Subgroups — #10618732

Order 640.

1022 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#552	C₂	1	1	yes	maximal, characteristic, complemented
2	#66039	C₂	1	2	yes	maximal, complemented
3	#66035	C₂	1	2	yes	maximal, complemented
4	#66028	C₂	1	1	yes	maximal, characteristic, complemented
5	#66027	C₂	1	2	yes	maximal, complemented
6	#66023	C₂	1	1	yes	maximal, characteristic, complemented
7	#66022	C₂	1	2	yes	maximal, complemented
8	#65996	C₂	1	2	yes	maximal, complemented
9	#65993	C₂	1	2	yes	maximal, complemented
10	#65975	C₂	1	1	yes	maximal, characteristic, complemented
11	#65973	C₂	1	1	yes	maximal, characteristic, complemented
12	#65962	C₂	1	1	yes	maximal, characteristic, complemented
13	D₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
14	#65913	C₂	1	1	yes	maximal, characteristic, complemented
15	#65906	C₂	1	1	yes	maximal, characteristic, complemented
16	#65881	C₂	1	1	yes	maximal, characteristic
17	#65876	C₂	1	1	yes	maximal, characteristic, complemented
18	#65863	C₂	1	1	yes	maximal, characteristic, complemented
19	#65863	C₂	1	2	yes	maximal, complemented
20	#65862	C₂	1	2	yes	maximal, complemented
21	D₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
22	#65845	C₂	1	1	yes	maximal, characteristic, complemented
23	#65838	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×Q₈×D₅	C₂²	1	1	yes	characteristic
25	C₂×#709	C₂²	1	1	yes	characteristic
26	C₂²×C₄×D₅	C₂²	1	1	yes	characteristic
27	C₅×#126	C₂²	1	2	yes	—
28	C₅×#125	C₂²	1	2	yes	complemented
29	C₅×#125	C₂²	1	1	yes	characteristic, complemented
30	C₅×#123	C₂²	1	2	yes	—
31	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
32	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
33	C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₄×C₅×D₄	C₂²	1	1	yes	characteristic
35	C₅×#117	C₂²	1	1	yes	characteristic
36	C₅×#117	C₂²	1	2	yes	complemented
37	C₂×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
38	#4092	C₂²	1	1	yes	characteristic
39	#4092	C₂²	1	1	yes	characteristic, complemented
40	Q₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
41	#4085	C₂²	1	1	yes	characteristic
42	#4083	C₂²	1	1	yes	characteristic
43	#4082	C₂²	1	2	yes	—
44	C₄×C₂²⋊D₅	C₂²	1	2	yes	—
45	C₄×C₂²⋊D₅	C₂²	1	2	yes	—
46	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
47	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
48	C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
49	#4072	C₂²	1	1	yes	characteristic
50	#4072	C₂²	1	1	yes	characteristic, complemented
51	#4070	C₂²	1	1	yes	characteristic
