Subgroups — #10618062

Order 640.

1152 conjugacy classes of subgroups.

The subgroup lattice has 678 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	#66043	C₂	1	2	yes	maximal, complemented
3	#66039	C₂	1	2	yes	maximal, complemented
4	#66026	C₂	1	2	yes	maximal, complemented
5	#66012	C₂	1	2	yes	maximal, complemented
6	#65990	C₂	1	2	yes	maximal, complemented
7	D₅×#123	C₂	1	2	yes	maximal, complemented
8	#65971	C₂	1	2	yes	maximal, complemented
9	#65944	C₂	1	2	yes	maximal, complemented
10	#65919	C₂	1	1	yes	maximal, characteristic, complemented
11	#65913	C₂	1	1	yes	maximal, characteristic, complemented
12	#65899	C₂	1	1	yes	maximal, characteristic, complemented
13	#65889	C₂	1	1	yes	maximal, characteristic, complemented
14	#65884	C₂	1	1	yes	maximal, characteristic, complemented
15	#65884	C₂	1	1	yes	maximal, characteristic, complemented
16	D₄×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
17	#65875	C₂	1	1	yes	maximal, characteristic, complemented
18	#65869	C₂	1	1	yes	maximal, characteristic, complemented
19	#65868	C₂	1	1	yes	maximal, characteristic, complemented
20	#65857	C₂	1	1	yes	maximal, characteristic, complemented
21	#65855	C₂	1	1	yes	maximal, characteristic, complemented
22	#65813	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₄×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#711	C₂²	1	2	yes	complemented
25	C₂×D₄×D₅	C₂²	1	2	yes	—
26	C₂×#709	C₂²	1	1	yes	characteristic
27	C₂²×D₂₀	C₂²	1	1	yes	characteristic
28	C₂²×D₂₀	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₅	C₂²	1	2	yes	complemented
30	C₅×#126	C₂²	1	1	yes	characteristic, complemented
31	C₅×#126	C₂²	1	1	yes	characteristic, complemented
32	C₅×#125	C₂²	1	1	yes	characteristic, complemented
33	C₅×#124	C₂²	1	1	yes	characteristic, complemented
34	C₅×#123	C₂²	1	1	yes	characteristic
35	C₅×#123	C₂²	1	1	yes	characteristic, complemented
36	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, 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	C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
41	C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
42	C₅×#117	C₂²	1	1	yes	characteristic, complemented
43	C₅×#117	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
45	#4093	C₂²	1	2	yes	complemented
46	#4092	C₂²	1	2	yes	complemented
47	#4085	C₂²	1	2	yes	complemented
48	#4083	C₂²	1	2	yes	complemented
49	#4083	C₂²	1	2	yes	complemented
50	#4081	C₂²	1	2	yes	—
51	#4076	C₂²	1	1	yes	characteristic
52	#4076	C₂²	1	1	yes	characteristic
53	#4076	C₂²	1	1	yes	characteristic, complemented
54	#4076	C₂²	1	1	yes	characteristic, complemented
55	#4075	C₂²	1	2	yes	complemented
56	C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
57	C₂×#685	C₂²	1	2	yes	complemented
58	#4072	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₄⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₄⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
