Subgroups — C₅×#23010 #11945730

Order 1280.

1046 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#460	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#440	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₅×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2366	C₂	1	1	yes	maximal, characteristic
5	C₅×#2351	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1961	C₂	1	1	yes	maximal, characteristic
7	C₅×#1949	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1936	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1934	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1880	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1880	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1864	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1862	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1771	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1763	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₅×SD₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₅×SD₁₆	C₂²	1	1	yes	characteristic
18	C₂×C₅×#127	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₅×D₄	—	2	1	no	—
23	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
25	C₅×#460	C₄	1	8	yes	complemented
26	C₅×#440	—	2	4	no	—
27	C₄×C₅×SD₁₆	—	2	4	no	—
28	C₂×C₅×#107	C₂²	1	1	yes	characteristic
29	C₂×C₅×#106	C₂²	1	1	yes	characteristic
30	C₂×C₅×C₄⋊C₈	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×#102	C₂²	1	1	yes	characteristic
34	C₂×C₅×#102	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×#102	C₂²	1	1	yes	characteristic
39	C₂×C₅×#97	C₂²	1	1	yes	characteristic
40	C₂×C₅×#97	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
42	C₅×#390	—	2	1	no	—
43	C₅×#390	C₂²	1	1	yes	characteristic
44	C₅×#390	C₂²	1	1	yes	characteristic
45	C₅×#389	—	2	1	no	—
46	C₅×#389	—	2	1	no	—
47	C₅×#389	C₂²	1	1	yes	characteristic
48	C₅×#389	C₂²	1	1	yes	characteristic
49	C₅×#386	—	2	1	no	—
50	C₅×#386	—	2	1	no	—
51	C₅×#382	—	2	1	no	—
52	C₅×#382	C₂²	1	1	yes	characteristic
53	C₄×C₅×C₄⋊C₄	—	2	1	no	—
54	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
55	C₄×C₅×C₄⋊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	#23010	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
63	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
64	C₂²×C₅×D₄	—	2	1	no	—
65	C₂²×C₅×D₄	—	2	1	no	—
66	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
67	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₅	—	2	1	no	—
69	C₂³×C₄×C₅	—	2	1	no	—
70	C₂×C₅×SD₁₆	—	2	2	no	—
71	C₂×C₅×SD₁₆	—	2	2	no	—
72	C₂×C₅×SD₁₆	—	2	2	no	—
73	C₂×C₅×SD₁₆	—	2	2	no	—
74	C₂×C₅×SD₁₆	C₂×C₄	1	4	yes	complemented
75	C₂×C₅×SD₁₆	C₂×C₄	1	4	yes	complemented
76	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
77	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
