Subgroups — #10618470

Order 640.

1032 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	#66067	C₂	1	1	yes	maximal, characteristic, complemented
3	#66062	C₂	1	1	yes	maximal, characteristic, complemented
4	#66046	C₂	1	2	yes	maximal, complemented
5	#66039	C₂	1	2	yes	maximal, complemented
6	#66016	C₂	1	2	yes	maximal, complemented
7	#66012	C₂	1	2	yes	maximal, complemented
8	#66009	C₂	1	1	yes	maximal, characteristic, complemented
9	D₅×#124	C₂	1	1	yes	maximal, characteristic, complemented
10	#66001	C₂	1	2	yes	maximal, complemented
11	#65992	C₂	1	2	yes	maximal, complemented
12	#65977	C₂	1	2	yes	maximal, complemented
13	#65968	C₂	1	2	yes	maximal, complemented
14	#65967	C₂	1	1	yes	maximal, characteristic, complemented
15	#65966	C₂	1	1	yes	maximal, characteristic, complemented
16	#65946	C₂	1	1	yes	maximal, characteristic, complemented
17	#65932	C₂	1	1	yes	maximal, characteristic, complemented
18	Q₈×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
19	#65902	C₂	1	1	yes	maximal, characteristic, complemented
20	#65888	C₂	1	1	yes	maximal, characteristic, complemented
21	#65876	C₂	1	1	yes	maximal, characteristic, complemented
22	#65862	C₂	1	1	yes	maximal, characteristic, complemented
23	#65860	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×Q₈×D₅	C₂²	1	1	yes	characteristic
25	C₂×Q₈×D₅	C₂²	1	1	yes	characteristic, complemented
26	C₂×#711	C₂²	1	1	yes	characteristic
27	C₂×D₄×D₅	C₂²	1	1	yes	characteristic
28	C₂×#709	C₂²	1	1	yes	characteristic
29	C₂²×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
30	C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₅×#126	C₂²	1	2	yes	complemented
32	C₅×#124	C₂²	1	1	yes	characteristic
33	C₅×#124	C₂²	1	2	yes	complemented
34	C₅×#123	C₂²	1	2	yes	complemented
35	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
36	C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
37	C₅×#121	C₂²	1	1	yes	characteristic
38	C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
39	C₄×C₅×D₄	C₂²	1	1	yes	characteristic
40	C₅×#117	C₂²	1	1	yes	characteristic, complemented
41	#4093	C₂²	1	1	yes	characteristic
42	#4093	C₂²	1	2	yes	complemented
43	#4092	C₂²	1	2	yes	—
44	#4092	C₂²	1	2	yes	complemented
45	Q₈×Dic₅	C₂²	1	2	yes	complemented
46	#4090	C₂²	1	1	yes	characteristic, complemented
47	#4085	C₂²	1	2	yes	complemented
48	#4084	C₂²	1	2	yes	—
49	#4083	C₂²	1	2	yes	—
50	#4082	C₂²	1	1	yes	characteristic
51	#4082	C₂²	1	1	yes	characteristic
52	D₄×Dic₅	C₂²	1	2	yes	complemented
53	#4076	C₂²	1	2	yes	—
54	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
55	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
56	C₂×#685	C₂²	1	2	yes	—
57	#4072	C₂²	1	2	yes	complemented
58	#4070	C₂²	1	2	yes	complemented
59	#4044	C₂²	1	2	yes	complemented