61	#4070	C₂²	1	1	yes	characteristic, complemented
62	#4070	C₂²	1	1	yes	characteristic, complemented
63	#4044	C₂²	1	2	yes	complemented
64	#4044	C₂²	1	2	yes	complemented
65	#4043	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	2	yes	—
70	#4040	C₂²	1	2	yes	complemented
71	#4040	C₂²	1	2	yes	complemented
72	#4040	C₂²	1	2	yes	complemented
73	#4040	C₂²	1	2	yes	complemented
74	#4040	C₂²	1	2	yes	complemented
75	#4040	C₂²	1	2	yes	complemented
76	#4039	C₂²	1	2	yes	complemented
77	#4039	C₂²	1	2	yes	complemented
78	#4039	C₂²	1	2	yes	complemented
79	#4038	C₂²	1	2	yes	complemented
80	D₅×C₄⋊C₄	C₂²	1	2	yes	complemented
81	D₅×C₄⋊C₄	C₂²	1	2	yes	complemented
82	#4035	C₂²	1	2	yes	complemented
83	#4032	C₂²	1	2	yes	complemented
84	#4032	C₂²	1	2	yes	complemented
85	#4031	C₂²	1	2	yes	complemented
86	#4030	C₂²	1	2	yes	complemented
87	#4030	C₂²	1	2	yes	complemented
88	#4030	C₂²	1	2	yes	complemented
89	#4030	C₂²	1	2	yes	complemented
90	#4029	C₂²	1	2	yes	complemented
91	#4029	C₂²	1	2	yes	complemented
92	#4028	C₂²	1	2	yes	—
93	#4028	C₂²	1	2	yes	—
94	#4027	C₂²	1	2	yes	complemented
95	#4027	C₂²	1	2	yes	complemented
96	#4027	C₂²	1	2	yes	complemented
97	D₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
98	D₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
99	D₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
100	D₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
101	#4025	C₂²	1	2	yes	complemented
102	#4023	C₂²	1	2	yes	complemented
103	#4022	C₂²	1	2	yes	complemented
104	#4021	C₂²	1	1	yes	characteristic, complemented
105	#4021	C₂²	1	1	yes	characteristic, complemented
106	#4020	C₂²	1	1	yes	characteristic
107	C₄×D₂₀	C₂²	1	1	yes	characteristic
108	C₄×D₂₀	C₂²	1	1	yes	characteristic
109	C₄×D₂₀	C₂²	1	1	yes	characteristic
110	C₄×D₂₀	C₂²	1	1	yes	characteristic
111	C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
112	C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
113	C₄×D₂₀	C₂²	1	2	yes	complemented
114	C₄×D₂₀	C₂²	1	2	yes	complemented
115	C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
116	C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
117	#4018	C₂²	1	2	yes	complemented
118	#4016	C₂²	1	1	yes	characteristic, complemented
119	#4016	C₂²	1	1	yes	characteristic, 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	#3513	—	5	1	no	maximal, Sylow
124	C₂³×D₅	C₂³	1	2	yes	—
125	C₂³×D₅	C₂³	1	2	yes	—
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	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	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
134	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
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	C₂²×Dic₅	C₂³	1	2	yes	—
141	C₂²×Dic₅	C₂³	1	2	yes	—
142	#711	—	4	4	no	—
143	D₄×D₅	—	4	4	no	—
144	#709	—	2	4	no	—
145	C₂×D₂₀	—	2	4	no	—
