic, complemented
187	C₂×#95	C₂²	1	1	yes	characteristic, complemented
188	C₂⁵	C₂³	1	1	yes	characteristic
189	C₂⁵	C₂³	1	1	yes	characteristic
190	C₂×#41	—	4	2	no	—
191	C₂×#41	—	4	2	no	—
192	C₂×#41	C₂×C₄	1	8	yes	complemented
193	C₂²×Q₈	C₂³	1	1	yes	characteristic
194	C₂²×D₄	—	4	2	no	—
195	C₂²×D₄	—	4	2	no	—
196	C₂²×D₄	C₂×C₄	1	8	yes	complemented
197	C₂²×D₄	C₂³	1	1	yes	characteristic
198	C₂²×D₄	C₂³	1	1	yes	characteristic
199	C₂²×D₄	C₂³	1	1	yes	characteristic
200	C₂²×D₄	C₂³	1	1	yes	characteristic
201	C₂²×D₄	C₂³	1	1	yes	characteristic
202	C₂²×D₄	C₂³	1	1	yes	characteristic
203	C₂²×D₄	C₂³	1	1	yes	characteristic
204	C₂²×D₄	C₂³	1	1	yes	characteristic
205	C₂²×D₄	C₂³	1	1	yes	characteristic
206	C₂³×C₄	C₂³	1	1	yes	characteristic
207	C₂³×C₄	C₂³	1	1	yes	characteristic
208	C₂³×C₄	C₂³	1	1	yes	characteristic
209	C₂³×C₄	C₂³	1	1	yes	characteristic
210	C₂³×C₄	C₂³	1	1	yes	characteristic
211	C₂³×C₄	C₂³	1	1	yes	characteristic
212	C₂³×C₄	C₂³	1	1	yes	characteristic
213	C₂³×C₄	C₂³	1	1	yes	characteristic
214	C₂³×C₄	C₂³	1	1	yes	characteristic
215	C₂³×C₄	C₂³	1	1	yes	characteristic
216	C₂³×C₄	C₂³	1	1	yes	characteristic
217	C₂³×C₄	C₂³	1	1	yes	characteristic
218	C₂³×C₄	C₂³	1	1	yes	characteristic
219	C₂³×C₄	C₂³	1	1	yes	characteristic
220	C₂³×C₄	C₂³	1	1	yes	characteristic
221	C₂³×C₄	C₂³	1	1	yes	characteristic
222	#124	C₂×C₄	1	8	yes	complemented
223	#123	C₂×C₄	1	8	yes	complemented
224	#123	C₂×C₄	1	8	yes	complemented
225	C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
226	#121	C₂×C₄	1	8	yes	complemented
227	#121	C₂×C₄	1	8	yes	complemented
228	#121	C₂×C₄	1	8	yes	complemented
229	#120	C₂×C₄	1	8	yes	complemented
230	#120	C₂×C₄	1	8	yes	complemented
231	C₄×D₄	—	4	2	no	—
232	C₄×D₄	—	4	2	no	—
233	C₄×D₄	—	4	2	no	—
234	C₄×D₄	—	4	2	no	—
235	C₄×D₄	—	4	2	no	—
236	C₄×D₄	—	4	2	no	—
237	C₄×D₄	C₂×C₄	1	8	yes	complemented
238	C₄×D₄	C₂×C₄	1	8	yes	complemented
239	#117	—	4	2	no	—
240	#117	—	4	2	no	—
241	C₂×C₄⋊C₄	—	4	2	no	—
242	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
243	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
244	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
245	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
246	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
247	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
248	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
249	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
250	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
251	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
252	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
253	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
254	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
255	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
