Subgroups — #10618074

Order 640.

1060 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	#66044	C₂	1	2	yes	maximal, complemented
3	#66038	C₂	1	2	yes	maximal, complemented
4	#66034	C₂	1	1	yes	maximal, characteristic, complemented
5	#66033	C₂	1	1	yes	maximal, characteristic, complemented
6	#66018	C₂	1	1	yes	maximal, characteristic, complemented
7	#66017	C₂	1	1	yes	maximal, characteristic, complemented
8	#65987	C₂	1	2	yes	maximal, complemented
9	#65982	C₂	1	2	yes	maximal, complemented
10	#65971	C₂	1	2	yes	maximal, complemented
11	#65944	C₂	1	2	yes	maximal, complemented
12	#65916	C₂	1	2	yes	maximal, complemented
13	#65894	C₂	1	2	yes	maximal, complemented
14	#65890	C₂	1	2	yes	maximal, complemented
15	#65888	C₂	1	2	yes	maximal, complemented
16	#65866	C₂	1	2	yes	maximal, complemented
17	#65861	C₂	1	2	yes	maximal, complemented
18	#65813	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#4021	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#711	C₂²	1	2	yes	—
21	C₂×D₄×D₅	C₂²	1	2	yes	complemented
22	C₂²×D₂₀	C₂²	1	1	yes	characteristic
23	C₂²×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
24	C₅×#126	C₂²	1	2	yes	complemented
25	C₅×#125	C₂²	1	1	yes	characteristic, complemented
26	C₅×#124	C₂²	1	1	yes	characteristic, complemented
27	C₅×#123	C₂²	1	2	yes	complemented
28	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₅×#121	C₂²	1	1	yes	characteristic
30	C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₄×C₅×D₄	C₂²	1	2	yes	complemented
32	C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
33	C₅×#117	C₂²	1	2	yes	complemented
34	C₂×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
35	#4093	C₂²	1	2	yes	complemented
36	#4092	C₂²	1	2	yes	complemented
37	#4085	C₂²	1	2	yes	complemented
38	#4083	C₂²	1	2	yes	—
39	#4083	C₂²	1	2	yes	complemented
40	#4081	C₂²	1	2	yes	complemented
41	#4076	C₂²	1	1	yes	characteristic
42	#4076	C₂²	1	2	yes	complemented
43	#4075	C₂²	1	2	yes	complemented
44	#4075	C₂²	1	2	yes	complemented
45	C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
46	C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
47	C₂×#685	C₂²	1	2	yes	complemented
48	C₂×#685	C₂²	1	2	yes	complemented
49	C₂×#685	C₂²	1	2	yes	complemented
50	#4070	C₂²	1	1	yes	characteristic, complemented
51	#4044	C₂²	1	2	yes	complemented
52	#4044	C₂²	1	2	yes	complemented
53	#4044	C₂²	1	2	yes	complemented
54	#4043	C₂²	1	2	yes	complemented
55	#4042	C₂²	1	2	yes	complemented
56	#4042	C₂²	1	2	yes	complemented
57	#4042	C₂²	1	2	yes	complemented
