Subgroups — #10618618

Order 640.

1142 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×#548	C₂	1	1	yes	maximal, characteristic, complemented
2	#66166	C₂	1	1	yes	maximal, characteristic, complemented
3	#66163	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#4093	C₂	1	1	yes	maximal, characteristic, complemented
6	#66015	C₂	1	1	yes	maximal, characteristic, complemented
7	#66012	C₂	1	2	yes	maximal, complemented
8	D₅×#124	C₂	1	1	yes	maximal, characteristic, complemented
9	#66004	C₂	1	2	yes	maximal, complemented
10	#65974	C₂	1	2	yes	maximal, complemented
11	#65971	C₂	1	2	yes	maximal, complemented
12	#65967	C₂	1	1	yes	maximal, characteristic, complemented
13	#65958	C₂	1	1	yes	maximal, characteristic, complemented
14	#65951	C₂	1	2	yes	maximal, complemented
15	#65944	C₂	1	2	yes	maximal, complemented
16	#65943	C₂	1	1	yes	maximal, characteristic, complemented
17	#65934	C₂	1	1	yes	maximal, characteristic, complemented
18	#65914	C₂	1	1	yes	maximal, characteristic, complemented
19	#65902	C₂	1	1	yes	maximal, characteristic, complemented
20	#65890	C₂	1	2	yes	maximal, complemented
21	#65884	C₂	1	1	yes	maximal, characteristic, complemented
22	#65879	C₂	1	2	yes	maximal, complemented
23	C₄×#711	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₅×#41	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
26	C₂×Q₈×D₅	C₂²	1	1	yes	characteristic, complemented
27	C₂×#711	C₂²	1	1	yes	characteristic
28	C₂×D₄×D₅	C₂²	1	2	yes	—
29	C₂×D₄×D₅	C₂²	1	1	yes	characteristic
30	C₂×#709	C₂²	1	1	yes	characteristic, complemented
31	C₂²×D₂₀	C₂²	1	1	yes	characteristic
32	C₅×#124	C₂²	1	2	yes	complemented
33	C₅×#124	C₂²	1	1	yes	characteristic, complemented
34	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
36	C₅×#121	C₂²	1	1	yes	characteristic
37	C₅×#121	C₂²	1	2	yes	complemented
38	C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
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	#4093	C₂²	1	1	yes	characteristic
43	#4093	C₂²	1	1	yes	characteristic, complemented
44	#4093	C₂²	1	1	yes	characteristic, complemented
45	#4093	C₂²	1	2	yes	complemented
46	#4093	C₂²	1	2	yes	complemented
47	#4092	C₂²	1	1	yes	characteristic, complemented
48	#4092	C₂²	1	2	yes	complemented
49	Q₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
50	#4090	C₂²	1	1	yes	characteristic, complemented
51	#4090	C₂²	1	2	yes	complemented
52	#4086	C₂²	1	1	yes	characteristic
53	#4085	C₂²	1	2	yes	complemented
54	#4085	C₂²	1	2	yes	complemented
55	#4085	C₂²	1	2	yes	complemented
56	#4083	C₂²	1	2	yes	—
57	#4083	C₂²	1	2	yes	complemented
58	#4083	C₂²	1	2	yes	complemented
59	#4082	C₂²	1	1	yes	characteristic, complemented
60	#4081	C₂²	1	2	yes	complemented
61	D₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
62	D₄×Dic₅	C₂²	1	2	yes	complemented
63	D₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
64	#4076	C₂²	1	1	yes	characteristic
