Subgroups — #10618452

Order 640.

1022 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	#66063	C₂	1	1	yes	maximal, characteristic, complemented
3	#66062	C₂	1	1	yes	maximal, characteristic, complemented
4	#66042	C₂	1	2	yes	maximal, complemented
5	#66042	C₂	1	2	yes	maximal, complemented
6	#66014	C₂	1	1	yes	maximal, characteristic, complemented
7	#66013	C₂	1	2	yes	maximal, complemented
8	#66009	C₂	1	1	yes	maximal, characteristic, complemented
9	#66005	C₂	1	2	yes	maximal, complemented
10	#65993	C₂	1	2	yes	maximal, complemented
11	#65984	C₂	1	2	yes	maximal, complemented
12	#65973	C₂	1	2	yes	maximal, complemented
13	#65970	C₂	1	2	yes	maximal, complemented
14	D₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
15	#65959	C₂	1	1	yes	maximal, characteristic, complemented
16	#65940	C₂	1	1	yes	maximal, characteristic
17	#65937	C₂	1	1	yes	maximal, characteristic, complemented
18	#65912	C₂	1	1	yes	maximal, characteristic, complemented
19	#65906	C₂	1	1	yes	maximal, characteristic, complemented
20	#65891	C₂	1	1	yes	maximal, characteristic, complemented
21	#65880	C₂	1	1	yes	maximal, characteristic, complemented
22	D₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
23	#65852	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×Q₈×D₅	C₂²	1	1	yes	characteristic
25	C₂×#711	C₂²	1	1	yes	characteristic
26	C₂²×C₄×D₅	C₂²	1	1	yes	characteristic
27	C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
28	C₅×#126	C₂²	1	2	yes	complemented
29	C₅×#124	C₂²	1	2	yes	—
30	C₅×#124	C₂²	1	1	yes	characteristic, complemented
31	C₅×#123	C₂²	1	2	yes	—
32	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
33	C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
34	C₅×#121	C₂²	1	1	yes	characteristic
35	C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
36	C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
37	C₅×#117	C₂²	1	1	yes	characteristic
38	#4092	C₂²	1	2	yes	—
39	#4092	C₂²	1	2	yes	—
40	#4092	C₂²	1	1	yes	characteristic
41	Q₈×Dic₅	C₂²	1	2	yes	complemented
42	Q₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
43	#4090	C₂²	1	2	yes	complemented
44	#4090	C₂²	1	1	yes	characteristic, complemented
45	#4084	C₂²	1	1	yes	characteristic
46	#4083	C₂²	1	2	yes	—
47	#4082	C₂²	1	2	yes	—
48	#4082	C₂²	1	1	yes	characteristic, complemented
49	#4081	C₂²	1	2	yes	—
50	D₄×Dic₅	C₂²	1	2	yes	—
51	D₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
52	C₄×C₂²⋊D₅	C₂²	1	2	yes	—
53	C₄×C₂²⋊D₅	C₂²	1	2	yes	—
54	#4072	C₂²	1	1	yes	characteristic
55	#4072	C₂²	1	2	yes	complemented
