Subgroups — #10618622

Order 640.

1124 conjugacy classes of subgroups.

The subgroup lattice has 686 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	#66162	C₂	1	1	yes	maximal, characteristic, complemented
3	#66158	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#4092	C₂	1	1	yes	maximal, characteristic, complemented
6	#66014	C₂	1	1	yes	maximal, characteristic, complemented
7	#66013	C₂	1	2	yes	maximal, complemented
8	#66011	C₂	1	1	yes	maximal, characteristic, complemented
9	#66003	C₂	1	2	yes	maximal, complemented
10	#65975	C₂	1	1	yes	maximal, characteristic, complemented
11	#65972	C₂	1	2	yes	maximal, complemented
12	#65970	C₂	1	2	yes	maximal, complemented
13	D₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
14	#65945	C₂	1	1	yes	maximal, characteristic, complemented
15	#65944	C₂	1	2	yes	maximal, complemented
16	#65940	C₂	1	1	yes	maximal, characteristic, complemented
17	#65936	C₂	1	2	yes	maximal, complemented
18	#65915	C₂	1	1	yes	maximal, characteristic, complemented
19	#65912	C₂	1	1	yes	maximal, characteristic, complemented
20	#65890	C₂	1	2	yes	maximal, complemented
21	#65880	C₂	1	2	yes	maximal, complemented
22	C₄×D₄×D₅	C₂	1	1	yes	maximal, characteristic, complemented
23	#65875	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	2	yes	—
28	C₂×#711	C₂²	1	1	yes	characteristic, complemented
29	C₂×D₄×D₅	C₂²	1	1	yes	characteristic
30	C₂²×C₄×D₅	C₂²	1	1	yes	characteristic
31	C₂²×C₄×D₅	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	2	yes	—
37	C₅×#121	C₂²	1	1	yes	characteristic, complemented
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	2	yes	complemented
41	#4092	C₂²	1	1	yes	characteristic
42	#4092	C₂²	1	1	yes	characteristic
43	#4092	C₂²	1	2	yes	—
44	#4092	C₂²	1	1	yes	characteristic, complemented
45	#4092	C₂²	1	2	yes	complemented
46	#4092	C₂²	1	1	yes	characteristic, 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	#4085	C₂²	1	2	yes	—
53	#4084	C₂²	1	1	yes	characteristic
54	#4084	C₂²	1	1	yes	characteristic, complemented
55	#4083	C₂²	1	2	yes	—
56	#4083	C₂²	1	2	yes	—
57	#4081	C₂²	1	2	yes	—
58	#4081	C₂²	1	2	yes	complemented
59	#4081	C₂²	1	2	yes	complemented
60	#4081	C₂²	1	2	yes	complemented
61	D₄×Dic₅	C₂²	1	1	yes	characteristic
62	D₄×Dic₅	C₂²	1	2	yes	complemented
63	D₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
64	#4075	C₂²	1	2	yes	complemented
65	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
66	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
67	C₄×C₂²⋊D₅	C₂²	1	2	yes	—
68	C₄×C₂²⋊D₅	C₂²	1	2	yes	—
69	C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