52	#4070	C₂²	1	2	yes	complemented
53	#4070	C₂²	1	1	yes	characteristic, complemented
54	#4044	C₂²	1	2	yes	complemented
55	#4044	C₂²	1	2	yes	complemented
56	#4043	C₂²	1	1	yes	characteristic
57	#4043	C₂²	1	2	yes	—
58	#4043	C₂²	1	1	yes	characteristic, complemented
59	#4042	C₂²	1	2	yes	—
60	#4042	C₂²	1	2	yes	—
61	#4042	C₂²	1	1	yes	characteristic
62	#4042	C₂²	1	2	yes	—
63	#4042	C₂²	1	2	yes	—
64	#4042	C₂²	1	2	yes	complemented
65	#4040	C₂²	1	2	yes	—
66	#4040	C₂²	1	1	yes	characteristic
67	#4040	C₂²	1	2	yes	—
68	#4039	C₂²	1	2	yes	—
69	#4038	C₂²	1	1	yes	characteristic
70	#4038	C₂²	1	1	yes	characteristic
71	#4038	C₂²	1	2	yes	—
72	#4038	C₂²	1	2	yes	—
73	#4038	C₂²	1	2	yes	—
74	#4038	C₂²	1	1	yes	characteristic, complemented
75	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
76	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
77	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
78	D₅×C₄⋊C₄	C₂²	1	2	yes	—
79	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
80	#4036	C₂²	1	1	yes	characteristic, complemented
81	#4036	C₂²	1	2	yes	complemented
82	#4035	C₂²	1	2	yes	complemented
83	#4035	C₂²	1	2	yes	complemented
84	#4035	C₂²	1	2	yes	complemented
85	#4034	C₂²	1	1	yes	characteristic, complemented
86	#4034	C₂²	1	2	yes	complemented
87	#4034	C₂²	1	2	yes	complemented
88	#4033	C₂²	1	2	yes	complemented
89	#4033	C₂²	1	1	yes	characteristic, complemented
90	#4033	C₂²	1	2	yes	complemented
91	#4033	C₂²	1	2	yes	complemented
92	#4033	C₂²	1	2	yes	complemented
93	#4031	C₂²	1	2	yes	—
94	#4031	C₂²	1	2	yes	complemented
95	#4030	C₂²	1	1	yes	characteristic
96	#4029	C₂²	1	2	yes	—
97	#4029	C₂²	1	1	yes	characteristic
98	#4029	C₂²	1	2	yes	—
99	#4029	C₂²	1	2	yes	—
100	#4028	C₂²	1	1	yes	characteristic
101	D₅×C₂²⋊C₄	C₂²	1	2	yes	—
102	D₅×C₂²⋊C₄	C₂²	1	2	yes	—
103	#4025	C₂²	1	2	yes	—
104	#4025	C₂²	1	2	yes	—
105	#4025	C₂²	1	2	yes	—
106	#4025	C₂²	1	2	yes	complemented
107	#4025	C₂²	1	2	yes	complemented
108	#4024	C₂²	1	1	yes	characteristic
109	#4024	C₂²	1	2	yes	—
110	#4023	C₂²	1	2	yes	—
111	C₄×D₂₀	C₂²	1	2	yes	—
112	C₄×D₂₀	C₂²	1	1	yes	characteristic
113	#4018	C₂²	1	2	yes	—
114	#4018	C₂²	1	2	yes	—
115	#4018	C₂²	1	1	yes	characteristic
116	#4018	C₂²	1	2	yes	complemented
117	C₄²×D₅	C₂²	1	2	yes	—
118	#4016	C₂²	1	2	yes	complemented
119	#4016	C₂²	1	2	yes	complemented
120	#4015	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₁₀	C₂²	1	2	yes	complemented
122	C₄×Dic₁₀	C₂²	1	1	yes	characteristic, 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×D₄	C₂³	1	1	yes	characteristic
