Subgroups — #13033939

Order 1280.

886 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	#10617128	C₂	1	1	yes	maximal, characteristic
2	D₅⋊#433	C₂	1	1	yes	maximal, characteristic
3	D₅×#433	C₂	1	1	yes	maximal, characteristic
4	#10604035	C₂	1	1	yes	maximal, characteristic, complemented
5	#10604035	C₂	1	1	yes	maximal, characteristic, complemented
6	#10604034	C₂	1	1	yes	maximal, characteristic, complemented
7	#10604033	C₂	1	1	yes	maximal, characteristic, complemented
8	#10603909	C₂	1	1	yes	maximal, characteristic
9	#10603909	C₂	1	1	yes	maximal, characteristic
10	#10603908	C₂	1	1	yes	maximal, characteristic
11	AGL(1,𝔽₅)×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
12	#10603880	C₂	1	1	yes	maximal, characteristic, complemented
13	#10603880	C₂	1	1	yes	maximal, characteristic, complemented
14	#10603842	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×C₄⋊AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#4130	C₂²	1	1	yes	characteristic
17	C₂²×C₄×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
18	D₅×#117	C₂²	1	1	yes	characteristic
19	D₅⋊(C₂²⋊C₈)	C₂²	1	1	yes	characteristic
20	D₅⋊(C₂²⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×#3992	C₂²	1	1	yes	characteristic
22	C₂×#3992	C₂²	1	1	yes	characteristic
23	C₂×#3992	C₂²	1	1	yes	characteristic
24	C₂×#3992	C₂²	1	1	yes	characteristic
25	C₂×C₈×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
26	C₂×C₈×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
27	C₂×C₈×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
28	C₂×C₈×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
29	#65712	C₄	1	2	yes	—
30	#65712	C₄	1	2	yes	—
31	#65706	C₄	1	2	yes	complemented
32	#65706	C₄	1	2	yes	complemented
33	#65699	C₄	1	2	yes	—
34	#65699	C₄	1	2	yes	—
35	#65697	C₄	1	2	yes	complemented
36	#65697	C₄	1	2	yes	complemented
37	C₄×C₄⋊AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
41	D₅⋊(C₄⋊C₈)	C₂²	1	1	yes	characteristic
42	D₅⋊(C₄⋊C₈)	C₂²	1	1	yes	characteristic
43	#65676	C₂²	1	1	yes	characteristic
44	C₄×D₅⋊C₈	C₂²	1	1	yes	characteristic
45	C₅×#433	C₄	1	1	yes	characteristic, complemented
46	#65289	C₄	1	1	yes	characteristic, complemented
47	#65129	C₄	1	1	yes	characteristic, complemented
48	#65129	C₄	1	1	yes	characteristic, complemented
49	D₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
50	D₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
51	D₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
52	D₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
53	#65009	C₄	1	1	yes	characteristic, complemented
54	#65009	C₄	1	1	yes	characteristic, complemented
55	#64998	C₄	1	1	yes	characteristic, complemented
56	D₅×#97	C₂²	1	1	yes	characteristic
57	#64979	C₄	1	1	yes	characteristic, complemented
58	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
59	(C₂×AGL(1,𝔽₅))⋊C₈	C₂²	1	1	yes	characteristic
60	(C₂×AGL(1,𝔽₅))⋊C₈	C₂²	1	1	yes	characteristic
61	(C₂×AGL(1,𝔽₅))⋊C₈	C₂²	1	1	yes	characteristic
62	(C₂×AGL(1,𝔽₅))⋊C₈	C₂²	1	1	yes	characteristic
