Subgroups — #10618961

Order 640.

1050 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#559	C₂	1	1	yes	maximal, characteristic, complemented
2	#66052	C₂	1	1	yes	maximal, characteristic, complemented
3	#66049	C₂	1	1	yes	maximal, characteristic, complemented
4	#66018	C₂	1	2	yes	maximal, complemented
5	#66012	C₂	1	2	yes	maximal, complemented
6	#66011	C₂	1	1	yes	maximal, characteristic, complemented
7	#66010	C₂	1	1	yes	maximal, characteristic, complemented
8	#66009	C₂	1	1	yes	maximal, characteristic, complemented
9	#66002	C₂	1	1	yes	maximal, characteristic, complemented
10	#66000	C₂	1	2	yes	maximal, complemented
11	#65999	C₂	1	2	yes	maximal, complemented
12	#65997	C₂	1	2	yes	maximal, complemented
13	#65992	C₂	1	2	yes	maximal, complemented
14	#65918	C₂	1	1	yes	maximal, characteristic, complemented
15	#65917	C₂	1	1	yes	maximal, characteristic, complemented
16	#65914	C₂	1	1	yes	maximal, characteristic, complemented
17	#65910	C₂	1	1	yes	maximal, characteristic, complemented
18	#65899	C₂	1	2	yes	maximal, complemented
19	#65896	C₂	1	1	yes	maximal, characteristic, complemented
20	#65894	C₂	1	2	yes	maximal, complemented
21	#65891	C₂	1	1	yes	maximal, characteristic, complemented
22	#65889	C₂	1	1	yes	maximal, characteristic, complemented
23	#65888	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#713	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×#711	C₂²	1	1	yes	characteristic
28	C₂×#711	C₂²	1	1	yes	characteristic, complemented
29	C₂×D₄×D₅	C₂²	1	1	yes	characteristic
30	C₅×#127	C₂²	1	1	yes	characteristic
31	C₅×#124	C₂²	1	1	yes	characteristic
32	C₅×#124	C₂²	1	1	yes	characteristic, complemented
33	C₅×#124	C₂²	1	2	yes	complemented
34	C₅×#123	C₂²	1	2	yes	complemented
35	C₅×#123	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×D₄	C₂²	1	1	yes	characteristic
39	C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
40	C₄×C₅×D₄	C₂²	1	2	yes	complemented
41	#4093	C₂²	1	1	yes	characteristic
42	#4092	C₂²	1	1	yes	characteristic
43	#4092	C₂²	1	1	yes	characteristic, complemented
44	#4092	C₂²	1	2	yes	complemented
45	#4090	C₂²	1	1	yes	characteristic, complemented
46	#4086	C₂²	1	1	yes	characteristic
47	#4086	C₂²	1	2	yes	complemented
48	#4085	C₂²	1	2	yes	—
49	#4085	C₂²	1	2	yes	—
50	#4085	C₂²	1	2	yes	complemented
51	#4085	C₂²	1	2	yes	complemented
52	#4084	C₂²	1	1	yes	characteristic
53	#4084	C₂²	1	1	yes	characteristic, complemented
54	#4083	C₂²	1	2	yes	—
55	#4083	C₂²	1	2	yes	—
56	#4082	C₂²	1	1	yes	characteristic
57	D₄×Dic₅	C₂²	1	2	yes	complemented
58	#4076	C₂²	1	2	yes	—
59	#4076	C₂²	1	2	yes	—
60	#4076	C₂²	1	2	yes	complemented
61	#4075	C₂²	1	2	yes	complemented