127	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₅	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
131	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
132	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
133	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
134	C₂²×Dic₅	C₂³	1	1	yes	characteristic
135	Q₈×D₅	—	2	4	no	—
136	#709	—	2	4	no	—
137	C₂×D₂₀	C₂³	1	1	yes	characteristic
138	C₂×D₂₀	C₂³	1	1	yes	characteristic
139	C₂×C₄×D₅	—	2	4	no	—
140	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
153	C₂×Dic₁₀	C₂³	1	2	yes	—
154	C₂×Dic₁₀	C₂³	1	2	yes	—
155	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
156	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
157	C₅×C₄⋊C₄	C₂³	1	2	yes	—
158	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
159	C₅×C₄⋊C₄	C₂³	1	2	yes	—
160	C₅×C₄⋊C₄	C₂³	1	2	yes	—
161	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
162	C₅×C₄⋊C₄	C₂³	1	2	yes	—
163	C₅×C₄⋊C₄	C₂³	1	2	yes	—
164	C₅×C₄⋊C₄	C₂³	1	2	yes	—
165	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
166	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
167	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
169	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₄²×C₅	C₂³	1	2	yes	—
171	C₄²×C₅	C₂³	1	2	yes	—
172	C₄²×C₅	C₂³	1	1	yes	characteristic
173	C₂²⋊Dic₅	C₂³	1	2	yes	—
174	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
175	C₂²⋊Dic₅	C₂³	1	2	yes	—
176	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
177	C₂²⋊Dic₅	C₂³	1	2	yes	—
178	C₂²⋊Dic₅	C₂³	1	2	yes	—
179	#685	C₂³	1	1	yes	characteristic
180	#685	C₂³	1	2	yes	—
181	#685	C₂³	1	2	yes	—
182	#685	C₂³	1	1	yes	characteristic
183	#685	C₂³	1	1	yes	characteristic
184	#685	C₂³	1	2	yes	—
185	#685	C₂³	1	2	yes	—
186	#685	C₂³	1	2	yes	—
187	#685	C₂³	1	1	yes	characteristic
188	#685	C₂³	1	1	yes	characteristic
189	#685	C₂³	1	2	yes	—
190	#685	C₂³	1	1	yes	characteristic
191	#685	C₂³	1	2	yes	—
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	1	yes	characteristic
196	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
197	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
198	C₄⋊Dic₅	C₂³	1	2	yes	—
199	C₄⋊Dic₅	C₂³	1	2	yes	—
200	C₄⋊Dic₅	C₂³	1	2	yes	—
201	#683	C₂³	1	1	yes	characteristic
202	#683	C₂³	1	2	yes	—
203	#683	C₂³	1	2	yes	—
204	#683	C₂³	1	1	yes	characteristic
205	#683	C₂³	1	2	yes	—
206	#683	C₂³	1	2	yes	—
207	#683	C₂³	1	2	yes	—
208	#683	C₂³	1	2	yes	—
209	#683	C₂³	1	2	yes	—
210	#683	C₂³	1	2	yes	—
211	#683	C₂³	1	1	yes	characteristic
212	#683	C₂³	1	2	yes	—
213	#683	C₂³	1	2	yes	—
