Subgroups — C₅×#22873 #11945593

Order 1280.

1102 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#452	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#416	C₂	1	1	yes	maximal, characteristic
4	C₅×#2362	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2341	C₂	1	1	yes	maximal, characteristic
6	C₅×#1968	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1934	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1925	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1892	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1880	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1878	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1865	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1854	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₅×#103	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×C₈×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₅×#41	C₂²	1	1	yes	characteristic
17	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₅×SD₁₆	C₂²	1	1	yes	characteristic
19	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
20	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₅×#117	C₂²	1	1	yes	characteristic
25	C₅×#452	C₄	1	8	yes	complemented
26	C₄×C₅×Q₁₆	—	2	4	no	—
27	C₂×C₅×#107	C₂²	1	1	yes	characteristic
28	C₂×C₅×#106	C₂²	1	1	yes	characteristic
29	C₅×#416	—	2	4	no	—
30	C₂×C₅×#103	C₂²	1	1	yes	characteristic
31	C₂×C₅×#103	C₂²	1	1	yes	characteristic
32	C₂×C₅×#103	C₂²	1	1	yes	characteristic
33	C₂×C₅×#103	C₂²	1	1	yes	characteristic
34	C₂×C₅×#103	C₂²	1	1	yes	characteristic
35	C₂×C₅×#102	C₂²	1	1	yes	characteristic
36	C₂×C₅×#102	C₂²	1	1	yes	characteristic
37	C₂×C₅×#102	C₂²	1	1	yes	characteristic
38	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
41	C₅×#391	C₂²	1	1	yes	characteristic
42	C₅×#390	—	2	1	no	—
43	C₅×#390	—	2	1	no	—
44	C₅×#390	C₂²	1	1	yes	characteristic
45	C₅×#390	C₂²	1	1	yes	characteristic
46	C₅×#389	C₂²	1	1	yes	characteristic
47	C₅×#388	—	2	1	no	—
48	C₅×#388	—	2	1	no	—
49	C₅×#387	—	2	1	no	—
50	C₅×#380	—	2	1	no	—
51	C₅×#380	C₂²	1	1	yes	characteristic
52	C₄×C₅×C₄⋊C₄	—	2	1	no	—
53	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
54	C₄×C₅×C₂²⋊C₄	—	2	1	no	—
55	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
56	C₅×#340	C₂²	1	1	yes	characteristic
57	C₅×#340	C₂²	1	1	yes	characteristic
58	C₅×#340	C₂²	1	1	yes	characteristic
59	C₅×#340	C₂²	1	1	yes	characteristic
60	C₅×#336	C₂²	1	1	yes	characteristic
61	C₅×#336	C₂²	1	1	yes	characteristic
62	#22873	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
63	C₂×C₅×#41	—	2	2	no	—
64	C₂×C₅×#41	—	2	2	no	—
65	C₂×C₅×#41	—	2	2	no	—
66	C₂×C₅×#41	—	4	1	no	—
67	C₂×C₅×#41	—	4	1	no	—
68	C₂×C₅×#41	C₂×C₄	1	4	yes	—
69	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
70	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
71	C₂²×C₅×D₄	—	2	1	no	—
72	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₅	—	2	1	no	—
74	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
