Subgroups — C₅×#35079 #11957799

Order 1280.

2098 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2857	C₂	1	2	yes	maximal, complemented
2	C₅×#2851	C₂	1	2	yes	maximal, complemented
3	C₅×#2667	C₂	1	2	yes	maximal, complemented
4	C₅×#2665	C₂	1	2	yes	maximal, complemented
5	C₅×#2569	C₂	1	2	yes	maximal, complemented
6	C₅×#2549	C₂	1	2	yes	maximal, complemented
7	C₅×#2442	C₂	1	2	yes	maximal, complemented
8	C₅×#2441	C₂	1	2	yes	maximal, complemented
9	C₅×#2440	C₂	1	2	yes	maximal, complemented
10	C₅×#2439	C₂	1	2	yes	maximal, complemented
11	C₅×#2437	C₂	1	4	yes	maximal
12	C₅×#2329	C₂	1	4	yes	maximal, complemented
13	C₅×#2280	C₂	1	1	yes	maximal, characteristic
14	C₂×C₅×#380	C₂	1	1	yes	maximal, characteristic
15	C₂×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
16	C₂⁴×C₄×C₅	C₂²	1	1	yes	characteristic
17	C₂×C₅×C₄⋊Q₈	C₂²	1	2	yes	complemented
18	C₂×C₅×#125	C₂²	1	2	yes	complemented
19	C₂×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
20	C₂×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
21	C₂×C₅×#117	C₂²	1	2	yes	—
22	C₂²×C₅×C₄⋊C₄	C₂²	1	2	yes	—
23	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
24	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
25	C₂²×C₄²×C₅	C₂²	1	2	yes	—
26	C₅×#400	C₂²	1	4	yes	complemented
27	C₅×#399	C₂²	1	4	yes	—
28	C₅×#398	C₂²	1	4	yes	complemented
29	C₅×#398	C₂²	1	4	yes	complemented
30	C₅×#396	C₂²	1	4	yes	—
31	C₅×#396	C₂²	1	4	yes	—
32	C₅×#395	C₂²	1	4	yes	complemented
33	C₅×#393	C₂²	1	4	yes	—
34	C₅×#391	C₂²	1	4	yes	complemented
35	C₅×#391	C₂²	1	4	yes	complemented
36	C₅×#389	C₂²	1	4	yes	complemented
37	C₅×#389	C₂²	1	4	yes	complemented
38	C₅×#389	C₂²	1	2	yes	complemented
39	C₅×#389	C₂²	1	2	yes	complemented
40	C₅×#389	C₂²	1	2	yes	complemented
41	C₅×#389	C₂²	1	2	yes	complemented
42	C₅×#387	C₂²	1	4	yes	complemented
43	C₅×#387	C₂²	1	4	yes	complemented
44	C₅×#387	C₂²	1	4	yes	complemented
45	C₅×#387	C₂²	1	4	yes	complemented
46	C₅×#385	C₂²	1	4	yes	—
47	C₅×#385	C₂²	1	4	yes	—
48	C₅×#385	C₂²	1	4	yes	—
49	C₅×#385	C₂²	1	4	yes	—
50	C₅×#384	C₂²	1	2	yes	complemented
51	C₅×#382	C₂²	1	2	yes	complemented
52	C₅×#381	C₂²	1	2	yes	—
53	C₅×#380	C₂²	1	2	yes	—
54	C₅×#380	C₂²	1	2	yes	—
55	C₅×#380	C₂²	1	2	yes	—
56	C₅×#380	C₂²	1	1	yes	characteristic
57	C₅×#380	C₂²	1	1	yes	characteristic
58	C₅×#380	C₂²	1	1	yes	characteristic
59	C₅×#380	C₂²	1	1	yes	characteristic
60	C₅×#380	C₂²	1	2	yes	—
61	C₅×#380	C₂²	1	4	yes	—
62	C₅×#380	C₂²	1	4	yes	—
63	C₅×#379	C₂²	1	2	yes	—
64	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
65	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
66	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
67	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
68	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
69	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
70	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
71	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
72	C₂×C₅×#95	C₂²	1	1	yes	characteristic
