Subgroups — C₂×#3565 #62741

Order 256.

3277 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3565	C₂	1	32	yes	maximal, direct product factor
2	C₂×#563	C₂	1	2	yes	maximal, complemented
3	C₂×#562	C₂	1	2	yes	maximal, complemented
4	C₂×#557	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#556	C₂	1	2	yes	maximal, complemented
6	C₂×#556	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#555	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#554	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#553	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#553	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#552	C₂	1	2	yes	maximal, complemented
12	C₂×#552	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#552	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#544	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#544	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#542	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#542	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#542	C₂	1	2	yes	maximal, complemented
19	C₂×#542	C₂	1	2	yes	maximal, complemented
20	C₂×#541	C₂	1	2	yes	maximal, complemented
21	C₂×#539	C₂	1	2	yes	maximal, complemented
22	C₂×#533	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#529	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#529	C₂	1	1	yes	maximal, characteristic, complemented
25	#563	C₂²	1	32	yes	complemented
26	#562	C₂²	1	32	yes	complemented
27	#557	C₂²	1	16	yes	complemented
28	#556	C₂²	1	32	yes	complemented
29	#556	C₂²	1	16	yes	complemented
30	#555	C₂²	1	16	yes	complemented
31	#554	C₂²	1	16	yes	complemented
32	#553	C₂²	1	16	yes	complemented
33	#553	C₂²	1	16	yes	complemented
34	#552	C₂²	1	32	yes	complemented
35	#552	C₂²	1	16	yes	complemented
36	#552	C₂²	1	16	yes	complemented
37	#544	C₂²	1	16	yes	complemented
38	#544	C₂²	1	16	yes	complemented
39	#542	C₂²	1	16	yes	complemented
40	#542	C₂²	1	16	yes	complemented
41	#542	C₂²	1	32	yes	complemented
42	#542	C₂²	1	32	yes	complemented
43	#541	C₂²	1	32	yes	complemented
44	#539	C₂²	1	32	yes	complemented
45	#533	C₂²	1	16	yes	complemented
46	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic
47	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic
48	C₂×C₄⋊Q₈	C₂²	1	2	yes	—
49	C₂×C₄⋊Q₈	C₂²	1	2	yes	—
50	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic
51	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic
52	C₂×C₄⋊Q₈	C₂²	1	2	yes	—
53	#529	C₂²	1	16	yes	complemented