75	C₂×C₅×Q₁₆	—	2	2	no	—
76	C₂×C₅×Q₁₆	—	2	2	no	—
77	C₂×C₅×Q₁₆	C₂×C₄	1	4	yes	—
78	C₂×C₅×SD₁₆	—	4	1	no	—
79	C₂×C₅×SD₁₆	—	4	1	no	—
80	C₂×C₅×SD₁₆	C₂×C₄	1	4	yes	—
81	C₂²×C₅×C₈	—	2	2	no	—
82	C₂²×C₅×C₈	—	2	2	no	—
83	C₂²×C₅×C₈	—	4	1	no	—
84	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
85	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
86	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
87	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
88	C₅×C₂²⋊Q₈	—	2	2	no	—
89	C₅×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
90	C₄×C₅×Q₈	—	2	2	no	—
91	C₄×C₅×Q₈	—	2	2	no	—
92	C₄×C₅×Q₈	—	2	2	no	—
93	C₄×C₅×Q₈	—	4	1	no	—
94	C₄×C₅×Q₈	—	4	1	no	—
95	C₄×C₅×Q₈	—	4	1	no	—
96	C₅×#117	—	2	2	no	—
97	C₅×#117	—	4	1	no	—
98	C₂×C₅×C₄⋊C₄	—	2	1	no	—
99	C₂×C₅×C₄⋊C₄	—	2	1	no	—
100	C₂×C₅×C₄⋊C₄	—	2	1	no	—
101	C₂×C₅×C₄⋊C₄	—	2	1	no	—
102	C₂×C₅×C₄⋊C₄	—	2	1	no	—
103	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
104	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
105	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
106	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
107	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
109	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
110	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
111	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
112	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
113	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
114	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
115	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
116	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
117	C₂×C₄²×C₅	—	2	1	no	—
118	C₂×C₄²×C₅	—	2	1	no	—
119	C₂×C₄²×C₅	—	2	1	no	—
120	C₂×C₄²×C₅	—	2	1	no	—
121	C₂×C₄²×C₅	—	2	1	no	—
122	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
123	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
124	C₅×#107	—	2	2	no	—
125	C₅×#106	—	4	1	no	—
126	C₅×#103	—	2	2	no	—
127	C₅×#103	—	2	2	no	—
128	C₅×#103	—	4	1	no	—
129	C₅×#103	C₂×C₄	1	4	yes	—
130	C₅×#103	D₄	1	4	yes	—
131	C₅×#102	—	2	2	no	—
132	C₅×#102	—	2	2	no	—
133	C₅×#102	C₂×C₄	1	4	yes	—
134	C₅×C₂²⋊C₈	C₂×C₄	1	4	yes	—
135	C₄×C₅×C₈	—	2	2	no	—
136	C₄×C₅×C₈	—	4	1	no	—
137	C₅×#95	—	2	1	no	—
138	C₅×#95	—	2	1	no	—
139	C₅×#95	—	2	1	no	—
140	C₅×#95	—	2	1	no	—
141	C₅×#95	—	2	1	no	—
142	C₅×#95	D₄	1	1	yes	characteristic
143	C₅×#95	D₄	1	1	yes	characteristic
144	C₂×#452	C₂×C₅	1	1	yes	characteristic
145	C₂×C₄×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
146	C₂×#416	C₂×C₅	1	1	yes	characteristic
147	#2362	C₂×C₅	1	1	yes	characteristic, complemented
148	#2341	C₂×C₅	1	1	yes	characteristic
149	#1968	C₂×C₅	1	1	yes	characteristic, complemented
150	#1934	C₂×C₅	1	1	yes	characteristic, complemented
151	#1925	C₂×C₅	1	1	yes	characteristic, complemented
152	#1892	C₂×C₅	1	1	yes	characteristic, complemented
153	#1880	C₂×C₅	1	1	yes	characteristic, complemented
154	#1878	C₂×C₅	1	1	yes	characteristic, complemented
