Subgroups — #10618248

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×#536	C₂	1	1	yes	maximal, characteristic, complemented
2	#66163	C₂	1	2	yes	maximal, complemented
3	#66150	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#4093	C₂	1	1	yes	maximal, characteristic, complemented
5	#66069	C₂	1	1	yes	maximal, characteristic, complemented
6	#66068	C₂	1	1	yes	maximal, characteristic, complemented
7	#66067	C₂	1	2	yes	maximal, complemented
8	#66017	C₂	1	1	yes	maximal, characteristic, complemented
9	#66012	C₂	1	2	yes	maximal, complemented
10	#66004	C₂	1	1	yes	maximal, characteristic, complemented
11	#65992	C₂	1	2	yes	maximal, complemented
12	#65988	C₂	1	2	yes	maximal, complemented
13	#65987	C₂	1	2	yes	maximal, complemented
14	#65983	C₂	1	2	yes	maximal, complemented
15	#65981	C₂	1	2	yes	maximal, complemented
16	#65978	C₂	1	2	yes	maximal, complemented
17	#65974	C₂	1	2	yes	maximal, complemented
18	#65971	C₂	1	2	yes	maximal, complemented
19	#65861	C₂	1	2	yes	maximal, complemented
20	C₂×C₅×#41	C₂²	1	1	yes	characteristic
21	C₂²×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
22	C₂×D₄×D₅	C₂²	1	2	yes	complemented
23	C₂×#709	C₂²	1	1	yes	characteristic
24	C₂²×D₂₀	C₂²	1	1	yes	characteristic
25	C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
26	C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
27	C₅×#124	C₂²	1	1	yes	characteristic, complemented
28	C₅×#124	C₂²	1	1	yes	characteristic, complemented
29	C₅×#123	C₂²	1	2	yes	complemented
30	C₅×#123	C₂²	1	2	yes	complemented
31	C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
32	C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
33	C₅×#117	C₂²	1	1	yes	characteristic, complemented
34	#4093	C₂²	1	1	yes	characteristic
35	#4093	C₂²	1	1	yes	characteristic
36	#4093	C₂²	1	2	yes	complemented
37	#4093	C₂²	1	2	yes	complemented
38	#4093	C₂²	1	1	yes	characteristic, complemented
39	#4093	C₂²	1	1	yes	characteristic, complemented
40	#4093	C₂²	1	2	yes	complemented
41	#4093	C₂²	1	1	yes	characteristic, complemented
42	#4093	C₂²	1	1	yes	characteristic, complemented
43	#4092	C₂²	1	2	yes	complemented
44	#4092	C₂²	1	2	yes	complemented
45	#4092	C₂²	1	2	yes	complemented
46	#4090	C₂²	1	1	yes	characteristic, complemented
47	#4090	C₂²	1	1	yes	characteristic, complemented
48	#4085	C₂²	1	2	yes	—
49	#4085	C₂²	1	2	yes	complemented
50	#4083	C₂²	1	2	yes	—
51	#4083	C₂²	1	2	yes	complemented
52	D₄×Dic₅	C₂²	1	2	yes	complemented
53	#4076	C₂²	1	2	yes	complemented
54	#4075	C₂²	1	2	yes	complemented
55	#4075	C₂²	1	2	yes	complemented
56	#4075	C₂²	1	2	yes	complemented
57	C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
