Subgroups — #10618898

Order 640.

930 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	#66066	C₂	1	1	yes	maximal, characteristic, complemented
3	#66065	C₂	1	1	yes	maximal, characteristic, complemented
4	#66046	C₂	1	2	yes	maximal, complemented
5	#66044	C₂	1	2	yes	maximal, complemented
6	#66042	C₂	1	2	yes	maximal, complemented
7	#66041	C₂	1	2	yes	maximal, complemented
8	#66016	C₂	1	1	yes	maximal, characteristic, complemented
9	#66015	C₂	1	1	yes	maximal, characteristic, complemented
10	#66015	C₂	1	1	yes	maximal, characteristic, complemented
11	#66014	C₂	1	1	yes	maximal, characteristic, complemented
12	#65980	C₂	1	2	yes	maximal, complemented
13	#65979	C₂	1	2	yes	maximal, complemented
14	#65916	C₂	1	1	yes	maximal, characteristic, complemented
15	#65914	C₂	1	1	yes	maximal, characteristic, complemented
16	#65913	C₂	1	1	yes	maximal, characteristic, complemented
17	#65912	C₂	1	1	yes	maximal, characteristic, complemented
18	#65904	C₂	1	1	yes	maximal, characteristic, complemented
19	#65903	C₂	1	1	yes	maximal, characteristic, complemented
20	#65896	C₂	1	1	yes	maximal, characteristic
21	#65873	C₂	1	1	yes	maximal, characteristic, complemented
22	#65868	C₂	1	2	yes	maximal, complemented
23	#65865	C₂	1	2	yes	maximal, complemented
24	C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₅×#126	C₂²	1	2	yes	—
26	C₅×#126	C₂²	1	2	yes	—
27	C₅×#124	C₂²	1	1	yes	characteristic
28	C₅×#124	C₂²	1	1	yes	characteristic
29	C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
30	C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
31	C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
32	C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
33	C₄×C₅×D₄	C₂²	1	1	yes	characteristic
34	C₅×#117	C₂²	1	2	yes	—
35	#4093	C₂²	1	1	yes	characteristic
36	#4093	C₂²	1	1	yes	characteristic
37	#4092	C₂²	1	1	yes	characteristic
38	#4092	C₂²	1	1	yes	characteristic
39	#4092	C₂²	1	1	yes	characteristic
40	#4092	C₂²	1	2	yes	—
41	Q₈×Dic₅	C₂²	1	1	yes	characteristic
42	Q₈×Dic₅	C₂²	1	1	yes	characteristic
43	Q₈×Dic₅	C₂²	1	1	yes	characteristic
44	Q₈×Dic₅	C₂²	1	1	yes	characteristic
45	#4090	C₂²	1	1	yes	characteristic
46	#4086	C₂²	1	1	yes	characteristic
47	#4084	C₂²	1	1	yes	characteristic
48	D₄×Dic₅	C₂²	1	1	yes	characteristic
49	D₄×Dic₅	C₂²	1	1	yes	characteristic
50	#4076	C₂²	1	2	yes	—
51	#4075	C₂²	1	2	yes	—
52	#4070	C₂²	1	2	yes	—
53	C₂×#683	C₂²	1	2	yes	—
54	#4044	C₂²	1	2	yes	—
55	#4044	C₂²	1	2	yes	—
56	#4044	C₂²	1	2	yes	—
57	#4044	C₂²	1	2	yes	—
58	#4044	C₂²	1	2	yes	—
59	#4043	C₂²	1	2	yes	—
60	#4043	C₂²	1	1	yes	characteristic
61	#4042	C₂²	1	2	yes	—
62	#4042	C₂²	1	1	yes	characteristic
63	#4042	C₂²	1	1	yes	characteristic
