Subgroups — C₂×#3534 #62721

Order 256.

4083 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3534	C₂	1	32	yes	maximal, direct product factor
2	C₂×#562	C₂	1	2	yes	maximal, complemented
3	C₂×#560	C₂	1	2	yes	maximal, complemented
4	C₂×#553	C₂	1	2	yes	maximal, complemented
5	C₂×#551	C₂	1	2	yes	maximal, complemented
6	C₂×#546	C₂	1	2	yes	maximal, complemented
7	C₂×#546	C₂	1	2	yes	maximal, complemented
8	C₂×#546	C₂	1	2	yes	maximal, complemented
9	C₂×D₄²	C₂	1	2	yes	maximal, complemented
10	C₂×#540	C₂	1	2	yes	maximal, complemented
11	C₂×#539	C₂	1	2	yes	maximal, complemented
12	C₂×#539	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#538	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#538	C₂	1	2	yes	maximal, complemented
15	C₂×#537	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#534	C₂	1	2	yes	maximal, complemented
17	C₂×#534	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#525	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×#123	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×#121	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂²×#41	C₂²	1	1	yes	characteristic, complemented
22	C₂²×#41	C₂²	1	2	yes	complemented
23	C₂³×D₄	C₂²	1	1	yes	characteristic
24	C₂³×D₄	C₂²	1	1	yes	characteristic, complemented
25	C₂³×D₄	C₂²	1	2	yes	complemented
26	C₂³×D₄	C₂²	1	2	yes	complemented
27	C₂³×D₄	C₂²	1	2	yes	complemented
28	C₂⁴×C₄	C₂²	1	1	yes	characteristic, complemented
29	#562	C₂²	1	32	yes	complemented
30	#560	C₂²	1	32	yes	complemented
31	#553	C₂²	1	32	yes	complemented
32	#551	C₂²	1	32	yes	complemented
33	#546	C₂²	1	32	yes	complemented
34	#546	C₂²	1	32	yes	complemented
35	#546	C₂²	1	32	yes	complemented
36	D₄²	C₂²	1	32	yes	complemented
37	#540	C₂²	1	32	yes	complemented
38	#539	C₂²	1	32	yes	complemented
39	#539	C₂²	1	16	yes	complemented
40	#538	C₂²	1	16	yes	complemented
41	#538	C₂²	1	32	yes	complemented
42	#537	C₂²	1	16	yes	complemented
43	#534	C₂²	1	32	yes	complemented
44	#534	C₂²	1	16	yes	complemented
45	C₂×#127	C₂²	1	2	yes	complemented
46	C₂×#126	C₂²	1	2	yes	complemented
47	C₂×#126	C₂²	1	2	yes	complemented
48	C₂×#126	C₂²	1	2	yes	complemented
49	C₂×#126	C₂²	1	2	yes	complemented
50	C₂×#125	C₂²	1	2	yes	complemented
51	C₂×#125	C₂²	1	2	yes	complemented
52	C₂×#124	C₂²	1	2	yes	complemented
53	C₂×#124	C₂²	1	2	yes	complemented
54	C₂×#124	C₂²	1	2	yes	complemented
55	#525	C₂²	1	16	yes	complemented
56	C₂×#123	C₂²	1	2	yes	complemented
57	C₂×#123	C₂²	1	2	yes	complemented
58	C₂×#123	C₂²	1	2	yes	complemented
59	C₂×#123	C₂²	1	2	yes	complemented
60	C₂×#123	C₂²	1	2	yes	complemented
61	C₂×#123	C₂²	1	2	yes	complemented
62	C₂×#123	C₂²	1	2	yes	complemented
63	C₂×#123	C₂²	1	2	yes	complemented
64	C₂×#123	C₂²	1	2	yes	complemented
65	C₂×#123	C₂²	1	2	yes	complemented
66	C₂×#123	C₂²	1	2	yes	complemented
67	C₂×#123	C₂²	1	2	yes	complemented
68	C₂×#123	C₂²	1	2	yes	complemented
69	C₂×#123	C₂²	1	2	yes	complemented
70	C₂×#123	C₂²	1	16	yes	complemented
71	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
72	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
73	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
74	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