58	#4042	C₂²	1	2	yes	complemented
59	#4041	C₂²	1	2	yes	—
60	#4041	C₂²	1	2	yes	complemented
61	#4041	C₂²	1	2	yes	complemented
62	#4040	C₂²	1	2	yes	—
63	#4040	C₂²	1	2	yes	complemented
64	#4040	C₂²	1	2	yes	complemented
65	#4040	C₂²	1	2	yes	complemented
66	#4040	C₂²	1	2	yes	complemented
67	#4039	C₂²	1	2	yes	complemented
68	#4038	C₂²	1	2	yes	complemented
69	#4034	C₂²	1	2	yes	complemented
70	#4034	C₂²	1	2	yes	complemented
71	#4032	C₂²	1	2	yes	complemented
72	#4032	C₂²	1	2	yes	complemented
73	#4031	C₂²	1	2	yes	complemented
74	#4031	C₂²	1	2	yes	complemented
75	#4031	C₂²	1	2	yes	complemented
76	#4031	C₂²	1	2	yes	complemented
77	#4030	C₂²	1	2	yes	—
78	#4030	C₂²	1	2	yes	complemented
79	#4030	C₂²	1	2	yes	complemented
80	#4029	C₂²	1	2	yes	complemented
81	#4028	C₂²	1	2	yes	—
82	#4028	C₂²	1	2	yes	—
83	#4028	C₂²	1	2	yes	complemented
84	#4028	C₂²	1	2	yes	complemented
85	#4027	C₂²	1	2	yes	complemented
86	D₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
87	D₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
88	#4024	C₂²	1	2	yes	complemented
89	#4024	C₂²	1	2	yes	complemented
90	#4023	C₂²	1	2	yes	complemented
91	#4022	C₂²	1	2	yes	complemented
92	#4022	C₂²	1	2	yes	complemented
93	#4021	C₂²	1	1	yes	characteristic
94	#4021	C₂²	1	1	yes	characteristic
95	#4021	C₂²	1	1	yes	characteristic, complemented
96	#4021	C₂²	1	2	yes	complemented
97	#4021	C₂²	1	1	yes	characteristic, complemented
98	#4021	C₂²	1	2	yes	complemented
99	#4021	C₂²	1	1	yes	characteristic, complemented
100	#4021	C₂²	1	2	yes	complemented
101	C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
102	C₄×D₂₀	C₂²	1	2	yes	complemented
103	#4018	C₂²	1	2	yes	complemented
104	#4018	C₂²	1	2	yes	complemented
105	#4016	C₂²	1	1	yes	characteristic, complemented
106	C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
107	#3545	—	5	1	no	maximal, Sylow
108	C₂³×D₅	C₂³	1	2	yes	—
109	C₂³×D₅	C₂³	1	2	yes	—
110	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
111	C₂×C₅×D₄	C₂³	1	2	yes	—
112	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
113	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
114	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
115	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
116	C₂²×C₄×C₅	C₂³	1	2	yes	—
117	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
118	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
119	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
120	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