60	#4044	C₂²	1	1	yes	characteristic, complemented
61	#4044	C₂²	1	2	yes	complemented
62	#4043	C₂²	1	1	yes	characteristic
63	#4043	C₂²	1	1	yes	characteristic
64	#4043	C₂²	1	2	yes	—
65	#4043	C₂²	1	1	yes	characteristic, complemented
66	#4043	C₂²	1	2	yes	complemented
67	#4043	C₂²	1	2	yes	complemented
68	#4043	C₂²	1	2	yes	complemented
69	#4042	C₂²	1	1	yes	characteristic
70	#4042	C₂²	1	2	yes	—
71	#4042	C₂²	1	2	yes	complemented
72	#4042	C₂²	1	2	yes	complemented
73	#4041	C₂²	1	1	yes	characteristic
74	#4040	C₂²	1	1	yes	characteristic
75	#4040	C₂²	1	2	yes	complemented
76	#4039	C₂²	1	1	yes	characteristic
77	#4039	C₂²	1	2	yes	complemented
78	#4038	C₂²	1	2	yes	—
79	#4036	C₂²	1	2	yes	complemented
80	#4035	C₂²	1	1	yes	characteristic, complemented
81	#4034	C₂²	1	2	yes	complemented
82	#4033	C₂²	1	1	yes	characteristic, complemented
83	#4033	C₂²	1	1	yes	characteristic, complemented
84	#4033	C₂²	1	1	yes	characteristic, complemented
85	#4032	C₂²	1	2	yes	—
86	#4032	C₂²	1	2	yes	complemented
87	#4032	C₂²	1	2	yes	complemented
88	#4031	C₂²	1	2	yes	—
89	#4031	C₂²	1	2	yes	—
90	#4031	C₂²	1	1	yes	characteristic, complemented
91	#4031	C₂²	1	2	yes	complemented
92	#4031	C₂²	1	2	yes	complemented
93	#4030	C₂²	1	1	yes	characteristic
94	#4030	C₂²	1	2	yes	complemented
95	#4029	C₂²	1	1	yes	characteristic
96	#4029	C₂²	1	2	yes	—
97	#4029	C₂²	1	2	yes	complemented
98	#4029	C₂²	1	2	yes	complemented
99	#4028	C₂²	1	2	yes	—
100	#4027	C₂²	1	2	yes	—
101	D₅×C₂²⋊C₄	C₂²	1	2	yes	—
102	D₅×C₂²⋊C₄	C₂²	1	2	yes	—
103	D₅×C₂²⋊C₄	C₂²	1	2	yes	—
104	#4025	C₂²	1	1	yes	characteristic, complemented
105	#4025	C₂²	1	2	yes	complemented
106	#4025	C₂²	1	2	yes	complemented
107	#4024	C₂²	1	2	yes	complemented
108	#4024	C₂²	1	2	yes	complemented
109	#4024	C₂²	1	2	yes	complemented
110	#4024	C₂²	1	2	yes	complemented
111	#4022	C₂²	1	2	yes	complemented
112	#4021	C₂²	1	1	yes	characteristic
113	#4021	C₂²	1	1	yes	characteristic
114	C₄×D₂₀	C₂²	1	1	yes	characteristic
115	C₄×D₂₀	C₂²	1	2	yes	—
116	#4018	C₂²	1	1	yes	characteristic, complemented
117	#4018	C₂²	1	2	yes	complemented
118	C₄²×D₅	C₂²	1	1	yes	characteristic
119	#4015	C₂²	1	1	yes	characteristic, complemented
120	#4015	C₂²	1	1	yes	characteristic, complemented
121	#4015	C₂²	1	2	yes	complemented
122	C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
123	#3561	—	5	1	no	maximal, Sylow
124	C₂³×D₅	C₂³	1	2	yes	—
125	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
126	C₂×C₅×Q₈	C₂³	1	2	yes	—
127	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
128	C₂×C₅×D₄	C₂³	1	2	yes	—
129	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₅	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
132	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
136	C₂²×Dic₅	C₂³	1	2	yes	—
137	C₂²×Dic₅	C₂³	1	2	yes	—
138	Q₈×D₅	—	4	2	no	—