78	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
79	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
80	C₅×#127	—	2	2	no	—
81	C₅×#127	C₂×C₄	1	4	yes	—
82	C₄×C₅×Q₈	—	2	2	no	—
83	C₄×C₅×Q₈	—	2	2	no	—
84	C₄×C₅×Q₈	—	2	2	no	—
85	C₄×C₅×Q₈	—	4	1	no	—
86	C₄×C₅×Q₈	—	4	1	no	—
87	C₄×C₅×Q₈	C₂×C₄	1	4	yes	complemented
88	C₄×C₅×D₄	—	2	2	no	—
89	C₄×C₅×D₄	—	2	2	no	—
90	C₄×C₅×D₄	—	4	1	no	—
91	C₄×C₅×D₄	—	4	1	no	—
92	C₄×C₅×D₄	—	4	4	no	—
93	C₂×C₅×C₄⋊C₄	—	2	1	no	—
94	C₂×C₅×C₄⋊C₄	—	2	1	no	—
95	C₂×C₅×C₄⋊C₄	—	2	1	no	—
96	C₂×C₅×C₄⋊C₄	—	2	1	no	—
97	C₂×C₅×C₄⋊C₄	—	2	1	no	—
98	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
99	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
100	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
101	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
102	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
103	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
104	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
105	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
106	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
107	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
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×C₄²×C₅	—	2	1	no	—
112	C₂×C₄²×C₅	—	2	1	no	—
113	C₂×C₄²×C₅	—	2	1	no	—
114	C₂×C₄²×C₅	—	2	1	no	—
115	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
118	C₅×#107	—	2	2	no	—
119	C₅×#106	—	2	2	no	—
120	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
121	C₅×#103	—	2	2	no	—
122	C₅×#103	D₄	1	4	yes	complemented
123	C₅×#102	—	2	2	no	—
124	C₅×#102	—	2	2	no	—
125	C₅×#102	—	4	1	no	—
126	C₅×#102	—	4	1	no	—
127	C₅×#102	C₂×C₄	1	4	yes	complemented
128	C₅×#102	C₂×C₄	1	4	yes	complemented
129	C₅×#97	—	2	2	no	—
130	C₅×#97	—	2	2	no	—
131	C₄×C₅×C₈	—	2	2	no	—
132	C₅×#95	—	2	1	no	—
133	C₅×#95	—	2	1	no	—
134	C₅×#95	—	2	1	no	—
135	C₅×#95	—	2	1	no	—
136	C₅×#95	—	2	1	no	—
137	C₅×#95	D₄	1	1	yes	characteristic
138	C₅×#95	D₄	1	1	yes	characteristic
139	C₂×#460	C₂×C₅	1	1	yes	characteristic
140	C₂×#440	C₂×C₅	1	1	yes	characteristic, complemented
141	C₂×C₄×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
142	#2366	C₂×C₅	1	1	yes	characteristic
143	#2351	C₂×C₅	1	1	yes	characteristic, complemented
144	#1961	C₂×C₅	1	1	yes	characteristic
145	#1949	C₂×C₅	1	1	yes	characteristic, complemented
146	#1936	C₂×C₅	1	1	yes	characteristic, complemented
147	#1934	C₂×C₅	1	1	yes	characteristic, complemented
148	#1880	C₂×C₅	1	1	yes	characteristic, complemented
149	#1880	C₂×C₅	1	1	yes	characteristic, complemented
150	#1864	C₂×C₅	1	1	yes	characteristic, complemented
151	#1862	C₂×C₅	1	1	yes	characteristic, complemented
152	#1771	C₂×C₅	1	1	yes	characteristic, complemented
153	#1763	C₂×C₅	1	1	yes	characteristic, complemented
154	C₂⁴×C₅	—	2	1	no	—
155	C₂⁴×C₅	—	2	1	no	—