256	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
257	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
258	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
260	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
261	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
262	C₂×C₂²⋊C₄	—	4	2	no	—
263	C₂×C₂²⋊C₄	—	4	2	no	—
264	C₂×C₂²⋊C₄	—	4	2	no	—
265	C₂×C₂²⋊C₄	—	4	2	no	—
266	C₂×C₂²⋊C₄	C₂×C₄	1	8	yes	complemented
267	C₂×C₂²⋊C₄	C₂×C₄	1	8	yes	complemented
268	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
269	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
270	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
271	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
272	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
273	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
274	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
275	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
276	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
277	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
278	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
279	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
280	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
281	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
282	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
283	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
284	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
285	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
286	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
287	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
288	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
289	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
290	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
291	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
292	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
293	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
294	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
295	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
296	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
297	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
298	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
299	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
300	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
301	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
302	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
303	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
304	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
305	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
306	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
307	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
308	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
309	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
310	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
311	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
312	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
313	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
314	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
315	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
316	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
317	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
318	C₂×C₄²	—	4	2	no	—
319	C₂×C₄²	C₂³	1	1	yes	characteristic
320	C₂×C₄²	C₂³	1	1	yes	characteristic
321	C₂×C₄²	C₂³	1	1	yes	characteristic
322	C₂×C₄²	C₂³	1	1	yes	characteristic
323	C₂×C₄²	C₂³	1	1	yes	characteristic
324	C₂×C₄²	C₂³	1	1	yes	characteristic
325	C₂×C₄²	C₂³	1	1	yes	characteristic
326	C₂×C₄²	C₂³	1	1	yes	characteristic
327	C₂×C₄²	C₂³	1	1	yes	characteristic
328	C₂×C₄²	C₂³	1	1	yes	characteristic
329	C₂×C₄²	C₂³	1	1	yes	characteristic
330	C₂×C₄²	C₂³	1	1	yes	characteristic
331	C₂×C₄²	C₂³	1	1	yes	characteristic
332	C₂×C₄²	C₂³	1	1	yes	characteristic
333	C₂×C₄²	C₂³	1	1	yes	characteristic
334	C₂×C₄²	C₂³	1	1	yes	characteristic
335	C₂×C₄²	C₂³	1	1	yes	characteristic
336	#95	C₂³	1	1	yes	characteristic
337	#95	C₂³	1	1	yes	characteristic
338	#95	C₂³	1	1	yes	characteristic
339	#95	C₂³	1	1	yes	characteristic
340	#95	C₂³	1	1	yes	characteristic
341	#95	C₂³	1	1	yes	characteristic
342	#95	C₂³	1	1	yes	characteristic
343	#95	C₂³	1	1	yes	characteristic
344	#95	C₂³	1	1	yes	characteristic
345	#95	C₂³	1	1	yes	characteristic
346	#95	C₂³	1	1	yes	characteristic
347	#95	C₂³	1	1	yes	characteristic
348	#95	C₂³	1	1	yes	characteristic
349	#95	C₂³	1	1	yes	characteristic
350	#95	C₂³	1	1	yes	characteristic
351	#95	C₂³	1	1	yes	characteristic
352	#95	C₂³	1	1	yes	characteristic
353	#95	C₂³	1	1	yes	characteristic
354	#95	C₂³	1	1	yes	characteristic
355	#95	C₂³	1	1	yes	characteristic
356	#95	C₂³	1	1	yes	characteristic
357	#95	C₂³	1	1	yes	characteristic
358	#95	C₂³	1	1	yes	characteristic
359	#95	C₂³	1	1	yes	characteristic
360	#95	C₂³	1	1	yes	characteristic
361	#95	C₂³	1	1	yes	characteristic
362	#95	C₂³	1	1	yes	characteristic
363	#95	C₂³	1	1	yes	characteristic
364	#95	C₂³	1	1	yes	characteristic
365	#95	C₂³	1	1	yes	characteristic
366	#95	C₂³	1	1	yes	characteristic
367	#95	C₂³	1	1	yes	characteristic
368	#95	C₂³	1	1	yes	characteristic
369	#95	C₂³	1	1	yes	characteristic
370	#95	C₂³	1	1	yes	characteristic
371	#95	C₂³	1	1	yes	characteristic
372	#95	C₂³	1	1	yes	characteristic
373	#95	C₂³	1	1	yes	characteristic
374	#95	C₂³	1	1	yes	characteristic
375	#95	C₂³	1	1	yes	characteristic
