Subgroups — #10618505

Order 640.

912 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#544	C₂	1	1	yes	maximal, characteristic, complemented
2	#66065	C₂	1	2	yes	maximal, complemented
3	#66064	C₂	1	1	yes	maximal, characteristic, complemented
4	#66063	C₂	1	1	yes	maximal, characteristic, complemented
5	#66063	C₂	1	2	yes	maximal, complemented
6	#66062	C₂	1	1	yes	maximal, characteristic, complemented
7	#66055	C₂	1	1	yes	maximal, characteristic, complemented
8	#66031	C₂	1	1	yes	maximal, characteristic, complemented
9	#66028	C₂	1	1	yes	maximal, characteristic, complemented
10	#66027	C₂	1	2	yes	maximal, complemented
11	D₅×#125	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅⋊#564	C₂	1	2	yes	maximal, complemented
13	#66019	C₂	1	1	yes	maximal, characteristic, complemented
14	#65980	C₂	1	2	yes	maximal, complemented
15	#65973	C₂	1	2	yes	maximal, complemented
16	#65972	C₂	1	2	yes	maximal
17	#65959	C₂	1	2	yes	maximal, complemented
18	#65863	C₂	1	1	yes	maximal, characteristic, complemented
19	#65863	C₂	1	1	yes	maximal, characteristic, complemented
20	#65862	C₂	1	1	yes	maximal, characteristic
21	#65852	C₂	1	1	yes	maximal, characteristic, complemented
22	#65847	C₂	1	1	yes	maximal, characteristic, complemented
23	#65845	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₅×C₄⋊Q₈	C₂²	1	2	yes	—
27	C₅×#125	C₂²	1	1	yes	characteristic
28	C₅×#125	C₂²	1	2	yes	—
29	C₅×#125	C₂²	1	1	yes	characteristic
30	C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
31	C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
32	C₅×#117	C₂²	1	1	yes	characteristic
33	C₅×#117	C₂²	1	1	yes	characteristic
34	C₂×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	#4092	C₂²	1	2	yes	—
36	#4092	C₂²	1	2	yes	—
37	#4092	C₂²	1	2	yes	—
38	#4092	C₂²	1	2	yes	—
39	Q₈×Dic₅	C₂²	1	2	yes	—
40	Q₈×Dic₅	C₂²	1	2	yes	—
41	#4090	C₂²	1	2	yes	—
42	#4090	C₂²	1	2	yes	—
43	#4075	C₂²	1	2	yes	—
44	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
45	C₄×C₂²⋊D₅	C₂²	1	2	yes	—
46	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
47	#4072	C₂²	1	2	yes	—
48	#4070	C₂²	1	1	yes	characteristic
49	#4070	C₂²	1	2	yes	—
50	#4070	C₂²	1	1	yes	characteristic
51	#4044	C₂²	1	1	yes	characteristic
52	#4044	C₂²	1	2	yes	—
53	#4044	C₂²	1	2	yes	—
54	#4044	C₂²	1	2	yes	—
55	#4044	C₂²	1	2	yes	—
56	#4043	C₂²	1	1	yes	characteristic
57	#4043	C₂²	1	1	yes	characteristic
58	#4043	C₂²	1	1	yes	characteristic
59	#4043	C₂²	1	1	yes	characteristic
60	#4042	C₂²	1	1	yes	characteristic
61	#4042	C₂²	1	2	yes	—
62	#4042	C₂²	1	2	yes	—
63	#4040	C₂²	1	1	yes	characteristic
64	#4040	C₂²	1	2	yes	—
65	#4039	C₂²	1	2	yes	—