155	#1865	C₂×C₅	1	1	yes	characteristic, complemented
156	#1854	C₂×C₅	1	1	yes	characteristic, complemented
157	C₄×#103	C₂×C₅	1	1	yes	characteristic, complemented
158	C₈×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
159	C₂⁴×C₅	—	2	1	no	—
160	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
161	C₅×#41	—	2	8	no	—
162	C₅×#41	—	4	4	no	—
163	C₅×#41	—	4	4	no	—
164	C₅×#41	—	4	4	no	—
165	C₂×C₅×Q₈	—	2	1	no	—
166	C₂×C₅×Q₈	—	2	1	no	—
167	C₂×C₅×Q₈	—	2	1	no	—
168	C₂×C₅×Q₈	—	2	1	no	—
169	C₂×C₅×Q₈	—	2	1	no	—
170	C₂×C₅×Q₈	—	2	1	no	—
171	C₂×C₅×Q₈	—	2	1	no	—
172	C₂×C₅×Q₈	—	2	1	no	—
173	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
174	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
175	C₂×C₅×Q₈	C₂×D₄	1	2	yes	—
176	C₂×C₅×Q₈	#41	1	2	yes	—
177	C₂×C₅×D₄	—	2	4	no	—
178	C₂×C₅×D₄	—	2	1	no	—
179	C₂×C₅×D₄	—	2	1	no	—
180	C₂×C₅×D₄	—	2	1	no	—
181	C₂×C₅×D₄	—	2	1	no	—
182	C₂×C₅×D₄	—	2	1	no	—
183	C₂×C₅×D₄	—	4	2	no	—
184	C₂×C₅×D₄	—	4	2	no	—
185	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
186	C₂²×C₄×C₅	—	2	1	no	—
187	C₂²×C₄×C₅	—	2	1	no	—
188	C₂²×C₄×C₅	—	2	1	no	—
189	C₂²×C₄×C₅	—	2	1	no	—
190	C₂²×C₄×C₅	—	2	1	no	—
191	C₂²×C₄×C₅	—	2	1	no	—
192	C₂²×C₄×C₅	—	2	1	no	—
193	C₂²×C₄×C₅	—	2	1	no	—
194	C₂²×C₄×C₅	—	2	4	no	—
195	C₂²×C₄×C₅	—	2	1	no	—
196	C₂²×C₄×C₅	—	2	1	no	—
197	C₂²×C₄×C₅	—	2	1	no	—
198	C₂²×C₄×C₅	—	4	2	no	—
199	C₂²×C₄×C₅	—	4	2	no	—
200	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
201	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₅	#41	1	2	yes	—
207	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
208	C₅×Q₁₆	—	2	8	no	—
209	C₅×SD₁₆	—	4	4	no	—
210	C₂×C₅×C₈	—	2	1	no	—
211	C₂×C₅×C₈	—	2	1	no	—
212	C₂×C₅×C₈	—	2	1	no	—
213	C₂×C₅×C₈	—	2	1	no	—
214	C₂×C₅×C₈	—	2	1	no	—
215	C₂×C₅×C₈	—	2	1	no	—
216	C₂×C₅×C₈	—	2	1	no	—
217	C₂×C₅×C₈	—	2	1	no	—
218	C₂×C₅×C₈	—	2	1	no	—
219	C₂×C₅×C₈	—	4	4	no	—
220	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
221	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
222	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
223	C₅×C₄⋊C₄	—	2	4	no	—
224	C₅×C₄⋊C₄	—	2	1	no	—
225	C₅×C₄⋊C₄	—	2	1	no	—
226	C₅×C₄⋊C₄	—	2	1	no	—
227	C₅×C₄⋊C₄	—	2	1	no	—
228	C₅×C₄⋊C₄	—	2	1	no	—
229	C₅×C₄⋊C₄	—	2	1	no	—
230	C₅×C₄⋊C₄	—	2	1	no	—
231	C₅×C₄⋊C₄	—	2	1	no	—
232	C₅×C₄⋊C₄	—	4	2	no	—
233	C₅×C₄⋊C₄	—	4	2	no	—
234	C₅×C₄⋊C₄	—	4	2	no	—
235	C₅×C₄⋊C₄	—	4	2	no	—
236	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
237	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
238	C₅×C₂²⋊C₄	—	2	4	no	—
239	C₅×C₂²⋊C₄	—	2	2	no	—
240	C₅×C₂²⋊C₄	—	2	2	no	—
241	C₅×C₂²⋊C₄	—	4	2	no	—
242	C₅×C₂²⋊C₄	—	4	2	no	—
243	C₅×C₂²⋊C₄	—	4	2	no	—
244	C₅×C₂²⋊C₄	—	8	1	no	—
245	C₅×C₂²⋊C₄	—	8	1	no	—
246	C₅×C₂²⋊C₄	—	8	1	no	—
247	C₄²×C₅	—	2	1	no	—
248	C₄²×C₅	—	2	1	no	—
249	C₄²×C₅	—	2	1	no	—
250	C₄²×C₅	—	2	1	no	—
251	C₄²×C₅	—	4	2	no	—
252	C₄²×C₅	—	4	2	no	—
253	C₄²×C₅	—	4	2	no	—
254	C₄²×C₅	—	4	2	no	—
255	C₄²×C₅	—	4	2	no	—