73	C₂×C₅×#95	C₂²	1	1	yes	characteristic
74	C₂×C₅×#95	C₂²	1	2	yes	—
75	#35079	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
76	C₂⁵×C₅	C₂³	1	1	yes	characteristic
77	C₂²×C₅×Q₈	C₂³	1	4	yes	—
78	C₂³×C₄×C₅	—	4	4	no	—
79	C₂³×C₄×C₅	Q₈	1	8	yes	complemented
80	C₂³×C₄×C₅	C₂³	1	2	yes	—
81	C₂³×C₄×C₅	C₂³	1	2	yes	—
82	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₅	C₂³	1	4	yes	—
86	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
89	C₅×C₄⋊Q₈	—	4	4	no	—
90	C₅×#125	—	4	4	no	—
91	C₅×C₂²⋊Q₈	—	2	16	no	—
92	C₅×C₂²⋊Q₈	—	4	8	no	—
93	C₅×#117	—	4	4	no	—
94	C₂×C₅×C₄⋊C₄	—	4	4	no	—
95	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
96	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
97	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
98	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
99	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
100	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
101	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
102	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
103	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
104	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
105	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
106	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
107	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
108	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
109	C₂×C₅×C₂²⋊C₄	—	2	8	no	—
110	C₂×C₅×C₂²⋊C₄	—	4	4	no	—
111	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
112	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
113	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
114	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
115	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
116	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
117	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
118	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
119	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
120	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
121	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
122	C₂×C₄²×C₅	—	4	4	no	—
123	C₂×C₄²×C₅	C₂³	1	2	yes	—
124	C₂×C₄²×C₅	C₂³	1	2	yes	—
125	C₂×C₄²×C₅	C₂³	1	2	yes	—
126	C₂×C₄²×C₅	C₂³	1	4	yes	—
127	C₂×C₄²×C₅	C₂³	1	2	yes	—
128	C₅×#95	C₂³	1	2	yes	—
129	C₅×#95	C₂³	1	2	yes	—
130	C₅×#95	C₂³	1	1	yes	characteristic
131	C₅×#95	C₂³	1	1	yes	characteristic
132	C₅×#95	C₂³	1	1	yes	characteristic
133	C₅×#95	C₂³	1	1	yes	characteristic
134	C₅×#95	C₂³	1	2	yes	—
135	C₅×#95	C₂³	1	4	yes	—
136	C₅×#95	C₂³	1	2	yes	—
137	C₅×#95	C₂³	1	2	yes	—
138	C₅×#95	C₂³	1	2	yes	—
139	C₅×#95	C₂³	1	4	yes	—
140	C₅×#95	C₂³	1	4	yes	—
141	C₅×#95	C₂³	1	4	yes	—
142	C₅×#95	C₂³	1	4	yes	—
143	C₅×#95	C₂³	1	4	yes	—
144	C₅×#95	C₂³	1	4	yes	—
145	C₅×#95	C₂³	1	4	yes	—
146	#2857	C₂×C₅	1	2	yes	complemented
147	#2851	C₂×C₅	1	2	yes	complemented
148	#2667	C₂×C₅	1	2	yes	complemented
149	#2665	C₂×C₅	1	2	yes	complemented