75	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
76	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
77	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
78	C₂×#121	C₂²	1	1	yes	characteristic
79	C₂×#121	C₂²	1	2	yes	—
80	C₂×#121	C₂²	1	1	yes	characteristic, complemented
81	C₂×#121	C₂²	1	1	yes	characteristic, complemented
82	C₂×#121	C₂²	1	1	yes	characteristic, complemented
83	C₂×#121	C₂²	1	2	yes	complemented
84	C₂×#121	C₂²	1	2	yes	complemented
85	C₂×#121	C₂²	1	1	yes	characteristic, complemented
86	C₂×#121	C₂²	1	1	yes	characteristic, complemented
87	C₂×#121	C₂²	1	2	yes	complemented
88	C₂×#121	C₂²	1	2	yes	complemented
89	C₂×#121	C₂²	1	2	yes	complemented
90	C₂×#121	C₂²	1	2	yes	complemented
91	C₂×#121	C₂²	1	2	yes	complemented
92	C₂×#121	C₂²	1	2	yes	complemented
93	C₂×#121	C₂²	1	2	yes	complemented
94	C₂×#121	C₂²	1	2	yes	complemented
95	C₂×#121	C₂²	1	2	yes	complemented
96	C₂×#121	C₂²	1	2	yes	complemented
97	C₂×#121	C₂²	1	2	yes	complemented
98	C₂×#121	C₂²	1	2	yes	complemented
99	C₂×#121	C₂²	1	16	yes	complemented
100	C₂×#120	C₂²	1	2	yes	—
101	C₂×#120	C₂²	1	2	yes	complemented
102	C₂×#120	C₂²	1	2	yes	complemented
103	C₂×#120	C₂²	1	2	yes	complemented
104	C₂×#120	C₂²	1	2	yes	complemented
105	C₂×#120	C₂²	1	2	yes	complemented
106	C₂×#120	C₂²	1	2	yes	complemented
107	C₂×#120	C₂²	1	2	yes	complemented
108	C₂×C₄×D₄	C₂²	1	2	yes	complemented
109	C₂×C₄×D₄	C₂²	1	2	yes	complemented
110	C₂×C₄×D₄	C₂²	1	2	yes	complemented
111	C₂×C₄×D₄	C₂²	1	2	yes	complemented
112	C₂×C₄×D₄	C₂²	1	2	yes	complemented
113	C₂×C₄×D₄	C₂²	1	2	yes	complemented
114	C₂×C₄×D₄	C₂²	1	2	yes	complemented
115	C₂×C₄×D₄	C₂²	1	2	yes	complemented
116	C₂×#117	C₂²	1	1	yes	characteristic, complemented
117	C₂×#117	C₂²	1	2	yes	complemented
118	C₂²×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
119	C₂²×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
120	C₂²×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
121	C₂²×C₂²⋊C₄	C₂²	1	2	yes	complemented
122	C₂²×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
123	C₂²×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
124	C₂²×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
125	C₂²×C₂²⋊C₄	C₂²	1	2	yes	complemented
126	C₂²×C₂²⋊C₄	C₂²	1	2	yes	complemented
127	C₂⁵	C₂³	1	1	yes	characteristic
128	C₂⁵	C₂³	1	2	yes	—
129	C₂⁵	C₂³	1	1	yes	characteristic
130	C₂⁵	C₂³	1	2	yes	—
131	C₂×#41	—	4	4	no	—
132	C₂×#41	—	4	8	no	—
133	C₂×#41	C₂³	1	8	yes	complemented
134	C₂×#41	C₂³	1	16	yes	complemented
135	C₂²×Q₈	C₂³	1	1	yes	characteristic
136	C₂²×Q₈	C₂³	1	2	yes	—
137	C₂²×D₄	—	4	4	no	—
138	C₂²×D₄	—	4	4	no	—
139	C₂²×D₄	—	4	8	no	—
140	C₂²×D₄	—	4	8	no	—
141	C₂²×D₄	—	4	8	no	—
142	C₂²×D₄	C₂³	1	2	yes	—
143	C₂²×D₄	C₂³	1	2	yes	—
144	C₂²×D₄	C₂³	1	2	yes	—
145	C₂²×D₄	C₂³	1	2	yes	—
146	C₂²×D₄	C₂³	1	2	yes	—
147	C₂²×D₄	C₂³	1	2	yes	—
148	C₂²×D₄	C₂³	1	2	yes	—
149	C₂²×D₄	C₂³	1	2	yes	—
150	C₂²×D₄	C₂³	1	2	yes	—
151	C₂²×D₄	C₂³	1	1	yes	characteristic
152	C₂²×D₄	C₂³	1	2	yes	—
153	C₂²×D₄	C₂³	1	1	yes	characteristic
154	C₂²×D₄	C₂³	1	2	yes	—
155	C₂²×D₄	C₂³	1	2	yes	—
156	C₂²×D₄	C₂³	1	2	yes	—
157	C₂²×D₄	C₂³	1	2	yes	—
158	C₂²×D₄	C₂³	1	2	yes	—
159	C₂²×D₄	C₂³	1	1	yes	characteristic
160	C₂²×D₄	C₂³	1	2	yes	—
161	C₂²×D₄	C₂³	1	2	yes	—
162	C₂²×D₄	C₂³	1	8	yes	—