63	(C₂×AGL(1,𝔽₅))⋊C₈	C₂²	1	1	yes	characteristic
64	(C₂×AGL(1,𝔽₅))⋊C₈	C₂²	1	1	yes	characteristic
65	(C₂×AGL(1,𝔽₅))⋊C₈	C₂²	1	1	yes	characteristic
66	(C₂×AGL(1,𝔽₅))⋊C₈	C₂²	1	1	yes	characteristic
67	#20541	—	5	1	no	maximal, Sylow
68	C₂³×AGL(1,𝔽₅)	C₂×C₄	1	2	yes	—
69	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
70	C₂×C₂²⋊AGL(1,𝔽₅)	C₂×C₄	1	2	yes	—
71	#4130	—	4	1	no	—
72	#4130	—	4	1	no	—
73	C₂×C₄⋊AGL(1,𝔽₅)	C₂×C₄	1	2	yes	—
74	C₂×C₄⋊AGL(1,𝔽₅)	C₂×C₄	1	2	yes	—
75	C₂×C₄⋊AGL(1,𝔽₅)	C₂×C₄	1	2	yes	—
76	C₂×C₄⋊AGL(1,𝔽₅)	C₂×C₄	1	2	yes	—
77	C₂×C₄⋊AGL(1,𝔽₅)	C₂×C₄	1	2	yes	—
78	C₂×C₄×AGL(1,𝔽₅)	—	4	1	no	—
79	C₂×C₄×AGL(1,𝔽₅)	—	4	1	no	—
80	C₂×C₄×AGL(1,𝔽₅)	C₂×C₄	1	2	yes	—
81	C₂×C₄×AGL(1,𝔽₅)	C₂³	1	1	yes	characteristic
82	C₂×C₄×AGL(1,𝔽₅)	C₂³	1	1	yes	characteristic
83	C₂×C₄×AGL(1,𝔽₅)	C₂³	1	1	yes	characteristic
84	C₂×C₄×AGL(1,𝔽₅)	C₂³	1	1	yes	characteristic
85	C₂×D₅⋊C₈	C₂³	1	1	yes	characteristic
86	C₂×D₅⋊C₈	C₂³	1	1	yes	characteristic
87	C₂×D₅⋊C₈	C₂³	1	1	yes	characteristic
88	C₂×D₅⋊C₈	C₂³	1	1	yes	characteristic
89	C₅×#117	C₂×C₄	1	1	yes	characteristic
90	#4072	C₂×C₄	1	1	yes	characteristic
91	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
92	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
93	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
94	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
95	#4038	C₂×C₄	1	1	yes	characteristic
96	#4038	C₂×C₄	1	1	yes	characteristic
97	D₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
98	D₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
99	D₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
100	D₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
101	#4023	C₂×C₄	1	1	yes	characteristic
102	#4023	C₂×C₄	1	1	yes	characteristic
103	#4018	C₂×C₄	1	1	yes	characteristic
104	#4018	C₂×C₄	1	1	yes	characteristic
105	C₄²×D₅	C₂³	1	1	yes	characteristic
106	C₄²×D₅	C₂³	1	1	yes	characteristic
107	C₂²⋊#170	C₂×C₄	1	2	yes	—
108	C₂²⋊#170	C₂×C₄	1	2	yes	—
109	(C₂×AGL(1,𝔽₅))⋊C₄	C₂×C₄	1	2	yes	—
110	(C₂×AGL(1,𝔽₅))⋊C₄	C₂×C₄	1	2	yes	—
111	(C₂×AGL(1,𝔽₅))⋊C₄	C₂×C₄	1	2	yes	—
112	(C₂×AGL(1,𝔽₅))⋊C₄	C₂×C₄	1	2	yes	—
113	#4004	C₂×C₄	1	2	yes	complemented
114	#4004	C₂×C₄	1	2	yes	complemented
115	#4003	C₂×C₄	1	2	yes	—
116	#4003	C₂×C₄	1	2	yes	—
117	#4002	C₂×C₄	1	2	yes	complemented
118	#4002	C₂×C₄	1	2	yes	complemented
119	C₄⋊#170	C₂×C₄	1	2	yes	complemented
120	C₄⋊#170	C₂×C₄	1	2	yes	complemented
121	C₄×#170	C₂×C₄	1	2	yes	complemented
122	C₄×#170	C₂×C₄	1	2	yes	complemented
123	#3992	—	4	1	no	—
124	#3992	—	4	1	no	—
125	#3992	—	4	1	no	—
126	#3992	—	4	1	no	—
127	C₈×AGL(1,𝔽₅)	—	4	1	no	—
128	C₈×AGL(1,𝔽₅)	—	4	1	no	—
129	C₈×AGL(1,𝔽₅)	—	4	1	no	—
130	C₈×AGL(1,𝔽₅)	—	4	1	no	—
131	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic, complemented
132	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic, complemented
133	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
134	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
135	C₅×#97	C₂×C₄	1	1	yes	characteristic, complemented