256	C₂²×#41	C₂²×C₅	1	1	yes	characteristic
257	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
258	C₂²×SD₁₆	C₂²×C₅	1	1	yes	characteristic
259	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
260	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
261	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
262	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
263	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
264	C₂×#117	C₂²×C₅	1	1	yes	characteristic
265	#452	C₄×C₅	1	8	yes	complemented
266	C₄×Q₁₆	—	2	4	no	—
267	C₂×#107	C₂²×C₅	1	1	yes	characteristic
268	C₂×#106	C₂²×C₅	1	1	yes	characteristic
269	#416	—	2	4	no	—
270	C₂×#103	C₂²×C₅	1	1	yes	characteristic
271	C₂×#103	C₂²×C₅	1	1	yes	characteristic
272	C₂×#103	C₂²×C₅	1	1	yes	characteristic
273	C₂×#103	C₂²×C₅	1	1	yes	characteristic
274	C₂×#103	C₂²×C₅	1	1	yes	characteristic
275	C₂×#102	C₂²×C₅	1	1	yes	characteristic
276	C₂×#102	C₂²×C₅	1	1	yes	characteristic
277	C₂×#102	C₂²×C₅	1	1	yes	characteristic
278	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
279	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
280	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
281	#391	C₂²×C₅	1	1	yes	characteristic
282	#390	—	2	1	no	—
283	#390	—	2	1	no	—
284	#390	C₂²×C₅	1	1	yes	characteristic
285	#390	C₂²×C₅	1	1	yes	characteristic
286	#389	C₂²×C₅	1	1	yes	characteristic
287	#388	—	2	1	no	—
288	#388	—	2	1	no	—
289	#387	—	2	1	no	—
290	#380	—	2	1	no	—
291	#380	C₂²×C₅	1	1	yes	characteristic
292	C₄×C₄⋊C₄	—	2	1	no	—
293	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
294	C₄×C₂²⋊C₄	—	2	1	no	—
295	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
296	#340	C₂²×C₅	1	1	yes	characteristic
297	#340	C₂²×C₅	1	1	yes	characteristic
298	#340	C₂²×C₅	1	1	yes	characteristic
299	#340	C₂²×C₅	1	1	yes	characteristic
300	#336	C₂²×C₅	1	1	yes	characteristic
301	#336	C₂²×C₅	1	1	yes	characteristic
302	C₂³×C₅	—	2	1	no	—
303	C₂³×C₅	—	2	1	no	—
304	C₂³×C₅	—	2	1	no	—
305	C₂³×C₅	—	2	1	no	—
306	C₂³×C₅	—	2	1	no	—
307	C₂³×C₅	—	2	1	no	—
308	C₂³×C₅	—	2	2	no	—
309	C₂³×C₅	—	4	1	no	—
310	C₂³×C₅	—	4	1	no	—
311	C₂³×C₅	—	4	1	no	—
312	C₂³×C₅	—	4	1	no	—
313	C₂³×C₅	—	4	1	no	—
314	C₂³×C₅	—	4	1	no	—
315	C₂³×C₅	C₄×D₄	1	2	yes	—
316	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
317	C₅×Q₈	—	2	2	no	—
318	C₅×Q₈	—	2	2	no	—
319	C₅×Q₈	—	2	2	no	—
320	C₅×Q₈	—	2	2	no	—
321	C₅×Q₈	—	2	2	no	—
322	C₅×Q₈	—	4	1	no	—
323	C₅×Q₈	—	4	1	no	—
324	C₅×Q₈	C₄×D₄	1	4	yes	—
325	C₅×D₄	—	2	2	no	—
326	C₅×D₄	—	2	2	no	—
327	C₅×D₄	—	4	8	no	—
328	C₅×D₄	—	4	1	no	—
329	C₅×D₄	—	4	1	no	—
330	C₂×C₄×C₅	—	2	2	no	—
331	C₂×C₄×C₅	—	2	1	no	—
332	C₂×C₄×C₅	—	2	1	no	—
333	C₂×C₄×C₅	—	2	2	no	—
334	C₂×C₄×C₅	—	2	1	no	—
335	C₂×C₄×C₅	—	2	2	no	—
336	C₂×C₄×C₅	—	2	1	no	—
337	C₂×C₄×C₅	—	2	1	no	—
338	C₂×C₄×C₅	—	2	1	no	—
339	C₂×C₄×C₅	—	2	2	no	—
340	C₂×C₄×C₅	—	2	2	no	—
341	C₂×C₄×C₅	—	2	2	no	—
342	C₂×C₄×C₅	—	2	2	no	—
343	C₂×C₄×C₅	—	2	2	no	—
344	C₂×C₄×C₅	—	2	2	no	—
345	C₂×C₄×C₅	—	2	1	no	—
346	C₂×C₄×C₅	—	2	2	no	—