163	C₂²×D₄	C₂³	1	8	yes	complemented
164	C₂²×D₄	C₂³	1	16	yes	complemented
165	C₂²×D₄	C₂³	1	16	yes	complemented
166	C₂²×D₄	C₂³	1	16	yes	complemented
167	C₂³×C₄	—	4	4	no	—
168	C₂³×C₄	C₂³	1	1	yes	characteristic
169	C₂³×C₄	C₂³	1	1	yes	characteristic
170	C₂³×C₄	C₂³	1	1	yes	characteristic
171	C₂³×C₄	C₂³	1	1	yes	characteristic
172	C₂³×C₄	C₂³	1	2	yes	—
173	C₂³×C₄	C₂³	1	1	yes	characteristic
174	C₂³×C₄	C₂³	1	1	yes	characteristic
175	C₂³×C₄	C₂³	1	2	yes	—
176	C₂³×C₄	C₂³	1	2	yes	—
177	C₂³×C₄	C₂³	1	2	yes	—
178	C₂³×C₄	C₂³	1	2	yes	—
179	C₂³×C₄	C₂³	1	1	yes	characteristic
180	C₂³×C₄	C₂³	1	1	yes	characteristic
181	C₂³×C₄	C₂³	1	2	yes	—
182	C₂³×C₄	C₂³	1	2	yes	—
183	C₂³×C₄	C₂³	1	1	yes	characteristic
184	C₂³×C₄	C₂³	1	8	yes	complemented
185	#127	C₂³	1	16	yes	complemented
186	#126	C₂³	1	16	yes	complemented
187	#126	C₂³	1	16	yes	complemented
188	#126	C₂³	1	16	yes	complemented
189	#126	C₂³	1	16	yes	complemented
190	#125	C₂³	1	16	yes	complemented
191	#125	C₂³	1	16	yes	complemented
192	#124	C₂³	1	16	yes	complemented
193	#124	C₂³	1	16	yes	complemented
194	#124	C₂³	1	16	yes	complemented
195	#123	C₂³	1	16	yes	complemented
196	#123	C₂³	1	16	yes	complemented
197	#123	C₂³	1	16	yes	complemented
198	#123	C₂³	1	16	yes	complemented
199	#123	C₂³	1	16	yes	complemented
200	#123	C₂³	1	16	yes	complemented
201	#123	C₂³	1	16	yes	complemented
202	#123	C₂³	1	16	yes	complemented
203	#123	C₂³	1	16	yes	complemented
204	#123	C₂³	1	16	yes	complemented
205	#123	C₂³	1	16	yes	complemented
206	#123	C₂³	1	16	yes	complemented
207	#123	C₂³	1	16	yes	complemented
208	#123	C₂³	1	16	yes	complemented
209	C₂²⋊Q₈	C₂³	1	8	yes	complemented
210	C₂²⋊Q₈	C₂³	1	8	yes	complemented
211	C₂²⋊Q₈	C₂³	1	16	yes	complemented
212	C₂²⋊Q₈	C₂³	1	16	yes	complemented
213	C₂²⋊Q₈	C₂³	1	16	yes	complemented
214	C₂²⋊Q₈	C₂³	1	16	yes	complemented
215	C₂²⋊Q₈	C₂³	1	16	yes	complemented
216	#121	C₂³	1	8	yes	—
217	#121	C₂³	1	16	yes	—
218	#121	C₂³	1	8	yes	complemented
219	#121	C₂³	1	8	yes	complemented
220	#121	C₂³	1	8	yes	complemented
221	#121	C₂³	1	16	yes	complemented
222	#121	C₂³	1	16	yes	complemented
223	#121	C₂³	1	8	yes	complemented
224	#121	C₂³	1	8	yes	complemented
225	#121	C₂³	1	16	yes	complemented
226	#121	C₂³	1	16	yes	complemented
227	#121	C₂³	1	16	yes	complemented
228	#121	C₂³	1	16	yes	complemented
229	#121	C₂³	1	16	yes	complemented
230	#121	C₂³	1	16	yes	complemented
231	#121	C₂³	1	16	yes	complemented
232	#121	C₂³	1	16	yes	complemented
233	#121	C₂³	1	16	yes	complemented
234	#121	C₂³	1	16	yes	complemented
235	#121	C₂³	1	16	yes	complemented
236	#121	C₂³	1	16	yes	complemented
237	#120	C₂³	1	16	yes	—
238	#120	C₂³	1	16	yes	complemented
239	#120	C₂³	1	16	yes	complemented
240	#120	C₂³	1	16	yes	complemented
241	#120	C₂³	1	16	yes	complemented
242	#120	C₂³	1	16	yes	complemented
243	#120	C₂³	1	16	yes	complemented
244	#120	C₂³	1	16	yes	complemented
245	C₄×D₄	C₂³	1	16	yes	complemented
246	C₄×D₄	C₂³	1	16	yes	complemented
247	C₄×D₄	C₂³	1	16	yes	complemented
248	C₄×D₄	C₂³	1	16	yes	complemented
249	C₄×D₄	C₂³	1	16	yes	complemented
250	C₄×D₄	C₂³	1	16	yes	complemented
251	C₄×D₄	C₂³	1	16	yes	complemented
252	C₄×D₄	C₂³	1	16	yes	complemented
253	#117	C₂³	1	8	yes	complemented
