Subgroups — #10618180

Order 640.

1022 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	#66067	C₂	1	1	yes	maximal, characteristic, complemented
3	#66065	C₂	1	1	yes	maximal, characteristic, complemented
4	#66063	C₂	1	1	yes	maximal, characteristic, complemented
5	#66058	C₂	1	1	yes	maximal, characteristic, complemented
6	#66027	C₂	1	2	yes	maximal, complemented
7	#66027	C₂	1	2	yes	maximal, complemented
8	#65971	C₂	1	2	yes	maximal, complemented
9	#65970	C₂	1	2	yes	maximal, complemented
10	#65961	C₂	1	1	yes	maximal, characteristic
11	D₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
12	#65958	C₂	1	1	yes	maximal, characteristic, complemented
13	#65956	C₂	1	1	yes	maximal, characteristic, complemented
14	#65917	C₂	1	1	yes	maximal, characteristic, complemented
15	#65916	C₂	1	1	yes	maximal, characteristic, complemented
16	#65915	C₂	1	2	yes	maximal, complemented
17	#65908	C₂	1	1	yes	maximal, characteristic, complemented
18	#65906	C₂	1	1	yes	maximal, characteristic, complemented
19	#65902	C₂	1	2	yes	maximal, complemented
20	#65865	C₂	1	2	yes	maximal, complemented
21	#65861	C₂	1	2	yes	maximal, complemented
22	#65813	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#4018	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#713	C₂²	1	1	yes	characteristic
25	C₂×Q₈×D₅	C₂²	1	1	yes	characteristic
26	C₂²×C₄×D₅	C₂²	1	1	yes	characteristic
27	C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
28	C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₅×#125	C₂²	1	2	yes	complemented
30	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
32	C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
33	C₄×C₅×Q₈	C₂²	1	2	yes	complemented
34	C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
36	C₅×#117	C₂²	1	2	yes	—
37	C₂×C₄²×C₅	C₂²	1	1	yes	characteristic
38	#4093	C₂²	1	2	yes	—
39	#4093	C₂²	1	1	yes	characteristic, complemented
40	#4092	C₂²	1	2	yes	—
41	#4092	C₂²	1	1	yes	characteristic
42	#4092	C₂²	1	1	yes	characteristic
43	#4092	C₂²	1	2	yes	complemented
44	Q₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
45	Q₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
46	#4090	C₂²	1	1	yes	characteristic, complemented
47	#4090	C₂²	1	2	yes	complemented
48	#4076	C₂²	1	1	yes	characteristic
49	#4075	C₂²	1	2	yes	—
50	C₄×C₂²⋊D₅	C₂²	1	2	yes	—
51	C₂×#685	C₂²	1	1	yes	characteristic
52	C₂×#685	C₂²	1	1	yes	characteristic
53	#4070	C₂²	1	1	yes	characteristic
54	C₂×#683	C₂²	1	1	yes	characteristic
55	C₂×#683	C₂²	1	1	yes	characteristic
56	C₂×C₄×Dic₅	C₂²	1	1	yes	characteristic
57	#4044	C₂²	1	2	yes	—
58	#4044	C₂²	1	2	yes	—
59	#4044	C₂²	1	2	yes	—