136	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic, complemented
137	C₂²⋊#168	C₂×C₄	1	1	yes	characteristic
138	C₂²⋊#168	C₂×C₄	1	1	yes	characteristic
139	#3952	C₂×C₄	1	1	yes	characteristic
140	#3952	C₂×C₄	1	1	yes	characteristic
141	#3952	C₂×C₄	1	1	yes	characteristic
142	#3952	C₂×C₄	1	1	yes	characteristic
143	#3947	C₂×C₄	1	1	yes	characteristic, complemented
144	#3947	C₂×C₄	1	1	yes	characteristic, complemented
145	#3946	C₂×C₄	1	1	yes	characteristic, complemented
146	#3946	C₂×C₄	1	1	yes	characteristic, complemented
147	#3946	C₂×C₄	1	1	yes	characteristic, complemented
148	#3946	C₂×C₄	1	1	yes	characteristic, complemented
149	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic, complemented
150	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic, complemented
151	C₄⋊#168	C₂×C₄	1	1	yes	characteristic, complemented
152	C₄⋊#168	C₂×C₄	1	1	yes	characteristic, complemented
153	#3935	C₂×C₄	1	1	yes	characteristic, complemented
154	C₄×#168	C₂×C₄	1	1	yes	characteristic, complemented
155	C₂×#433	—	5	1	no	—
156	C₂×#433	—	5	1	no	—
157	#2296	—	5	1	no	—
158	#1771	—	5	1	no	—
159	#1771	—	5	1	no	—
160	#1771	—	5	1	no	—
161	#1771	—	5	1	no	—
162	#1770	—	5	1	no	—
163	#1770	—	5	1	no	—
164	C₈×C₄⋊C₄	—	5	1	no	—
165	C₈×C₄⋊C₄	—	5	1	no	—
166	#1750	—	5	1	no	—
167	#1750	—	5	1	no	—
168	#1749	—	5	1	no	—
169	C₄×C₂²⋊C₈	—	5	1	no	—
170	C₂³×D₅	C₂²×C₄	1	1	yes	characteristic
171	C₂²×AGL(1,𝔽₅)	—	2	4	no	—
172	C₂²×AGL(1,𝔽₅)	—	4	2	no	—
173	C₂²×AGL(1,𝔽₅)	—	4	2	no	—
174	C₂²×AGL(1,𝔽₅)	C₂²×C₄	1	2	yes	—
175	C₂²×AGL(1,𝔽₅)	C₂²×C₄	1	2	yes	—
176	C₂²×AGL(1,𝔽₅)	C₂²×C₄	1	2	yes	—
177	C₂²×AGL(1,𝔽₅)	C₂²×C₄	1	2	yes	—
178	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
179	C₂²×Dic₅	C₂²×C₄	1	1	yes	characteristic
180	C₂×C₄×D₅	—	2	1	no	—
181	C₂×C₄×D₅	—	2	1	no	—
182	C₂×C₄×D₅	—	2	1	no	—
183	C₂×C₄×D₅	—	2	1	no	—
184	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
185	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
186	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
187	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
188	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
189	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
190	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
191	C₂×C₄×D₅	C₂⁴	1	1	yes	characteristic
192	C₂²⋊AGL(1,𝔽₅)	—	4	2	no	—
193	C₂×#170	C₂²×C₄	1	2	yes	—
194	C₂×#170	C₂²×C₄	1	2	yes	—
195	C₂×#170	C₂²×C₄	1	2	yes	—
196	C₂×#170	C₂²×C₄	1	2	yes	—
197	C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
198	C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
199	C₄⋊AGL(1,𝔽₅)	—	4	2	no	—
200	C₄⋊AGL(1,𝔽₅)	—	4	2	no	—
201	C₄⋊AGL(1,𝔽₅)	—	4	2	no	—
202	C₄×AGL(1,𝔽₅)	—	2	1	no	—
203	C₄×AGL(1,𝔽₅)	—	2	1	no	—
204	C₄×AGL(1,𝔽₅)	—	2	1	no	—
205	C₄×AGL(1,𝔽₅)	—	2	1	no	—
206	C₄×AGL(1,𝔽₅)	—	2	1	no	—
207	C₄×AGL(1,𝔽₅)	—	2	1	no	—
208	C₄×AGL(1,𝔽₅)	—	2	1	no	—
209	C₄×AGL(1,𝔽₅)	—	2	1	no	—
210	C₄×AGL(1,𝔽₅)	—	4	2	no	—
211	D₅⋊C₈	—	2	1	no	—
212	D₅⋊C₈	—	2	1	no	—
213	D₅⋊C₈	—	2	1	no	—
214	D₅⋊C₈	—	2	1	no	—
215	D₅⋊C₈	—	2	1	no	—