70	C₂×#685	C₂²	1	2	yes	—
71	#4072	C₂²	1	1	yes	characteristic, complemented
72	C₂×C₄⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
73	#4070	C₂²	1	1	yes	characteristic, complemented
74	#4070	C₂²	1	1	yes	characteristic, complemented
75	#4070	C₂²	1	2	yes	complemented
76	C₂×#683	C₂²	1	2	yes	complemented
77	C₂×#683	C₂²	1	2	yes	complemented
78	#4044	C₂²	1	2	yes	complemented
79	#4043	C₂²	1	1	yes	characteristic
80	#4042	C₂²	1	2	yes	—
81	#4042	C₂²	1	2	yes	—
82	#4040	C₂²	1	2	yes	—
83	#4039	C₂²	1	1	yes	characteristic
84	#4038	C₂²	1	1	yes	characteristic, complemented
85	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
86	D₅×C₄⋊C₄	C₂²	1	2	yes	complemented
87	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
88	#4035	C₂²	1	2	yes	complemented
89	#4035	C₂²	1	2	yes	complemented
90	#4035	C₂²	1	2	yes	complemented
91	#4034	C₂²	1	1	yes	characteristic, complemented
92	#4033	C₂²	1	2	yes	complemented
93	#4031	C₂²	1	2	yes	—
94	#4031	C₂²	1	2	yes	complemented
95	#4030	C₂²	1	2	yes	—
96	#4029	C₂²	1	2	yes	—
97	#4029	C₂²	1	2	yes	complemented
98	#4029	C₂²	1	2	yes	complemented
99	#4027	C₂²	1	1	yes	characteristic
100	#4027	C₂²	1	1	yes	characteristic
101	#4027	C₂²	1	2	yes	—
102	#4027	C₂²	1	2	yes	—
103	#4027	C₂²	1	2	yes	complemented
104	D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
105	D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
106	D₅×C₂²⋊C₄	C₂²	1	2	yes	—
107	#4025	C₂²	1	2	yes	complemented
108	#4025	C₂²	1	2	yes	complemented
109	#4025	C₂²	1	2	yes	complemented
110	#4024	C₂²	1	2	yes	complemented
111	#4024	C₂²	1	2	yes	complemented
112	#4024	C₂²	1	2	yes	complemented
113	#4023	C₂²	1	2	yes	complemented
114	#4023	C₂²	1	2	yes	complemented
115	#4022	C₂²	1	2	yes	complemented
116	C₄×D₂₀	C₂²	1	1	yes	characteristic
117	#4018	C₂²	1	2	yes	—
118	#4018	C₂²	1	2	yes	complemented
119	C₄²×D₅	C₂²	1	1	yes	characteristic
120	#4016	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₁₀	C₂²	1	2	yes	complemented
123	#3520	—	5	1	no	maximal, Sylow
124	C₂³×D₅	C₂³	1	1	yes	characteristic
125	C₂³×D₅	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
132	C₂×C₅×D₄	C₂³	1	2	yes	—
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	1	yes	characteristic
140	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
144	C₂²×Dic₅	C₂³	1	2	yes	—
145	C₂²×Dic₅	C₂³	1	2	yes	—
146	C₂²×Dic₅	C₂³	1	1	yes	characteristic
147	C₂²×Dic₅	C₂³	1	1	yes	characteristic
148	C₂²×Dic₅	C₂³	1	2	yes	—
149	Q₈×D₅	—	4	2	no	—
150	#711	—	2	8	no	—
151	#711	—	4	2	no	—
152	D₄×D₅	—	2	4	no	—
