Subgroups — #10618025

Order 640.

1012 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	#66042	C₂	1	2	yes	maximal, complemented
3	#66036	C₂	1	2	yes	maximal, complemented
4	#66030	C₂	1	2	yes	maximal, complemented
5	#66003	C₂	1	2	yes	maximal, complemented
6	#65983	C₂	1	2	yes	maximal, complemented
7	#65983	C₂	1	2	yes	maximal, complemented
8	#65970	C₂	1	2	yes	maximal, complemented
9	#65935	C₂	1	2	yes	maximal, complemented
10	#65918	C₂	1	1	yes	maximal, characteristic, complemented
11	#65901	C₂	1	1	yes	maximal, characteristic, complemented
12	#65899	C₂	1	1	yes	maximal, characteristic, complemented
13	#65886	C₂	1	1	yes	maximal, characteristic, complemented
14	#65886	C₂	1	1	yes	maximal, characteristic, complemented
15	#65877	C₂	1	1	yes	maximal, characteristic, complemented
16	#65875	C₂	1	1	yes	maximal, characteristic, complemented
17	D₄×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
18	#65868	C₂	1	1	yes	maximal, characteristic, complemented
19	#65857	C₂	1	1	yes	maximal, characteristic, complemented
20	#65852	C₂	1	1	yes	maximal, characteristic, complemented
21	#65850	C₂	1	1	yes	maximal, characteristic, complemented
22	#65813	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₄×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#709	C₂²	1	1	yes	characteristic
25	C₂²×Dic₁₀	C₂²	1	1	yes	characteristic
26	C₂²×Dic₁₀	C₂²	1	1	yes	characteristic
27	C₅×#126	C₂²	1	1	yes	characteristic
28	C₅×#126	C₂²	1	1	yes	characteristic
29	C₅×#125	C₂²	1	1	yes	characteristic
30	C₅×#124	C₂²	1	1	yes	characteristic
31	C₅×#123	C₂²	1	1	yes	characteristic
32	C₅×#123	C₂²	1	1	yes	characteristic
33	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
34	C₅×#121	C₂²	1	1	yes	characteristic
35	C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
36	C₄×C₅×D₄	C₂²	1	1	yes	characteristic
37	C₄×C₅×D₄	C₂²	1	1	yes	characteristic
38	C₄×C₅×D₄	C₂²	1	1	yes	characteristic
39	C₅×#117	C₂²	1	1	yes	characteristic
40	C₅×#117	C₂²	1	1	yes	characteristic
41	C₂×C₄²×C₅	C₂²	1	1	yes	characteristic
42	#4092	C₂²	1	2	yes	—
43	#4090	C₂²	1	2	yes	—
44	#4085	C₂²	1	2	yes	—
45	#4085	C₂²	1	2	yes	—
46	#4085	C₂²	1	2	yes	—
47	#4081	C₂²	1	2	yes	—
48	D₄×Dic₅	C₂²	1	2	yes	—
49	D₄×Dic₅	C₂²	1	2	yes	—
50	#4076	C₂²	1	1	yes	characteristic
51	#4076	C₂²	1	1	yes	characteristic
52	#4075	C₂²	1	2	yes	—
53	C₄×C₂²⋊D₅	C₂²	1	2	yes	—
54	#4072	C₂²	1	1	yes	characteristic
55	C₂×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
56	C₂×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
57	#4070	C₂²	1	1	yes	characteristic
58	#4070	C₂²	1	1	yes	characteristic
59	#4070	C₂²	1	1	yes	characteristic
60	#4070	C₂²	1	1	yes	characteristic
61	C₂×#683	C₂²	1	2	yes	—
62	C₂×C₄×Dic₅	C₂²	1	2	yes	—
63	#4044	C₂²	1	2	yes	—
64	#4044	C₂²	1	2	yes	—
65	#4044	C₂²	1	2	yes	—
66	#4044	C₂²	1	2	yes	—
