Subgroups — #10618899

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×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	#66061	C₂	1	1	yes	maximal, characteristic, complemented
3	#66058	C₂	1	1	yes	maximal, characteristic, complemented
4	#66046	C₂	1	2	yes	maximal, complemented
5	#66044	C₂	1	2	yes	maximal, complemented
6	#66039	C₂	1	2	yes	maximal, complemented
7	#66038	C₂	1	2	yes	maximal, complemented
8	#66011	C₂	1	1	yes	maximal, characteristic, complemented
9	#66010	C₂	1	1	yes	maximal, characteristic, complemented
10	#66009	C₂	1	1	yes	maximal, characteristic, complemented
11	D₅×#124	C₂	1	1	yes	maximal, characteristic, complemented
12	#65981	C₂	1	2	yes	maximal, complemented
13	#65968	C₂	1	2	yes	maximal, complemented
14	#65918	C₂	1	1	yes	maximal, characteristic, complemented
15	#65916	C₂	1	1	yes	maximal, characteristic, complemented
16	#65914	C₂	1	1	yes	maximal, characteristic, complemented
17	#65912	C₂	1	1	yes	maximal, characteristic, complemented
18	#65910	C₂	1	1	yes	maximal, characteristic, complemented
19	Q₈×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
20	#65895	C₂	1	1	yes	maximal, characteristic, complemented
21	#65888	C₂	1	1	yes	maximal, characteristic, complemented
22	#65868	C₂	1	2	yes	maximal, complemented
23	#65861	C₂	1	2	yes	maximal, complemented
24	C₂×#713	C₂²	1	1	yes	characteristic
25	C₂×Q₈×D₅	C₂²	1	1	yes	characteristic
26	C₂×Q₈×D₅	C₂²	1	1	yes	characteristic, complemented
27	C₂×Q₈×D₅	C₂²	1	1	yes	characteristic, complemented
28	C₂×#711	C₂²	1	1	yes	characteristic
29	C₂×D₄×D₅	C₂²	1	1	yes	characteristic
30	C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₅×#126	C₂²	1	2	yes	complemented
32	C₅×#126	C₂²	1	2	yes	complemented
33	C₅×#124	C₂²	1	1	yes	characteristic
34	C₅×#124	C₂²	1	1	yes	characteristic
35	C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
36	C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
38	C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
39	C₄×C₅×D₄	C₂²	1	1	yes	characteristic
40	C₅×#117	C₂²	1	2	yes	complemented
41	#4093	C₂²	1	1	yes	characteristic
42	#4093	C₂²	1	1	yes	characteristic, complemented
43	#4092	C₂²	1	1	yes	characteristic
44	#4092	C₂²	1	1	yes	characteristic
45	#4092	C₂²	1	1	yes	characteristic, complemented
46	#4092	C₂²	1	2	yes	complemented
47	#4090	C₂²	1	1	yes	characteristic, complemented
48	#4084	C₂²	1	1	yes	characteristic
49	#4082	C₂²	1	1	yes	characteristic
50	#4076	C₂²	1	2	yes	—
51	#4075	C₂²	1	2	yes	complemented
52	C₂×#685	C₂²	1	2	yes	—
53	#4070	C₂²	1	2	yes	complemented
54	#4044	C₂²	1	2	yes	complemented
55	#4044	C₂²	1	1	yes	characteristic, complemented
56	#4044	C₂²	1	1	yes	characteristic, complemented