62	C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
63	C₂×#685	C₂²	1	2	yes	—
64	#4072	C₂²	1	2	yes	complemented
65	C₂×C₄⋊Dic₅	C₂²	1	2	yes	complemented
66	#4044	C₂²	1	1	yes	characteristic
67	#4044	C₂²	1	2	yes	—
68	#4044	C₂²	1	2	yes	complemented
69	#4044	C₂²	1	1	yes	characteristic, complemented
70	#4044	C₂²	1	2	yes	complemented
71	#4043	C₂²	1	1	yes	characteristic
72	#4043	C₂²	1	1	yes	characteristic, complemented
73	#4043	C₂²	1	2	yes	complemented
74	#4041	C₂²	1	1	yes	characteristic
75	#4041	C₂²	1	1	yes	characteristic
76	#4041	C₂²	1	2	yes	complemented
77	#4040	C₂²	1	1	yes	characteristic
78	#4040	C₂²	1	1	yes	characteristic, complemented
79	#4038	C₂²	1	2	yes	complemented
80	#4036	C₂²	1	1	yes	characteristic, complemented
81	#4036	C₂²	1	1	yes	characteristic, complemented
82	#4035	C₂²	1	2	yes	complemented
83	#4032	C₂²	1	2	yes	—
84	#4032	C₂²	1	2	yes	—
85	#4032	C₂²	1	2	yes	complemented
86	#4031	C₂²	1	2	yes	—
87	#4030	C₂²	1	2	yes	—
88	#4030	C₂²	1	2	yes	—
89	#4030	C₂²	1	2	yes	complemented
90	#4030	C₂²	1	2	yes	complemented
91	#4030	C₂²	1	2	yes	complemented
92	#4029	C₂²	1	2	yes	—
93	#4029	C₂²	1	2	yes	complemented
94	#4029	C₂²	1	2	yes	complemented
95	#4029	C₂²	1	2	yes	complemented
96	#4029	C₂²	1	2	yes	complemented
97	#4028	C₂²	1	2	yes	—
98	#4028	C₂²	1	2	yes	—
99	#4027	C₂²	1	2	yes	complemented
100	#4027	C₂²	1	2	yes	complemented
101	#4027	C₂²	1	2	yes	complemented
102	D₅×C₂²⋊C₄	C₂²	1	2	yes	—
103	#4025	C₂²	1	2	yes	complemented
104	#4024	C₂²	1	2	yes	complemented
105	#4024	C₂²	1	2	yes	complemented
106	#4024	C₂²	1	2	yes	complemented
107	#4022	C₂²	1	2	yes	—
108	#4021	C₂²	1	1	yes	characteristic
109	#4021	C₂²	1	1	yes	characteristic
110	#4021	C₂²	1	2	yes	complemented
111	C₄×D₂₀	C₂²	1	1	yes	characteristic
112	C₄×D₂₀	C₂²	1	1	yes	characteristic
113	C₄×D₂₀	C₂²	1	1	yes	characteristic
114	C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
115	C₄×D₂₀	C₂²	1	2	yes	complemented
116	#4018	C₂²	1	1	yes	characteristic
117	#4018	C₂²	1	1	yes	characteristic, complemented
118	C₄²×D₅	C₂²	1	1	yes	characteristic, complemented
119	#4016	C₂²	1	2	yes	complemented
120	#4015	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
123	#3562	—	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×D₄	C₂³	1	1	yes	characteristic
128	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
129	C₂×C₅×D₄	C₂³	1	2	yes	—
130	C₂×C₅×D₄	C₂³	1	2	yes	—
131	C₂²×C₄×C₅	C₂³	1	2	yes	—
132	C₂²×C₄×C₅	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	2	yes	—
136	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
141	C₂²×Dic₅	C₂³	1	2	yes	—
142	C₂²×Dic₅	C₂³	1	2	yes	—
143	C₂²×Dic₅	C₂³	1	2	yes	—
144	#713	—	4	2	no	—