60	#4044	C₂²	1	2	yes	complemented
61	#4044	C₂²	1	2	yes	complemented
62	#4043	C₂²	1	1	yes	characteristic
63	#4042	C₂²	1	2	yes	—
64	#4042	C₂²	1	2	yes	—
65	#4042	C₂²	1	2	yes	complemented
66	#4042	C₂²	1	2	yes	complemented
67	#4042	C₂²	1	2	yes	complemented
68	#4041	C₂²	1	1	yes	characteristic
69	#4040	C₂²	1	2	yes	—
70	#4040	C₂²	1	2	yes	—
71	#4040	C₂²	1	2	yes	—
72	#4040	C₂²	1	2	yes	—
73	#4040	C₂²	1	2	yes	—
74	#4039	C₂²	1	2	yes	—
75	#4039	C₂²	1	2	yes	—
76	#4039	C₂²	1	1	yes	characteristic, complemented
77	#4038	C₂²	1	1	yes	characteristic
78	#4038	C₂²	1	2	yes	—
79	#4038	C₂²	1	2	yes	complemented
80	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
81	D₅×C₄⋊C₄	C₂²	1	2	yes	—
82	D₅×C₄⋊C₄	C₂²	1	2	yes	complemented
83	#4036	C₂²	1	1	yes	characteristic, complemented
84	#4035	C₂²	1	2	yes	complemented
85	#4035	C₂²	1	2	yes	complemented
86	#4035	C₂²	1	2	yes	complemented
87	#4035	C₂²	1	2	yes	complemented
88	#4035	C₂²	1	2	yes	complemented
89	#4034	C₂²	1	1	yes	characteristic, complemented
90	#4033	C₂²	1	1	yes	characteristic, complemented
91	#4033	C₂²	1	2	yes	complemented
92	#4033	C₂²	1	2	yes	complemented
93	#4032	C₂²	1	2	yes	—
94	#4028	C₂²	1	2	yes	—
95	#4027	C₂²	1	2	yes	—
96	#4027	C₂²	1	2	yes	—
97	D₅×C₂²⋊C₄	C₂²	1	2	yes	—
98	#4024	C₂²	1	2	yes	—
99	#4024	C₂²	1	2	yes	—
100	#4023	C₂²	1	2	yes	—
101	#4022	C₂²	1	2	yes	—
102	#4022	C₂²	1	2	yes	complemented
103	#4022	C₂²	1	2	yes	complemented
104	#4021	C₂²	1	2	yes	—
105	#4021	C₂²	1	1	yes	characteristic, complemented
106	C₄×D₂₀	C₂²	1	2	yes	—
107	C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
108	#4018	C₂²	1	1	yes	characteristic
109	#4018	C₂²	1	1	yes	characteristic
110	#4018	C₂²	1	1	yes	characteristic
111	#4018	C₂²	1	1	yes	characteristic
112	#4018	C₂²	1	1	yes	characteristic
113	#4018	C₂²	1	1	yes	characteristic
114	#4018	C₂²	1	1	yes	characteristic
115	#4018	C₂²	1	1	yes	characteristic
116	#4018	C₂²	1	2	yes	—
117	#4018	C₂²	1	2	yes	complemented
118	#4018	C₂²	1	2	yes	complemented
119	#4016	C₂²	1	1	yes	characteristic, complemented
120	#4016	C₂²	1	2	yes	complemented
121	C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₁₀	C₂²	1	2	yes	complemented
123	#3495	—	5	1	no	maximal, Sylow
124	C₂³×D₅	C₂³	1	1	yes	characteristic
125	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
126	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
127	C₂×C₅×Q₈	C₂³	1	2	yes	—
128	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
131	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
132	C₂²×Dic₅	C₂³	1	1	yes	characteristic
133	C₂²×Dic₅	C₂³	1	1	yes	characteristic
134	C₂²×Dic₅	C₂³	1	1	yes	characteristic
135	#713	—	2	4	no	—
136	Q₈×D₅	—	2	4	no	—