121	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
122	C₂²×Dic₅	C₂³	1	2	yes	—
123	C₂²×Dic₅	C₂³	1	2	yes	—
124	#711	—	4	4	no	—
125	D₄×D₅	—	4	4	no	—
126	C₂×D₂₀	—	4	2	no	—
127	C₂×D₂₀	C₂³	1	1	yes	characteristic
128	C₂×D₂₀	C₂³	1	2	yes	—
129	C₂×D₂₀	C₂³	1	1	yes	characteristic
130	C₂×D₂₀	C₂³	1	2	yes	—
131	C₂×D₂₀	C₂³	1	1	yes	characteristic
132	C₂×D₂₀	C₂³	1	2	yes	—
133	C₂×D₂₀	C₂³	1	2	yes	—
134	C₂×C₄×D₅	C₂³	1	2	yes	—
135	C₂×C₄×D₅	C₂³	1	2	yes	—
136	C₂×C₄×D₅	C₂³	1	2	yes	—
137	C₂×C₄×D₅	C₂³	1	2	yes	—
138	C₂×C₄×D₅	C₂³	1	2	yes	—
139	C₂×Dic₁₀	—	4	2	no	—
140	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
141	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
142	C₂×Dic₁₀	C₂³	1	2	yes	—
143	C₂×Dic₁₀	C₂³	1	2	yes	—
144	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
145	C₅×C₄⋊C₄	C₂³	1	2	yes	—
146	C₅×C₄⋊C₄	C₂³	1	2	yes	—
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×C₂²⋊C₄	C₂³	1	2	yes	—
152	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
153	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
154	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
155	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
156	C₄²×C₅	C₂³	1	1	yes	characteristic
157	C₄²×C₅	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	2	yes	—
164	#685	C₂³	1	2	yes	—
165	#685	C₂³	1	2	yes	—
166	#685	C₂³	1	2	yes	—
167	#685	C₂³	1	2	yes	—
168	#685	C₂³	1	2	yes	—
169	#685	C₂³	1	2	yes	—
170	#685	C₂³	1	2	yes	—
171	#685	C₂³	1	2	yes	—
172	#685	C₂³	1	2	yes	—
173	#685	C₂³	1	2	yes	—
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	#685	C₂³	1	2	yes	—
183	#685	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	2	yes	—
187	C₄⋊Dic₅	C₂³	1	2	yes	—
188	#683	C₂³	1	2	yes	—
189	#683	C₂³	1	2	yes	—
190	#683	C₂³	1	2	yes	—
191	#683	C₂³	1	2	yes	—
192	#683	C₂³	1	2	yes	—
193	#683	C₂³	1	2	yes	—
194	#683	C₂³	1	2	yes	—
195	#683	C₂³	1	2	yes	—
196	C₄×Dic₅	C₂³	1	2	yes	—
197	C₄×Dic₅	C₂³	1	2	yes	—
198	C₄×Dic₅	C₂³	1	2	yes	—
199	#563	—	5	1	no	—
200	#562	—	5	1	no	—
201	#562	—	5	1	no	—
202	H(3,𝔽₄)	—	5	1	no	—
203	#555	—	5	2	no	—
204	#551	—	5	2	no	—
205	#551	—	5	2	no	—
206	#551	—	5	2	no	—
207	#546	—	5	2	no	—
208	#546	—	5	2	no	—
209	#542	—	5	2	no	—
210	#542	—	5	2	no	—
211	#538	—	5	2	no	—
212	#538	—	5	2	no	—
213	#536	—	5	2	no	—
214	#534	—	5	2	no	—
215	#529	—	5	1	no	—
216	#529	D₅	1	1	yes	characteristic, complemented
217	C₂×#124	—	5	1	no	—
218	C₂³×C₅	C₂⁴	1	2	yes	—
219	C₂³×C₅	C₂⁴	1	1	yes	characteristic
220	C₂²×D₅	—	2	4	no	—
221	C₂²×D₅	—	4	2	no	—
222	C₂²×D₅	—	4	2	no	—