64	#4042	C₂²	1	2	yes	—
65	#4042	C₂²	1	2	yes	—
66	#4041	C₂²	1	1	yes	characteristic
67	#4040	C₂²	1	2	yes	—
68	#4040	C₂²	1	2	yes	—
69	#4038	C₂²	1	2	yes	—
70	D₅×C₄⋊C₄	C₂²	1	2	yes	—
71	#4036	C₂²	1	1	yes	characteristic
72	#4036	C₂²	1	1	yes	characteristic
73	#4036	C₂²	1	2	yes	—
74	#4036	C₂²	1	2	yes	—
75	#4036	C₂²	1	2	yes	—
76	#4035	C₂²	1	2	yes	—
77	#4035	C₂²	1	2	yes	—
78	#4035	C₂²	1	1	yes	characteristic
79	#4035	C₂²	1	1	yes	characteristic
80	#4034	C₂²	1	1	yes	characteristic
81	#4034	C₂²	1	2	yes	—
82	#4034	C₂²	1	1	yes	characteristic
83	#4032	C₂²	1	2	yes	—
84	#4032	C₂²	1	2	yes	—
85	#4032	C₂²	1	2	yes	—
86	#4031	C₂²	1	2	yes	—
87	#4031	C₂²	1	2	yes	—
88	#4031	C₂²	1	2	yes	—
89	#4030	C₂²	1	2	yes	—
90	#4029	C₂²	1	2	yes	—
91	#4029	C₂²	1	2	yes	—
92	#4029	C₂²	1	2	yes	—
93	#4029	C₂²	1	2	yes	—
94	#4027	C₂²	1	2	yes	—
95	#4027	C₂²	1	2	yes	—
96	#4027	C₂²	1	2	yes	—
97	#4025	C₂²	1	2	yes	—
98	#4025	C₂²	1	2	yes	—
99	#4024	C₂²	1	2	yes	—
100	#4024	C₂²	1	2	yes	—
101	#4024	C₂²	1	2	yes	—
102	#4023	C₂²	1	2	yes	—
103	#4022	C₂²	1	2	yes	—
104	#4021	C₂²	1	2	yes	—
105	C₄×D₂₀	C₂²	1	1	yes	characteristic
106	C₄×D₂₀	C₂²	1	2	yes	—
107	C₄×D₂₀	C₂²	1	1	yes	characteristic
108	C₄×D₂₀	C₂²	1	1	yes	characteristic
109	#4018	C₂²	1	1	yes	characteristic
110	#4018	C₂²	1	2	yes	—
111	#4018	C₂²	1	1	yes	characteristic
112	C₄²×D₅	C₂²	1	1	yes	characteristic
113	#4016	C₂²	1	1	yes	characteristic
114	#4016	C₂²	1	2	yes	—
115	#4016	C₂²	1	1	yes	characteristic
116	#4015	C₂²	1	2	yes	—
117	#4015	C₂²	1	1	yes	characteristic
118	C₄×Dic₁₀	C₂²	1	1	yes	characteristic
119	C₄×Dic₁₀	C₂²	1	2	yes	—
120	C₄×Dic₁₀	C₂²	1	2	yes	—
121	C₄×Dic₁₀	C₂²	1	1	yes	characteristic
122	C₄×Dic₁₀	C₂²	1	1	yes	characteristic
123	#3557	—	5	1	no	maximal, Sylow
124	C₂×C₅×Q₈	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×D₄	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₅	C₂³	1	2	yes	—
129	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
132	C₂²×Dic₅	C₂³	1	2	yes	—
133	C₂²×Dic₅	C₂³	1	2	yes	—
134	C₂×D₂₀	C₂³	1	1	yes	characteristic
135	C₂×D₂₀	C₂³	1	2	yes	—
136	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
137	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
138	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
139	C₂×C₄×D₅	C₂³	1	2	yes	—
140	C₂×C₄×D₅	C₂³	1	2	yes	—
141	C₂×C₄×D₅	C₂³	1	2	yes	—
142	C₂×Dic₁₀	C₂³	1	2	yes	—
143	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
144	C₂×Dic₁₀	C₂³	1	2	yes	—
145	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
146	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
147	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
148	C₅×C₄⋊C₄	C₂³	1	2	yes	—
149	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