347	C₂×C₄×C₅	—	2	1	no	—
348	C₂×C₄×C₅	—	2	1	no	—
349	C₂×C₄×C₅	—	2	1	no	—
350	C₂×C₄×C₅	—	2	1	no	—
351	C₂×C₄×C₅	—	2	1	no	—
352	C₂×C₄×C₅	—	4	8	no	—
353	C₂×C₄×C₅	—	4	1	no	—
354	C₂×C₄×C₅	—	4	1	no	—
355	C₂×C₄×C₅	—	4	1	no	—
356	C₂×C₄×C₅	—	4	1	no	—
357	C₂×C₄×C₅	—	4	1	no	—
358	C₂×C₄×C₅	—	4	1	no	—
359	C₂×C₄×C₅	—	4	1	no	—
360	C₂×C₄×C₅	—	4	1	no	—
361	C₂×C₄×C₅	—	4	1	no	—
362	C₂×C₄×C₅	—	4	1	no	—
363	C₂×C₄×C₅	—	4	1	no	—
364	C₂×C₄×C₅	—	4	1	no	—
365	C₂×C₄×C₅	—	4	1	no	—
366	C₂×C₄×C₅	—	4	1	no	—
367	C₂×C₄×C₅	—	4	1	no	—
368	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
369	C₂×C₄×C₅	#135	1	2	yes	—
370	C₂×C₄×C₅	#135	1	2	yes	—
371	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
372	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
373	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
374	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
375	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
376	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
377	C₅×C₈	—	2	2	no	—
378	C₅×C₈	—	2	2	no	—
379	C₅×C₈	—	2	2	no	—
380	C₅×C₈	—	4	1	no	—
381	C₂×#41	—	2	2	no	—
382	C₂×#41	—	2	2	no	—
383	C₂×#41	—	2	2	no	—
384	C₂×#41	—	4	1	no	—
385	C₂×#41	—	4	1	no	—
386	C₂×#41	C₂×C₄×C₅	1	4	yes	—
387	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
388	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
389	C₂²×D₄	—	2	1	no	—
390	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
391	C₂³×C₄	—	2	1	no	—
392	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
393	C₂×Q₁₆	—	2	2	no	—
394	C₂×Q₁₆	—	2	2	no	—
395	C₂×Q₁₆	C₂×C₄×C₅	1	4	yes	—
396	C₂×SD₁₆	—	4	1	no	—
397	C₂×SD₁₆	—	4	1	no	—
398	C₂×SD₁₆	C₂×C₄×C₅	1	4	yes	—
399	C₂²×C₈	—	2	2	no	—
400	C₂²×C₈	—	2	2	no	—
401	C₂²×C₈	—	4	1	no	—
402	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
403	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
404	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
405	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
406	C₂²⋊Q₈	—	2	2	no	—
407	C₂²⋊Q₈	C₂×C₄×C₅	1	4	yes	—
408	C₄×Q₈	—	2	2	no	—
409	C₄×Q₈	—	2	2	no	—
410	C₄×Q₈	—	2	2	no	—
411	C₄×Q₈	—	4	1	no	—
412	C₄×Q₈	—	4	1	no	—
413	C₄×Q₈	—	4	1	no	—
414	#117	—	2	2	no	—
415	#117	—	4	1	no	—
416	C₂×C₄⋊C₄	—	2	1	no	—
417	C₂×C₄⋊C₄	—	2	1	no	—
418	C₂×C₄⋊C₄	—	2	1	no	—
419	C₂×C₄⋊C₄	—	2	1	no	—
420	C₂×C₄⋊C₄	—	2	1	no	—
421	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
422	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
423	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
424	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
425	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
426	C₂×C₂²⋊C₄	—	2	1	no	—
427	C₂×C₂²⋊C₄	—	2	1	no	—
428	C₂×C₂²⋊C₄	—	2	1	no	—
429	C₂×C₂²⋊C₄	—	2	1	no	—
430	C₂×C₂²⋊C₄	—	2	1	no	—
431	C₂×C₂²⋊C₄	—	2	1	no	—
432	C₂×C₂²⋊C₄	—	2	1	no	—
433	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
434	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
435	C₂×C₄²	—	2	1	no	—
436	C₂×C₄²	—	2	1	no	—