66	#4038	C₂²	1	2	yes	—
67	#4038	C₂²	1	1	yes	characteristic
68	#4038	C₂²	1	2	yes	—
69	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
70	D₅×C₄⋊C₄	C₂²	1	2	yes	—
71	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
72	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
73	D₅×C₄⋊C₄	C₂²	1	2	yes	—
74	#4036	C₂²	1	1	yes	characteristic
75	#4036	C₂²	1	1	yes	characteristic
76	#4036	C₂²	1	2	yes	—
77	#4036	C₂²	1	2	yes	—
78	#4036	C₂²	1	2	yes	—
79	#4036	C₂²	1	1	yes	characteristic
80	#4036	C₂²	1	2	yes	—
81	#4036	C₂²	1	2	yes	—
82	#4035	C₂²	1	2	yes	—
83	#4035	C₂²	1	2	yes	—
84	#4035	C₂²	1	2	yes	—
85	#4035	C₂²	1	2	yes	—
86	#4035	C₂²	1	2	yes	—
87	#4035	C₂²	1	2	yes	—
88	#4035	C₂²	1	2	yes	—
89	#4035	C₂²	1	2	yes	—
90	#4035	C₂²	1	2	yes	—
91	#4035	C₂²	1	1	yes	characteristic
92	#4035	C₂²	1	2	yes	—
93	#4035	C₂²	1	2	yes	—
94	#4034	C₂²	1	1	yes	characteristic
95	#4034	C₂²	1	2	yes	—
96	#4033	C₂²	1	1	yes	characteristic
97	#4033	C₂²	1	1	yes	characteristic
98	#4033	C₂²	1	1	yes	characteristic
99	#4033	C₂²	1	1	yes	characteristic
100	#4033	C₂²	1	2	yes	—
101	#4031	C₂²	1	1	yes	characteristic
102	#4030	C₂²	1	1	yes	characteristic
103	#4029	C₂²	1	1	yes	characteristic
104	#4029	C₂²	1	2	yes	—
105	#4029	C₂²	1	2	yes	—
106	#4025	C₂²	1	2	yes	—
107	#4025	C₂²	1	2	yes	—
108	#4025	C₂²	1	1	yes	characteristic
109	#4025	C₂²	1	2	yes	—
110	#4025	C₂²	1	2	yes	—
111	C₄×D₂₀	C₂²	1	1	yes	characteristic
112	#4018	C₂²	1	1	yes	characteristic
113	#4018	C₂²	1	2	yes	—
114	#4018	C₂²	1	2	yes	—
115	C₄²×D₅	C₂²	1	1	yes	characteristic
116	#4016	C₂²	1	1	yes	characteristic
117	#4016	C₂²	1	2	yes	—
118	#4016	C₂²	1	2	yes	—
119	#4015	C₂²	1	1	yes	characteristic
120	C₄×Dic₁₀	C₂²	1	1	yes	characteristic
121	C₄×Dic₁₀	C₂²	1	1	yes	characteristic
122	C₄×Dic₁₀	C₂²	1	1	yes	characteristic
123	#3563	—	5	1	no	maximal, Sylow
124	C₂×C₅×Q₈	C₂³	1	2	yes	—
125	C₂×C₅×Q₈	C₂³	1	2	yes	—
126	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
127	C₂²×C₄×C₅	C₂³	1	2	yes	—
128	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
129	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
130	C₂×D₂₀	C₂³	1	1	yes	characteristic
131	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
132	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
133	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
134	C₂×C₄×D₅	C₂³	1	2	yes	—
135	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
136	C₂×C₄×D₅	C₂³	1	2	yes	—
137	C₂×C₄×D₅	C₂³	1	2	yes	—
138	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
139	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
140	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