223	C₂²×D₅	—	4	2	no	—
224	C₂²×D₅	—	4	2	no	—
225	C₂²×D₅	—	4	2	no	—
226	C₂²×D₅	C₂⁴	1	2	yes	—
227	C₂²×D₅	C₂⁴	1	2	yes	—
228	C₂²×D₅	C₂⁴	1	2	yes	—
229	C₅×Q₈	—	4	1	no	—
230	C₅×D₄	—	2	4	no	—
231	C₅×D₄	—	4	1	no	—
232	C₂×C₄×C₅	—	2	2	no	—
233	C₂×C₄×C₅	—	4	1	no	—
234	C₂×C₄×C₅	—	4	1	no	—
235	C₂×C₄×C₅	—	4	2	no	—
236	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
237	C₂×C₄×C₅	C₂⁴	1	2	yes	—
238	C₂×C₄×C₅	C₂⁴	1	2	yes	—
239	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
240	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
241	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
242	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
243	C₂×C₄×C₅	C₂⁴	1	2	yes	—
244	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
245	C₂²⋊D₅	—	2	4	no	—
246	C₂²⋊D₅	—	4	2	no	—
247	C₂²⋊D₅	—	4	2	no	—
248	C₂²⋊D₅	—	4	2	no	—
249	C₂²⋊D₅	—	4	2	no	—
250	C₂×Dic₅	—	2	4	no	—
251	C₂×Dic₅	—	4	2	no	—
252	C₂×Dic₅	C₂⁴	1	2	yes	—
253	C₂×Dic₅	C₂⁴	1	2	yes	—
254	C₂×Dic₅	C₂⁴	1	2	yes	—
255	C₂×Dic₅	C₂⁴	1	2	yes	—
256	C₂×Dic₅	C₂⁴	1	2	yes	—
257	D₂₀	—	4	1	no	—
258	D₂₀	—	4	2	no	—
259	D₂₀	—	4	1	no	—
260	D₂₀	—	4	1	no	—
261	D₂₀	—	4	2	no	—
262	D₂₀	—	4	2	no	—
263	D₂₀	—	4	2	no	—
264	C₄×D₅	—	4	2	no	—
265	C₄×D₅	—	4	2	no	—
266	C₄×D₅	—	4	2	no	—
267	C₄×D₅	—	4	2	no	—
268	C₄×D₅	—	4	2	no	—
269	Dic₁₀	—	4	1	no	—
270	Dic₁₀	—	4	2	no	—
271	Dic₁₀	—	4	1	no	—
272	Dic₁₀	—	4	1	no	—
273	Dic₁₀	—	4	2	no	—
274	C₂×#41	—	5	2	no	—
275	C₂²×Q₈	—	5	1	no	—
276	C₂²×D₄	—	5	2	no	—
277	C₂²×D₄	—	5	1	no	—
278	C₄⋊Q₈	—	5	2	no	—
279	C₄⋊Q₈	—	5	2	no	—
280	#126	—	5	2	no	—
281	#126	—	5	2	no	—
282	#126	—	5	2	no	—
283	#126	—	5	2	no	—
284	#126	—	5	2	no	—
285	#126	C₂×D₅	1	2	yes	complemented
286	#125	—	5	1	no	—
287	#125	C₂×D₅	1	1	yes	characteristic, complemented
288	#124	—	5	2	no	—
289	#124	—	5	2	no	—
290	#124	—	5	2	no	—
291	#124	—	5	2	no	—
292	#124	—	5	2	no	—
293	#124	—	5	2	no	—
294	#124	—	5	2	no	—
295	#124	—	5	1	no	—
296	#124	—	5	1	no	—
297	#124	—	5	1	no	—
298	#124	—	5	1	no	—
299	#124	—	5	1	no	—
300	#124	—	5	2	no	—
301	#124	C₂×D₅	1	1	yes	characteristic, complemented
302	#123	—	5	2	no	—
303	#123	—	5	2	no	—
304	#123	—	5	2	no	—
305	#123	—	5	2	no	—
306	#123	—	5	2	no	—
307	#123	—	5	2	no	—
308	#123	—	5	2	no	—
309	#123	—	5	2	no	—
310	#123	—	5	2	no	—
311	#123	—	5	2	no	—
312	#123	—	5	2	no	—
313	#123	C₂×D₅	1	2	yes	complemented
314	C₂²⋊Q₈	—	5	2	no	—
315	C₂²⋊Q₈	—	5	1	no	—
316	C₂²⋊Q₈	—	5	2	no	—
317	C₂²⋊Q₈	—	5	2	no	—
318	C₂²⋊Q₈	—	5	2	no	—
319	C₂²⋊Q₈	—	5	2	no	—
320	C₂²⋊Q₈	—	5	2	no	—
321	C₂²⋊Q₈	—	5	2	no	—
322	C₂²⋊Q₈	—	5	2	no	—