65	#4075	C₂²	1	2	yes	complemented
66	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
67	C₄×C₂²⋊D₅	C₂²	1	2	yes	—
68	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
69	C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
70	C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
71	C₂×#685	C₂²	1	2	yes	complemented
72	C₂×#685	C₂²	1	2	yes	complemented
73	C₂×#685	C₂²	1	2	yes	complemented
74	#4070	C₂²	1	1	yes	characteristic, complemented
75	#4070	C₂²	1	2	yes	complemented
76	C₂×C₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
77	C₂×C₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
78	#4044	C₂²	1	2	yes	complemented
79	#4044	C₂²	1	2	yes	complemented
80	#4044	C₂²	1	2	yes	complemented
81	#4042	C₂²	1	2	yes	complemented
82	#4042	C₂²	1	2	yes	complemented
83	#4041	C₂²	1	1	yes	characteristic
84	#4040	C₂²	1	2	yes	complemented
85	#4040	C₂²	1	2	yes	complemented
86	#4039	C₂²	1	1	yes	characteristic
87	#4039	C₂²	1	2	yes	complemented
88	#4038	C₂²	1	1	yes	characteristic, complemented
89	#4038	C₂²	1	2	yes	complemented
90	#4036	C₂²	1	1	yes	characteristic, complemented
91	#4033	C₂²	1	1	yes	characteristic, complemented
92	#4033	C₂²	1	1	yes	characteristic, complemented
93	#4032	C₂²	1	2	yes	complemented
94	#4032	C₂²	1	2	yes	complemented
95	#4031	C₂²	1	2	yes	complemented
96	#4031	C₂²	1	2	yes	complemented
97	#4031	C₂²	1	2	yes	complemented
98	#4031	C₂²	1	2	yes	complemented
99	#4030	C₂²	1	2	yes	—
100	#4030	C₂²	1	2	yes	complemented
101	#4030	C₂²	1	2	yes	complemented
102	#4029	C₂²	1	2	yes	complemented
103	#4028	C₂²	1	2	yes	—
104	#4027	C₂²	1	1	yes	characteristic
105	#4027	C₂²	1	1	yes	characteristic, complemented
106	#4027	C₂²	1	2	yes	complemented
107	#4027	C₂²	1	2	yes	complemented
108	D₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
109	D₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
110	D₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
111	#4025	C₂²	1	2	yes	complemented
112	#4023	C₂²	1	1	yes	characteristic, complemented
113	#4023	C₂²	1	1	yes	characteristic, complemented
114	#4023	C₂²	1	2	yes	complemented
115	#4022	C₂²	1	2	yes	complemented
116	#4021	C₂²	1	1	yes	characteristic
117	C₄×D₂₀	C₂²	1	2	yes	complemented
118	C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
119	#4018	C₂²	1	2	yes	complemented
120	#4018	C₂²	1	2	yes	complemented
121	C₄²×D₅	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
123	#3514	—	5	1	no	maximal, Sylow
124	C₂³×D₅	C₂³	1	2	yes	—
125	C₂³×D₅	C₂³	1	2	yes	—
126	C₅×#41	—	4	2	no	—
127	C₂×C₅×Q₈	—	4	2	no	—
128	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
129	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
130	C₂×C₅×Q₈	C₂³	1	2	yes	—
131	C₂×C₅×D₄	C₂³	1	2	yes	—
132	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
133	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
134	C₂×C₅×D₄	C₂³	1	2	yes	—