214	#683	C₂³	1	1	yes	characteristic
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	2	yes	—
221	C₄×Dic₅	C₂³	1	2	yes	—
222	C₄×Dic₅	C₂³	1	2	yes	—
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	1	no	—
227	#556	—	5	1	no	—
228	#554	—	5	1	no	—
229	#554	—	5	1	no	—
230	#552	—	5	2	no	—
231	#552	—	5	1	no	—
232	#552	—	5	1	no	—
233	#552	—	5	1	no	—
234	#552	—	5	2	no	—
235	#552	D₅	1	1	yes	characteristic, complemented
236	#551	—	5	2	no	—
237	#551	—	5	2	no	—
238	#544	—	5	1	no	—
239	#542	—	5	2	no	—
240	#541	—	5	2	no	—
241	#536	—	5	1	no	—
242	#533	—	5	2	no	—
243	#529	—	5	2	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	C₂³×C₅	C₂⁴	1	1	yes	characteristic
251	C₂²×D₅	—	2	2	no	—
252	C₂²×D₅	—	2	2	no	—
253	C₂²×D₅	—	4	1	no	—
254	C₂²×D₅	C₂⁴	1	1	yes	characteristic
255	C₂²×D₅	C₂⁴	1	1	yes	characteristic
256	C₂²×D₅	C₂⁴	1	1	yes	characteristic
257	C₅×Q₈	—	2	2	no	—
258	C₅×D₄	—	4	1	no	—
259	C₂×C₄×C₅	—	2	2	no	—
260	C₂×C₄×C₅	—	2	2	no	—
261	C₂×C₄×C₅	—	4	2	no	—
262	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
263	C₂×C₄×C₅	C₂⁴	1	2	yes	—
264	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
265	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
266	C₂×C₄×C₅	C₂⁴	1	2	yes	—
267	C₂×C₄×C₅	C₂⁴	1	2	yes	—
268	C₂×C₄×C₅	C₂⁴	1	2	yes	—
269	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
270	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
271	C₂²⋊D₅	—	2	2	no	—
272	C₂²⋊D₅	—	2	2	no	—
273	C₂²⋊D₅	—	2	2	no	—
274	C₂²⋊D₅	—	4	1	no	—
275	C₂×Dic₅	—	2	2	no	—
276	C₂×Dic₅	C₂⁴	1	2	yes	—
277	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
278	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
279	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
280	C₂×Dic₅	C₂⁴	1	2	yes	—
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	2	no	—
286	D₂₀	—	2	2	no	—
287	C₄×D₅	—	2	2	no	—
288	C₄×D₅	—	2	4	no	—
289	C₄×D₅	—	2	4	no	—
290	C₄×D₅	—	2	2	no	—
291	C₄×D₅	—	2	2	no	—
292	C₄×D₅	—	2	2	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	2	no	—
299	Dic₁₀	—	2	4	no	—
300	Dic₁₀	—	4	2	no	—
301	Dic₁₀	—	4	2	no	—
302	C₂×#41	—	5	1	no	—
303	C₂²×Q₈	—	5	1	no	—
304	C₂³×C₄	—	5	1	no	—
305	C₄⋊Q₈	—	5	2	no	—
306	C₄⋊Q₈	—	5	2	no	—
307	C₄⋊Q₈	—	5	1	no	—
308	C₄⋊Q₈	—	5	1	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	#126	C₂×D₅	1	2	yes	—
317	#125	—	5	2	no	—
318	#125	—	5	2	no	—
319	#125	—	5	2	no	—
320	#125	—	5	2	no	—
321	#125	—	5	1	no	—
322	#125	—	5	2	no	—
323	#125	—	5	2	no	—
324	#125	C₂×D₅	1	2	yes	complemented
325	#125	C₂×D₅	1	1	yes	characteristic, complemented
326	#124	—	5	2	no	—