146	C₂×D₂₀	—	2	4	no	—
147	C₂×D₂₀	C₂³	1	1	yes	characteristic
148	C₂×D₂₀	C₂³	1	1	yes	characteristic
149	C₂×D₂₀	C₂³	1	2	yes	—
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	1	yes	characteristic
154	C₂×C₄×D₅	—	4	4	no	—
155	C₂×C₄×D₅	C₂³	1	2	yes	—
156	C₂×C₄×D₅	C₂³	1	2	yes	—
157	C₂×C₄×D₅	C₂³	1	2	yes	—
158	C₂×C₄×D₅	C₂³	1	2	yes	—
159	C₂×C₄×D₅	C₂³	1	2	yes	—
160	C₂×C₄×D₅	C₂³	1	2	yes	—
161	C₂×C₄×D₅	C₂³	1	2	yes	—
162	C₂×C₄×D₅	C₂³	1	2	yes	—
163	C₂×C₄×D₅	C₂³	1	2	yes	—
164	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
165	C₂×Dic₁₀	C₂³	1	2	yes	—
166	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
167	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
168	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
169	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
170	C₅×C₄⋊C₄	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	1	yes	characteristic
174	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
175	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
177	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
178	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
179	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
180	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
181	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
182	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
183	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
184	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
185	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
186	C₄²×C₅	C₂³	1	1	yes	characteristic
187	C₄²×C₅	C₂³	1	1	yes	characteristic
188	C₄²×C₅	C₂³	1	1	yes	characteristic
189	C₄²×C₅	C₂³	1	1	yes	characteristic
190	C₄²×C₅	C₂³	1	1	yes	characteristic
191	C₄²×C₅	C₂³	1	1	yes	characteristic
192	C₂²⋊Dic₅	C₂³	1	2	yes	—
193	C₂²⋊Dic₅	C₂³	1	2	yes	—
194	C₂²⋊Dic₅	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	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	#685	C₂³	1	2	yes	—
206	#685	C₂³	1	2	yes	—
207	#685	C₂³	1	2	yes	—
208	#685	C₂³	1	2	yes	—
209	#685	C₂³	1	2	yes	—
210	#685	C₂³	1	2	yes	—
211	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
212	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
213	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
214	C₄⋊Dic₅	C₂³	1	2	yes	—
215	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
216	C₄⋊Dic₅	C₂³	1	2	yes	—
217	C₄⋊Dic₅	C₂³	1	2	yes	—
218	#683	C₂³	1	2	yes	—
219	#683	C₂³	1	2	yes	—
220	#683	C₂³	1	2	yes	—
221	#683	C₂³	1	2	yes	—
222	#683	C₂³	1	2	yes	—
223	#683	C₂³	1	2	yes	—
224	#683	C₂³	1	2	yes	—
225	#683	C₂³	1	2	yes	—
226	C₄×Dic₅	C₂³	1	2	yes	—
227	C₄×Dic₅	C₂³	1	2	yes	—
228	C₄×Dic₅	C₂³	1	2	yes	—
229	#559	—	5	1	no	—
230	#554	—	5	1	no	—
231	#553	—	5	2	no	—
232	#553	—	5	1	no	—
233	#552	—	5	1	no	—
234	#551	—	5	2	no	—
235	#551	—	5	2	no	—
236	#547	—	5	1	no	—
237	#546	—	5	2	no	—