323	C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
324	#121	—	5	2	no	—
325	#121	—	5	1	no	—
326	#121	—	5	2	no	—
327	#121	—	5	2	no	—
328	#121	—	5	2	no	—
329	#121	—	5	2	no	—
330	#121	—	5	2	no	—
331	#121	—	5	2	no	—
332	#121	—	5	2	no	—
333	#121	C₂×D₅	1	1	yes	characteristic
334	#120	—	5	2	no	—
335	#120	—	5	2	no	—
336	#120	—	5	2	no	—
337	#120	—	5	2	no	—
338	#120	—	5	2	no	—
339	#120	—	5	2	no	—
340	C₄×Q₈	—	5	1	no	—
341	C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
342	C₄×D₄	—	5	2	no	—
343	C₄×D₄	—	5	2	no	—
344	C₄×D₄	—	5	2	no	—
345	C₄×D₄	—	5	2	no	—
346	C₄×D₄	—	5	1	no	—
347	C₄×D₄	—	5	2	no	—
348	C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
349	C₄×D₄	C₂×D₅	1	2	yes	complemented
350	#117	—	5	2	no	—
351	#117	—	5	2	no	—
352	#117	—	5	2	no	—
353	#117	—	5	2	no	—
354	#117	C₂×D₅	1	2	yes	complemented
355	C₂×C₂²⋊C₄	—	5	2	no	—
356	C₂×C₂²⋊C₄	—	5	2	no	—
357	C₂×C₂²⋊C₄	—	5	2	no	—
358	C₂×C₂²⋊C₄	—	5	2	no	—
359	C₂×C₂²⋊C₄	—	5	2	no	—
360	C₂×C₄²	C₂×D₅	1	1	yes	characteristic, complemented
361	C₂²×C₅	—	2	1	no	—
362	C₂²×C₅	—	2	1	no	—
363	C₂²×C₅	—	2	2	no	—
364	C₂²×C₅	—	2	2	no	—
365	C₂²×C₅	—	2	2	no	—
366	C₂²×C₅	H(5,𝔽₂)	1	2	yes	—
367	C₂²×C₅	C₂⁵	1	1	yes	characteristic
368	C₂×D₅	—	2	2	no	—
369	C₂×D₅	—	2	2	no	—
370	C₂×D₅	—	2	2	no	—
371	C₂×D₅	—	2	2	no	—
372	C₂×D₅	—	2	2	no	—
373	C₂×D₅	—	2	2	no	—
374	C₂×D₅	—	2	2	no	—
375	C₂×D₅	—	2	2	no	—
376	C₂×D₅	—	2	2	no	—
377	C₂×D₅	—	8	4	no	—
378	C₂×D₅	—	8	4	no	—
379	C₄×C₅	—	2	1	no	—
380	C₄×C₅	—	2	1	no	—
381	C₄×C₅	—	2	2	no	—
382	C₄×C₅	—	2	1	no	—
383	C₄×C₅	—	2	1	no	—
384	C₄×C₅	—	2	2	no	—
385	C₄×C₅	—	2	2	no	—
386	C₄×C₅	—	2	1	no	—
387	C₄×C₅	—	2	1	no	—
388	Dic₅	—	2	2	no	—
389	Dic₅	—	2	2	no	—
390	Dic₅	—	2	2	no	—
391	Dic₅	—	2	2	no	—
392	Dic₅	—	2	2	no	—
393	C₂⁴	—	5	2	no	—
394	C₂⁴	—	5	2	no	—
395	#41	—	20	4	no	—
396	C₂×Q₈	—	5	1	no	—
397	C₂×Q₈	—	5	1	no	—
398	C₂×Q₈	—	5	2	no	—
399	C₂×Q₈	—	5	2	no	—
400	C₂×Q₈	—	5	1	no	—
401	C₂×Q₈	—	20	2	no	—
402	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
403	C₂×D₄	—	5	2	no	—
404	C₂×D₄	—	5	2	no	—
405	C₂×D₄	—	5	2	no	—
406	C₂×D₄	—	5	2	no	—
407	C₂×D₄	—	5	2	no	—
408	C₂×D₄	—	5	2	no	—
409	C₂×D₄	—	5	2	no	—
410	C₂×D₄	—	5	1	no	—
411	C₂×D₄	—	5	1	no	—
412	C₂×D₄	—	5	2	no	—
413	C₂×D₄	—	5	2	no	—
414	C₂×D₄	—	5	1	no	—
415	C₂×D₄	—	20	2	no	—
416	C₂×D₄	—	20	4	no	—
417	C₂×D₄	C₂²×D₅	1	2	yes	—
418	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
419	C₂²×C₄	—	5	2	no	—
420	C₂²×C₄	—	5	2	no	—
421	C₂²×C₄	—	5	2	no	—
422	C₂²×C₄	—	5	2	no	—
423	C₂²×C₄	—	5	2	no	—
424	C₂²×C₄	—	5	2	no	—
425	C₂²×C₄	—	5	2	no	—