153	C₂×D₂₀	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₅	—	4	2	no	—
155	C₂×C₄×D₅	—	4	2	no	—
156	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
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	2	yes	—
161	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
162	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
163	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
164	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
165	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
166	C₂×C₄×D₅	C₂³	1	2	yes	—
167	C₂×Dic₁₀	C₂³	1	2	yes	—
168	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
169	C₂×Dic₁₀	C₂³	1	2	yes	—
170	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₅×C₄⋊C₄	C₂³	1	2	yes	—
172	C₅×C₄⋊C₄	C₂³	1	2	yes	—
173	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
174	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
175	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
176	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
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	C₄²×C₅	C₂³	1	1	yes	characteristic
181	C₄²×C₅	C₂³	1	2	yes	—
182	C₂²⋊Dic₅	C₂³	1	2	yes	—
183	C₂²⋊Dic₅	C₂³	1	2	yes	—
184	C₂²⋊Dic₅	C₂³	1	2	yes	—
185	C₂²⋊Dic₅	C₂³	1	2	yes	—
186	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
187	C₂²⋊Dic₅	C₂³	1	2	yes	—
188	C₂²⋊Dic₅	C₂³	1	2	yes	—
189	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
190	#685	C₂³	1	2	yes	—
191	#685	C₂³	1	2	yes	—
192	#685	C₂³	1	1	yes	characteristic
193	#685	C₂³	1	2	yes	—
194	#685	C₂³	1	1	yes	characteristic
195	#685	C₂³	1	2	yes	—
196	#685	C₂³	1	2	yes	—
197	#685	C₂³	1	2	yes	—
198	#685	C₂³	1	1	yes	characteristic
199	#685	C₂³	1	1	yes	characteristic
200	#685	C₂³	1	2	yes	—
201	C₄⋊Dic₅	C₂³	1	2	yes	—
202	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
203	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
204	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
205	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
206	C₄⋊Dic₅	C₂³	1	2	yes	—
207	C₄⋊Dic₅	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	#683	C₂³	1	2	yes	—
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	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	2	yes	—
229	C₄×Dic₅	C₂³	1	2	yes	—
230	C₄×Dic₅	C₂³	1	2	yes	—
231	#556	—	5	1	no	—
232	#554	—	5	2	no	—
233	#552	—	5	1	no	—
234	#552	—	5	1	no	—
235	#551	—	5	2	no	—
236	#551	—	5	2	no	—
237	D₄×Q₈	—	5	1	no	—
238	#548	—	5	1	no	—
239	#548	D₅	1	1	yes	characteristic, complemented
240	#547	—	5	1	no	—
241	#547	—	5	1	no	—
242	#546	—	5	2	no	—
243	#542	—	5	2	no	—
244	#539	—	5	2	no	—
245	#539	—	5	2	no	—