376	C₂⁴	—	2	2	no	—
377	C₂⁴	—	2	2	no	—
378	C₂⁴	—	4	1	no	—
379	C₂⁴	—	4	1	no	—
380	C₂⁴	—	4	1	no	—
381	C₂⁴	—	4	1	no	—
382	C₂⁴	—	4	1	no	—
383	C₂⁴	—	4	1	no	—
384	C₂⁴	—	4	1	no	—
385	C₂⁴	—	4	1	no	—
386	C₂⁴	—	4	1	no	—
387	C₂⁴	—	4	1	no	—
388	C₂⁴	C₂²×C₄	1	4	yes	—
389	C₂⁴	C₂²×C₄	1	4	yes	—
390	C₂⁴	C₂⁴	1	1	yes	characteristic
391	C₂⁴	C₂⁴	1	1	yes	characteristic
392	C₂⁴	C₂⁴	1	1	yes	characteristic
393	C₂⁴	C₂⁴	1	1	yes	characteristic
394	C₂⁴	C₂⁴	1	1	yes	characteristic
395	C₂⁴	C₂⁴	1	1	yes	characteristic
396	#41	—	4	16	no	—
397	C₂×Q₈	—	4	1	no	—
398	C₂×Q₈	—	4	1	no	—
399	C₂×Q₈	C₂²×C₄	1	4	yes	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	2	2	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	—	2	2	no	—
404	C₂×D₄	—	2	2	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	4	1	no	—
407	C₂×D₄	—	4	1	no	—
408	C₂×D₄	—	4	1	no	—
409	C₂×D₄	—	4	1	no	—
410	C₂×D₄	—	4	1	no	—
411	C₂×D₄	—	4	1	no	—
412	C₂×D₄	—	4	1	no	—
413	C₂×D₄	—	4	1	no	—
414	C₂×D₄	—	4	1	no	—
415	C₂×D₄	—	4	1	no	—
416	C₂×D₄	—	4	1	no	—
417	C₂×D₄	—	4	1	no	—
418	C₂×D₄	—	4	16	no	—
419	C₂×D₄	C₂²×C₄	1	4	yes	—
420	C₂×D₄	C₂²×C₄	1	4	yes	—
421	C₂×D₄	C₂²×C₄	1	4	yes	—
422	C₂×D₄	C₂²×C₄	1	4	yes	—
423	C₂×D₄	C₂²×C₄	1	4	yes	—
424	C₂×D₄	C₂²×C₄	1	4	yes	—
425	C₂×D₄	C₂²×C₄	1	4	yes	—
426	C₂×D₄	C₂²×C₄	1	4	yes	—
427	C₂×D₄	C₂²×C₄	1	4	yes	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	2	2	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	4	1	no	—
437	C₂²×C₄	—	4	1	no	—
438	C₂²×C₄	—	4	1	no	—
439	C₂²×C₄	—	4	1	no	—
440	C₂²×C₄	—	4	1	no	—
441	C₂²×C₄	—	4	1	no	—
442	C₂²×C₄	—	4	1	no	—
443	C₂²×C₄	—	4	1	no	—
444	C₂²×C₄	—	4	1	no	—
445	C₂²×C₄	—	4	1	no	—
446	C₂²×C₄	—	4	1	no	—
447	C₂²×C₄	—	4	1	no	—
448	C₂²×C₄	—	4	1	no	—
449	C₂²×C₄	—	4	1	no	—
450	C₂²×C₄	—	4	1	no	—
451	C₂²×C₄	—	4	1	no	—
452	C₂²×C₄	—	4	1	no	—
453	C₂²×C₄	—	4	1	no	—
454	C₂²×C₄	—	4	1	no	—
455	C₂²×C₄	—	4	1	no	—
456	C₂²×C₄	—	4	1	no	—
457	C₂²×C₄	—	4	1	no	—
458	C₂²×C₄	—	4	1	no	—
459	C₂²×C₄	—	4	1	no	—
460	C₂²×C₄	—	4	1	no	—
461	C₂²×C₄	—	4	1	no	—
462	C₂²×C₄	—	4	1	no	—
463	C₂²×C₄	—	4	1	no	—
464	C₂²×C₄	—	4	1	no	—
465	C₂²×C₄	—	4	1	no	—
466	C₂²×C₄	—	4	1	no	—
467	C₂²×C₄	—	4	1	no	—
468	C₂²×C₄	—	4	1	no	—
469	C₂²×C₄	—	4	1	no	—
470	C₂²×C₄	C₂²×C₄	1	4	yes	—
471	C₂²×C₄	C₂²×C₄	1	4	yes	—
472	C₂²×C₄	C₂²×C₄	1	4	yes	—
473	C₂²×C₄	C₂²×C₄	1	4	yes	—
474	C₂²×C₄	C₂²×C₄	1	4	yes	—
475	C₂²×C₄	C₂²×C₄	1	4	yes	—
476	C₂²×C₄	C₂⁴	1	1	yes	characteristic
477	C₂²×C₄	C₂⁴	1	1	yes	characteristic
478	C₂²×C₄	C₂⁴	1	1	yes	characteristic
479	C₂²×C₄	C₂⁴	1	1	yes	characteristic
480	C₂²×C₄	C₂⁴	1	1	yes	characteristic
481	C₂²×C₄	C₂⁴	1	1	yes	characteristic
482	C₂²×C₄	C₂⁴	1	1	yes	characteristic
483	C₂²×C₄	C₂⁴	1	1	yes	characteristic
484	C₂²×C₄	C₂⁴	1	1	yes	characteristic
485	C₂²×C₄	C₂⁴	1	1	yes	characteristic
486	C₂²×C₄	C₂⁴	1	1	yes	characteristic