238	#546	—	5	1	no	—
239	#546	—	5	1	no	—
240	D₄²	—	5	1	no	—
241	#542	—	5	1	no	—
242	#540	—	5	1	no	—
243	#539	—	5	2	no	—
244	#538	—	5	2	no	—
245	#529	—	5	1	no	—
246	#529	D₅	1	1	yes	characteristic, complemented
247	#525	—	5	2	no	—
248	C₂×#123	—	5	2	no	—
249	#520	—	5	1	no	—
250	#518	—	5	1	no	—
251	C₂×C₄×D₄	—	5	1	no	—
252	C₂³×C₅	C₂⁴	1	1	yes	characteristic
253	C₂³×C₅	C₂⁴	1	1	yes	characteristic
254	C₂³×C₅	C₂⁴	1	1	yes	characteristic
255	C₂²×D₅	—	2	4	no	—
256	C₂²×D₅	—	2	4	no	—
257	C₂²×D₅	—	2	4	no	—
258	C₂²×D₅	—	4	2	no	—
259	C₂²×D₅	—	4	2	no	—
260	C₂²×D₅	—	4	2	no	—
261	C₂²×D₅	C₂⁴	1	2	yes	—
262	C₂²×D₅	C₂⁴	1	2	yes	—
263	C₂²×D₅	C₂⁴	1	2	yes	—
264	C₅×Q₈	—	4	1	no	—
265	C₅×D₄	—	2	2	no	—
266	C₅×D₄	—	2	2	no	—
267	C₅×D₄	—	4	1	no	—
268	C₂×C₄×C₅	—	2	2	no	—
269	C₂×C₄×C₅	—	2	2	no	—
270	C₂×C₄×C₅	—	2	2	no	—
271	C₂×C₄×C₅	—	2	2	no	—
272	C₂×C₄×C₅	—	4	1	no	—
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	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
277	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
278	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
279	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
280	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
281	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
282	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
283	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
284	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
285	C₂²⋊D₅	—	2	4	no	—
286	C₂²⋊D₅	—	2	4	no	—
287	C₂²⋊D₅	—	4	2	no	—
288	C₂²⋊D₅	—	4	2	no	—
289	C₂²⋊D₅	—	4	2	no	—
290	C₂×Dic₅	—	2	4	no	—
291	C₂×Dic₅	—	4	2	no	—
292	C₂×Dic₅	C₂⁴	1	2	yes	—
293	C₂×Dic₅	C₂⁴	1	2	yes	—
294	C₂×Dic₅	C₂⁴	1	2	yes	—
295	C₂×Dic₅	C₂⁴	1	2	yes	—
296	C₂×Dic₅	C₂⁴	1	2	yes	—
297	D₂₀	—	2	4	no	—
298	D₂₀	—	2	4	no	—
299	D₂₀	—	2	2	no	—
300	D₂₀	—	2	2	no	—
301	D₂₀	—	4	2	no	—
302	D₂₀	—	4	2	no	—
303	D₂₀	#41	1	4	yes	complemented
304	C₄×D₅	—	2	4	no	—
305	C₄×D₅	—	4	2	no	—
306	C₄×D₅	—	4	2	no	—
307	C₄×D₅	—	4	2	no	—
308	C₄×D₅	—	4	2	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	Dic₁₀	—	2	2	no	—
314	Dic₁₀	—	4	2	no	—
315	C₂×#41	—	5	2	no	—
316	C₂×#41	—	5	1	no	—
317	C₂²×D₄	—	5	2	no	—
318	C₂²×D₄	—	5	1	no	—
319	C₂²×D₄	—	5	1	no	—
320	C₂³×C₄	—	5	2	no	—
321	C₄⋊Q₈	—	5	1	no	—
322	#127	—	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	1	yes	characteristic, complemented
328	#126	C₂×D₅	1	1	yes	characteristic, complemented
329	#125	—	5	2	no	—
330	#125	—	5	1	no	—
331	#125	—	5	1	no	—
332	#125	C₂×D₅	1	1	yes	characteristic, complemented
333	#124	—	5	2	no	—
334	#124	—	5	2	no	—
335	#124	—	5	1	no	—
336	#124	—	5	1	no	—
337	#124	C₂×D₅	1	1	yes	characteristic, complemented
338	#123	—	5	2	no	—
339	#123	—	5	2	no	—
340	#123	—	5	2	no	—
341	#123	—	5	2	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	2	no	—
350	#123	C₂×D₅	1	1	yes	characteristic
351	#123	C₂×D₅	1	1	yes	characteristic, complemented