150	#2569	C₂×C₅	1	2	yes	complemented
151	#2549	C₂×C₅	1	2	yes	complemented
152	#2442	C₂×C₅	1	2	yes	complemented
153	#2441	C₂×C₅	1	2	yes	complemented
154	#2440	C₂×C₅	1	2	yes	complemented
155	#2439	C₂×C₅	1	2	yes	complemented
156	#2437	C₂×C₅	1	4	yes	—
157	#2329	C₂×C₅	1	4	yes	complemented
158	#2280	C₂×C₅	1	1	yes	characteristic
159	C₂×#380	C₂×C₅	1	1	yes	characteristic
160	C₂×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic
161	C₂⁴×C₅	—	2	4	no	—
162	C₂⁴×C₅	—	2	2	no	—
163	C₂⁴×C₅	—	2	2	no	—
164	C₂⁴×C₅	—	4	2	no	—
165	C₂⁴×C₅	C₂×Q₈	1	4	yes	—
166	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
167	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
168	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
169	C₂×C₅×Q₈	—	2	8	no	—
170	C₂×C₅×Q₈	—	4	4	no	—
171	C₂×C₅×Q₈	—	4	4	no	—
172	C₂²×C₄×C₅	—	2	4	no	—
173	C₂²×C₄×C₅	—	2	4	no	—
174	C₂²×C₄×C₅	—	2	4	no	—
175	C₂²×C₄×C₅	—	2	4	no	—
176	C₂²×C₄×C₅	—	2	4	no	—
177	C₂²×C₄×C₅	—	2	8	no	—
178	C₂²×C₄×C₅	—	2	4	no	—
179	C₂²×C₄×C₅	—	2	4	no	—
180	C₂²×C₄×C₅	—	4	16	no	—
181	C₂²×C₄×C₅	—	4	2	no	—
182	C₂²×C₄×C₅	—	4	2	no	—
183	C₂²×C₄×C₅	—	4	2	no	—
184	C₂²×C₄×C₅	—	4	2	no	—
185	C₂²×C₄×C₅	—	4	2	no	—
186	C₂²×C₄×C₅	—	4	4	no	—
187	C₂²×C₄×C₅	—	4	4	no	—
188	C₂²×C₄×C₅	C₂×Q₈	1	4	yes	—
189	C₂²×C₄×C₅	C₂×Q₈	1	4	yes	—
190	C₂²×C₄×C₅	C₂×Q₈	1	4	yes	—
191	C₂²×C₄×C₅	C₂×Q₈	1	4	yes	—
192	C₂²×C₄×C₅	C₂×Q₈	1	4	yes	—
193	C₂²×C₄×C₅	C₂×Q₈	1	4	yes	—
194	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
195	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
196	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
197	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
198	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
199	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
200	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
201	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
202	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
203	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
204	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
206	C₅×C₄⋊C₄	—	2	8	no	—
207	C₅×C₄⋊C₄	—	2	8	no	—
208	C₅×C₄⋊C₄	—	2	8	no	—
209	C₅×C₄⋊C₄	—	2	4	no	—
210	C₅×C₄⋊C₄	—	2	4	no	—
211	C₅×C₄⋊C₄	—	2	4	no	—
212	C₅×C₄⋊C₄	—	2	4	no	—
213	C₅×C₄⋊C₄	—	4	4	no	—
214	C₅×C₄⋊C₄	—	4	4	no	—
215	C₅×C₄⋊C₄	—	4	4	no	—
216	C₅×C₄⋊C₄	—	4	4	no	—
217	C₅×C₄⋊C₄	—	4	4	no	—
218	C₅×C₄⋊C₄	—	4	4	no	—
219	C₅×C₄⋊C₄	—	4	4	no	—
220	C₅×C₂²⋊C₄	—	2	4	no	—
221	C₅×C₂²⋊C₄	—	2	8	no	—
222	C₅×C₂²⋊C₄	—	2	8	no	—
223	C₅×C₂²⋊C₄	—	2	4	no	—
224	C₅×C₂²⋊C₄	—	2	4	no	—
225	C₅×C₂²⋊C₄	—	2	4	no	—
226	C₅×C₂²⋊C₄	—	2	4	no	—
227	C₅×C₂²⋊C₄	—	4	2	no	—
228	C₅×C₂²⋊C₄	—	4	2	no	—
229	C₅×C₂²⋊C₄	—	4	4	no	—
230	C₅×C₂²⋊C₄	#41	1	8	yes	—
231	C₄²×C₅	—	2	4	no	—
232	C₄²×C₅	—	2	4	no	—
233	C₄²×C₅	—	4	2	no	—
234	C₄²×C₅	—	4	2	no	—
235	C₄²×C₅	—	4	4	no	—
236	C₂⁴×C₄	C₂²×C₅	1	1	yes	characteristic
237	C₂×C₄⋊Q₈	C₂²×C₅	1	2	yes	complemented
238	C₂×#125	C₂²×C₅	1	2	yes	complemented
239	C₂×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