487	C₂²×C₄	C₂⁴	1	1	yes	characteristic
488	C₂²×C₄	C₂⁴	1	1	yes	characteristic
489	C₂²×C₄	C₂⁴	1	1	yes	characteristic
490	C₂²×C₄	C₂⁴	1	1	yes	characteristic
491	C₂²×C₄	C₂⁴	1	1	yes	characteristic
492	C₂²×C₄	C₂⁴	1	1	yes	characteristic
493	C₂²×C₄	C₂⁴	1	1	yes	characteristic
494	C₂²×C₄	C₂⁴	1	1	yes	characteristic
495	C₂²×C₄	C₂⁴	1	1	yes	characteristic
496	C₂²×C₄	C₂⁴	1	1	yes	characteristic
497	C₂²×C₄	C₂⁴	1	1	yes	characteristic
498	C₂²×C₄	C₂⁴	1	1	yes	characteristic
499	C₂²×C₄	C₂⁴	1	1	yes	characteristic
500	C₂²×C₄	C₂⁴	1	1	yes	characteristic
501	C₄⋊C₄	—	2	2	no	—
502	C₄⋊C₄	—	2	2	no	—
503	C₄⋊C₄	—	4	1	no	—
504	C₄⋊C₄	—	4	1	no	—
505	C₄⋊C₄	—	4	1	no	—
506	C₄⋊C₄	—	4	1	no	—
507	C₄⋊C₄	—	4	1	no	—
508	C₄⋊C₄	—	4	1	no	—
509	C₄⋊C₄	—	4	1	no	—
510	C₄⋊C₄	—	4	1	no	—
511	C₄⋊C₄	—	4	1	no	—
512	C₄⋊C₄	—	4	1	no	—
513	C₄⋊C₄	—	4	1	no	—
514	C₄⋊C₄	—	4	1	no	—
515	C₄⋊C₄	—	4	1	no	—
516	C₄⋊C₄	—	4	1	no	—
517	C₄⋊C₄	C₂²×C₄	1	4	yes	—
518	C₄⋊C₄	C₂²×C₄	1	4	yes	—
519	C₄⋊C₄	C₂²×C₄	1	4	yes	—
520	C₄⋊C₄	C₂²×C₄	1	4	yes	—
521	C₂²⋊C₄	—	2	2	no	—
522	C₂²⋊C₄	—	2	2	no	—
523	C₂²⋊C₄	—	2	2	no	—
524	C₂²⋊C₄	—	2	2	no	—
525	C₂²⋊C₄	—	2	2	no	—
526	C₂²⋊C₄	—	2	2	no	—
527	C₂²⋊C₄	—	2	2	no	—
528	C₂²⋊C₄	—	2	2	no	—
529	C₂²⋊C₄	—	4	1	no	—
530	C₂²⋊C₄	—	4	1	no	—
531	C₂²⋊C₄	—	4	1	no	—
532	C₂²⋊C₄	—	4	1	no	—
533	C₂²⋊C₄	—	4	1	no	—
534	C₂²⋊C₄	—	4	1	no	—
535	C₂²⋊C₄	—	4	1	no	—
536	C₂²⋊C₄	—	4	1	no	—
537	C₂²⋊C₄	—	4	1	no	—
538	C₂²⋊C₄	—	4	1	no	—
539	C₂²⋊C₄	—	4	1	no	—
540	C₂²⋊C₄	—	4	1	no	—
541	C₂²⋊C₄	—	4	1	no	—
542	C₂²⋊C₄	—	4	1	no	—
543	C₂²⋊C₄	—	4	1	no	—
544	C₂²⋊C₄	—	4	1	no	—
545	C₂²⋊C₄	—	4	1	no	—
546	C₂²⋊C₄	—	4	1	no	—
547	C₂²⋊C₄	—	4	1	no	—
548	C₂²⋊C₄	—	4	1	no	—
549	C₂²⋊C₄	—	4	1	no	—
550	C₂²⋊C₄	—	4	1	no	—
551	C₂²⋊C₄	—	4	1	no	—
552	C₂²⋊C₄	—	4	1	no	—
553	C₂²⋊C₄	—	4	1	no	—
554	C₂²⋊C₄	—	4	1	no	—
555	C₂²⋊C₄	—	4	1	no	—
556	C₂²⋊C₄	—	4	1	no	—
557	C₂²⋊C₄	—	4	1	no	—
558	C₂²⋊C₄	—	4	1	no	—
559	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
560	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
561	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
562	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
563	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
564	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
565	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
566	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
567	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
568	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
569	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
570	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
571	C₄²	—	2	2	no	—
572	C₄²	—	4	1	no	—
573	C₄²	—	4	1	no	—
574	C₄²	—	4	1	no	—
575	C₄²	—	4	1	no	—
576	C₄²	—	4	1	no	—
577	C₄²	—	4	1	no	—
578	C₄²	—	4	1	no	—
579	C₄²	—	4	1	no	—
580	C₄²	—	4	1	no	—
581	C₄²	—	4	1	no	—