150	C₅×C₄⋊C₄	C₂³	1	2	yes	—
151	C₅×C₄⋊C₄	C₂³	1	2	yes	—
152	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
153	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
154	C₅×C₄⋊C₄	C₂³	1	2	yes	—
155	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
156	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
157	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
158	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
159	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
160	C₄²×C₅	C₂³	1	2	yes	—
161	C₄²×C₅	C₂³	1	2	yes	—
162	C₄²×C₅	C₂³	1	1	yes	characteristic
163	C₄²×C₅	C₂³	1	1	yes	characteristic
164	C₄²×C₅	C₂³	1	1	yes	characteristic
165	C₂²⋊Dic₅	C₂³	1	2	yes	—
166	C₂²⋊Dic₅	C₂³	1	2	yes	—
167	C₂²⋊Dic₅	C₂³	1	2	yes	—
168	#685	C₂³	1	1	yes	characteristic
169	#685	C₂³	1	2	yes	—
170	#685	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	2	yes	—
175	#685	C₂³	1	2	yes	—
176	#685	C₂³	1	2	yes	—
177	#685	C₂³	1	2	yes	—
178	#685	C₂³	1	2	yes	—
179	#685	C₂³	1	2	yes	—
180	#685	C₂³	1	2	yes	—
181	#685	C₂³	1	2	yes	—
182	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
183	C₄⋊Dic₅	C₂³	1	2	yes	—
184	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
185	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
186	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
187	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
188	C₄⋊Dic₅	C₂³	1	2	yes	—
189	C₄⋊Dic₅	C₂³	1	2	yes	—
190	C₄⋊Dic₅	C₂³	1	2	yes	—
191	C₄⋊Dic₅	C₂³	1	2	yes	—
192	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
193	C₄⋊Dic₅	C₂³	1	2	yes	—
194	C₄⋊Dic₅	C₂³	1	2	yes	—
195	#683	C₂³	1	1	yes	characteristic
196	#683	C₂³	1	2	yes	—
197	#683	C₂³	1	1	yes	characteristic
198	#683	C₂³	1	2	yes	—
199	#683	C₂³	1	2	yes	—
200	#683	C₂³	1	1	yes	characteristic
201	#683	C₂³	1	1	yes	characteristic
202	#683	C₂³	1	1	yes	characteristic
203	#683	C₂³	1	1	yes	characteristic
204	#683	C₂³	1	2	yes	—
205	#683	C₂³	1	2	yes	—
206	#683	C₂³	1	2	yes	—
207	#683	C₂³	1	2	yes	—
208	#683	C₂³	1	1	yes	characteristic
209	#683	C₂³	1	2	yes	—
210	#683	C₂³	1	1	yes	characteristic
211	#683	C₂³	1	1	yes	characteristic
212	#683	C₂³	1	1	yes	characteristic
213	#683	C₂³	1	2	yes	—
214	C₄×Dic₅	C₂³	1	1	yes	characteristic
215	C₄×Dic₅	C₂³	1	1	yes	characteristic
216	C₄×Dic₅	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
222	C₄×Dic₅	C₂³	1	1	yes	characteristic
223	#563	—	5	2	no	—
224	#563	—	5	2	no	—
225	#559	—	5	1	no	—
226	#559	—	5	1	no	—
227	#557	—	5	1	no	—
228	#557	—	5	1	no	—
229	#556	—	5	1	no	—
230	#556	D₅	1	1	yes	characteristic, complemented
231	#554	—	5	1	no	—
232	#554	—	5	1	no	—
233	#552	—	5	2	no	—
234	#552	—	5	2	no	—
235	#542	—	5	2	no	—
236	#542	—	5	1	no	—
237	#542	—	5	1	no	—