145	Q₈×D₅	—	4	2	no	—
146	#711	—	4	2	no	—
147	#711	—	4	2	no	—
148	#711	—	4	2	no	—
149	D₄×D₅	—	4	2	no	—
150	C₂×D₂₀	C₂³	1	1	yes	characteristic
151	C₂×D₂₀	C₂³	1	2	yes	—
152	C₂×D₂₀	C₂³	1	1	yes	characteristic
153	C₂×D₂₀	C₂³	1	1	yes	characteristic
154	C₂×D₂₀	C₂³	1	2	yes	—
155	C₂×D₂₀	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₅	C₂³	1	2	yes	—
160	C₂×C₄×D₅	C₂³	1	2	yes	—
161	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
162	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
163	C₂×C₄×D₅	C₂³	1	2	yes	—
164	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
165	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
166	C₂×Dic₁₀	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×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₄²×C₅	C₂³	1	1	yes	characteristic
179	C₄²×C₅	C₂³	1	1	yes	characteristic
180	C₄²×C₅	C₂³	1	2	yes	—
181	C₄²×C₅	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₅	C₂³	1	2	yes	—
183	C₂²⋊Dic₅	C₂³	1	2	yes	—
184	C₂²⋊Dic₅	C₂³	1	2	yes	—
185	C₂²⋊Dic₅	C₂³	1	2	yes	—
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	1	yes	characteristic
190	#685	C₂³	1	1	yes	characteristic
191	#685	C₂³	1	1	yes	characteristic
192	#685	C₂³	1	2	yes	—
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	2	yes	—
209	C₄⋊Dic₅	C₂³	1	2	yes	—
210	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
211	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
212	C₄⋊Dic₅	C₂³	1	2	yes	—
213	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
214	#683	C₂³	1	2	yes	—
215	#683	C₂³	1	2	yes	—
216	#683	C₂³	1	1	yes	characteristic
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	2	yes	—
223	#683	C₂³	1	2	yes	—
224	C₄×Dic₅	C₂³	1	2	yes	—
225	C₄×Dic₅	C₂³	1	2	yes	—
226	C₄×Dic₅	C₂³	1	1	yes	characteristic
227	C₄×Dic₅	C₂³	1	1	yes	characteristic
228	C₄×Dic₅	C₂³	1	1	yes	characteristic
229	#562	—	5	2	no	—
230	#560	—	5	2	no	—
231	#559	D₅	1	1	yes	characteristic, complemented
232	#556	—	5	1	no	—
233	#553	—	5	2	no	—
234	#551	—	5	2	no	—
235	#550	—	5	1	no	—
236	#548	—	5	1	no	—
237	#548	—	5	1	no	—
238	#547	—	5	1	no	—
239	#546	—	5	1	no	—
240	#546	—	5	1	no	—
241	#541	—	5	1	no	—
242	#540	—	5	2	no	—
243	#540	—	5	1	no	—
244	#539	—	5	2	no	—
245	#538	—	5	2	no	—
246	#538	—	5	2	no	—
247	#536	—	5	1	no	—
248	#535	—	5	1	no	—
249	#532	—	5	1	no	—
250	#529	—	5	1	no	—
251	#529	—	5	1	no	—
252	C₂³×C₅	C₂⁴	1	2	yes	—
253	C₂³×C₅	C₂⁴	1	2	yes	—
254	C₂²×D₅	—	4	2	no	—
255	C₂²×D₅	—	4	2	no	—
256	C₂²×D₅	—	4	2	no	—
257	C₂²×D₅	C₂⁴	1	1	yes	characteristic
258	C₂²×D₅	C₂⁴	1	2	yes	—
259	C₂²×D₅	C₂⁴	1	1	yes	characteristic
260	C₂²×D₅	C₂⁴	1	1	yes	characteristic
261	C₅×Q₈	—	2	2	no	—
262	C₅×Q₈	—	4	1	no	—