437	C₂×C₄²	—	2	1	no	—
438	C₂×C₄²	—	2	1	no	—
439	C₂×C₄²	—	2	1	no	—
440	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
441	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
442	#107	—	2	2	no	—
443	#106	—	4	1	no	—
444	#103	—	2	2	no	—
445	#103	—	2	2	no	—
446	#103	—	4	1	no	—
447	#103	C₂×C₄×C₅	1	4	yes	—
448	#103	C₅×D₄	1	4	yes	—
449	#102	—	2	2	no	—
450	#102	—	2	2	no	—
451	#102	C₂×C₄×C₅	1	4	yes	—
452	C₂²⋊C₈	C₂×C₄×C₅	1	4	yes	—
453	C₄×C₈	—	2	2	no	—
454	C₄×C₈	—	4	1	no	—
455	#95	—	2	1	no	—
456	#95	—	2	1	no	—
457	#95	—	2	1	no	—
458	#95	—	2	1	no	—
459	#95	—	2	1	no	—
460	#95	C₅×D₄	1	1	yes	characteristic
461	#95	C₅×D₄	1	1	yes	characteristic
462	C₂²×C₅	—	2	2	no	—
463	C₂²×C₅	—	2	2	no	—
464	C₂²×C₅	—	2	2	no	—
465	C₂²×C₅	—	4	1	no	—
466	C₂²×C₅	—	4	1	no	—
467	C₂²×C₅	—	4	1	no	—
468	C₂²×C₅	—	4	1	no	—
469	C₂²×C₅	—	4	2	no	—
470	C₂²×C₅	—	4	2	no	—
471	C₂²×C₅	—	4	2	no	—
472	C₂²×C₅	—	8	1	no	—
473	C₂²×C₅	—	8	1	no	—
474	C₂²×C₅	—	8	1	no	—
475	C₂²×C₅	—	8	1	no	—
476	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
477	C₂²×C₅	D₄²	1	1	yes	characteristic
478	C₂²×C₅	#546	1	1	yes	characteristic
479	C₂²×C₅	C₂×#135	1	1	yes	characteristic
480	C₂²×C₅	C₂×#135	1	1	yes	characteristic
481	C₂²×C₅	#577	1	1	yes	characteristic
482	C₂²×C₅	#578	1	1	yes	characteristic
483	C₄×C₅	—	2	2	no	—
484	C₄×C₅	—	2	4	no	—
485	C₄×C₅	—	2	2	no	—
486	C₄×C₅	—	2	2	no	—
487	C₄×C₅	—	4	2	no	—
488	C₄×C₅	—	4	2	no	—
489	C₄×C₅	—	4	1	no	—
490	C₄×C₅	—	4	2	no	—
491	C₄×C₅	—	4	1	no	—
492	C₄×C₅	—	8	1	no	—
493	C₄×C₅	—	8	1	no	—
494	C₄×C₅	—	8	1	no	—
495	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
496	C₄×C₅	#518	1	1	yes	characteristic
497	C₄×C₅	#546	1	1	yes	characteristic
498	C₄×C₅	#551	1	1	yes	characteristic
499	C₂⁴	—	2	1	no	—
500	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
501	#41	—	2	8	no	—
502	#41	—	4	4	no	—
503	#41	—	4	4	no	—
504	#41	—	4	4	no	—
505	C₂×Q₈	—	2	1	no	—
506	C₂×Q₈	—	2	1	no	—
507	C₂×Q₈	—	2	1	no	—
508	C₂×Q₈	—	2	1	no	—
509	C₂×Q₈	—	2	1	no	—
510	C₂×Q₈	—	2	1	no	—
511	C₂×Q₈	—	2	1	no	—
512	C₂×Q₈	—	2	1	no	—
513	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
514	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
515	C₂×Q₈	C₂×C₅×D₄	1	2	yes	—
516	C₂×Q₈	C₅×#41	1	2	yes	—
517	C₂×D₄	—	2	4	no	—
518	C₂×D₄	—	2	1	no	—
519	C₂×D₄	—	2	1	no	—
520	C₂×D₄	—	2	1	no	—
521	C₂×D₄	—	2	1	no	—
522	C₂×D₄	—	2	1	no	—
523	C₂×D₄	—	4	2	no	—
524	C₂×D₄	—	4	2	no	—
525	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
526	C₂²×C₄	—	2	1	no	—
527	C₂²×C₄	—	2	1	no	—
528	C₂²×C₄	—	2	1	no	—
529	C₂²×C₄	—	2	1	no	—
530	C₂²×C₄	—	2	1	no	—
531	C₂²×C₄	—	2	1	no	—
532	C₂²×C₄	—	2	1	no	—
533	C₂²×C₄	—	2	1	no	—
534	C₂²×C₄	—	2	4	no	—
535	C₂²×C₄	—	2	1	no	—
536	C₂²×C₄	—	2	1	no	—
537	C₂²×C₄	—	2	1	no	—
538	C₂²×C₄	—	4	2	no	—
539	C₂²×C₄	—	4	2	no	—
540	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
541	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
542	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
543	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