240	C₂×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
241	C₂×#117	C₂²×C₅	1	2	yes	—
242	C₂²×C₄⋊C₄	C₂²×C₅	1	2	yes	—
243	C₂²×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
244	C₂²×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
245	C₂²×C₄²	C₂²×C₅	1	2	yes	—
246	#400	C₂²×C₅	1	4	yes	complemented
247	#399	C₂²×C₅	1	4	yes	—
248	#398	C₂²×C₅	1	4	yes	complemented
249	#398	C₂²×C₅	1	4	yes	complemented
250	#396	C₂²×C₅	1	4	yes	—
251	#396	C₂²×C₅	1	4	yes	—
252	#395	C₂²×C₅	1	4	yes	complemented
253	#393	C₂²×C₅	1	4	yes	—
254	#391	C₂²×C₅	1	4	yes	complemented
255	#391	C₂²×C₅	1	4	yes	complemented
256	#389	C₂²×C₅	1	4	yes	complemented
257	#389	C₂²×C₅	1	4	yes	complemented
258	#389	C₂²×C₅	1	2	yes	complemented
259	#389	C₂²×C₅	1	2	yes	complemented
260	#389	C₂²×C₅	1	2	yes	complemented
261	#389	C₂²×C₅	1	2	yes	complemented
262	#387	C₂²×C₅	1	4	yes	complemented
263	#387	C₂²×C₅	1	4	yes	complemented
264	#387	C₂²×C₅	1	4	yes	complemented
265	#387	C₂²×C₅	1	4	yes	complemented
266	#385	C₂²×C₅	1	4	yes	—
267	#385	C₂²×C₅	1	4	yes	—
268	#385	C₂²×C₅	1	4	yes	—
269	#385	C₂²×C₅	1	4	yes	—
270	#384	C₂²×C₅	1	2	yes	complemented
271	#382	C₂²×C₅	1	2	yes	complemented
272	#381	C₂²×C₅	1	2	yes	—
273	#380	C₂²×C₅	1	4	yes	—
274	#380	C₂²×C₅	1	2	yes	—
275	#380	C₂²×C₅	1	4	yes	—
276	#380	C₂²×C₅	1	1	yes	characteristic
277	#380	C₂²×C₅	1	2	yes	—
278	#380	C₂²×C₅	1	1	yes	characteristic
279	#380	C₂²×C₅	1	2	yes	—
280	#380	C₂²×C₅	1	1	yes	characteristic
281	#380	C₂²×C₅	1	2	yes	—
282	#380	C₂²×C₅	1	1	yes	characteristic
283	#379	C₂²×C₅	1	2	yes	—
284	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
285	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
286	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
287	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
288	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
289	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
290	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
291	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
292	C₂×#95	C₂²×C₅	1	1	yes	characteristic
293	C₂×#95	C₂²×C₅	1	2	yes	—
294	C₂×#95	C₂²×C₅	1	1	yes	characteristic
295	C₂³×C₅	—	2	2	no	—
296	C₂³×C₅	—	2	2	no	—
297	C₂³×C₅	—	2	2	no	—
298	C₂³×C₅	—	2	1	no	—
299	C₂³×C₅	—	2	1	no	—
300	C₂³×C₅	—	2	8	no	—
301	C₂³×C₅	—	2	8	no	—
302	C₂³×C₅	—	2	2	no	—
303	C₂³×C₅	—	2	1	no	—
304	C₂³×C₅	—	2	2	no	—
305	C₂³×C₅	—	2	1	no	—
306	C₂³×C₅	—	4	4	no	—
307	C₂³×C₅	—	4	8	no	—
308	C₂³×C₅	—	4	8	no	—
309	C₂³×C₅	C₂²×Q₈	1	2	yes	—
310	C₂³×C₅	C₂²×Q₈	1	2	yes	—
311	C₂³×C₅	C₂²×Q₈	1	2	yes	—
312	C₂³×C₅	C₂×#41	1	4	yes	—
313	C₂³×C₅	H(5,𝔽₂)	1	2	yes	—
314	C₂³×C₅	2₋¹⁺⁴	1	2	yes	—
315	C₂³×C₅	C₂⁵	1	1	yes	characteristic
316	C₅×Q₈	—	8	8	no	—
317	C₂×C₄×C₅	—	2	2	no	—
318	C₂×C₄×C₅	—	2	2	no	—
319	C₂×C₄×C₅	—	2	2	no	—
320	C₂×C₄×C₅	—	2	2	no	—
321	C₂×C₄×C₅	—	2	2	no	—
322	C₂×C₄×C₅	—	2	2	no	—
323	C₂×C₄×C₅	—	2	2	no	—
324	C₂×C₄×C₅	—	2	8	no	—
325	C₂×C₄×C₅	—	2	8	no	—
326	C₂×C₄×C₅	—	2	8	no	—
327	C₂×C₄×C₅	—	2	2	no	—