352	C₂²⋊Q₈	—	5	2	no	—
353	C₂²⋊Q₈	—	5	1	no	—
354	C₂²⋊Q₈	—	5	1	no	—
355	C₂²⋊Q₈	—	5	2	no	—
356	C₂²⋊Q₈	—	5	2	no	—
357	C₂²⋊Q₈	—	5	2	no	—
358	C₂²⋊Q₈	—	5	2	no	—
359	C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
360	#121	—	5	2	no	—
361	#121	—	5	1	no	—
362	#121	—	5	1	no	—
363	#121	—	5	1	no	—
364	#121	—	5	1	no	—
365	#121	—	5	2	no	—
366	#121	—	5	2	no	—
367	#121	—	5	2	no	—
368	#121	—	5	2	no	—
369	#121	—	5	2	no	—
370	#121	C₂×D₅	1	1	yes	characteristic
371	#120	—	5	2	no	—
372	#120	—	5	2	no	—
373	#120	—	5	2	no	—
374	#120	—	5	2	no	—
375	C₄×Q₈	—	5	1	no	—
376	C₄×Q₈	—	5	1	no	—
377	C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
378	C₄×D₄	—	5	2	no	—
379	C₄×D₄	—	5	2	no	—
380	C₄×D₄	—	5	2	no	—
381	C₄×D₄	—	5	2	no	—
382	C₄×D₄	—	5	2	no	—
383	C₄×D₄	—	5	2	no	—
384	C₄×D₄	—	5	2	no	—
385	C₄×D₄	—	5	1	no	—
386	C₄×D₄	—	5	2	no	—
387	C₄×D₄	—	5	1	no	—
388	C₄×D₄	—	5	1	no	—
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	1	no	—
394	C₄×D₄	—	5	1	no	—
395	C₄×D₄	C₂×D₅	1	1	yes	characteristic
396	C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
397	C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
398	#117	—	5	1	no	—
399	#117	—	5	2	no	—
400	#117	—	5	2	no	—
401	#117	—	5	2	no	—
402	#117	C₂×D₅	1	1	yes	characteristic, complemented
403	#117	C₂×D₅	1	1	yes	characteristic, complemented
404	C₂×C₄⋊C₄	—	5	1	no	—
405	C₂×C₄⋊C₄	—	5	1	no	—
406	C₂×C₄⋊C₄	—	5	2	no	—
407	C₂×C₄⋊C₄	—	5	2	no	—
408	C₂×C₂²⋊C₄	—	5	2	no	—
409	C₂×C₂²⋊C₄	—	5	2	no	—
410	C₂×C₂²⋊C₄	—	5	2	no	—
411	C₂×C₂²⋊C₄	—	5	2	no	—
412	C₂×C₂²⋊C₄	—	5	2	no	—
413	C₂×C₄²	C₂×D₅	1	1	yes	characteristic, complemented
414	C₂²×C₅	—	2	1	no	—
415	C₂²×C₅	—	2	1	no	—
416	C₂²×C₅	—	2	1	no	—
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	H(5,𝔽₂)	1	2	yes	—
423	C₂²×C₅	C₂⁵	1	1	yes	characteristic
424	C₂×D₅	—	2	2	no	—
425	C₂×D₅	—	2	2	no	—
426	C₂×D₅	—	2	2	no	—
427	C₂×D₅	—	2	2	no	—
428	C₂×D₅	—	2	2	no	—
429	C₂×D₅	—	2	2	no	—
430	C₂×D₅	—	2	2	no	—
431	C₂×D₅	—	2	2	no	—
432	C₂×D₅	—	4	8	no	—
433	C₂×D₅	—	8	4	no	—
434	C₂×D₅	C₂×#41	1	4	yes	—
435	C₄×C₅	—	2	1	no	—
436	C₄×C₅	—	2	1	no	—
437	C₄×C₅	—	2	1	no	—
438	C₄×C₅	—	2	1	no	—
439	C₄×C₅	—	2	1	no	—
440	C₄×C₅	—	2	1	no	—
441	C₄×C₅	—	2	1	no	—
442	C₄×C₅	—	2	1	no	—
443	C₄×C₅	—	2	1	no	—
444	C₄×C₅	—	2	1	no	—
445	C₄×C₅	—	2	1	no	—
446	C₄×C₅	C₂×#41	1	2	yes	—
447	Dic₅	—	2	2	no	—
448	Dic₅	—	2	2	no	—
449	Dic₅	—	2	2	no	—
450	Dic₅	—	2	2	no	—
451	Dic₅	—	2	2	no	—
452	C₂⁴	—	5	2	no	—
453	C₂⁴	—	5	2	no	—
454	#41	—	10	4	no	—
455	#41	—	20	4	no	—
456	C₂×Q₈	—	5	1	no	—
457	C₂×Q₈	—	5	2	no	—
458	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
459	C₂×D₄	—	5	2	no	—
460	C₂×D₄	—	5	2	no	—
461	C₂×D₄	—	5	2	no	—
462	C₂×D₄	—	5	2	no	—
463	C₂×D₄	—	5	2	no	—
464	C₂×D₄	—	5	1	no	—
465	C₂×D₄	—	5	2	no	—
466	C₂×D₄	—	5	2	no	—
467	C₂×D₄	—	5	1	no	—
468	C₂×D₄	—	5	1	no	—
469	C₂×D₄	—	5	2	no	—
470	C₂×D₄	—	5	2	no	—
471	C₂×D₄	—	10	4	no	—
472	C₂×D₄	—	10	4	no	—