544	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
545	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
546	C₂²×C₄	C₅×#41	1	2	yes	—
547	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
548	Q₁₆	—	2	8	no	—
549	SD₁₆	—	4	4	no	—
550	C₂×C₈	—	2	1	no	—
551	C₂×C₈	—	2	1	no	—
552	C₂×C₈	—	2	1	no	—
553	C₂×C₈	—	2	1	no	—
554	C₂×C₈	—	2	1	no	—
555	C₂×C₈	—	2	1	no	—
556	C₂×C₈	—	2	1	no	—
557	C₂×C₈	—	2	1	no	—
558	C₂×C₈	—	2	1	no	—
559	C₂×C₈	—	4	4	no	—
560	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
561	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
562	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
563	C₄⋊C₄	—	2	4	no	—
564	C₄⋊C₄	—	2	1	no	—
565	C₄⋊C₄	—	2	1	no	—
566	C₄⋊C₄	—	2	1	no	—
567	C₄⋊C₄	—	2	1	no	—
568	C₄⋊C₄	—	2	1	no	—
569	C₄⋊C₄	—	2	1	no	—
570	C₄⋊C₄	—	2	1	no	—
571	C₄⋊C₄	—	2	1	no	—
572	C₄⋊C₄	—	4	2	no	—
573	C₄⋊C₄	—	4	2	no	—
574	C₄⋊C₄	—	4	2	no	—
575	C₄⋊C₄	—	4	2	no	—
576	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
577	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
578	C₂²⋊C₄	—	2	4	no	—
579	C₂²⋊C₄	—	2	2	no	—
580	C₂²⋊C₄	—	2	2	no	—
581	C₂²⋊C₄	—	4	2	no	—
582	C₂²⋊C₄	—	4	2	no	—
583	C₂²⋊C₄	—	4	2	no	—
584	C₂²⋊C₄	—	8	1	no	—
585	C₂²⋊C₄	—	8	1	no	—
586	C₂²⋊C₄	—	8	1	no	—
587	C₄²	—	2	1	no	—
588	C₄²	—	2	1	no	—
589	C₄²	—	2	1	no	—
590	C₄²	—	2	1	no	—
591	C₄²	—	4	2	no	—
592	C₄²	—	4	2	no	—
593	C₄²	—	4	2	no	—
594	C₄²	—	4	2	no	—
595	C₄²	—	4	2	no	—
596	C₂×C₅	—	4	2	no	—
597	C₂×C₅	—	8	2	no	—
598	C₂×C₅	#2358	1	1	yes	characteristic
599	C₂×C₅	C₄×#135	1	1	yes	characteristic
600	C₂×C₅	#2947	1	1	yes	characteristic
601	C₂×C₅	#3284	1	1	yes	characteristic
602	C₂×C₅	#3285	1	1	yes	characteristic
603	C₂×C₅	#3300	1	1	yes	characteristic
604	C₂×C₅	#3304	1	1	yes	characteristic
605	C₂³	—	2	1	no	—
606	C₂³	—	2	1	no	—
607	C₂³	—	2	1	no	—
608	C₂³	—	2	1	no	—
609	C₂³	—	2	1	no	—
610	C₂³	—	2	1	no	—
611	C₂³	—	2	2	no	—
612	C₂³	—	4	1	no	—
613	C₂³	—	4	1	no	—
614	C₂³	—	4	1	no	—
615	C₂³	—	4	1	no	—
616	C₂³	—	4	1	no	—
617	C₂³	—	4	1	no	—
618	C₂³	C₄×C₅×D₄	1	2	yes	—
619	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
620	Q₈	—	2	2	no	—
621	Q₈	—	2	2	no	—
622	Q₈	—	2	2	no	—
623	Q₈	—	2	2	no	—
624	Q₈	—	2	2	no	—
625	Q₈	—	4	1	no	—
626	Q₈	—	4	1	no	—
627	Q₈	C₄×C₅×D₄	1	4	yes	—
628	D₄	—	2	2	no	—
629	D₄	—	2	2	no	—
630	D₄	—	4	8	no	—
631	D₄	—	4	1	no	—
632	D₄	—	4	1	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	4	8	no	—
656	C₂×C₄	—	4	1	no	—
657	C₂×C₄	—	4	1	no	—
658	C₂×C₄	—	4	1	no	—
659	C₂×C₄	—	4	1	no	—
660	C₂×C₄	—	4	1	no	—
661	C₂×C₄	—	4	1	no	—
662	C₂×C₄	—	4	1	no	—
663	C₂×C₄	—	4	1	no	—
664	C₂×C₄	—	4	1	no	—
665	C₂×C₄	—	4	1	no	—
666	C₂×C₄	—	4	1	no	—
667	C₂×C₄	—	4	1	no	—
668	C₂×C₄	—	4	1	no	—
669	C₂×C₄	—	4	1	no	—
670	C₂×C₄	—	4	1	no	—
671	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
672	C₂×C₄	C₅×#135	1	2	yes	—
673	C₂×C₄	C₅×#135	1	2	yes	—
674	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
675	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