135	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
136	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
137	C₂²×C₄×C₅	C₂³	1	2	yes	—
138	C₂²×C₄×C₅	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
145	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
146	C₂²×Dic₅	C₂³	1	1	yes	characteristic
147	C₂²×Dic₅	C₂³	1	1	yes	characteristic
148	C₂²×Dic₅	C₂³	1	2	yes	—
149	C₂²×Dic₅	C₂³	1	1	yes	characteristic
150	C₂²×Dic₅	C₂³	1	1	yes	characteristic
151	Q₈×D₅	—	4	2	no	—
152	#711	—	2	4	no	—
153	D₄×D₅	—	2	8	no	—
154	D₄×D₅	—	4	2	no	—
155	#709	—	4	2	no	—
156	C₂×D₂₀	—	4	2	no	—
157	C₂×D₂₀	C₂³	1	1	yes	characteristic
158	C₂×D₂₀	C₂³	1	1	yes	characteristic
159	C₂×D₂₀	C₂³	1	2	yes	—
160	C₂×D₂₀	C₂³	1	2	yes	—
161	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
162	C₂×C₄×D₅	C₂³	1	2	yes	—
163	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
164	C₂×C₄×D₅	C₂³	1	2	yes	—
165	C₂×C₄×D₅	C₂³	1	2	yes	—
166	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
167	C₂×C₄×D₅	C₂³	1	2	yes	—
168	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
169	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
170	C₂×Dic₁₀	C₂³	1	2	yes	—
171	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
172	C₅×C₄⋊C₄	C₂³	1	2	yes	—
173	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
174	C₅×C₄⋊C₄	C₂³	1	2	yes	—
175	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
176	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
177	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₄²×C₅	C₂³	1	1	yes	characteristic
182	C₄²×C₅	C₂³	1	2	yes	—
183	C₂²⋊Dic₅	C₂³	1	2	yes	—
184	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
185	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
186	C₂²⋊Dic₅	C₂³	1	2	yes	—
187	C₂²⋊Dic₅	C₂³	1	2	yes	—
188	C₂²⋊Dic₅	C₂³	1	2	yes	—
189	#685	C₂³	1	2	yes	—
190	#685	C₂³	1	2	yes	—
191	#685	C₂³	1	2	yes	—
192	#685	C₂³	1	2	yes	—
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	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	1	yes	characteristic
203	#685	C₂³	1	1	yes	characteristic
204	#685	C₂³	1	2	yes	—
205	#685	C₂³	1	2	yes	—
206	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
207	C₄⋊Dic₅	C₂³	1	2	yes	—
208	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
209	C₄⋊Dic₅	C₂³	1	2	yes	—
210	#683	C₂³	1	1	yes	characteristic
211	#683	C₂³	1	1	yes	characteristic
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	#683	C₂³	1	2	yes	—
218	#683	C₂³	1	1	yes	characteristic
219	#683	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	1	yes	characteristic
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	C₄×Dic₅	C₂³	1	1	yes	characteristic
230	C₄×Dic₅	C₂³	1	2	yes	—
231	#559	—	5	1	no	—
232	#556	—	5	1	no	—
233	#555	—	5	2	no	—
234	#551	—	5	2	no	—
235	#551	—	5	2	no	—
236	D₄×Q₈	—	5	1	no	—
237	#548	—	5	1	no	—
238	#548	D₅	1	1	yes	characteristic, complemented
239	#546	—	5	1	no	—