137	C₂×D₂₀	C₂³	1	2	yes	—
138	C₂×D₂₀	C₂³	1	1	yes	characteristic
139	C₂×D₂₀	C₂³	1	2	yes	—
140	C₂×C₄×D₅	—	2	4	no	—
141	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
142	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
143	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₅	C₂³	1	2	yes	—
145	C₂×C₄×D₅	C₂³	1	2	yes	—
146	C₂×C₄×D₅	C₂³	1	2	yes	—
147	C₂×C₄×D₅	C₂³	1	2	yes	—
148	C₂×C₄×D₅	C₂³	1	2	yes	—
149	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
150	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
151	C₂×Dic₁₀	C₂³	1	2	yes	—
152	C₂×Dic₁₀	C₂³	1	2	yes	—
153	C₅×C₄⋊C₄	C₂³	1	2	yes	—
154	C₅×C₄⋊C₄	C₂³	1	2	yes	—
155	C₅×C₄⋊C₄	C₂³	1	2	yes	—
156	C₅×C₄⋊C₄	C₂³	1	2	yes	—
157	C₅×C₄⋊C₄	C₂³	1	2	yes	—
158	C₅×C₄⋊C₄	C₂³	1	2	yes	—
159	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
160	C₅×C₄⋊C₄	C₂³	1	2	yes	—
161	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
162	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
163	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₄²×C₅	C₂³	1	1	yes	characteristic
165	C₄²×C₅	C₂³	1	1	yes	characteristic
166	C₄²×C₅	C₂³	1	1	yes	characteristic
167	C₄²×C₅	C₂³	1	1	yes	characteristic
168	C₄²×C₅	C₂³	1	2	yes	—
169	C₄²×C₅	C₂³	1	2	yes	—
170	C₂²⋊Dic₅	C₂³	1	2	yes	—
171	#685	C₂³	1	1	yes	characteristic
172	#685	C₂³	1	1	yes	characteristic
173	#685	C₂³	1	1	yes	characteristic
174	#685	C₂³	1	1	yes	characteristic
175	#685	C₂³	1	1	yes	characteristic
176	#685	C₂³	1	1	yes	characteristic
177	#685	C₂³	1	1	yes	characteristic
178	#685	C₂³	1	1	yes	characteristic
179	#685	C₂³	1	2	yes	—
180	#685	C₂³	1	2	yes	—
181	#685	C₂³	1	2	yes	—
182	#685	C₂³	1	2	yes	—
183	#685	C₂³	1	2	yes	—
184	#685	C₂³	1	2	yes	—
185	#685	C₂³	1	2	yes	—
186	#685	C₂³	1	2	yes	—
187	#685	C₂³	1	2	yes	—
188	#685	C₂³	1	2	yes	—
189	#685	C₂³	1	2	yes	—
190	#685	C₂³	1	2	yes	—
191	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
192	C₄⋊Dic₅	C₂³	1	2	yes	—
193	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
194	C₄⋊Dic₅	C₂³	1	2	yes	—
195	C₄⋊Dic₅	C₂³	1	2	yes	—
196	C₄⋊Dic₅	C₂³	1	2	yes	—
197	#683	C₂³	1	2	yes	—
198	#683	C₂³	1	1	yes	characteristic
199	#683	C₂³	1	1	yes	characteristic
200	#683	C₂³	1	2	yes	—
201	#683	C₂³	1	2	yes	—
202	#683	C₂³	1	2	yes	—
203	#683	C₂³	1	2	yes	—
204	#683	C₂³	1	1	yes	characteristic
205	#683	C₂³	1	1	yes	characteristic
206	#683	C₂³	1	1	yes	characteristic
207	#683	C₂³	1	1	yes	characteristic
208	#683	C₂³	1	1	yes	characteristic
209	#683	C₂³	1	1	yes	characteristic
210	#683	C₂³	1	2	yes	—
211	#683	C₂³	1	2	yes	—
212	#683	C₂³	1	2	yes	—
213	#683	C₂³	1	2	yes	—
214	#683	C₂³	1	2	yes	—
215	#683	C₂³	1	2	yes	—
216	#683	C₂³	1	2	yes	—
217	C₄×Dic₅	C₂³	1	2	yes	—