328	C₂×C₄×C₅	—	2	2	no	—
329	C₂×C₄×C₅	—	2	4	no	—
330	C₂×C₄×C₅	—	2	4	no	—
331	C₂×C₄×C₅	—	2	4	no	—
332	C₂×C₄×C₅	—	2	4	no	—
333	C₂×C₄×C₅	—	2	2	no	—
334	C₂×C₄×C₅	—	2	2	no	—
335	C₂×C₄×C₅	—	2	4	no	—
336	C₂×C₄×C₅	—	2	4	no	—
337	C₂×C₄×C₅	—	2	4	no	—
338	C₂×C₄×C₅	—	2	4	no	—
339	C₂×C₄×C₅	—	2	4	no	—
340	C₂×C₄×C₅	—	2	4	no	—
341	C₂×C₄×C₅	—	2	4	no	—
342	C₂×C₄×C₅	—	2	2	no	—
343	C₂×C₄×C₅	—	2	4	no	—
344	C₂×C₄×C₅	—	2	2	no	—
345	C₂×C₄×C₅	—	4	4	no	—
346	C₂×C₄×C₅	—	4	4	no	—
347	C₂×C₄×C₅	—	4	4	no	—
348	C₂×C₄×C₅	—	4	8	no	—
349	C₂×C₄×C₅	—	4	8	no	—
350	C₂×C₄×C₅	—	8	8	no	—
351	C₂×C₄×C₅	C₂²×Q₈	1	2	yes	—
352	C₂×C₄×C₅	C₂²×Q₈	1	2	yes	—
353	C₂×C₄×C₅	C₂²×Q₈	1	2	yes	—
354	C₂×C₄×C₅	C₂²×Q₈	1	2	yes	—
355	C₂×C₄×C₅	C₂×#41	1	4	yes	—
356	C₂×C₄×C₅	C₂×#41	1	4	yes	—
357	C₂×C₄×C₅	H(5,𝔽₂)	1	4	yes	—
358	C₂⁵	C₂³×C₅	1	1	yes	characteristic
359	C₂²×Q₈	C₂³×C₅	1	4	yes	—
360	C₂³×C₄	—	4	4	no	—
361	C₂³×C₄	C₅×Q₈	1	8	yes	complemented
362	C₂³×C₄	C₂³×C₅	1	2	yes	—
363	C₂³×C₄	C₂³×C₅	1	2	yes	—
364	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
365	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
366	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
367	C₂³×C₄	C₂³×C₅	1	4	yes	—
368	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
369	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
370	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
371	C₄⋊Q₈	—	4	4	no	—
372	#125	—	4	4	no	—
373	C₂²⋊Q₈	—	2	16	no	—
374	C₂²⋊Q₈	—	4	8	no	—
375	#117	—	4	4	no	—
376	C₂×C₄⋊C₄	—	4	4	no	—
377	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
378	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
379	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
380	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
381	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
382	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
383	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
384	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
385	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
386	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
387	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
388	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
389	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
390	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
391	C₂×C₂²⋊C₄	—	2	8	no	—
392	C₂×C₂²⋊C₄	—	4	4	no	—
393	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
394	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
395	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
396	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
397	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
398	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
399	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
400	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
401	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
402	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