56	#4070	C₂²	1	1	yes	characteristic
57	#4070	C₂²	1	1	yes	characteristic
58	C₂×#683	C₂²	1	2	yes	complemented
59	#4043	C₂²	1	1	yes	characteristic
60	#4043	C₂²	1	1	yes	characteristic
61	#4042	C₂²	1	2	yes	—
62	#4042	C₂²	1	2	yes	—
63	#4042	C₂²	1	2	yes	—
64	#4038	C₂²	1	2	yes	—
65	#4038	C₂²	1	1	yes	characteristic
66	#4038	C₂²	1	1	yes	characteristic
67	#4038	C₂²	1	1	yes	characteristic
68	#4038	C₂²	1	2	yes	—
69	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
70	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
71	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
72	D₅×C₄⋊C₄	C₂²	1	2	yes	—
73	#4036	C₂²	1	2	yes	complemented
74	#4036	C₂²	1	1	yes	characteristic, complemented
75	#4036	C₂²	1	2	yes	complemented
76	#4035	C₂²	1	2	yes	complemented
77	#4035	C₂²	1	2	yes	complemented
78	#4035	C₂²	1	2	yes	complemented
79	#4035	C₂²	1	2	yes	complemented
80	#4035	C₂²	1	2	yes	complemented
81	#4034	C₂²	1	1	yes	characteristic, complemented
82	#4033	C₂²	1	1	yes	characteristic, complemented
83	#4033	C₂²	1	1	yes	characteristic, complemented
84	#4033	C₂²	1	2	yes	complemented
85	#4029	C₂²	1	2	yes	—
86	#4029	C₂²	1	2	yes	—
87	#4029	C₂²	1	2	yes	—
88	#4029	C₂²	1	2	yes	—
89	#4029	C₂²	1	2	yes	—
90	#4027	C₂²	1	2	yes	—
91	#4027	C₂²	1	2	yes	—
92	#4027	C₂²	1	2	yes	—
93	D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
94	D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
95	D₅×C₂²⋊C₄	C₂²	1	2	yes	—
96	#4025	C₂²	1	2	yes	—
97	#4025	C₂²	1	2	yes	—
98	#4025	C₂²	1	2	yes	—
99	#4025	C₂²	1	2	yes	—
100	#4025	C₂²	1	2	yes	complemented
101	#4025	C₂²	1	2	yes	complemented
102	#4025	C₂²	1	2	yes	complemented
103	#4024	C₂²	1	2	yes	—
104	#4024	C₂²	1	2	yes	complemented
105	#4024	C₂²	1	2	yes	complemented
106	#4024	C₂²	1	2	yes	complemented
107	#4023	C₂²	1	1	yes	characteristic
108	#4023	C₂²	1	1	yes	characteristic
109	#4023	C₂²	1	2	yes	complemented
110	#4023	C₂²	1	2	yes	complemented
111	#4018	C₂²	1	1	yes	characteristic
112	#4018	C₂²	1	1	yes	characteristic
113	#4018	C₂²	1	2	yes	—
114	#4018	C₂²	1	2	yes	—
115	C₄²×D₅	C₂²	1	1	yes	characteristic
116	C₄²×D₅	C₂²	1	1	yes	characteristic
117	#4016	C₂²	1	1	yes	characteristic, complemented
118	#4015	C₂²	1	1	yes	characteristic, complemented
119	C₄×Dic₁₀	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	2	yes	complemented
123	#3495	—	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×Q₈	C₂³	1	2	yes	—
127	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
128	C₂×C₅×D₄	C₂³	1	2	yes	—