218	C₄×Dic₅	C₂³	1	2	yes	—
219	C₄×Dic₅	C₂³	1	2	yes	—
220	C₄×Dic₅	C₂³	1	1	yes	characteristic
221	C₄×Dic₅	C₂³	1	1	yes	characteristic
222	C₄×Dic₅	C₂³	1	1	yes	characteristic
223	C₄×Dic₅	C₂³	1	1	yes	characteristic
224	C₄×Dic₅	C₂³	1	2	yes	—
225	C₄×Dic₅	C₂³	1	2	yes	—
226	#556	—	5	2	no	—
227	#554	—	5	2	no	—
228	#552	—	5	2	no	—
229	#552	—	5	2	no	—
230	#552	—	5	2	no	—
231	#552	—	5	2	no	—
232	#551	—	5	2	no	—
233	#551	—	5	2	no	—
234	#544	—	5	1	no	—
235	#542	—	5	1	no	—
236	#542	—	5	1	no	—
237	#541	—	5	1	no	—
238	#541	—	5	1	no	—
239	#536	—	5	1	no	—
240	#533	—	5	1	no	—
241	#533	D₅	1	1	yes	characteristic, complemented
242	#529	—	5	1	no	—
243	#529	—	5	1	no	—
244	#525	—	5	1	no	—
245	C₂×C₂²⋊Q₈	—	5	1	no	—
246	#520	—	5	1	no	—
247	#519	—	5	1	no	—
248	C₂×#117	—	5	1	no	—
249	C₂³×C₅	C₂⁴	1	1	yes	characteristic
250	C₂²×D₅	—	2	2	no	—
251	C₂²×D₅	—	2	2	no	—
252	C₂²×D₅	—	4	1	no	—
253	C₂²×D₅	C₂⁴	1	1	yes	characteristic
254	C₂²×D₅	C₂⁴	1	2	yes	—
255	C₂²×D₅	C₂⁴	1	1	yes	characteristic
256	C₅×Q₈	—	2	2	no	—
257	C₅×Q₈	—	2	2	no	—
258	C₅×Q₈	—	4	2	no	—
259	C₂×C₄×C₅	—	2	2	no	—
260	C₂×C₄×C₅	—	2	2	no	—
261	C₂×C₄×C₅	—	4	1	no	—
262	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
263	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
264	C₂×C₄×C₅	C₂⁴	1	2	yes	—
265	C₂×C₄×C₅	C₂⁴	1	2	yes	—
266	C₂×C₄×C₅	C₂⁴	1	2	yes	—
267	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
268	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
269	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
270	C₂×C₄×C₅	C₂⁴	1	2	yes	—
271	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
272	C₂²⋊D₅	—	2	4	no	—
273	C₂×Dic₅	—	2	2	no	—
274	C₂×Dic₅	—	2	2	no	—
275	C₂×Dic₅	—	4	1	no	—
276	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
277	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
278	C₂×Dic₅	C₂⁴	1	2	yes	—
279	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
280	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
281	C₂×Dic₅	C₂⁴	1	2	yes	—
282	C₂×Dic₅	C₂⁴	1	2	yes	—
283	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
284	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
285	D₂₀	—	2	4	no	—
286	D₂₀	—	2	2	no	—
287	D₂₀	—	4	2	no	—
288	C₄×D₅	—	2	2	no	—
289	C₄×D₅	—	2	4	no	—
290	C₄×D₅	—	2	2	no	—
291	C₄×D₅	—	2	2	no	—
292	C₄×D₅	—	2	4	no	—
293	C₄×D₅	—	4	2	no	—
294	C₄×D₅	—	4	2	no	—
295	C₄×D₅	—	4	2	no	—
296	C₄×D₅	#41	1	4	yes	—
297	Dic₁₀	—	2	2	no	—
298	Dic₁₀	—	2	4	no	—
299	Dic₁₀	—	4	2	no	—
300	C₂×#41	—	5	1	no	—
301	C₂²×Q₈	—	5	1	no	—
302	C₂³×C₄	—	5	1	no	—
303	C₄⋊Q₈	—	5	1	no	—
304	C₄⋊Q₈	—	5	2	no	—
305	C₄⋊Q₈	—	5	1	no	—
306	C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