327	#124	—	5	2	no	—
328	#124	—	5	2	no	—
329	#123	—	5	1	no	—
330	#123	—	5	2	no	—
331	#123	—	5	2	no	—
332	#123	—	5	1	no	—
333	#123	—	5	2	no	—
334	#123	—	5	2	no	—
335	#123	—	5	2	no	—
336	#123	C₂×D₅	1	2	yes	—
337	C₂²⋊Q₈	—	5	1	no	—
338	C₂²⋊Q₈	—	5	1	no	—
339	C₂²⋊Q₈	—	5	1	no	—
340	C₂²⋊Q₈	—	5	1	no	—
341	C₂²⋊Q₈	—	5	2	no	—
342	C₂²⋊Q₈	—	5	2	no	—
343	C₂²⋊Q₈	—	5	1	no	—
344	C₂²⋊Q₈	—	5	1	no	—
345	C₂²⋊Q₈	—	5	2	no	—
346	C₂²⋊Q₈	—	5	2	no	—
347	C₂²⋊Q₈	—	5	1	no	—
348	C₂²⋊Q₈	—	5	2	no	—
349	C₂²⋊Q₈	—	5	2	no	—
350	C₂²⋊Q₈	—	5	2	no	—
351	C₂²⋊Q₈	—	5	2	no	—
352	C₂²⋊Q₈	—	5	1	no	—
353	C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic
354	C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
355	#121	—	5	1	no	—
356	#121	—	5	1	no	—
357	#120	—	5	1	no	—
358	#120	—	5	1	no	—
359	C₄×Q₈	—	5	1	no	—
360	C₄×Q₈	—	5	2	no	—
361	C₄×Q₈	—	5	1	no	—
362	C₄×Q₈	—	5	2	no	—
363	C₄×Q₈	—	5	2	no	—
364	C₄×Q₈	—	5	2	no	—
365	C₄×Q₈	—	5	2	no	—
366	C₄×Q₈	—	5	1	no	—
367	C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
368	C₄×D₄	—	5	2	no	—
369	C₄×D₄	—	5	2	no	—
370	C₄×D₄	—	5	1	no	—
371	C₄×D₄	—	5	1	no	—
372	C₄×D₄	—	5	2	no	—
373	C₄×D₄	—	5	2	no	—
374	C₄×D₄	—	5	1	no	—
375	C₄×D₄	—	5	2	no	—
376	C₄×D₄	C₂×D₅	1	1	yes	characteristic
377	#117	—	5	1	no	—
378	#117	—	5	1	no	—
379	#117	—	5	1	no	—
380	#117	—	5	1	no	—
381	#117	—	5	2	no	—
382	#117	—	5	1	no	—
383	#117	—	5	2	no	—
384	#117	—	5	2	no	—
385	#117	—	5	2	no	—
386	#117	—	5	2	no	—
387	#117	—	5	1	no	—
388	#117	—	5	2	no	—
389	#117	—	5	2	no	—
390	#117	C₂×D₅	1	1	yes	characteristic
391	#117	C₂×D₅	1	2	yes	complemented
392	C₂×C₄⋊C₄	—	5	1	no	—
393	C₂×C₄⋊C₄	—	5	1	no	—
394	C₂×C₄⋊C₄	—	5	1	no	—
395	C₂×C₄⋊C₄	—	5	1	no	—
396	C₂×C₄⋊C₄	—	5	2	no	—
397	C₂×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
398	C₂×C₂²⋊C₄	—	5	2	no	—
399	C₂×C₂²⋊C₄	—	5	2	no	—
400	C₂×C₄²	—	5	2	no	—
401	C₂²×C₅	—	2	1	no	—
402	C₂²×C₅	—	2	1	no	—
403	C₂²×C₅	—	2	1	no	—
404	C₂²×C₅	—	2	1	no	—
405	C₂²×C₅	—	2	1	no	—
406	C₂²×C₅	—	2	1	no	—
407	C₂²×C₅	C₂⁵	1	1	yes	characteristic
408	C₂×D₅	—	2	1	no	—
409	C₂×D₅	—	2	1	no	—
410	C₂×D₅	—	2	1	no	—
411	C₂×D₅	—	2	1	no	—
412	C₂×D₅	—	2	1	no	—
413	C₂×D₅	—	2	1	no	—
414	C₂×D₅	—	2	1	no	—
415	C₂×D₅	—	4	4	no	—
416	C₂×D₅	C₂×#41	1	2	yes	—
417	C₂×D₅	2₋¹⁺⁴	1	2	yes	—
418	C₄×C₅	—	2	2	no	—
419	C₄×C₅	—	2	1	no	—
420	C₄×C₅	—	2	1	no	—
421	C₄×C₅	—	2	2	no	—
422	C₄×C₅	—	2	1	no	—
423	C₄×C₅	—	2	1	no	—
424	C₄×C₅	—	2	2	no	—
425	C₄×C₅	—	2	2	no	—
426	C₄×C₅	C₂×#41	1	2	yes	—
427	Dic₅	—	2	2	no	—
428	Dic₅	—	2	1	no	—
429	Dic₅	—	2	1	no	—
430	Dic₅	—	2	2	no	—
431	Dic₅	—	2	1	no	—
432	Dic₅	—	2	2	no	—