582	C₄²	—	4	1	no	—
583	C₄²	—	4	1	no	—
584	C₄²	—	4	1	no	—
585	C₄²	—	4	1	no	—
586	C₄²	—	4	1	no	—
587	C₄²	C₂²×C₄	1	4	yes	—
588	C₂³	—	2	1	no	—
589	C₂³	—	2	1	no	—
590	C₂³	—	2	1	no	—
591	C₂³	—	2	1	no	—
592	C₂³	—	2	1	no	—
593	C₂³	—	2	1	no	—
594	C₂³	—	2	1	no	—
595	C₂³	—	2	1	no	—
596	C₂³	—	2	1	no	—
597	C₂³	—	2	1	no	—
598	C₂³	—	2	1	no	—
599	C₂³	—	2	1	no	—
600	C₂³	—	2	1	no	—
601	C₂³	—	2	1	no	—
602	C₂³	—	2	1	no	—
603	C₂³	—	2	1	no	—
604	C₂³	—	2	1	no	—
605	C₂³	—	2	1	no	—
606	C₂³	—	2	1	no	—
607	C₂³	—	2	1	no	—
608	C₂³	—	2	1	no	—
609	C₂³	—	2	1	no	—
610	C₂³	—	2	1	no	—
611	C₂³	—	2	1	no	—
612	C₂³	—	2	1	no	—
613	C₂³	—	2	1	no	—
614	C₂³	—	2	1	no	—
615	C₂³	—	2	1	no	—
616	C₂³	—	2	1	no	—
617	C₂³	—	2	1	no	—
618	C₂³	—	2	1	no	—
619	C₂³	—	2	1	no	—
620	C₂³	—	2	1	no	—
621	C₂³	—	2	1	no	—
622	C₂³	—	2	8	no	—
623	C₂³	—	4	4	no	—
624	C₂³	—	4	4	no	—
625	C₂³	—	4	4	no	—
626	C₂³	—	4	4	no	—
627	C₂³	—	4	4	no	—
628	C₂³	—	8	2	no	—
629	C₂³	—	8	2	no	—
630	C₂³	—	8	2	no	—
631	C₂³	—	8	2	no	—
632	C₂³	—	8	2	no	—
633	C₂³	—	8	2	no	—
634	C₂³	—	8	2	no	—
635	C₂³	—	8	2	no	—
636	C₂³	C₂³×C₄	1	2	yes	—
637	C₂³	C₂³×C₄	1	2	yes	—
638	C₂³	C₂³×C₄	1	2	yes	—
639	C₂³	C₂³×C₄	1	2	yes	—
640	C₂³	C₂³×C₄	1	2	yes	—
641	C₂³	C₂³×C₄	1	2	yes	—
642	C₂³	H(5,𝔽₂)	1	2	yes	—
643	C₂³	H(5,𝔽₂)	1	2	yes	—
644	C₂³	C₂⁵	1	1	yes	characteristic
645	Q₈	—	4	4	no	—
646	D₄	—	2	8	no	—
647	D₄	—	2	8	no	—
648	D₄	—	2	8	no	—
649	D₄	—	4	4	no	—
650	D₄	—	4	4	no	—
651	D₄	—	4	4	no	—
652	D₄	—	4	4	no	—
653	D₄	—	4	4	no	—
654	D₄	—	4	4	no	—
655	C₂×C₄	—	2	8	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	1	no	—
717	C₂×C₄	—	2	1	no	—
718	C₂×C₄	—	2	1	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	4	4	no	—
722	C₂×C₄	—	4	4	no	—
723	C₂×C₄	—	4	4	no	—
724	C₂×C₄	—	4	4	no	—
725	C₂×C₄	—	4	4	no	—
726	C₂×C₄	—	4	4	no	—
727	C₂×C₄	—	4	4	no	—
728	C₂×C₄	—	8	2	no	—
729	C₂×C₄	—	8	2	no	—
730	C₂×C₄	—	8	2	no	—
731	C₂×C₄	—	8	2	no	—
732	C₂×C₄	—	8	2	no	—
733	C₂×C₄	—	8	2	no	—
734	C₂×C₄	—	8	2	no	—
735	C₂×C₄	—	8	2	no	—
736	C₂×C₄	C₂³×C₄	1	2	yes	—
737	C₂×C₄	C₂³×C₄	1	2	yes	—
738	C₂×C₄	C₂³×C₄	1	2	yes	—
739	C₂×C₄	C₂³×C₄	1	2	yes	—
740	C₂×C₄	C₂³×C₄	1	2	yes	—
741	C₂×C₄	C₂³×C₄	1	2	yes	—
742	C₂×C₄	C₂³×C₄	1	2	yes	—
743	C₂×C₄	C₂³×C₄	1	2	yes	—
744	C₂×C₄	C₂³×C₄	1	2	yes	—
745	C₂×C₄	H(5,𝔽₂)	1	2	yes	—
746	C₂²	—	2	2	no	—
747	C₂²	—	2	2	no	—
748	C₂²	—	2	2	no	—
749	C₂²	—	2	2	no	—
750	C₂²	—	2	2	no	—
751	C₂²	—	2	2	no	—
752	C₂²	—	2	2	no	—
753	C₂²	—	2	2	no	—
754	C₂²	—	2	2	no	—
755	C₂²	—	2	2	no	—
756	C₂²	—	2	2	no	—
757	C₂²	—	2	2	no	—
758	C₂²	—	2	2	no	—
759	C₂²	—	2	2	no	—
760	C₂²	—	2	2	no	—
761	C₂²	—	2	2	no	—
762	C₂²	—	2	2	no	—
763	C₂²	—	2	2	no	—
764	C₂²	—	2	2	no	—
765	C₂²	—	2	2	no	—
766	C₂²	—	2	2	no	—
767	C₂²	—	4	1	no	—
768	C₂²	—	4	1	no	—
769	C₂²	—	4	1	no	—
770	C₂²	—	4	1	no	—
771	C₂²	—	4	1	no	—
772	C₂²	—	4	1	no	—