141	C₂×Dic₁₀	C₂³	1	2	yes	—
142	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
143	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
144	C₅×C₄⋊C₄	C₂³	1	2	yes	—
145	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
146	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
147	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
148	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
149	C₅×C₄⋊C₄	C₂³	1	2	yes	—
150	C₅×C₄⋊C₄	C₂³	1	2	yes	—
151	C₅×C₄⋊C₄	C₂³	1	2	yes	—
152	C₅×C₄⋊C₄	C₂³	1	2	yes	—
153	C₅×C₄⋊C₄	C₂³	1	2	yes	—
154	C₅×C₄⋊C₄	C₂³	1	2	yes	—
155	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
156	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
157	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
158	C₄²×C₅	C₂³	1	1	yes	characteristic
159	C₄²×C₅	C₂³	1	1	yes	characteristic
160	C₄²×C₅	C₂³	1	2	yes	—
161	C₂²⋊Dic₅	C₂³	1	2	yes	—
162	C₂²⋊Dic₅	C₂³	1	2	yes	—
163	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
164	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
165	#685	C₂³	1	1	yes	characteristic
166	#685	C₂³	1	1	yes	characteristic
167	#685	C₂³	1	2	yes	—
168	#685	C₂³	1	2	yes	—
169	#685	C₂³	1	1	yes	characteristic
170	#685	C₂³	1	1	yes	characteristic
171	#685	C₂³	1	1	yes	characteristic
172	#685	C₂³	1	1	yes	characteristic
173	#685	C₂³	1	2	yes	—
174	#685	C₂³	1	2	yes	—
175	#685	C₂³	1	2	yes	—
176	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
177	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
178	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
179	C₄⋊Dic₅	C₂³	1	2	yes	—
180	C₄⋊Dic₅	C₂³	1	2	yes	—
181	C₄⋊Dic₅	C₂³	1	2	yes	—
182	C₄⋊Dic₅	C₂³	1	2	yes	—
183	C₄⋊Dic₅	C₂³	1	2	yes	—
184	C₄⋊Dic₅	C₂³	1	2	yes	—
185	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
186	C₄⋊Dic₅	C₂³	1	2	yes	—
187	C₄⋊Dic₅	C₂³	1	2	yes	—
188	C₄⋊Dic₅	C₂³	1	2	yes	—
189	#683	C₂³	1	1	yes	characteristic
190	#683	C₂³	1	2	yes	—
191	#683	C₂³	1	2	yes	—
192	#683	C₂³	1	1	yes	characteristic
193	#683	C₂³	1	1	yes	characteristic
194	#683	C₂³	1	1	yes	characteristic
195	#683	C₂³	1	2	yes	—
196	#683	C₂³	1	2	yes	—
197	#683	C₂³	1	2	yes	—
198	#683	C₂³	1	2	yes	—
199	#683	C₂³	1	2	yes	—
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	2	yes	—
205	#683	C₂³	1	1	yes	characteristic
206	#683	C₂³	1	1	yes	characteristic
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	2	yes	—
212	C₄×Dic₅	C₂³	1	1	yes	characteristic
213	C₄×Dic₅	C₂³	1	1	yes	characteristic
214	C₄×Dic₅	C₂³	1	2	yes	—
215	C₄×Dic₅	C₂³	1	2	yes	—
216	C₄×Dic₅	C₂³	1	1	yes	characteristic
217	C₄×Dic₅	C₂³	1	1	yes	characteristic