57	#4044	C₂²	1	2	yes	complemented
58	#4043	C₂²	1	1	yes	characteristic
59	#4043	C₂²	1	2	yes	—
60	#4043	C₂²	1	1	yes	characteristic, complemented
61	#4043	C₂²	1	2	yes	complemented
62	#4043	C₂²	1	2	yes	complemented
63	#4042	C₂²	1	2	yes	—
64	#4042	C₂²	1	2	yes	—
65	#4042	C₂²	1	2	yes	complemented
66	#4042	C₂²	1	2	yes	complemented
67	#4042	C₂²	1	2	yes	complemented
68	#4042	C₂²	1	2	yes	complemented
69	#4041	C₂²	1	1	yes	characteristic
70	#4041	C₂²	1	1	yes	characteristic
71	#4041	C₂²	1	2	yes	complemented
72	#4040	C₂²	1	1	yes	characteristic
73	#4040	C₂²	1	1	yes	characteristic
74	#4040	C₂²	1	2	yes	complemented
75	#4040	C₂²	1	2	yes	complemented
76	#4040	C₂²	1	2	yes	complemented
77	#4039	C₂²	1	2	yes	—
78	#4038	C₂²	1	2	yes	complemented
79	#4036	C₂²	1	1	yes	characteristic, complemented
80	#4035	C₂²	1	2	yes	complemented
81	#4034	C₂²	1	2	yes	complemented
82	#4034	C₂²	1	1	yes	characteristic, complemented
83	#4032	C₂²	1	2	yes	—
84	#4031	C₂²	1	2	yes	—
85	#4031	C₂²	1	2	yes	—
86	#4031	C₂²	1	2	yes	complemented
87	#4031	C₂²	1	2	yes	complemented
88	#4030	C₂²	1	2	yes	—
89	#4030	C₂²	1	2	yes	complemented
90	#4029	C₂²	1	2	yes	—
91	#4029	C₂²	1	2	yes	complemented
92	#4029	C₂²	1	2	yes	complemented
93	#4028	C₂²	1	2	yes	—
94	#4028	C₂²	1	2	yes	—
95	#4027	C₂²	1	2	yes	complemented
96	D₅×C₂²⋊C₄	C₂²	1	2	yes	—
97	D₅×C₂²⋊C₄	C₂²	1	2	yes	—
98	D₅×C₂²⋊C₄	C₂²	1	2	yes	—
99	#4025	C₂²	1	2	yes	complemented
100	#4024	C₂²	1	2	yes	complemented
101	#4024	C₂²	1	2	yes	complemented
102	#4024	C₂²	1	2	yes	complemented
103	#4022	C₂²	1	2	yes	complemented
104	#4021	C₂²	1	1	yes	characteristic
105	#4021	C₂²	1	1	yes	characteristic
106	#4021	C₂²	1	2	yes	complemented
107	#4021	C₂²	1	2	yes	complemented
108	C₄×D₂₀	C₂²	1	1	yes	characteristic
109	C₄×D₂₀	C₂²	1	2	yes	—
110	C₄×D₂₀	C₂²	1	1	yes	characteristic
111	C₄×D₂₀	C₂²	1	1	yes	characteristic
112	C₄×D₂₀	C₂²	1	2	yes	complemented
113	C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
114	#4018	C₂²	1	2	yes	—
115	#4018	C₂²	1	1	yes	characteristic, complemented
116	#4018	C₂²	1	1	yes	characteristic, complemented
117	C₄²×D₅	C₂²	1	1	yes	characteristic
118	#4015	C₂²	1	2	yes	complemented
119	#4015	C₂²	1	1	yes	characteristic, complemented
120	C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₁₀	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	1	yes	characteristic
127	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
128	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₅	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
133	C₂²×Dic₅	C₂³	1	2	yes	—
134	#713	—	4	2	no	—
135	Q₈×D₅	—	4	2	no	—
136	Q₈×D₅	—	4	2	no	—
137	Q₈×D₅	—	4	2	no	—
138	#711	—	4	2	no	—
139	D₄×D₅	—	4	2	no	—
