Subgroups — #10618767

Order 640.

1050 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#552	C₂	1	1	yes	maximal, characteristic, complemented
2	#66045	C₂	1	2	yes	maximal, complemented
3	#66041	C₂	1	2	yes	maximal, complemented
4	#66032	C₂	1	1	yes	maximal, characteristic, complemented
5	#66029	C₂	1	2	yes	maximal, complemented
6	#66028	C₂	1	1	yes	maximal, characteristic, complemented
7	#66026	C₂	1	2	yes	maximal, complemented
8	#66000	C₂	1	2	yes	maximal, complemented
9	#65997	C₂	1	2	yes	maximal, complemented
10	#65965	C₂	1	1	yes	maximal, characteristic, complemented
11	#65965	C₂	1	1	yes	maximal, characteristic, complemented
12	#65963	C₂	1	1	yes	maximal, characteristic, complemented
13	#65961	C₂	1	1	yes	maximal, characteristic, complemented
14	#65917	C₂	1	1	yes	maximal, characteristic, complemented
15	#65911	C₂	1	1	yes	maximal, characteristic, complemented
16	#65887	C₂	1	1	yes	maximal, characteristic, complemented
17	#65881	C₂	1	1	yes	maximal, characteristic, complemented
18	#65869	C₂	1	2	yes	maximal, complemented
19	#65864	C₂	1	1	yes	maximal, characteristic, complemented
20	#65864	C₂	1	2	yes	maximal, complemented
21	#65858	C₂	1	1	yes	maximal, characteristic, complemented
22	#65848	C₂	1	1	yes	maximal, characteristic, complemented
23	#65844	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#713	C₂²	1	1	yes	characteristic
25	C₂×#713	C₂²	1	1	yes	characteristic, complemented
26	C₂×#709	C₂²	1	1	yes	characteristic
27	C₂×#709	C₂²	1	1	yes	characteristic
28	C₂×#709	C₂²	1	1	yes	characteristic, complemented
29	C₂²×C₄×D₅	C₂²	1	1	yes	characteristic
30	C₅×#126	C₂²	1	2	yes	—
31	C₅×#125	C₂²	1	2	yes	complemented
32	C₅×#125	C₂²	1	1	yes	characteristic, complemented
33	C₅×#123	C₂²	1	2	yes	—
34	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
35	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
36	C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₄×C₅×D₄	C₂²	1	1	yes	characteristic
38	C₅×#117	C₂²	1	1	yes	characteristic
39	C₅×#117	C₂²	1	2	yes	complemented
40	C₂×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
41	#4092	C₂²	1	1	yes	characteristic
42	#4090	C₂²	1	1	yes	characteristic, complemented
43	#4086	C₂²	1	2	yes	—
44	#4085	C₂²	1	1	yes	characteristic
45	#4083	C₂²	1	1	yes	characteristic
46	#4076	C₂²	1	2	yes	—
47	#4076	C₂²	1	2	yes	—
48	#4076	C₂²	1	1	yes	characteristic
49	#4076	C₂²	1	2	yes	complemented
50	#4076	C₂²	1	1	yes	characteristic, complemented
51	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
52	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
53	C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
54	#4044	C₂²	1	2	yes	—
55	#4044	C₂²	1	2	yes	—
56	#4044	C₂²	1	2	yes	complemented
57	#4043	C₂²	1	1	yes	characteristic