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	#564	—	5	2	no	—
224	#563	—	5	2	no	—
225	#557	—	5	1	no	—
226	#557	—	5	1	no	—
227	#554	—	5	1	no	—
228	#554	—	5	1	no	—
229	#552	—	5	2	no	—
230	#552	—	5	1	no	—
231	#552	—	5	2	no	—
232	#552	—	5	1	no	—
233	#552	—	5	1	no	—
234	#552	—	5	1	no	—
235	#544	—	5	2	no	—
236	#544	—	5	1	no	—
237	#544	D₅	1	1	yes	characteristic, complemented
238	#541	—	5	2	no	—
239	#541	—	5	1	no	—
240	#541	—	5	2	no	—
241	#541	—	5	1	no	—
242	#539	—	5	2	no	—
243	#533	—	5	1	no	—
244	#529	—	5	1	no	—
245	C₂×#125	—	5	1	no	—
246	C₂³×C₅	C₂⁴	1	1	yes	characteristic
247	C₂²×D₅	C₂⁴	1	1	yes	characteristic
248	C₂²×D₅	C₂⁴	1	1	yes	characteristic
249	C₅×Q₈	—	4	2	no	—
250	C₅×Q₈	—	4	2	no	—
251	C₂×C₄×C₅	—	2	2	no	—
252	C₂×C₄×C₅	—	4	2	no	—
253	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
255	C₂×C₄×C₅	C₂⁴	1	2	yes	—
256	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
257	C₂×C₄×C₅	C₂⁴	1	2	yes	—
258	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
259	C₂×C₄×C₅	C₂⁴	1	2	yes	—
260	C₂×C₄×C₅	C₂⁴	1	2	yes	—
261	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
262	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
263	C₂²⋊D₅	—	2	2	no	—
264	C₂²⋊D₅	—	4	1	no	—
265	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
266	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
267	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
268	C₂×Dic₅	C₂⁴	1	2	yes	—
269	C₂×Dic₅	C₂⁴	1	2	yes	—
270	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
271	C₂×Dic₅	C₂⁴	1	2	yes	—
272	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
273	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
274	C₂×Dic₅	C₂⁴	1	2	yes	—
275	D₂₀	—	2	2	no	—
276	C₄×D₅	—	2	2	no	—
277	C₄×D₅	—	2	4	no	—
278	C₄×D₅	—	2	2	no	—
279	C₄×D₅	—	2	2	no	—
280	C₄×D₅	—	4	2	no	—
281	C₄×D₅	—	4	2	no	—
282	C₄×D₅	—	4	1	no	—
283	Dic₁₀	—	2	2	no	—
284	Dic₁₀	—	2	2	no	—
285	Dic₁₀	—	4	2	no	—
286	Dic₁₀	—	4	1	no	—
287	C₄⋊Q₈	—	5	2	no	—
288	C₄⋊Q₈	—	5	2	no	—
289	C₄⋊Q₈	—	5	1	no	—
290	C₄⋊Q₈	—	5	2	no	—
291	C₄⋊Q₈	—	5	1	no	—
292	C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic
293	C₄⋊Q₈	C₂×D₅	1	2	yes	—
294	C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic
295	#126	—	5	1	no	—
296	#126	—	5	2	no	—
297	#126	—	5	2	no	—
298	#126	—	5	2	no	—
299	#126	—	5	2	no	—
300	#126	—	5	1	no	—
301	#126	—	5	2	no	—
302	#126	—	5	2	no	—
303	#126	—	5	2	no	—
304	#126	—	5	2	no	—
305	#125	—	5	2	no	—
306	#125	—	5	1	no	—
307	#125	—	5	1	no	—
308	#125	—	5	2	no	—
309	#125	—	5	1	no	—
310	#125	—	5	2	no	—
311	#125	—	5	2	no	—
312	#125	—	5	2	no	—
313	#125	—	5	2	no	—
314	#125	—	5	2	no	—
315	#125	—	5	2	no	—