473	C₂×D₄	—	20	4	no	—
474	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
475	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
476	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
477	C₂²×C₄	—	5	2	no	—
478	C₂²×C₄	—	5	2	no	—
479	C₂²×C₄	—	5	2	no	—
480	C₂²×C₄	—	5	2	no	—
481	C₂²×C₄	—	5	2	no	—
482	C₂²×C₄	—	5	2	no	—
483	C₂²×C₄	—	5	2	no	—
484	C₂²×C₄	—	5	2	no	—
485	C₂²×C₄	—	5	2	no	—
486	C₂²×C₄	—	5	2	no	—
487	C₂²×C₄	—	5	2	no	—
488	C₂²×C₄	—	20	4	no	—
489	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
490	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
491	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
492	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
493	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
494	C₄⋊C₄	—	5	1	no	—
495	C₄⋊C₄	—	5	2	no	—
496	C₄⋊C₄	—	5	2	no	—
497	C₄⋊C₄	—	5	1	no	—
498	C₄⋊C₄	—	5	2	no	—
499	C₄⋊C₄	—	5	1	no	—
500	C₄⋊C₄	—	5	2	no	—
501	C₄⋊C₄	—	5	2	no	—
502	C₄⋊C₄	—	5	2	no	—
503	C₄⋊C₄	—	5	2	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	C₂²×D₅	1	1	yes	characteristic
510	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
511	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
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	1	yes	characteristic
516	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
517	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
518	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
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	2	no	—
526	C₂²⋊C₄	—	5	2	no	—
527	C₂²⋊C₄	—	5	2	no	—
528	C₂²⋊C₄	—	5	2	no	—
529	C₂²⋊C₄	—	5	2	no	—
530	C₂²⋊C₄	—	5	2	no	—
531	C₂²⋊C₄	—	5	2	no	—
532	C₂²⋊C₄	—	5	2	no	—
533	C₂²⋊C₄	—	5	2	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	C₂²×D₅	1	1	yes	characteristic
539	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
540	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
541	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
542	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
543	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
544	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
545	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
546	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
547	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
548	C₄²	—	5	2	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	1	yes	characteristic
555	C₄²	C₂²×D₅	1	1	yes	characteristic
556	C₄²	C₂²×D₅	1	1	yes	characteristic
557	C₂×C₅	—	2	2	no	—
558	C₂×C₅	—	4	1	no	—
559	C₂×C₅	—	4	1	no	—
560	C₂×C₅	C₂²×#41	1	1	yes	characteristic
561	C₂×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
562	C₂×C₅	#585	1	1	yes	characteristic
563	D₅	—	2	4	no	—
564	D₅	—	4	2	no	—
565	D₅	—	4	2	no	—
566	C₂³	—	5	2	no	—
567	C₂³	—	5	2	no	—
568	C₂³	—	5	2	no	—
569	C₂³	—	10	4	no	—
570	C₂³	—	10	4	no	—
571	C₂³	—	10	4	no	—