140	C₂×D₂₀	C₂³	1	1	yes	characteristic
141	C₂×D₂₀	C₂³	1	1	yes	characteristic
142	C₂×D₂₀	C₂³	1	1	yes	characteristic
143	C₂×D₂₀	C₂³	1	2	yes	—
144	C₂×D₂₀	C₂³	1	2	yes	—
145	C₂×D₂₀	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
150	C₂×C₄×D₅	C₂³	1	2	yes	—
151	C₂×C₄×D₅	C₂³	1	2	yes	—
152	C₂×C₄×D₅	C₂³	1	2	yes	—
153	C₂×C₄×D₅	C₂³	1	2	yes	—
154	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₅	C₂³	1	2	yes	—
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	2	yes	—
162	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
163	C₅×C₄⋊C₄	C₂³	1	2	yes	—
164	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
165	C₅×C₄⋊C₄	C₂³	1	2	yes	—
166	C₅×C₄⋊C₄	C₂³	1	2	yes	—
167	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
168	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
169	C₅×C₄⋊C₄	C₂³	1	2	yes	—
170	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
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	C₄²×C₅	C₂³	1	2	yes	—
176	C₄²×C₅	C₂³	1	2	yes	—
177	C₄²×C₅	C₂³	1	1	yes	characteristic
178	C₄²×C₅	C₂³	1	1	yes	characteristic
179	C₄²×C₅	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	#685	C₂³	1	2	yes	—
184	#685	C₂³	1	2	yes	—
185	#685	C₂³	1	1	yes	characteristic
186	#685	C₂³	1	1	yes	characteristic
187	#685	C₂³	1	1	yes	characteristic
188	#685	C₂³	1	1	yes	characteristic
189	#685	C₂³	1	2	yes	—
190	#685	C₂³	1	2	yes	—
191	#685	C₂³	1	1	yes	characteristic
192	#685	C₂³	1	1	yes	characteristic
193	#685	C₂³	1	1	yes	characteristic
194	#685	C₂³	1	1	yes	characteristic
195	#685	C₂³	1	1	yes	characteristic
196	#685	C₂³	1	2	yes	—
197	#685	C₂³	1	1	yes	characteristic
198	#685	C₂³	1	2	yes	—
199	#685	C₂³	1	2	yes	—
200	#685	C₂³	1	2	yes	—
201	#685	C₂³	1	2	yes	—
202	#685	C₂³	1	2	yes	—
203	#685	C₂³	1	2	yes	—
204	#685	C₂³	1	2	yes	—
205	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
206	C₄⋊Dic₅	C₂³	1	2	yes	—
207	C₄⋊Dic₅	C₂³	1	2	yes	—
208	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
209	C₄⋊Dic₅	C₂³	1	2	yes	—
210	C₄⋊Dic₅	C₂³	1	2	yes	—
211	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
212	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
213	#683	C₂³	1	2	yes	—
214	#683	C₂³	1	2	yes	—
215	#683	C₂³	1	2	yes	—
216	#683	C₂³	1	2	yes	—
217	#683	C₂³	1	2	yes	—
218	#683	C₂³	1	2	yes	—
219	#683	C₂³	1	1	yes	characteristic
220	#683	C₂³	1	1	yes	characteristic
221	#683	C₂³	1	1	yes	characteristic
222	#683	C₂³	1	1	yes	characteristic
223	#683	C₂³	1	2	yes	—
224	C₄×Dic₅	C₂³	1	1	yes	characteristic
225	C₄×Dic₅	C₂³	1	2	yes	—
226	C₄×Dic₅	C₂³	1	2	yes	—
227	C₄×Dic₅	C₂³	1	1	yes	characteristic
228	C₄×Dic₅	C₂³	1	1	yes	characteristic
229	#563	—	5	2	no	—
230	#562	—	5	2	no	—
231	#556	—	5	1	no	—