58	#4043	C₂²	1	1	yes	characteristic
59	#4043	C₂²	1	1	yes	characteristic, complemented
60	#4043	C₂²	1	2	yes	complemented
61	#4042	C₂²	1	1	yes	characteristic
62	#4042	C₂²	1	2	yes	complemented
63	#4041	C₂²	1	1	yes	characteristic
64	#4041	C₂²	1	2	yes	—
65	#4041	C₂²	1	1	yes	characteristic
66	#4041	C₂²	1	1	yes	characteristic
67	#4041	C₂²	1	2	yes	—
68	#4041	C₂²	1	2	yes	—
69	#4041	C₂²	1	2	yes	—
70	#4041	C₂²	1	2	yes	—
71	#4041	C₂²	1	1	yes	characteristic, complemented
72	#4041	C₂²	1	2	yes	complemented
73	#4040	C₂²	1	2	yes	—
74	#4040	C₂²	1	2	yes	—
75	#4040	C₂²	1	2	yes	—
76	#4040	C₂²	1	1	yes	characteristic
77	#4040	C₂²	1	2	yes	—
78	#4040	C₂²	1	2	yes	complemented
79	#4040	C₂²	1	2	yes	complemented
80	#4040	C₂²	1	2	yes	complemented
81	#4039	C₂²	1	2	yes	—
82	#4039	C₂²	1	1	yes	characteristic, complemented
83	#4039	C₂²	1	1	yes	characteristic, complemented
84	#4039	C₂²	1	2	yes	complemented
85	#4038	C₂²	1	1	yes	characteristic
86	#4038	C₂²	1	2	yes	complemented
87	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
88	D₅×C₄⋊C₄	C₂²	1	2	yes	complemented
89	D₅×C₄⋊C₄	C₂²	1	2	yes	complemented
90	#4036	C₂²	1	1	yes	characteristic, complemented
91	#4036	C₂²	1	2	yes	complemented
92	#4035	C₂²	1	2	yes	complemented
93	#4032	C₂²	1	2	yes	—
94	#4030	C₂²	1	2	yes	—
95	#4030	C₂²	1	2	yes	—
96	#4030	C₂²	1	1	yes	characteristic
97	#4030	C₂²	1	2	yes	—
98	#4030	C₂²	1	2	yes	—
99	#4030	C₂²	1	2	yes	—
100	#4030	C₂²	1	2	yes	complemented
101	#4030	C₂²	1	2	yes	complemented
102	#4029	C₂²	1	1	yes	characteristic
103	#4029	C₂²	1	2	yes	—
104	#4029	C₂²	1	2	yes	—
105	#4029	C₂²	1	2	yes	complemented
106	#4028	C₂²	1	2	yes	—
107	#4028	C₂²	1	1	yes	characteristic
108	#4028	C₂²	1	2	yes	—
109	#4027	C₂²	1	2	yes	—
110	#4024	C₂²	1	1	yes	characteristic
111	#4022	C₂²	1	2	yes	—
112	#4022	C₂²	1	2	yes	complemented
113	#4020	C₂²	1	2	yes	—
114	#4020	C₂²	1	1	yes	characteristic, complemented
115	C₄×D₂₀	C₂²	1	2	yes	—
116	C₄×D₂₀	C₂²	1	2	yes	—
117	C₄×D₂₀	C₂²	1	1	yes	characteristic
118	C₄×D₂₀	C₂²	1	2	yes	complemented
119	C₄×D₂₀	C₂²	1	2	yes	complemented
120	#4018	C₂²	1	1	yes	characteristic
121	#4016	C₂²	1	2	yes	complemented
122	C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
123	#3539	—	5	1	no	maximal, Sylow
124	C₂³×D₅	C₂³	1	1	yes	characteristic
125	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
126	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
127	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₅	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	1	yes	characteristic
132	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
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	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