129	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₅	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	1	yes	characteristic
134	C₂²×Dic₅	C₂³	1	2	yes	—
135	C₂²×Dic₅	C₂³	1	2	yes	—
136	Q₈×D₅	—	2	4	no	—
137	#711	—	2	4	no	—
138	C₂×C₄×D₅	—	2	4	no	—
139	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
140	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
141	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
142	C₂×C₄×D₅	C₂³	1	2	yes	—
143	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
145	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
147	C₂×C₄×D₅	C₂³	1	2	yes	—
148	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
149	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
150	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
151	C₂×Dic₁₀	C₂³	1	2	yes	—
152	C₂×Dic₁₀	C₂³	1	2	yes	—
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	2	yes	—
158	C₅×C₄⋊C₄	C₂³	1	2	yes	—
159	C₅×C₄⋊C₄	C₂³	1	2	yes	—
160	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
161	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
162	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
163	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
165	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
166	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
167	C₄²×C₅	C₂³	1	1	yes	characteristic
168	C₄²×C₅	C₂³	1	1	yes	characteristic
169	C₄²×C₅	C₂³	1	2	yes	—
170	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
171	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
172	C₂²⋊Dic₅	C₂³	1	2	yes	—
173	C₂²⋊Dic₅	C₂³	1	2	yes	—
174	C₂²⋊Dic₅	C₂³	1	2	yes	—
175	C₂²⋊Dic₅	C₂³	1	2	yes	—
176	C₂²⋊Dic₅	C₂³	1	2	yes	—
177	C₂²⋊Dic₅	C₂³	1	2	yes	—
178	#685	C₂³	1	1	yes	characteristic
179	#685	C₂³	1	2	yes	—
180	#685	C₂³	1	1	yes	characteristic
181	#685	C₂³	1	1	yes	characteristic
182	#685	C₂³	1	1	yes	characteristic
183	#685	C₂³	1	2	yes	—
184	#685	C₂³	1	2	yes	—
185	#685	C₂³	1	2	yes	—
186	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
187	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
188	C₄⋊Dic₅	C₂³	1	2	yes	—
189	C₄⋊Dic₅	C₂³	1	2	yes	—
190	C₄⋊Dic₅	C₂³	1	2	yes	—
191	C₄⋊Dic₅	C₂³	1	2	yes	—
192	C₄⋊Dic₅	C₂³	1	2	yes	—
193	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
194	C₄⋊Dic₅	C₂³	1	2	yes	—
195	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
196	#683	C₂³	1	1	yes	characteristic
197	#683	C₂³	1	2	yes	—
198	#683	C₂³	1	2	yes	—
199	#683	C₂³	1	2	yes	—
200	#683	C₂³	1	2	yes	—
201	#683	C₂³	1	2	yes	—
202	#683	C₂³	1	2	yes	—
203	#683	C₂³	1	1	yes	characteristic
204	#683	C₂³	1	1	yes	characteristic