67	#4042	C₂²	1	2	yes	—
68	#4042	C₂²	1	2	yes	—
69	#4042	C₂²	1	2	yes	—
70	#4038	C₂²	1	2	yes	—
71	#4038	C₂²	1	2	yes	—
72	D₅×C₄⋊C₄	C₂²	1	2	yes	—
73	#4036	C₂²	1	2	yes	—
74	#4035	C₂²	1	2	yes	—
75	#4035	C₂²	1	2	yes	—
76	#4035	C₂²	1	2	yes	—
77	#4035	C₂²	1	2	yes	—
78	#4035	C₂²	1	2	yes	—
79	#4034	C₂²	1	2	yes	—
80	#4033	C₂²	1	2	yes	—
81	#4033	C₂²	1	2	yes	—
82	#4033	C₂²	1	2	yes	—
83	#4031	C₂²	1	2	yes	—
84	#4031	C₂²	1	2	yes	—
85	#4031	C₂²	1	2	yes	—
86	#4029	C₂²	1	2	yes	—
87	#4029	C₂²	1	2	yes	—
88	#4027	C₂²	1	2	yes	—
89	#4027	C₂²	1	2	yes	—
90	#4027	C₂²	1	2	yes	—
91	#4027	C₂²	1	2	yes	—
92	#4027	C₂²	1	2	yes	—
93	#4025	C₂²	1	2	yes	—
94	#4025	C₂²	1	2	yes	—
95	#4025	C₂²	1	2	yes	—
96	#4024	C₂²	1	2	yes	—
97	#4024	C₂²	1	2	yes	—
98	#4024	C₂²	1	2	yes	—
99	#4024	C₂²	1	2	yes	—
100	#4023	C₂²	1	2	yes	—
101	#4023	C₂²	1	2	yes	—
102	#4023	C₂²	1	2	yes	—
103	#4022	C₂²	1	2	yes	—
104	#4021	C₂²	1	1	yes	characteristic
105	#4021	C₂²	1	1	yes	characteristic
106	C₄×D₂₀	C₂²	1	1	yes	characteristic
107	C₄×D₂₀	C₂²	1	1	yes	characteristic
108	#4018	C₂²	1	2	yes	—
109	#4016	C₂²	1	1	yes	characteristic
110	#4016	C₂²	1	1	yes	characteristic
111	#4015	C₂²	1	1	yes	characteristic
112	#4015	C₂²	1	1	yes	characteristic
113	C₄×Dic₁₀	C₂²	1	1	yes	characteristic
114	C₄×Dic₁₀	C₂²	1	1	yes	characteristic
115	C₄×Dic₁₀	C₂²	1	1	yes	characteristic
116	C₄×Dic₁₀	C₂²	1	1	yes	characteristic
117	C₄×Dic₁₀	C₂²	1	2	yes	—
118	C₄×Dic₁₀	C₂²	1	2	yes	—
119	C₄×Dic₁₀	C₂²	1	1	yes	characteristic
120	C₄×Dic₁₀	C₂²	1	1	yes	characteristic
121	C₄×Dic₁₀	C₂²	1	1	yes	characteristic
122	C₄×Dic₁₀	C₂²	1	1	yes	characteristic
123	#3516	—	5	1	no	maximal, Sylow
124	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
125	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
126	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
127	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
132	C₂²×C₄×C₅	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	2	yes	—
136	C₂²×Dic₅	C₂³	1	2	yes	—
137	C₂²×Dic₅	C₂³	1	2	yes	—
138	C₂²×Dic₅	C₂³	1	2	yes	—
139	C₂²×Dic₅	C₂³	1	2	yes	—
140	#709	—	2	4	no	—
141	C₂×D₂₀	C₂³	1	1	yes	characteristic
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	—	2	4	no	—
146	C₂×Dic₁₀	—	2	4	no	—
147	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
148	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
149	C₂×Dic₁₀	C₂³	1	2	yes	—
150	C₂×Dic₁₀	C₂³	1	2	yes	—
151	C₂×Dic₁₀	C₂³	1	2	yes	—
152	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
153	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
154	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
155	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
156	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
157	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
158	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