139	Q₈×D₅	—	4	2	no	—
140	#711	—	4	2	no	—
141	D₄×D₅	—	4	2	no	—
142	#709	—	4	2	no	—
143	C₂×D₂₀	C₂³	1	1	yes	characteristic
144	C₂×D₂₀	C₂³	1	1	yes	characteristic
145	C₂×D₂₀	C₂³	1	2	yes	—
146	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
147	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₅	C₂³	1	2	yes	—
150	C₂×C₄×D₅	C₂³	1	2	yes	—
151	C₂×C₄×D₅	C₂³	1	2	yes	—
152	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₅	C₂³	1	2	yes	—
154	C₂×Dic₁₀	—	4	2	no	—
155	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
156	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
157	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
158	C₂×Dic₁₀	C₂³	1	2	yes	—
159	C₂×Dic₁₀	C₂³	1	2	yes	—
160	C₂×Dic₁₀	C₂³	1	2	yes	—
161	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
162	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
163	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
164	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
165	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
166	C₅×C₄⋊C₄	C₂³	1	2	yes	—
167	C₅×C₄⋊C₄	C₂³	1	2	yes	—
168	C₅×C₄⋊C₄	C₂³	1	2	yes	—
169	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
170	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
171	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₄²×C₅	C₂³	1	1	yes	characteristic
177	C₄²×C₅	C₂³	1	1	yes	characteristic
178	C₄²×C₅	C₂³	1	2	yes	—
179	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
180	C₂²⋊Dic₅	C₂³	1	2	yes	—
181	C₂²⋊Dic₅	C₂³	1	2	yes	—
182	C₂²⋊Dic₅	C₂³	1	2	yes	—
183	C₂²⋊Dic₅	C₂³	1	2	yes	—
184	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
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	#685	C₂³	1	1	yes	characteristic
193	#685	C₂³	1	2	yes	—
194	#685	C₂³	1	2	yes	—
195	#685	C₂³	1	2	yes	—
196	#685	C₂³	1	2	yes	—
197	#685	C₂³	1	2	yes	—
198	#685	C₂³	1	1	yes	characteristic
199	#685	C₂³	1	2	yes	—
200	#685	C₂³	1	1	yes	characteristic
201	#685	C₂³	1	2	yes	—
202	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
203	C₄⋊Dic₅	C₂³	1	2	yes	—
204	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
205	C₄⋊Dic₅	C₂³	1	2	yes	—
206	C₄⋊Dic₅	C₂³	1	2	yes	—
207	C₄⋊Dic₅	C₂³	1	2	yes	—
208	C₄⋊Dic₅	C₂³	1	2	yes	—
209	C₄⋊Dic₅	C₂³	1	2	yes	—
210	C₄⋊Dic₅	C₂³	1	2	yes	—
211	#683	C₂³	1	1	yes	characteristic
212	#683	C₂³	1	1	yes	characteristic
213	#683	C₂³	1	1	yes	characteristic
214	#683	C₂³	1	1	yes	characteristic
215	#683	C₂³	1	2	yes	—
216	#683	C₂³	1	2	yes	—
217	#683	C₂³	1	2	yes	—
218	#683	C₂³	1	1	yes	characteristic
219	#683	C₂³	1	2	yes	—
220	#683	C₂³	1	2	yes	—
221	#683	C₂³	1	1	yes	characteristic
222	C₄×Dic₅	C₂³	1	1	yes	characteristic
223	C₄×Dic₅	C₂³	1	1	yes	characteristic
224	C₄×Dic₅	C₂³	1	1	yes	characteristic
225	C₄×Dic₅	C₂³	1	1	yes	characteristic
226	C₄×Dic₅	C₂³	1	2	yes	—