58	C₂×#685	C₂²	1	2	yes	complemented
59	C₂×#685	C₂²	1	2	yes	complemented
60	C₂×#685	C₂²	1	2	yes	complemented
61	#4072	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
63	#4044	C₂²	1	2	yes	complemented
64	#4044	C₂²	1	2	yes	complemented
65	#4044	C₂²	1	2	yes	complemented
66	#4044	C₂²	1	2	yes	complemented
67	#4043	C₂²	1	2	yes	complemented
68	#4042	C₂²	1	2	yes	complemented
69	#4042	C₂²	1	2	yes	complemented
70	#4041	C₂²	1	2	yes	—
71	#4041	C₂²	1	2	yes	complemented
72	#4041	C₂²	1	2	yes	complemented
73	#4040	C₂²	1	2	yes	—
74	#4040	C₂²	1	2	yes	complemented
75	#4040	C₂²	1	2	yes	complemented
76	#4040	C₂²	1	2	yes	complemented
77	#4040	C₂²	1	2	yes	complemented
78	#4039	C₂²	1	2	yes	complemented
79	#4038	C₂²	1	2	yes	complemented
80	#4038	C₂²	1	2	yes	complemented
81	#4035	C₂²	1	2	yes	complemented
82	#4033	C₂²	1	2	yes	complemented
83	#4032	C₂²	1	2	yes	complemented
84	#4031	C₂²	1	2	yes	complemented
85	#4031	C₂²	1	2	yes	complemented
86	#4031	C₂²	1	2	yes	complemented
87	#4030	C₂²	1	2	yes	—
88	#4030	C₂²	1	2	yes	complemented
89	#4030	C₂²	1	2	yes	complemented
90	#4029	C₂²	1	2	yes	complemented
91	#4028	C₂²	1	2	yes	—
92	#4028	C₂²	1	2	yes	—
93	#4028	C₂²	1	2	yes	complemented
94	#4028	C₂²	1	2	yes	complemented
95	#4027	C₂²	1	2	yes	complemented
96	#4027	C₂²	1	2	yes	complemented
97	#4027	C₂²	1	2	yes	complemented
98	D₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
99	D₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
100	#4025	C₂²	1	2	yes	complemented
101	#4024	C₂²	1	2	yes	complemented
102	#4023	C₂²	1	2	yes	complemented
103	#4022	C₂²	1	2	yes	complemented
104	#4021	C₂²	1	2	yes	complemented
105	C₄×D₂₀	C₂²	1	2	yes	complemented
106	#4018	C₂²	1	2	yes	complemented
107	#3545	—	5	1	no	maximal, Sylow
108	C₂³×D₅	C₂³	1	2	yes	—
109	C₂³×D₅	C₂³	1	2	yes	—
110	C₅×#41	—	4	2	no	—
111	C₂×C₅×Q₈	—	4	2	no	—
112	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
113	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
114	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
115	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
116	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
117	C₂×C₅×D₄	C₂³	1	2	yes	—
118	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
119	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
120	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
121	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
122	C₂²×C₄×C₅	C₂³	1	2	yes	—
123	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
124	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
125	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