676	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
677	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
678	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
679	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
680	C₈	—	2	2	no	—
681	C₈	—	2	2	no	—
682	C₈	—	2	2	no	—
683	C₈	—	4	1	no	—
684	C₅	#22873	1	1	yes	characteristic, direct product factor, Sylow
685	C₂²	—	2	2	no	—
686	C₂²	—	2	2	no	—
687	C₂²	—	2	2	no	—
688	C₂²	—	4	1	no	—
689	C₂²	—	4	1	no	—
690	C₂²	—	4	1	no	—
691	C₂²	—	4	1	no	—
692	C₂²	—	4	2	no	—
693	C₂²	—	4	2	no	—
694	C₂²	—	4	2	no	—
695	C₂²	—	8	1	no	—
696	C₂²	—	8	1	no	—
697	C₂²	—	8	1	no	—
698	C₂²	—	8	1	no	—
699	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
700	C₂²	C₅×D₄²	1	1	yes	characteristic
701	C₂²	C₅×#546	1	1	yes	characteristic
702	C₂²	C₂×C₅×#135	1	1	yes	characteristic
703	C₂²	C₂×C₅×#135	1	1	yes	characteristic
704	C₂²	C₅×#577	1	1	yes	characteristic
705	C₂²	C₅×#578	1	1	yes	characteristic
706	C₄	—	2	2	no	—
707	C₄	—	2	2	no	—
708	C₄	—	2	2	no	—
709	C₄	—	2	4	no	—
710	C₄	—	4	1	no	—
711	C₄	—	4	2	no	—
712	C₄	—	4	1	no	—
713	C₄	—	4	2	no	—
714	C₄	—	4	2	no	—
715	C₄	—	8	1	no	—
716	C₄	—	8	1	no	—
717	C₄	—	8	1	no	—
718	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
719	C₄	C₅×#518	1	1	yes	characteristic
720	C₄	C₅×#546	1	1	yes	characteristic
721	C₄	C₅×#551	1	1	yes	characteristic
722	C₂	—	4	2	no	—
723	C₂	—	8	2	no	—
724	C₂	C₅×#2358	1	1	yes	characteristic
725	C₂	C₄×C₅×#135	1	1	yes	characteristic
726	C₂	C₅×#2947	1	1	yes	characteristic
727	C₂	C₅×#3284	1	1	yes	characteristic
728	C₂	C₅×#3285	1	1	yes	characteristic
729	C₂	C₅×#3300	1	1	yes	characteristic
730	C₂	C₅×#3304	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂²×C₅×#41	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₄×C₅×C₂²⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₅×Q₁₆	C₂	semidirect
4. C₅×#2362	C₂	semidirect
6. C₅×#1968	C₂	semidirect
7. C₅×#1934	C₂	semidirect
8. C₅×#1925	C₂	semidirect
9. C₅×#1892	C₂	semidirect
10. C₅×#1880	C₂	semidirect
11. C₅×#1878	C₂	semidirect
12. C₅×#1865	C₂	semidirect
13. C₅×#1854	C₂	semidirect
14. C₄×C₅×#103	C₂	semidirect
15. C₅×C₈×C₂²⋊C₄	C₂	semidirect
25. C₅×#452	C₄	semidirect
62. #22873	C₅	direct (N × H)
145. C₂×C₄×Q₁₆	C₂×C₅	semidirect
147. #2362	C₂×C₅	semidirect
149. #1968	C₂×C₅	semidirect
150. #1934	C₂×C₅	semidirect
151. #1925	C₂×C₅	semidirect
152. #1892	C₂×C₅	semidirect
153. #1880	C₂×C₅	semidirect
154. #1878	C₂×C₅	semidirect
155. #1865	C₂×C₅	semidirect
156. #1854	C₂×C₅	semidirect
157. C₄×#103	C₂×C₅	semidirect
158. C₈×C₂²⋊C₄	C₂×C₅	semidirect
265. #452	C₄×C₅	semidirect
684. C₅	#22873	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#452	2
C₂×C₄×C₅×Q₁₆	2
C₂×C₅×#416	2
C₅×#2362	2
C₅×#2341	2
C₅×#1968	2
C₅×#1934	2
C₅×#1925	2
C₅×#1892	2
C₅×#1880	2
C₅×#1878	2
C₅×#1865	2
C₅×#1854	2
C₄×C₅×#103	2
C₅×C₈×C₂²⋊C₄	2
#22873	5

Subgroups — C5×#22873 #11945593

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22873 #11945593