426	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
427	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
428	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
429	C₂²×C₄	C₂²×D₅	1	2	yes	—
430	C₄⋊C₄	—	5	2	no	—
431	C₄⋊C₄	—	5	2	no	—
432	C₄⋊C₄	—	5	2	no	—
433	C₄⋊C₄	—	5	2	no	—
434	C₄⋊C₄	—	5	2	no	—
435	C₄⋊C₄	—	5	2	no	—
436	C₄⋊C₄	—	5	2	no	—
437	C₄⋊C₄	—	5	2	no	—
438	C₄⋊C₄	—	5	2	no	—
439	C₄⋊C₄	—	5	1	no	—
440	C₄⋊C₄	—	5	1	no	—
441	C₄⋊C₄	—	5	2	no	—
442	C₄⋊C₄	C₂²×D₅	1	2	yes	—
443	C₄⋊C₄	C₂²×D₅	1	2	yes	—
444	C₄⋊C₄	C₂²×D₅	1	2	yes	—
445	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
446	C₄⋊C₄	C₂²×D₅	1	2	yes	—
447	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
448	C₂²⋊C₄	—	5	2	no	—
449	C₂²⋊C₄	—	5	2	no	—
450	C₂²⋊C₄	—	5	2	no	—
451	C₂²⋊C₄	—	5	2	no	—
452	C₂²⋊C₄	—	5	2	no	—
453	C₂²⋊C₄	—	5	2	no	—
454	C₂²⋊C₄	—	5	2	no	—
455	C₂²⋊C₄	—	5	2	no	—
456	C₂²⋊C₄	—	5	2	no	—
457	C₂²⋊C₄	—	5	2	no	—
458	C₂²⋊C₄	—	5	2	no	—
459	C₂²⋊C₄	—	5	2	no	—
460	C₂²⋊C₄	—	5	2	no	—
461	C₂²⋊C₄	—	5	2	no	—
462	C₂²⋊C₄	—	5	2	no	—
463	C₂²⋊C₄	—	5	2	no	—
464	C₂²⋊C₄	—	5	2	no	—
465	C₂²⋊C₄	—	5	2	no	—
466	C₂²⋊C₄	—	5	2	no	—
467	C₂²⋊C₄	—	5	2	no	—
468	C₂²⋊C₄	—	5	2	no	—
469	C₂²⋊C₄	—	5	2	no	—
470	C₂²⋊C₄	—	5	2	no	—
471	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
472	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
473	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
474	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
475	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
476	C₄²	—	5	2	no	—
477	C₄²	—	5	2	no	—
478	C₄²	—	5	2	no	—
479	C₄²	C₂²×D₅	1	1	yes	characteristic
480	C₄²	C₂²×D₅	1	1	yes	characteristic
481	C₄²	C₂²×D₅	1	1	yes	characteristic
482	C₄²	C₂²×D₅	1	1	yes	characteristic
483	C₄²	C₂²×D₅	1	2	yes	—
484	C₂×C₅	—	2	2	no	—
485	C₂×C₅	—	4	2	no	—
486	C₂×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
487	C₂×C₅	#585	1	1	yes	characteristic
488	C₂×C₅	#585	1	1	yes	characteristic
489	D₅	—	4	2	no	—
490	D₅	—	4	2	no	—
491	D₅	—	4	2	no	—
492	C₂³	—	5	2	no	—
493	C₂³	—	5	2	no	—
494	C₂³	—	5	2	no	—
495	C₂³	—	10	4	no	—
496	C₂³	—	20	2	no	—
497	C₂³	—	20	2	no	—
498	C₂³	—	20	2	no	—
499	C₂³	—	20	2	no	—
500	C₂³	—	20	2	no	—
501	C₂³	C₂³×D₅	1	2	yes	—
502	C₂³	C₂³×D₅	1	1	yes	characteristic
503	Q₈	—	4	1	no	—
504	Q₈	—	20	1	no	—
505	Q₈	—	20	2	no	—
506	Q₈	—	20	1	no	—
507	Q₈	—	20	2	no	—
508	Q₈	—	20	1	no	—
509	D₄	—	2	4	no	—
510	D₄	—	4	1	no	—
511	D₄	—	10	4	no	—
512	D₄	—	20	1	no	—
513	D₄	—	20	2	no	—
514	D₄	—	20	1	no	—
515	D₄	—	20	2	no	—
516	D₄	—	20	2	no	—
517	D₄	—	20	1	no	—