159	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
160	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
161	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
162	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
163	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
164	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
165	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
166	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
167	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
168	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
169	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
170	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
171	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
172	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
173	C₄²×C₅	C₂³	1	1	yes	characteristic
174	C₄²×C₅	C₂³	1	1	yes	characteristic
175	C₄²×C₅	C₂³	1	1	yes	characteristic
176	C₄²×C₅	C₂³	1	1	yes	characteristic
177	C₄²×C₅	C₂³	1	1	yes	characteristic
178	C₄²×C₅	C₂³	1	1	yes	characteristic
179	C₂²⋊Dic₅	C₂³	1	2	yes	—
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	#685	C₂³	1	2	yes	—
185	#685	C₂³	1	2	yes	—
186	#685	C₂³	1	2	yes	—
187	#685	C₂³	1	2	yes	—
188	#685	C₂³	1	2	yes	—
189	#685	C₂³	1	2	yes	—
190	#685	C₂³	1	2	yes	—
191	#685	C₂³	1	2	yes	—
192	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
193	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
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	2	yes	—
198	C₄⋊Dic₅	C₂³	1	2	yes	—
199	C₄⋊Dic₅	C₂³	1	2	yes	—
200	C₄⋊Dic₅	C₂³	1	2	yes	—
201	#683	C₂³	1	2	yes	—
202	#683	C₂³	1	2	yes	—
203	#683	C₂³	1	2	yes	—
204	#683	C₂³	1	2	yes	—
205	#683	C₂³	1	2	yes	—
206	#683	C₂³	1	2	yes	—
207	#683	C₂³	1	2	yes	—
208	#683	C₂³	1	2	yes	—
209	#683	C₂³	1	2	yes	—
210	#683	C₂³	1	2	yes	—
211	#683	C₂³	1	2	yes	—
212	#683	C₂³	1	2	yes	—
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	C₄×Dic₅	C₂³	1	2	yes	—
218	C₄×Dic₅	C₂³	1	2	yes	—
219	C₄×Dic₅	C₂³	1	2	yes	—
220	C₄×Dic₅	C₂³	1	2	yes	—
221	C₄×Dic₅	C₂³	1	2	yes	—
222	C₄×Dic₅	C₂³	1	2	yes	—
223	C₄×Dic₅	C₂³	1	2	yes	—
224	C₄×Dic₅	C₂³	1	2	yes	—
225	C₄×Dic₅	C₂³	1	2	yes	—
226	#557	—	5	1	no	—
227	#556	—	5	2	no	—
228	#556	—	5	1	no	—
229	#554	—	5	2	no	—
230	#554	—	5	1	no	—
231	#553	—	5	2	no	—
232	#553	—	5	1	no	—
233	#552	—	5	2	no	—
234	#552	—	5	1	no	—
235	D₄×Q₈	—	5	1	no	—
236	#548	—	5	1	no	—
237	#548	—	5	1	no	—
238	#542	—	5	2	no	—
239	#542	—	5	1	no	—
240	#541	—	5	2	no	—
241	#541	—	5	1	no	—
242	#529	—	5	2	no	—
243	#529	—	5	2	no	—
244	#529	—	5	1	no	—
245	#529	D₅	1	1	yes	characteristic, complemented
246	#520	—	5	1	no	—
247	#519	—	5	1	no	—
248	C₂×C₄×Q₈	—	5	1	no	—
249	C₂³×C₅	C₂⁴	1	1	yes	characteristic
250	C₂³×C₅	C₂⁴	1	1	yes	characteristic
251	C₂³×C₅	C₂⁴	1	1	yes	characteristic