54	#529	C₂²	1	16	yes	complemented
55	C₂×#126	C₂²	1	2	yes	—
56	C₂×#126	C₂²	1	1	yes	characteristic
57	C₂×#126	C₂²	1	1	yes	characteristic
58	C₂×#126	C₂²	1	2	yes	—
59	C₂×#126	C₂²	1	2	yes	—
60	C₂×#126	C₂²	1	2	yes	—
61	C₂×#126	C₂²	1	2	yes	—
62	C₂×#126	C₂²	1	2	yes	—
63	C₂×#126	C₂²	1	2	yes	—
64	C₂×#126	C₂²	1	2	yes	—
65	C₂×#126	C₂²	1	2	yes	—
66	C₂×#125	C₂²	1	1	yes	characteristic
67	C₂×#125	C₂²	1	1	yes	characteristic
68	C₂×#125	C₂²	1	1	yes	characteristic
69	C₂×#125	C₂²	1	1	yes	characteristic
70	C₂×#125	C₂²	1	2	yes	—
71	C₂×#125	C₂²	1	2	yes	—
72	C₂×#125	C₂²	1	2	yes	—
73	C₂×#125	C₂²	1	2	yes	—
74	C₂×#125	C₂²	1	2	yes	—
75	C₂×#125	C₂²	1	1	yes	characteristic
76	C₂×#125	C₂²	1	2	yes	—
77	C₂×#125	C₂²	1	1	yes	characteristic
78	C₂×#124	C₂²	1	1	yes	characteristic
79	C₂×#124	C₂²	1	1	yes	characteristic
80	C₂×#124	C₂²	1	2	yes	—
81	C₂×#124	C₂²	1	2	yes	—
82	C₂×#124	C₂²	1	2	yes	—
83	C₂×#124	C₂²	1	2	yes	—
84	C₂×#124	C₂²	1	2	yes	—
85	C₂×#123	C₂²	1	1	yes	characteristic
86	C₂×#123	C₂²	1	1	yes	characteristic
87	C₂×#123	C₂²	1	2	yes	—
88	C₂×#123	C₂²	1	2	yes	—
89	C₂×#123	C₂²	1	2	yes	—
90	C₂×#123	C₂²	1	2	yes	—
91	C₂×#123	C₂²	1	2	yes	—
92	C₂×#123	C₂²	1	2	yes	—
93	C₂×#123	C₂²	1	2	yes	—
94	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
95	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
96	C₂×C₂²⋊Q₈	C₂²	1	2	yes	—
97	C₂×C₂²⋊Q₈	C₂²	1	2	yes	—
98	C₂×C₂²⋊Q₈	C₂²	1	2	yes	—
99	C₂×C₂²⋊Q₈	C₂²	1	2	yes	—
100	C₂×C₂²⋊Q₈	C₂²	1	2	yes	—
101	C₂×C₂²⋊Q₈	C₂²	1	2	yes	—
102	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
103	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
104	C₂×C₂²⋊Q₈	C₂²	1	2	yes	—
105	C₂×C₂²⋊Q₈	C₂²	1	2	yes	—
106	C₂×C₂²⋊Q₈	C₂²	1	2	yes	—
107	C₂×C₂²⋊Q₈	C₂²	1	2	yes	—
108	C₂×C₂²⋊Q₈	C₂²	1	2	yes	—
109	C₂×#121	C₂²	1	1	yes	characteristic
110	C₂×#121	C₂²	1	1	yes	characteristic
111	C₂×#121	C₂²	1	2	yes	—
112	C₂×#121	C₂²	1	1	yes	characteristic
113	C₂×#121	C₂²	1	1	yes	characteristic
114	C₂×#121	C₂²	1	2	yes	—
115	C₂×#121	C₂²	1	2	yes	—
116	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic
117	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic
118	C₂×C₄×Q₈	C₂²	1	2	yes	—
119	C₂×C₄×Q₈	C₂²	1	2	yes	—
120	C₂×C₄×Q₈	C₂²	1	2	yes	—
121	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic
122	C₂×C₄×Q₈	C₂²	1	2	yes	—
123	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic
124	C₂×C₄×D₄	C₂²	1	2	yes	—
125	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
126	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