156	C₂×C₅×Q₈	—	2	1	no	—
157	C₂×C₅×Q₈	—	2	1	no	—
158	C₂×C₅×Q₈	—	2	1	no	—
159	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
160	C₂×C₅×Q₈	C₂×D₄	1	2	yes	—
161	C₂×C₅×Q₈	#41	1	2	yes	—
162	C₂×C₅×D₄	—	2	4	no	—
163	C₂×C₅×D₄	—	2	4	no	—
164	C₂×C₅×D₄	—	2	1	no	—
165	C₂×C₅×D₄	—	2	1	no	—
166	C₂×C₅×D₄	—	2	1	no	—
167	C₂×C₅×D₄	—	2	1	no	—
168	C₂×C₅×D₄	—	2	1	no	—
169	C₂×C₅×D₄	—	2	1	no	—
170	C₂×C₅×D₄	—	2	1	no	—
171	C₂×C₅×D₄	—	2	1	no	—
172	C₂×C₅×D₄	—	2	1	no	—
173	C₂×C₅×D₄	—	2	1	no	—
174	C₂×C₅×D₄	—	4	2	no	—
175	C₂×C₅×D₄	—	4	2	no	—
176	C₂×C₅×D₄	—	8	1	no	—
177	C₂×C₅×D₄	—	8	1	no	—
178	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
179	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
180	C₂²×C₄×C₅	—	2	1	no	—
181	C₂²×C₄×C₅	—	2	1	no	—
182	C₂²×C₄×C₅	—	2	1	no	—
183	C₂²×C₄×C₅	—	2	1	no	—
184	C₂²×C₄×C₅	—	2	1	no	—
185	C₂²×C₄×C₅	—	2	1	no	—
186	C₂²×C₄×C₅	—	4	2	no	—
187	C₂²×C₄×C₅	—	4	2	no	—
188	C₂²×C₄×C₅	—	4	2	no	—
189	C₂²×C₄×C₅	—	4	2	no	—
190	C₂²×C₄×C₅	—	8	1	no	—
191	C₂²×C₄×C₅	—	8	1	no	—
192	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
199	C₅×SD₁₆	—	2	8	no	—
200	C₅×SD₁₆	—	2	8	no	—
201	C₂×C₅×C₈	—	2	1	no	—
202	C₂×C₅×C₈	—	2	1	no	—
203	C₂×C₅×C₈	—	2	1	no	—
204	C₂×C₅×C₈	—	2	1	no	—
205	C₂×C₅×C₈	—	2	1	no	—
206	C₂×C₅×C₈	—	2	1	no	—
207	C₂×C₅×C₈	—	2	1	no	—
208	C₂×C₅×C₈	—	2	1	no	—
209	C₂×C₅×C₈	—	2	1	no	—
210	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
211	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
212	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
213	C₅×C₄⋊C₄	—	2	4	no	—
214	C₅×C₄⋊C₄	—	2	2	no	—
215	C₅×C₄⋊C₄	—	2	1	no	—
216	C₅×C₄⋊C₄	—	2	1	no	—
217	C₅×C₄⋊C₄	—	2	1	no	—
218	C₅×C₄⋊C₄	—	2	1	no	—
219	C₅×C₄⋊C₄	—	2	1	no	—
220	C₅×C₄⋊C₄	—	2	1	no	—
221	C₅×C₄⋊C₄	—	2	1	no	—
222	C₅×C₄⋊C₄	—	2	1	no	—
223	C₅×C₄⋊C₄	—	4	1	no	—
224	C₅×C₄⋊C₄	—	4	2	no	—
225	C₅×C₄⋊C₄	—	4	2	no	—
226	C₅×C₄⋊C₄	—	4	2	no	—
227	C₅×C₄⋊C₄	—	4	2	no	—
228	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
229	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
230	C₅×C₂²⋊C₄	—	4	2	no	—
231	C₅×C₂²⋊C₄	—	4	2	no	—
232	C₅×C₂²⋊C₄	—	4	2	no	—
233	C₅×C₂²⋊C₄	—	4	2	no	—
234	C₅×C₂²⋊C₄	—	8	1	no	—
235	C₅×C₂²⋊C₄	—	8	1	no	—
236	C₄²×C₅	—	2	4	no	—
237	C₄²×C₅	—	2	1	no	—
238	C₄²×C₅	—	2	1	no	—
239	C₄²×C₅	—	2	1	no	—
240	C₄²×C₅	—	2	1	no	—
241	C₄²×C₅	—	4	2	no	—
242	C₄²×C₅	—	4	2	no	—
243	C₄²×C₅	—	4	2	no	—
244	C₄²×C₅	C₂²×C₄	1	2	yes	—
245	C₄²×C₅	#41	1	2	yes	—
246	C₂²×SD₁₆	C₂²×C₅	1	1	yes	characteristic
247	C₂²×SD₁₆	C₂²×C₅	1	1	yes	characteristic
248	C₂×#127	C₂²×C₅	1	1	yes	characteristic
249	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
250	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
251	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
252	C₂×C₄×D₄	—	2	1	no	—
253	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
254	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