246	#533	—	5	1	no	—
247	#529	—	5	1	no	—
248	#525	—	5	1	no	—
249	#525	—	5	1	no	—
250	C₂×C₂²⋊Q₈	—	5	1	no	—
251	C₂×C₂²⋊Q₈	—	5	1	no	—
252	#520	—	5	2	no	—
253	C₂×C₄×D₄	—	5	1	no	—
254	C₂³×C₅	C₂⁴	1	1	yes	characteristic
255	C₂³×C₅	C₂⁴	1	2	yes	—
256	C₂³×C₅	C₂⁴	1	1	yes	characteristic
257	C₂²×D₅	—	2	2	no	—
258	C₂²×D₅	—	2	2	no	—
259	C₂²×D₅	—	2	2	no	—
260	C₂²×D₅	—	2	2	no	—
261	C₂²×D₅	—	4	1	no	—
262	C₂²×D₅	—	4	1	no	—
263	C₂²×D₅	C₂⁴	1	1	yes	characteristic
264	C₂²×D₅	C₂⁴	1	1	yes	characteristic
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	2	no	—
270	C₅×D₄	—	2	4	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	1	yes	characteristic
280	C₂×C₄×C₅	C₂⁴	1	2	yes	—
281	C₂×C₄×C₅	C₂⁴	1	2	yes	—
282	C₂×C₄×C₅	C₂⁴	1	2	yes	—
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	—	2	2	no	—
288	C₂²⋊D₅	—	4	2	no	—
289	C₂²⋊D₅	#41	1	4	yes	complemented
290	C₂×Dic₅	—	2	4	no	—
291	C₂×Dic₅	—	2	4	no	—
292	C₂×Dic₅	—	4	1	no	—
293	C₂×Dic₅	—	4	1	no	—
294	C₂×Dic₅	—	4	2	no	—
295	C₂×Dic₅	C₂⁴	1	2	yes	—
296	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
297	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
298	C₂×Dic₅	C₂⁴	1	2	yes	—
299	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
300	C₂×Dic₅	C₂⁴	1	2	yes	—
301	C₂×Dic₅	C₂⁴	1	2	yes	—
302	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
303	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
304	D₂₀	—	2	2	no	—
305	C₄×D₅	—	2	4	no	—
306	C₄×D₅	—	2	2	no	—
307	C₄×D₅	—	2	2	no	—
308	C₄×D₅	—	2	2	no	—
309	C₄×D₅	—	2	2	no	—
310	C₄×D₅	—	2	2	no	—
311	C₄×D₅	—	4	1	no	—
312	C₄×D₅	—	4	1	no	—
313	C₄×D₅	—	4	1	no	—
314	C₄×D₅	—	4	1	no	—
315	C₄×D₅	—	4	2	no	—
316	Dic₁₀	—	2	2	no	—
317	Dic₁₀	—	2	4	no	—
318	Dic₁₀	—	4	2	no	—
319	C₂×#41	—	5	2	no	—
320	C₂×#41	—	5	1	no	—
321	C₂×#41	C₂×D₅	1	1	yes	characteristic, complemented
322	C₂²×Q₈	—	5	1	no	—
323	C₂²×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
324	C₂²×D₄	—	5	1	no	—
325	C₂³×C₄	—	5	1	no	—
326	C₂³×C₄	—	5	1	no	—
327	C₄⋊Q₈	—	5	1	no	—
328	C₄⋊Q₈	—	5	2	no	—
329	C₄⋊Q₈	—	5	1	no	—
330	#126	—	5	2	no	—
331	#126	—	5	2	no	—
332	#126	—	5	2	no	—
333	#126	—	5	2	no	—
334	#126	—	5	2	no	—
335	#125	—	5	2	no	—
336	#125	—	5	2	no	—
337	#125	—	5	2	no	—
338	#125	—	5	1	no	—
339	#124	—	5	2	no	—
340	#124	—	5	2	no	—
341	#124	C₂×D₅	1	1	yes	characteristic, complemented
342	#124	C₂×D₅	1	2	yes	complemented
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	—	5	2	no	—
351	#123	—	5	2	no	—
352	C₂²⋊Q₈	—	5	1	no	—
353	C₂²⋊Q₈	—	5	1	no	—
354	C₂²⋊Q₈	—	5	2	no	—
355	C₂²⋊Q₈	—	5	1	no	—
356	C₂²⋊Q₈	—	5	1	no	—
357	C₂²⋊Q₈	—	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	1	no	—