232	#556	D₅	1	1	yes	characteristic, complemented
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	2	no	—
243	#542	—	5	1	no	—
244	#542	—	5	1	no	—
245	#542	—	5	2	no	—
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	C₂²×D₅	—	2	4	no	—
254	C₂²×D₅	—	4	2	no	—
255	C₂²×D₅	—	4	2	no	—
256	C₂²×D₅	C₂⁴	1	2	yes	—
257	C₂²×D₅	C₂⁴	1	1	yes	characteristic
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	—	2	2	no	—
262	C₅×Q₈	—	4	1	no	—
263	C₅×D₄	—	2	2	no	—
264	C₂×C₄×C₅	—	4	2	no	—
265	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
266	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
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	2	yes	—
274	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
275	C₂²⋊D₅	—	4	2	no	—
276	C₂²⋊D₅	—	4	2	no	—
277	C₂²⋊D₅	—	4	2	no	—
278	C₂×Dic₅	—	4	2	no	—
279	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
280	C₂×Dic₅	C₂⁴	1	2	yes	—
281	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
282	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
283	C₂×Dic₅	C₂⁴	1	2	yes	—
284	C₂×Dic₅	C₂⁴	1	2	yes	—
285	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
286	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
287	D₂₀	—	2	2	no	—
288	D₂₀	—	2	2	no	—
289	D₂₀	—	2	2	no	—
290	D₂₀	—	4	2	no	—
291	D₂₀	—	4	1	no	—
292	D₂₀	—	4	2	no	—
293	C₄×D₅	—	2	2	no	—
294	C₄×D₅	—	2	2	no	—
295	C₄×D₅	—	2	2	no	—
296	C₄×D₅	—	2	2	no	—
297	C₄×D₅	—	4	1	no	—
298	C₄×D₅	—	4	2	no	—
299	C₄×D₅	—	4	2	no	—
300	C₄×D₅	—	4	2	no	—
301	C₄×D₅	—	4	2	no	—
302	C₄×D₅	—	4	2	no	—
303	Dic₁₀	—	2	2	no	—
304	Dic₁₀	—	2	2	no	—
305	Dic₁₀	—	4	2	no	—
306	Dic₁₀	—	4	2	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	1	no	—
317	C₄⋊Q₈	—	5	2	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	1	no	—
323	#126	—	5	2	no	—
324	#126	—	5	2	no	—
325	#126	—	5	2	no	—
326	#126	—	5	2	no	—
327	#126	C₂×D₅	1	2	yes	complemented
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	1	no	—
333	#124	—	5	1	no	—
334	#124	—	5	2	no	—
335	#124	—	5	2	no	—
336	#124	—	5	2	no	—
337	#124	—	5	2	no	—
338	#124	—	5	1	no	—
339	#124	—	5	1	no	—
340	#124	—	5	2	no	—
341	#124	—	5	2	no	—
342	#124	C₂×D₅	1	1	yes	characteristic
343	#124	C₂×D₅	1	1	yes	characteristic
344	#123	—	5	2	no	—
345	#123	—	5	1	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	—	5	2	no	—
354	C₂²⋊Q₈	—	5	1	no	—
355	C₂²⋊Q₈	—	5	1	no	—
356	C₂²⋊Q₈	—	5	1	no	—
357	C₂²⋊Q₈	—	5	2	no	—
358	C₂²⋊Q₈	—	5	2	no	—
359	C₂²⋊Q₈	—	5	2	no	—
360	C₂²⋊Q₈	—	5	1	no	—
361	C₂²⋊Q₈	—	5	2	no	—
362	C₂²⋊Q₈	—	5	2	no	—
363	C₂²⋊Q₈	—	5	2	no	—
364	C₂²⋊Q₈	—	5	1	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	—	5	2	no	—
373	C₂²⋊Q₈	C₂×D₅	1	2	yes	complemented
374	#121	—	5	1	no	—
375	#121	—	5	2	no	—
376	#121	—	5	1	no	—