252	C₂²×D₅	C₂⁴	1	2	yes	—
253	C₅×Q₈	—	4	1	no	—
254	C₅×D₄	—	2	2	no	—
255	C₅×D₄	—	2	2	no	—
256	C₅×D₄	—	4	1	no	—
257	C₂×C₄×C₅	—	2	2	no	—
258	C₂×C₄×C₅	—	2	2	no	—
259	C₂×C₄×C₅	—	2	2	no	—
260	C₂×C₄×C₅	—	2	2	no	—
261	C₂×C₄×C₅	—	4	1	no	—
262	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
263	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
264	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
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	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	1	yes	characteristic
274	C₂²⋊D₅	—	2	4	no	—
275	C₂²⋊D₅	—	2	4	no	—
276	C₂²⋊D₅	—	4	2	no	—
277	C₂×Dic₅	—	2	4	no	—
278	C₂×Dic₅	—	2	4	no	—
279	C₂×Dic₅	—	4	2	no	—
280	C₂×Dic₅	—	4	2	no	—
281	C₂×Dic₅	C₂⁴	1	2	yes	—
282	C₂×Dic₅	C₂⁴	1	2	yes	—
283	C₂×Dic₅	C₂⁴	1	2	yes	—
284	C₂×Dic₅	C₂⁴	1	2	yes	—
285	C₂×Dic₅	C₂⁴	1	2	yes	—
286	C₂×Dic₅	C₂⁴	1	2	yes	—
287	C₂×Dic₅	C₂⁴	1	2	yes	—
288	D₂₀	—	2	2	no	—
289	C₄×D₅	—	2	4	no	—
290	C₄×D₅	—	4	2	no	—
291	C₄×D₅	—	4	2	no	—
292	Dic₁₀	—	2	2	no	—
293	Dic₁₀	—	2	2	no	—
294	Dic₁₀	—	2	4	no	—
295	Dic₁₀	—	2	4	no	—
296	Dic₁₀	—	4	2	no	—
297	Dic₁₀	#41	1	4	yes	—
298	C₂×#41	—	5	1	no	—
299	C₂²×Q₈	—	5	1	no	—
300	C₂²×Q₈	—	5	1	no	—
301	C₄⋊Q₈	—	5	2	no	—
302	C₄⋊Q₈	—	5	2	no	—
303	C₄⋊Q₈	—	5	1	no	—
304	C₄⋊Q₈	—	5	1	no	—
305	#126	—	5	2	no	—
306	#126	—	5	2	no	—
307	#126	—	5	2	no	—
308	#126	—	5	2	no	—
309	#126	—	5	2	no	—
310	#126	—	5	2	no	—
311	#126	—	5	2	no	—
312	#126	—	5	2	no	—
313	#126	C₂×D₅	1	1	yes	characteristic
314	#126	C₂×D₅	1	1	yes	characteristic
315	#125	—	5	2	no	—
316	#125	—	5	2	no	—
317	#125	—	5	2	no	—
318	#125	—	5	2	no	—
319	#125	—	5	2	no	—
320	#125	—	5	2	no	—
321	#125	—	5	1	no	—
322	#125	—	5	1	no	—
323	#125	C₂×D₅	1	1	yes	characteristic
324	#124	—	5	2	no	—
325	#124	—	5	2	no	—
326	#124	—	5	2	no	—
327	#124	—	5	1	no	—
328	#124	—	5	1	no	—
329	#124	C₂×D₅	1	1	yes	characteristic
330	#123	—	5	2	no	—
331	#123	—	5	2	no	—
332	#123	—	5	2	no	—
333	#123	—	5	2	no	—
334	#123	C₂×D₅	1	1	yes	characteristic
335	#123	C₂×D₅	1	1	yes	characteristic
336	C₂²⋊Q₈	—	5	2	no	—
337	C₂²⋊Q₈	—	5	1	no	—
338	C₂²⋊Q₈	—	5	1	no	—
339	C₂²⋊Q₈	—	5	1	no	—
340	C₂²⋊Q₈	—	5	1	no	—
341	C₂²⋊Q₈	—	5	2	no	—
342	C₂²⋊Q₈	—	5	2	no	—
343	C₂²⋊Q₈	—	5	2	no	—
344	C₂²⋊Q₈	—	5	2	no	—
345	C₂²⋊Q₈	—	5	2	no	—
346	C₂²⋊Q₈	—	5	2	no	—
347	C₂²⋊Q₈	—	5	2	no	—
348	C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic
349	#121	—	5	2	no	—
350	#121	—	5	2	no	—
351	#121	—	5	2	no	—
352	#121	—	5	1	no	—
353	#121	—	5	1	no	—
354	#121	C₂×D₅	1	1	yes	characteristic
355	C₄×Q₈	—	5	2	no	—
356	C₄×Q₈	—	5	2	no	—
357	C₄×Q₈	—	5	2	no	—
358	C₄×Q₈	—	5	1	no	—
359	C₄×Q₈	—	5	2	no	—
360	C₄×Q₈	—	5	1	no	—
361	C₄×Q₈	—	5	1	no	—
362	C₄×Q₈	—	5	1	no	—
363	C₄×Q₈	—	5	2	no	—
364	C₄×Q₈	—	5	1	no	—
365	C₄×Q₈	—	5	1	no	—
366	C₄×Q₈	—	5	1	no	—
367	C₄×Q₈	—	5	1	no	—
368	C₄×Q₈	C₂×D₅	1	1	yes	characteristic
369	C₄×D₄	—	5	2	no	—