227	C₄×Dic₅	C₂³	1	2	yes	—
228	C₄×Dic₅	C₂³	1	2	yes	—
229	#563	—	5	2	no	—
230	#562	—	5	2	no	—
231	#556	—	5	1	no	—
232	#556	—	5	1	no	—
233	#551	—	5	2	no	—
234	#551	—	5	2	no	—
235	D₄×Q₈	—	5	1	no	—
236	D₄×Q₈	—	5	1	no	—
237	#548	—	5	1	no	—
238	#548	—	5	1	no	—
239	#546	—	5	1	no	—
240	#546	—	5	1	no	—
241	#543	—	5	2	no	—
242	#542	—	5	1	no	—
243	#542	—	5	2	no	—
244	#542	—	5	2	no	—
245	#542	D₅	1	1	yes	characteristic, complemented
246	#538	—	5	2	no	—
247	#536	—	5	1	no	—
248	#536	—	5	1	no	—
249	#533	—	5	1	no	—
250	#529	—	5	1	no	—
251	C₂×#124	—	5	1	no	—
252	C₂³×C₅	C₂⁴	1	2	yes	—
253	C₂³×C₅	C₂⁴	1	1	yes	characteristic
254	C₂²×D₅	—	2	4	no	—
255	C₂²×D₅	—	4	2	no	—
256	C₂²×D₅	—	4	2	no	—
257	C₂²×D₅	C₂⁴	1	2	yes	—
258	C₂²×D₅	C₂⁴	1	1	yes	characteristic
259	C₂²×D₅	C₂⁴	1	1	yes	characteristic
260	C₅×Q₈	—	2	2	no	—
261	C₅×Q₈	—	4	2	no	—
262	C₅×D₄	—	2	2	no	—
263	C₅×D₄	—	4	2	no	—
264	C₂×C₄×C₅	—	2	2	no	—
265	C₂×C₄×C₅	—	4	2	no	—
266	C₂×C₄×C₅	C₂⁴	1	2	yes	—
267	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
268	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
269	C₂×C₄×C₅	C₂⁴	1	2	yes	—
270	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
271	C₂×C₄×C₅	C₂⁴	1	2	yes	—
272	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
273	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
274	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
275	C₂²⋊D₅	—	2	2	no	—
276	C₂²⋊D₅	—	4	2	no	—
277	C₂²⋊D₅	—	4	2	no	—
278	C₂²⋊D₅	—	4	2	no	—
279	C₂²⋊D₅	—	4	1	no	—
280	C₂×Dic₅	—	4	2	no	—
281	C₂×Dic₅	—	4	2	no	—
282	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
283	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
284	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
285	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
286	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
287	C₂×Dic₅	C₂⁴	1	2	yes	—
288	C₂×Dic₅	C₂⁴	1	2	yes	—
289	C₂×Dic₅	C₂⁴	1	2	yes	—
290	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
291	D₂₀	—	2	2	no	—
292	D₂₀	—	2	2	no	—
293	D₂₀	—	4	2	no	—
294	C₄×D₅	—	2	2	no	—
295	C₄×D₅	—	2	2	no	—
296	C₄×D₅	—	2	2	no	—
297	C₄×D₅	—	4	2	no	—
298	C₄×D₅	—	4	1	no	—
299	C₄×D₅	—	4	2	no	—
300	C₄×D₅	—	4	2	no	—
301	C₄×D₅	—	4	2	no	—
302	Dic₁₀	—	2	2	no	—
303	Dic₁₀	—	2	2	no	—
304	Dic₁₀	—	2	2	no	—
305	Dic₁₀	—	4	2	no	—
306	Dic₁₀	—	4	1	no	—
307	Dic₁₀	—	4	2	no	—
308	Dic₁₀	—	4	2	no	—
309	C₂×#41	—	5	1	no	—
310	C₂×#41	—	5	1	no	—
311	C₂²×Q₈	—	5	1	no	—
312	C₂²×Q₈	—	5	1	no	—
313	C₂²×Q₈	—	5	1	no	—
314	C₂²×D₄	—	5	1	no	—
315	C₄⋊Q₈	—	5	1	no	—
316	C₄⋊Q₈	—	5	2	no	—
317	C₄⋊Q₈	—	5	1	no	—
318	C₄⋊Q₈	—	5	1	no	—
319	C₄⋊Q₈	—	5	2	no	—
320	C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
321	#126	—	5	1	no	—
322	#126	—	5	2	no	—
323	#126	—	5	2	no	—
324	#126	—	5	1	no	—
325	#126	—	5	2	no	—
326	#126	—	5	2	no	—