205	#683	C₂³	1	1	yes	characteristic
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	C₄×Dic₅	C₂³	1	1	yes	characteristic
215	C₄×Dic₅	C₂³	1	2	yes	—
216	C₄×Dic₅	C₂³	1	2	yes	—
217	C₄×Dic₅	C₂³	1	2	yes	—
218	C₄×Dic₅	C₂³	1	2	yes	—
219	C₄×Dic₅	C₂³	1	1	yes	characteristic
220	C₄×Dic₅	C₂³	1	1	yes	characteristic
221	C₄×Dic₅	C₂³	1	1	yes	characteristic
222	C₄×Dic₅	C₂³	1	1	yes	characteristic
223	C₄×Dic₅	C₂³	1	1	yes	characteristic
224	C₄×Dic₅	C₂³	1	2	yes	—
225	C₄×Dic₅	C₂³	1	2	yes	—
226	#556	—	5	2	no	—
227	#554	—	5	2	no	—
228	#552	—	5	2	no	—
229	#552	—	5	2	no	—
230	#552	—	5	2	no	—
231	#552	—	5	2	no	—
232	#551	—	5	2	no	—
233	#551	—	5	2	no	—
234	#544	—	5	1	no	—
235	#542	—	5	1	no	—
236	#542	D₅	1	1	yes	characteristic, complemented
237	#541	—	5	1	no	—
238	#541	—	5	1	no	—
239	#536	—	5	1	no	—
240	#533	—	5	1	no	—
241	#533	—	5	1	no	—
242	#529	—	5	1	no	—
243	#529	—	5	1	no	—
244	#525	—	5	1	no	—
245	C₂×C₂²⋊Q₈	—	5	1	no	—
246	#520	—	5	1	no	—
247	#519	—	5	1	no	—
248	C₂×#117	—	5	1	no	—
249	C₂³×C₅	C₂⁴	1	1	yes	characteristic
250	C₂³×C₅	C₂⁴	1	2	yes	—
251	C₂²×D₅	—	2	2	no	—
252	C₂²×D₅	—	2	2	no	—
253	C₂²×D₅	—	4	1	no	—
254	C₂²×D₅	C₂⁴	1	1	yes	characteristic
255	C₂²×D₅	C₂⁴	1	1	yes	characteristic
256	C₅×Q₈	—	2	2	no	—
257	C₅×Q₈	—	4	2	no	—
258	C₅×D₄	—	2	2	no	—
259	C₅×D₄	—	4	2	no	—
260	C₂×C₄×C₅	—	2	2	no	—
261	C₂×C₄×C₅	—	4	2	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	2	yes	—
265	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
266	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
267	C₂×C₄×C₅	C₂⁴	1	2	yes	—
268	C₂×C₄×C₅	C₂⁴	1	2	yes	—
269	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
270	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
271	C₂²⋊D₅	—	2	4	no	—
272	C₂²⋊D₅	—	2	4	no	—
273	C₂×Dic₅	—	2	2	no	—
274	C₂×Dic₅	—	2	4	no	—
275	C₂×Dic₅	—	4	2	no	—
276	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
277	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
278	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
279	C₂×Dic₅	C₂⁴	1	2	yes	—
280	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
281	C₂×Dic₅	C₂⁴	1	2	yes	—
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	C₄×D₅	—	2	2	no	—
287	C₄×D₅	—	2	4	no	—
288	C₄×D₅	—	2	2	no	—
289	C₄×D₅	—	2	2	no	—
290	C₄×D₅	—	2	2	no	—
291	C₄×D₅	—	2	2	no	—
292	C₄×D₅	—	4	1	no	—
293	C₄×D₅	—	4	2	no	—
294	C₄×D₅	—	4	1	no	—
295	C₄×D₅	#41	1	4	yes	—
296	Dic₁₀	—	2	2	no	—
297	Dic₁₀	—	2	2	no	—
298	Dic₁₀	—	2	4	no	—
299	Dic₁₀	—	4	2	no	—
300	C₂×#41	—	5	1	no	—
301	C₂²×Q₈	—	5	1	no	—
302	C₂³×C₄	—	5	1	no	—