127	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
128	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
129	C₂×C₄×D₄	C₂²	1	2	yes	—
130	C₂×C₄×D₄	C₂²	1	2	yes	—
131	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
132	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
133	C₂×#117	C₂²	1	1	yes	characteristic
134	C₂×#117	C₂²	1	1	yes	characteristic
135	C₂×#117	C₂²	1	2	yes	—
136	C₂×#117	C₂²	1	1	yes	characteristic
137	C₂×#117	C₂²	1	1	yes	characteristic
138	C₂×#117	C₂²	1	2	yes	—
139	C₂×#117	C₂²	1	2	yes	—
140	C₂×#117	C₂²	1	2	yes	—
141	C₂×#117	C₂²	1	1	yes	characteristic
142	C₂×#117	C₂²	1	1	yes	characteristic
143	C₂²×C₄⋊C₄	C₂²	1	2	yes	—
144	C₂²×C₄⋊C₄	C₂²	1	1	yes	characteristic
145	C₂²×C₄⋊C₄	C₂²	1	1	yes	characteristic
146	C₂²×C₄²	C₂²	1	1	yes	characteristic
147	C₂²×Q₈	C₂³	1	1	yes	characteristic
148	C₂²×Q₈	C₂³	1	1	yes	characteristic
149	C₂²×Q₈	C₂³	1	2	yes	—
150	C₂²×Q₈	C₂³	1	2	yes	—
151	C₂²×Q₈	C₂³	1	2	yes	—
152	C₂²×Q₈	C₂³	1	2	yes	—
153	C₂²×D₄	C₂³	1	1	yes	characteristic
154	C₂²×D₄	C₂³	1	1	yes	characteristic
155	C₂²×D₄	C₂³	1	2	yes	—
156	C₂²×D₄	C₂³	1	1	yes	characteristic
157	C₂²×D₄	C₂³	1	2	yes	—
158	C₂²×D₄	C₂³	1	1	yes	characteristic
159	C₂²×D₄	C₂³	1	2	yes	—
160	C₂³×C₄	C₂³	1	1	yes	characteristic
161	C₂³×C₄	C₂³	1	1	yes	characteristic
162	C₂³×C₄	C₂³	1	1	yes	characteristic
163	C₂³×C₄	C₂³	1	2	yes	—
164	C₂³×C₄	C₂³	1	2	yes	—
165	C₂³×C₄	C₂³	1	2	yes	—
166	C₂³×C₄	C₂³	1	2	yes	—
167	C₂³×C₄	C₂³	1	2	yes	—
168	C₂³×C₄	C₂³	1	1	yes	characteristic
169	C₂³×C₄	C₂³	1	1	yes	characteristic
170	C₄⋊Q₈	C₂³	1	8	yes	—
171	C₄⋊Q₈	C₂³	1	8	yes	—
172	C₄⋊Q₈	C₂³	1	16	yes	—
173	C₄⋊Q₈	C₂³	1	16	yes	—
174	C₄⋊Q₈	C₂³	1	8	yes	—
175	C₄⋊Q₈	C₂³	1	8	yes	—
176	C₄⋊Q₈	C₂³	1	16	yes	—
177	#126	C₂³	1	16	yes	—
178	#126	C₂³	1	8	yes	—
179	#126	C₂³	1	8	yes	—
180	#126	C₂³	1	16	yes	—
181	#126	C₂³	1	16	yes	—
182	#126	C₂³	1	16	yes	—
183	#126	C₂³	1	16	yes	—
184	#126	C₂³	1	16	yes	—
185	#126	C₂³	1	16	yes	—
186	#126	C₂³	1	16	yes	—
187	#126	C₂³	1	16	yes	—
188	#125	C₂³	1	8	yes	—
189	#125	C₂³	1	8	yes	—
190	#125	C₂³	1	8	yes	—
191	#125	C₂³	1	8	yes	—
192	#125	C₂³	1	16	yes	—
193	#125	C₂³	1	16	yes	—
194	#125	C₂³	1	16	yes	—
195	#125	C₂³	1	16	yes	—
196	#125	C₂³	1	16	yes	—
197	#125	C₂³	1	8	yes	—
198	#125	C₂³	1	16	yes	—
199	#125	C₂³	1	8	yes	—
200	#124	C₂³	1	8	yes	—
201	#124	C₂³	1	8	yes	—
202	#124	C₂³	1	16	yes	—
203	#124	C₂³	1	16	yes	—
204	#124	C₂³	1	16	yes	—
205	#124	C₂³	1	16	yes	—
206	#124	C₂³	1	16	yes	—
207	#123	C₂³	1	8	yes	—
208	#123	C₂³	1	8	yes	—
209	#123	C₂³	1	16	yes	—