362	C₂²⋊Q₈	—	5	2	no	—
363	C₂²⋊Q₈	—	5	1	no	—
364	C₂²⋊Q₈	—	5	2	no	—
365	C₂²⋊Q₈	—	5	2	no	—
366	C₂²⋊Q₈	—	5	2	no	—
367	C₂²⋊Q₈	—	5	2	no	—
368	C₂²⋊Q₈	—	5	2	no	—
369	C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
370	C₂²⋊Q₈	C₂×D₅	1	2	yes	complemented
371	#121	—	5	1	no	—
372	#121	—	5	1	no	—
373	#121	—	5	2	no	—
374	#121	—	5	2	no	—
375	#121	C₂×D₅	1	2	yes	—
376	#121	C₂×D₅	1	1	yes	characteristic, complemented
377	#120	—	5	2	no	—
378	#120	—	5	2	no	—
379	C₄×Q₈	—	5	1	no	—
380	C₄×Q₈	—	5	2	no	—
381	C₄×Q₈	—	5	2	no	—
382	C₄×Q₈	—	5	1	no	—
383	C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
384	C₄×D₄	—	5	1	no	—
385	C₄×D₄	—	5	2	no	—
386	C₄×D₄	—	5	1	no	—
387	C₄×D₄	—	5	1	no	—
388	C₄×D₄	—	5	1	no	—
389	C₄×D₄	—	5	2	no	—
390	C₄×D₄	—	5	2	no	—
391	C₄×D₄	—	5	2	no	—
392	C₄×D₄	—	5	1	no	—
393	C₄×D₄	—	5	1	no	—
394	C₄×D₄	—	5	1	no	—
395	C₄×D₄	—	5	2	no	—
396	C₄×D₄	—	5	2	no	—
397	C₄×D₄	—	5	2	no	—
398	C₄×D₄	—	5	1	no	—
399	C₄×D₄	C₂×D₅	1	1	yes	characteristic
400	C₄×D₄	C₂×D₅	1	2	yes	complemented
401	#117	—	5	1	no	—
402	#117	—	5	1	no	—
403	#117	—	5	2	no	—
404	#117	—	5	2	no	—
405	#117	—	5	2	no	—
406	#117	—	5	2	no	—
407	C₂×C₄⋊C₄	—	5	2	no	—
408	C₂×C₄⋊C₄	—	5	2	no	—
409	C₂×C₄⋊C₄	—	5	1	no	—
410	C₂×C₄⋊C₄	—	5	1	no	—
411	C₂×C₄⋊C₄	—	5	2	no	—
412	C₂×C₄⋊C₄	—	5	1	no	—
413	C₂×C₂²⋊C₄	—	5	2	no	—
414	C₂×C₂²⋊C₄	—	5	1	no	—
415	C₂×C₂²⋊C₄	—	5	1	no	—
416	C₂×C₂²⋊C₄	—	5	2	no	—
417	C₂×C₄²	—	5	1	no	—
418	C₂²×C₅	—	2	1	no	—
419	C₂²×C₅	—	2	1	no	—
420	C₂²×C₅	—	2	2	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	C₂×#41	1	2	yes	—
427	C₂²×C₅	C₂⁵	1	1	yes	characteristic
428	C₂×D₅	—	2	1	no	—
429	C₂×D₅	—	2	1	no	—
430	C₂×D₅	—	2	1	no	—
431	C₂×D₅	—	2	1	no	—
432	C₂×D₅	—	2	1	no	—
433	C₂×D₅	—	2	1	no	—
434	C₂×D₅	—	2	1	no	—
435	C₂×D₅	—	4	4	no	—
436	C₂×D₅	—	4	4	no	—
437	C₂×D₅	C₂×#41	1	2	yes	—
438	C₂×D₅	2₋¹⁺⁴	1	2	yes	—
439	C₄×C₅	—	2	2	no	—
440	C₄×C₅	—	2	1	no	—
441	C₄×C₅	—	2	2	no	—
442	C₄×C₅	—	2	1	no	—
443	C₄×C₅	—	2	1	no	—
444	C₄×C₅	—	2	2	no	—
445	C₄×C₅	—	2	1	no	—
446	C₄×C₅	H(5,𝔽₂)	1	2	yes	—
447	Dic₅	—	2	2	no	—
448	Dic₅	—	2	2	no	—
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	2	no	—
455	Dic₅	C₂×#41	1	2	yes	—
456	C₂⁴	—	5	1	no	—
457	C₂⁴	—	5	1	no	—
458	#41	—	4	2	no	—
459	#41	—	10	8	no	—
460	#41	—	20	2	no	—
461	C₂×Q₈	—	4	2	no	—
462	C₂×Q₈	—	5	2	no	—
463	C₂×Q₈	—	5	1	no	—
464	C₂×Q₈	—	5	2	no	—
465	C₂×Q₈	—	20	2	no	—
466	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
467	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
468	C₂×Q₈	C₂²×D₅	1	2	yes	—
469	C₂×D₄	—	5	1	no	—
470	C₂×D₄	—	5	2	no	—
471	C₂×D₄	—	5	2	no	—