572	C₂³	—	20	2	no	—
573	C₂³	—	20	2	no	—
574	C₂³	—	20	2	no	—
575	C₂³	C₂³×D₅	1	1	yes	characteristic
576	C₂³	C₂³×D₅	1	1	yes	characteristic
577	C₂³	C₂³×D₅	1	1	yes	characteristic
578	Q₈	—	4	1	no	—
579	Q₈	—	10	2	no	—
580	Q₈	—	20	2	no	—
581	D₄	—	2	2	no	—
582	D₄	—	2	2	no	—
583	D₄	—	4	1	no	—
584	D₄	—	5	4	no	—
585	D₄	—	10	4	no	—
586	D₄	—	10	4	no	—
587	D₄	—	10	4	no	—
588	D₄	—	10	4	no	—
589	D₄	—	10	2	no	—
590	D₄	—	10	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	—	2	2	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	5	2	no	—
602	C₂×C₄	—	5	2	no	—
603	C₂×C₄	—	5	2	no	—
604	C₂×C₄	—	5	2	no	—
605	C₂×C₄	—	5	2	no	—
606	C₂×C₄	—	10	4	no	—
607	C₂×C₄	—	10	4	no	—
608	C₂×C₄	—	20	2	no	—
609	C₂×C₄	—	20	2	no	—
610	C₂×C₄	—	20	2	no	—
611	C₂×C₄	—	20	2	no	—
612	C₂×C₄	—	20	2	no	—
613	C₂×C₄	—	20	2	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	1	yes	characteristic
624	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
625	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
626	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
627	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
628	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
629	C₅	#3513	1	1	yes	characteristic, complemented, Sylow
630	C₂²	—	2	1	no	—
631	C₂²	—	2	1	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	1	no	—
634	C₂²	—	2	1	no	—
635	C₂²	—	2	1	no	—
636	C₂²	—	2	1	no	—
637	C₂²	—	2	1	no	—
638	C₂²	—	5	4	no	—
639	C₂²	—	10	2	no	—
640	C₂²	—	10	2	no	—
641	C₂²	—	10	2	no	—
642	C₂²	—	10	2	no	—
643	C₂²	—	10	2	no	—
644	C₂²	—	10	2	no	—
645	C₂²	—	10	2	no	—
646	C₂²	—	10	2	no	—
647	C₂²	—	20	8	no	—
648	C₂²	—	40	4	no	—
649	C₂²	#4149	1	2	yes	—
650	C₂²	C₂⁴×D₅	1	1	yes	characteristic
651	C₄	—	2	1	no	—
652	C₄	—	2	1	no	—
653	C₄	—	2	1	no	—
654	C₄	—	2	1	no	—
655	C₄	—	2	1	no	—
656	C₄	—	2	1	no	—
657	C₄	—	2	1	no	—
658	C₄	—	2	1	no	—
659	C₄	—	2	1	no	—
660	C₄	—	2	1	no	—
661	C₄	—	2	1	no	—
662	C₄	—	10	2	no	—
663	C₄	—	10	2	no	—
664	C₄	—	10	2	no	—
665	C₄	—	10	2	no	—
666	C₄	—	10	2	no	—
667	C₄	D₅×#41	1	2	yes	—
668	C₂	—	2	2	no	—
669	C₂	—	4	1	no	—
670	C₂	—	4	1	no	—
671	C₂	—	10	4	no	—
672	C₂	—	20	2	no	—
673	C₂	—	20	2	no	—
674	C₂	C₂×D₅×#41	1	1	yes	characteristic
675	C₂	C₂×#4149	1	1	yes	characteristic
676	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	#3513
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. #66043	C₂	semidirect
3. #66039	C₂	semidirect
4. #66026	C₂	semidirect
5. #66012	C₂	semidirect
6. #65990	C₂	semidirect
7. D₅×#123	C₂	semidirect
8. #65971	C₂	semidirect
9. #65944	C₂	semidirect
10. #65919	C₂	semidirect
11. #65913	C₂	semidirect
12. #65899	C₂	semidirect
13. #65889	C₂	semidirect
14. #65884	C₂	semidirect
15. #65884	C₂	semidirect
16. D₄×D₂₀	C₂	semidirect
17. #65875	C₂	semidirect
18. #65869	C₂	semidirect
19. #65868	C₂	semidirect
20. #65857	C₂	semidirect
21. #65855	C₂	semidirect
22. #65813	C₂	semidirect