126	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
127	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
128	C₂²×Dic₅	C₂³	1	2	yes	—
129	C₂²×Dic₅	C₂³	1	2	yes	—
130	D₄×D₅	—	4	4	no	—
131	#709	—	4	2	no	—
132	C₂×D₂₀	—	4	2	no	—
133	C₂×D₂₀	C₂³	1	1	yes	characteristic
134	C₂×D₂₀	C₂³	1	2	yes	—
135	C₂×D₂₀	C₂³	1	1	yes	characteristic
136	C₂×D₂₀	C₂³	1	1	yes	characteristic
137	C₂×D₂₀	C₂³	1	2	yes	—
138	C₂×D₂₀	C₂³	1	2	yes	—
139	C₂×D₂₀	C₂³	1	2	yes	—
140	C₂×C₄×D₅	C₂³	1	2	yes	—
141	C₂×C₄×D₅	C₂³	1	2	yes	—
142	C₂×C₄×D₅	C₂³	1	2	yes	—
143	C₂×C₄×D₅	C₂³	1	2	yes	—
144	C₂×C₄×D₅	C₂³	1	2	yes	—
145	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
146	C₂×Dic₁₀	C₂³	1	2	yes	—
147	C₅×C₄⋊C₄	C₂³	1	2	yes	—
148	C₅×C₄⋊C₄	C₂³	1	2	yes	—
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×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	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
157	C₄²×C₅	C₂³	1	1	yes	characteristic
158	C₄²×C₅	C₂³	1	1	yes	characteristic
159	C₂²⋊Dic₅	C₂³	1	2	yes	—
160	C₂²⋊Dic₅	C₂³	1	2	yes	—
161	C₂²⋊Dic₅	C₂³	1	2	yes	—
162	#685	C₂³	1	2	yes	—
163	#685	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	C₄⋊Dic₅	C₂³	1	2	yes	—
183	C₄⋊Dic₅	C₂³	1	2	yes	—
184	C₄⋊Dic₅	C₂³	1	2	yes	—
185	#683	C₂³	1	2	yes	—
186	#683	C₂³	1	2	yes	—
187	#683	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	C₄×Dic₅	C₂³	1	2	yes	—
194	C₄×Dic₅	C₂³	1	1	yes	characteristic
195	C₄×Dic₅	C₂³	1	2	yes	—
196	C₄×Dic₅	C₂³	1	1	yes	characteristic
197	C₄×Dic₅	C₂³	1	1	yes	characteristic
198	C₄×Dic₅	C₂³	1	1	yes	characteristic
199	C₄×Dic₅	C₂³	1	2	yes	—
200	#563	—	5	1	no	—
201	#562	—	5	2	no	—
202	H(3,𝔽₄)	—	5	1	no	—
203	#555	—	5	1	no	—
204	#555	—	5	1	no	—
205	#551	—	5	2	no	—
206	#551	—	5	2	no	—
207	#551	—	5	2	no	—
208	#546	—	5	2	no	—
209	#546	—	5	2	no	—
210	#542	—	5	2	no	—
211	#542	—	5	2	no	—
212	#538	—	5	2	no	—
213	#538	—	5	2	no	—
214	#536	—	5	1	no	—
215	#536	D₅	1	1	yes	characteristic, complemented
216	#534	—	5	2	no	—
217	#529	—	5	2	no	—
218	C₂×#124	—	5	1	no	—
219	C₂³×C₅	C₂⁴	1	2	yes	—
220	C₂³×C₅	C₂⁴	1	1	yes	characteristic
221	C₂²×D₅	—	2	4	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	—	4	2	no	—
227	C₂²×D₅	C₂⁴	1	2	yes	—
228	C₂²×D₅	C₂⁴	1	2	yes	—
229	C₂²×D₅	C₂⁴	1	2	yes	—
230	C₅×Q₈	—	4	1	no	—
231	C₅×Q₈	—	4	1	no	—
232	C₅×Q₈	—	4	1	no	—
233	C₅×Q₈	—	4	1	no	—
234	C₅×Q₈	—	4	1	no	—
235	C₅×D₄	—	2	4	no	—
236	C₅×D₄	—	4	1	no	—
237	C₂×C₄×C₅	—	2	2	no	—
238	C₂×C₄×C₅	—	2	2	no	—
239	C₂×C₄×C₅	—	2	2	no	—
240	C₂×C₄×C₅	—	4	2	no	—
241	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
242	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