240	#546	—	5	2	no	—
241	#546	—	5	1	no	—
242	D₄²	—	5	1	no	—
243	#542	—	5	2	no	—
244	#538	—	5	2	no	—
245	#538	—	5	2	no	—
246	#532	—	5	1	no	—
247	#529	—	5	1	no	—
248	#529	—	5	1	no	—
249	#529	—	5	1	no	—
250	C₂×#124	—	5	1	no	—
251	C₂×#124	—	5	1	no	—
252	#518	—	5	2	no	—
253	C₄×#41	—	5	1	no	—
254	C₂³×C₅	C₂⁴	1	2	yes	—
255	C₂³×C₅	C₂⁴	1	1	yes	characteristic
256	C₂³×C₅	C₂⁴	1	1	yes	characteristic
257	C₂²×D₅	—	2	4	no	—
258	C₂²×D₅	—	2	4	no	—
259	C₂²×D₅	—	4	2	no	—
260	C₂²×D₅	—	4	2	no	—
261	C₂²×D₅	—	4	2	no	—
262	C₂²×D₅	—	4	2	no	—
263	C₂²×D₅	C₂⁴	1	2	yes	—
264	C₂²×D₅	C₂⁴	1	2	yes	—
265	C₂²×D₅	C₂⁴	1	1	yes	characteristic
266	C₅×Q₈	—	2	2	no	—
267	C₅×Q₈	—	2	2	no	—
268	C₅×Q₈	—	4	2	no	—
269	C₅×D₄	—	2	4	no	—
270	C₅×D₄	—	2	2	no	—
271	C₅×D₄	—	2	2	no	—
272	C₅×D₄	—	4	2	no	—
273	C₂×C₄×C₅	—	2	2	no	—
274	C₂×C₄×C₅	—	2	2	no	—
275	C₂×C₄×C₅	—	4	2	no	—
276	C₂×C₄×C₅	—	4	2	no	—
277	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
278	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
279	C₂×C₄×C₅	C₂⁴	1	2	yes	—
280	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
281	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
282	C₂×C₄×C₅	C₂⁴	1	2	yes	—
283	C₂×C₄×C₅	C₂⁴	1	2	yes	—
284	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
285	C₂²⋊D₅	—	2	2	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	C₂²⋊D₅	—	4	2	no	—
291	C₂²⋊D₅	#41	1	4	yes	complemented
292	C₂×Dic₅	—	2	2	no	—
293	C₂×Dic₅	—	2	2	no	—
294	C₂×Dic₅	—	4	1	no	—
295	C₂×Dic₅	—	4	1	no	—
296	C₂×Dic₅	—	4	2	no	—
297	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
298	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
299	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
300	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
301	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
302	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
303	C₂×Dic₅	C₂⁴	1	2	yes	—
304	C₂×Dic₅	C₂⁴	1	2	yes	—
305	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
306	D₂₀	—	2	4	no	—
307	D₂₀	—	2	2	no	—
308	D₂₀	—	2	2	no	—
309	D₂₀	—	4	2	no	—
310	C₄×D₅	—	2	2	no	—
311	C₄×D₅	—	2	2	no	—
312	C₄×D₅	—	2	4	no	—
313	C₄×D₅	—	4	1	no	—
314	C₄×D₅	—	4	2	no	—
315	C₄×D₅	—	4	2	no	—
316	C₄×D₅	—	4	2	no	—
317	Dic₁₀	—	2	2	no	—
318	Dic₁₀	—	2	2	no	—
319	Dic₁₀	—	4	2	no	—
320	C₂×#41	—	5	1	no	—
321	C₂×#41	—	5	1	no	—
322	C₂×#41	C₂×D₅	1	1	yes	characteristic, complemented
323	C₂²×Q₈	—	5	1	no	—
324	C₂²×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
325	C₂²×D₄	—	5	2	no	—
326	C₂²×D₄	—	5	1	no	—
327	C₂²×D₄	—	5	1	no	—
328	C₄⋊Q₈	—	5	1	no	—
329	C₄⋊Q₈	—	5	2	no	—
330	#127	—	5	1	no	—
331	#126	—	5	2	no	—
332	#126	—	5	2	no	—
333	#126	—	5	2	no	—
334	#126	—	5	2	no	—
335	#126	—	5	2	no	—
336	#125	—	5	1	no	—
337	#124	—	5	1	no	—
338	#124	—	5	1	no	—
339	#124	—	5	2	no	—
340	#124	—	5	1	no	—
341	#124	—	5	1	no	—
342	#124	—	5	2	no	—
343	#124	—	5	1	no	—
344	#124	—	5	2	no	—
345	#124	—	5	2	no	—