327	#126	—	5	2	no	—
328	#126	C₂×D₅	1	2	yes	complemented
329	#125	—	5	1	no	—
330	#125	—	5	2	no	—
331	#124	—	5	1	no	—
332	#124	—	5	2	no	—
333	#124	—	5	1	no	—
334	#124	—	5	1	no	—
335	#124	—	5	2	no	—
336	#124	—	5	2	no	—
337	#124	—	5	1	no	—
338	#124	—	5	2	no	—
339	#124	—	5	2	no	—
340	#124	—	5	1	no	—
341	#124	—	5	1	no	—
342	#124	C₂×D₅	1	1	yes	characteristic
343	#124	C₂×D₅	1	2	yes	complemented
344	#123	—	5	1	no	—
345	#123	—	5	2	no	—
346	#123	—	5	1	no	—
347	#123	—	5	2	no	—
348	#123	—	5	2	no	—
349	#123	—	5	2	no	—
350	#123	—	5	2	no	—
351	#123	—	5	2	no	—
352	#123	—	5	2	no	—
353	#123	C₂×D₅	1	2	yes	complemented
354	C₂²⋊Q₈	—	5	2	no	—
355	C₂²⋊Q₈	—	5	2	no	—
356	C₂²⋊Q₈	—	5	2	no	—
357	C₂²⋊Q₈	—	5	1	no	—
358	C₂²⋊Q₈	—	5	1	no	—
359	C₂²⋊Q₈	—	5	1	no	—
360	C₂²⋊Q₈	—	5	2	no	—
361	C₂²⋊Q₈	—	5	2	no	—
362	C₂²⋊Q₈	—	5	1	no	—
363	C₂²⋊Q₈	—	5	2	no	—
364	C₂²⋊Q₈	—	5	2	no	—
365	C₂²⋊Q₈	—	5	2	no	—
366	C₂²⋊Q₈	—	5	2	no	—
367	C₂²⋊Q₈	—	5	2	no	—
368	C₂²⋊Q₈	—	5	2	no	—
369	C₂²⋊Q₈	—	5	2	no	—
370	C₂²⋊Q₈	—	5	2	no	—
371	C₂²⋊Q₈	—	5	2	no	—
372	C₂²⋊Q₈	C₂×D₅	1	2	yes	complemented
373	C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
374	#121	—	5	2	no	—
375	#121	—	5	2	no	—
376	#121	—	5	2	no	—
377	#121	—	5	1	no	—
378	#121	—	5	1	no	—
379	#121	—	5	2	no	—
380	#121	C₂×D₅	1	1	yes	characteristic
381	#120	—	5	2	no	—
382	#120	—	5	2	no	—
383	C₄×Q₈	—	5	2	no	—
384	C₄×Q₈	—	5	1	no	—
385	C₄×Q₈	—	5	1	no	—
386	C₄×Q₈	—	5	1	no	—
387	C₄×Q₈	—	5	1	no	—
388	C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
389	C₄×D₄	—	5	2	no	—
390	C₄×D₄	—	5	1	no	—
391	C₄×D₄	—	5	1	no	—
392	C₄×D₄	—	5	1	no	—
393	C₄×D₄	—	5	2	no	—
394	C₄×D₄	—	5	2	no	—
395	C₄×D₄	—	5	1	no	—
396	C₄×D₄	—	5	2	no	—
397	C₄×D₄	C₂×D₅	1	1	yes	characteristic
398	#117	—	5	2	no	—
399	#117	—	5	2	no	—
400	#117	—	5	1	no	—
401	#117	—	5	2	no	—
402	#117	C₂×D₅	1	1	yes	characteristic, complemented
403	C₂×C₂²⋊C₄	—	5	2	no	—
404	C₂×C₂²⋊C₄	—	5	2	no	—
405	C₂×C₂²⋊C₄	—	5	2	no	—
406	C₂×C₂²⋊C₄	—	5	2	no	—
407	C₂×C₄²	—	5	1	no	—
408	C₂²×C₅	—	2	1	no	—
409	C₂²×C₅	—	2	2	no	—
410	C₂²×C₅	—	2	1	no	—
411	C₂²×C₅	—	2	2	no	—
412	C₂²×C₅	—	2	1	no	—
413	C₂²×C₅	—	2	2	no	—
414	C₂²×C₅	C₂⁵	1	1	yes	characteristic
415	C₂×D₅	—	2	1	no	—
416	C₂×D₅	—	2	1	no	—
417	C₂×D₅	—	2	1	no	—
418	C₂×D₅	—	2	2	no	—
419	C₂×D₅	—	2	1	no	—
420	C₂×D₅	—	2	2	no	—
421	C₂×D₅	—	2	2	no	—
422	C₂×D₅	—	2	1	no	—
423	C₂×D₅	—	8	4	no	—
424	C₂×D₅	2₋¹⁺⁴	1	2	yes	—
425	C₄×C₅	—	2	1	no	—
426	C₄×C₅	—	2	2	no	—
427	C₄×C₅	—	2	1	no	—
428	C₄×C₅	—	2	1	no	—
429	C₄×C₅	—	2	1	no	—
430	C₄×C₅	—	2	2	no	—
431	C₄×C₅	—	2	1	no	—
432	C₄×C₅	—	2	2	no	—
433	C₄×C₅	H(5,𝔽₂)	1	2	yes	—
434	Dic₅	—	2	2	no	—
435	Dic₅	—	2	2	no	—
436	Dic₅	—	2	2	no	—
437	Dic₅	—	2	1	no	—
438	Dic₅	—	2	1	no	—
439	Dic₅	—	2	1	no	—
440	Dic₅	—	2	1	no	—
441	Dic₅	—	2	1	no	—
442	Dic₅	—	2	1	no	—
443	C₂⁴	—	5	2	no	—
444	#41	—	20	2	no	—