377	#121	—	5	2	no	—
378	#121	—	5	1	no	—
379	#121	—	5	2	no	—
380	#121	—	5	2	no	—
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	C₂×D₅	1	1	yes	characteristic, complemented
387	C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
388	C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
389	C₄×D₄	—	5	2	no	—
390	C₄×D₄	—	5	2	no	—
391	C₄×D₄	—	5	1	no	—
392	C₄×D₄	—	5	1	no	—
393	C₄×D₄	—	5	1	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	1	no	—
400	#117	—	5	1	no	—
401	#117	—	5	2	no	—
402	#117	C₂×D₅	1	2	yes	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	2	no	—
409	C₂²×C₅	—	2	2	no	—
410	C₂²×C₅	—	2	2	no	—
411	C₂²×C₅	C₂⁵	1	1	yes	characteristic
412	C₂×D₅	—	2	1	no	—
413	C₂×D₅	—	2	1	no	—
414	C₂×D₅	—	2	1	no	—
415	C₂×D₅	—	2	1	no	—
416	C₂×D₅	—	2	2	no	—
417	C₂×D₅	—	2	1	no	—
418	C₂×D₅	—	2	1	no	—
419	C₂×D₅	—	2	2	no	—
420	C₂×D₅	—	2	2	no	—
421	C₂×D₅	—	2	1	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	2	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	1	no	—
433	C₄×C₅	—	2	1	no	—
434	C₄×C₅	H(5,𝔽₂)	1	2	yes	—
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	2	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	2	no	—
449	C₂×Q₈	—	5	2	no	—
450	C₂×Q₈	—	5	2	no	—
451	C₂×Q₈	—	5	2	no	—
452	C₂×Q₈	—	20	2	no	—
453	C₂×Q₈	—	20	2	no	—
454	C₂×Q₈	—	20	2	no	—
455	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
456	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
457	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
458	C₂×D₄	—	5	2	no	—
459	C₂×D₄	—	5	2	no	—
460	C₂×D₄	—	5	2	no	—
461	C₂×D₄	—	5	1	no	—
462	C₂×D₄	—	5	1	no	—
463	C₂×D₄	—	5	1	no	—
464	C₂×D₄	—	5	2	no	—
465	C₂×D₄	—	5	1	no	—
466	C₂×D₄	—	5	2	no	—
467	C₂×D₄	—	20	2	no	—
468	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
469	C₂²×C₄	—	5	2	no	—
470	C₂²×C₄	—	5	1	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	—	5	2	no	—
480	C₂²×C₄	C₂²×D₅	1	2	yes	—
481	C₄⋊C₄	—	5	1	no	—
482	C₄⋊C₄	—	5	1	no	—
483	C₄⋊C₄	—	5	2	no	—
484	C₄⋊C₄	—	5	2	no	—
485	C₄⋊C₄	—	5	1	no	—
486	C₄⋊C₄	—	5	1	no	—
487	C₄⋊C₄	—	5	2	no	—
488	C₄⋊C₄	—	5	1	no	—
489	C₄⋊C₄	—	5	1	no	—
490	C₄⋊C₄	—	5	2	no	—
491	C₄⋊C₄	—	5	2	no	—
492	C₄⋊C₄	—	5	2	no	—
493	C₄⋊C₄	—	5	1	no	—
494	C₄⋊C₄	—	5	1	no	—
495	C₄⋊C₄	—	5	2	no	—
496	C₄⋊C₄	—	5	2	no	—
497	C₄⋊C₄	—	5	2	no	—
498	C₄⋊C₄	—	5	2	no	—
499	C₄⋊C₄	—	5	2	no	—
500	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
501	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
502	C₄⋊C₄	C₂²×D₅	1	2	yes	—
503	C₄⋊C₄	C₂²×D₅	1	2	yes	—
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	1	no	—
512	C₂²⋊C₄	—	5	1	no	—
513	C₂²⋊C₄	—	5	2	no	—
514	C₂²⋊C₄	—	5	2	no	—
515	C₂²⋊C₄	—	5	2	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	1	no	—