773	C₂²	—	4	1	no	—
774	C₂²	—	4	1	no	—
775	C₂²	—	4	1	no	—
776	C₂²	—	4	1	no	—
777	C₂²	—	4	1	no	—
778	C₂²	—	4	1	no	—
779	C₂²	—	4	1	no	—
780	C₂²	—	4	1	no	—
781	C₂²	—	4	1	no	—
782	C₂²	—	4	1	no	—
783	C₂²	—	4	1	no	—
784	C₂²	—	4	1	no	—
785	C₂²	—	4	1	no	—
786	C₂²	—	4	1	no	—
787	C₂²	—	8	8	no	—
788	C₂²	—	8	8	no	—
789	C₂²	#518	1	4	yes	—
790	C₂²	C₂⁴×C₄	1	1	yes	characteristic
791	C₂²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
792	C₂²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
793	C₂²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
794	C₂²	#585	1	1	yes	characteristic
795	C₂²	#585	1	1	yes	characteristic
796	C₂²	#585	1	1	yes	characteristic
797	C₄	—	2	2	no	—
798	C₄	—	2	2	no	—
799	C₄	—	2	2	no	—
800	C₄	—	2	2	no	—
801	C₄	—	2	2	no	—
802	C₄	—	2	2	no	—
803	C₄	—	2	2	no	—
804	C₄	—	2	2	no	—
805	C₄	—	2	2	no	—
806	C₄	—	2	2	no	—
807	C₄	—	4	1	no	—
808	C₄	—	4	1	no	—
809	C₄	—	4	1	no	—
810	C₄	—	4	1	no	—
811	C₄	—	4	1	no	—
812	C₄	—	4	1	no	—
813	C₄	—	4	1	no	—
814	C₄	—	4	1	no	—
815	C₄	—	4	1	no	—
816	C₄	—	4	1	no	—
817	C₄	—	4	1	no	—
818	C₄	—	4	1	no	—
819	C₄	—	4	1	no	—
820	C₄	—	4	1	no	—
821	C₄	—	4	1	no	—
822	C₂	—	2	4	no	—
823	C₂	—	4	2	no	—
824	C₂	—	4	2	no	—
825	C₂	—	4	2	no	—
826	C₂	—	4	2	no	—
827	C₂	—	4	2	no	—
828	C₂	C₂×#518	1	1	yes	characteristic
829	C₂	#3428	1	1	yes	characteristic
830	C₂	C₄×H(5,𝔽₂)	1	1	yes	characteristic
831	C₂	#3533	1	1	yes	characteristic
832	C₂	#3534	1	1	yes	characteristic
833	C₂	#3558	1	1	yes	characteristic
834	C₂	#3560	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. #2379	C₂	semidirect
3. #2378	C₂	semidirect
4. #2377	C₂	semidirect
5. #2375	C₂	semidirect
6. #2374	C₂	semidirect
7. #2364	C₂	semidirect
8. #2361	C₂	semidirect
9. #2359	C₂	semidirect
10. #2358	C₂	semidirect
11. #2357	C₂	semidirect
12. #2352	C₂	semidirect
13. #2342	C₂	semidirect
14. #2342	C₂	semidirect
15. #2339	C₂	semidirect
16. D₄×C₂²⋊C₄	C₂	semidirect
17. #2337	C₂	semidirect
18. #2335	C₂	semidirect
19. #2333	C₂	semidirect
20. #2332	C₂	semidirect
21. #2325	C₂	semidirect
22. #2324	C₂	semidirect
23. #2321	C₂	semidirect
24. #2321	C₂	semidirect
25. #2318	C₂	semidirect
26. #2318	C₂	semidirect
27. #2312	C₂	semidirect
28. #2308	C₂	semidirect
29. C₄×#123	C₂	semidirect
30. #2297	C₂	semidirect
31. C₂×#388	C₂	semidirect
34. #546	C₄	semidirect
48. C₂×C₄×D₄	C₂²	semidirect
49. C₂×C₄×D₄	C₂²	semidirect
50. C₂×C₄×D₄	C₂²	semidirect
51. C₂×C₄×D₄	C₂²	semidirect
52. C₂×#117	C₂²	semidirect
53. C₂×#117	C₂²	semidirect
54. C₂²×C₄⋊C₄	C₂²	semidirect
61. C₂²×C₄²	C₂²	semidirect
62. #391	C₂²	semidirect
63. #391	C₂²	semidirect
64. #391	C₂²	semidirect
65. #391	C₂²	semidirect
70. #390	C₂²	semidirect
71. #390	C₂²	semidirect
72. #390	C₂²	semidirect
73. #390	C₂²	semidirect
74. #389	C₂²	semidirect
75. #389	C₂²	semidirect
88. #388	C₂²	semidirect