243	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₅	C₂⁴	1	2	yes	—
245	C₂×C₄×C₅	C₂⁴	1	2	yes	—
246	C₂×C₄×C₅	C₂⁴	1	2	yes	—
247	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
250	C₂²⋊D₅	—	2	4	no	—
251	C₂²⋊D₅	—	4	2	no	—
252	C₂²⋊D₅	—	4	2	no	—
253	C₂²⋊D₅	—	4	2	no	—
254	C₂²⋊D₅	—	4	2	no	—
255	C₂×Dic₅	—	4	2	no	—
256	C₂×Dic₅	—	4	2	no	—
257	C₂×Dic₅	C₂⁴	1	2	yes	—
258	C₂×Dic₅	C₂⁴	1	2	yes	—
259	C₂×Dic₅	C₂⁴	1	2	yes	—
260	C₂×Dic₅	C₂⁴	1	2	yes	—
261	C₂×Dic₅	C₂⁴	1	2	yes	—
262	D₂₀	—	4	1	no	—
263	D₂₀	—	4	2	no	—
264	D₂₀	—	4	1	no	—
265	D₂₀	—	4	2	no	—
266	D₂₀	—	4	2	no	—
267	D₂₀	—	4	1	no	—
268	D₂₀	—	4	2	no	—
269	C₄×D₅	—	4	2	no	—
270	C₄×D₅	—	4	2	no	—
271	C₄×D₅	—	4	2	no	—
272	C₄×D₅	—	4	2	no	—
273	C₄×D₅	—	4	2	no	—
274	Dic₁₀	—	4	2	no	—
275	Dic₁₀	—	4	1	no	—
276	C₂×#41	—	5	1	no	—
277	C₂×#41	C₂×D₅	1	1	yes	characteristic
278	C₂²×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
279	C₂²×D₄	—	5	2	no	—
280	C₂²×D₄	—	5	1	no	—
281	C₄⋊Q₈	—	5	1	no	—
282	C₄⋊Q₈	—	5	1	no	—
283	C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
284	C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
285	#126	—	5	2	no	—
286	#126	—	5	2	no	—
287	#126	—	5	2	no	—
288	#126	—	5	2	no	—
289	#126	—	5	2	no	—
290	#126	—	5	2	no	—
291	#125	—	5	2	no	—
292	#124	—	5	2	no	—
293	#124	—	5	2	no	—
294	#124	—	5	1	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	—	5	2	no	—
302	#124	—	5	2	no	—
303	#124	—	5	2	no	—
304	#124	—	5	2	no	—
305	#124	C₂×D₅	1	1	yes	characteristic, complemented
306	#124	C₂×D₅	1	1	yes	characteristic, complemented
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	—	5	2	no	—
314	#123	—	5	2	no	—
315	#123	—	5	2	no	—
316	#123	—	5	2	no	—
317	#123	C₂×D₅	1	2	yes	complemented
318	#123	C₂×D₅	1	2	yes	complemented
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	—	5	2	no	—
324	C₂²⋊Q₈	—	5	2	no	—
325	C₂²⋊Q₈	—	5	2	no	—
326	C₂²⋊Q₈	C₂×D₅	1	2	yes	complemented
327	C₂²⋊Q₈	C₂×D₅	1	2	yes	complemented
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	—	5	2	no	—
334	#121	—	5	2	no	—
335	#121	—	5	2	no	—
336	#121	—	5	2	no	—
337	#120	—	5	2	no	—
338	#120	—	5	2	no	—
339	#120	—	5	2	no	—
340	#120	—	5	2	no	—
341	#120	—	5	2	no	—
342	#120	—	5	2	no	—
343	C₄×Q₈	—	5	2	no	—
344	C₄×D₄	—	5	2	no	—
345	C₄×D₄	—	5	2	no	—
346	C₄×D₄	—	5	2	no	—
347	C₄×D₄	—	5	2	no	—
348	C₄×D₄	—	5	2	no	—
349	C₄×D₄	—	5	2	no	—
350	C₄×D₄	—	5	2	no	—
351	#117	—	5	1	no	—
352	#117	—	5	2	no	—
353	#117	—	5	2	no	—
354	#117	—	5	2	no	—
355	#117	—	5	2	no	—
356	#117	C₂×D₅	1	1	yes	characteristic, complemented
357	C₂×C₂²⋊C₄	—	5	2	no	—
358	C₂×C₂²⋊C₄	—	5	2	no	—
359	C₂×C₂²⋊C₄	—	5	2	no	—
360	C₂×C₂²⋊C₄	—	5	2	no	—
361	C₂×C₂²⋊C₄	—	5	2	no	—