370	C₄×D₄	—	5	2	no	—
371	C₄×D₄	—	5	2	no	—
372	C₄×D₄	—	5	2	no	—
373	C₄×D₄	—	5	2	no	—
374	C₄×D₄	—	5	2	no	—
375	C₄×D₄	—	5	2	no	—
376	C₄×D₄	—	5	2	no	—
377	C₄×D₄	—	5	1	no	—
378	C₄×D₄	—	5	1	no	—
379	C₄×D₄	C₂×D₅	1	1	yes	characteristic
380	C₄×D₄	C₂×D₅	1	1	yes	characteristic
381	C₄×D₄	C₂×D₅	1	1	yes	characteristic
382	#117	—	5	1	no	—
383	#117	—	5	2	no	—
384	#117	—	5	2	no	—
385	#117	—	5	2	no	—
386	#117	—	5	2	no	—
387	#117	—	5	2	no	—
388	#117	—	5	2	no	—
389	#117	C₂×D₅	1	1	yes	characteristic
390	#117	C₂×D₅	1	1	yes	characteristic
391	C₂×C₄⋊C₄	—	5	2	no	—
392	C₂×C₄⋊C₄	—	5	1	no	—
393	C₂×C₄⋊C₄	—	5	1	no	—
394	C₂×C₄⋊C₄	—	5	2	no	—
395	C₂×C₄²	—	5	2	no	—
396	C₂×C₄²	C₂×D₅	1	1	yes	characteristic
397	C₂²×C₅	—	2	1	no	—
398	C₂²×C₅	—	2	1	no	—
399	C₂²×C₅	—	2	1	no	—
400	C₂²×C₅	—	2	1	no	—
401	C₂²×C₅	—	2	1	no	—
402	C₂²×C₅	—	2	1	no	—
403	C₂²×C₅	—	2	1	no	—
404	C₂²×C₅	—	2	1	no	—
405	C₂²×C₅	2₋¹⁺⁴	1	2	yes	—
406	C₂²×C₅	C₂⁵	1	1	yes	characteristic
407	C₂×D₅	—	2	2	no	—
408	C₂×D₅	—	2	2	no	—
409	C₂×D₅	—	2	2	no	—
410	C₄×C₅	—	2	1	no	—
411	C₄×C₅	—	2	1	no	—
412	C₄×C₅	—	2	1	no	—
413	C₄×C₅	—	2	1	no	—
414	C₄×C₅	—	2	1	no	—
415	C₄×C₅	—	2	1	no	—
416	C₄×C₅	—	2	1	no	—
417	C₄×C₅	—	2	1	no	—
418	C₄×C₅	—	2	1	no	—
419	C₄×C₅	—	2	1	no	—
420	C₄×C₅	—	2	1	no	—
421	C₄×C₅	C₂×#41	1	2	yes	—
422	Dic₅	—	2	2	no	—
423	Dic₅	—	2	2	no	—
424	Dic₅	—	2	2	no	—
425	Dic₅	—	2	2	no	—
426	Dic₅	—	2	2	no	—
427	Dic₅	—	2	2	no	—
428	Dic₅	C₂×#41	1	4	yes	—
429	#41	—	10	4	no	—
430	C₂×Q₈	—	5	1	no	—
431	C₂×Q₈	—	5	2	no	—
432	C₂×Q₈	—	5	2	no	—
433	C₂×Q₈	—	5	1	no	—
434	C₂×Q₈	—	5	1	no	—
435	C₂×Q₈	—	5	2	no	—
436	C₂×Q₈	—	10	4	no	—
437	C₂×Q₈	—	10	4	no	—
438	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
439	C₂×D₄	—	5	2	no	—
440	C₂×D₄	—	5	2	no	—
441	C₂×D₄	—	5	2	no	—
442	C₂×D₄	—	5	1	no	—
443	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
444	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
445	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
446	C₂²×C₄	—	5	2	no	—
447	C₂²×C₄	—	5	2	no	—
448	C₂²×C₄	—	5	2	no	—
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	C₂²×D₅	1	1	yes	characteristic
454	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
455	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
456	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
457	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
458	C₄⋊C₄	—	5	2	no	—
459	C₄⋊C₄	—	5	1	no	—
460	C₄⋊C₄	—	5	2	no	—
461	C₄⋊C₄	—	5	2	no	—
462	C₄⋊C₄	—	5	1	no	—
463	C₄⋊C₄	—	5	2	no	—
464	C₄⋊C₄	—	5	1	no	—
465	C₄⋊C₄	—	5	2	no	—
466	C₄⋊C₄	—	5	2	no	—
467	C₄⋊C₄	—	5	2	no	—
468	C₄⋊C₄	—	5	2	no	—
469	C₄⋊C₄	—	5	2	no	—
470	C₄⋊C₄	—	5	1	no	—
471	C₄⋊C₄	—	5	2	no	—
472	C₄⋊C₄	—	5	2	no	—
473	C₄⋊C₄	—	5	2	no	—
474	C₄⋊C₄	—	5	2	no	—
475	C₄⋊C₄	—	5	2	no	—
476	C₄⋊C₄	—	5	2	no	—
477	C₄⋊C₄	—	5	2	no	—
478	C₄⋊C₄	—	5	2	no	—
479	C₄⋊C₄	—	5	2	no	—