346	#124	—	5	2	no	—
347	#124	—	5	2	no	—
348	#124	—	5	1	no	—
349	#124	C₂×D₅	1	1	yes	characteristic, complemented
350	#124	C₂×D₅	1	2	yes	complemented
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	—	5	2	no	—
357	#123	—	5	2	no	—
358	C₂²⋊Q₈	—	5	1	no	—
359	C₂²⋊Q₈	—	5	2	no	—
360	C₂²⋊Q₈	—	5	1	no	—
361	C₂²⋊Q₈	—	5	2	no	—
362	C₂²⋊Q₈	—	5	2	no	—
363	C₂²⋊Q₈	—	5	2	no	—
364	C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
365	C₂²⋊Q₈	C₂×D₅	1	2	yes	complemented
366	#121	—	5	2	no	—
367	#121	—	5	2	no	—
368	#121	—	5	2	no	—
369	#121	—	5	1	no	—
370	#121	—	5	1	no	—
371	#121	—	5	2	no	—
372	#121	—	5	2	no	—
373	#121	—	5	2	no	—
374	#121	C₂×D₅	1	1	yes	characteristic
375	#121	C₂×D₅	1	2	yes	complemented
376	#120	—	5	2	no	—
377	#120	—	5	2	no	—
378	#120	—	5	2	no	—
379	#120	—	5	2	no	—
380	C₄×Q₈	—	5	1	no	—
381	C₄×Q₈	—	5	1	no	—
382	C₄×Q₈	—	5	1	no	—
383	C₄×Q₈	—	5	1	no	—
384	C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
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	1	no	—
390	C₄×D₄	—	5	2	no	—
391	C₄×D₄	—	5	2	no	—
392	C₄×D₄	—	5	2	no	—
393	C₄×D₄	—	5	2	no	—
394	C₄×D₄	—	5	1	no	—
395	C₄×D₄	—	5	1	no	—
396	C₄×D₄	—	5	1	no	—
397	C₄×D₄	—	5	2	no	—
398	C₄×D₄	—	5	2	no	—
399	C₄×D₄	—	5	2	no	—
400	C₄×D₄	—	5	1	no	—
401	C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
402	C₄×D₄	C₂×D₅	1	2	yes	complemented
403	#117	—	5	1	no	—
404	#117	—	5	2	no	—
405	#117	—	5	1	no	—
406	#117	—	5	1	no	—
407	#117	—	5	2	no	—
408	#117	—	5	2	no	—
409	#117	—	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×C₂²⋊C₄	—	5	2	no	—
414	C₂×C₂²⋊C₄	—	5	2	no	—
415	C₂×C₂²⋊C₄	—	5	2	no	—
416	C₂×C₄²	—	5	1	no	—
417	C₂×C₄²	—	5	1	no	—
418	C₂×C₄²	—	5	1	no	—
419	C₂²×C₅	—	2	1	no	—
420	C₂²×C₅	—	2	1	no	—
421	C₂²×C₅	—	2	1	no	—
422	C₂²×C₅	—	2	2	no	—
423	C₂²×C₅	—	2	1	no	—
424	C₂²×C₅	—	2	2	no	—
425	C₂²×C₅	—	2	1	no	—
426	C₂²×C₅	—	2	2	no	—
427	C₂²×C₅	C₂×#41	1	2	yes	—
428	C₂²×C₅	C₂⁵	1	1	yes	characteristic
429	C₂×D₅	—	2	1	no	—
430	C₂×D₅	—	2	1	no	—
431	C₂×D₅	—	2	2	no	—
432	C₂×D₅	—	2	2	no	—
433	C₂×D₅	—	2	2	no	—
434	C₂×D₅	—	2	2	no	—
435	C₂×D₅	—	2	2	no	—
436	C₂×D₅	—	2	2	no	—
437	C₂×D₅	—	8	4	no	—
438	C₂×D₅	—	8	4	no	—
439	C₂×D₅	C₂×#41	1	2	yes	—
440	C₄×C₅	—	2	1	no	—
441	C₄×C₅	—	2	2	no	—
442	C₄×C₅	—	2	2	no	—
443	C₄×C₅	—	2	1	no	—
444	C₄×C₅	—	2	1	no	—
445	C₄×C₅	—	2	2	no	—
446	C₄×C₅	—	2	1	no	—
447	C₄×C₅	H(5,𝔽₂)	1	2	yes	—
448	Dic₅	—	2	1	no	—
449	Dic₅	—	2	1	no	—
450	Dic₅	—	2	2	no	—
451	Dic₅	—	2	1	no	—
452	Dic₅	—	2	1	no	—
453	Dic₅	—	2	2	no	—
454	Dic₅	—	2	1	no	—
455	Dic₅	—	2	1	no	—
456	Dic₅	C₂×#41	1	2	yes	—
457	C₂⁴	—	5	2	no	—
458	C₂⁴	—	5	2	no	—
459	#41	—	4	2	no	—
460	#41	—	10	4	no	—
461	#41	—	20	2	no	—
462	C₂×Q₈	—	4	2	no	—
463	C₂×Q₈	—	5	1	no	—
464	C₂×Q₈	—	5	1	no	—
465	C₂×Q₈	—	5	2	no	—
466	C₂×Q₈	—	20	2	no	—
467	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
468	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
469	C₂×Q₈	C₂²×D₅	1	2	yes	—