138	C₂²×Dic₅	C₂³	1	1	yes	characteristic
139	#713	—	4	2	no	—
140	#713	—	4	2	no	—
141	#709	—	4	2	no	—
142	#709	—	4	2	no	—
143	#709	—	4	2	no	—
144	C₂×D₂₀	C₂³	1	1	yes	characteristic
145	C₂×D₂₀	C₂³	1	1	yes	characteristic
146	C₂×D₂₀	C₂³	1	1	yes	characteristic
147	C₂×D₂₀	C₂³	1	2	yes	—
148	C₂×D₂₀	C₂³	1	2	yes	—
149	C₂×D₂₀	C₂³	1	1	yes	characteristic
150	C₂×D₂₀	C₂³	1	2	yes	—
151	C₂×D₂₀	C₂³	1	2	yes	—
152	C₂×D₂₀	C₂³	1	2	yes	—
153	C₂×D₂₀	C₂³	1	2	yes	—
154	C₂×D₂₀	C₂³	1	2	yes	—
155	C₂×D₂₀	C₂³	1	2	yes	—
156	C₂×C₄×D₅	—	4	2	no	—
157	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
160	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
161	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
162	C₂×C₄×D₅	C₂³	1	2	yes	—
163	C₂×C₄×D₅	C₂³	1	2	yes	—
164	C₂×C₄×D₅	C₂³	1	2	yes	—
165	C₂×C₄×D₅	C₂³	1	2	yes	—
166	C₂×C₄×D₅	C₂³	1	2	yes	—
167	C₂×C₄×D₅	C₂³	1	2	yes	—
168	C₂×C₄×D₅	C₂³	1	2	yes	—
169	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
170	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
171	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
172	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
173	C₅×C₄⋊C₄	C₂³	1	2	yes	—
174	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
175	C₅×C₄⋊C₄	C₂³	1	2	yes	—
176	C₅×C₄⋊C₄	C₂³	1	2	yes	—
177	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
178	C₅×C₄⋊C₄	C₂³	1	2	yes	—
179	C₅×C₄⋊C₄	C₂³	1	2	yes	—
180	C₅×C₄⋊C₄	C₂³	1	2	yes	—
181	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
183	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
184	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
185	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₄²×C₅	C₂³	1	2	yes	—
187	C₄²×C₅	C₂³	1	2	yes	—
188	C₄²×C₅	C₂³	1	1	yes	characteristic
189	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
190	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
191	#685	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
198	#685	C₂³	1	1	yes	characteristic
199	#685	C₂³	1	1	yes	characteristic
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	#685	C₂³	1	2	yes	—
206	#685	C₂³	1	1	yes	characteristic
207	#685	C₂³	1	2	yes	—
208	#685	C₂³	1	2	yes	—
209	#685	C₂³	1	2	yes	—
210	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
211	C₄⋊Dic₅	C₂³	1	2	yes	—
212	C₄⋊Dic₅	C₂³	1	2	yes	—
213	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
214	C₄⋊Dic₅	C₂³	1	2	yes	—
215	C₄⋊Dic₅	C₂³	1	2	yes	—
216	#683	C₂³	1	2	yes	—
217	#683	C₂³	1	1	yes	characteristic
218	#683	C₂³	1	2	yes	—
219	#683	C₂³	1	2	yes	—
220	#683	C₂³	1	1	yes	characteristic
221	#683	C₂³	1	2	yes	—
222	#683	C₂³	1	2	yes	—
223	#683	C₂³	1	1	yes	characteristic
224	#683	C₂³	1	2	yes	—
225	#683	C₂³	1	1	yes	characteristic
226	C₄×Dic₅	C₂³	1	2	yes	—
227	C₄×Dic₅	C₂³	1	1	yes	characteristic