210	#123	C₂³	1	16	yes	—
211	#123	C₂³	1	16	yes	—
212	#123	C₂³	1	16	yes	—
213	#123	C₂³	1	16	yes	—
214	#123	C₂³	1	16	yes	—
215	#123	C₂³	1	16	yes	—
216	C₂²⋊Q₈	C₂³	1	8	yes	—
217	C₂²⋊Q₈	C₂³	1	8	yes	—
218	C₂²⋊Q₈	C₂³	1	16	yes	—
219	C₂²⋊Q₈	C₂³	1	16	yes	—
220	C₂²⋊Q₈	C₂³	1	16	yes	—
221	C₂²⋊Q₈	C₂³	1	16	yes	—
222	C₂²⋊Q₈	C₂³	1	16	yes	—
223	C₂²⋊Q₈	C₂³	1	16	yes	—
224	C₂²⋊Q₈	C₂³	1	8	yes	—
225	C₂²⋊Q₈	C₂³	1	8	yes	—
226	C₂²⋊Q₈	C₂³	1	16	yes	—
227	C₂²⋊Q₈	C₂³	1	16	yes	—
228	C₂²⋊Q₈	C₂³	1	16	yes	—
229	C₂²⋊Q₈	C₂³	1	16	yes	—
230	C₂²⋊Q₈	C₂³	1	16	yes	—
231	#121	C₂³	1	8	yes	—
232	#121	C₂³	1	8	yes	—
233	#121	C₂³	1	16	yes	—
234	#121	C₂³	1	8	yes	—
235	#121	C₂³	1	8	yes	—
236	#121	C₂³	1	16	yes	—
237	#121	C₂³	1	16	yes	—
238	C₄×Q₈	C₂³	1	8	yes	—
239	C₄×Q₈	C₂³	1	8	yes	—
240	C₄×Q₈	C₂³	1	16	yes	—
241	C₄×Q₈	C₂³	1	16	yes	—
242	C₄×Q₈	C₂³	1	16	yes	—
243	C₄×Q₈	C₂³	1	8	yes	—
244	C₄×Q₈	C₂³	1	16	yes	—
245	C₄×Q₈	C₂³	1	8	yes	—
246	C₄×D₄	C₂³	1	16	yes	—
247	C₄×D₄	C₂³	1	8	yes	—
248	C₄×D₄	C₂³	1	8	yes	—
249	C₄×D₄	C₂³	1	8	yes	—
250	C₄×D₄	C₂³	1	8	yes	—
251	C₄×D₄	C₂³	1	16	yes	—
252	C₄×D₄	C₂³	1	16	yes	—
253	C₄×D₄	C₂³	1	8	yes	—
254	C₄×D₄	C₂³	1	8	yes	—
255	#117	C₂³	1	8	yes	—
256	#117	C₂³	1	8	yes	—
257	#117	C₂³	1	16	yes	—
258	#117	C₂³	1	8	yes	—
259	#117	C₂³	1	8	yes	—
260	#117	C₂³	1	16	yes	—
261	#117	C₂³	1	16	yes	—
262	#117	C₂³	1	16	yes	—
263	#117	C₂³	1	8	yes	—
264	#117	C₂³	1	8	yes	—
265	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
266	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
267	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
268	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
269	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
270	C₂×C₄⋊C₄	C₂³	1	2	yes	—
271	C₂×C₄⋊C₄	C₂³	1	2	yes	—
272	C₂×C₄⋊C₄	C₂³	1	2	yes	—
273	C₂×C₄⋊C₄	C₂³	1	2	yes	—
274	C₂×C₄⋊C₄	C₂³	1	2	yes	—
275	C₂×C₄⋊C₄	C₂³	1	16	yes	—
276	C₂×C₄⋊C₄	C₂³	1	8	yes	—
277	C₂×C₄⋊C₄	C₂³	1	8	yes	—
278	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
279	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
280	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
281	C₂×C₄⋊C₄	C₂³	1	2	yes	—
282	C₂×C₄⋊C₄	C₂³	1	2	yes	—
283	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
284	C₂×C₄⋊C₄	C₂³	1	2	yes	—
285	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
286	C₂×C₄⋊C₄	C₂³	1	2	yes	—
287	C₂×C₄⋊C₄	C₂³	1	2	yes	—
288	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
289	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
290	C₂×C₄⋊C₄	C₂³	1	2	yes	—