238	#542	—	5	2	no	—
239	#541	—	5	1	no	—
240	#540	—	5	1	no	—
241	#539	—	5	2	no	—
242	#539	—	5	2	no	—
243	#533	—	5	1	no	—
244	#529	—	5	1	no	—
245	#529	—	5	1	no	—
246	C₂³×C₅	C₂⁴	1	2	yes	—
247	C₂²×D₅	C₂⁴	1	1	yes	characteristic
248	C₂²×D₅	C₂⁴	1	2	yes	—
249	C₅×Q₈	—	2	2	no	—
250	C₅×Q₈	—	2	2	no	—
251	C₅×Q₈	—	4	1	no	—
252	C₅×D₄	—	2	2	no	—
253	C₂×C₄×C₅	—	4	2	no	—
254	C₂×C₄×C₅	C₂⁴	1	2	yes	—
255	C₂×C₄×C₅	C₂⁴	1	2	yes	—
256	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
257	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
258	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
259	C₂×C₄×C₅	C₂⁴	1	2	yes	—
260	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
261	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
262	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
263	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
264	C₂²⋊D₅	—	4	2	no	—
265	C₂²⋊D₅	—	4	2	no	—
266	C₂²⋊D₅	—	4	2	no	—
267	C₂×Dic₅	—	4	2	no	—
268	C₂×Dic₅	—	4	2	no	—
269	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
270	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
271	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
272	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
273	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
274	C₂×Dic₅	C₂⁴	1	2	yes	—
275	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
276	C₂×Dic₅	C₂⁴	1	2	yes	—
277	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
278	C₂×Dic₅	C₂⁴	1	2	yes	—
279	D₂₀	—	2	2	no	—
280	D₂₀	—	4	2	no	—
281	C₄×D₅	—	2	2	no	—
282	C₄×D₅	—	4	1	no	—
283	C₄×D₅	—	4	2	no	—
284	C₄×D₅	—	4	2	no	—
285	C₄×D₅	—	4	2	no	—
286	C₄×D₅	—	4	1	no	—
287	Dic₁₀	—	4	2	no	—
288	Dic₁₀	—	4	1	no	—
289	Dic₁₀	—	4	1	no	—
290	Dic₁₀	—	4	1	no	—
291	Dic₁₀	—	4	2	no	—
292	C₄⋊Q₈	—	5	1	no	—
293	C₄⋊Q₈	—	5	1	no	—
294	C₄⋊Q₈	—	5	1	no	—
295	C₄⋊Q₈	—	5	2	no	—
296	C₄⋊Q₈	—	5	1	no	—
297	C₄⋊Q₈	—	5	2	no	—
298	C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic
299	#127	—	5	1	no	—
300	#126	—	5	2	no	—
301	#126	—	5	2	no	—
302	#126	—	5	2	no	—
303	#126	—	5	2	no	—
304	#126	—	5	2	no	—
305	#126	—	5	2	no	—
306	#126	—	5	2	no	—
307	#126	—	5	2	no	—
308	#126	C₂×D₅	1	2	yes	—
309	#126	C₂×D₅	1	2	yes	—
310	#125	—	5	1	no	—
311	#125	—	5	1	no	—
312	#125	—	5	1	no	—
313	#125	—	5	2	no	—
314	#125	—	5	2	no	—
315	#125	—	5	2	no	—
316	#125	—	5	1	no	—
317	#125	—	5	2	no	—
318	#125	—	5	2	no	—
319	#125	—	5	1	no	—
320	#125	—	5	2	no	—
321	#125	—	5	1	no	—
322	#124	—	5	1	no	—
323	#124	—	5	1	no	—
324	#124	—	5	2	no	—
325	#124	—	5	2	no	—
326	#124	—	5	2	no	—
327	#124	—	5	2	no	—
328	#124	C₂×D₅	1	1	yes	characteristic
329	#124	C₂×D₅	1	1	yes	characteristic
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	#123	—	5	2	no	—