470	C₂×D₄	—	5	1	no	—
471	C₂×D₄	—	5	1	no	—
472	C₂×D₄	—	5	2	no	—
473	C₂×D₄	—	5	2	no	—
474	C₂×D₄	—	5	2	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	1	no	—
480	C₂×D₄	—	5	2	no	—
481	C₂×D₄	—	10	8	no	—
482	C₂×D₄	—	20	2	no	—
483	C₂×D₄	—	20	2	no	—
484	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
485	C₂×D₄	C₂²×D₅	1	2	yes	—
486	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
487	C₂×D₄	C₂²×D₅	1	2	yes	—
488	C₂²×C₄	—	5	1	no	—
489	C₂²×C₄	—	5	1	no	—
490	C₂²×C₄	—	5	1	no	—
491	C₂²×C₄	—	5	1	no	—
492	C₂²×C₄	—	5	2	no	—
493	C₂²×C₄	—	5	1	no	—
494	C₂²×C₄	—	5	1	no	—
495	C₂²×C₄	—	5	2	no	—
496	C₂²×C₄	—	5	1	no	—
497	C₂²×C₄	—	5	2	no	—
498	C₂²×C₄	—	5	2	no	—
499	C₂²×C₄	—	5	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	C₂²×C₄	C₂²×D₅	1	2	yes	—
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	1	no	—
509	C₄⋊C₄	—	5	1	no	—
510	C₄⋊C₄	—	5	1	no	—
511	C₄⋊C₄	—	5	1	no	—
512	C₄⋊C₄	—	5	2	no	—
513	C₄⋊C₄	—	5	2	no	—
514	C₄⋊C₄	—	5	1	no	—
515	C₄⋊C₄	—	5	2	no	—
516	C₄⋊C₄	—	5	2	no	—
517	C₄⋊C₄	—	5	2	no	—
518	C₄⋊C₄	C₂²×D₅	1	2	yes	—
519	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
520	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
521	C₄⋊C₄	C₂²×D₅	1	2	yes	—
522	C₂²⋊C₄	—	5	2	no	—
523	C₂²⋊C₄	—	5	2	no	—
524	C₂²⋊C₄	—	5	2	no	—
525	C₂²⋊C₄	—	5	1	no	—
526	C₂²⋊C₄	—	5	1	no	—
527	C₂²⋊C₄	—	5	2	no	—
528	C₂²⋊C₄	—	5	1	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	—	5	2	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	2	no	—
544	C₂²⋊C₄	—	5	2	no	—
545	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
546	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
547	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
548	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
549	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
550	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
551	C₄²	—	5	1	no	—
552	C₄²	—	5	1	no	—
553	C₄²	—	5	1	no	—
554	C₄²	—	5	1	no	—
555	C₄²	—	5	1	no	—
556	C₄²	—	5	1	no	—
557	C₄²	—	5	1	no	—
558	C₄²	—	5	1	no	—
559	C₄²	—	5	1	no	—
560	C₄²	—	5	2	no	—
561	C₄²	—	5	2	no	—
562	C₄²	C₂²×D₅	1	1	yes	characteristic
563	C₄²	C₂²×D₅	1	2	yes	—
564	C₂×C₅	—	2	2	no	—
565	C₂×C₅	—	4	2	no	—
566	C₂×C₅	—	4	1	no	—
567	C₂×C₅	C₂²×#41	1	1	yes	characteristic
568	C₂×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
569	C₂×C₅	#585	1	1	yes	characteristic
570	D₅	—	2	2	no	—
571	D₅	—	4	2	no	—
572	D₅	—	4	2	no	—
573	C₂³	—	5	1	no	—
574	C₂³	—	5	2	no	—
575	C₂³	—	5	2	no	—
576	C₂³	—	10	4	no	—
577	C₂³	—	10	4	no	—
578	C₂³	—	20	2	no	—
579	C₂³	—	20	2	no	—
580	C₂³	—	20	2	no	—
581	C₂³	—	20	2	no	—
582	C₂³	C₂³×D₅	1	2	yes	—
583	C₂³	C₂³×D₅	1	1	yes	characteristic
584	C₂³	C₂³×D₅	1	1	yes	characteristic
585	Q₈	—	2	2	no	—
586	Q₈	—	2	2	no	—
587	Q₈	—	4	2	no	—
588	Q₈	—	10	2	no	—
589	Q₈	—	10	2	no	—
590	Q₈	—	20	2	no	—
591	D₄	—	2	4	no	—
592	D₄	—	2	2	no	—
593	D₄	—	2	2	no	—
594	D₄	—	4	2	no	—