263	C₅×D₄	—	2	2	no	—
264	C₅×D₄	—	2	2	no	—
265	C₅×D₄	—	4	2	no	—
266	C₅×D₄	—	4	2	no	—
267	C₂×C₄×C₅	—	4	2	no	—
268	C₂×C₄×C₅	—	4	2	no	—
269	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
270	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
271	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
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	C₂×C₄×C₅	C₂⁴	1	2	yes	—
276	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
277	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
278	C₂²⋊D₅	—	4	2	no	—
279	C₂²⋊D₅	—	4	2	no	—
280	C₂²⋊D₅	—	4	2	no	—
281	C₂²⋊D₅	—	4	2	no	—
282	C₂²⋊D₅	—	4	2	no	—
283	C₂²⋊D₅	—	4	2	no	—
284	C₂²⋊D₅	—	4	2	no	—
285	C₂²⋊D₅	—	4	2	no	—
286	C₂×Dic₅	—	4	2	no	—
287	C₂×Dic₅	—	4	2	no	—
288	C₂×Dic₅	—	4	2	no	—
289	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
290	C₂×Dic₅	C₂⁴	1	2	yes	—
291	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
292	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
293	C₂×Dic₅	C₂⁴	1	2	yes	—
294	C₂×Dic₅	C₂⁴	1	2	yes	—
295	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
296	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
297	D₂₀	—	2	2	no	—
298	D₂₀	—	4	1	no	—
299	D₂₀	—	4	1	no	—
300	D₂₀	—	4	2	no	—
301	D₂₀	—	4	1	no	—
302	D₂₀	—	4	2	no	—
303	C₄×D₅	—	2	2	no	—
304	C₄×D₅	—	2	2	no	—
305	C₄×D₅	—	2	2	no	—
306	C₄×D₅	—	4	2	no	—
307	C₄×D₅	—	4	1	no	—
308	C₄×D₅	—	4	1	no	—
309	C₄×D₅	—	4	2	no	—
310	C₄×D₅	—	4	2	no	—
311	Dic₁₀	—	2	2	no	—
312	Dic₁₀	—	2	2	no	—
313	Dic₁₀	—	4	2	no	—
314	C₂×#41	—	5	1	no	—
315	C₂×#41	—	5	1	no	—
316	C₂×#41	—	5	1	no	—
317	C₂×#41	—	5	1	no	—
318	C₂²×Q₈	—	5	1	no	—
319	C₂²×D₄	—	5	1	no	—
320	C₄⋊Q₈	—	5	1	no	—
321	C₄⋊Q₈	—	5	1	no	—
322	#127	—	5	1	no	—
323	#127	—	5	2	no	—
324	#127	C₂×D₅	1	1	yes	characteristic
325	#126	—	5	1	no	—
326	#126	—	5	1	no	—
327	#126	—	5	2	no	—
328	#126	—	5	2	no	—
329	#126	—	5	2	no	—
330	#126	—	5	2	no	—
331	#126	—	5	2	no	—
332	#125	—	5	1	no	—
333	#125	—	5	1	no	—
334	#125	—	5	2	no	—
335	#125	—	5	2	no	—
336	#124	—	5	1	no	—
337	#124	—	5	1	no	—
338	#124	—	5	2	no	—
339	#124	—	5	1	no	—
340	#124	—	5	1	no	—
341	#124	—	5	2	no	—
342	#124	C₂×D₅	1	1	yes	characteristic
343	#124	C₂×D₅	1	1	yes	characteristic, complemented
344	#124	C₂×D₅	1	2	yes	complemented
345	#123	—	5	2	no	—
346	#123	—	5	1	no	—
347	#123	—	5	1	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	#123	—	5	2	no	—
355	#123	—	5	2	no	—
356	#123	C₂×D₅	1	2	yes	complemented
357	#123	C₂×D₅	1	2	yes	complemented
358	C₂²⋊Q₈	—	5	1	no	—
359	C₂²⋊Q₈	—	5	2	no	—
360	C₂²⋊Q₈	—	5	1	no	—
361	C₂²⋊Q₈	—	5	1	no	—
362	C₂²⋊Q₈	—	5	2	no	—
363	C₂²⋊Q₈	—	5	1	no	—
364	C₂²⋊Q₈	—	5	2	no	—
365	C₂²⋊Q₈	—	5	2	no	—
366	C₂²⋊Q₈	—	5	2	no	—