403	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
404	C₂×C₄²	—	4	4	no	—
405	C₂×C₄²	C₂³×C₅	1	2	yes	—
406	C₂×C₄²	C₂³×C₅	1	2	yes	—
407	C₂×C₄²	C₂³×C₅	1	4	yes	—
408	C₂×C₄²	C₂³×C₅	1	2	yes	—
409	C₂×C₄²	C₂³×C₅	1	2	yes	—
410	#95	C₂³×C₅	1	2	yes	—
411	#95	C₂³×C₅	1	2	yes	—
412	#95	C₂³×C₅	1	1	yes	characteristic
413	#95	C₂³×C₅	1	1	yes	characteristic
414	#95	C₂³×C₅	1	1	yes	characteristic
415	#95	C₂³×C₅	1	1	yes	characteristic
416	#95	C₂³×C₅	1	2	yes	—
417	#95	C₂³×C₅	1	4	yes	—
418	#95	C₂³×C₅	1	2	yes	—
419	#95	C₂³×C₅	1	2	yes	—
420	#95	C₂³×C₅	1	2	yes	—
421	#95	C₂³×C₅	1	4	yes	—
422	#95	C₂³×C₅	1	4	yes	—
423	#95	C₂³×C₅	1	4	yes	—
424	#95	C₂³×C₅	1	4	yes	—
425	#95	C₂³×C₅	1	4	yes	—
426	#95	C₂³×C₅	1	4	yes	—
427	#95	C₂³×C₅	1	4	yes	—
428	C₂²×C₅	—	2	2	no	—
429	C₂²×C₅	—	2	2	no	—
430	C₂²×C₅	—	2	2	no	—
431	C₂²×C₅	—	2	2	no	—
432	C₂²×C₅	—	2	4	no	—
433	C₂²×C₅	—	2	4	no	—
434	C₂²×C₅	—	2	4	no	—
435	C₂²×C₅	—	2	4	no	—
436	C₂²×C₅	—	2	2	no	—
437	C₂²×C₅	—	2	2	no	—
438	C₂²×C₅	—	2	2	no	—
439	C₂²×C₅	—	4	16	no	—
440	C₂²×C₅	—	4	2	no	—
441	C₂²×C₅	—	4	2	no	—
442	C₂²×C₅	#533	1	4	yes	—
443	C₂²×C₅	#544	1	4	yes	—
444	C₂²×C₅	C₂³×Q₈	1	1	yes	characteristic
445	C₂²×C₅	C₂²×#41	1	2	yes	—
446	C₂²×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
447	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
448	C₂²×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
449	C₄×C₅	—	2	2	no	—
450	C₄×C₅	—	2	2	no	—
451	C₄×C₅	—	2	2	no	—
452	C₄×C₅	—	2	4	no	—
453	C₄×C₅	—	2	4	no	—
454	C₄×C₅	—	4	2	no	—
455	C₄×C₅	—	4	4	no	—
456	C₄×C₅	—	4	4	no	—
457	C₄×C₅	—	4	4	no	—
458	C₄×C₅	—	4	4	no	—
459	C₄×C₅	—	4	2	no	—
460	C₄×C₅	#543	1	4	yes	—
461	C₂⁴	—	2	4	no	—
462	C₂⁴	—	2	2	no	—
463	C₂⁴	—	2	2	no	—
464	C₂⁴	—	4	2	no	—
465	C₂⁴	C₂×C₅×Q₈	1	4	yes	—
466	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
467	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
468	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
469	C₂×Q₈	—	2	8	no	—
470	C₂×Q₈	—	4	4	no	—
471	C₂×Q₈	—	4	4	no	—
472	C₂²×C₄	—	2	4	no	—
473	C₂²×C₄	—	2	4	no	—
474	C₂²×C₄	—	2	4	no	—
475	C₂²×C₄	—	2	4	no	—
476	C₂²×C₄	—	2	4	no	—
477	C₂²×C₄	—	2	8	no	—
478	C₂²×C₄	—	2	4	no	—
479	C₂²×C₄	—	2	4	no	—
480	C₂²×C₄	—	4	16	no	—
481	C₂²×C₄	—	4	2	no	—
482	C₂²×C₄	—	4	2	no	—
483	C₂²×C₄	—	4	2	no	—
484	C₂²×C₄	—	4	2	no	—
485	C₂²×C₄	—	4	2	no	—
486	C₂²×C₄	—	4	4	no	—
487	C₂²×C₄	—	4	4	no	—
488	C₂²×C₄	C₂×C₅×Q₈	1	4	yes	—
489	C₂²×C₄	C₂×C₅×Q₈	1	4	yes	—
490	C₂²×C₄	C₂×C₅×Q₈	1	4	yes	—
491	C₂²×C₄	C₂×C₅×Q₈	1	4	yes	—
492	C₂²×C₄	C₂×C₅×Q₈	1	4	yes	—
493	C₂²×C₄	C₂×C₅×Q₈	1	4	yes	—
494	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
495	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
496	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
497	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
498	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
499	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
500	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