89. #388	C₂²	semidirect
90. #388	C₂²	semidirect
91. #388	C₂²	semidirect
92. #388	C₂²	semidirect
93. #388	C₂²	semidirect
94. #388	C₂²	semidirect
95. #388	C₂²	semidirect
96. #388	C₂²	semidirect
97. #388	C₂²	semidirect
98. #388	C₂²	semidirect
99. #388	C₂²	semidirect
100. #388	C₂²	semidirect
101. #388	C₂²	semidirect
102. #388	C₂²	semidirect
103. #388	C₂²	semidirect
104. #388	C₂²	semidirect
105. #388	C₂²	semidirect
106. #387	C₂²	semidirect
107. #387	C₂²	semidirect
108. #387	C₂²	semidirect
109. #387	C₂²	semidirect
110. #387	C₂²	semidirect
111. #387	C₂²	semidirect
112. #387	C₂²	semidirect
113. #387	C₂²	semidirect
114. #387	C₂²	semidirect
115. #387	C₂²	semidirect
130. #386	C₂²	semidirect
131. #386	C₂²	semidirect
132. #386	C₂²	semidirect
133. #386	C₂²	semidirect
134. #386	C₂²	semidirect
135. #386	C₂²	semidirect
136. #386	C₂²	semidirect
137. #386	C₂²	semidirect
138. #385	C₂²	semidirect
139. #385	C₂²	semidirect
140. #385	C₂²	semidirect
141. #385	C₂²	semidirect
142. #385	C₂²	semidirect
143. #385	C₂²	semidirect
144. #385	C₂²	semidirect
145. #385	C₂²	semidirect
146. #385	C₂²	semidirect
147. #385	C₂²	semidirect
148. #383	C₂²	semidirect
149. #382	C₂²	semidirect
150. #382	C₂²	semidirect
153. #381	C₂²	semidirect
154. #381	C₂²	semidirect
155. #381	C₂²	semidirect
157. #380	C₂²	semidirect
158. #380	C₂²	semidirect
159. #380	C₂²	semidirect
160. #380	C₂²	semidirect
165. C₄×C₄⋊C₄	C₂²	semidirect
166. C₄×C₄⋊C₄	C₂²	semidirect
167. C₄×C₄⋊C₄	C₂²	semidirect
168. C₄×C₄⋊C₄	C₂²	semidirect
169. C₄×C₄⋊C₄	C₂²	semidirect
171. C₄×C₂²⋊C₄	C₂²	semidirect
172. C₄×C₂²⋊C₄	C₂²	semidirect
173. C₄×C₂²⋊C₄	C₂²	semidirect
174. C₄×C₂²⋊C₄	C₂²	semidirect
175. C₄×C₂²⋊C₄	C₂²	semidirect
176. C₄×C₂²⋊C₄	C₂²	semidirect
177. C₄×C₂²⋊C₄	C₂²	semidirect
178. C₄×C₂²⋊C₄	C₂²	semidirect
179. C₄×C₂²⋊C₄	C₂²	semidirect
180. C₄×C₂²⋊C₄	C₂²	semidirect
181. C₄×C₂²⋊C₄	C₂²	semidirect
182. C₄×C₂²⋊C₄	C₂²	semidirect
183. C₄×C₂²⋊C₄	C₂²	semidirect
184. C₄×C₂²⋊C₄	C₂²	semidirect
185. C₂×#95	C₂²	semidirect
186. C₂×#95	C₂²	semidirect
187. C₂×#95	C₂²	semidirect
192. C₂×#41	C₂×C₄	semidirect
196. C₂²×D₄	C₂×C₄	semidirect
222. #124	C₂×C₄	semidirect
223. #123	C₂×C₄	semidirect
224. #123	C₂×C₄	semidirect
225. C₂²⋊Q₈	C₂×C₄	semidirect
226. #121	C₂×C₄	semidirect
227. #121	C₂×C₄	semidirect
228. #121	C₂×C₄	semidirect
229. #120	C₂×C₄	semidirect
230. #120	C₂×C₄	semidirect
237. C₄×D₄	C₂×C₄	semidirect
238. C₄×D₄	C₂×C₄	semidirect
266. C₂×C₂²⋊C₄	C₂×C₄	semidirect
267. C₂×C₂²⋊C₄	C₂×C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×#546	2
#2379	2
#2378	2
#2377	2
#2375	2
#2374	2
#2364	2
#2361	2
#2359	2
#2358	2
#2357	2
#2352	2
#2342	2
#2339	2
D₄×C₂²⋊C₄	2
#2337	2
#2335	2
#2333	2
#2332	2
#2325	2
#2324	2
#2321	2
#2318	2
#2312	2
#2308	2
C₄×#123	2
#2297	2
C₂×#388	2