228	C₄×Dic₅	C₂³	1	2	yes	—
229	#560	—	5	2	no	—
230	#560	—	5	2	no	—
231	#553	—	5	2	no	—
232	#553	—	5	1	no	—
233	#553	—	5	2	no	—
234	#553	—	5	1	no	—
235	#552	—	5	1	no	—
236	#552	D₅	1	1	yes	characteristic, complemented
237	#550	—	5	1	no	—
238	#550	—	5	1	no	—
239	#547	—	5	1	no	—
240	#547	—	5	1	no	—
241	#541	—	5	1	no	—
242	#540	—	5	1	no	—
243	#540	—	5	2	no	—
244	#540	—	5	2	no	—
245	#539	—	5	2	no	—
246	#539	—	5	2	no	—
247	#537	—	5	1	no	—
248	#537	—	5	1	no	—
249	#525	—	5	1	no	—
250	#525	—	5	1	no	—
251	#525	—	5	1	no	—
252	C₂³×C₅	C₂⁴	1	1	yes	characteristic
253	C₂³×C₅	C₂⁴	1	1	yes	characteristic
254	C₂²×D₅	—	4	1	no	—
255	C₂²×D₅	—	4	1	no	—
256	C₂²×D₅	—	4	1	no	—
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	C₂²×D₅	C₂⁴	1	2	yes	—
261	C₂²×D₅	C₂⁴	1	2	yes	—
262	C₅×Q₈	—	2	2	no	—
263	C₅×D₄	—	4	1	no	—
264	C₂×C₄×C₅	—	2	2	no	—
265	C₂×C₄×C₅	—	2	2	no	—
266	C₂×C₄×C₅	—	4	2	no	—
267	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
268	C₂×C₄×C₅	C₂⁴	1	2	yes	—
269	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
270	C₂×C₄×C₅	C₂⁴	1	2	yes	—
271	C₂×C₄×C₅	C₂⁴	1	2	yes	—
272	C₂×C₄×C₅	C₂⁴	1	2	yes	—
273	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
274	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
275	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
276	C₂²⋊D₅	—	4	2	no	—
277	C₂²⋊D₅	—	4	2	no	—
278	C₂²⋊D₅	—	4	1	no	—
279	C₂²⋊D₅	—	4	1	no	—
280	C₂²⋊D₅	—	4	1	no	—
281	C₂²⋊D₅	—	4	1	no	—
282	C₂²⋊D₅	—	4	2	no	—
283	C₂²⋊D₅	—	4	2	no	—
284	C₂×Dic₅	—	4	1	no	—
285	C₂×Dic₅	C₂⁴	1	2	yes	—
286	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
287	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
288	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
289	C₂×Dic₅	C₂⁴	1	2	yes	—
290	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
291	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
292	D₂₀	—	2	2	no	—
293	D₂₀	—	2	2	no	—
294	D₂₀	—	4	2	no	—
295	D₂₀	—	4	2	no	—
296	D₂₀	—	4	1	no	—
297	D₂₀	—	4	2	no	—
298	D₂₀	—	4	2	no	—
299	D₂₀	—	4	2	no	—
300	D₂₀	—	4	2	no	—
301	D₂₀	—	4	1	no	—
302	D₂₀	—	4	2	no	—
303	D₂₀	—	4	2	no	—
304	C₄×D₅	—	2	2	no	—
305	C₄×D₅	—	2	2	no	—
306	C₄×D₅	—	2	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	C₄×D₅	—	4	2	no	—
312	C₄×D₅	—	4	2	no	—
313	C₄×D₅	—	4	2	no	—
314	C₄×D₅	—	4	2	no	—
315	C₄×D₅	—	4	2	no	—
316	Dic₁₀	—	2	2	no	—
317	Dic₁₀	—	4	1	no	—
318	C₂×#41	—	5	1	no	—
319	C₂×#41	—	5	1	no	—
320	C₂×#41	—	5	1	no	—
321	C₂×#41	—	5	1	no	—
322	C₂×#41	—	5	1	no	—
323	C₂³×C₄	—	5	1	no	—
324	C₄⋊Q₈	—	5	1	no	—
325	#127	—	5	2	no	—
326	#127	—	5	1	no	—
327	#127	—	5	2	no	—
328	#126	—	5	2	no	—
329	#126	—	5	2	no	—
330	#126	—	5	2	no	—
331	#126	—	5	2	no	—
332	#126	—	5	2	no	—
333	#126	C₂×D₅	1	2	yes	—
334	#125	—	5	2	no	—