216	D₅⋊C₈	—	2	1	no	—
217	D₅⋊C₈	—	2	1	no	—
218	D₅⋊C₈	—	2	1	no	—
219	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
220	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
221	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
222	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
223	C₅×C₄⋊C₄	C₄²	1	1	yes	characteristic
224	C₅×C₄⋊C₄	C₄²	1	1	yes	characteristic
225	C₅×C₂²⋊C₄	C₄²	1	1	yes	characteristic
226	C₅×C₂²⋊C₄	C₄²	1	1	yes	characteristic
227	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
228	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
229	C₂²⋊Dic₅	C₄²	1	1	yes	characteristic
230	C₂²⋊Dic₅	C₄²	1	1	yes	characteristic
231	#685	C₄²	1	1	yes	characteristic
232	#685	C₄²	1	1	yes	characteristic
233	#685	C₄²	1	1	yes	characteristic
234	#685	C₄²	1	1	yes	characteristic
235	C₄⋊Dic₅	C₄²	1	1	yes	characteristic
236	C₄⋊Dic₅	C₄²	1	1	yes	characteristic
237	#683	C₄²	1	1	yes	characteristic
238	#683	C₄²	1	1	yes	characteristic
239	#683	C₄²	1	1	yes	characteristic
240	#683	C₄²	1	1	yes	characteristic
241	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
242	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
243	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
244	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
245	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
246	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
247	C₂×#168	C₂²×C₄	1	1	yes	characteristic
248	C₂×#168	C₂²×C₄	1	1	yes	characteristic
249	C₂×#168	C₂²×C₄	1	1	yes	characteristic
250	C₂×#168	C₂²×C₄	1	1	yes	characteristic
251	C₈×D₅	—	2	1	no	—
252	C₈×D₅	—	2	1	no	—
253	C₈×D₅	—	2	1	no	—
254	C₈×D₅	—	2	1	no	—
255	C₈×D₅	—	2	1	no	—
256	C₈×D₅	—	2	1	no	—
257	C₈×D₅	—	2	1	no	—
258	C₈×D₅	—	2	1	no	—
259	C₂×#117	—	5	1	no	—
260	C₂×#117	—	5	1	no	—
261	C₂²×C₄²	—	5	1	no	—
262	#433	—	5	2	no	—
263	#433	—	5	2	no	—
264	#433	—	5	2	no	—
265	#433	—	5	2	no	—
266	#433	—	5	1	no	—
267	#433	—	5	1	no	—
268	#433	—	5	1	no	—
269	#433	—	5	1	no	—
270	#433	—	5	1	no	—
271	#433	—	5	1	no	—
272	#433	—	5	1	no	—
273	#433	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
274	C₂×C₄⋊C₈	—	5	1	no	—
275	C₂×C₄⋊C₈	—	5	1	no	—
276	C₂×C₄⋊C₈	—	5	1	no	—
277	C₂×C₄⋊C₈	—	5	1	no	—
278	C₂×C₂²⋊C₈	—	5	1	no	—
279	C₂×C₂²⋊C₈	—	5	1	no	—
280	C₂×C₂²⋊C₈	—	5	1	no	—
281	C₂×C₂²⋊C₈	—	5	1	no	—
282	C₂×#97	—	5	1	no	—
283	C₂×#97	—	5	1	no	—
284	C₂×#97	—	5	1	no	—
285	C₂×#97	—	5	1	no	—
286	C₂×#97	—	5	1	no	—
287	C₂×#97	—	5	1	no	—
288	C₂×C₄×C₈	—	5	1	no	—
289	C₂×C₄×C₈	—	5	1	no	—
290	C₂×C₄×C₈	—	5	1	no	—
291	C₂×C₄×C₈	—	5	1	no	—
292	C₂×C₄×C₈	—	5	1	no	—
293	C₂×C₄×C₈	—	5	1	no	—
294	#389	—	5	2	no	—
295	#389	—	5	2	no	—
296	#385	—	5	2	no	—
297	#385	—	5	2	no	—
298	C₄×C₄⋊C₄	—	5	1	no	—
299	C₄×C₄⋊C₄	—	5	1	no	—
300	C₄×C₄⋊C₄	—	5	1	no	—
301	C₄×C₄⋊C₄	—	5	1	no	—
302	#336	—	5	1	no	—
303	#336	—	5	1	no	—
304	#336	—	5	1	no	—
305	#336	—	5	1	no	—
306	#336	—	5	1	no	—
307	#336	—	5	1	no	—
308	#336	—	5	1	no	—
309	#336	—	5	1	no	—
310	C₂³×C₅	C₂×C₄²	1	1	yes	characteristic
311	C₂²×D₅	—	2	1	no	—