595	D₄	—	5	4	no	—
596	D₄	—	10	4	no	—
597	D₄	—	10	4	no	—
598	D₄	—	10	2	no	—
599	D₄	—	10	2	no	—
600	D₄	—	10	2	no	—
601	D₄	—	20	2	no	—
602	D₄	—	20	2	no	—
603	D₄	—	20	2	no	—
604	D₄	—	20	2	no	—
605	D₄	—	20	2	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	4	2	no	—
609	C₂×C₄	—	4	2	no	—
610	C₂×C₄	—	5	1	no	—
611	C₂×C₄	—	5	1	no	—
612	C₂×C₄	—	5	1	no	—
613	C₂×C₄	—	5	1	no	—
614	C₂×C₄	—	5	1	no	—
615	C₂×C₄	—	5	1	no	—
616	C₂×C₄	—	5	1	no	—
617	C₂×C₄	—	5	2	no	—
618	C₂×C₄	—	5	2	no	—
619	C₂×C₄	—	10	4	no	—
620	C₂×C₄	—	10	2	no	—
621	C₂×C₄	—	10	2	no	—
622	C₂×C₄	—	10	2	no	—
623	C₂×C₄	—	10	2	no	—
624	C₂×C₄	—	20	2	no	—
625	C₂×C₄	—	20	2	no	—
626	C₂×C₄	—	20	1	no	—
627	C₂×C₄	—	20	2	no	—
628	C₂×C₄	—	20	1	no	—
629	C₂×C₄	—	20	2	no	—
630	C₂×C₄	—	20	1	no	—
631	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
632	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
633	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
634	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
635	C₂×C₄	C₂³×D₅	1	2	yes	—
636	C₂×C₄	C₂³×D₅	1	2	yes	—
637	C₂×C₄	C₂³×D₅	1	2	yes	—
638	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
639	C₅	#3514	1	1	yes	characteristic, complemented, Sylow
640	C₂²	—	2	1	no	—
641	C₂²	—	2	1	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	1	no	—
645	C₂²	—	2	2	no	—
646	C₂²	—	2	1	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	5	2	no	—
649	C₂²	—	10	1	no	—
650	C₂²	—	10	1	no	—
651	C₂²	—	10	2	no	—
652	C₂²	—	10	2	no	—
653	C₂²	—	10	2	no	—
654	C₂²	—	10	2	no	—
655	C₂²	—	10	2	no	—
656	C₂²	—	10	2	no	—
657	C₂²	—	40	4	no	—
658	C₂²	—	40	4	no	—
659	C₂²	D₅×#41	1	2	yes	—
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	1	no	—
668	C₄	—	5	2	no	—
669	C₄	—	10	1	no	—
670	C₄	—	10	2	no	—
671	C₄	—	10	1	no	—
672	C₄	—	10	1	no	—
673	C₄	—	10	1	no	—
674	C₄	—	10	1	no	—
675	C₄	—	10	2	no	—
676	C₄	—	10	1	no	—
677	C₄	#4144	1	2	yes	—
678	C₂	—	2	2	no	—
679	C₂	—	4	2	no	—
680	C₂	—	4	1	no	—
681	C₂	—	10	2	no	—
682	C₂	—	20	2	no	—
683	C₂	—	20	2	no	—
684	C₂	C₂×#4144	1	1	yes	characteristic
685	C₂	C₂×D₅×#41	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×#548	C₂
hypercenter	#548	D₅
hypocenter	C₅	#3514
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ #548

Complements

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

N	H ≅ G/N	type
1. C₅×#548	C₂	semidirect
2. #66166	C₂	semidirect
3. #66163	C₂	semidirect
4. Q₈×C₂²⋊D₅	C₂	semidirect
5. C₂×#4093	C₂	semidirect
6. #66015	C₂	semidirect
7. #66012	C₂	semidirect
8. D₅×#124	C₂	semidirect
9. #66004	C₂	semidirect
10. #65974	C₂	semidirect
11. #65971	C₂	semidirect
12. #65967	C₂	semidirect
13. #65958	C₂	semidirect
14. #65951	C₂	semidirect
15. #65944	C₂	semidirect
16. #65943	C₂	semidirect
17. #65934	C₂	semidirect
18. #65914	C₂	semidirect
19. #65902	C₂	semidirect
20. #65890	C₂	semidirect
21. #65884	C₂	semidirect
22. #65879	C₂	semidirect
23. C₄×#711	C₂	semidirect