518	D₄	—	20	2	no	—
519	D₄	—	20	2	no	—
520	D₄	—	20	2	no	—
521	D₄	—	20	2	no	—
522	D₄	—	20	2	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	5	2	no	—
528	C₂×C₄	—	5	2	no	—
529	C₂×C₄	—	5	2	no	—
530	C₂×C₄	—	5	2	no	—
531	C₂×C₄	—	5	2	no	—
532	C₂×C₄	—	10	4	no	—
533	C₂×C₄	—	20	2	no	—
534	C₂×C₄	—	20	2	no	—
535	C₂×C₄	—	20	2	no	—
536	C₂×C₄	—	20	2	no	—
537	C₂×C₄	—	20	2	no	—
538	C₂×C₄	—	20	2	no	—
539	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
540	C₂×C₄	C₂³×D₅	1	2	yes	—
541	C₂×C₄	C₂³×D₅	1	2	yes	—
542	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
543	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
544	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
545	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
546	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
547	C₂×C₄	C₂³×D₅	1	2	yes	—
548	C₅	#3545	1	1	yes	characteristic, complemented, Sylow
549	C₂²	—	2	1	no	—
550	C₂²	—	2	1	no	—
551	C₂²	—	2	2	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	10	2	no	—
555	C₂²	—	10	2	no	—
556	C₂²	—	10	2	no	—
557	C₂²	—	10	2	no	—
558	C₂²	—	10	2	no	—
559	C₂²	—	10	2	no	—
560	C₂²	—	10	2	no	—
561	C₂²	—	10	2	no	—
562	C₂²	—	10	2	no	—
563	C₂²	—	40	4	no	—
564	C₂²	—	40	4	no	—
565	C₂²	#4149	1	2	yes	—
566	C₂²	C₂⁴×D₅	1	1	yes	characteristic
567	C₄	—	2	1	no	—
568	C₄	—	2	1	no	—
569	C₄	—	2	2	no	—
570	C₄	—	2	1	no	—
571	C₄	—	2	1	no	—
572	C₄	—	2	2	no	—
573	C₄	—	2	1	no	—
574	C₄	—	2	1	no	—
575	C₄	—	2	2	no	—
576	C₄	—	10	2	no	—
577	C₄	—	10	2	no	—
578	C₄	—	10	2	no	—
579	C₄	—	10	2	no	—
580	C₄	—	10	2	no	—
581	C₂	—	2	2	no	—
582	C₂	—	4	2	no	—
583	C₂	—	20	2	no	—
584	C₂	—	20	2	no	—
585	C₂	—	20	2	no	—
586	C₂	C₂×#4149	1	1	yes	characteristic
587	C₂	#66283	1	1	yes	characteristic
588	C₂	#66283	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅
commutator, socle, cosocle	C₂²×C₅	C₂⁵
Fitting	C₅×#529	C₂
hypercenter	#529	D₅
hypocenter	C₅	#3545
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
1. C₅×#529	C₂	semidirect
2. #66044	C₂	semidirect
3. #66038	C₂	semidirect
4. #66034	C₂	semidirect
5. #66033	C₂	semidirect
6. #66018	C₂	semidirect
7. #66017	C₂	semidirect
8. #65987	C₂	semidirect
9. #65982	C₂	semidirect
10. #65971	C₂	semidirect
11. #65944	C₂	semidirect
12. #65916	C₂	semidirect
13. #65894	C₂	semidirect
14. #65890	C₂	semidirect
15. #65888	C₂	semidirect
16. #65866	C₂	semidirect
17. #65861	C₂	semidirect
18. #65813	C₂	semidirect
19. C₂×#4021	C₂	semidirect
21. C₂×D₄×D₅	C₂²	semidirect
23. C₂²×Dic₁₀	C₂²	semidirect
24. C₅×#126	C₂²	semidirect