303	C₄⋊Q₈	—	5	1	no	—
304	C₄⋊Q₈	—	5	2	no	—
305	C₄⋊Q₈	—	5	1	no	—
306	C₄⋊Q₈	—	5	1	no	—
307	C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
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	—	5	2	no	—
314	#126	—	5	2	no	—
315	#126	C₂×D₅	1	2	yes	complemented
316	#125	—	5	1	no	—
317	#125	—	5	2	no	—
318	#125	—	5	2	no	—
319	#125	—	5	2	no	—
320	#125	—	5	2	no	—
321	#125	—	5	2	no	—
322	#125	—	5	2	no	—
323	#125	—	5	2	no	—
324	#125	—	5	1	no	—
325	#124	—	5	1	no	—
326	#124	—	5	2	no	—
327	#124	C₂×D₅	1	2	yes	—
328	#124	C₂×D₅	1	1	yes	characteristic, complemented
329	#123	—	5	2	no	—
330	#123	—	5	2	no	—
331	#123	—	5	2	no	—
332	#123	—	5	2	no	—
333	#123	—	5	2	no	—
334	#123	—	5	2	no	—
335	#123	C₂×D₅	1	2	yes	—
336	C₂²⋊Q₈	—	5	1	no	—
337	C₂²⋊Q₈	—	5	2	no	—
338	C₂²⋊Q₈	—	5	2	no	—
339	C₂²⋊Q₈	—	5	1	no	—
340	C₂²⋊Q₈	—	5	1	no	—
341	C₂²⋊Q₈	—	5	1	no	—
342	C₂²⋊Q₈	—	5	2	no	—
343	C₂²⋊Q₈	—	5	1	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	—	5	2	no	—
349	C₂²⋊Q₈	—	5	2	no	—
350	C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic
351	C₂²⋊Q₈	C₂×D₅	1	2	yes	complemented
352	#121	—	5	1	no	—
353	#121	C₂×D₅	1	1	yes	characteristic
354	#120	—	5	2	no	—
355	C₄×Q₈	—	5	1	no	—
356	C₄×Q₈	—	5	2	no	—
357	C₄×Q₈	—	5	1	no	—
358	C₄×Q₈	—	5	2	no	—
359	C₄×Q₈	—	5	1	no	—
360	C₄×Q₈	—	5	1	no	—
361	C₄×Q₈	—	5	2	no	—
362	C₄×Q₈	—	5	1	no	—
363	C₄×Q₈	—	5	2	no	—
364	C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
365	C₄×D₄	—	5	1	no	—
366	C₄×D₄	—	5	2	no	—
367	C₄×D₄	—	5	2	no	—
368	C₄×D₄	—	5	2	no	—
369	C₄×D₄	—	5	2	no	—
370	C₄×D₄	—	5	2	no	—
371	C₄×D₄	—	5	2	no	—
372	C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
373	#117	—	5	1	no	—
374	#117	—	5	2	no	—
375	#117	—	5	1	no	—
376	#117	—	5	1	no	—
377	#117	—	5	1	no	—
378	#117	—	5	2	no	—
379	#117	—	5	2	no	—
380	#117	—	5	1	no	—
381	#117	—	5	1	no	—
382	#117	—	5	2	no	—
383	#117	—	5	2	no	—
384	#117	—	5	1	no	—
385	#117	—	5	1	no	—
386	#117	—	5	2	no	—
387	#117	—	5	2	no	—
388	#117	C₂×D₅	1	1	yes	characteristic
389	C₂×C₄⋊C₄	—	5	2	no	—
390	C₂×C₄⋊C₄	—	5	1	no	—
391	C₂×C₄⋊C₄	—	5	1	no	—
392	C₂×C₄⋊C₄	—	5	1	no	—
393	C₂×C₄⋊C₄	—	5	2	no	—
394	C₂×C₂²⋊C₄	—	5	1	no	—
395	C₂×C₂²⋊C₄	—	5	1	no	—
396	C₂×C₂²⋊C₄	—	5	2	no	—
397	C₂×C₄²	—	5	1	no	—
398	C₂×C₄²	—	5	1	no	—
399	C₂²×C₅	—	2	2	no	—
400	C₂²×C₅	—	2	1	no	—
401	C₂²×C₅	—	2	2	no	—
402	C₂²×C₅	—	2	1	no	—
403	C₂²×C₅	—	2	2	no	—
404	C₂²×C₅	—	2	1	no	—
405	C₂²×C₅	C₂⁵	1	1	yes	characteristic
406	C₂×D₅	—	2	1	no	—
407	C₂×D₅	—	2	1	no	—
408	C₂×D₅	—	2	1	no	—
409	C₂×D₅	—	2	1	no	—
410	C₂×D₅	—	4	4	no	—
411	C₂×D₅	C₂×#41	1	2	yes	—