523	C₂²⋊C₄	—	5	1	no	—
524	C₂²⋊C₄	—	5	1	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	1	no	—
531	C₂²⋊C₄	—	5	2	no	—
532	C₂²⋊C₄	—	5	2	no	—
533	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
534	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
535	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
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	C₂²×D₅	1	1	yes	characteristic
544	C₄²	C₂²×D₅	1	2	yes	—
545	C₄²	C₂²×D₅	1	1	yes	characteristic
546	C₄²	C₂²×D₅	1	1	yes	characteristic
547	C₄²	C₂²×D₅	1	2	yes	—
548	C₂×C₅	—	4	2	no	—
549	C₂×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
550	C₂×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
551	C₂×C₅	#585	1	1	yes	characteristic
552	D₅	—	2	2	no	—
553	D₅	—	4	1	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	—	5	1	no	—
560	C₂³	—	10	4	no	—
561	C₂³	—	20	2	no	—
562	C₂³	—	20	2	no	—
563	C₂³	C₂³×D₅	1	2	yes	—
564	Q₈	—	2	2	no	—
565	Q₈	—	2	2	no	—
566	Q₈	—	4	1	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	2	no	—
573	D₄	—	2	2	no	—
574	D₄	—	10	2	no	—
575	D₄	—	10	2	no	—
576	D₄	—	10	2	no	—
577	D₄	—	20	2	no	—
578	D₄	—	20	2	no	—
579	D₄	—	20	1	no	—
580	D₄	—	20	2	no	—
581	D₄	—	20	2	no	—
582	D₄	—	20	2	no	—
583	C₂×C₄	—	4	2	no	—
584	C₂×C₄	—	5	1	no	—
585	C₂×C₄	—	5	1	no	—
586	C₂×C₄	—	5	2	no	—
587	C₂×C₄	—	5	1	no	—
588	C₂×C₄	—	5	2	no	—
589	C₂×C₄	—	5	2	no	—
590	C₂×C₄	—	5	1	no	—
591	C₂×C₄	—	5	1	no	—
592	C₂×C₄	—	10	2	no	—
593	C₂×C₄	—	10	2	no	—
594	C₂×C₄	—	10	2	no	—
595	C₂×C₄	—	10	2	no	—
596	C₂×C₄	—	20	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	C₂³×D₅	1	1	yes	characteristic
604	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
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	2	yes	—
612	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
613	C₅	#3561	1	1	yes	characteristic, complemented, Sylow
614	C₂²	—	2	2	no	—
615	C₂²	—	2	2	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	5	2	no	—
618	C₂²	—	10	1	no	—
619	C₂²	—	10	1	no	—
620	C₂²	—	10	1	no	—
621	C₂²	—	10	1	no	—
622	C₂²	—	10	2	no	—
623	C₂²	—	10	2	no	—
624	C₂²	—	10	1	no	—
625	C₂²	—	10	1	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	2	no	—
632	C₄	—	2	2	no	—
633	C₄	—	2	1	no	—
634	C₄	—	2	2	no	—
635	C₄	—	2	1	no	—
636	C₄	—	2	1	no	—
637	C₄	—	2	1	no	—
638	C₄	—	2	1	no	—
639	C₄	—	2	1	no	—
640	C₄	—	10	1	no	—
641	C₄	—	10	1	no	—
642	C₄	—	10	1	no	—
643	C₄	—	10	2	no	—
644	C₄	—	10	2	no	—
645	C₄	—	10	2	no	—
646	C₄	—	10	1	no	—
647	C₄	—	10	1	no	—
648	C₄	#4149	1	2	yes	—
649	C₂	—	4	2	no	—
650	C₂	—	10	2	no	—
651	C₂	—	20	2	no	—
652	C₂	—	20	1	no	—
653	C₂	—	20	1	no	—
654	C₂	C₂×#4149	1	1	yes	characteristic