255	#460	C₄×C₅	1	8	yes	complemented
256	#440	—	2	4	no	—
257	C₄×SD₁₆	—	2	4	no	—
258	C₂×#107	C₂²×C₅	1	1	yes	characteristic
259	C₂×#106	C₂²×C₅	1	1	yes	characteristic
260	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
261	C₂×#103	C₂²×C₅	1	1	yes	characteristic
262	C₂×#103	C₂²×C₅	1	1	yes	characteristic
263	C₂×#102	C₂²×C₅	1	1	yes	characteristic
264	C₂×#102	C₂²×C₅	1	1	yes	characteristic
265	C₂×#102	C₂²×C₅	1	1	yes	characteristic
266	C₂×#102	C₂²×C₅	1	1	yes	characteristic
267	C₂×#102	C₂²×C₅	1	1	yes	characteristic
268	C₂×#102	C₂²×C₅	1	1	yes	characteristic
269	C₂×#97	C₂²×C₅	1	1	yes	characteristic
270	C₂×#97	C₂²×C₅	1	1	yes	characteristic
271	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
272	#390	—	2	1	no	—
273	#390	C₂²×C₅	1	1	yes	characteristic
274	#390	C₂²×C₅	1	1	yes	characteristic
275	#389	—	2	1	no	—
276	#389	—	2	1	no	—
277	#389	C₂²×C₅	1	1	yes	characteristic
278	#389	C₂²×C₅	1	1	yes	characteristic
279	#386	—	2	1	no	—
280	#386	—	2	1	no	—
281	#382	—	2	1	no	—
282	#382	C₂²×C₅	1	1	yes	characteristic
283	C₄×C₄⋊C₄	—	2	1	no	—
284	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
285	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
286	#340	C₂²×C₅	1	1	yes	characteristic
287	#340	C₂²×C₅	1	1	yes	characteristic
288	#340	C₂²×C₅	1	1	yes	characteristic
289	#340	C₂²×C₅	1	1	yes	characteristic
290	#336	C₂²×C₅	1	1	yes	characteristic
291	#336	C₂²×C₅	1	1	yes	characteristic
292	C₂³×C₅	—	2	2	no	—
293	C₂³×C₅	—	2	2	no	—
294	C₂³×C₅	—	4	1	no	—
295	C₂³×C₅	—	4	1	no	—
296	C₂³×C₅	—	4	1	no	—
297	C₂³×C₅	—	4	1	no	—
298	C₂³×C₅	—	4	1	no	—
299	C₂³×C₅	—	4	1	no	—
300	C₂³×C₅	—	4	1	no	—
301	C₂³×C₅	—	4	1	no	—
302	C₂³×C₅	—	4	1	no	—
303	C₂³×C₅	—	4	1	no	—
304	C₂³×C₅	—	4	1	no	—
305	C₂³×C₅	—	4	1	no	—
306	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
307	C₅×Q₈	—	2	2	no	—
308	C₅×Q₈	—	2	2	no	—
309	C₅×Q₈	—	2	2	no	—
310	C₅×Q₈	C₄×D₄	1	4	yes	complemented
311	C₅×D₄	—	2	2	no	—
312	C₅×D₄	—	2	2	no	—
313	C₅×D₄	—	2	2	no	—
314	C₅×D₄	—	2	2	no	—
315	C₅×D₄	—	4	8	no	—
316	C₅×D₄	—	4	1	no	—
317	C₅×D₄	—	4	1	no	—
318	C₅×D₄	—	4	1	no	—
319	C₅×D₄	—	4	1	no	—
320	C₅×D₄	—	8	4	no	—
321	C₂×C₄×C₅	—	2	2	no	—
322	C₂×C₄×C₅	—	2	1	no	—
323	C₂×C₄×C₅	—	2	2	no	—
324	C₂×C₄×C₅	—	2	2	no	—
325	C₂×C₄×C₅	—	2	1	no	—
326	C₂×C₄×C₅	—	2	1	no	—
327	C₂×C₄×C₅	—	2	1	no	—
328	C₂×C₄×C₅	—	2	1	no	—
329	C₂×C₄×C₅	—	2	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	1	no	—
334	C₂×C₄×C₅	—	2	2	no	—
335	C₂×C₄×C₅	—	2	1	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	1	no	—
340	C₂×C₄×C₅	—	2	1	no	—
341	C₂×C₄×C₅	—	4	1	no	—
342	C₂×C₄×C₅	—	4	1	no	—
343	C₂×C₄×C₅	—	4	1	no	—
344	C₂×C₄×C₅	—	4	1	no	—
345	C₂×C₄×C₅	—	4	1	no	—
346	C₂×C₄×C₅	—	4	1	no	—
347	C₂×C₄×C₅	—	4	1	no	—
348	C₂×C₄×C₅	—	4	1	no	—
349	C₂×C₄×C₅	—	4	1	no	—
350	C₂×C₄×C₅	—	4	1	no	—
351	C₂×C₄×C₅	—	4	1	no	—