335	#125	—	5	2	no	—
336	#125	—	5	1	no	—
337	#125	—	5	2	no	—
338	#125	C₂×D₅	1	2	yes	complemented
339	#125	C₂×D₅	1	1	yes	characteristic, complemented
340	#123	—	5	2	no	—
341	#123	—	5	1	no	—
342	#123	—	5	2	no	—
343	#123	—	5	2	no	—
344	#123	—	5	2	no	—
345	#123	—	5	2	no	—
346	#123	—	5	2	no	—
347	#123	—	5	2	no	—
348	#123	—	5	2	no	—
349	#123	—	5	1	no	—
350	#123	—	5	2	no	—
351	#123	—	5	2	no	—
352	#123	—	5	2	no	—
353	#123	C₂×D₅	1	2	yes	—
354	C₂²⋊Q₈	—	5	1	no	—
355	C₂²⋊Q₈	—	5	1	no	—
356	C₂²⋊Q₈	—	5	1	no	—
357	C₂²⋊Q₈	—	5	1	no	—
358	C₂²⋊Q₈	—	5	2	no	—
359	C₂²⋊Q₈	—	5	2	no	—
360	C₂²⋊Q₈	—	5	1	no	—
361	C₂²⋊Q₈	—	5	1	no	—
362	C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic
363	C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
364	#121	—	5	1	no	—
365	#121	—	5	1	no	—
366	#121	—	5	2	no	—
367	#121	—	5	1	no	—
368	#121	—	5	2	no	—
369	#121	—	5	2	no	—
370	#121	—	5	1	no	—
371	#121	—	5	1	no	—
372	#121	—	5	1	no	—
373	#121	—	5	1	no	—
374	#121	—	5	2	no	—
375	#121	—	5	2	no	—
376	#121	—	5	2	no	—
377	#121	—	5	2	no	—
378	#121	—	5	2	no	—
379	#121	—	5	2	no	—
380	#121	—	5	1	no	—
381	#121	—	5	2	no	—
382	#121	—	5	2	no	—
383	#121	—	5	2	no	—
384	#121	—	5	2	no	—
385	#121	—	5	2	no	—
386	#121	—	5	2	no	—
387	#121	—	5	2	no	—
388	#120	—	5	1	no	—
389	#120	—	5	1	no	—
390	#120	—	5	2	no	—
391	#120	—	5	2	no	—
392	C₄×Q₈	—	5	1	no	—
393	C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
394	C₄×D₄	—	5	1	no	—
395	C₄×D₄	—	5	1	no	—
396	C₄×D₄	—	5	2	no	—
397	C₄×D₄	—	5	2	no	—
398	C₄×D₄	—	5	2	no	—
399	C₄×D₄	—	5	1	no	—
400	C₄×D₄	—	5	1	no	—
401	C₄×D₄	—	5	2	no	—
402	C₄×D₄	—	5	2	no	—
403	C₄×D₄	—	5	1	no	—
404	C₄×D₄	—	5	2	no	—
405	C₄×D₄	—	5	2	no	—
406	C₄×D₄	—	5	2	no	—
407	C₄×D₄	C₂×D₅	1	1	yes	characteristic
408	#117	—	5	1	no	—
409	#117	—	5	2	no	—
410	#117	—	5	1	no	—
411	#117	C₂×D₅	1	1	yes	characteristic
412	#117	C₂×D₅	1	2	yes	complemented
413	C₂×C₄⋊C₄	—	5	1	no	—
414	C₂×C₄⋊C₄	—	5	2	no	—
415	C₂×C₄⋊C₄	—	5	2	no	—
416	C₂×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
417	C₂²×C₅	—	2	1	no	—
418	C₂²×C₅	—	2	1	no	—
419	C₂²×C₅	—	2	1	no	—
420	C₂²×C₅	—	2	1	no	—
421	C₂²×C₅	—	2	1	no	—
422	C₂²×C₅	—	2	1	no	—
423	C₂²×C₅	C₂⁵	1	1	yes	characteristic
424	C₂×D₅	—	2	1	no	—
425	C₂×D₅	—	2	1	no	—
426	C₂×D₅	—	2	1	no	—
427	C₂×D₅	—	2	2	no	—
428	C₂×D₅	—	2	2	no	—
429	C₂×D₅	—	2	1	no	—
430	C₂×D₅	—	2	2	no	—
431	C₂×D₅	—	2	2	no	—
432	C₂×D₅	—	2	2	no	—
433	C₂×D₅	—	2	1	no	—
434	C₂×D₅	—	2	2	no	—
435	C₂×D₅	—	2	1	no	—
436	C₂×D₅	—	2	1	no	—
437	C₂×D₅	—	2	1	no	—
438	C₂×D₅	—	2	1	no	—
439	C₂×D₅	—	4	4	no	—
440	C₄×C₅	—	2	1	no	—
441	C₄×C₅	—	2	1	no	—
442	C₄×C₅	—	2	2	no	—
443	C₄×C₅	—	2	2	no	—
444	C₄×C₅	—	2	2	no	—
445	C₄×C₅	—	2	1	no	—
446	C₄×C₅	—	2	2	no	—
447	C₄×C₅	—	2	1	no	—
448	C₄×C₅	H(5,𝔽₂)	1	2	yes	—