362	C₂×C₄²	—	5	1	no	—
363	C₂²×C₅	—	2	2	no	—
364	C₂²×C₅	—	2	2	no	—
365	C₂²×C₅	—	2	2	no	—
366	C₂²×C₅	—	2	2	no	—
367	C₂²×C₅	H(5,𝔽₂)	1	2	yes	—
368	C₂²×C₅	C₂⁵	1	1	yes	characteristic
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	—	2	2	no	—
378	C₂×D₅	—	8	4	no	—
379	C₂×D₅	—	8	4	no	—
380	C₄×C₅	—	2	1	no	—
381	C₄×C₅	—	2	1	no	—
382	C₄×C₅	—	2	2	no	—
383	C₄×C₅	—	2	1	no	—
384	C₄×C₅	—	2	1	no	—
385	C₄×C₅	—	2	1	no	—
386	C₄×C₅	—	2	1	no	—
387	C₄×C₅	—	2	2	no	—
388	C₄×C₅	—	2	2	no	—
389	Dic₅	—	2	2	no	—
390	Dic₅	—	2	2	no	—
391	Dic₅	—	2	2	no	—
392	Dic₅	—	2	2	no	—
393	Dic₅	—	2	2	no	—
394	C₂⁴	—	5	2	no	—
395	C₂⁴	—	5	2	no	—
396	#41	—	4	2	no	—
397	#41	—	20	2	no	—
398	C₂×Q₈	—	4	2	no	—
399	C₂×Q₈	—	5	2	no	—
400	C₂×Q₈	—	5	1	no	—
401	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
402	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
403	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
404	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
405	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
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	2	no	—
411	C₂×D₄	—	5	2	no	—
412	C₂×D₄	—	5	2	no	—
413	C₂×D₄	—	5	1	no	—
414	C₂×D₄	—	5	1	no	—
415	C₂×D₄	—	5	2	no	—
416	C₂×D₄	—	5	2	no	—
417	C₂×D₄	—	5	1	no	—
418	C₂×D₄	—	20	2	no	—
419	C₂×D₄	—	20	4	no	—
420	C₂×D₄	C₂²×D₅	1	2	yes	—
421	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
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	—	5	2	no	—
427	C₂²×C₄	—	5	2	no	—
428	C₂²×C₄	—	5	2	no	—
429	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
430	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
431	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
432	C₂²×C₄	C₂²×D₅	1	2	yes	—
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	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	C₂²×D₅	1	2	yes	—
445	C₄⋊C₄	C₂²×D₅	1	2	yes	—
446	C₄⋊C₄	C₂²×D₅	1	2	yes	—
447	C₄⋊C₄	C₂²×D₅	1	2	yes	—
448	C₄⋊C₄	C₂²×D₅	1	2	yes	—
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	—	5	2	no	—
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	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
477	C₄²	—	5	1	no	—
478	C₄²	—	5	2	no	—
479	C₄²	—	5	1	no	—
480	C₄²	—	5	1	no	—
481	C₄²	—	5	2	no	—
482	C₄²	—	5	2	no	—
483	C₄²	—	5	1	no	—
484	C₄²	C₂²×D₅	1	1	yes	characteristic
485	C₄²	C₂²×D₅	1	1	yes	characteristic
486	C₂×C₅	—	2	2	no	—
487	C₂×C₅	—	4	2	no	—
488	C₂×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
489	C₂×C₅	#585	1	2	yes	—
490	D₅	—	4	2	no	—
491	D₅	—	4	2	no	—
492	D₅	—	4	2	no	—
493	C₂³	—	5	2	no	—
494	C₂³	—	5	2	no	—
495	C₂³	—	5	2	no	—
496	C₂³	—	10	4	no	—
497	C₂³	—	20	2	no	—