501	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
502	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
503	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
504	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
505	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
506	C₄⋊C₄	—	2	8	no	—
507	C₄⋊C₄	—	2	8	no	—
508	C₄⋊C₄	—	2	8	no	—
509	C₄⋊C₄	—	2	4	no	—
510	C₄⋊C₄	—	2	4	no	—
511	C₄⋊C₄	—	2	4	no	—
512	C₄⋊C₄	—	2	4	no	—
513	C₄⋊C₄	—	4	4	no	—
514	C₄⋊C₄	—	4	4	no	—
515	C₄⋊C₄	—	4	4	no	—
516	C₄⋊C₄	—	4	4	no	—
517	C₄⋊C₄	—	4	4	no	—
518	C₄⋊C₄	—	4	4	no	—
519	C₄⋊C₄	—	4	4	no	—
520	C₂²⋊C₄	—	2	4	no	—
521	C₂²⋊C₄	—	2	8	no	—
522	C₂²⋊C₄	—	2	8	no	—
523	C₂²⋊C₄	—	2	4	no	—
524	C₂²⋊C₄	—	2	4	no	—
525	C₂²⋊C₄	—	2	4	no	—
526	C₂²⋊C₄	—	2	4	no	—
527	C₂²⋊C₄	—	4	2	no	—
528	C₂²⋊C₄	—	4	2	no	—
529	C₂²⋊C₄	—	4	4	no	—
530	C₂²⋊C₄	C₅×#41	1	8	yes	—
531	C₄²	—	2	4	no	—
532	C₄²	—	2	4	no	—
533	C₄²	—	4	2	no	—
534	C₄²	—	4	2	no	—
535	C₄²	—	4	4	no	—
536	C₂×C₅	—	2	4	no	—
537	C₂×C₅	—	2	4	no	—
538	C₂×C₅	—	4	2	no	—
539	C₂×C₅	C₂×#533	1	1	yes	characteristic
540	C₂×C₅	C₂×#543	1	1	yes	characteristic
541	C₂×C₅	C₂×#544	1	1	yes	characteristic
542	C₂×C₅	#3519	1	2	yes	—
543	C₂×C₅	#3520	1	2	yes	—
544	C₂³	—	2	2	no	—
545	C₂³	—	2	2	no	—
546	C₂³	—	2	2	no	—
547	C₂³	—	2	1	no	—
548	C₂³	—	2	1	no	—
549	C₂³	—	2	8	no	—
550	C₂³	—	2	8	no	—
551	C₂³	—	2	2	no	—
552	C₂³	—	2	1	no	—
553	C₂³	—	2	2	no	—
554	C₂³	—	2	1	no	—
555	C₂³	—	4	4	no	—
556	C₂³	—	4	8	no	—
557	C₂³	—	4	8	no	—
558	C₂³	C₂²×C₅×Q₈	1	2	yes	—
559	C₂³	C₂²×C₅×Q₈	1	2	yes	—
560	C₂³	C₂²×C₅×Q₈	1	2	yes	—
561	C₂³	C₂×C₅×#41	1	4	yes	—
562	C₂³	C₅×H(5,𝔽₂)	1	2	yes	—
563	C₂³	C₅×2₋¹⁺⁴	1	2	yes	—
564	C₂³	C₂⁵×C₅	1	1	yes	characteristic
565	Q₈	—	8	8	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	8	no	—
574	C₂×C₄	—	2	8	no	—
575	C₂×C₄	—	2	8	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	4	no	—
579	C₂×C₄	—	2	4	no	—
580	C₂×C₄	—	2	4	no	—
581	C₂×C₄	—	2	4	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	4	no	—
585	C₂×C₄	—	2	4	no	—
586	C₂×C₄	—	2	4	no	—
587	C₂×C₄	—	2	4	no	—
588	C₂×C₄	—	2	4	no	—
589	C₂×C₄	—	2	4	no	—
590	C₂×C₄	—	2	4	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	4	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	4	4	no	—
595	C₂×C₄	—	4	4	no	—
596	C₂×C₄	—	4	4	no	—
597	C₂×C₄	—	4	8	no	—
598	C₂×C₄	—	4	8	no	—
599	C₂×C₄	—	8	8	no	—
600	C₂×C₄	C₂²×C₅×Q₈	1	2	yes	—
601	C₂×C₄	C₂²×C₅×Q₈	1	2	yes	—
602	C₂×C₄	C₂²×C₅×Q₈	1	2	yes	—
603	C₂×C₄	C₂²×C₅×Q₈	1	2	yes	—
604	C₂×C₄	C₂×C₅×#41	1	4	yes	—
605	C₂×C₄	C₂×C₅×#41	1	4	yes	—
606	C₂×C₄	C₅×H(5,𝔽₂)	1	4	yes	—
607	C₅	#35079	1	1	yes	characteristic, direct product factor, Sylow
608	C₂²	—	2	2	no	—
609	C₂²	—	2	2	no	—
610	C₂²	—	2	2	no	—
611	C₂²	—	2	2	no	—
612	C₂²	—	2	4	no	—
613	C₂²	—	2	4	no	—
614	C₂²	—	2	4	no	—
615	C₂²	—	2	4	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	2	2	no	—
618	C₂²	—	2	2	no	—
619	C₂²	—	4	16	no	—
620	C₂²	—	4	2	no	—
621	C₂²	—	4	2	no	—
622	C₂²	C₅×#533	1	4	yes	—
623	C₂²	C₅×#544	1	4	yes	—
624	C₂²	C₂³×C₅×Q₈	1	1	yes	characteristic