449	Dic₅	—	2	2	no	—
450	Dic₅	—	2	1	no	—
451	Dic₅	—	2	1	no	—
452	Dic₅	—	2	1	no	—
453	Dic₅	—	2	1	no	—
454	Dic₅	—	2	1	no	—
455	Dic₅	—	2	2	no	—
456	C₂⁴	—	5	1	no	—
457	#41	—	20	2	no	—
458	#41	—	20	2	no	—
459	#41	—	20	2	no	—
460	#41	—	20	2	no	—
461	#41	—	20	2	no	—
462	C₂×Q₈	—	5	1	no	—
463	C₂×Q₈	—	5	1	no	—
464	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
465	C₂×D₄	—	5	1	no	—
466	C₂×D₄	—	5	1	no	—
467	C₂×D₄	—	5	2	no	—
468	C₂×D₄	—	5	2	no	—
469	C₂×D₄	—	5	1	no	—
470	C₂×D₄	—	5	2	no	—
471	C₂×D₄	—	5	1	no	—
472	C₂×D₄	—	5	2	no	—
473	C₂×D₄	—	5	1	no	—
474	C₂×D₄	—	5	1	no	—
475	C₂×D₄	—	5	2	no	—
476	C₂×D₄	—	5	2	no	—
477	C₂×D₄	—	5	2	no	—
478	C₂×D₄	—	5	1	no	—
479	C₂×D₄	—	5	2	no	—
480	C₂×D₄	—	5	2	no	—
481	C₂×D₄	—	5	2	no	—
482	C₂×D₄	—	5	1	no	—
483	C₂×D₄	—	5	2	no	—
484	C₂×D₄	—	5	2	no	—
485	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
486	C₂²×C₄	—	5	1	no	—
487	C₂²×C₄	—	5	1	no	—
488	C₂²×C₄	—	5	1	no	—
489	C₂²×C₄	—	5	1	no	—
490	C₂²×C₄	—	5	2	no	—
491	C₂²×C₄	—	5	2	no	—
492	C₂²×C₄	—	5	2	no	—
493	C₂²×C₄	—	5	2	no	—
494	C₂²×C₄	—	5	2	no	—
495	C₂²×C₄	—	5	2	no	—
496	C₂²×C₄	—	5	2	no	—
497	C₂²×C₄	—	5	1	no	—
498	C₂²×C₄	—	5	1	no	—
499	C₂²×C₄	—	20	2	no	—
500	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
501	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
502	C₂²×C₄	C₂²×D₅	1	2	yes	—
503	C₄⋊C₄	—	5	1	no	—
504	C₄⋊C₄	—	5	1	no	—
505	C₄⋊C₄	—	5	2	no	—
506	C₄⋊C₄	—	5	1	no	—
507	C₄⋊C₄	—	5	2	no	—
508	C₄⋊C₄	—	5	2	no	—
509	C₄⋊C₄	—	5	2	no	—
510	C₄⋊C₄	—	5	2	no	—
511	C₄⋊C₄	—	5	1	no	—
512	C₄⋊C₄	—	5	1	no	—
513	C₄⋊C₄	—	5	1	no	—
514	C₄⋊C₄	—	5	2	no	—
515	C₄⋊C₄	—	5	2	no	—
516	C₄⋊C₄	—	5	2	no	—
517	C₄⋊C₄	—	5	2	no	—
518	C₄⋊C₄	—	5	2	no	—
519	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
520	C₄⋊C₄	C₂²×D₅	1	2	yes	—
521	C₄⋊C₄	C₂²×D₅	1	2	yes	—
522	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
523	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
524	C₄⋊C₄	C₂²×D₅	1	2	yes	—
525	C₄⋊C₄	C₂²×D₅	1	2	yes	—
526	C₄⋊C₄	C₂²×D₅	1	2	yes	—
527	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
528	C₄⋊C₄	C₂²×D₅	1	2	yes	—
529	C₂²⋊C₄	—	5	1	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	2	no	—
538	C₂²⋊C₄	—	5	1	no	—
539	C₂²⋊C₄	—	5	2	no	—
540	C₂²⋊C₄	—	5	2	no	—
541	C₂²⋊C₄	—	5	1	no	—
542	C₂²⋊C₄	—	5	2	no	—
543	C₂²⋊C₄	—	5	1	no	—
544	C₂²⋊C₄	—	5	2	no	—
545	C₂²⋊C₄	—	5	2	no	—
546	C₂²⋊C₄	—	5	2	no	—
547	C₂²⋊C₄	—	5	2	no	—
548	C₂²⋊C₄	—	5	2	no	—
549	C₂²⋊C₄	—	5	2	no	—
550	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
551	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
552	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
553	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
554	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
555	C₄²	—	5	2	no	—