291	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
292	C₂×C₄⋊C₄	C₂³	1	2	yes	—
293	C₂×C₄⋊C₄	C₂³	1	2	yes	—
294	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
295	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
296	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
297	C₂×C₄⋊C₄	C₂³	1	2	yes	—
298	C₂×C₄⋊C₄	C₂³	1	2	yes	—
299	C₂×C₄⋊C₄	C₂³	1	2	yes	—
300	C₂×C₄⋊C₄	C₂³	1	2	yes	—
301	C₂×C₄⋊C₄	C₂³	1	2	yes	—
302	C₂×C₄⋊C₄	C₂³	1	2	yes	—
303	C₂×C₄⋊C₄	C₂³	1	2	yes	—
304	C₂×C₄⋊C₄	C₂³	1	2	yes	—
305	C₂×C₄⋊C₄	C₂³	1	2	yes	—
306	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
311	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
312	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
313	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
314	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
315	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
316	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
317	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
318	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
319	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
320	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
321	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
322	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
323	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
324	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
325	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
326	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
327	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
328	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
329	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
330	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
331	C₂×C₄²	C₂³	1	2	yes	—
332	C₂×C₄²	C₂³	1	2	yes	—
333	C₂×C₄²	C₂³	1	2	yes	—
334	C₂×C₄²	C₂³	1	2	yes	—
335	C₂×C₄²	C₂³	1	1	yes	characteristic
336	C₂×C₄²	C₂³	1	1	yes	characteristic
337	C₂×C₄²	C₂³	1	1	yes	characteristic
338	C₂×C₄²	C₂³	1	1	yes	characteristic
339	C₂×C₄²	C₂³	1	2	yes	—
340	C₂×C₄²	C₂³	1	2	yes	—
341	C₂×C₄²	C₂³	1	1	yes	characteristic
342	C₂×C₄²	C₂³	1	2	yes	—
343	C₂×C₄²	C₂³	1	1	yes	characteristic
344	C₂×C₄²	C₂³	1	8	yes	—
345	C₂⁴	C₂⁴	1	1	yes	characteristic
346	C₂⁴	C₂⁴	1	1	yes	characteristic
347	C₂⁴	C₂⁴	1	1	yes	characteristic
348	C₂⁴	C₂⁴	1	2	yes	—
349	C₂×Q₈	—	2	4	no	—
350	C₂×Q₈	—	4	2	no	—
351	C₂×Q₈	—	4	4	no	—
352	C₂×Q₈	—	4	4	no	—
353	C₂×Q₈	—	4	4	no	—
354	C₂×Q₈	—	4	4	no	—
355	C₂×Q₈	C₂⁴	1	4	yes	—