412	C₂×D₅	2₋¹⁺⁴	1	2	yes	—
413	C₄×C₅	—	2	2	no	—
414	C₄×C₅	—	2	1	no	—
415	C₄×C₅	—	2	1	no	—
416	C₄×C₅	—	2	1	no	—
417	C₄×C₅	—	2	2	no	—
418	C₄×C₅	—	2	1	no	—
419	C₄×C₅	—	2	2	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	1	no	—
425	Dic₅	—	2	1	no	—
426	Dic₅	—	2	1	no	—
427	Dic₅	—	2	2	no	—
428	Dic₅	—	2	1	no	—
429	Dic₅	—	2	2	no	—
430	Dic₅	—	2	1	no	—
431	Dic₅	C₂×#41	1	2	yes	—
432	C₂⁴	—	5	1	no	—
433	#41	—	10	4	no	—
434	C₂×Q₈	—	5	2	no	—
435	C₂×Q₈	—	5	1	no	—
436	C₂×Q₈	—	5	1	no	—
437	C₂×Q₈	—	5	2	no	—
438	C₂×Q₈	—	10	4	no	—
439	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
440	C₂×Q₈	C₂²×D₅	1	2	yes	—
441	C₂×D₄	—	5	2	no	—
442	C₂×D₄	—	5	2	no	—
443	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
444	C₂×D₄	C₂²×D₅	1	2	yes	—
445	C₂²×C₄	—	5	1	no	—
446	C₂²×C₄	—	5	2	no	—
447	C₂²×C₄	—	5	1	no	—
448	C₂²×C₄	—	5	2	no	—
449	C₂²×C₄	—	5	1	no	—
450	C₂²×C₄	—	5	1	no	—
451	C₂²×C₄	—	5	1	no	—
452	C₂²×C₄	—	5	2	no	—
453	C₂²×C₄	—	5	1	no	—
454	C₂²×C₄	—	5	1	no	—
455	C₂²×C₄	—	5	1	no	—
456	C₂²×C₄	—	5	1	no	—
457	C₂²×C₄	—	5	2	no	—
458	C₂²×C₄	—	10	4	no	—
459	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
460	C₂²×C₄	C₂²×D₅	1	2	yes	—
461	C₄⋊C₄	—	5	1	no	—
462	C₄⋊C₄	—	5	2	no	—
463	C₄⋊C₄	—	5	1	no	—
464	C₄⋊C₄	—	5	1	no	—
465	C₄⋊C₄	—	5	1	no	—
466	C₄⋊C₄	—	5	1	no	—
467	C₄⋊C₄	—	5	1	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	1	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	—	5	2	no	—
484	C₄⋊C₄	—	5	2	no	—
485	C₄⋊C₄	—	5	2	no	—
486	C₄⋊C₄	—	5	2	no	—
487	C₄⋊C₄	—	5	2	no	—
488	C₄⋊C₄	—	5	2	no	—
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	2	yes	—
493	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
494	C₄⋊C₄	C₂²×D₅	1	2	yes	—
495	C₄⋊C₄	C₂²×D₅	1	2	yes	—
496	C₂²⋊C₄	—	5	1	no	—
497	C₂²⋊C₄	—	5	1	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	1	no	—
505	C₂²⋊C₄	—	5	1	no	—
506	C₂²⋊C₄	—	5	1	no	—
507	C₂²⋊C₄	—	5	1	no	—
508	C₂²⋊C₄	—	5	2	no	—
509	C₂²⋊C₄	—	5	2	no	—
510	C₂²⋊C₄	—	5	2	no	—
511	C₂²⋊C₄	—	5	2	no	—
512	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
513	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
514	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
515	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
516	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
517	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
518	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
519	C₄²	—	5	1	no	—
520	C₄²	—	5	1	no	—
521	C₄²	—	5	1	no	—
522	C₄²	—	5	1	no	—
523	C₄²	—	5	1	no	—
524	C₄²	—	5	1	no	—
525	C₄²	—	5	2	no	—
526	C₄²	—	5	2	no	—