307	C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
308	#126	—	5	2	no	—
309	#126	—	5	2	no	—
310	#126	—	5	2	no	—
311	#126	—	5	2	no	—
312	#126	—	5	2	no	—
313	#126	—	5	2	no	—
314	#126	—	5	2	no	—
315	#126	—	5	2	no	—
316	#125	—	5	1	no	—
317	#125	—	5	2	no	—
318	#125	—	5	2	no	—
319	#125	—	5	2	no	—
320	#125	—	5	2	no	—
321	#125	—	5	2	no	—
322	#125	—	5	1	no	—
323	#125	—	5	2	no	—
324	#125	C₂×D₅	1	2	yes	complemented
325	#124	—	5	1	no	—
326	#124	—	5	2	no	—
327	#124	—	5	1	no	—
328	#124	—	5	2	no	—
329	#123	—	5	2	no	—
330	#123	—	5	2	no	—
331	#123	—	5	2	no	—
332	#123	—	5	2	no	—
333	#123	—	5	2	no	—
334	#123	—	5	2	no	—
335	#123	—	5	2	no	—
336	C₂²⋊Q₈	—	5	1	no	—
337	C₂²⋊Q₈	—	5	1	no	—
338	C₂²⋊Q₈	—	5	2	no	—
339	C₂²⋊Q₈	—	5	2	no	—
340	C₂²⋊Q₈	—	5	1	no	—
341	C₂²⋊Q₈	—	5	1	no	—
342	C₂²⋊Q₈	—	5	2	no	—
343	C₂²⋊Q₈	—	5	2	no	—
344	C₂²⋊Q₈	—	5	2	no	—
345	C₂²⋊Q₈	—	5	2	no	—
346	C₂²⋊Q₈	—	5	2	no	—
347	C₂²⋊Q₈	—	5	2	no	—
348	C₂²⋊Q₈	—	5	2	no	—
349	C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic
350	C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic
351	C₂²⋊Q₈	C₂×D₅	1	2	yes	—
352	#121	—	5	1	no	—
353	#121	—	5	1	no	—
354	#120	—	5	2	no	—
355	C₄×Q₈	—	5	1	no	—
356	C₄×Q₈	—	5	1	no	—
357	C₄×Q₈	—	5	1	no	—
358	C₄×Q₈	—	5	2	no	—
359	C₄×Q₈	—	5	2	no	—
360	C₄×Q₈	—	5	1	no	—
361	C₄×Q₈	—	5	2	no	—
362	C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
363	C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
364	C₄×Q₈	C₂×D₅	1	2	yes	complemented
365	C₄×D₄	—	5	2	no	—
366	C₄×D₄	—	5	1	no	—
367	C₄×D₄	—	5	2	no	—
368	C₄×D₄	—	5	2	no	—
369	C₄×D₄	—	5	2	no	—
370	C₄×D₄	—	5	2	no	—
371	C₄×D₄	—	5	1	no	—
372	C₄×D₄	—	5	2	no	—
373	#117	—	5	1	no	—
374	#117	—	5	2	no	—
375	#117	—	5	2	no	—
376	#117	—	5	2	no	—
377	#117	—	5	1	no	—
378	#117	—	5	1	no	—
379	#117	—	5	1	no	—
380	#117	—	5	1	no	—
381	#117	—	5	1	no	—
382	#117	—	5	1	no	—
383	#117	—	5	1	no	—
384	#117	—	5	1	no	—
385	#117	—	5	2	no	—
386	#117	—	5	2	no	—
387	#117	—	5	2	no	—
388	#117	C₂×D₅	1	2	yes	—
389	C₂×C₄⋊C₄	—	5	1	no	—
390	C₂×C₄⋊C₄	—	5	1	no	—
391	C₂×C₄⋊C₄	—	5	1	no	—
392	C₂×C₄⋊C₄	—	5	2	no	—
393	C₂×C₄⋊C₄	—	5	2	no	—
394	C₂×C₂²⋊C₄	—	5	1	no	—
395	C₂×C₂²⋊C₄	—	5	1	no	—
396	C₂×C₂²⋊C₄	—	5	2	no	—
397	C₂×C₄²	—	5	1	no	—
398	C₂×C₄²	C₂×D₅	1	1	yes	characteristic
399	C₂²×C₅	—	2	1	no	—
400	C₂²×C₅	—	2	1	no	—
401	C₂²×C₅	2₋¹⁺⁴	1	2	yes	—
402	C₂²×C₅	C₂⁵	1	1	yes	characteristic
403	C₂×D₅	—	2	1	no	—
404	C₂×D₅	—	2	1	no	—
405	C₂×D₅	—	2	1	no	—
406	C₂×D₅	—	2	2	no	—
407	C₂×D₅	—	2	2	no	—
408	C₂×D₅	—	2	1	no	—
409	C₂×D₅	—	2	2	no	—
410	C₂×D₅	—	2	1	no	—
411	C₂×D₅	—	4	4	no	—
412	C₂×D₅	C₂×#41	1	2	yes	—
413	C₄×C₅	—	2	2	no	—
414	C₄×C₅	—	2	1	no	—
415	C₄×C₅	—	2	2	no	—
416	C₄×C₅	—	2	1	no	—