356	C₂×Q₈	C₂⁴	1	4	yes	—
357	C₂×Q₈	C₂⁴	1	8	yes	—
358	C₂×Q₈	C₂⁴	1	8	yes	—
359	C₂×Q₈	C₂⁴	1	8	yes	—
360	C₂×Q₈	C₂⁴	1	8	yes	—
361	C₂×D₄	—	2	4	no	—
362	C₂×D₄	—	4	2	no	—
363	C₂×D₄	—	4	2	no	—
364	C₂×D₄	—	4	4	no	—
365	C₂×D₄	—	4	4	no	—
366	C₂×D₄	—	4	2	no	—
367	C₂×D₄	—	4	4	no	—
368	C₂×D₄	C₂⁴	1	4	yes	—
369	C₂×D₄	C₂⁴	1	4	yes	—
370	C₂×D₄	C₂⁴	1	8	yes	—
371	C₂×D₄	C₂⁴	1	4	yes	—
372	C₂×D₄	C₂⁴	1	8	yes	—
373	C₂×D₄	C₂⁴	1	4	yes	—
374	C₂×D₄	C₂⁴	1	8	yes	—
375	C₂²×C₄	—	2	4	no	—
376	C₂²×C₄	—	2	4	no	—
377	C₂²×C₄	—	2	4	no	—
378	C₂²×C₄	—	4	4	no	—
379	C₂²×C₄	—	4	2	no	—
380	C₂²×C₄	—	4	4	no	—
381	C₂²×C₄	—	4	4	no	—
382	C₂²×C₄	—	4	4	no	—
383	C₂²×C₄	—	4	4	no	—
384	C₂²×C₄	—	4	2	no	—
385	C₂²×C₄	C₂⁴	1	4	yes	—
386	C₂²×C₄	C₂⁴	1	4	yes	—
387	C₂²×C₄	C₂⁴	1	4	yes	—
388	C₂²×C₄	C₂⁴	1	1	yes	characteristic
389	C₂²×C₄	C₂⁴	1	1	yes	characteristic
390	C₂²×C₄	C₂⁴	1	2	yes	—
391	C₂²×C₄	C₂⁴	1	1	yes	characteristic
392	C₂²×C₄	C₂⁴	1	2	yes	—
393	C₂²×C₄	C₂⁴	1	1	yes	characteristic
394	C₂²×C₄	C₂⁴	1	1	yes	characteristic
395	C₂²×C₄	C₂⁴	1	1	yes	characteristic
396	C₂²×C₄	C₂⁴	1	2	yes	—
397	C₂²×C₄	C₂⁴	1	1	yes	characteristic
398	C₂²×C₄	C₂⁴	1	1	yes	characteristic
399	C₂²×C₄	C₂⁴	1	2	yes	—
400	C₂²×C₄	C₂⁴	1	2	yes	—
401	C₂²×C₄	C₂⁴	1	1	yes	characteristic
402	C₂²×C₄	C₂⁴	1	2	yes	—
403	C₂²×C₄	C₂⁴	1	1	yes	characteristic
404	C₂²×C₄	C₂⁴	1	2	yes	—
405	C₂²×C₄	C₂⁴	1	1	yes	characteristic
406	C₂²×C₄	C₂⁴	1	4	yes	—
407	C₂²×C₄	C₂⁴	1	4	yes	—
408	C₂²×C₄	C₂⁴	1	8	yes	—
409	C₂²×C₄	C₂⁴	1	8	yes	—
410	C₂²×C₄	C₂⁴	1	8	yes	—
411	C₂²×C₄	C₂⁴	1	8	yes	—
412	C₂²×C₄	C₂⁴	1	8	yes	—
413	C₂²×C₄	C₂⁴	1	1	yes	characteristic
414	C₄⋊C₄	C₂⁴	1	4	yes	—
415	C₄⋊C₄	C₂⁴	1	4	yes	—
416	C₄⋊C₄	C₂⁴	1	4	yes	—
417	C₄⋊C₄	C₂⁴	1	4	yes	—
418	C₄⋊C₄	C₂⁴	1	4	yes	—
419	C₄⋊C₄	C₂⁴	1	8	yes	—
420	C₄⋊C₄	C₂⁴	1	8	yes	—
421	C₄⋊C₄	C₂⁴	1	8	yes	—
422	C₄⋊C₄	C₂⁴	1	8	yes	—
423	C₄⋊C₄	C₂⁴	1	8	yes	—
424	C₄⋊C₄	C₂⁴	1	4	yes	—
425	C₄⋊C₄	C₂⁴	1	4	yes	—
426	C₄⋊C₄	C₂⁴	1	4	yes	—
427	C₄⋊C₄	C₂⁴	1	8	yes	—
428	C₄⋊C₄	C₂⁴	1	8	yes	—
429	C₄⋊C₄	C₂⁴	1	4	yes	—
430	C₄⋊C₄	C₂⁴	1	8	yes	—
431	C₄⋊C₄	C₂⁴	1	4	yes	—
432	C₄⋊C₄	C₂⁴	1	8	yes	—
433	C₄⋊C₄	C₂⁴	1	8	yes	—
434	C₄⋊C₄	C₂⁴	1	4	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	4	yes	—
441	C₄⋊C₄	C₂⁴	1	4	yes	—
442	C₄⋊C₄	C₂⁴	1	4	yes	—
443	C₄⋊C₄	C₂⁴	1	8	yes	—
444	C₄⋊C₄	C₂⁴	1	8	yes	—
445	C₄⋊C₄	C₂⁴	1	8	yes	—
446	C₄⋊C₄	C₂⁴	1	8	yes	—
447	C₄⋊C₄	C₂⁴	1	8	yes	—
448	C₄⋊C₄	C₂⁴	1	8	yes	—
449	C₄⋊C₄	C₂⁴	1	8	yes	—
450	C₄⋊C₄	C₂⁴	1	8	yes	—
451	C₄⋊C₄	C₂⁴	1	8	yes	—
452	C₂²⋊C₄	C₂⁴	1	8	yes	—
453	C₂²⋊C₄	C₂⁴	1	4	yes	—