556	C₄²	—	5	1	no	—
557	C₄²	—	5	2	no	—
558	C₄²	C₂²×D₅	1	1	yes	characteristic
559	C₄²	C₂²×D₅	1	2	yes	—
560	C₄²	C₂²×D₅	1	2	yes	—
561	C₂×C₅	—	4	1	no	—
562	C₂×C₅	—	4	1	no	—
563	C₂×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
564	C₂×C₅	#585	1	1	yes	characteristic
565	C₂×C₅	#585	1	1	yes	characteristic
566	D₅	—	4	1	no	—
567	D₅	—	4	2	no	—
568	D₅	—	4	2	no	—
569	D₅	—	4	1	no	—
570	D₅	—	4	1	no	—
571	C₂³	—	5	1	no	—
572	C₂³	—	5	1	no	—
573	C₂³	—	5	1	no	—
574	C₂³	—	5	2	no	—
575	C₂³	—	5	2	no	—
576	C₂³	—	20	1	no	—
577	C₂³	—	20	1	no	—
578	C₂³	—	20	1	no	—
579	C₂³	C₂³×D₅	1	1	yes	characteristic
580	C₂³	C₂³×D₅	1	1	yes	characteristic
581	Q₈	—	2	2	no	—
582	Q₈	—	10	2	no	—
583	Q₈	—	20	1	no	—
584	D₄	—	4	1	no	—
585	D₄	—	10	2	no	—
586	D₄	—	10	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	1	no	—
596	D₄	—	20	2	no	—
597	D₄	—	20	1	no	—
598	D₄	—	20	1	no	—
599	D₄	—	20	2	no	—
600	D₄	—	20	2	no	—
601	D₄	—	20	1	no	—
602	D₄	—	20	1	no	—
603	D₄	—	20	2	no	—
604	D₄	—	20	2	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	4	2	no	—
608	C₂×C₄	—	5	2	no	—
609	C₂×C₄	—	5	1	no	—
610	C₂×C₄	—	5	1	no	—
611	C₂×C₄	—	5	1	no	—
612	C₂×C₄	—	5	2	no	—
613	C₂×C₄	—	5	1	no	—
614	C₂×C₄	—	5	1	no	—
615	C₂×C₄	—	10	2	no	—
616	C₂×C₄	—	10	2	no	—
617	C₂×C₄	—	10	2	no	—
618	C₂×C₄	—	20	1	no	—
619	C₂×C₄	—	20	1	no	—
620	C₂×C₄	—	20	2	no	—
621	C₂×C₄	—	20	2	no	—
622	C₂×C₄	—	20	2	no	—
623	C₂×C₄	—	20	2	no	—
624	C₂×C₄	—	20	2	no	—
625	C₂×C₄	—	20	2	no	—
626	C₂×C₄	—	20	2	no	—
627	C₂×C₄	—	20	1	no	—
628	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
629	C₂×C₄	C₂³×D₅	1	2	yes	—
630	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
631	C₂×C₄	C₂³×D₅	1	2	yes	—
632	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
633	C₂×C₄	C₂³×D₅	1	2	yes	—
634	C₂×C₄	C₂³×D₅	1	2	yes	—
635	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
636	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
637	C₅	#3539	1	1	yes	characteristic, complemented, Sylow
638	C₂²	—	2	1	no	—
639	C₂²	—	2	1	no	—
640	C₂²	—	2	1	no	—
641	C₂²	—	2	1	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	10	1	no	—
645	C₂²	—	10	1	no	—
646	C₂²	—	10	1	no	—
647	C₂²	—	10	2	no	—
648	C₂²	—	10	2	no	—
649	C₂²	—	10	2	no	—
650	C₂²	—	10	2	no	—
651	C₂²	—	10	1	no	—
652	C₂²	—	10	1	no	—
653	C₂²	—	10	1	no	—
654	C₂²	—	10	1	no	—
655	C₂²	—	10	2	no	—
656	C₂²	—	10	2	no	—
657	C₂²	—	10	1	no	—
658	C₂²	—	10	1	no	—
659	C₂²	—	20	4	no	—
660	C₂²	C₂⁴×D₅	1	1	yes	characteristic
661	C₄	—	2	1	no	—
662	C₄	—	2	1	no	—
663	C₄	—	2	2	no	—
664	C₄	—	2	2	no	—
665	C₄	—	2	2	no	—
666	C₄	—	2	1	no	—
667	C₄	—	2	2	no	—
668	C₄	—	2	1	no	—
669	C₄	—	10	1	no	—
670	C₄	—	10	1	no	—
671	C₄	—	10	1	no	—
672	C₄	—	10	2	no	—
673	C₄	—	10	1	no	—
674	C₄	—	10	1	no	—
675	C₄	—	10	2	no	—