312	C₂²×D₅	—	2	1	no	—
313	C₂²×D₅	—	2	2	no	—
314	C₂²×D₅	—	2	2	no	—
315	C₂²×D₅	C₂×C₄²	1	1	yes	characteristic
316	C₂²×D₅	C₂³×C₄	1	1	yes	characteristic
317	C₂×AGL(1,𝔽₅)	—	2	2	no	—
318	C₂×AGL(1,𝔽₅)	—	2	2	no	—
319	C₂×AGL(1,𝔽₅)	—	2	2	no	—
320	C₂×AGL(1,𝔽₅)	—	2	2	no	—
321	C₂×AGL(1,𝔽₅)	—	2	2	no	—
322	C₂×AGL(1,𝔽₅)	—	2	2	no	—
323	C₂×AGL(1,𝔽₅)	—	2	2	no	—
324	C₂×AGL(1,𝔽₅)	—	2	2	no	—
325	C₂×AGL(1,𝔽₅)	—	2	2	no	—
326	C₂×AGL(1,𝔽₅)	—	2	2	no	—
327	C₂×AGL(1,𝔽₅)	—	2	2	no	—
328	C₂×AGL(1,𝔽₅)	—	4	8	no	—
329	C₂×AGL(1,𝔽₅)	#131	1	4	yes	—
330	C₂×C₄×C₅	—	2	1	no	—
331	C₂×C₄×C₅	—	2	1	no	—
332	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
333	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
334	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
335	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
336	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
337	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
338	C₂×Dic₅	—	2	1	no	—
339	C₂×Dic₅	—	2	1	no	—
340	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
341	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
342	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
343	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
344	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
345	C₂×Dic₅	C₂³×C₄	1	1	yes	characteristic
346	C₄×D₅	—	2	1	no	—
347	C₄×D₅	—	2	1	no	—
348	C₄×D₅	—	2	2	no	—
349	C₄×D₅	—	2	2	no	—
350	C₄×D₅	—	2	2	no	—
351	C₄×D₅	—	2	2	no	—
352	C₄×D₅	—	2	1	no	—
353	C₄×D₅	—	2	1	no	—
354	C₄×D₅	—	2	1	no	—
355	C₄×D₅	—	2	1	no	—
356	C₄×D₅	H(5,𝔽₂)	1	1	yes	characteristic
357	C₄×D₅	H(5,𝔽₂)	1	1	yes	characteristic
358	C₄×D₅	2₋¹⁺⁴	1	1	yes	characteristic
359	C₄×D₅	2₋¹⁺⁴	1	1	yes	characteristic
360	#170	—	2	2	no	—
361	#170	—	2	2	no	—
362	#170	—	2	2	no	—
363	#170	—	2	2	no	—
364	C₅×C₈	—	2	1	no	—
365	C₅×C₈	—	2	1	no	—
366	C₅×C₈	—	2	1	no	—
367	C₅×C₈	—	2	1	no	—
368	#168	—	2	1	no	—
369	#168	—	2	1	no	—
370	#168	—	2	1	no	—
371	#168	—	2	1	no	—
372	C₂³×C₄	—	5	1	no	—
373	C₂³×C₄	—	5	2	no	—
374	C₂²×C₈	—	5	1	no	—
375	C₂²×C₈	—	5	1	no	—
376	C₂²×C₈	—	5	1	no	—
377	C₂²×C₈	—	5	1	no	—
378	C₂²×C₈	—	5	1	no	—
379	C₂²×C₈	—	5	1	no	—
380	C₂²×C₈	—	5	1	no	—
381	C₂²×C₈	—	5	1	no	—
382	#117	—	5	1	no	—
383	#117	—	5	1	no	—
384	#117	—	5	1	no	—
385	#117	—	5	1	no	—
386	#117	—	5	1	no	—
387	#117	—	5	1	no	—
388	#117	—	5	1	no	—
389	#117	—	20	1	no	—
390	#117	—	20	1	no	—
391	#117	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
392	C₂×C₄⋊C₄	—	5	1	no	—
393	C₂×C₄⋊C₄	—	5	1	no	—
394	C₂×C₄⋊C₄	—	5	2	no	—
395	C₂×C₄⋊C₄	—	5	2	no	—
396	C₂×C₄⋊C₄	—	5	2	no	—
397	C₂×C₄⋊C₄	—	5	2	no	—
398	C₂×C₄⋊C₄	—	5	2	no	—
399	C₂×C₂²⋊C₄	—	5	1	no	—
400	C₂×C₂²⋊C₄	—	5	1	no	—
401	C₂×C₂²⋊C₄	—	5	2	no	—
402	C₂×C₄²	—	5	1	no	—
403	C₂×C₄²	—	5	1	no	—
404	C₂×C₄²	—	5	1	no	—
405	C₂×C₄²	—	5	1	no	—
406	C₂×C₄²	—	5	1	no	—
407	C₂×C₄²	—	5	1	no	—
408	C₂×C₄²	—	5	2	no	—
409	C₂×C₄²	—	20	1	no	—
410	C₂×C₄²	—	20	1	no	—
411	C₄⋊C₈	—	5	2	no	—
412	C₄⋊C₈	—	5	2	no	—
413	C₄⋊C₈	—	5	2	no	—
414	C₄⋊C₈	—	5	2	no	—
415	C₄⋊C₈	—	5	1	no	—
416	C₄⋊C₈	—	5	1	no	—