254	#117	C₂³	1	16	yes	complemented
255	C₂×C₄⋊C₄	C₂³	1	2	yes	—
256	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
257	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
258	C₂×C₄⋊C₄	C₂³	1	2	yes	—
259	C₂×C₄⋊C₄	C₂³	1	2	yes	—
260	C₂×C₄⋊C₄	C₂³	1	2	yes	—
261	C₂×C₄⋊C₄	C₂³	1	2	yes	—
262	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
263	C₂×C₄⋊C₄	C₂³	1	2	yes	—
264	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
265	C₂×C₄⋊C₄	C₂³	1	2	yes	—
266	C₂×C₄⋊C₄	C₂³	1	2	yes	—
267	C₂×C₄⋊C₄	C₂³	1	2	yes	—
268	C₂×C₄⋊C₄	C₂³	1	2	yes	—
269	C₂×C₄⋊C₄	C₂³	1	2	yes	—
270	C₂×C₄⋊C₄	C₂³	1	2	yes	—
271	C₂×C₄⋊C₄	C₂³	1	2	yes	—
272	C₂×C₄⋊C₄	C₂³	1	8	yes	complemented
273	C₂×C₄⋊C₄	C₂³	1	8	yes	complemented
274	C₂×C₄⋊C₄	C₂³	1	8	yes	complemented
275	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
276	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
277	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
278	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
279	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
280	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
281	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
282	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
283	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
284	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
285	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
286	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
287	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
288	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
289	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
290	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
291	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
292	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
293	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
294	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
295	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
296	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
297	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
298	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
299	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
300	C₂×C₂²⋊C₄	C₂³	1	16	yes	complemented
301	C₂×C₂²⋊C₄	C₂³	1	8	yes	complemented
302	C₂×C₂²⋊C₄	C₂³	1	8	yes	complemented
303	C₂×C₂²⋊C₄	C₂³	1	8	yes	complemented
304	C₂×C₂²⋊C₄	C₂³	1	16	yes	complemented
305	C₂×C₂²⋊C₄	C₂³	1	16	yes	complemented
306	C₂×C₄²	C₂³	1	2	yes	—
307	C₂×C₄²	C₂³	1	2	yes	—
308	C₂×C₄²	C₂³	1	2	yes	—
309	C₂⁴	—	2	4	no	—
310	C₂⁴	—	2	4	no	—
311	C₂⁴	—	2	4	no	—
312	C₂⁴	—	2	8	no	—
313	C₂⁴	—	4	2	no	—
314	C₂⁴	—	4	2	no	—
315	C₂⁴	—	4	4	no	—
316	C₂⁴	—	4	4	no	—
317	C₂⁴	—	4	4	no	—
318	C₂⁴	—	4	2	no	—
319	C₂⁴	—	4	4	no	—
320	C₂⁴	—	4	4	no	—
321	C₂⁴	C₂⁴	1	2	yes	—
322	C₂⁴	C₂⁴	1	2	yes	—
323	C₂⁴	C₂⁴	1	1	yes	characteristic
324	C₂⁴	C₂⁴	1	2	yes	—
325	C₂⁴	C₂⁴	1	2	yes	—
326	C₂⁴	C₂⁴	1	4	yes	—
327	C₂⁴	C₂⁴	1	1	yes	characteristic
328	C₂⁴	C₂⁴	1	1	yes	characteristic
329	C₂⁴	C₂⁴	1	8	yes	—
330	C₂⁴	C₂⁴	1	4	yes	—
331	C₂⁴	C₂⁴	1	8	yes	—
332	#41	—	4	16	no	—
333	#41	—	4	32	no	—
334	C₂×Q₈	—	4	2	no	—
335	C₂×Q₈	—	4	4	no	—
336	C₂×Q₈	C₂⁴	1	4	yes	—
337	C₂×Q₈	C₂⁴	1	8	yes	—
338	C₂×D₄	—	2	8	no	—