472	C₂×D₄	—	5	1	no	—
473	C₂×D₄	—	5	2	no	—
474	C₂×D₄	—	5	1	no	—
475	C₂×D₄	—	10	4	no	—
476	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
477	C₂×D₄	C₂²×D₅	1	2	yes	—
478	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
479	C₂×D₄	C₂²×D₅	1	2	yes	—
480	C₂²×C₄	—	5	2	no	—
481	C₂²×C₄	—	5	2	no	—
482	C₂²×C₄	—	5	1	no	—
483	C₂²×C₄	—	5	2	no	—
484	C₂²×C₄	—	5	1	no	—
485	C₂²×C₄	—	5	1	no	—
486	C₂²×C₄	—	5	1	no	—
487	C₂²×C₄	—	5	1	no	—
488	C₂²×C₄	—	5	2	no	—
489	C₂²×C₄	—	5	1	no	—
490	C₂²×C₄	—	5	1	no	—
491	C₂²×C₄	—	5	2	no	—
492	C₂²×C₄	—	5	1	no	—
493	C₂²×C₄	—	5	1	no	—
494	C₂²×C₄	—	5	1	no	—
495	C₂²×C₄	—	5	1	no	—
496	C₂²×C₄	—	20	2	no	—
497	C₂²×C₄	—	20	2	no	—
498	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
499	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
500	C₂²×C₄	C₂²×D₅	1	2	yes	—
501	C₂²×C₄	C₂²×D₅	1	2	yes	—
502	C₄⋊C₄	—	5	1	no	—
503	C₄⋊C₄	—	5	2	no	—
504	C₄⋊C₄	—	5	2	no	—
505	C₄⋊C₄	—	5	2	no	—
506	C₄⋊C₄	—	5	1	no	—
507	C₄⋊C₄	—	5	1	no	—
508	C₄⋊C₄	—	5	1	no	—
509	C₄⋊C₄	—	5	1	no	—
510	C₄⋊C₄	—	5	2	no	—
511	C₄⋊C₄	—	5	2	no	—
512	C₄⋊C₄	—	5	2	no	—
513	C₄⋊C₄	—	5	2	no	—
514	C₄⋊C₄	—	5	2	no	—
515	C₄⋊C₄	—	5	2	no	—
516	C₄⋊C₄	—	5	2	no	—
517	C₄⋊C₄	—	5	1	no	—
518	C₄⋊C₄	—	5	2	no	—
519	C₄⋊C₄	—	5	2	no	—
520	C₄⋊C₄	—	5	2	no	—
521	C₄⋊C₄	—	5	2	no	—
522	C₄⋊C₄	—	5	2	no	—
523	C₄⋊C₄	—	5	2	no	—
524	C₄⋊C₄	—	5	2	no	—
525	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
526	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
527	C₄⋊C₄	C₂²×D₅	1	2	yes	—
528	C₄⋊C₄	C₂²×D₅	1	2	yes	—
529	C₂²⋊C₄	—	5	1	no	—
530	C₂²⋊C₄	—	5	1	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	1	no	—
539	C₂²⋊C₄	—	5	2	no	—
540	C₂²⋊C₄	—	5	2	no	—
541	C₂²⋊C₄	—	5	1	no	—
542	C₂²⋊C₄	—	5	1	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	C₂²×D₅	1	1	yes	characteristic
549	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
550	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
551	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
552	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
553	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
554	C₄²	—	5	1	no	—
555	C₄²	—	5	1	no	—
556	C₄²	—	5	1	no	—
557	C₄²	—	5	2	no	—
558	C₄²	—	5	2	no	—
559	C₄²	—	5	2	no	—
560	C₄²	—	5	2	no	—
561	C₄²	C₂²×D₅	1	1	yes	characteristic
562	C₄²	C₂²×D₅	1	2	yes	—
563	C₂×C₅	—	2	2	no	—
564	C₂×C₅	—	4	1	no	—
565	C₂×C₅	—	4	2	no	—
566	C₂×C₅	C₂²×#41	1	1	yes	characteristic
567	C₂×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
568	C₂×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
569	D₅	—	2	2	no	—
570	D₅	—	2	2	no	—
571	D₅	—	4	1	no	—