337	#123	—	5	2	no	—
338	#123	—	5	2	no	—
339	#123	—	5	2	no	—
340	C₂²⋊Q₈	—	5	1	no	—
341	C₂²⋊Q₈	—	5	1	no	—
342	C₂²⋊Q₈	—	5	1	no	—
343	C₂²⋊Q₈	—	5	2	no	—
344	C₂²⋊Q₈	—	5	2	no	—
345	C₂²⋊Q₈	—	5	1	no	—
346	C₂²⋊Q₈	—	5	1	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	2	no	—
353	C₂²⋊Q₈	—	5	2	no	—
354	C₂²⋊Q₈	—	5	2	no	—
355	C₂²⋊Q₈	C₂×D₅	1	2	yes	—
356	#121	—	5	1	no	—
357	#121	—	5	2	no	—
358	#121	—	5	1	no	—
359	#121	—	5	2	no	—
360	C₄×Q₈	—	5	1	no	—
361	C₄×Q₈	—	5	1	no	—
362	C₄×Q₈	—	5	1	no	—
363	C₄×Q₈	—	5	1	no	—
364	C₄×Q₈	—	5	1	no	—
365	C₄×Q₈	—	5	1	no	—
366	C₄×Q₈	—	5	1	no	—
367	C₄×Q₈	—	5	2	no	—
368	C₄×Q₈	—	5	2	no	—
369	C₄×Q₈	C₂×D₅	1	1	yes	characteristic
370	C₄×Q₈	C₂×D₅	1	1	yes	characteristic
371	C₄×Q₈	C₂×D₅	1	1	yes	characteristic
372	C₄×D₄	—	5	1	no	—
373	C₄×D₄	—	5	1	no	—
374	C₄×D₄	—	5	2	no	—
375	C₄×D₄	—	5	2	no	—
376	C₄×D₄	—	5	2	no	—
377	C₄×D₄	—	5	2	no	—
378	C₄×D₄	—	5	1	no	—
379	C₄×D₄	—	5	1	no	—
380	C₄×D₄	—	5	1	no	—
381	C₄×D₄	C₂×D₅	1	1	yes	characteristic
382	#117	—	5	2	no	—
383	#117	—	5	2	no	—
384	#117	—	5	2	no	—
385	#117	—	5	1	no	—
386	#117	—	5	1	no	—
387	#117	C₂×D₅	1	2	yes	—
388	C₂×C₄⋊C₄	—	5	2	no	—
389	C₂×C₄⋊C₄	—	5	2	no	—
390	C₂×C₄²	—	5	1	no	—
391	C₂²×C₅	—	2	2	no	—
392	C₂²×C₅	—	2	2	no	—
393	C₂²×C₅	—	2	2	no	—
394	C₂²×C₅	C₂⁵	1	1	yes	characteristic
395	C₂×D₅	—	2	1	no	—
396	C₂×D₅	—	2	2	no	—
397	C₂×D₅	—	2	2	no	—
398	C₂×D₅	—	2	1	no	—
399	C₂×D₅	—	2	2	no	—
400	C₂×D₅	—	2	1	no	—
401	C₄×C₅	—	2	2	no	—
402	C₄×C₅	—	2	2	no	—
403	C₄×C₅	—	2	1	no	—
404	C₄×C₅	—	2	1	no	—
405	C₄×C₅	—	2	1	no	—
406	C₄×C₅	—	2	2	no	—
407	C₄×C₅	—	2	1	no	—
408	C₄×C₅	—	2	1	no	—
409	C₄×C₅	—	2	1	no	—
410	C₄×C₅	2₋¹⁺⁴	1	2	yes	—
411	Dic₅	—	2	1	no	—
412	Dic₅	—	2	1	no	—
413	Dic₅	—	2	1	no	—
414	Dic₅	—	2	2	no	—
415	Dic₅	—	2	2	no	—
416	Dic₅	—	2	2	no	—
417	Dic₅	—	2	1	no	—
418	Dic₅	—	2	1	no	—
419	Dic₅	—	2	1	no	—
420	Dic₅	—	2	1	no	—
421	C₂×Q₈	—	5	1	no	—
422	C₂×Q₈	—	5	2	no	—
423	C₂×Q₈	—	5	2	no	—
424	C₂×Q₈	—	5	1	no	—
425	C₂×Q₈	—	5	1	no	—
426	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
427	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
428	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
429	C₂×D₄	—	5	2	no	—
430	C₂×D₄	—	5	2	no	—
431	C₂×D₄	—	5	2	no	—
432	C₂×D₄	—	5	1	no	—
433	C₂×D₄	—	5	2	no	—
434	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
435	C₂²×C₄	—	5	2	no	—
436	C₂²×C₄	—	5	2	no	—
437	C₂²×C₄	—	5	1	no	—
438	C₂²×C₄	—	5	1	no	—
439	C₂²×C₄	—	5	1	no	—
440	C₂²×C₄	—	5	2	no	—
441	C₂²×C₄	—	5	2	no	—
442	C₂²×C₄	—	5	2	no	—
443	C₂²×C₄	C₂²×D₅	1	2	yes	—
444	C₄⋊C₄	—	5	1	no	—
445	C₄⋊C₄	—	5	2	no	—
446	C₄⋊C₄	—	5	2	no	—
447	C₄⋊C₄	—	5	2	no	—
448	C₄⋊C₄	—	5	2	no	—
449	C₄⋊C₄	—	5	2	no	—
450	C₄⋊C₄	—	5	2	no	—
451	C₄⋊C₄	—	5	1	no	—