433	Dic₅	—	2	1	no	—
434	Dic₅	—	2	2	no	—
435	Dic₅	C₂×#41	1	2	yes	—
436	C₂⁴	—	5	1	no	—
437	#41	—	10	4	no	—
438	C₂×Q₈	—	5	1	no	—
439	C₂×Q₈	—	5	2	no	—
440	C₂×Q₈	—	5	1	no	—
441	C₂×Q₈	—	5	2	no	—
442	C₂×Q₈	—	5	2	no	—
443	C₂×Q₈	—	10	4	no	—
444	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
445	C₂×D₄	—	5	1	no	—
446	C₂×D₄	—	5	1	no	—
447	C₂×D₄	—	5	1	no	—
448	C₂×D₄	—	5	1	no	—
449	C₂×D₄	—	5	1	no	—
450	C₂×D₄	—	5	1	no	—
451	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
452	C₂²×C₄	—	5	1	no	—
453	C₂²×C₄	—	5	1	no	—
454	C₂²×C₄	—	5	1	no	—
455	C₂²×C₄	—	5	2	no	—
456	C₂²×C₄	—	5	2	no	—
457	C₂²×C₄	—	5	1	no	—
458	C₂²×C₄	—	5	1	no	—
459	C₂²×C₄	—	5	1	no	—
460	C₂²×C₄	—	5	2	no	—
461	C₂²×C₄	—	5	2	no	—
462	C₂²×C₄	—	5	2	no	—
463	C₂²×C₄	—	10	4	no	—
464	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
465	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
466	C₂²×C₄	C₂²×D₅	1	2	yes	—
467	C₄⋊C₄	—	5	1	no	—
468	C₄⋊C₄	—	5	1	no	—
469	C₄⋊C₄	—	5	2	no	—
470	C₄⋊C₄	—	5	1	no	—
471	C₄⋊C₄	—	5	2	no	—
472	C₄⋊C₄	—	5	2	no	—
473	C₄⋊C₄	—	5	2	no	—
474	C₄⋊C₄	—	5	2	no	—
475	C₄⋊C₄	—	5	2	no	—
476	C₄⋊C₄	—	5	2	no	—
477	C₄⋊C₄	—	5	1	no	—
478	C₄⋊C₄	—	5	1	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	1	no	—
486	C₄⋊C₄	—	5	1	no	—
487	C₄⋊C₄	—	5	1	no	—
488	C₄⋊C₄	—	5	2	no	—
489	C₄⋊C₄	—	5	2	no	—
490	C₄⋊C₄	—	5	2	no	—
491	C₄⋊C₄	—	5	2	no	—
492	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
493	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
494	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
495	C₄⋊C₄	C₂²×D₅	1	2	yes	—
496	C₄⋊C₄	C₂²×D₅	1	2	yes	—
497	C₄⋊C₄	C₂²×D₅	1	2	yes	—
498	C₄⋊C₄	C₂²×D₅	1	2	yes	—
499	C₄⋊C₄	C₂²×D₅	1	2	yes	—
500	C₄⋊C₄	C₂²×D₅	1	2	yes	—
501	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
502	C₂²⋊C₄	—	5	2	no	—
503	C₂²⋊C₄	—	5	2	no	—
504	C₂²⋊C₄	—	5	2	no	—
505	C₂²⋊C₄	—	5	1	no	—
506	C₂²⋊C₄	—	5	1	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	1	no	—
513	C₂²⋊C₄	—	5	1	no	—
514	C₂²⋊C₄	—	5	1	no	—
515	C₂²⋊C₄	—	5	1	no	—
516	C₂²⋊C₄	—	5	1	no	—
517	C₂²⋊C₄	—	5	2	no	—
518	C₂²⋊C₄	—	5	2	no	—
519	C₂²⋊C₄	—	5	1	no	—
520	C₂²⋊C₄	—	5	2	no	—
521	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
522	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
523	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
524	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
525	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
526	C₄²	—	5	2	no	—
527	C₄²	—	5	2	no	—
528	C₄²	—	5	2	no	—
529	C₄²	—	5	2	no	—
530	C₄²	—	5	2	no	—
531	C₄²	—	5	2	no	—
532	C₄²	—	5	2	no	—
533	C₄²	—	5	2	no	—