527	C₄²	—	5	2	no	—
528	C₄²	—	5	2	no	—
529	C₄²	—	5	2	no	—
530	C₄²	—	5	2	no	—
531	C₄²	C₂²×D₅	1	1	yes	characteristic
532	C₄²	C₂²×D₅	1	1	yes	characteristic
533	C₄²	C₂²×D₅	1	2	yes	—
534	C₂×C₅	—	4	1	no	—
535	C₂×C₅	—	4	2	no	—
536	C₂×C₅	C₂²×#41	1	1	yes	characteristic
537	C₂×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
538	C₂×C₅	#585	1	1	yes	characteristic
539	D₅	—	2	2	no	—
540	D₅	—	2	2	no	—
541	C₂³	—	5	1	no	—
542	C₂³	—	5	1	no	—
543	C₂³	—	10	2	no	—
544	C₂³	—	10	2	no	—
545	C₂³	—	20	1	no	—
546	C₂³	C₂³×D₅	1	1	yes	characteristic
547	C₂³	C₂³×D₅	1	2	yes	—
548	Q₈	—	2	2	no	—
549	Q₈	—	4	2	no	—
550	Q₈	—	10	4	no	—
551	Q₈	—	10	2	no	—
552	Q₈	—	10	2	no	—
553	Q₈	—	20	2	no	—
554	D₄	—	2	2	no	—
555	D₄	—	4	2	no	—
556	D₄	—	10	4	no	—
557	D₄	—	10	4	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	4	2	no	—
560	C₂×C₄	—	5	1	no	—
561	C₂×C₄	—	5	4	no	—
562	C₂×C₄	—	5	1	no	—
563	C₂×C₄	—	5	1	no	—
564	C₂×C₄	—	5	1	no	—
565	C₂×C₄	—	5	2	no	—
566	C₂×C₄	—	5	1	no	—
567	C₂×C₄	—	5	2	no	—
568	C₂×C₄	—	5	1	no	—
569	C₂×C₄	—	5	2	no	—
570	C₂×C₄	—	5	2	no	—
571	C₂×C₄	—	10	2	no	—
572	C₂×C₄	—	10	2	no	—
573	C₂×C₄	—	10	4	no	—
574	C₂×C₄	—	10	2	no	—
575	C₂×C₄	—	10	2	no	—
576	C₂×C₄	—	10	2	no	—
577	C₂×C₄	—	10	4	no	—
578	C₂×C₄	—	10	2	no	—
579	C₂×C₄	—	20	1	no	—
580	C₂×C₄	—	20	2	no	—
581	C₂×C₄	—	20	1	no	—
582	C₂×C₄	—	20	2	no	—
583	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
584	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
585	C₂×C₄	C₂³×D₅	1	2	yes	—
586	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
587	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
588	C₂×C₄	C₂³×D₅	1	2	yes	—
589	C₂×C₄	C₂³×D₅	1	2	yes	—
590	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
591	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
592	C₅	#3495	1	1	yes	characteristic, complemented, Sylow
593	C₂²	—	2	1	no	—
594	C₂²	—	2	2	no	—
595	C₂²	—	2	2	no	—
596	C₂²	—	2	1	no	—
597	C₂²	—	2	2	no	—
598	C₂²	—	2	1	no	—
599	C₂²	—	5	2	no	—
600	C₂²	—	5	2	no	—
601	C₂²	—	10	1	no	—
602	C₂²	—	10	1	no	—
603	C₂²	—	10	1	no	—
604	C₂²	—	10	1	no	—
605	C₂²	—	20	4	no	—
606	C₂²	C₂⁴×D₅	1	1	yes	characteristic
607	C₄	—	2	1	no	—
608	C₄	—	2	2	no	—
609	C₄	—	2	1	no	—
610	C₄	—	2	2	no	—
611	C₄	—	2	1	no	—
612	C₄	—	2	2	no	—
613	C₄	—	2	1	no	—
614	C₄	—	2	1	no	—
615	C₄	—	5	2	no	—
616	C₄	—	10	1	no	—
617	C₄	—	10	2	no	—
618	C₄	—	10	2	no	—
619	C₄	—	10	1	no	—
620	C₄	—	10	2	no	—
621	C₄	—	10	1	no	—
622	C₄	—	10	1	no	—
623	C₄	—	10	1	no	—
624	C₄	—	10	2	no	—
625	C₄	D₅×#41	1	2	yes	—
626	C₂	—	4	1	no	—
627	C₂	—	4	2	no	—
628	C₂	—	10	2	no	—