655	C₂	#66283	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×#556	C₂
hypercenter	#556	D₅
hypocenter	C₅	#3561
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. #66061	C₂	semidirect
3. #66058	C₂	semidirect
4. #66046	C₂	semidirect
5. #66044	C₂	semidirect
6. #66039	C₂	semidirect
7. #66038	C₂	semidirect
8. #66011	C₂	semidirect
9. #66010	C₂	semidirect
10. #66009	C₂	semidirect
11. D₅×#124	C₂	semidirect
12. #65981	C₂	semidirect
13. #65968	C₂	semidirect
14. #65918	C₂	semidirect
15. #65916	C₂	semidirect
16. #65914	C₂	semidirect
17. #65912	C₂	semidirect
18. #65910	C₂	semidirect
19. Q₈×D₂₀	C₂	semidirect
20. #65895	C₂	semidirect
21. #65888	C₂	semidirect
22. #65868	C₂	semidirect
23. #65861	C₂	semidirect
26. C₂×Q₈×D₅	C₂²	semidirect
27. C₂×Q₈×D₅	C₂²	semidirect
30. C₅×C₄⋊Q₈	C₂²	semidirect
31. C₅×#126	C₂²	semidirect
32. C₅×#126	C₂²	semidirect
35. C₅×C₂²⋊Q₈	C₂²	semidirect
36. C₄×C₅×Q₈	C₂²	semidirect
37. C₄×C₅×Q₈	C₂²	semidirect
38. C₄×C₅×Q₈	C₂²	semidirect
40. C₅×#117	C₂²	semidirect
42. #4093	C₂²	semidirect
45. #4092	C₂²	semidirect
46. #4092	C₂²	semidirect
47. #4090	C₂²	semidirect
51. #4075	C₂²	semidirect
53. #4070	C₂²	semidirect
54. #4044	C₂²	semidirect
55. #4044	C₂²	semidirect
56. #4044	C₂²	semidirect
57. #4044	C₂²	semidirect
60. #4043	C₂²	semidirect
61. #4043	C₂²	semidirect
62. #4043	C₂²	semidirect
65. #4042	C₂²	semidirect
66. #4042	C₂²	semidirect
67. #4042	C₂²	semidirect
68. #4042	C₂²	semidirect
71. #4041	C₂²	semidirect
74. #4040	C₂²	semidirect
75. #4040	C₂²	semidirect
76. #4040	C₂²	semidirect
78. #4038	C₂²	semidirect
79. #4036	C₂²	semidirect
80. #4035	C₂²	semidirect
81. #4034	C₂²	semidirect
82. #4034	C₂²	semidirect
86. #4031	C₂²	semidirect
87. #4031	C₂²	semidirect
89. #4030	C₂²	semidirect
91. #4029	C₂²	semidirect
92. #4029	C₂²	semidirect
95. #4027	C₂²	semidirect
99. #4025	C₂²	semidirect
100. #4024	C₂²	semidirect
101. #4024	C₂²	semidirect
102. #4024	C₂²	semidirect
103. #4022	C₂²	semidirect
106. #4021	C₂²	semidirect
107. #4021	C₂²	semidirect
112. C₄×D₂₀	C₂²	semidirect
113. C₄×D₂₀	C₂²	semidirect
115. #4018	C₂²	semidirect
116. #4018	C₂²	semidirect
118. #4015	C₂²	semidirect
119. #4015	C₂²	semidirect
120. C₄×Dic₁₀	C₂²	semidirect
121. C₄×Dic₁₀	C₂²	semidirect
122. C₄×Dic₁₀	C₂²	semidirect
232. #556	D₅	semidirect
320. C₄⋊Q₈	C₂×D₅	semidirect
327. #126	C₂×D₅	semidirect
328. #126	C₂×D₅	semidirect
373. C₂²⋊Q₈	C₂×D₅	semidirect
386. C₄×Q₈	C₂×D₅	semidirect
387. C₄×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×#556	2
#66061	2
#66058	2
#66046	2
#66044	2
#66039	2
#66038	2
#66011	2
#66010	2
#66009	2
D₅×#124	2
#65981	2
#65968	2
#65918	2
#65916	2
#65914	2
#65912	2
#65910	2
Q₈×D₂₀	2
#65895	2
#65888	2
#65868	2
#65861	2
#3561	5