367	#121	—	5	1	no	—
368	#121	—	5	2	no	—
369	#121	—	5	2	no	—
370	#121	—	5	2	no	—
371	#121	—	5	2	no	—
372	#121	—	5	1	no	—
373	#121	—	5	2	no	—
374	#121	—	5	2	no	—
375	#121	—	5	2	no	—
376	#121	—	5	1	no	—
377	#121	—	5	1	no	—
378	#121	—	5	2	no	—
379	#121	—	5	2	no	—
380	#121	—	5	2	no	—
381	#121	—	5	2	no	—
382	#121	—	5	2	no	—
383	#121	—	5	2	no	—
384	#120	—	5	2	no	—
385	#120	—	5	2	no	—
386	#120	—	5	2	no	—
387	#120	—	5	2	no	—
388	C₄×Q₈	—	5	1	no	—
389	C₄×Q₈	—	5	1	no	—
390	C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
391	C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
392	C₄×D₄	—	5	2	no	—
393	C₄×D₄	—	5	2	no	—
394	C₄×D₄	—	5	2	no	—
395	C₄×D₄	—	5	2	no	—
396	C₄×D₄	—	5	2	no	—
397	C₄×D₄	—	5	1	no	—
398	C₄×D₄	—	5	1	no	—
399	C₄×D₄	—	5	1	no	—
400	C₄×D₄	—	5	2	no	—
401	C₄×D₄	—	5	1	no	—
402	C₄×D₄	C₂×D₅	1	1	yes	characteristic
403	C₄×D₄	C₂×D₅	1	2	yes	complemented
404	C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
405	#117	—	5	2	no	—
406	#117	—	5	2	no	—
407	#117	—	5	1	no	—
408	#117	—	5	1	no	—
409	C₂×C₄⋊C₄	—	5	2	no	—
410	C₂×C₂²⋊C₄	—	5	2	no	—
411	C₂×C₂²⋊C₄	—	5	2	no	—
412	C₂×C₄²	—	5	1	no	—
413	C₂²×C₅	—	2	2	no	—
414	C₂²×C₅	—	2	2	no	—
415	C₂²×C₅	—	2	2	no	—
416	C₂²×C₅	—	2	2	no	—
417	C₂²×C₅	—	2	2	no	—
418	C₂²×C₅	—	2	2	no	—
419	C₂²×C₅	C₂⁵	1	1	yes	characteristic
420	C₂×D₅	—	2	1	no	—
421	C₂×D₅	—	2	1	no	—
422	C₂×D₅	—	2	1	no	—
423	C₂×D₅	—	2	2	no	—
424	C₂×D₅	—	2	1	no	—
425	C₂×D₅	—	2	1	no	—
426	C₂×D₅	—	2	2	no	—
427	C₂×D₅	—	2	1	no	—
428	C₂×D₅	—	2	1	no	—
429	C₂×D₅	—	2	2	no	—
430	C₂×D₅	—	2	1	no	—
431	C₂×D₅	—	2	1	no	—
432	C₂×D₅	—	8	4	no	—
433	C₄×C₅	—	2	2	no	—
434	C₄×C₅	—	2	1	no	—
435	C₄×C₅	—	2	1	no	—
436	C₄×C₅	—	2	1	no	—
437	C₄×C₅	—	2	1	no	—
438	C₄×C₅	—	2	2	no	—
439	C₄×C₅	—	2	1	no	—
440	C₄×C₅	—	2	1	no	—
441	C₄×C₅	H(5,𝔽₂)	1	2	yes	—
442	Dic₅	—	2	2	no	—
443	Dic₅	—	2	2	no	—
444	Dic₅	—	2	1	no	—
445	Dic₅	—	2	1	no	—
446	Dic₅	—	2	1	no	—
447	Dic₅	—	2	2	no	—
448	Dic₅	—	2	1	no	—
449	Dic₅	—	2	1	no	—
450	C₂⁴	—	5	2	no	—
451	#41	—	20	2	no	—
452	#41	—	20	2	no	—
453	#41	—	20	2	no	—
454	#41	—	20	2	no	—
455	C₂×Q₈	—	5	1	no	—
456	C₂×Q₈	—	5	1	no	—
457	C₂×Q₈	—	5	2	no	—
458	C₂×Q₈	—	20	2	no	—
459	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
460	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
461	C₂×D₄	—	5	2	no	—
462	C₂×D₄	—	5	2	no	—
463	C₂×D₄	—	5	2	no	—
464	C₂×D₄	—	5	2	no	—
465	C₂×D₄	—	5	2	no	—
466	C₂×D₄	—	5	2	no	—
467	C₂×D₄	—	5	2	no	—
468	C₂×D₄	—	5	2	no	—
469	C₂×D₄	—	5	1	no	—
470	C₂×D₄	—	5	1	no	—
471	C₂×D₄	—	5	1	no	—
472	C₂×D₄	—	5	2	no	—
473	C₂×D₄	—	5	1	no	—
474	C₂×D₄	—	5	2	no	—
475	C₂×D₄	—	20	2	no	—
476	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