629	C₂	—	10	2	no	—
630	C₂	C₂×D₅×#41	1	1	yes	characteristic
631	C₂	#66285	1	1	yes	characteristic
632	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×#542	C₂
prime radical	#65940	C₂
hypercenter	#542	D₅
hypocenter	C₅	#3495
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ #542

Complements

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

N	H ≅ G/N	type
1. C₅×#542	C₂	semidirect
2. #66063	C₂	semidirect
3. #66062	C₂	semidirect
4. #66042	C₂	semidirect
5. #66042	C₂	semidirect
6. #66014	C₂	semidirect
7. #66013	C₂	semidirect
8. #66009	C₂	semidirect
9. #66005	C₂	semidirect
10. #65993	C₂	semidirect
11. #65984	C₂	semidirect
12. #65973	C₂	semidirect
13. #65970	C₂	semidirect
14. D₅×C₂²⋊Q₈	C₂	semidirect
15. #65959	C₂	semidirect
17. #65937	C₂	semidirect
18. #65912	C₂	semidirect
19. #65906	C₂	semidirect
20. #65891	C₂	semidirect
21. #65880	C₂	semidirect
22. D₅×#117	C₂	semidirect
23. #65852	C₂	semidirect
27. C₅×C₄⋊Q₈	C₂²	semidirect
28. C₅×#126	C₂²	semidirect
30. C₅×#124	C₂²	semidirect
33. C₅×C₂²⋊Q₈	C₂²	semidirect
35. C₄×C₅×Q₈	C₂²	semidirect
36. C₄×C₅×D₄	C₂²	semidirect
41. Q₈×Dic₅	C₂²	semidirect
42. Q₈×Dic₅	C₂²	semidirect
43. #4090	C₂²	semidirect
44. #4090	C₂²	semidirect
48. #4082	C₂²	semidirect
51. D₄×Dic₅	C₂²	semidirect
55. #4072	C₂²	semidirect
58. C₂×#683	C₂²	semidirect
73. #4036	C₂²	semidirect
74. #4036	C₂²	semidirect
75. #4036	C₂²	semidirect
76. #4035	C₂²	semidirect
77. #4035	C₂²	semidirect
78. #4035	C₂²	semidirect
79. #4035	C₂²	semidirect
80. #4035	C₂²	semidirect
81. #4034	C₂²	semidirect
82. #4033	C₂²	semidirect
83. #4033	C₂²	semidirect
84. #4033	C₂²	semidirect
100. #4025	C₂²	semidirect
101. #4025	C₂²	semidirect
102. #4025	C₂²	semidirect
104. #4024	C₂²	semidirect
105. #4024	C₂²	semidirect
106. #4024	C₂²	semidirect
109. #4023	C₂²	semidirect
110. #4023	C₂²	semidirect
117. #4016	C₂²	semidirect
118. #4015	C₂²	semidirect
119. C₄×Dic₁₀	C₂²	semidirect
120. C₄×Dic₁₀	C₂²	semidirect
121. C₄×Dic₁₀	C₂²	semidirect
122. C₄×Dic₁₀	C₂²	semidirect
236. #542	D₅	semidirect
307. C₄⋊Q₈	C₂×D₅	semidirect
315. #126	C₂×D₅	semidirect
328. #124	C₂×D₅	semidirect
351. C₂²⋊Q₈	C₂×D₅	semidirect
364. C₄×Q₈	C₂×D₅	semidirect
372. C₄×D₄	C₂×D₅	semidirect
592. C₅	#3495	semidirect

Maximal subgroups

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

subgroup	index
C₅×#542	2
#66063	2
#66062	2
#66042	2
#66014	2
#66013	2
#66009	2
#66005	2
#65993	2
#65984	2
#65973	2
#65970	2
D₅×C₂²⋊Q₈	2
#65959	2
#65940	2
#65937	2
#65912	2
#65906	2
#65891	2
#65880	2
D₅×#117	2
#65852	2
#3495	5