676	C₄	#4149	1	2	yes	—
677	C₂	—	4	1	no	—
678	C₂	—	4	1	no	—
679	C₂	—	20	1	no	—
680	C₂	—	20	1	no	—
681	C₂	—	20	1	no	—
682	C₂	—	20	2	no	—
683	C₂	—	20	2	no	—
684	C₂	C₂×#4149	1	1	yes	characteristic
685	C₂	#66283	1	1	yes	characteristic
686	C₂	#66287	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅
commutator, socle, cosocle	C₂²×C₅	C₂⁵
Fitting	C₅×#552	C₂
hypercenter	#552	D₅
hypocenter	C₅	#3539
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ #552

Complements

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

N	H ≅ G/N	type
1. C₅×#552	C₂	semidirect
2. #66045	C₂	semidirect
3. #66041	C₂	semidirect
4. #66032	C₂	semidirect
5. #66029	C₂	semidirect
6. #66028	C₂	semidirect
7. #66026	C₂	semidirect
8. #66000	C₂	semidirect
9. #65997	C₂	semidirect
10. #65965	C₂	semidirect
11. #65965	C₂	semidirect
12. #65963	C₂	semidirect
13. #65961	C₂	semidirect
14. #65917	C₂	semidirect
15. #65911	C₂	semidirect
16. #65887	C₂	semidirect
17. #65881	C₂	semidirect
18. #65869	C₂	semidirect
19. #65864	C₂	semidirect
20. #65864	C₂	semidirect
21. #65858	C₂	semidirect
22. #65848	C₂	semidirect
23. #65844	C₂	semidirect
25. C₂×#713	C₂²	semidirect
28. C₂×#709	C₂²	semidirect
31. C₅×#125	C₂²	semidirect
32. C₅×#125	C₂²	semidirect
35. C₅×C₂²⋊Q₈	C₂²	semidirect
36. C₄×C₅×Q₈	C₂²	semidirect
39. C₅×#117	C₂²	semidirect
40. C₂×C₅×C₄⋊C₄	C₂²	semidirect
42. #4090	C₂²	semidirect
49. #4076	C₂²	semidirect
50. #4076	C₂²	semidirect
53. C₄×C₂²⋊D₅	C₂²	semidirect
56. #4044	C₂²	semidirect
59. #4043	C₂²	semidirect
60. #4043	C₂²	semidirect
62. #4042	C₂²	semidirect
71. #4041	C₂²	semidirect
72. #4041	C₂²	semidirect
78. #4040	C₂²	semidirect
79. #4040	C₂²	semidirect
80. #4040	C₂²	semidirect
82. #4039	C₂²	semidirect
83. #4039	C₂²	semidirect
84. #4039	C₂²	semidirect
86. #4038	C₂²	semidirect
87. D₅×C₄⋊C₄	C₂²	semidirect
88. D₅×C₄⋊C₄	C₂²	semidirect
89. D₅×C₄⋊C₄	C₂²	semidirect
90. #4036	C₂²	semidirect
91. #4036	C₂²	semidirect
92. #4035	C₂²	semidirect
100. #4030	C₂²	semidirect
101. #4030	C₂²	semidirect
105. #4029	C₂²	semidirect
112. #4022	C₂²	semidirect
114. #4020	C₂²	semidirect
118. C₄×D₂₀	C₂²	semidirect
119. C₄×D₂₀	C₂²	semidirect
121. #4016	C₂²	semidirect
122. C₄×Dic₁₀	C₂²	semidirect
236. #552	D₅	semidirect
338. #125	C₂×D₅	semidirect
339. #125	C₂×D₅	semidirect
363. C₂²⋊Q₈	C₂×D₅	semidirect
393. C₄×Q₈	C₂×D₅	semidirect
412. #117	C₂×D₅	semidirect
416. C₂×C₄⋊C₄	C₂×D₅	semidirect
637. C₅	#3539	semidirect

Maximal subgroups

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

subgroup	index
C₅×#552	2
#66045	2
#66041	2
#66032	2
#66029	2
#66028	2
#66026	2
#66000	2
#65997	2
#65965	2
#65963	2
#65961	2
#65917	2
#65911	2
#65887	2
#65881	2
#65869	2
#65864	2
#65858	2
#65848	2
#65844	2
#3539	5