498	C₂³	—	20	2	no	—
499	C₂³	—	20	2	no	—
500	C₂³	—	20	2	no	—
501	C₂³	—	20	2	no	—
502	C₂³	C₂³×D₅	1	2	yes	—
503	C₂³	C₂³×D₅	1	1	yes	characteristic
504	Q₈	—	4	1	no	—
505	Q₈	—	4	1	no	—
506	Q₈	—	4	1	no	—
507	Q₈	—	4	1	no	—
508	Q₈	—	4	1	no	—
509	Q₈	—	20	1	no	—
510	Q₈	—	20	2	no	—
511	D₄	—	2	4	no	—
512	D₄	—	4	1	no	—
513	D₄	—	10	4	no	—
514	D₄	—	20	1	no	—
515	D₄	—	20	2	no	—
516	D₄	—	20	1	no	—
517	D₄	—	20	2	no	—
518	D₄	—	20	1	no	—
519	D₄	—	20	2	no	—
520	D₄	—	20	2	no	—
521	D₄	—	20	2	no	—
522	D₄	—	20	2	no	—
523	D₄	—	20	2	no	—
524	D₄	—	20	2	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	5	2	no	—
530	C₂×C₄	—	5	2	no	—
531	C₂×C₄	—	5	2	no	—
532	C₂×C₄	—	5	2	no	—
533	C₂×C₄	—	5	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	—	20	2	no	—
540	C₂×C₄	—	20	2	no	—
541	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
542	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
543	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
544	C₂×C₄	C₂³×D₅	1	2	yes	—
545	C₂×C₄	C₂³×D₅	1	2	yes	—
546	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
547	C₂×C₄	C₂³×D₅	1	2	yes	—
548	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
549	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
550	C₅	#3545	1	1	yes	characteristic, complemented, Sylow
551	C₂²	—	2	2	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	2	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	—	10	2	no	—
564	C₂²	—	40	4	no	—
565	C₂²	—	40	4	no	—
566	C₂²	#4144	1	2	yes	—
567	C₂²	C₂⁴×D₅	1	1	yes	characteristic
568	C₄	—	2	1	no	—
569	C₄	—	2	1	no	—
570	C₄	—	2	1	no	—
571	C₄	—	2	1	no	—
572	C₄	—	2	1	no	—
573	C₄	—	2	1	no	—
574	C₄	—	2	2	no	—
575	C₄	—	2	2	no	—
576	C₄	—	2	2	no	—
577	C₄	—	10	2	no	—
578	C₄	—	10	2	no	—
579	C₄	—	10	2	no	—
580	C₄	—	10	2	no	—
581	C₄	—	10	2	no	—
582	C₂	—	2	2	no	—
583	C₂	—	4	2	no	—
584	C₂	—	20	2	no	—
585	C₂	—	20	2	no	—
586	C₂	—	20	2	no	—
587	C₂	C₂×#4144	1	1	yes	characteristic
588	C₂	#66287	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅
commutator, socle, cosocle	C₂²×C₅	C₂⁵
Fitting	C₅×#536	C₂
hypercenter	#536	D₅
hypocenter	C₅	#3545
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ #536

Complements

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

N	H ≅ G/N	type
1. C₅×#536	C₂	semidirect
2. #66163	C₂	semidirect
3. #66150	C₂	semidirect
4. C₂×#4093	C₂	semidirect
5. #66069	C₂	semidirect
6. #66068	C₂	semidirect
7. #66067	C₂	semidirect
8. #66017	C₂	semidirect
9. #66012	C₂	semidirect
10. #66004	C₂	semidirect
11. #65992	C₂	semidirect
12. #65988	C₂	semidirect
13. #65987	C₂	semidirect
14. #65983	C₂	semidirect
15. #65981	C₂	semidirect
16. #65978	C₂	semidirect