452	C₄⋊C₄	—	5	2	no	—
453	C₄⋊C₄	—	5	2	no	—
454	C₄⋊C₄	—	5	1	no	—
455	C₄⋊C₄	—	5	1	no	—
456	C₄⋊C₄	—	5	1	no	—
457	C₄⋊C₄	—	5	1	no	—
458	C₄⋊C₄	—	5	1	no	—
459	C₄⋊C₄	—	5	1	no	—
460	C₄⋊C₄	—	5	1	no	—
461	C₄⋊C₄	—	5	1	no	—
462	C₄⋊C₄	—	5	1	no	—
463	C₄⋊C₄	—	5	2	no	—
464	C₄⋊C₄	—	5	2	no	—
465	C₄⋊C₄	—	5	1	no	—
466	C₄⋊C₄	—	5	1	no	—
467	C₄⋊C₄	—	5	2	no	—
468	C₄⋊C₄	—	5	2	no	—
469	C₄⋊C₄	—	5	1	no	—
470	C₄⋊C₄	—	5	2	no	—
471	C₄⋊C₄	—	5	1	no	—
472	C₄⋊C₄	—	5	1	no	—
473	C₄⋊C₄	—	5	2	no	—
474	C₄⋊C₄	—	5	2	no	—
475	C₄⋊C₄	—	5	2	no	—
476	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
477	C₄⋊C₄	C₂²×D₅	1	2	yes	—
478	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
479	C₄⋊C₄	C₂²×D₅	1	2	yes	—
480	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
481	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
482	C₄⋊C₄	C₂²×D₅	1	2	yes	—
483	C₄⋊C₄	C₂²×D₅	1	2	yes	—
484	C₂²⋊C₄	—	5	2	no	—
485	C₂²⋊C₄	—	5	2	no	—
486	C₂²⋊C₄	—	5	2	no	—
487	C₂²⋊C₄	—	5	2	no	—
488	C₂²⋊C₄	—	5	1	no	—
489	C₂²⋊C₄	—	5	1	no	—
490	C₂²⋊C₄	—	5	2	no	—
491	C₂²⋊C₄	—	5	1	no	—
492	C₂²⋊C₄	—	5	1	no	—
493	C₂²⋊C₄	—	5	2	no	—
494	C₂²⋊C₄	—	5	2	no	—
495	C₂²⋊C₄	—	5	2	no	—
496	C₂²⋊C₄	—	5	2	no	—
497	C₂²⋊C₄	—	5	2	no	—
498	C₂²⋊C₄	—	5	2	no	—
499	C₂²⋊C₄	—	5	2	no	—
500	C₂²⋊C₄	—	5	2	no	—
501	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
502	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
503	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
504	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
505	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
506	C₄²	—	5	1	no	—
507	C₄²	—	5	1	no	—
508	C₄²	—	5	1	no	—
509	C₄²	—	5	2	no	—
510	C₄²	—	5	1	no	—
511	C₄²	—	5	1	no	—
512	C₄²	—	5	2	no	—
513	C₄²	—	5	2	no	—
514	C₄²	—	5	2	no	—
515	C₄²	C₂²×D₅	1	1	yes	characteristic
516	C₄²	C₂²×D₅	1	2	yes	—
517	C₄²	C₂²×D₅	1	1	yes	characteristic
518	C₄²	C₂²×D₅	1	1	yes	characteristic
519	C₄²	C₂²×D₅	1	2	yes	—
520	C₂×C₅	—	4	2	no	—
521	C₂×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
522	C₂×C₅	#585	1	1	yes	characteristic
523	C₂×C₅	#585	1	1	yes	characteristic
524	D₅	—	4	1	no	—
525	D₅	—	4	2	no	—
526	C₂³	—	5	1	no	—
527	C₂³	—	5	2	no	—
528	C₂³	C₂³×D₅	1	2	yes	—
529	Q₈	—	2	2	no	—
530	Q₈	—	2	2	no	—
531	Q₈	—	4	1	no	—
532	Q₈	—	20	2	no	—
533	Q₈	—	20	1	no	—
534	Q₈	—	20	1	no	—
535	Q₈	—	20	2	no	—
536	Q₈	—	20	1	no	—
537	D₄	—	2	2	no	—
538	D₄	—	10	2	no	—
539	D₄	—	20	2	no	—
540	D₄	—	20	2	no	—
541	D₄	—	20	2	no	—
542	D₄	—	20	2	no	—
543	C₂×C₄	—	4	2	no	—
544	C₂×C₄	—	5	1	no	—
545	C₂×C₄	—	5	1	no	—
546	C₂×C₄	—	5	1	no	—
547	C₂×C₄	—	5	1	no	—
548	C₂×C₄	—	5	1	no	—
549	C₂×C₄	—	5	1	no	—
550	C₂×C₄	—	5	2	no	—
551	C₂×C₄	—	5	2	no	—
552	C₂×C₄	—	5	1	no	—
553	C₂×C₄	—	5	2	no	—
554	C₂×C₄	—	10	2	no	—
555	C₂×C₄	—	20	2	no	—