417	C₄⋊C₈	—	5	1	no	—
418	C₄⋊C₈	—	5	1	no	—
419	C₄⋊C₈	—	5	1	no	—
420	C₄⋊C₈	—	5	1	no	—
421	C₄⋊C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
422	C₄⋊C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
423	C₂²⋊C₈	—	5	2	no	—
424	C₂²⋊C₈	—	5	2	no	—
425	C₂²⋊C₈	—	5	2	no	—
426	C₂²⋊C₈	—	5	2	no	—
427	C₂²⋊C₈	—	5	1	no	—
428	C₂²⋊C₈	—	5	1	no	—
429	C₂²⋊C₈	—	5	1	no	—
430	C₂²⋊C₈	—	5	1	no	—
431	C₂²⋊C₈	—	5	1	no	—
432	C₂²⋊C₈	—	5	1	no	—
433	C₂²⋊C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
434	C₂²⋊C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
435	#97	—	5	2	no	—
436	#97	—	5	2	no	—
437	#97	—	5	1	no	—
438	#97	—	5	1	no	—
439	#97	—	5	1	no	—
440	#97	—	20	1	no	—
441	#97	—	20	1	no	—
442	#97	—	20	1	no	—
443	#97	—	20	1	no	—
444	#97	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
445	C₄×C₈	—	5	2	no	—
446	C₄×C₈	—	5	2	no	—
447	C₄×C₈	—	5	1	no	—
448	C₄×C₈	—	5	1	no	—
449	C₄×C₈	—	5	1	no	—
450	C₄×C₈	—	20	1	no	—
451	C₄×C₈	—	20	1	no	—
452	C₄×C₈	—	20	1	no	—
453	C₄×C₈	—	20	1	no	—
454	C₄×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
455	#95	—	5	2	no	—
456	#95	—	5	2	no	—
457	#95	—	5	2	no	—
458	#95	—	5	2	no	—
459	C₂²×C₅	—	2	1	no	—
460	C₂²×C₅	—	2	1	no	—
461	C₂²×C₅	—	2	1	no	—
462	C₂²×C₅	C₂²×C₄²	1	1	yes	characteristic
463	C₂×D₅	—	2	1	no	—
464	C₂×D₅	—	2	1	no	—
465	C₂×D₅	—	2	1	no	—
466	C₂×D₅	—	4	2	no	—
467	C₂×D₅	—	4	2	no	—
468	C₂×D₅	#518	1	1	yes	characteristic
469	C₂×D₅	#519	1	1	yes	characteristic
470	C₂×D₅	C₂×#131	1	2	yes	—
471	C₂×D₅	#568	1	2	yes	—
472	AGL(1,𝔽₅)	—	2	4	no	—
473	AGL(1,𝔽₅)	—	4	2	no	—
474	AGL(1,𝔽₅)	—	4	2	no	—
475	AGL(1,𝔽₅)	—	4	2	no	—
476	C₄×C₅	—	2	1	no	—
477	C₄×C₅	—	2	1	no	—
478	C₄×C₅	—	2	1	no	—
479	C₄×C₅	—	2	1	no	—
480	C₄×C₅	—	2	1	no	—
481	C₄×C₅	#520	1	1	yes	characteristic
482	C₄×C₅	#520	1	1	yes	characteristic
483	Dic₅	—	2	1	no	—
484	Dic₅	—	2	1	no	—
485	Dic₅	—	2	1	no	—
486	Dic₅	—	2	1	no	—
487	Dic₅	—	2	1	no	—
488	Dic₅	#520	1	1	yes	characteristic
489	Dic₅	#520	1	1	yes	characteristic
490	C₂⁴	—	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	1	no	—
496	C₂²×C₄	—	5	1	no	—
497	C₂²×C₄	—	5	1	no	—
498	C₂²×C₄	—	5	1	no	—
499	C₂²×C₄	—	5	1	no	—
500	C₂²×C₄	—	5	1	no	—
501	C₂²×C₄	—	5	2	no	—
502	C₂²×C₄	—	5	2	no	—
503	C₂²×C₄	—	5	2	no	—
504	C₂²×C₄	—	10	1	no	—
505	C₂²×C₄	—	10	1	no	—
506	C₂²×C₄	—	10	1	no	—
507	C₂²×C₄	—	10	1	no	—
508	C₂²×C₄	—	10	4	no	—
509	C₂²×C₄	—	20	2	no	—
510	C₂²×C₄	—	20	2	no	—
511	C₂²×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
512	C₂×C₈	—	5	2	no	—
513	C₂×C₈	—	5	2	no	—
514	C₂×C₈	—	5	2	no	—
515	C₂×C₈	—	5	2	no	—
516	C₂×C₈	—	5	1	no	—
517	C₂×C₈	—	5	1	no	—
518	C₂×C₈	—	5	1	no	—
519	C₂×C₈	—	5	1	no	—
520	C₂×C₈	—	10	1	no	—
521	C₂×C₈	—	10	1	no	—
522	C₂×C₈	—	10	1	no	—
523	C₂×C₈	—	10	1	no	—
524	C₂×C₈	—	10	1	no	—
525	C₂×C₈	—	10	1	no	—
526	C₂×C₈	—	10	1	no	—
527	C₂×C₈	—	10	1	no	—
528	C₂×C₈	—	10	1	no	—
529	C₂×C₈	—	10	1	no	—
530	C₂×C₈	—	10	1	no	—
531	C₂×C₈	—	10	1	no	—
532	C₂×C₈	—	10	1	no	—
533	C₂×C₈	—	10	1	no	—
534	C₂×C₈	—	10	1	no	—
535	C₂×C₈	—	10	1	no	—
536	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