454	C₂²⋊C₄	C₂⁴	1	4	yes	—
455	C₂²⋊C₄	C₂⁴	1	4	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	4	yes	—
460	C₂²⋊C₄	C₂⁴	1	8	yes	—
461	C₂²⋊C₄	C₂⁴	1	8	yes	—
462	C₂²⋊C₄	C₂⁴	1	4	yes	—
463	C₂²⋊C₄	C₂⁴	1	4	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	4	yes	—
468	C₂²⋊C₄	C₂⁴	1	4	yes	—
469	C₂²⋊C₄	C₂⁴	1	8	yes	—
470	C₂²⋊C₄	C₂⁴	1	8	yes	—
471	C₂²⋊C₄	C₂⁴	1	8	yes	—
472	C₂²⋊C₄	C₂⁴	1	8	yes	—
473	C₂²⋊C₄	C₂⁴	1	4	yes	—
474	C₂²⋊C₄	C₂⁴	1	8	yes	—
475	C₂²⋊C₄	C₂⁴	1	8	yes	—
476	C₂²⋊C₄	C₂⁴	1	4	yes	—
477	C₄²	C₂⁴	1	4	yes	—
478	C₄²	C₂⁴	1	4	yes	—
479	C₄²	C₂⁴	1	4	yes	—
480	C₄²	C₂⁴	1	4	yes	—
481	C₄²	C₂⁴	1	8	yes	—
482	C₄²	C₂⁴	1	8	yes	—
483	C₄²	C₂⁴	1	8	yes	—
484	C₄²	C₂⁴	1	8	yes	—
485	C₄²	C₂⁴	1	4	yes	—
486	C₄²	C₂⁴	1	4	yes	—
487	C₄²	C₂⁴	1	8	yes	—
488	C₄²	C₂⁴	1	8	yes	—
489	C₄²	C₂⁴	1	8	yes	—
490	C₂³	—	2	2	no	—
491	C₂³	—	2	2	no	—
492	C₂³	—	2	2	no	—
493	C₂³	—	2	4	no	—
494	C₂³	—	2	2	no	—
495	C₂³	—	2	2	no	—
496	C₂³	—	2	4	no	—
497	C₂³	—	2	2	no	—
498	C₂³	—	2	2	no	—
499	C₂³	—	2	4	no	—
500	C₂³	—	2	2	no	—
501	C₂³	—	2	2	no	—
502	C₂³	C₂⁵	1	2	yes	—
503	C₂³	C₂⁵	1	2	yes	—
504	C₂³	C₂⁵	1	2	yes	—
505	C₂³	C₂⁵	1	4	yes	—
506	C₂³	C₂⁵	1	1	yes	characteristic
507	Q₈	—	2	8	no	—
508	Q₈	—	4	4	no	—
509	Q₈	—	4	8	no	—
510	Q₈	—	4	8	no	—
511	Q₈	—	4	8	no	—
512	Q₈	—	4	8	no	—
513	D₄	—	2	8	no	—
514	D₄	—	4	4	no	—
515	D₄	—	4	4	no	—
516	D₄	—	4	8	no	—
517	D₄	—	4	8	no	—
518	D₄	—	4	4	no	—
519	D₄	—	4	8	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	4	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	4	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	2	4	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	4	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	8	no	—
539	C₂×C₄	—	2	8	no	—
540	C₂×C₄	—	2	8	no	—
541	C₂×C₄	—	4	8	no	—
542	C₂×C₄	—	4	4	no	—
543	C₂×C₄	—	4	8	no	—
544	C₂×C₄	—	4	8	no	—
545	C₂×C₄	—	4	8	no	—
546	C₂×C₄	—	4	8	no	—
547	C₂×C₄	—	4	4	no	—
548	C₂×C₄	2₋¹⁺⁴	1	4	yes	—
549	C₂×C₄	C₂⁵	1	2	yes	—
550	C₂×C₄	C₂⁵	1	2	yes	—
551	C₂×C₄	C₂⁵	1	4	yes	—
552	C₂×C₄	C₂⁵	1	2	yes	—
553	C₂×C₄	C₂⁵	1	4	yes	—
554	C₂×C₄	C₂⁵	1	2	yes	—
555	C₂×C₄	C₂⁵	1	2	yes	—
556	C₂×C₄	C₂⁵	1	2	yes	—
557	C₂×C₄	C₂⁵	1	2	yes	—
558	C₂×C₄	C₂⁵	1	2	yes	—
559	C₂×C₄	C₂⁵	1	4	yes	—
560	C₂×C₄	C₂⁵	1	2	yes	—
561	C₂×C₄	C₂⁵	1	4	yes	—
562	C₂×C₄	C₂⁵	1	4	yes	—
563	C₂×C₄	C₂⁵	1	4	yes	—
564	C₂×C₄	C₂⁵	1	2	yes	—
565	C₂×C₄	C₂⁵	1	4	yes	—
566	C₂×C₄	C₂⁵	1	2	yes	—
567	C₂×C₄	C₂⁵	1	2	yes	—
568	C₂²	—	2	2	no	—
569	C₂²	—	2	2	no	—
570	C₂²	—	2	2	no	—
571	C₂²	—	2	4	no	—
572	C₂²	—	2	2	no	—
573	C₂²	—	2	2	no	—
574	C₂²	—	2	4	no	—