556	C₂×C₄	—	20	1	no	—
557	C₂×C₄	—	20	2	no	—
558	C₂×C₄	—	20	1	no	—
559	C₂×C₄	—	20	2	no	—
560	C₂×C₄	—	20	2	no	—
561	C₂×C₄	—	20	2	no	—
562	C₂×C₄	C₂³×D₅	1	2	yes	—
563	C₂×C₄	C₂³×D₅	1	2	yes	—
564	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
565	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
566	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
567	C₂×C₄	C₂³×D₅	1	2	yes	—
568	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
569	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
570	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
571	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
572	C₅	#3557	1	1	yes	characteristic, complemented, Sylow
573	C₂²	—	2	2	no	—
574	C₂²	—	2	2	no	—
575	C₂²	—	2	2	no	—
576	C₂²	—	10	1	no	—
577	C₂²	—	10	2	no	—
578	C₂²	—	10	1	no	—
579	C₂²	—	10	2	no	—
580	C₂²	—	10	2	no	—
581	C₂²	—	10	1	no	—
582	C₂²	C₂⁴×D₅	1	1	yes	characteristic
583	C₄	—	2	2	no	—
584	C₄	—	2	2	no	—
585	C₄	—	2	1	no	—
586	C₄	—	2	2	no	—
587	C₄	—	2	1	no	—
588	C₄	—	2	1	no	—
589	C₄	—	2	1	no	—
590	C₄	—	2	1	no	—
591	C₄	—	2	1	no	—
592	C₄	—	10	1	no	—
593	C₄	—	10	1	no	—
594	C₄	—	10	2	no	—
595	C₄	—	10	1	no	—
596	C₄	—	10	1	no	—
597	C₄	—	10	2	no	—
598	C₄	—	10	1	no	—
599	C₄	—	10	2	no	—
600	C₄	—	10	1	no	—
601	C₄	—	10	1	no	—
602	C₄	#4150	1	2	yes	—
603	C₂	—	4	2	no	—
604	C₂	—	20	1	no	—
605	C₂	—	20	2	no	—
606	C₂	C₂×#4150	1	1	yes	characteristic
607	C₂	#66283	1	1	yes	characteristic
608	C₂	#66287	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅
commutator, socle, cosocle	C₂²×C₅	C₂⁵
Fitting	C₅×#556	C₂
prime radical	#65896	C₂
hypercenter	#556	D₅
hypocenter	C₅	#3557
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ #556

Complements

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

N	H ≅ G/N	type
1. C₅×#556	C₂	semidirect
2. #66066	C₂	semidirect
3. #66065	C₂	semidirect
4. #66046	C₂	semidirect
5. #66044	C₂	semidirect
6. #66042	C₂	semidirect
7. #66041	C₂	semidirect
8. #66016	C₂	semidirect
9. #66015	C₂	semidirect
10. #66015	C₂	semidirect
11. #66014	C₂	semidirect
12. #65980	C₂	semidirect
13. #65979	C₂	semidirect
14. #65916	C₂	semidirect
15. #65914	C₂	semidirect
16. #65913	C₂	semidirect
17. #65912	C₂	semidirect
18. #65904	C₂	semidirect
19. #65903	C₂	semidirect
21. #65873	C₂	semidirect
22. #65868	C₂	semidirect
23. #65865	C₂	semidirect
230. #556	D₅	semidirect
572. C₅	#3557	semidirect

Maximal subgroups

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

subgroup	index
C₅×#556	2
#66066	2
#66065	2
#66046	2
#66044	2
#66042	2
#66041	2
#66016	2
#66015	2
#66014	2
#65980	2
#65979	2
#65916	2
#65914	2
#65913	2
#65912	2
#65904	2
#65903	2
#65896	2
#65873	2
#65868	2
#65865	2
#3557	5