537	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
538	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
539	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
540	C₄⋊C₄	—	5	1	no	—
541	C₄⋊C₄	—	5	1	no	—
542	C₄⋊C₄	—	5	1	no	—
543	C₄⋊C₄	—	5	1	no	—
544	C₄⋊C₄	—	5	1	no	—
545	C₄⋊C₄	—	5	1	no	—
546	C₄⋊C₄	—	10	4	no	—
547	C₄⋊C₄	—	10	4	no	—
548	C₄⋊C₄	—	20	2	no	—
549	C₄⋊C₄	—	20	2	no	—
550	C₄⋊C₄	—	20	2	no	—
551	C₄⋊C₄	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
552	C₄⋊C₄	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
553	C₂²⋊C₄	—	5	1	no	—
554	C₂²⋊C₄	—	5	1	no	—
555	C₂²⋊C₄	—	5	1	no	—
556	C₂²⋊C₄	—	5	1	no	—
557	C₂²⋊C₄	—	5	1	no	—
558	C₂²⋊C₄	—	5	1	no	—
559	C₂²⋊C₄	—	20	2	no	—
560	C₂²⋊C₄	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
561	C₂²⋊C₄	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
562	C₄²	—	5	1	no	—
563	C₄²	—	5	1	no	—
564	C₄²	—	5	1	no	—
565	C₄²	—	5	1	no	—
566	C₄²	—	5	1	no	—
567	C₄²	—	5	1	no	—
568	C₄²	—	10	1	no	—
569	C₄²	—	10	1	no	—
570	C₄²	—	10	1	no	—
571	C₄²	—	10	1	no	—
572	C₄²	—	10	1	no	—
573	C₄²	—	10	1	no	—
574	C₄²	—	10	1	no	—
575	C₄²	—	10	1	no	—
576	C₄²	—	20	2	no	—
577	C₄²	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
578	C₄²	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
579	C₂×C₅	—	4	1	no	—
580	C₂×C₅	#2274	1	1	yes	characteristic
581	C₂×C₅	C₄×#131	1	1	yes	characteristic
582	C₂×C₅	#2875	1	1	yes	characteristic
583	D₅	—	4	1	no	—
584	D₅	#2976	1	2	yes	—
585	D₅	#2985	1	2	yes	—
586	C₂³	—	5	1	no	—
587	C₂³	—	5	1	no	—
588	C₂³	—	10	1	no	—
589	C₂³	—	10	1	no	—
590	C₂³	—	10	2	no	—
591	C₂³	—	10	2	no	—
592	C₂³	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	5	1	no	—
596	C₂×C₄	—	5	1	no	—
597	C₂×C₄	—	5	1	no	—
598	C₂×C₄	—	5	1	no	—
599	C₂×C₄	—	5	1	no	—
600	C₂×C₄	—	5	4	no	—
601	C₂×C₄	—	5	1	no	—
602	C₂×C₄	—	5	1	no	—
603	C₂×C₄	—	5	1	no	—
604	C₂×C₄	—	5	1	no	—
605	C₂×C₄	—	5	1	no	—
606	C₂×C₄	—	10	1	no	—
607	C₂×C₄	—	10	1	no	—
608	C₂×C₄	—	10	1	no	—
609	C₂×C₄	—	10	2	no	—
610	C₂×C₄	—	10	2	no	—
611	C₂×C₄	—	10	2	no	—
612	C₂×C₄	—	10	2	no	—
613	C₂×C₄	—	10	1	no	—
614	C₂×C₄	—	10	1	no	—
615	C₂×C₄	—	10	1	no	—
616	C₂×C₄	—	10	2	no	—
617	C₂×C₄	—	10	2	no	—
618	C₂×C₄	—	10	1	no	—
619	C₂×C₄	—	10	1	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	—	10	2	no	—
625	C₂×C₄	—	10	2	no	—
626	C₂×C₄	—	10	2	no	—
627	C₂×C₄	—	10	2	no	—
628	C₂×C₄	—	10	2	no	—
629	C₂×C₄	—	20	8	no	—
630	C₂×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
631	C₂×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
632	C₂×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
633	C₂×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
634	C₂×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
635	C₂×C₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
636	C₈	—	2	1	no	—
637	C₈	—	2	1	no	—
638	C₈	—	2	1	no	—
639	C₈	—	2	1	no	—
640	C₈	—	10	2	no	—
641	C₈	—	10	2	no	—
642	C₈	—	10	2	no	—
643	C₈	—	10	2	no	—
644	C₈	—	10	1	no	—
645	C₈	—	10	1	no	—
646	C₈	—	10	1	no	—
647	C₈	—	10	1	no	—