339	C₂×D₄	—	2	8	no	—
340	C₂×D₄	—	2	8	no	—
341	C₂×D₄	—	2	8	no	—
342	C₂×D₄	—	2	8	no	—
343	C₂×D₄	—	4	2	no	—
344	C₂×D₄	—	4	4	no	—
345	C₂×D₄	—	4	2	no	—
346	C₂×D₄	—	4	4	no	—
347	C₂×D₄	—	4	4	no	—
348	C₂×D₄	—	4	4	no	—
349	C₂×D₄	—	4	4	no	—
350	C₂×D₄	—	4	4	no	—
351	C₂×D₄	—	4	4	no	—
352	C₂×D₄	—	4	4	no	—
353	C₂×D₄	—	4	16	no	—
354	C₂×D₄	—	4	4	no	—
355	C₂×D₄	—	4	4	no	—
356	C₂×D₄	—	4	4	no	—
357	C₂×D₄	—	4	2	no	—
358	C₂×D₄	—	4	4	no	—
359	C₂×D₄	—	4	16	no	—
360	C₂×D₄	—	4	32	no	—
361	C₂×D₄	—	4	32	no	—
362	C₂×D₄	—	4	32	no	—
363	C₂×D₄	C₂⁴	1	8	yes	—
364	C₂×D₄	C₂⁴	1	8	yes	—
365	C₂×D₄	C₂⁴	1	8	yes	—
366	C₂×D₄	C₂⁴	1	8	yes	—
367	C₂×D₄	C₂⁴	1	8	yes	—
368	C₂×D₄	C₂⁴	1	8	yes	—
369	C₂×D₄	C₂⁴	1	8	yes	—
370	C₂×D₄	C₂⁴	1	8	yes	—
371	C₂×D₄	C₂⁴	1	8	yes	—
372	C₂×D₄	C₂⁴	1	4	yes	—
373	C₂×D₄	C₂⁴	1	8	yes	—
374	C₂×D₄	C₂⁴	1	4	yes	—
375	C₂×D₄	C₂⁴	1	8	yes	—
376	C₂×D₄	C₂⁴	1	8	yes	—
377	C₂×D₄	C₂⁴	1	8	yes	—
378	C₂×D₄	C₂⁴	1	8	yes	—
379	C₂×D₄	C₂⁴	1	8	yes	—
380	C₂×D₄	C₂⁴	1	4	yes	—
381	C₂×D₄	C₂⁴	1	8	yes	—
382	C₂×D₄	C₂⁴	1	8	yes	—
383	C₂²×C₄	—	2	4	no	—
384	C₂²×C₄	—	2	4	no	—
385	C₂²×C₄	—	2	4	no	—
386	C₂²×C₄	—	4	2	no	—
387	C₂²×C₄	—	4	2	no	—
388	C₂²×C₄	—	4	2	no	—
389	C₂²×C₄	—	4	2	no	—
390	C₂²×C₄	—	4	16	no	—
391	C₂²×C₄	—	4	2	no	—
392	C₂²×C₄	—	4	4	no	—
393	C₂²×C₄	—	4	2	no	—
394	C₂²×C₄	—	4	4	no	—
395	C₂²×C₄	—	4	4	no	—
396	C₂²×C₄	—	4	4	no	—
397	C₂²×C₄	—	4	4	no	—
398	C₂²×C₄	—	4	4	no	—
399	C₂²×C₄	—	4	4	no	—
400	C₂²×C₄	C₂⁴	1	4	yes	—
401	C₂²×C₄	C₂⁴	1	4	yes	—
402	C₂²×C₄	C₂⁴	1	4	yes	—
403	C₂²×C₄	C₂⁴	1	2	yes	—
404	C₂²×C₄	C₂⁴	1	1	yes	characteristic
405	C₂²×C₄	C₂⁴	1	2	yes	—
406	C₂²×C₄	C₂⁴	1	2	yes	—
407	C₂²×C₄	C₂⁴	1	2	yes	—
408	C₂²×C₄	C₂⁴	1	2	yes	—
409	C₂²×C₄	C₂⁴	1	2	yes	—
410	C₂²×C₄	C₂⁴	1	2	yes	—
411	C₂²×C₄	C₂⁴	1	2	yes	—
412	C₂²×C₄	C₂⁴	1	1	yes	characteristic
413	C₂²×C₄	C₂⁴	1	1	yes	characteristic
414	C₂²×C₄	C₂⁴	1	1	yes	characteristic
415	C₂²×C₄	C₂⁴	1	4	yes	—
416	C₂²×C₄	C₂⁴	1	8	yes	—
417	C₂²×C₄	C₂⁴	1	4	yes	—
418	C₂²×C₄	C₂⁴	1	4	yes	—
419	C₂²×C₄	C₂⁴	1	8	yes	—
420	C₂²×C₄	C₂⁴	1	8	yes	—
421	C₂²×C₄	C₂⁴	1	8	yes	—
422	C₂²×C₄	C₂⁴	1	8	yes	—
423	C₂²×C₄	C₂⁴	1	4	yes	—
424	C₂²×C₄	C₂⁴	1	4	yes	—
425	C₂²×C₄	C₂⁴	1	8	yes	—
426	C₂²×C₄	C₂⁴	1	8	yes	—
427	C₂²×C₄	C₂⁴	1	4	yes	—
428	C₄⋊C₄	C₂⁴	1	8	yes	—
429	C₄⋊C₄	C₂⁴	1	4	yes	—
430	C₄⋊C₄	C₂⁴	1	4	yes	—
431	C₄⋊C₄	C₂⁴	1	8	yes	—
432	C₄⋊C₄	C₂⁴	1	8	yes	—
433	C₄⋊C₄	C₂⁴	1	8	yes	—
434	C₄⋊C₄	C₂⁴	1	8	yes	—
435	C₄⋊C₄	C₂⁴	1	4	yes	—
436	C₄⋊C₄	C₂⁴	1	8	yes	—
437	C₄⋊C₄	C₂⁴	1	4	yes	—
438	C₄⋊C₄	C₂⁴	1	8	yes	—
439	C₄⋊C₄	C₂⁴	1	8	yes	—
440	C₄⋊C₄	C₂⁴	1	8	yes	—
441	C₄⋊C₄	C₂⁴	1	8	yes	—
442	C₄⋊C₄	C₂⁴	1	8	yes	—
443	C₄⋊C₄	C₂⁴	1	8	yes	—
444	C₄⋊C₄	C₂⁴	1	8	yes	—
445	C₂²⋊C₄	C₂⁴	1	8	yes	—
446	C₂²⋊C₄	C₂⁴	1	8	yes	—
447	C₂²⋊C₄	C₂⁴	1	8	yes	—
448	C₂²⋊C₄	C₂⁴	1	8	yes	—
449	C₂²⋊C₄	C₂⁴	1	8	yes	—
450	C₂²⋊C₄	C₂⁴	1	8	yes	—
451	C₂²⋊C₄	C₂⁴	1	8	yes	—
452	C₂²⋊C₄	C₂⁴	1	8	yes	—
453	C₂²⋊C₄	C₂⁴	1	8	yes	—
454	C₂²⋊C₄	C₂⁴	1	8	yes	—
455	C₂²⋊C₄	C₂⁴	1	8	yes	—
456	C₂²⋊C₄	C₂⁴	1	8	yes	—
457	C₂²⋊C₄	C₂⁴	1	8	yes	—
458	C₂²⋊C₄	C₂⁴	1	8	yes	—
459	C₂²⋊C₄	C₂⁴	1	8	yes	—
460	C₂²⋊C₄	C₂⁴	1	8	yes	—
461	C₂²⋊C₄	C₂⁴	1	8	yes	—
462	C₂²⋊C₄	C₂⁴	1	8	yes	—
463	C₂²⋊C₄	C₂⁴	1	8	yes	—
464	C₂²⋊C₄	C₂⁴	1	8	yes	—
465	C₂²⋊C₄	C₂⁴	1	8	yes	—
466	C₂²⋊C₄	C₂⁴	1	8	yes	—
467	C₂²⋊C₄	C₂⁴	1	8	yes	—
468	C₂²⋊C₄	C₂⁴	1	8	yes	—
469	C₂²⋊C₄	C₂⁴	1	8	yes	—