445	#41	—	20	2	no	—
446	C₂×Q₈	—	5	1	no	—
447	C₂×Q₈	—	5	1	no	—
448	C₂×Q₈	—	5	1	no	—
449	C₂×Q₈	—	5	1	no	—
450	C₂×Q₈	—	5	2	no	—
451	C₂×Q₈	—	5	2	no	—
452	C₂×Q₈	—	5	2	no	—
453	C₂×Q₈	—	20	2	no	—
454	C₂×Q₈	—	20	2	no	—
455	C₂×Q₈	—	20	2	no	—
456	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
457	C₂×Q₈	C₂²×D₅	1	2	yes	—
458	C₂×D₄	—	5	1	no	—
459	C₂×D₄	—	5	1	no	—
460	C₂×D₄	—	5	2	no	—
461	C₂×D₄	—	5	2	no	—
462	C₂×D₄	—	5	2	no	—
463	C₂×D₄	—	5	1	no	—
464	C₂×D₄	—	5	1	no	—
465	C₂×D₄	—	5	2	no	—
466	C₂×D₄	—	20	2	no	—
467	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
468	C₂×D₄	C₂²×D₅	1	2	yes	—
469	C₂²×C₄	—	5	2	no	—
470	C₂²×C₄	—	5	2	no	—
471	C₂²×C₄	—	5	1	no	—
472	C₂²×C₄	—	5	1	no	—
473	C₂²×C₄	—	5	1	no	—
474	C₂²×C₄	—	5	1	no	—
475	C₂²×C₄	—	5	2	no	—
476	C₂²×C₄	—	5	2	no	—
477	C₂²×C₄	—	5	2	no	—
478	C₂²×C₄	—	5	2	no	—
479	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
480	C₂²×C₄	C₂²×D₅	1	2	yes	—
481	C₄⋊C₄	—	5	1	no	—
482	C₄⋊C₄	—	5	1	no	—
483	C₄⋊C₄	—	5	1	no	—
484	C₄⋊C₄	—	5	2	no	—
485	C₄⋊C₄	—	5	2	no	—
486	C₄⋊C₄	—	5	2	no	—
487	C₄⋊C₄	—	5	1	no	—
488	C₄⋊C₄	—	5	1	no	—
489	C₄⋊C₄	—	5	2	no	—
490	C₄⋊C₄	—	5	2	no	—
491	C₄⋊C₄	—	5	2	no	—
492	C₄⋊C₄	—	5	1	no	—
493	C₄⋊C₄	—	5	1	no	—
494	C₄⋊C₄	—	5	2	no	—
495	C₄⋊C₄	—	5	2	no	—
496	C₄⋊C₄	—	5	2	no	—
497	C₄⋊C₄	—	5	2	no	—
498	C₄⋊C₄	—	5	1	no	—
499	C₄⋊C₄	—	5	2	no	—
500	C₄⋊C₄	—	5	2	no	—
501	C₄⋊C₄	C₂²×D₅	1	2	yes	—
502	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
503	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
504	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
505	C₄⋊C₄	C₂²×D₅	1	2	yes	—
506	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
507	C₄⋊C₄	C₂²×D₅	1	2	yes	—
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	2	no	—
517	C₂²⋊C₄	—	5	2	no	—
518	C₂²⋊C₄	—	5	2	no	—
519	C₂²⋊C₄	—	5	2	no	—
520	C₂²⋊C₄	—	5	2	no	—
521	C₂²⋊C₄	—	5	2	no	—
522	C₂²⋊C₄	—	5	2	no	—
523	C₂²⋊C₄	—	5	2	no	—
524	C₂²⋊C₄	—	5	2	no	—
525	C₂²⋊C₄	—	5	1	no	—
526	C₂²⋊C₄	—	5	1	no	—
527	C₂²⋊C₄	—	5	1	no	—
528	C₂²⋊C₄	—	5	2	no	—
529	C₂²⋊C₄	—	5	1	no	—
530	C₂²⋊C₄	—	5	2	no	—
531	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
532	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
533	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
534	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
535	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
536	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
537	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
538	C₄²	—	5	1	no	—
539	C₄²	—	5	1	no	—
540	C₄²	—	5	1	no	—
541	C₄²	—	5	2	no	—
542	C₄²	—	5	2	no	—
543	C₄²	—	5	1	no	—
544	C₄²	—	5	2	no	—
545	C₄²	C₂²×D₅	1	1	yes	characteristic
546	C₄²	C₂²×D₅	1	2	yes	—
547	C₄²	C₂²×D₅	1	1	yes	characteristic
548	C₂×C₅	—	4	2	no	—
549	C₂×C₅	—	4	1	no	—
550	C₂×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