648	C₅	#20541	1	1	yes	characteristic, complemented, Sylow
649	C₂²	—	2	1	no	—
650	C₂²	—	2	1	no	—
651	C₂²	—	2	1	no	—
652	C₂²	—	5	1	no	—
653	C₂²	—	5	1	no	—
654	C₂²	—	5	2	no	—
655	C₂²	—	5	2	no	—
656	C₂²	—	10	1	no	—
657	C₂²	—	10	1	no	—
658	C₂²	—	10	1	no	—
659	C₂²	—	20	2	no	—
660	C₂²	—	20	2	no	—
661	C₂²	C₂²×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
662	C₄	—	2	1	no	—
663	C₄	—	2	1	no	—
664	C₄	—	2	1	no	—
665	C₄	—	2	1	no	—
666	C₄	—	2	1	no	—
667	C₄	—	5	1	no	—
668	C₄	—	5	1	no	—
669	C₄	—	10	4	no	—
670	C₄	—	10	1	no	—
671	C₄	—	10	1	no	—
672	C₄	—	10	1	no	—
673	C₄	—	10	1	no	—
674	C₄	—	10	1	no	—
675	C₄	—	20	2	no	—
676	C₄	—	20	2	no	—
677	C₄	—	20	2	no	—
678	C₄	#66266	1	1	yes	characteristic
679	C₄	#66266	1	1	yes	characteristic
680	C₂	—	4	1	no	—
681	C₂	—	5	2	no	—
682	C₂	—	5	2	no	—
683	C₂	—	20	1	no	—
684	C₂	#10617127	1	1	yes	characteristic
685	C₂	AGL(1,𝔽₅)×#131	1	1	yes	characteristic
686	C₂	#10617415	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×AGL(1,𝔽₅)
commutator, socle	C₂²×C₅	C₂²×C₄²
Fitting	C₅×#433	C₄
prime radical	C₂³×D₅	C₂²×C₄
cosocle	C₂×C₄×D₅	C₂⁴
hypercenter	#433	AGL(1,𝔽₅)
hypocenter	C₅	#20541
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ #433

Complements

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

N	H ≅ G/N	type
4. #10604035	C₂	semidirect
5. #10604035	C₂	semidirect
6. #10604034	C₂	semidirect
7. #10604033	C₂	semidirect
12. #10603880	C₂	semidirect
13. #10603880	C₂	semidirect
14. #10603842	C₂	semidirect
15. C₈×C₄⋊AGL(1,𝔽₅)	C₂	semidirect
31. #65706	C₄	semidirect
32. #65706	C₄	semidirect
35. #65697	C₄	semidirect
36. #65697	C₄	semidirect
45. C₅×#433	C₄	semidirect
46. #65289	C₄	semidirect
47. #65129	C₄	semidirect
48. #65129	C₄	semidirect
53. #65009	C₄	semidirect
54. #65009	C₄	semidirect
55. #64998	C₄	semidirect
57. #64979	C₄	semidirect
113. #4004	C₂×C₄	semidirect
114. #4004	C₂×C₄	semidirect
117. #4002	C₂×C₄	semidirect
118. #4002	C₂×C₄	semidirect
119. C₄⋊#170	C₂×C₄	semidirect
120. C₄⋊#170	C₂×C₄	semidirect
121. C₄×#170	C₂×C₄	semidirect
122. C₄×#170	C₂×C₄	semidirect
131. C₅×C₄⋊C₈	C₂×C₄	semidirect
132. C₅×C₄⋊C₈	C₂×C₄	semidirect
135. C₅×#97	C₂×C₄	semidirect
136. C₄×C₅×C₈	C₂×C₄	semidirect
143. #3947	C₂×C₄	semidirect
144. #3947	C₂×C₄	semidirect
145. #3946	C₂×C₄	semidirect
146. #3946	C₂×C₄	semidirect
147. #3946	C₂×C₄	semidirect
148. #3946	C₂×C₄	semidirect
149. C₈×Dic₅	C₂×C₄	semidirect
150. C₈×Dic₅	C₂×C₄	semidirect
151. C₄⋊#168	C₂×C₄	semidirect
152. C₄⋊#168	C₂×C₄	semidirect
153. #3935	C₂×C₄	semidirect
154. C₄×#168	C₂×C₄	semidirect
273. #433	AGL(1,𝔽₅)	semidirect
421. C₄⋊C₈	C₂×AGL(1,𝔽₅)	semidirect
422. C₄⋊C₈	C₂×AGL(1,𝔽₅)	semidirect
444. #97	C₂×AGL(1,𝔽₅)	semidirect
454. C₄×C₈	C₂×AGL(1,𝔽₅)	semidirect
648. C₅	#20541	semidirect

Maximal subgroups

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

subgroup	index
#10617128	2
D₅⋊#433	2
D₅×#433	2
#10604035	2
#10604034	2
#10604033	2
#10603909	2
#10603908	2
AGL(1,𝔽₅)×C₂²⋊C₈	2
#10603880	2
#10603842	2
C₈×C₄⋊AGL(1,𝔽₅)	2
#20541	5