470	C₄²	C₂⁴	1	8	yes	—
471	C₄²	C₂⁴	1	8	yes	—
472	C₄²	C₂⁴	1	8	yes	—
473	C₂³	—	2	2	no	—
474	C₂³	—	2	2	no	—
475	C₂³	—	2	2	no	—
476	C₂³	—	2	2	no	—
477	C₂³	—	2	8	no	—
478	C₂³	—	2	2	no	—
479	C₂³	—	2	4	no	—
480	C₂³	—	2	4	no	—
481	C₂³	—	2	4	no	—
482	C₂³	—	2	4	no	—
483	C₂³	—	2	4	no	—
484	C₂³	—	2	4	no	—
485	C₂³	—	2	4	no	—
486	C₂³	—	2	8	no	—
487	C₂³	—	2	2	no	—
488	C₂³	—	2	4	no	—
489	C₂³	—	2	4	no	—
490	C₂³	—	2	2	no	—
491	C₂³	—	2	4	no	—
492	C₂³	—	2	4	no	—
493	C₂³	—	2	4	no	—
494	C₂³	—	2	8	no	—
495	C₂³	—	2	16	no	—
496	C₂³	—	4	4	no	—
497	C₂³	—	4	4	no	—
498	C₂³	—	4	8	no	—
499	C₂³	—	4	8	no	—
500	C₂³	—	4	8	no	—
501	C₂³	—	4	4	no	—
502	C₂³	—	4	8	no	—
503	C₂³	—	4	8	no	—
504	C₂³	—	4	16	no	—
505	C₂³	—	8	16	no	—
506	C₂³	—	8	8	no	—
507	C₂³	—	8	16	no	—
508	C₂³	H(5,𝔽₂)	1	4	yes	—
509	C₂³	H(5,𝔽₂)	1	4	yes	—
510	C₂³	C₂⁵	1	4	yes	—
511	C₂³	C₂⁵	1	4	yes	—
512	C₂³	C₂⁵	1	2	yes	—
513	C₂³	C₂⁵	1	4	yes	—
514	C₂³	C₂⁵	1	4	yes	—
515	C₂³	C₂⁵	1	2	yes	—
516	C₂³	C₂⁵	1	2	yes	—
517	C₂³	C₂⁵	1	1	yes	characteristic
518	Q₈	—	4	4	no	—
519	Q₈	—	4	8	no	—
520	D₄	—	2	16	no	—
521	D₄	—	2	16	no	—
522	D₄	—	2	16	no	—
523	D₄	—	2	16	no	—
524	D₄	—	2	16	no	—
525	D₄	—	4	4	no	—
526	D₄	—	4	8	no	—
527	D₄	—	4	4	no	—
528	D₄	—	4	8	no	—
529	D₄	—	4	8	no	—
530	D₄	—	4	8	no	—
531	D₄	—	4	8	no	—
532	D₄	—	4	8	no	—
533	D₄	—	4	8	no	—
534	D₄	—	4	8	no	—
535	D₄	—	4	8	no	—
536	D₄	—	4	8	no	—
537	D₄	—	4	8	no	—
538	D₄	—	4	4	no	—
539	D₄	—	4	8	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	8	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	4	no	—
546	C₂×C₄	—	2	8	no	—
547	C₂×C₄	—	2	8	no	—
548	C₂×C₄	—	2	4	no	—
549	C₂×C₄	—	2	4	no	—
550	C₂×C₄	—	2	4	no	—
551	C₂×C₄	—	2	4	no	—
552	C₂×C₄	—	2	4	no	—
553	C₂×C₄	—	2	4	no	—
554	C₂×C₄	—	2	4	no	—
555	C₂×C₄	—	4	4	no	—
556	C₂×C₄	—	4	4	no	—
557	C₂×C₄	—	4	4	no	—
558	C₂×C₄	—	4	4	no	—
559	C₂×C₄	—	4	4	no	—
560	C₂×C₄	—	4	8	no	—
561	C₂×C₄	—	4	4	no	—
562	C₂×C₄	—	4	8	no	—
563	C₂×C₄	—	4	8	no	—
564	C₂×C₄	—	4	8	no	—
565	C₂×C₄	—	4	8	no	—
566	C₂×C₄	—	4	8	no	—
567	C₂×C₄	—	4	8	no	—
568	C₂×C₄	C₂⁵	1	4	yes	—
569	C₂×C₄	C₂⁵	1	2	yes	—
570	C₂×C₄	C₂⁵	1	4	yes	—
571	C₂×C₄	C₂⁵	1	4	yes	—
572	C₂×C₄	C₂⁵	1	4	yes	—
573	C₂×C₄	C₂⁵	1	4	yes	—
574	C₂×C₄	C₂⁵	1	4	yes	—
575	C₂×C₄	C₂⁵	1	4	yes	—
576	C₂×C₄	C₂⁵	1	4	yes	—
577	C₂×C₄	C₂⁵	1	2	yes	—
578	C₂×C₄	C₂⁵	1	2	yes	—
579	C₂×C₄	C₂⁵	1	2	yes	—
580	C₂²	—	2	2	no	—
581	C₂²	—	2	2	no	—
582	C₂²	—	2	2	no	—
583	C₂²	—	2	2	no	—
584	C₂²	—	2	8	no	—
585	C₂²	—	2	8	no	—
586	C₂²	—	2	2	no	—
587	C₂²	—	2	4	no	—
588	C₂²	—	2	4	no	—
589	C₂²	—	2	4	no	—
590	C₂²	—	2	4	no	—
591	C₂²	—	2	4	no	—
592	C₂²	—	2	4	no	—
593	C₂²	—	2	4	no	—
594	C₂²	—	2	2	no	—
595	C₂²	—	2	4	no	—
596	C₂²	—	2	4	no	—
597	C₂²	—	2	2	no	—
598	C₂²	—	2	4	no	—
599	C₂²	—	2	4	no	—
600	C₂²	—	2	4	no	—
601	C₂²	—	4	16	no	—
602	C₂²	—	4	4	no	—
603	C₂²	—	4	8	no	—
604	C₂²	—	4	8	no	—
605	C₂²	—	4	8	no	—
606	C₂²	—	4	8	no	—
607	C₂²	—	8	16	no	—
608	C₂²	—	8	8	no	—
609	C₂²	—	8	16	no	—
610	C₂²	C₂×H(5,𝔽₂)	1	4	yes	—
611	C₂²	C₂×H(5,𝔽₂)	1	4	yes	—
612	C₂²	C₂×H(5,𝔽₂)	1	2	yes	—
613	C₂²	C₂×H(5,𝔽₂)	1	2	yes	—
614	C₂²	#585	1	2	yes	—
615	C₂²	C₂⁶	1	1	yes	characteristic
616	C₄	—	2	2	no	—
617	C₄	—	2	2	no	—
618	C₄	—	2	2	no	—
619	C₄	—	2	2	no	—
620	C₄	—	2	4	no	—
621	C₄	—	2	4	no	—
622	C₄	—	2	4	no	—
623	C₄	—	2	4	no	—