551	C₂×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
552	C₂×C₅	#585	1	1	yes	characteristic
553	D₅	—	2	2	no	—
554	D₅	—	4	1	no	—
555	D₅	—	4	2	no	—
556	C₂³	—	5	1	no	—
557	C₂³	—	5	2	no	—
558	C₂³	—	5	1	no	—
559	C₂³	—	10	4	no	—
560	C₂³	—	20	2	no	—
561	C₂³	—	20	2	no	—
562	C₂³	C₂³×D₅	1	2	yes	—
563	C₂³	C₂³×D₅	1	1	yes	characteristic
564	Q₈	—	2	2	no	—
565	Q₈	—	4	2	no	—
566	Q₈	—	10	2	no	—
567	Q₈	—	10	2	no	—
568	Q₈	—	10	2	no	—
569	Q₈	—	20	2	no	—
570	Q₈	—	20	2	no	—
571	Q₈	—	20	2	no	—
572	Q₈	—	20	1	no	—
573	D₄	—	2	2	no	—
574	D₄	—	4	2	no	—
575	D₄	—	10	2	no	—
576	D₄	—	10	2	no	—
577	D₄	—	10	2	no	—
578	D₄	—	20	2	no	—
579	D₄	—	20	2	no	—
580	D₄	—	20	2	no	—
581	D₄	—	20	2	no	—
582	D₄	—	20	1	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	4	2	no	—
585	C₂×C₄	—	5	1	no	—
586	C₂×C₄	—	5	1	no	—
587	C₂×C₄	—	5	1	no	—
588	C₂×C₄	—	5	1	no	—
589	C₂×C₄	—	5	1	no	—
590	C₂×C₄	—	5	2	no	—
591	C₂×C₄	—	5	2	no	—
592	C₂×C₄	—	5	2	no	—
593	C₂×C₄	—	5	1	no	—
594	C₂×C₄	—	10	2	no	—
595	C₂×C₄	—	10	2	no	—
596	C₂×C₄	—	10	2	no	—
597	C₂×C₄	—	20	2	no	—
598	C₂×C₄	—	20	2	no	—
599	C₂×C₄	—	20	2	no	—
600	C₂×C₄	—	20	2	no	—
601	C₂×C₄	—	20	1	no	—
602	C₂×C₄	—	20	2	no	—
603	C₂×C₄	—	20	2	no	—
604	C₂×C₄	C₂³×D₅	1	2	yes	—
605	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
606	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
607	C₂×C₄	C₂³×D₅	1	2	yes	—
608	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
609	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
610	C₂×C₄	C₂³×D₅	1	2	yes	—
611	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
612	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
613	C₅	#3561	1	1	yes	characteristic, complemented, Sylow
614	C₂²	—	2	1	no	—
615	C₂²	—	2	2	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	2	1	no	—
619	C₂²	—	2	2	no	—
620	C₂²	—	5	2	no	—
621	C₂²	—	10	1	no	—
622	C₂²	—	10	1	no	—
623	C₂²	—	10	1	no	—
624	C₂²	—	10	2	no	—
625	C₂²	—	10	2	no	—
626	C₂²	—	10	1	no	—
627	C₂²	—	10	1	no	—
628	C₂²	—	10	2	no	—
629	C₂²	—	40	4	no	—
630	C₂²	C₂⁴×D₅	1	1	yes	characteristic
631	C₄	—	2	1	no	—
632	C₄	—	2	2	no	—
633	C₄	—	2	1	no	—
634	C₄	—	2	2	no	—
635	C₄	—	2	2	no	—
636	C₄	—	2	1	no	—
637	C₄	—	2	1	no	—
638	C₄	—	2	1	no	—
639	C₄	—	10	1	no	—
640	C₄	—	10	1	no	—
641	C₄	—	10	2	no	—
642	C₄	—	10	2	no	—
643	C₄	—	10	2	no	—
644	C₄	—	10	1	no	—
645	C₄	—	10	1	no	—
646	C₄	—	10	1	no	—
647	C₄	—	10	1	no	—
648	C₄	#4149	1	2	yes	—
649	C₂	—	4	2	no	—
650	C₂	—	4	1	no	—
651	C₂	—	10	2	no	—
652	C₂	—	20	2	no	—
653	C₂	—	20	1	no	—
654	C₂	C₂×#4149	1	1	yes	characteristic
655	C₂	#66285	1	1	yes	characteristic
656	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×#542	C₂
hypercenter	#542	D₅
hypocenter	C₅	#3561
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ #542

Complements