477	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
478	C₂×D₄	C₂²×D₅	1	2	yes	—
479	C₂×D₄	C₂²×D₅	1	2	yes	—
480	C₂²×C₄	—	5	2	no	—
481	C₂²×C₄	—	5	2	no	—
482	C₂²×C₄	—	5	2	no	—
483	C₂²×C₄	—	5	1	no	—
484	C₂²×C₄	—	5	1	no	—
485	C₂²×C₄	—	5	1	no	—
486	C₂²×C₄	—	5	1	no	—
487	C₂²×C₄	—	5	1	no	—
488	C₂²×C₄	—	5	2	no	—
489	C₂²×C₄	—	5	2	no	—
490	C₂²×C₄	—	5	2	no	—
491	C₂²×C₄	C₂²×D₅	1	2	yes	—
492	C₂²×C₄	C₂²×D₅	1	2	yes	—
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	1	no	—
498	C₄⋊C₄	—	5	1	no	—
499	C₄⋊C₄	—	5	2	no	—
500	C₄⋊C₄	—	5	1	no	—
501	C₄⋊C₄	—	5	1	no	—
502	C₄⋊C₄	—	5	2	no	—
503	C₄⋊C₄	—	5	1	no	—
504	C₄⋊C₄	—	5	1	no	—
505	C₄⋊C₄	—	5	2	no	—
506	C₄⋊C₄	—	5	2	no	—
507	C₄⋊C₄	—	5	2	no	—
508	C₄⋊C₄	—	5	2	no	—
509	C₄⋊C₄	—	5	1	no	—
510	C₄⋊C₄	—	5	2	no	—
511	C₄⋊C₄	—	5	2	no	—
512	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
513	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
514	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
515	C₄⋊C₄	C₂²×D₅	1	2	yes	—
516	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
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	1	no	—
522	C₂²⋊C₄	—	5	1	no	—
523	C₂²⋊C₄	—	5	2	no	—
524	C₂²⋊C₄	—	5	2	no	—
525	C₂²⋊C₄	—	5	2	no	—
526	C₂²⋊C₄	—	5	2	no	—
527	C₂²⋊C₄	—	5	1	no	—
528	C₂²⋊C₄	—	5	1	no	—
529	C₂²⋊C₄	—	5	2	no	—
530	C₂²⋊C₄	—	5	1	no	—
531	C₂²⋊C₄	—	5	1	no	—
532	C₂²⋊C₄	—	5	1	no	—
533	C₂²⋊C₄	—	5	1	no	—
534	C₂²⋊C₄	—	5	2	no	—
535	C₂²⋊C₄	—	5	2	no	—
536	C₂²⋊C₄	—	5	2	no	—
537	C₂²⋊C₄	—	5	1	no	—
538	C₂²⋊C₄	—	5	2	no	—
539	C₂²⋊C₄	—	5	1	no	—
540	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
541	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
542	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
543	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
544	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
545	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
546	C₄²	—	5	1	no	—
547	C₄²	—	5	1	no	—
548	C₄²	—	5	1	no	—
549	C₄²	—	5	2	no	—
550	C₄²	—	5	2	no	—
551	C₄²	C₂²×D₅	1	1	yes	characteristic
552	C₄²	C₂²×D₅	1	1	yes	characteristic
553	C₄²	C₂²×D₅	1	1	yes	characteristic
554	C₄²	C₂²×D₅	1	2	yes	—
555	C₂×C₅	—	4	2	no	—
556	C₂×C₅	—	4	2	no	—
557	C₂×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
558	C₂×C₅	#585	1	1	yes	characteristic
559	C₂×C₅	#585	1	1	yes	characteristic
560	D₅	—	4	1	no	—
561	D₅	—	4	1	no	—
562	D₅	—	4	2	no	—
563	D₅	—	4	1	no	—
564	C₂³	—	5	1	no	—
565	C₂³	—	5	2	no	—
566	C₂³	—	5	1	no	—
567	C₂³	—	5	1	no	—
568	C₂³	—	20	2	no	—
569	C₂³	—	20	2	no	—
570	C₂³	—	20	2	no	—
571	C₂³	C₂³×D₅	1	2	yes	—
572	C₂³	C₂³×D₅	1	2	yes	—
573	Q₈	—	2	2	no	—
574	Q₈	—	4	1	no	—
575	Q₈	—	10	2	no	—
576	Q₈	—	10	2	no	—
577	Q₈	—	20	2	no	—