25. C₅×#125	C₂²	semidirect
26. C₅×#124	C₂²	semidirect
27. C₅×#123	C₂²	semidirect
28. C₅×C₂²⋊Q₈	C₂²	semidirect
30. C₄×C₅×Q₈	C₂²	semidirect
31. C₄×C₅×D₄	C₂²	semidirect
32. C₄×C₅×D₄	C₂²	semidirect
33. C₅×#117	C₂²	semidirect
34. C₂×C₄²×C₅	C₂²	semidirect
35. #4093	C₂²	semidirect
36. #4092	C₂²	semidirect
37. #4085	C₂²	semidirect
39. #4083	C₂²	semidirect
40. #4081	C₂²	semidirect
42. #4076	C₂²	semidirect
43. #4075	C₂²	semidirect
44. #4075	C₂²	semidirect
45. C₄×C₂²⋊D₅	C₂²	semidirect
46. C₄×C₂²⋊D₅	C₂²	semidirect
47. C₂×#685	C₂²	semidirect
48. C₂×#685	C₂²	semidirect
49. C₂×#685	C₂²	semidirect
50. #4070	C₂²	semidirect
51. #4044	C₂²	semidirect
52. #4044	C₂²	semidirect
53. #4044	C₂²	semidirect
54. #4043	C₂²	semidirect
55. #4042	C₂²	semidirect
56. #4042	C₂²	semidirect
57. #4042	C₂²	semidirect
58. #4042	C₂²	semidirect
60. #4041	C₂²	semidirect
61. #4041	C₂²	semidirect
63. #4040	C₂²	semidirect
64. #4040	C₂²	semidirect
65. #4040	C₂²	semidirect
66. #4040	C₂²	semidirect
67. #4039	C₂²	semidirect
68. #4038	C₂²	semidirect
69. #4034	C₂²	semidirect
70. #4034	C₂²	semidirect
71. #4032	C₂²	semidirect
72. #4032	C₂²	semidirect
73. #4031	C₂²	semidirect
74. #4031	C₂²	semidirect
75. #4031	C₂²	semidirect
76. #4031	C₂²	semidirect
78. #4030	C₂²	semidirect
79. #4030	C₂²	semidirect
80. #4029	C₂²	semidirect
83. #4028	C₂²	semidirect
84. #4028	C₂²	semidirect
85. #4027	C₂²	semidirect
86. D₅×C₂²⋊C₄	C₂²	semidirect
87. D₅×C₂²⋊C₄	C₂²	semidirect
88. #4024	C₂²	semidirect
89. #4024	C₂²	semidirect
90. #4023	C₂²	semidirect
91. #4022	C₂²	semidirect
92. #4022	C₂²	semidirect
95. #4021	C₂²	semidirect
96. #4021	C₂²	semidirect
97. #4021	C₂²	semidirect
98. #4021	C₂²	semidirect
99. #4021	C₂²	semidirect
100. #4021	C₂²	semidirect
101. C₄×D₂₀	C₂²	semidirect
102. C₄×D₂₀	C₂²	semidirect
103. #4018	C₂²	semidirect
104. #4018	C₂²	semidirect
105. #4016	C₂²	semidirect
106. C₄×Dic₁₀	C₂²	semidirect
216. #529	D₅	semidirect
285. #126	C₂×D₅	semidirect
287. #125	C₂×D₅	semidirect
301. #124	C₂×D₅	semidirect
313. #123	C₂×D₅	semidirect
323. C₂²⋊Q₈	C₂×D₅	semidirect
341. C₄×Q₈	C₂×D₅	semidirect
348. C₄×D₄	C₂×D₅	semidirect
349. C₄×D₄	C₂×D₅	semidirect
354. #117	C₂×D₅	semidirect
360. C₂×C₄²	C₂×D₅	semidirect
548. C₅	#3545	semidirect

Maximal subgroups

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

subgroup	index
C₅×#529	2
#66044	2
#66038	2
#66034	2
#66033	2
#66018	2
#66017	2
#65987	2
#65982	2
#65971	2
#65944	2
#65916	2
#65894	2
#65890	2
#65888	2
#65866	2
#65861	2
#65813	2
C₂×#4021	2
#3545	5