316	#125	—	5	2	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	—	5	2	no	—
325	#125	—	5	1	no	—
326	#125	—	5	2	no	—
327	#125	—	5	2	no	—
328	#125	C₂×D₅	1	1	yes	characteristic
329	#125	C₂×D₅	1	1	yes	characteristic
330	#125	C₂×D₅	1	2	yes	—
331	#124	—	5	1	no	—
332	#123	—	5	2	no	—
333	#123	—	5	1	no	—
334	#123	—	5	2	no	—
335	#123	—	5	1	no	—
336	#123	—	5	2	no	—
337	#123	—	5	2	no	—
338	C₂²⋊Q₈	—	5	2	no	—
339	C₂²⋊Q₈	—	5	2	no	—
340	C₂²⋊Q₈	—	5	2	no	—
341	C₂²⋊Q₈	—	5	2	no	—
342	C₂²⋊Q₈	—	5	1	no	—
343	C₂²⋊Q₈	—	5	1	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	1	no	—
349	C₂²⋊Q₈	—	5	1	no	—
350	C₂²⋊Q₈	—	5	2	no	—
351	C₂²⋊Q₈	—	5	2	no	—
352	C₂²⋊Q₈	C₂×D₅	1	2	yes	—
353	C₂²⋊Q₈	C₂×D₅	1	2	yes	—
354	#121	—	5	1	no	—
355	C₄×Q₈	—	5	2	no	—
356	C₄×Q₈	—	5	2	no	—
357	C₄×Q₈	—	5	1	no	—
358	C₄×Q₈	—	5	1	no	—
359	C₄×Q₈	—	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×D₄	—	5	1	no	—
366	C₄×D₄	—	5	1	no	—
367	C₄×D₄	—	5	2	no	—
368	C₄×D₄	—	5	2	no	—
369	C₄×D₄	—	5	1	no	—
370	#117	—	5	2	no	—
371	#117	—	5	2	no	—
372	#117	—	5	1	no	—
373	#117	—	5	2	no	—
374	#117	—	5	1	no	—
375	#117	—	5	2	no	—
376	#117	—	5	2	no	—
377	#117	C₂×D₅	1	1	yes	characteristic
378	#117	C₂×D₅	1	1	yes	characteristic
379	C₂×C₄⋊C₄	—	5	2	no	—
380	C₂×C₄⋊C₄	—	5	1	no	—
381	C₂×C₄⋊C₄	—	5	2	no	—
382	C₂×C₄⋊C₄	—	5	1	no	—
383	C₂×C₄⋊C₄	—	5	1	no	—
384	C₂×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
385	C₂×C₄²	—	5	1	no	—
386	C₂²×C₅	—	2	1	no	—
387	C₂²×C₅	—	2	1	no	—
388	C₂²×C₅	—	2	1	no	—
389	C₂²×C₅	C₂⁵	1	1	yes	characteristic
390	C₂×D₅	—	2	1	no	—
391	C₂×D₅	—	2	1	no	—
392	C₂×D₅	—	2	1	no	—
393	C₂×D₅	—	2	1	no	—
394	C₂×D₅	—	2	1	no	—
395	C₂×D₅	2₋¹⁺⁴	1	2	yes	—
396	C₄×C₅	—	2	1	no	—
397	C₄×C₅	—	2	2	no	—
398	C₄×C₅	—	2	1	no	—
399	C₄×C₅	—	2	1	no	—
400	C₄×C₅	—	2	2	no	—
401	C₄×C₅	—	2	1	no	—
402	C₄×C₅	—	2	2	no	—
403	C₄×C₅	—	2	2	no	—
404	C₄×C₅	—	2	1	no	—
405	C₄×C₅	2₋¹⁺⁴	1	2	yes	—
406	Dic₅	—	2	2	no	—
407	Dic₅	—	2	2	no	—
408	Dic₅	—	2	1	no	—
409	Dic₅	—	2	1	no	—
410	Dic₅	—	2	1	no	—
411	Dic₅	—	2	2	no	—
412	Dic₅	—	2	1	no	—
413	Dic₅	—	2	1	no	—
414	Dic₅	—	2	2	no	—
415	Dic₅	—	2	1	no	—
416	C₂×Q₈	—	5	1	no	—
417	C₂×Q₈	—	5	1	no	—
418	C₂×Q₈	—	5	2	no	—
419	C₂×Q₈	—	5	1	no	—
420	C₂×Q₈	C₂²×D₅	1	2	yes	—
421	C₂×Q₈	C₂²×D₅	1	2	yes	—
422	C₂×D₄	—	5	1	no	—
423	C₂×D₄	—	5	1	no	—
424	C₂×D₄	—	5	1	no	—
425	C₂²×C₄	—	5	1	no	—
426	C₂²×C₄	—	5	1	no	—
427	C₂²×C₄	—	5	2	no	—
428	C₂²×C₄	—	5	1	no	—
429	C₂²×C₄	—	5	1	no	—
430	C₂²×C₄	—	5	2	no	—
431	C₂²×C₄	—	5	2	no	—
432	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
433	C₂²×C₄	C₂²×D₅	1	2	yes	—
434	C₄⋊C₄	—	5	1	no	—
435	C₄⋊C₄	—	5	1	no	—
436	C₄⋊C₄	—	5	2	no	—
437	C₄⋊C₄	—	5	2	no	—
438	C₄⋊C₄	—	5	2	no	—