578	D₄	—	2	2	no	—
579	D₄	—	2	2	no	—
580	D₄	—	4	2	no	—
581	D₄	—	4	2	no	—
582	D₄	—	10	2	no	—
583	D₄	—	20	2	no	—
584	D₄	—	20	1	no	—
585	D₄	—	20	1	no	—
586	D₄	—	20	2	no	—
587	D₄	—	20	1	no	—
588	D₄	—	20	2	no	—
589	D₄	—	20	2	no	—
590	D₄	—	20	2	no	—
591	D₄	—	20	2	no	—
592	D₄	—	20	2	no	—
593	D₄	—	20	2	no	—
594	D₄	—	20	2	no	—
595	D₄	—	20	2	no	—
596	C₂×C₄	—	4	2	no	—
597	C₂×C₄	—	4	2	no	—
598	C₂×C₄	—	5	1	no	—
599	C₂×C₄	—	5	2	no	—
600	C₂×C₄	—	5	1	no	—
601	C₂×C₄	—	5	1	no	—
602	C₂×C₄	—	5	2	no	—
603	C₂×C₄	—	5	2	no	—
604	C₂×C₄	—	5	1	no	—
605	C₂×C₄	—	5	1	no	—
606	C₂×C₄	—	10	2	no	—
607	C₂×C₄	—	10	2	no	—
608	C₂×C₄	—	10	2	no	—
609	C₂×C₄	—	20	2	no	—
610	C₂×C₄	—	20	2	no	—
611	C₂×C₄	—	20	2	no	—
612	C₂×C₄	—	20	1	no	—
613	C₂×C₄	—	20	1	no	—
614	C₂×C₄	—	20	2	no	—
615	C₂×C₄	—	20	2	no	—
616	C₂×C₄	—	20	2	no	—
617	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
618	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
619	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
620	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
621	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
622	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
623	C₂×C₄	C₂³×D₅	1	2	yes	—
624	C₂×C₄	C₂³×D₅	1	2	yes	—
625	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
626	C₅	#3562	1	1	yes	characteristic, complemented, Sylow
627	C₂²	—	2	2	no	—
628	C₂²	—	2	2	no	—
629	C₂²	—	2	2	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	2	2	no	—
633	C₂²	—	10	1	no	—
634	C₂²	—	10	1	no	—
635	C₂²	—	10	1	no	—
636	C₂²	—	10	2	no	—
637	C₂²	—	10	1	no	—
638	C₂²	—	10	2	no	—
639	C₂²	—	10	1	no	—
640	C₂²	—	10	1	no	—
641	C₂²	—	10	1	no	—
642	C₂²	—	10	1	no	—
643	C₂²	—	10	2	no	—
644	C₂²	—	10	1	no	—
645	C₂²	—	40	4	no	—
646	C₂²	C₂⁴×D₅	1	1	yes	characteristic
647	C₄	—	2	2	no	—
648	C₄	—	2	1	no	—
649	C₄	—	2	1	no	—
650	C₄	—	2	1	no	—
651	C₄	—	2	1	no	—
652	C₄	—	2	2	no	—
653	C₄	—	2	1	no	—
654	C₄	—	2	1	no	—
655	C₄	—	10	1	no	—
656	C₄	—	10	1	no	—
657	C₄	—	10	1	no	—
658	C₄	—	10	2	no	—
659	C₄	—	10	2	no	—
660	C₄	—	10	1	no	—
661	C₄	—	10	2	no	—
662	C₄	—	10	1	no	—
663	C₄	#4149	1	2	yes	—
664	C₂	—	4	2	no	—
665	C₂	—	4	2	no	—
666	C₂	—	20	1	no	—
667	C₂	—	20	2	no	—
668	C₂	—	20	1	no	—
669	C₂	—	20	1	no	—
670	C₂	C₂×#4149	1	1	yes	characteristic
671	C₂	#66283	1	1	yes	characteristic
672	C₂	#66285	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅
commutator, socle, cosocle	C₂²×C₅	C₂⁵
Fitting	C₅×#559	C₂
hypercenter	#559	D₅
hypocenter	C₅	#3562
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ #559

Complements

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

N	H ≅ G/N	type
1. C₅×#559	C₂	semidirect
2. #66052	C₂	semidirect
3. #66049	C₂	semidirect