572	C₂³	—	5	1	no	—
573	C₂³	—	5	1	no	—
574	C₂³	—	5	1	no	—
575	C₂³	—	10	2	no	—
576	C₂³	—	10	2	no	—
577	C₂³	—	10	2	no	—
578	C₂³	—	10	2	no	—
579	C₂³	—	20	1	no	—
580	C₂³	—	20	1	no	—
581	C₂³	C₂³×D₅	1	1	yes	characteristic
582	C₂³	C₂³×D₅	1	2	yes	—
583	C₂³	C₂³×D₅	1	1	yes	characteristic
584	Q₈	—	2	2	no	—
585	Q₈	—	2	2	no	—
586	Q₈	—	4	2	no	—
587	Q₈	—	10	4	no	—
588	Q₈	—	10	2	no	—
589	Q₈	—	20	2	no	—
590	D₄	—	2	2	no	—
591	D₄	—	2	4	no	—
592	D₄	—	2	2	no	—
593	D₄	—	4	2	no	—
594	D₄	—	5	4	no	—
595	D₄	—	10	2	no	—
596	D₄	—	10	2	no	—
597	D₄	—	10	4	no	—
598	D₄	—	10	4	no	—
599	D₄	—	20	2	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	4	2	no	—
603	C₂×C₄	—	4	2	no	—
604	C₂×C₄	—	5	1	no	—
605	C₂×C₄	—	5	2	no	—
606	C₂×C₄	—	5	1	no	—
607	C₂×C₄	—	5	2	no	—
608	C₂×C₄	—	5	1	no	—
609	C₂×C₄	—	5	1	no	—
610	C₂×C₄	—	5	2	no	—
611	C₂×C₄	—	5	2	no	—
612	C₂×C₄	—	5	1	no	—
613	C₂×C₄	—	10	2	no	—
614	C₂×C₄	—	10	4	no	—
615	C₂×C₄	—	10	2	no	—
616	C₂×C₄	—	10	4	no	—
617	C₂×C₄	—	10	4	no	—
618	C₂×C₄	—	10	2	no	—
619	C₂×C₄	—	10	2	no	—
620	C₂×C₄	—	10	2	no	—
621	C₂×C₄	—	20	1	no	—
622	C₂×C₄	—	20	1	no	—
623	C₂×C₄	—	20	1	no	—
624	C₂×C₄	—	20	1	no	—
625	C₂×C₄	—	20	2	no	—
626	C₂×C₄	—	20	1	no	—
627	C₂×C₄	—	20	1	no	—
628	C₂×C₄	—	20	2	no	—
629	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
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	#3520	1	1	yes	characteristic, complemented, Sylow
638	C₂²	—	2	1	no	—
639	C₂²	—	2	1	no	—
640	C₂²	—	2	1	no	—
641	C₂²	—	2	2	no	—
642	C₂²	—	2	2	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	2	1	no	—
646	C₂²	—	5	2	no	—
647	C₂²	—	5	2	no	—
648	C₂²	—	10	1	no	—
649	C₂²	—	10	1	no	—
650	C₂²	—	10	1	no	—
651	C₂²	—	10	1	no	—
652	C₂²	—	10	1	no	—
653	C₂²	—	10	1	no	—
654	C₂²	—	10	1	no	—
655	C₂²	—	20	4	no	—
656	C₂²	—	20	4	no	—
657	C₂²	D₅×#41	1	2	yes	—
658	C₂²	C₂⁴×D₅	1	1	yes	characteristic
659	C₄	—	2	1	no	—
660	C₄	—	2	1	no	—
661	C₄	—	2	2	no	—
662	C₄	—	2	2	no	—
663	C₄	—	2	1	no	—
664	C₄	—	2	2	no	—
665	C₄	—	2	1	no	—
666	C₄	—	5	2	no	—
667	C₄	—	10	1	no	—
668	C₄	—	10	1	no	—
669	C₄	—	10	1	no	—
670	C₄	—	10	2	no	—
671	C₄	—	10	2	no	—
672	C₄	—	10	2	no	—
673	C₄	—	10	1	no	—
674	C₄	—	10	2	no	—
675	C₄	#4144	1	2	yes	—
676	C₂	—	2	2	no	—
677	C₂	—	4	1	no	—
678	C₂	—	4	2	no	—
679	C₂	—	10	2	no	—
680	C₂	—	10	2	no	—
681	C₂	—	20	1	no	—
682	C₂	C₂×#4144	1	1	yes	characteristic
683	C₂	C₂×D₅×#41	1	1	yes	characteristic
684	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×#548	C₂
hypercenter	#548	D₅
hypocenter	C₅	#3520
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. #66162	C₂	semidirect
3. #66158	C₂	semidirect
4. Q₈×C₂²⋊D₅	C₂	semidirect