24. C₂×C₅×#41	C₂²	semidirect
25. C₂²×C₅×Q₈	C₂²	semidirect
26. C₂×Q₈×D₅	C₂²	semidirect
30. C₂×#709	C₂²	semidirect
32. C₅×#124	C₂²	semidirect
33. C₅×#124	C₂²	semidirect
34. C₅×C₂²⋊Q₈	C₂²	semidirect
35. C₅×C₂²⋊Q₈	C₂²	semidirect
37. C₅×#121	C₂²	semidirect
38. C₄×C₅×Q₈	C₂²	semidirect
39. C₄×C₅×D₄	C₂²	semidirect
40. C₄×C₅×D₄	C₂²	semidirect
43. #4093	C₂²	semidirect
44. #4093	C₂²	semidirect
45. #4093	C₂²	semidirect
46. #4093	C₂²	semidirect
47. #4092	C₂²	semidirect
48. #4092	C₂²	semidirect
49. Q₈×Dic₅	C₂²	semidirect
50. #4090	C₂²	semidirect
51. #4090	C₂²	semidirect
53. #4085	C₂²	semidirect
54. #4085	C₂²	semidirect
55. #4085	C₂²	semidirect
57. #4083	C₂²	semidirect
58. #4083	C₂²	semidirect
59. #4082	C₂²	semidirect
60. #4081	C₂²	semidirect
61. D₄×Dic₅	C₂²	semidirect
62. D₄×Dic₅	C₂²	semidirect
63. D₄×Dic₅	C₂²	semidirect
65. #4075	C₂²	semidirect
68. C₄×C₂²⋊D₅	C₂²	semidirect
69. C₄×C₂²⋊D₅	C₂²	semidirect
70. C₄×C₂²⋊D₅	C₂²	semidirect
71. C₂×#685	C₂²	semidirect
72. C₂×#685	C₂²	semidirect
73. C₂×#685	C₂²	semidirect
74. #4070	C₂²	semidirect
75. #4070	C₂²	semidirect
76. C₂×C₄×Dic₅	C₂²	semidirect
77. C₂×C₄×Dic₅	C₂²	semidirect
78. #4044	C₂²	semidirect
79. #4044	C₂²	semidirect
80. #4044	C₂²	semidirect
81. #4042	C₂²	semidirect
82. #4042	C₂²	semidirect
84. #4040	C₂²	semidirect
85. #4040	C₂²	semidirect
87. #4039	C₂²	semidirect
88. #4038	C₂²	semidirect
89. #4038	C₂²	semidirect
90. #4036	C₂²	semidirect
91. #4033	C₂²	semidirect
92. #4033	C₂²	semidirect
93. #4032	C₂²	semidirect
94. #4032	C₂²	semidirect
95. #4031	C₂²	semidirect
96. #4031	C₂²	semidirect
97. #4031	C₂²	semidirect
98. #4031	C₂²	semidirect
100. #4030	C₂²	semidirect
101. #4030	C₂²	semidirect
102. #4029	C₂²	semidirect
105. #4027	C₂²	semidirect
106. #4027	C₂²	semidirect
107. #4027	C₂²	semidirect
108. D₅×C₂²⋊C₄	C₂²	semidirect
109. D₅×C₂²⋊C₄	C₂²	semidirect
110. D₅×C₂²⋊C₄	C₂²	semidirect
111. #4025	C₂²	semidirect
112. #4023	C₂²	semidirect
113. #4023	C₂²	semidirect
114. #4023	C₂²	semidirect
115. #4022	C₂²	semidirect
117. C₄×D₂₀	C₂²	semidirect
118. C₄×D₂₀	C₂²	semidirect
119. #4018	C₂²	semidirect
120. #4018	C₂²	semidirect
121. C₄²×D₅	C₂²	semidirect
122. C₄×Dic₁₀	C₂²	semidirect
238. #548	D₅	semidirect
291. C₂²⋊D₅	#41	semidirect
322. C₂×#41	C₂×D₅	semidirect
324. C₂²×Q₈	C₂×D₅	semidirect
349. #124	C₂×D₅	semidirect
350. #124	C₂×D₅	semidirect
364. C₂²⋊Q₈	C₂×D₅	semidirect
365. C₂²⋊Q₈	C₂×D₅	semidirect
375. #121	C₂×D₅	semidirect
384. C₄×Q₈	C₂×D₅	semidirect
401. C₄×D₄	C₂×D₅	semidirect
402. C₄×D₄	C₂×D₅	semidirect
639. C₅	#3514	semidirect

Maximal subgroups

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

subgroup	index
C₅×#548	2
#66166	2
#66163	2
Q₈×C₂²⋊D₅	2
C₂×#4093	2
#66015	2
#66012	2
D₅×#124	2
#66004	2
#65974	2
#65971	2
#65967	2
#65958	2
#65951	2
#65944	2
#65943	2
#65934	2
#65914	2
#65902	2
#65890	2
#65884	2
#65879	2
C₄×#711	2
#3514	5