23. C₂×C₄×D₂₀	C₂	semidirect
24. C₂×#711	C₂²	semidirect
29. C₂²×C₄×D₅	C₂²	semidirect
30. C₅×#126	C₂²	semidirect
31. C₅×#126	C₂²	semidirect
32. C₅×#125	C₂²	semidirect
33. C₅×#124	C₂²	semidirect
35. C₅×#123	C₂²	semidirect
36. C₅×C₂²⋊Q₈	C₂²	semidirect
38. C₄×C₅×Q₈	C₂²	semidirect
40. C₄×C₅×D₄	C₂²	semidirect
41. C₄×C₅×D₄	C₂²	semidirect
42. C₅×#117	C₂²	semidirect
43. C₅×#117	C₂²	semidirect
44. C₂×C₄²×C₅	C₂²	semidirect
45. #4093	C₂²	semidirect
46. #4092	C₂²	semidirect
47. #4085	C₂²	semidirect
48. #4083	C₂²	semidirect
49. #4083	C₂²	semidirect
53. #4076	C₂²	semidirect
54. #4076	C₂²	semidirect
55. #4075	C₂²	semidirect
56. C₄×C₂²⋊D₅	C₂²	semidirect
57. C₂×#685	C₂²	semidirect
58. #4072	C₂²	semidirect
59. C₂×C₄⋊Dic₅	C₂²	semidirect
60. C₂×C₄⋊Dic₅	C₂²	semidirect
61. #4070	C₂²	semidirect
62. #4070	C₂²	semidirect
63. #4044	C₂²	semidirect
64. #4044	C₂²	semidirect
65. #4043	C₂²	semidirect
66. #4042	C₂²	semidirect
67. #4042	C₂²	semidirect
68. #4042	C₂²	semidirect
70. #4040	C₂²	semidirect
71. #4040	C₂²	semidirect
72. #4040	C₂²	semidirect
73. #4040	C₂²	semidirect
74. #4040	C₂²	semidirect
75. #4040	C₂²	semidirect
76. #4039	C₂²	semidirect
77. #4039	C₂²	semidirect
78. #4039	C₂²	semidirect
79. #4038	C₂²	semidirect
80. D₅×C₄⋊C₄	C₂²	semidirect
81. D₅×C₄⋊C₄	C₂²	semidirect
82. #4035	C₂²	semidirect
83. #4032	C₂²	semidirect
84. #4032	C₂²	semidirect
85. #4031	C₂²	semidirect
86. #4030	C₂²	semidirect
87. #4030	C₂²	semidirect
88. #4030	C₂²	semidirect
89. #4030	C₂²	semidirect
90. #4029	C₂²	semidirect
91. #4029	C₂²	semidirect
94. #4027	C₂²	semidirect
95. #4027	C₂²	semidirect
96. #4027	C₂²	semidirect
97. D₅×C₂²⋊C₄	C₂²	semidirect
98. D₅×C₂²⋊C₄	C₂²	semidirect
99. D₅×C₂²⋊C₄	C₂²	semidirect
100. D₅×C₂²⋊C₄	C₂²	semidirect
101. #4025	C₂²	semidirect
102. #4023	C₂²	semidirect
103. #4022	C₂²	semidirect
104. #4021	C₂²	semidirect
105. #4021	C₂²	semidirect
111. C₄×D₂₀	C₂²	semidirect
112. C₄×D₂₀	C₂²	semidirect
113. C₄×D₂₀	C₂²	semidirect
114. C₄×D₂₀	C₂²	semidirect
115. C₄×D₂₀	C₂²	semidirect
116. C₄×D₂₀	C₂²	semidirect
117. #4018	C₂²	semidirect
118. #4016	C₂²	semidirect
119. #4016	C₂²	semidirect
120. #4015	C₂²	semidirect
121. C₄×Dic₁₀	C₂²	semidirect
122. C₄×Dic₁₀	C₂²	semidirect
246. #529	D₅	semidirect
303. D₂₀	#41	semidirect
327. #126	C₂×D₅	semidirect
328. #126	C₂×D₅	semidirect
332. #125	C₂×D₅	semidirect
337. #124	C₂×D₅	semidirect
351. #123	C₂×D₅	semidirect
359. C₂²⋊Q₈	C₂×D₅	semidirect
377. C₄×Q₈	C₂×D₅	semidirect
396. C₄×D₄	C₂×D₅	semidirect
397. C₄×D₄	C₂×D₅	semidirect
402. #117	C₂×D₅	semidirect
403. #117	C₂×D₅	semidirect
413. C₂×C₄²	C₂×D₅	semidirect
629. C₅	#3513	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
#66043	2
#66039	2
#66026	2
#66012	2
#65990	2
D₅×#123	2
#65971	2
#65944	2
#65919	2
#65913	2
#65899	2
#65889	2
#65884	2
D₄×D₂₀	2
#65875	2
#65869	2
#65868	2
#65857	2
#65855	2
#65813	2
C₂×C₄×D₂₀	2
#3513	5