575	C₂²	—	2	2	no	—
576	C₂²	—	2	2	no	—
577	C₂²	—	2	4	no	—
578	C₂²	—	2	2	no	—
579	C₂²	—	2	2	no	—
580	C₂²	—	4	4	no	—
581	C₂²	—	4	4	no	—
582	C₂²	—	4	4	no	—
583	C₂²	—	4	8	no	—
584	C₂²	C₂×2₋¹⁺⁴	1	2	yes	—
585	C₂²	#585	1	2	yes	—
586	C₂²	#585	1	2	yes	—
587	C₂²	C₂⁶	1	1	yes	characteristic
588	C₄	—	2	2	no	—
589	C₄	—	2	2	no	—
590	C₄	—	2	2	no	—
591	C₄	—	2	4	no	—
592	C₄	—	2	2	no	—
593	C₄	—	2	2	no	—
594	C₄	—	2	4	no	—
595	C₄	—	2	2	no	—
596	C₄	—	2	4	no	—
597	C₄	—	2	4	no	—
598	C₄	—	2	4	no	—
599	C₄	—	2	2	no	—
600	C₄	—	2	2	no	—
601	C₄	—	2	4	no	—
602	C₄	—	2	2	no	—
603	C₄	—	2	2	no	—
604	C₄	—	2	4	no	—
605	C₄	—	2	2	no	—
606	C₄	C₂×2₋¹⁺⁴	1	4	yes	—
607	C₂	—	4	2	no	—
608	C₂	—	4	2	no	—
609	C₂	—	4	2	no	—
610	C₂	—	4	4	no	—
611	C₂	#3565	1	4	yes	direct product factor
612	C₂	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
613	C₂	C₂×#585	1	1	yes	characteristic
614	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. #3565	C₂	direct (N × H)
2. C₂×#563	C₂	semidirect
3. C₂×#562	C₂	semidirect
4. C₂×#557	C₂	semidirect
5. C₂×#556	C₂	semidirect
6. C₂×#556	C₂	semidirect
7. C₂×#555	C₂	semidirect
8. C₂×#554	C₂	semidirect
9. C₂×#553	C₂	semidirect
10. C₂×#553	C₂	semidirect
11. C₂×#552	C₂	semidirect
12. C₂×#552	C₂	semidirect
13. C₂×#552	C₂	semidirect
14. C₂×#544	C₂	semidirect
15. C₂×#544	C₂	semidirect
16. C₂×#542	C₂	semidirect
17. C₂×#542	C₂	semidirect
18. C₂×#542	C₂	semidirect
19. C₂×#542	C₂	semidirect
20. C₂×#541	C₂	semidirect
21. C₂×#539	C₂	semidirect
22. C₂×#533	C₂	semidirect
23. C₂×#529	C₂	semidirect
24. C₂×#529	C₂	semidirect
25. #563	C₂²	semidirect
26. #562	C₂²	semidirect
27. #557	C₂²	semidirect
28. #556	C₂²	semidirect
29. #556	C₂²	semidirect
30. #555	C₂²	semidirect
31. #554	C₂²	semidirect
32. #553	C₂²	semidirect
33. #553	C₂²	semidirect
34. #552	C₂²	semidirect
35. #552	C₂²	semidirect
36. #552	C₂²	semidirect
37. #544	C₂²	semidirect
38. #544	C₂²	semidirect
39. #542	C₂²	semidirect
40. #542	C₂²	semidirect
41. #542	C₂²	semidirect
42. #542	C₂²	semidirect
43. #541	C₂²	semidirect
44. #539	C₂²	semidirect
45. #533	C₂²	semidirect
53. #529	C₂²	semidirect
54. #529	C₂²	semidirect
611. C₂	#3565	direct (N × H)

Maximal subgroups

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

subgroup	index
#3565	2
C₂×#563	2
C₂×#562	2
C₂×#557	2
C₂×#556	2
C₂×#555	2
C₂×#554	2
C₂×#553	2
C₂×#552	2
C₂×#544	2
C₂×#542	2
C₂×#541	2
C₂×#539	2
C₂×#533	2
C₂×#529	2

Subgroups — C2×#3565 #62741

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#3565 #62741