417	C₄×C₅	—	2	1	no	—
418	C₄×C₅	—	2	2	no	—
419	C₄×C₅	—	2	1	no	—
420	C₄×C₅	—	2	2	no	—
421	C₄×C₅	—	2	1	no	—
422	C₄×C₅	C₂×#41	1	2	yes	—
423	Dic₅	—	2	2	no	—
424	Dic₅	—	2	1	no	—
425	Dic₅	—	2	1	no	—
426	Dic₅	—	2	1	no	—
427	Dic₅	—	2	2	no	—
428	Dic₅	—	2	1	no	—
429	Dic₅	—	2	2	no	—
430	Dic₅	—	2	1	no	—
431	Dic₅	C₂×#41	1	2	yes	—
432	C₂⁴	—	5	1	no	—
433	#41	—	10	4	no	—
434	C₂×Q₈	—	5	2	no	—
435	C₂×Q₈	—	5	1	no	—
436	C₂×Q₈	—	5	2	no	—
437	C₂×Q₈	—	10	4	no	—
438	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
439	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
440	C₂×Q₈	C₂²×D₅	1	2	yes	—
441	C₂×D₄	—	5	2	no	—
442	C₂×D₄	—	5	2	no	—
443	C₂×D₄	—	5	1	no	—
444	C₂×D₄	—	5	2	no	—
445	C₂²×C₄	—	5	1	no	—
446	C₂²×C₄	—	5	1	no	—
447	C₂²×C₄	—	5	1	no	—
448	C₂²×C₄	—	5	1	no	—
449	C₂²×C₄	—	5	2	no	—
450	C₂²×C₄	—	5	1	no	—
451	C₂²×C₄	—	5	2	no	—
452	C₂²×C₄	—	5	1	no	—
453	C₂²×C₄	—	5	1	no	—
454	C₂²×C₄	—	5	2	no	—
455	C₂²×C₄	—	5	2	no	—
456	C₂²×C₄	—	5	2	no	—
457	C₂²×C₄	—	10	4	no	—
458	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
459	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
460	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
461	C₄⋊C₄	—	5	1	no	—
462	C₄⋊C₄	—	5	2	no	—
463	C₄⋊C₄	—	5	1	no	—
464	C₄⋊C₄	—	5	1	no	—
465	C₄⋊C₄	—	5	1	no	—
466	C₄⋊C₄	—	5	1	no	—
467	C₄⋊C₄	—	5	1	no	—
468	C₄⋊C₄	—	5	1	no	—
469	C₄⋊C₄	—	5	1	no	—
470	C₄⋊C₄	—	5	2	no	—
471	C₄⋊C₄	—	5	1	no	—
472	C₄⋊C₄	—	5	2	no	—
473	C₄⋊C₄	—	5	2	no	—
474	C₄⋊C₄	—	5	2	no	—
475	C₄⋊C₄	—	5	1	no	—
476	C₄⋊C₄	—	5	2	no	—
477	C₄⋊C₄	—	5	2	no	—
478	C₄⋊C₄	—	5	2	no	—
479	C₄⋊C₄	—	5	2	no	—
480	C₄⋊C₄	—	5	2	no	—
481	C₄⋊C₄	—	5	2	no	—
482	C₄⋊C₄	—	5	2	no	—
483	C₄⋊C₄	—	5	2	no	—
484	C₄⋊C₄	—	5	2	no	—
485	C₄⋊C₄	—	5	2	no	—
486	C₄⋊C₄	—	5	2	no	—
487	C₄⋊C₄	C₂²×D₅	1	2	yes	—
488	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
489	C₄⋊C₄	C₂²×D₅	1	2	yes	—
490	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
491	C₄⋊C₄	C₂²×D₅	1	2	yes	—
492	C₄⋊C₄	C₂²×D₅	1	2	yes	—
493	C₄⋊C₄	C₂²×D₅	1	2	yes	—
494	C₄⋊C₄	C₂²×D₅	1	2	yes	—
495	C₄⋊C₄	C₂²×D₅	1	2	yes	—
496	C₂²⋊C₄	—	5	2	no	—
497	C₂²⋊C₄	—	5	1	no	—
498	C₂²⋊C₄	—	5	1	no	—
499	C₂²⋊C₄	—	5	1	no	—
500	C₂²⋊C₄	—	5	1	no	—
501	C₂²⋊C₄	—	5	1	no	—
502	C₂²⋊C₄	—	5	1	no	—
503	C₂²⋊C₄	—	5	1	no	—
504	C₂²⋊C₄	—	5	1	no	—
505	C₂²⋊C₄	—	5	2	no	—
506	C₂²⋊C₄	—	5	2	no	—
507	C₂²⋊C₄	—	5	2	no	—
508	C₂²⋊C₄	—	5	2	no	—
509	C₂²⋊C₄	—	5	2	no	—
510	C₂²⋊C₄	—	5	2	no	—
511	C₂²⋊C₄	—	5	2	no	—
512	C₂²⋊C₄	—	5	2	no	—
513	C₂²⋊C₄	—	5	2	no	—
514	C₂²⋊C₄	—	5	2	no	—
515	C₂²⋊C₄	—	5	2	no	—
516	C₂²⋊C₄	—	5	2	no	—
517	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
518	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
519	C₄²	—	5	1	no	—