439	C₄⋊C₄	—	5	2	no	—
440	C₄⋊C₄	—	5	2	no	—
441	C₄⋊C₄	—	5	2	no	—
442	C₄⋊C₄	—	5	2	no	—
443	C₄⋊C₄	—	5	2	no	—
444	C₄⋊C₄	—	5	2	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	1	no	—
450	C₄⋊C₄	—	5	2	no	—
451	C₄⋊C₄	—	5	1	no	—
452	C₄⋊C₄	—	5	2	no	—
453	C₄⋊C₄	—	5	1	no	—
454	C₄⋊C₄	—	5	2	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	2	no	—
461	C₄⋊C₄	—	5	2	no	—
462	C₄⋊C₄	—	5	2	no	—
463	C₄⋊C₄	—	5	2	no	—
464	C₄⋊C₄	—	5	2	no	—
465	C₄⋊C₄	—	5	2	no	—
466	C₄⋊C₄	—	5	2	no	—
467	C₄⋊C₄	—	5	2	no	—
468	C₄⋊C₄	—	5	2	no	—
469	C₄⋊C₄	—	5	2	no	—
470	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
471	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
472	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
473	C₄⋊C₄	C₂²×D₅	1	2	yes	—
474	C₄⋊C₄	C₂²×D₅	1	2	yes	—
475	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
476	C₄⋊C₄	C₂²×D₅	1	2	yes	—
477	C₄⋊C₄	C₂²×D₅	1	2	yes	—
478	C₄⋊C₄	C₂²×D₅	1	2	yes	—
479	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
480	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
481	C₄⋊C₄	C₂²×D₅	1	2	yes	—
482	C₄⋊C₄	C₂²×D₅	1	2	yes	—
483	C₂²⋊C₄	—	5	1	no	—
484	C₂²⋊C₄	—	5	2	no	—
485	C₂²⋊C₄	—	5	2	no	—
486	C₂²⋊C₄	—	5	1	no	—
487	C₂²⋊C₄	—	5	2	no	—
488	C₂²⋊C₄	—	5	2	no	—
489	C₂²⋊C₄	—	5	1	no	—
490	C₂²⋊C₄	—	5	1	no	—
491	C₂²⋊C₄	—	5	1	no	—
492	C₂²⋊C₄	—	5	1	no	—
493	C₂²⋊C₄	—	5	2	no	—
494	C₂²⋊C₄	—	5	1	no	—
495	C₂²⋊C₄	—	5	2	no	—
496	C₂²⋊C₄	—	5	2	no	—
497	C₂²⋊C₄	—	5	1	no	—
498	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
499	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
500	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
501	C₄²	—	5	1	no	—
502	C₄²	—	5	1	no	—
503	C₄²	—	5	1	no	—
504	C₄²	—	5	2	no	—
505	C₄²	—	5	2	no	—
506	C₄²	—	5	2	no	—
507	C₄²	—	5	1	no	—
508	C₄²	—	5	2	no	—
509	C₄²	—	5	2	no	—
510	C₄²	—	5	2	no	—
511	C₄²	—	5	2	no	—
512	C₄²	C₂²×D₅	1	1	yes	characteristic
513	C₄²	C₂²×D₅	1	2	yes	—
514	C₄²	C₂²×D₅	1	1	yes	characteristic
515	C₂×C₅	—	4	1	no	—
516	C₂×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
517	C₂×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
518	C₂×C₅	#585	1	1	yes	characteristic
519	D₅	—	2	2	no	—
520	D₅	—	4	1	no	—
521	C₂³	—	5	1	no	—
522	C₂³	—	5	1	no	—
523	C₂³	C₂³×D₅	1	1	yes	characteristic
524	Q₈	—	4	2	no	—
525	Q₈	—	4	2	no	—
526	Q₈	—	10	2	no	—
527	Q₈	—	10	2	no	—
528	Q₈	—	20	2	no	—
529	Q₈	—	20	1	no	—
530	D₄	—	10	2	no	—
531	D₄	—	10	2	no	—
532	D₄	—	20	1	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	5	1	no	—
536	C₂×C₄	—	5	2	no	—
537	C₂×C₄	—	5	2	no	—
538	C₂×C₄	—	5	1	no	—
539	C₂×C₄	—	5	1	no	—
540	C₂×C₄	—	5	1	no	—
541	C₂×C₄	—	5	1	no	—
542	C₂×C₄	—	5	2	no	—