5. C₂×#4092	C₂	semidirect
6. #66014	C₂	semidirect
7. #66013	C₂	semidirect
8. #66011	C₂	semidirect
9. #66003	C₂	semidirect
10. #65975	C₂	semidirect
11. #65972	C₂	semidirect
12. #65970	C₂	semidirect
13. D₅×C₂²⋊Q₈	C₂	semidirect
14. #65945	C₂	semidirect
15. #65944	C₂	semidirect
16. #65940	C₂	semidirect
17. #65936	C₂	semidirect
18. #65915	C₂	semidirect
19. #65912	C₂	semidirect
20. #65890	C₂	semidirect
21. #65880	C₂	semidirect
22. C₄×D₄×D₅	C₂	semidirect
23. #65875	C₂	semidirect
24. C₂×C₅×#41	C₂²	semidirect
25. C₂²×C₅×Q₈	C₂²	semidirect
26. C₂×Q₈×D₅	C₂²	semidirect
28. C₂×#711	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
40. C₄×C₅×D₄	C₂²	semidirect
44. #4092	C₂²	semidirect
45. #4092	C₂²	semidirect
46. #4092	C₂²	semidirect
47. #4092	C₂²	semidirect
48. #4092	C₂²	semidirect
49. Q₈×Dic₅	C₂²	semidirect
50. #4090	C₂²	semidirect
51. #4090	C₂²	semidirect
54. #4084	C₂²	semidirect
58. #4081	C₂²	semidirect
59. #4081	C₂²	semidirect
60. #4081	C₂²	semidirect
62. D₄×Dic₅	C₂²	semidirect
63. D₄×Dic₅	C₂²	semidirect
64. #4075	C₂²	semidirect
69. C₄×C₂²⋊D₅	C₂²	semidirect
71. #4072	C₂²	semidirect
72. C₂×C₄⋊Dic₅	C₂²	semidirect
73. #4070	C₂²	semidirect
74. #4070	C₂²	semidirect
75. #4070	C₂²	semidirect
76. C₂×#683	C₂²	semidirect
77. C₂×#683	C₂²	semidirect
78. #4044	C₂²	semidirect
84. #4038	C₂²	semidirect
86. D₅×C₄⋊C₄	C₂²	semidirect
87. D₅×C₄⋊C₄	C₂²	semidirect
88. #4035	C₂²	semidirect
89. #4035	C₂²	semidirect
90. #4035	C₂²	semidirect
91. #4034	C₂²	semidirect
92. #4033	C₂²	semidirect
94. #4031	C₂²	semidirect
97. #4029	C₂²	semidirect
98. #4029	C₂²	semidirect
103. #4027	C₂²	semidirect
107. #4025	C₂²	semidirect
108. #4025	C₂²	semidirect
109. #4025	C₂²	semidirect
110. #4024	C₂²	semidirect
111. #4024	C₂²	semidirect
112. #4024	C₂²	semidirect
113. #4023	C₂²	semidirect
114. #4023	C₂²	semidirect
115. #4022	C₂²	semidirect
118. #4018	C₂²	semidirect
120. #4016	C₂²	semidirect
121. C₄×Dic₁₀	C₂²	semidirect
122. C₄×Dic₁₀	C₂²	semidirect
239. #548	D₅	semidirect
289. C₂²⋊D₅	#41	semidirect
321. C₂×#41	C₂×D₅	semidirect
323. C₂²×Q₈	C₂×D₅	semidirect
341. #124	C₂×D₅	semidirect
342. #124	C₂×D₅	semidirect
369. C₂²⋊Q₈	C₂×D₅	semidirect
370. C₂²⋊Q₈	C₂×D₅	semidirect
376. #121	C₂×D₅	semidirect
383. C₄×Q₈	C₂×D₅	semidirect
400. C₄×D₄	C₂×D₅	semidirect
637. C₅	#3520	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
#66162	2
#66158	2
Q₈×C₂²⋊D₅	2
C₂×#4092	2
#66014	2
#66013	2
#66011	2
#66003	2
#65975	2
#65972	2
#65970	2
D₅×C₂²⋊Q₈	2
#65945	2
#65944	2
#65940	2
#65936	2
#65915	2
#65912	2
#65890	2
#65880	2
C₄×D₄×D₅	2
#65875	2
#3520	5