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

N	H ≅ G/N	type
1. C₅×#542	C₂	semidirect
2. #66067	C₂	semidirect
3. #66062	C₂	semidirect
4. #66046	C₂	semidirect
5. #66039	C₂	semidirect
6. #66016	C₂	semidirect
7. #66012	C₂	semidirect
8. #66009	C₂	semidirect
9. D₅×#124	C₂	semidirect
10. #66001	C₂	semidirect
11. #65992	C₂	semidirect
12. #65977	C₂	semidirect
13. #65968	C₂	semidirect
14. #65967	C₂	semidirect
15. #65966	C₂	semidirect
16. #65946	C₂	semidirect
17. #65932	C₂	semidirect
18. Q₈×D₂₀	C₂	semidirect
19. #65902	C₂	semidirect
20. #65888	C₂	semidirect
21. #65876	C₂	semidirect
22. #65862	C₂	semidirect
23. #65860	C₂	semidirect
25. C₂×Q₈×D₅	C₂²	semidirect
29. C₂²×Dic₁₀	C₂²	semidirect
30. C₅×C₄⋊Q₈	C₂²	semidirect
31. C₅×#126	C₂²	semidirect
33. C₅×#124	C₂²	semidirect
34. C₅×#123	C₂²	semidirect
35. C₅×C₂²⋊Q₈	C₂²	semidirect
36. C₅×C₂²⋊Q₈	C₂²	semidirect
38. C₄×C₅×Q₈	C₂²	semidirect
40. C₅×#117	C₂²	semidirect
42. #4093	C₂²	semidirect
44. #4092	C₂²	semidirect
45. Q₈×Dic₅	C₂²	semidirect
46. #4090	C₂²	semidirect
47. #4085	C₂²	semidirect
52. D₄×Dic₅	C₂²	semidirect
55. C₄×C₂²⋊D₅	C₂²	semidirect
57. #4072	C₂²	semidirect
58. #4070	C₂²	semidirect
59. #4044	C₂²	semidirect
60. #4044	C₂²	semidirect
61. #4044	C₂²	semidirect
65. #4043	C₂²	semidirect
66. #4043	C₂²	semidirect
67. #4043	C₂²	semidirect
68. #4043	C₂²	semidirect
71. #4042	C₂²	semidirect
72. #4042	C₂²	semidirect
75. #4040	C₂²	semidirect
77. #4039	C₂²	semidirect
79. #4036	C₂²	semidirect
80. #4035	C₂²	semidirect
81. #4034	C₂²	semidirect
82. #4033	C₂²	semidirect
83. #4033	C₂²	semidirect
84. #4033	C₂²	semidirect
86. #4032	C₂²	semidirect
87. #4032	C₂²	semidirect
90. #4031	C₂²	semidirect
91. #4031	C₂²	semidirect
92. #4031	C₂²	semidirect
94. #4030	C₂²	semidirect
97. #4029	C₂²	semidirect
98. #4029	C₂²	semidirect
104. #4025	C₂²	semidirect
105. #4025	C₂²	semidirect
106. #4025	C₂²	semidirect
107. #4024	C₂²	semidirect
108. #4024	C₂²	semidirect
109. #4024	C₂²	semidirect
110. #4024	C₂²	semidirect
111. #4022	C₂²	semidirect
116. #4018	C₂²	semidirect
117. #4018	C₂²	semidirect
119. #4015	C₂²	semidirect
120. #4015	C₂²	semidirect
121. #4015	C₂²	semidirect
122. C₄×Dic₁₀	C₂²	semidirect
245. #542	D₅	semidirect
320. C₄⋊Q₈	C₂×D₅	semidirect
328. #126	C₂×D₅	semidirect
343. #124	C₂×D₅	semidirect
353. #123	C₂×D₅	semidirect
372. C₂²⋊Q₈	C₂×D₅	semidirect
373. C₂²⋊Q₈	C₂×D₅	semidirect
388. C₄×Q₈	C₂×D₅	semidirect
402. #117	C₂×D₅	semidirect
613. C₅	#3561	semidirect

Maximal subgroups

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

subgroup	index
C₅×#542	2
#66067	2
#66062	2
#66046	2
#66039	2
#66016	2
#66012	2
#66009	2
D₅×#124	2
#66001	2
#65992	2
#65977	2
#65968	2
#65967	2
#65966	2
#65946	2
#65932	2
Q₈×D₂₀	2
#65902	2
#65888	2
#65876	2
#65862	2
#65860	2
#3561	5