4. #66018	C₂	semidirect
5. #66012	C₂	semidirect
6. #66011	C₂	semidirect
7. #66010	C₂	semidirect
8. #66009	C₂	semidirect
9. #66002	C₂	semidirect
10. #66000	C₂	semidirect
11. #65999	C₂	semidirect
12. #65997	C₂	semidirect
13. #65992	C₂	semidirect
14. #65918	C₂	semidirect
15. #65917	C₂	semidirect
16. #65914	C₂	semidirect
17. #65910	C₂	semidirect
18. #65899	C₂	semidirect
19. #65896	C₂	semidirect
20. #65894	C₂	semidirect
21. #65891	C₂	semidirect
22. #65889	C₂	semidirect
23. #65888	C₂	semidirect
25. C₂×Q₈×D₅	C₂²	semidirect
28. C₂×#711	C₂²	semidirect
32. C₅×#124	C₂²	semidirect
33. C₅×#124	C₂²	semidirect
34. C₅×#123	C₂²	semidirect
35. C₅×#123	C₂²	semidirect
36. C₄×C₅×Q₈	C₂²	semidirect
37. C₄×C₅×Q₈	C₂²	semidirect
39. C₄×C₅×D₄	C₂²	semidirect
40. C₄×C₅×D₄	C₂²	semidirect
43. #4092	C₂²	semidirect
44. #4092	C₂²	semidirect
45. #4090	C₂²	semidirect
47. #4086	C₂²	semidirect
50. #4085	C₂²	semidirect
51. #4085	C₂²	semidirect
53. #4084	C₂²	semidirect
57. D₄×Dic₅	C₂²	semidirect
60. #4076	C₂²	semidirect
61. #4075	C₂²	semidirect
62. C₄×C₂²⋊D₅	C₂²	semidirect
64. #4072	C₂²	semidirect
65. C₂×C₄⋊Dic₅	C₂²	semidirect
68. #4044	C₂²	semidirect
69. #4044	C₂²	semidirect
70. #4044	C₂²	semidirect
72. #4043	C₂²	semidirect
73. #4043	C₂²	semidirect
76. #4041	C₂²	semidirect
78. #4040	C₂²	semidirect
79. #4038	C₂²	semidirect
80. #4036	C₂²	semidirect
81. #4036	C₂²	semidirect
82. #4035	C₂²	semidirect
85. #4032	C₂²	semidirect
89. #4030	C₂²	semidirect
90. #4030	C₂²	semidirect
91. #4030	C₂²	semidirect
93. #4029	C₂²	semidirect
94. #4029	C₂²	semidirect
95. #4029	C₂²	semidirect
96. #4029	C₂²	semidirect
99. #4027	C₂²	semidirect
100. #4027	C₂²	semidirect
101. #4027	C₂²	semidirect
103. #4025	C₂²	semidirect
104. #4024	C₂²	semidirect
105. #4024	C₂²	semidirect
106. #4024	C₂²	semidirect
110. #4021	C₂²	semidirect
114. C₄×D₂₀	C₂²	semidirect
115. C₄×D₂₀	C₂²	semidirect
117. #4018	C₂²	semidirect
118. C₄²×D₅	C₂²	semidirect
119. #4016	C₂²	semidirect
120. #4015	C₂²	semidirect
121. C₄×Dic₁₀	C₂²	semidirect
122. C₄×Dic₁₀	C₂²	semidirect
231. #559	D₅	semidirect
343. #124	C₂×D₅	semidirect
344. #124	C₂×D₅	semidirect
356. #123	C₂×D₅	semidirect
357. #123	C₂×D₅	semidirect
390. C₄×Q₈	C₂×D₅	semidirect
391. C₄×Q₈	C₂×D₅	semidirect
403. C₄×D₄	C₂×D₅	semidirect
404. C₄×D₄	C₂×D₅	semidirect
626. C₅	#3562	semidirect

Maximal subgroups

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

subgroup	index
C₅×#559	2
#66052	2
#66049	2
#66018	2
#66012	2
#66011	2
#66010	2
#66009	2
#66002	2
#66000	2
#65999	2
#65997	2
#65992	2
#65918	2
#65917	2
#65914	2
#65910	2
#65899	2
#65896	2
#65894	2
#65891	2
#65889	2
#65888	2
#3562	5