624	C₄	—	2	4	no	—
625	C₄	—	2	4	no	—
626	C₄	—	2	4	no	—
627	C₄	—	2	4	no	—
628	C₂	—	2	4	no	—
629	C₂	—	2	4	no	—
630	C₂	—	4	2	no	—
631	C₂	—	4	4	no	—
632	C₂	—	4	4	no	—
633	C₂	—	4	4	no	—
634	C₂	—	4	4	no	—
635	C₂	#3534	1	4	yes	direct product factor
636	C₂	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
637	C₂	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
638	C₂	C₂×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³ ◁ G
LECS	G ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #3534	C₂	direct (N × H)
2. C₂×#562	C₂	semidirect
3. C₂×#560	C₂	semidirect
4. C₂×#553	C₂	semidirect
5. C₂×#551	C₂	semidirect
6. C₂×#546	C₂	semidirect
7. C₂×#546	C₂	semidirect
8. C₂×#546	C₂	semidirect
9. C₂×D₄²	C₂	semidirect
10. C₂×#540	C₂	semidirect
11. C₂×#539	C₂	semidirect
12. C₂×#539	C₂	semidirect
13. C₂×#538	C₂	semidirect
14. C₂×#538	C₂	semidirect
15. C₂×#537	C₂	semidirect
16. C₂×#534	C₂	semidirect
17. C₂×#534	C₂	semidirect
18. C₂×#525	C₂	semidirect
19. C₂²×#123	C₂	semidirect
20. C₂²×#121	C₂	semidirect
21. C₂²×#41	C₂²	semidirect
22. C₂²×#41	C₂²	semidirect
24. C₂³×D₄	C₂²	semidirect
25. C₂³×D₄	C₂²	semidirect
26. C₂³×D₄	C₂²	semidirect
27. C₂³×D₄	C₂²	semidirect
28. C₂⁴×C₄	C₂²	semidirect
29. #562	C₂²	semidirect
30. #560	C₂²	semidirect
31. #553	C₂²	semidirect
32. #551	C₂²	semidirect
33. #546	C₂²	semidirect
34. #546	C₂²	semidirect
35. #546	C₂²	semidirect
36. D₄²	C₂²	semidirect
37. #540	C₂²	semidirect
38. #539	C₂²	semidirect
39. #539	C₂²	semidirect
40. #538	C₂²	semidirect
41. #538	C₂²	semidirect
42. #537	C₂²	semidirect
43. #534	C₂²	semidirect
44. #534	C₂²	semidirect
45. C₂×#127	C₂²	semidirect
46. C₂×#126	C₂²	semidirect
47. C₂×#126	C₂²	semidirect
48. C₂×#126	C₂²	semidirect
49. C₂×#126	C₂²	semidirect
50. C₂×#125	C₂²	semidirect
51. C₂×#125	C₂²	semidirect
52. C₂×#124	C₂²	semidirect
53. C₂×#124	C₂²	semidirect
54. C₂×#124	C₂²	semidirect
55. #525	C₂²	semidirect
56. C₂×#123	C₂²	semidirect
57. C₂×#123	C₂²	semidirect
58. C₂×#123	C₂²	semidirect
59. C₂×#123	C₂²	semidirect
60. C₂×#123	C₂²	semidirect
61. C₂×#123	C₂²	semidirect
62. C₂×#123	C₂²	semidirect
63. C₂×#123	C₂²	semidirect
64. C₂×#123	C₂²	semidirect
65. C₂×#123	C₂²	semidirect
66. C₂×#123	C₂²	semidirect
67. C₂×#123	C₂²	semidirect
68. C₂×#123	C₂²	semidirect
69. C₂×#123	C₂²	semidirect
70. C₂×#123	C₂²	semidirect
71. C₂×C₂²⋊Q₈	C₂²	semidirect
72. C₂×C₂²⋊Q₈	C₂²	semidirect
73. C₂×C₂²⋊Q₈	C₂²	semidirect
74. C₂×C₂²⋊Q₈	C₂²	semidirect
75. C₂×C₂²⋊Q₈	C₂²	semidirect
76. C₂×C₂²⋊Q₈	C₂²	semidirect
77. C₂×C₂²⋊Q₈	C₂²	semidirect
80. C₂×#121	C₂²	semidirect
81. C₂×#121	C₂²	semidirect
82. C₂×#121	C₂²	semidirect
83. C₂×#121	C₂²	semidirect
84. C₂×#121	C₂²	semidirect
85. C₂×#121	C₂²	semidirect
86. C₂×#121	C₂²	semidirect
87. C₂×#121	C₂²	semidirect
88. C₂×#121	C₂²	semidirect
89. C₂×#121	C₂²	semidirect
90. C₂×#121	C₂²	semidirect
91. C₂×#121	C₂²	semidirect
92. C₂×#121	C₂²	semidirect
93. C₂×#121	C₂²	semidirect
94. C₂×#121	C₂²	semidirect
95. C₂×#121	C₂²	semidirect
96. C₂×#121	C₂²	semidirect
97. C₂×#121	C₂²	semidirect
98. C₂×#121	C₂²	semidirect
99. C₂×#121	C₂²	semidirect
101. C₂×#120	C₂²	semidirect
102. C₂×#120	C₂²	semidirect
103. C₂×#120	C₂²	semidirect
104. C₂×#120	C₂²	semidirect
105. C₂×#120	C₂²	semidirect