17. #65974	C₂	semidirect
18. #65971	C₂	semidirect
19. #65861	C₂	semidirect
21. C₂²×C₅×Q₈	C₂²	semidirect
22. C₂×D₄×D₅	C₂²	semidirect
25. C₅×C₄⋊Q₈	C₂²	semidirect
26. C₅×C₄⋊Q₈	C₂²	semidirect
27. C₅×#124	C₂²	semidirect
28. C₅×#124	C₂²	semidirect
29. C₅×#123	C₂²	semidirect
30. C₅×#123	C₂²	semidirect
31. C₅×C₂²⋊Q₈	C₂²	semidirect
32. C₅×C₂²⋊Q₈	C₂²	semidirect
33. C₅×#117	C₂²	semidirect
36. #4093	C₂²	semidirect
37. #4093	C₂²	semidirect
38. #4093	C₂²	semidirect
39. #4093	C₂²	semidirect
40. #4093	C₂²	semidirect
41. #4093	C₂²	semidirect
42. #4093	C₂²	semidirect
43. #4092	C₂²	semidirect
44. #4092	C₂²	semidirect
45. #4092	C₂²	semidirect
46. #4090	C₂²	semidirect
47. #4090	C₂²	semidirect
49. #4085	C₂²	semidirect
51. #4083	C₂²	semidirect
52. D₄×Dic₅	C₂²	semidirect
53. #4076	C₂²	semidirect
54. #4075	C₂²	semidirect
55. #4075	C₂²	semidirect
56. #4075	C₂²	semidirect
57. C₄×C₂²⋊D₅	C₂²	semidirect
58. C₂×#685	C₂²	semidirect
59. C₂×#685	C₂²	semidirect
60. C₂×#685	C₂²	semidirect
61. #4072	C₂²	semidirect
62. C₂×C₄×Dic₅	C₂²	semidirect
63. #4044	C₂²	semidirect
64. #4044	C₂²	semidirect
65. #4044	C₂²	semidirect
66. #4044	C₂²	semidirect
67. #4043	C₂²	semidirect
68. #4042	C₂²	semidirect
69. #4042	C₂²	semidirect
71. #4041	C₂²	semidirect
72. #4041	C₂²	semidirect
74. #4040	C₂²	semidirect
75. #4040	C₂²	semidirect
76. #4040	C₂²	semidirect
77. #4040	C₂²	semidirect
78. #4039	C₂²	semidirect
79. #4038	C₂²	semidirect
80. #4038	C₂²	semidirect
81. #4035	C₂²	semidirect
82. #4033	C₂²	semidirect
83. #4032	C₂²	semidirect
84. #4031	C₂²	semidirect
85. #4031	C₂²	semidirect
86. #4031	C₂²	semidirect
88. #4030	C₂²	semidirect
89. #4030	C₂²	semidirect
90. #4029	C₂²	semidirect
93. #4028	C₂²	semidirect
94. #4028	C₂²	semidirect
95. #4027	C₂²	semidirect
96. #4027	C₂²	semidirect
97. #4027	C₂²	semidirect
98. D₅×C₂²⋊C₄	C₂²	semidirect
99. D₅×C₂²⋊C₄	C₂²	semidirect
100. #4025	C₂²	semidirect
101. #4024	C₂²	semidirect
102. #4023	C₂²	semidirect
103. #4022	C₂²	semidirect
104. #4021	C₂²	semidirect
105. C₄×D₂₀	C₂²	semidirect
106. #4018	C₂²	semidirect
215. #536	D₅	semidirect
278. C₂²×Q₈	C₂×D₅	semidirect
283. C₄⋊Q₈	C₂×D₅	semidirect
284. C₄⋊Q₈	C₂×D₅	semidirect
305. #124	C₂×D₅	semidirect
306. #124	C₂×D₅	semidirect
317. #123	C₂×D₅	semidirect
318. #123	C₂×D₅	semidirect
326. C₂²⋊Q₈	C₂×D₅	semidirect
327. C₂²⋊Q₈	C₂×D₅	semidirect
356. #117	C₂×D₅	semidirect
550. 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×#536	2
#66163	2
#66150	2
C₂×#4093	2
#66069	2
#66068	2
#66067	2
#66017	2
#66012	2
#66004	2
#65992	2
#65988	2
#65987	2
#65983	2
#65981	2
#65978	2
#65974	2
#65971	2
#65861	2
#3545	5