480	C₄⋊C₄	—	5	2	no	—
481	C₄⋊C₄	—	5	2	no	—
482	C₄⋊C₄	—	5	2	no	—
483	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
484	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
485	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
486	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
487	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
488	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
489	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
490	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
491	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
492	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
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	2	no	—
498	C₂²⋊C₄	—	5	2	no	—
499	C₂²⋊C₄	—	5	2	no	—
500	C₂²⋊C₄	—	5	2	no	—
501	C₂²⋊C₄	—	5	2	no	—
502	C₂²⋊C₄	—	5	2	no	—
503	C₂²⋊C₄	—	5	2	no	—
504	C₂²⋊C₄	—	5	2	no	—
505	C₂²⋊C₄	—	5	2	no	—
506	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
507	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
508	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
509	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
510	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
511	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
512	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
513	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
514	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
515	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
516	C₄²	—	5	2	no	—
517	C₄²	—	5	2	no	—
518	C₄²	—	5	2	no	—
519	C₄²	—	5	2	no	—
520	C₄²	—	5	2	no	—
521	C₄²	—	5	2	no	—
522	C₄²	—	5	2	no	—
523	C₄²	—	5	2	no	—
524	C₄²	—	5	2	no	—
525	C₄²	C₂²×D₅	1	1	yes	characteristic
526	C₄²	C₂²×D₅	1	1	yes	characteristic
527	C₄²	C₂²×D₅	1	1	yes	characteristic
528	C₄²	C₂²×D₅	1	1	yes	characteristic
529	C₄²	C₂²×D₅	1	1	yes	characteristic
530	C₄²	C₂²×D₅	1	1	yes	characteristic
531	C₂×C₅	—	2	2	no	—
532	C₂×C₅	—	4	1	no	—
533	C₂×C₅	—	4	1	no	—
534	C₂×C₅	C₂²×#41	1	1	yes	characteristic
535	C₂×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
536	C₂×C₅	#585	1	1	yes	characteristic
537	D₅	—	4	2	no	—
538	C₂³	—	5	2	no	—
539	C₂³	C₂³×D₅	1	1	yes	characteristic
540	C₂³	C₂³×D₅	1	1	yes	characteristic
541	C₂³	C₂³×D₅	1	1	yes	characteristic
542	Q₈	—	4	1	no	—
543	Q₈	—	5	4	no	—
544	Q₈	—	10	4	no	—
545	Q₈	—	10	4	no	—
546	Q₈	—	10	2	no	—
547	Q₈	—	10	2	no	—
548	Q₈	—	20	2	no	—
549	D₄	—	2	2	no	—
550	D₄	—	2	2	no	—
551	D₄	—	4	1	no	—
552	D₄	—	10	4	no	—
553	D₄	—	10	4	no	—
554	D₄	—	10	2	no	—
555	D₄	—	20	2	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	5	2	no	—
562	C₂×C₄	—	5	2	no	—
563	C₂×C₄	—	5	2	no	—
564	C₂×C₄	—	5	2	no	—
565	C₂×C₄	—	5	2	no	—
566	C₂×C₄	—	5	2	no	—
567	C₂×C₄	—	5	2	no	—
568	C₂×C₄	—	10	4	no	—
569	C₂×C₄	—	10	4	no	—
570	C₂×C₄	—	10	4	no	—
571	C₂×C₄	—	20	2	no	—