534	C₄²	—	5	1	no	—
535	C₄²	C₂²×D₅	1	2	yes	—
536	C₄²	C₂²×D₅	1	2	yes	—
537	C₄²	C₂²×D₅	1	1	yes	characteristic
538	C₂×C₅	—	4	1	no	—
539	C₂×C₅	—	4	1	no	—
540	C₂×C₅	C₂²×#41	1	1	yes	characteristic
541	C₂×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
542	C₂×C₅	#585	1	1	yes	characteristic
543	D₅	—	2	2	no	—
544	D₅	—	2	2	no	—
545	D₅	—	4	1	no	—
546	C₂³	—	5	1	no	—
547	C₂³	—	5	1	no	—
548	C₂³	—	5	1	no	—
549	C₂³	—	10	2	no	—
550	C₂³	—	10	2	no	—
551	C₂³	—	20	1	no	—
552	C₂³	C₂³×D₅	1	1	yes	characteristic
553	C₂³	C₂³×D₅	1	1	yes	characteristic
554	Q₈	—	2	2	no	—
555	Q₈	—	10	4	no	—
556	Q₈	—	10	2	no	—
557	Q₈	—	10	2	no	—
558	Q₈	—	20	2	no	—
559	Q₈	—	20	2	no	—
560	D₄	—	4	1	no	—
561	D₄	—	10	2	no	—
562	D₄	—	10	2	no	—
563	D₄	—	10	2	no	—
564	D₄	—	10	2	no	—
565	D₄	—	10	2	no	—
566	D₄	—	20	1	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	4	2	no	—
570	C₂×C₄	—	5	1	no	—
571	C₂×C₄	—	5	4	no	—
572	C₂×C₄	—	5	2	no	—
573	C₂×C₄	—	5	1	no	—
574	C₂×C₄	—	5	1	no	—
575	C₂×C₄	—	5	2	no	—
576	C₂×C₄	—	5	2	no	—
577	C₂×C₄	—	5	1	no	—
578	C₂×C₄	—	5	2	no	—
579	C₂×C₄	—	5	1	no	—
580	C₂×C₄	—	10	2	no	—
581	C₂×C₄	—	10	2	no	—
582	C₂×C₄	—	10	4	no	—
583	C₂×C₄	—	10	4	no	—
584	C₂×C₄	—	10	2	no	—
585	C₂×C₄	—	10	2	no	—
586	C₂×C₄	—	10	2	no	—
587	C₂×C₄	—	20	2	no	—
588	C₂×C₄	—	20	2	no	—
589	C₂×C₄	—	20	2	no	—
590	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
591	C₂×C₄	C₂³×D₅	1	2	yes	—
592	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
593	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
594	C₂×C₄	C₂³×D₅	1	2	yes	—
595	C₂×C₄	C₂³×D₅	1	2	yes	—
596	C₂×C₄	C₂³×D₅	1	2	yes	—
597	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
598	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
599	C₅	#3495	1	1	yes	characteristic, complemented, Sylow
600	C₂²	—	2	1	no	—
601	C₂²	—	2	1	no	—
602	C₂²	—	2	1	no	—
603	C₂²	—	2	1	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	5	2	no	—
607	C₂²	—	5	2	no	—
608	C₂²	—	10	1	no	—
609	C₂²	—	10	1	no	—
610	C₂²	—	10	1	no	—
611	C₂²	—	10	1	no	—
612	C₂²	—	10	1	no	—
613	C₂²	—	10	1	no	—
614	C₂²	—	10	1	no	—
615	C₂²	—	20	4	no	—
616	C₂²	C₂⁴×D₅	1	1	yes	characteristic
617	C₄	—	2	1	no	—
618	C₄	—	2	1	no	—
619	C₄	—	2	2	no	—
620	C₄	—	2	2	no	—
621	C₄	—	2	2	no	—
622	C₄	—	2	1	no	—
623	C₄	—	2	2	no	—
624	C₄	—	2	1	no	—
625	C₄	—	5	2	no	—
626	C₄	—	10	1	no	—
627	C₄	—	10	1	no	—
628	C₄	—	10	2	no	—
629	C₄	—	10	2	no	—
630	C₄	—	10	2	no	—
631	C₄	—	10	1	no	—
632	C₄	—	10	2	no	—
633	C₄	—	10	1	no	—
634	C₄	D₅×#41	1	2	yes	—
635	C₂	—	4	1	no	—
636	C₂	—	4	1	no	—
637	C₂	—	10	2	no	—