106. C₂×#120	C₂²	semidirect
107. C₂×#120	C₂²	semidirect
108. C₂×C₄×D₄	C₂²	semidirect
109. C₂×C₄×D₄	C₂²	semidirect
110. C₂×C₄×D₄	C₂²	semidirect
111. C₂×C₄×D₄	C₂²	semidirect
112. C₂×C₄×D₄	C₂²	semidirect
113. C₂×C₄×D₄	C₂²	semidirect
114. C₂×C₄×D₄	C₂²	semidirect
115. C₂×C₄×D₄	C₂²	semidirect
116. C₂×#117	C₂²	semidirect
117. C₂×#117	C₂²	semidirect
118. C₂²×C₄⋊C₄	C₂²	semidirect
119. C₂²×C₄⋊C₄	C₂²	semidirect
120. C₂²×C₄⋊C₄	C₂²	semidirect
121. C₂²×C₂²⋊C₄	C₂²	semidirect
122. C₂²×C₂²⋊C₄	C₂²	semidirect
123. C₂²×C₂²⋊C₄	C₂²	semidirect
124. C₂²×C₂²⋊C₄	C₂²	semidirect
125. C₂²×C₂²⋊C₄	C₂²	semidirect
126. C₂²×C₂²⋊C₄	C₂²	semidirect
133. C₂×#41	C₂³	semidirect
134. C₂×#41	C₂³	semidirect
163. C₂²×D₄	C₂³	semidirect
164. C₂²×D₄	C₂³	semidirect
165. C₂²×D₄	C₂³	semidirect
166. C₂²×D₄	C₂³	semidirect
184. C₂³×C₄	C₂³	semidirect
185. #127	C₂³	semidirect
186. #126	C₂³	semidirect
187. #126	C₂³	semidirect
188. #126	C₂³	semidirect
189. #126	C₂³	semidirect
190. #125	C₂³	semidirect
191. #125	C₂³	semidirect
192. #124	C₂³	semidirect
193. #124	C₂³	semidirect
194. #124	C₂³	semidirect
195. #123	C₂³	semidirect
196. #123	C₂³	semidirect
197. #123	C₂³	semidirect
198. #123	C₂³	semidirect
199. #123	C₂³	semidirect
200. #123	C₂³	semidirect
201. #123	C₂³	semidirect
202. #123	C₂³	semidirect
203. #123	C₂³	semidirect
204. #123	C₂³	semidirect
205. #123	C₂³	semidirect
206. #123	C₂³	semidirect
207. #123	C₂³	semidirect
208. #123	C₂³	semidirect
209. C₂²⋊Q₈	C₂³	semidirect
210. C₂²⋊Q₈	C₂³	semidirect
211. C₂²⋊Q₈	C₂³	semidirect
212. C₂²⋊Q₈	C₂³	semidirect
213. C₂²⋊Q₈	C₂³	semidirect
214. C₂²⋊Q₈	C₂³	semidirect
215. C₂²⋊Q₈	C₂³	semidirect
218. #121	C₂³	semidirect
219. #121	C₂³	semidirect
220. #121	C₂³	semidirect
221. #121	C₂³	semidirect
222. #121	C₂³	semidirect
223. #121	C₂³	semidirect
224. #121	C₂³	semidirect
225. #121	C₂³	semidirect
226. #121	C₂³	semidirect
227. #121	C₂³	semidirect
228. #121	C₂³	semidirect
229. #121	C₂³	semidirect
230. #121	C₂³	semidirect
231. #121	C₂³	semidirect
232. #121	C₂³	semidirect
233. #121	C₂³	semidirect
234. #121	C₂³	semidirect
235. #121	C₂³	semidirect
236. #121	C₂³	semidirect
238. #120	C₂³	semidirect
239. #120	C₂³	semidirect
240. #120	C₂³	semidirect
241. #120	C₂³	semidirect
242. #120	C₂³	semidirect
243. #120	C₂³	semidirect
244. #120	C₂³	semidirect
245. C₄×D₄	C₂³	semidirect
246. C₄×D₄	C₂³	semidirect
247. C₄×D₄	C₂³	semidirect
248. C₄×D₄	C₂³	semidirect
249. C₄×D₄	C₂³	semidirect
250. C₄×D₄	C₂³	semidirect
251. C₄×D₄	C₂³	semidirect
252. C₄×D₄	C₂³	semidirect
253. #117	C₂³	semidirect
254. #117	C₂³	semidirect
272. C₂×C₄⋊C₄	C₂³	semidirect
273. C₂×C₄⋊C₄	C₂³	semidirect
274. C₂×C₄⋊C₄	C₂³	semidirect
300. C₂×C₂²⋊C₄	C₂³	semidirect
301. C₂×C₂²⋊C₄	C₂³	semidirect
302. C₂×C₂²⋊C₄	C₂³	semidirect
303. C₂×C₂²⋊C₄	C₂³	semidirect
304. C₂×C₂²⋊C₄	C₂³	semidirect
305. C₂×C₂²⋊C₄	C₂³	semidirect
635. C₂	#3534	direct (N × H)

Maximal subgroups

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

subgroup	index
#3534	2
C₂×#562	2
C₂×#560	2
C₂×#553	2
C₂×#551	2
C₂×#546	2
C₂×D₄²	2
C₂×#540	2
C₂×#539	2
C₂×#538	2
C₂×#537	2
C₂×#534	2
C₂×#525	2
C₂²×#123	2
C₂²×#121	2

Subgroups — C2×#3534 #62721

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#3534 #62721