625	C₂²	C₂²×C₅×#41	1	2	yes	—
626	C₂²	C₂×C₅×H(5,𝔽₂)	1	2	yes	—
627	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
628	C₂²	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
629	C₄	—	2	2	no	—
630	C₄	—	2	2	no	—
631	C₄	—	2	2	no	—
632	C₄	—	2	4	no	—
633	C₄	—	2	4	no	—
634	C₄	—	4	2	no	—
635	C₄	—	4	4	no	—
636	C₄	—	4	4	no	—
637	C₄	—	4	4	no	—
638	C₄	—	4	2	no	—
639	C₄	—	4	4	no	—
640	C₄	C₅×#543	1	4	yes	—
641	C₂	—	2	4	no	—
642	C₂	—	2	4	no	—
643	C₂	—	4	2	no	—
644	C₂	C₂×C₅×#533	1	1	yes	characteristic
645	C₂	C₂×C₅×#543	1	1	yes	characteristic
646	C₂	C₂×C₅×#544	1	1	yes	characteristic
647	C₂	C₅×#3519	1	2	yes	—
648	C₂	C₅×#3520	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅
prime radical	C₂⁵×C₅	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#2857	C₂	semidirect
2. C₅×#2851	C₂	semidirect
3. C₅×#2667	C₂	semidirect
4. C₅×#2665	C₂	semidirect
5. C₅×#2569	C₂	semidirect
6. C₅×#2549	C₂	semidirect
7. C₅×#2442	C₂	semidirect
8. C₅×#2441	C₂	semidirect
9. C₅×#2440	C₂	semidirect
10. C₅×#2439	C₂	semidirect
12. C₅×#2329	C₂	semidirect
17. C₂×C₅×C₄⋊Q₈	C₂²	semidirect
18. C₂×C₅×#125	C₂²	semidirect
26. C₅×#400	C₂²	semidirect
28. C₅×#398	C₂²	semidirect
29. C₅×#398	C₂²	semidirect
32. C₅×#395	C₂²	semidirect
34. C₅×#391	C₂²	semidirect
35. C₅×#391	C₂²	semidirect
36. C₅×#389	C₂²	semidirect
37. C₅×#389	C₂²	semidirect
38. C₅×#389	C₂²	semidirect
39. C₅×#389	C₂²	semidirect
40. C₅×#389	C₂²	semidirect
41. C₅×#389	C₂²	semidirect
42. C₅×#387	C₂²	semidirect
43. C₅×#387	C₂²	semidirect
44. C₅×#387	C₂²	semidirect
45. C₅×#387	C₂²	semidirect
50. C₅×#384	C₂²	semidirect
51. C₅×#382	C₂²	semidirect
75. #35079	C₅	direct (N × H)
79. C₂³×C₄×C₅	Q₈	semidirect
146. #2857	C₂×C₅	semidirect
147. #2851	C₂×C₅	semidirect
148. #2667	C₂×C₅	semidirect
149. #2665	C₂×C₅	semidirect
150. #2569	C₂×C₅	semidirect
151. #2549	C₂×C₅	semidirect
152. #2442	C₂×C₅	semidirect
153. #2441	C₂×C₅	semidirect
154. #2440	C₂×C₅	semidirect
155. #2439	C₂×C₅	semidirect
157. #2329	C₂×C₅	semidirect
237. C₂×C₄⋊Q₈	C₂²×C₅	semidirect
238. C₂×#125	C₂²×C₅	semidirect
246. #400	C₂²×C₅	semidirect
248. #398	C₂²×C₅	semidirect
249. #398	C₂²×C₅	semidirect
252. #395	C₂²×C₅	semidirect
254. #391	C₂²×C₅	semidirect
255. #391	C₂²×C₅	semidirect
256. #389	C₂²×C₅	semidirect
257. #389	C₂²×C₅	semidirect
258. #389	C₂²×C₅	semidirect
259. #389	C₂²×C₅	semidirect
260. #389	C₂²×C₅	semidirect
261. #389	C₂²×C₅	semidirect
262. #387	C₂²×C₅	semidirect
263. #387	C₂²×C₅	semidirect
264. #387	C₂²×C₅	semidirect
265. #387	C₂²×C₅	semidirect
270. #384	C₂²×C₅	semidirect
271. #382	C₂²×C₅	semidirect
361. C₂³×C₄	C₅×Q₈	semidirect
607. C₅	#35079	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#2857	2
C₅×#2851	2
C₅×#2667	2
C₅×#2665	2
C₅×#2569	2
C₅×#2549	2
C₅×#2442	2
C₅×#2441	2
C₅×#2440	2
C₅×#2439	2
C₅×#2437	2
C₅×#2329	2
C₅×#2280	2
C₂×C₅×#380	2
C₂×C₄×C₅×C₂²⋊C₄	2
#35079	5

Subgroups — C5×#35079 #11957799

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#35079 #11957799