638	C₂	—	10	2	no	—
639	C₂	—	20	1	no	—
640	C₂	C₂×D₅×#41	1	1	yes	characteristic
641	C₂	#66283	1	1	yes	characteristic
642	C₂	D₅×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅
commutator, socle, cosocle	C₂²×C₅	C₂⁵
Fitting	C₅×#552	C₂
prime radical	#65881	C₂
hypercenter	#552	D₅
hypocenter	C₅	#3495
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ #552

Complements

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

N	H ≅ G/N	type
1. C₅×#552	C₂	semidirect
2. #66039	C₂	semidirect
3. #66035	C₂	semidirect
4. #66028	C₂	semidirect
5. #66027	C₂	semidirect
6. #66023	C₂	semidirect
7. #66022	C₂	semidirect
8. #65996	C₂	semidirect
9. #65993	C₂	semidirect
10. #65975	C₂	semidirect
11. #65973	C₂	semidirect
12. #65962	C₂	semidirect
13. D₅×C₂²⋊Q₈	C₂	semidirect
14. #65913	C₂	semidirect
15. #65906	C₂	semidirect
17. #65876	C₂	semidirect
18. #65863	C₂	semidirect
19. #65863	C₂	semidirect
20. #65862	C₂	semidirect
21. D₅×#117	C₂	semidirect
22. #65845	C₂	semidirect
23. #65838	C₂	semidirect
28. C₅×#125	C₂²	semidirect
29. C₅×#125	C₂²	semidirect
32. C₅×C₂²⋊Q₈	C₂²	semidirect
33. C₄×C₅×Q₈	C₂²	semidirect
36. C₅×#117	C₂²	semidirect
37. C₂×C₅×C₄⋊C₄	C₂²	semidirect
39. #4092	C₂²	semidirect
40. Q₈×Dic₅	C₂²	semidirect
48. C₄×C₂²⋊D₅	C₂²	semidirect
50. #4072	C₂²	semidirect
52. #4070	C₂²	semidirect
53. #4070	C₂²	semidirect
54. #4044	C₂²	semidirect
55. #4044	C₂²	semidirect
58. #4043	C₂²	semidirect
64. #4042	C₂²	semidirect
74. #4038	C₂²	semidirect
79. D₅×C₄⋊C₄	C₂²	semidirect
80. #4036	C₂²	semidirect
81. #4036	C₂²	semidirect
82. #4035	C₂²	semidirect
83. #4035	C₂²	semidirect
84. #4035	C₂²	semidirect
85. #4034	C₂²	semidirect
86. #4034	C₂²	semidirect
87. #4034	C₂²	semidirect
88. #4033	C₂²	semidirect
89. #4033	C₂²	semidirect
90. #4033	C₂²	semidirect
91. #4033	C₂²	semidirect
92. #4033	C₂²	semidirect
94. #4031	C₂²	semidirect
106. #4025	C₂²	semidirect
107. #4025	C₂²	semidirect
116. #4018	C₂²	semidirect
118. #4016	C₂²	semidirect
119. #4016	C₂²	semidirect
120. #4015	C₂²	semidirect
121. C₄×Dic₁₀	C₂²	semidirect
122. C₄×Dic₁₀	C₂²	semidirect
235. #552	D₅	semidirect
324. #125	C₂×D₅	semidirect
325. #125	C₂×D₅	semidirect
354. C₂²⋊Q₈	C₂×D₅	semidirect
367. C₄×Q₈	C₂×D₅	semidirect
391. #117	C₂×D₅	semidirect
397. C₂×C₄⋊C₄	C₂×D₅	semidirect
599. 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×#552	2
#66039	2
#66035	2
#66028	2
#66027	2
#66023	2
#66022	2
#65996	2
#65993	2
#65975	2
#65973	2
#65962	2
D₅×C₂²⋊Q₈	2
#65913	2
#65906	2
#65881	2
#65876	2
#65863	2
#65862	2
D₅×#117	2
#65845	2
#65838	2
#3495	5