520	C₄²	—	5	1	no	—
521	C₄²	—	5	1	no	—
522	C₄²	—	5	1	no	—
523	C₄²	—	5	2	no	—
524	C₄²	—	5	2	no	—
525	C₄²	—	5	2	no	—
526	C₄²	—	5	2	no	—
527	C₄²	—	5	2	no	—
528	C₄²	C₂²×D₅	1	1	yes	characteristic
529	C₄²	C₂²×D₅	1	1	yes	characteristic
530	C₄²	C₂²×D₅	1	1	yes	characteristic
531	C₄²	C₂²×D₅	1	1	yes	characteristic
532	C₄²	C₂²×D₅	1	2	yes	—
533	C₄²	C₂²×D₅	1	2	yes	—
534	C₂×C₅	—	2	2	no	—
535	C₂×C₅	C₂²×#41	1	1	yes	characteristic
536	C₂×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
537	C₂×C₅	#585	1	1	yes	characteristic
538	D₅	—	2	2	no	—
539	D₅	—	4	2	no	—
540	D₅	—	4	1	no	—
541	C₂³	—	5	1	no	—
542	C₂³	—	5	1	no	—
543	C₂³	—	5	2	no	—
544	C₂³	—	10	2	no	—
545	C₂³	—	10	2	no	—
546	C₂³	—	20	1	no	—
547	C₂³	C₂³×D₅	1	1	yes	characteristic
548	Q₈	—	2	2	no	—
549	Q₈	—	2	2	no	—
550	Q₈	—	4	2	no	—
551	Q₈	—	10	4	no	—
552	Q₈	—	10	2	no	—
553	Q₈	—	20	2	no	—
554	D₄	—	10	4	no	—
555	D₄	—	10	4	no	—
556	D₄	—	10	2	no	—
557	D₄	—	20	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	5	1	no	—
562	C₂×C₄	—	5	4	no	—
563	C₂×C₄	—	5	1	no	—
564	C₂×C₄	—	5	1	no	—
565	C₂×C₄	—	5	2	no	—
566	C₂×C₄	—	5	1	no	—
567	C₂×C₄	—	5	2	no	—
568	C₂×C₄	—	5	1	no	—
569	C₂×C₄	—	5	2	no	—
570	C₂×C₄	—	5	1	no	—
571	C₂×C₄	—	10	2	no	—
572	C₂×C₄	—	10	4	no	—
573	C₂×C₄	—	10	2	no	—
574	C₂×C₄	—	10	4	no	—
575	C₂×C₄	—	10	2	no	—
576	C₂×C₄	—	10	2	no	—
577	C₂×C₄	—	10	2	no	—
578	C₂×C₄	—	20	2	no	—
579	C₂×C₄	—	20	2	no	—
580	C₂×C₄	—	20	2	no	—
581	C₂×C₄	—	20	1	no	—
582	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
583	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
584	C₂×C₄	C₂³×D₅	1	2	yes	—
585	C₂×C₄	C₂³×D₅	1	2	yes	—
586	C₂×C₄	C₂³×D₅	1	2	yes	—
587	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
588	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
589	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
590	C₂×C₄	C₂³×D₅	1	2	yes	—
591	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
592	C₅	#3495	1	1	yes	characteristic, complemented, Sylow
593	C₂²	—	2	1	no	—
594	C₂²	—	2	1	no	—
595	C₂²	—	5	2	no	—
596	C₂²	—	10	1	no	—
597	C₂²	—	10	1	no	—
598	C₂²	—	10	2	no	—
599	C₂²	—	10	1	no	—
600	C₂²	—	10	1	no	—
601	C₂²	—	10	2	no	—
602	C₂²	—	10	2	no	—
603	C₂²	—	10	1	no	—
604	C₂²	—	20	4	no	—
605	C₂²	#4147	1	2	yes	—
606	C₂²	C₂⁴×D₅	1	1	yes	characteristic
607	C₄	—	2	1	no	—
608	C₄	—	2	1	no	—
609	C₄	—	2	1	no	—
610	C₄	—	2	2	no	—
611	C₄	—	2	2	no	—
612	C₄	—	2	1	no	—
613	C₄	—	2	1	no	—
614	C₄	—	2	2	no	—
615	C₄	—	2	2	no	—
616	C₄	—	5	2	no	—
617	C₄	—	10	1	no	—
618	C₄	—	10	1	no	—
619	C₄	—	10	2	no	—
620	C₄	—	10	1	no	—
621	C₄	—	10	2	no	—
622	C₄	—	10	1	no	—
623	C₄	—	10	2	no	—
624	C₄	—	10	1	no	—
625	C₄	D₅×#41	1	2	yes	—
626	C₂	—	2	2	no	—