572	C₂×C₄	—	20	2	no	—
573	C₂×C₄	—	20	2	no	—
574	C₂×C₄	—	20	2	no	—
575	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
576	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
577	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
578	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
579	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
580	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
581	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
582	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
583	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
584	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
585	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
586	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
587	C₅	#3516	1	1	yes	characteristic, complemented, Sylow
588	C₂²	—	2	1	no	—
589	C₂²	—	2	1	no	—
590	C₂²	—	2	1	no	—
591	C₂²	—	2	1	no	—
592	C₂²	—	2	1	no	—
593	C₂²	—	2	1	no	—
594	C₂²	—	2	1	no	—
595	C₂²	—	2	1	no	—
596	C₂²	—	10	2	no	—
597	C₂²	—	10	2	no	—
598	C₂²	—	10	2	no	—
599	C₂²	#4150	1	2	yes	—
600	C₂²	C₂⁴×D₅	1	1	yes	characteristic
601	C₄	—	2	1	no	—
602	C₄	—	2	1	no	—
603	C₄	—	2	1	no	—
604	C₄	—	2	1	no	—
605	C₄	—	2	1	no	—
606	C₄	—	2	1	no	—
607	C₄	—	2	1	no	—
608	C₄	—	2	1	no	—
609	C₄	—	2	1	no	—
610	C₄	—	2	1	no	—
611	C₄	—	2	1	no	—
612	C₄	—	5	4	no	—
613	C₄	—	10	2	no	—
614	C₄	—	10	2	no	—
615	C₄	—	10	2	no	—
616	C₄	—	10	2	no	—
617	C₄	—	10	2	no	—
618	C₄	—	10	2	no	—
619	C₄	D₅×#41	1	2	yes	—
620	C₂	—	2	2	no	—
621	C₂	—	4	1	no	—
622	C₂	—	4	1	no	—
623	C₂	—	20	2	no	—
624	C₂	C₂×D₅×#41	1	1	yes	characteristic
625	C₂	C₂×#4150	1	1	yes	characteristic
626	C₂	#66283	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅
commutator, socle, cosocle	C₂²×C₅	C₂⁵
Fitting	C₅×#529	C₂
hypercenter	#529	D₅
hypocenter	C₅	#3516
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
1. C₅×#529	C₂	semidirect
2. #66042	C₂	semidirect
3. #66036	C₂	semidirect
4. #66030	C₂	semidirect
5. #66003	C₂	semidirect
6. #65983	C₂	semidirect
7. #65983	C₂	semidirect
8. #65970	C₂	semidirect
9. #65935	C₂	semidirect
10. #65918	C₂	semidirect
11. #65901	C₂	semidirect
12. #65899	C₂	semidirect
13. #65886	C₂	semidirect
14. #65886	C₂	semidirect
15. #65877	C₂	semidirect
16. #65875	C₂	semidirect
17. D₄×Dic₁₀	C₂	semidirect
18. #65868	C₂	semidirect
19. #65857	C₂	semidirect
20. #65852	C₂	semidirect
21. #65850	C₂	semidirect
22. #65813	C₂	semidirect
23. C₂×C₄×Dic₁₀	C₂	semidirect
245. #529	D₅	semidirect
587. C₅	#3516	semidirect

Maximal subgroups

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

subgroup	index
C₅×#529	2
#66042	2
#66036	2
#66030	2
#66003	2
#65983	2
#65970	2
#65935	2
#65918	2
#65901	2
#65899	2
#65886	2
#65877	2
#65875	2
D₄×Dic₁₀	2
#65868	2
#65857	2
#65852	2
#65850	2
#65813	2
C₂×C₄×Dic₁₀	2
#3516	5