543	C₂×C₄	—	5	1	no	—
544	C₂×C₄	—	5	2	no	—
545	C₂×C₄	—	10	2	no	—
546	C₂×C₄	—	10	4	no	—
547	C₂×C₄	—	10	2	no	—
548	C₂×C₄	—	10	2	no	—
549	C₂×C₄	—	20	2	no	—
550	C₂×C₄	—	20	2	no	—
551	C₂×C₄	—	20	1	no	—
552	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
553	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
554	C₂×C₄	C₂³×D₅	1	2	yes	—
555	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
556	C₂×C₄	C₂³×D₅	1	2	yes	—
557	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
558	C₂×C₄	C₂³×D₅	1	2	yes	—
559	C₂×C₄	C₂³×D₅	1	2	yes	—
560	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
561	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
562	C₅	#3563	1	1	yes	characteristic, complemented, Sylow
563	C₂²	—	2	1	no	—
564	C₂²	—	2	1	no	—
565	C₂²	—	2	1	no	—
566	C₂²	—	5	2	no	—
567	C₂²	—	10	1	no	—
568	C₂²	—	10	1	no	—
569	C₂²	—	10	1	no	—
570	C₂²	—	10	1	no	—
571	C₂²	—	10	1	no	—
572	C₂²	C₂⁴×D₅	1	1	yes	characteristic
573	C₄	—	2	1	no	—
574	C₄	—	2	2	no	—
575	C₄	—	2	2	no	—
576	C₄	—	2	2	no	—
577	C₄	—	2	1	no	—
578	C₄	—	2	1	no	—
579	C₄	—	2	1	no	—
580	C₄	—	2	2	no	—
581	C₄	—	2	1	no	—
582	C₄	—	10	1	no	—
583	C₄	—	10	1	no	—
584	C₄	—	10	2	no	—
585	C₄	—	10	2	no	—
586	C₄	—	10	2	no	—
587	C₄	—	10	1	no	—
588	C₄	—	10	1	no	—
589	C₄	—	10	1	no	—
590	C₄	—	10	2	no	—
591	C₄	—	10	1	no	—
592	C₄	#4147	1	2	yes	—
593	C₂	—	4	1	no	—
594	C₂	—	10	2	no	—
595	C₂	—	20	1	no	—
596	C₂	C₂×#4147	1	1	yes	characteristic
597	C₂	#66285	1	1	yes	characteristic
598	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×#544	C₂
prime radical	#4030	C₂²
hypercenter	#544	D₅
hypocenter	C₅	#3563
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ #544

Complements

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

N	H ≅ G/N	type
1. C₅×#544	C₂	semidirect
2. #66065	C₂	semidirect
3. #66064	C₂	semidirect
4. #66063	C₂	semidirect
5. #66063	C₂	semidirect
6. #66062	C₂	semidirect
7. #66055	C₂	semidirect
8. #66031	C₂	semidirect
9. #66028	C₂	semidirect
10. #66027	C₂	semidirect
11. D₅×#125	C₂	semidirect
12. C₅⋊#564	C₂	semidirect
13. #66019	C₂	semidirect
14. #65980	C₂	semidirect
15. #65973	C₂	semidirect
17. #65959	C₂	semidirect
18. #65863	C₂	semidirect
19. #65863	C₂	semidirect
21. #65852	C₂	semidirect
22. #65847	C₂	semidirect
23. #65845	C₂	semidirect
237. #544	D₅	semidirect
562. C₅	#3563	semidirect

Maximal subgroups

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

subgroup	index
C₅×#544	2
#66065	2
#66064	2
#66063	2
#66062	2
#66055	2
#66031	2
#66028	2
#66027	2
D₅×#125	2
C₅⋊#564	2
#66019	2
#65980	2
#65973	2
#65972	2
#65959	2
#65863	2
#65862	2
#65852	2
#65847	2
#65845	2
#3563	5