627	C₂	—	10	2	no	—
628	C₂	—	20	1	no	—
629	C₂	—	20	2	no	—
630	C₂	C₂×#4147	1	1	yes	characteristic
631	C₂	C₂×D₅×#41	1	1	yes	characteristic
632	C₂	#66283	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅
commutator, socle, cosocle	C₂²×C₅	C₂⁵
Fitting	C₅×#533	C₂
prime radical	#65961	C₂
hypercenter	#533	D₅
hypocenter	C₅	#3495
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ #533

Complements

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

N	H ≅ G/N	type
1. C₅×#533	C₂	semidirect
2. #66067	C₂	semidirect
3. #66065	C₂	semidirect
4. #66063	C₂	semidirect
5. #66058	C₂	semidirect
6. #66027	C₂	semidirect
7. #66027	C₂	semidirect
8. #65971	C₂	semidirect
9. #65970	C₂	semidirect
11. D₅×C₂²⋊Q₈	C₂	semidirect
12. #65958	C₂	semidirect
13. #65956	C₂	semidirect
14. #65917	C₂	semidirect
15. #65916	C₂	semidirect
16. #65915	C₂	semidirect
17. #65908	C₂	semidirect
18. #65906	C₂	semidirect
19. #65902	C₂	semidirect
20. #65865	C₂	semidirect
21. #65861	C₂	semidirect
22. #65813	C₂	semidirect
23. C₂×#4018	C₂	semidirect
27. C₅×C₄⋊Q₈	C₂²	semidirect
28. C₅×C₄⋊Q₈	C₂²	semidirect
29. C₅×#125	C₂²	semidirect
33. C₄×C₅×Q₈	C₂²	semidirect
34. C₄×C₅×Q₈	C₂²	semidirect
35. C₄×C₅×Q₈	C₂²	semidirect
39. #4093	C₂²	semidirect
43. #4092	C₂²	semidirect
44. Q₈×Dic₅	C₂²	semidirect
45. Q₈×Dic₅	C₂²	semidirect
46. #4090	C₂²	semidirect
47. #4090	C₂²	semidirect
60. #4044	C₂²	semidirect
61. #4044	C₂²	semidirect
65. #4042	C₂²	semidirect
66. #4042	C₂²	semidirect
67. #4042	C₂²	semidirect
76. #4039	C₂²	semidirect
79. #4038	C₂²	semidirect
82. D₅×C₄⋊C₄	C₂²	semidirect
83. #4036	C₂²	semidirect
84. #4035	C₂²	semidirect
85. #4035	C₂²	semidirect
86. #4035	C₂²	semidirect
87. #4035	C₂²	semidirect
88. #4035	C₂²	semidirect
89. #4034	C₂²	semidirect
90. #4033	C₂²	semidirect
91. #4033	C₂²	semidirect
92. #4033	C₂²	semidirect
102. #4022	C₂²	semidirect
103. #4022	C₂²	semidirect
105. #4021	C₂²	semidirect
107. C₄×D₂₀	C₂²	semidirect
117. #4018	C₂²	semidirect
118. #4018	C₂²	semidirect
119. #4016	C₂²	semidirect
120. #4016	C₂²	semidirect
121. C₄×Dic₁₀	C₂²	semidirect
122. C₄×Dic₁₀	C₂²	semidirect
241. #533	D₅	semidirect
306. C₄⋊Q₈	C₂×D₅	semidirect
307. C₄⋊Q₈	C₂×D₅	semidirect
324. #125	C₂×D₅	semidirect
362. C₄×Q₈	C₂×D₅	semidirect
363. C₄×Q₈	C₂×D₅	semidirect
364. C₄×Q₈	C₂×D₅	semidirect
592. C₅	#3495	semidirect

Maximal subgroups

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

subgroup	index
C₅×#533	2
#66067	2
#66065	2
#66063	2
#66058	2
#66027	2
#65971	2
#65970	2
#65961	2
D₅×C₂²⋊Q₈	2
#65958	2
#65956	2
#65917	2
#65916	2
#65915	2
#65908	2
#65906	2
#65902	2
#65865	2
#65861	2
#65813	2
C₂×#4018	2
#3495	5