352	C₂×C₄×C₅	—	4	1	no	—
353	C₂×C₄×C₅	—	4	1	no	—
354	C₂×C₄×C₅	—	8	4	no	—
355	C₂×C₄×C₅	—	8	4	no	—
356	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
357	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
358	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
359	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
360	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
361	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
362	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
363	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
364	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
365	C₅×C₈	—	2	2	no	—
366	C₅×C₈	—	2	2	no	—
367	C₅×C₈	—	2	2	no	—
368	C₅×C₈	—	4	1	no	—
369	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
370	C₂²×D₄	—	2	1	no	—
371	C₂²×D₄	—	2	1	no	—
372	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
373	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
374	C₂³×C₄	—	2	1	no	—
375	C₂³×C₄	—	2	1	no	—
376	C₂×SD₁₆	—	2	2	no	—
377	C₂×SD₁₆	—	2	2	no	—
378	C₂×SD₁₆	—	2	2	no	—
379	C₂×SD₁₆	—	2	2	no	—
380	C₂×SD₁₆	C₂×C₄×C₅	1	4	yes	complemented
381	C₂×SD₁₆	C₂×C₄×C₅	1	4	yes	complemented
382	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
383	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
384	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
385	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
386	#127	—	2	2	no	—
387	#127	C₂×C₄×C₅	1	4	yes	—
388	C₄×Q₈	—	2	2	no	—
389	C₄×Q₈	—	2	2	no	—
390	C₄×Q₈	—	2	2	no	—
391	C₄×Q₈	—	4	1	no	—
392	C₄×Q₈	—	4	1	no	—
393	C₄×Q₈	C₂×C₄×C₅	1	4	yes	complemented
394	C₄×D₄	—	2	2	no	—
395	C₄×D₄	—	2	2	no	—
396	C₄×D₄	—	4	1	no	—
397	C₄×D₄	—	4	1	no	—
398	C₄×D₄	—	4	4	no	—
399	C₂×C₄⋊C₄	—	2	1	no	—
400	C₂×C₄⋊C₄	—	2	1	no	—
401	C₂×C₄⋊C₄	—	2	1	no	—
402	C₂×C₄⋊C₄	—	2	1	no	—
403	C₂×C₄⋊C₄	—	2	1	no	—
404	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
405	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
406	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
407	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
408	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
409	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
410	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
411	C₂×C₂²⋊C₄	—	2	1	no	—
412	C₂×C₂²⋊C₄	—	2	1	no	—
413	C₂×C₂²⋊C₄	—	2	1	no	—
414	C₂×C₂²⋊C₄	—	2	1	no	—
415	C₂×C₂²⋊C₄	—	2	1	no	—
416	C₂×C₂²⋊C₄	—	2	1	no	—
417	C₂×C₄²	—	2	1	no	—
418	C₂×C₄²	—	2	1	no	—
419	C₂×C₄²	—	2	1	no	—
420	C₂×C₄²	—	2	1	no	—
421	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
422	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
423	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
424	#107	—	2	2	no	—
425	#106	—	2	2	no	—
426	C₄⋊C₈	C₂×C₄×C₅	1	4	yes	complemented
427	#103	—	2	2	no	—
428	#103	C₅×D₄	1	4	yes	complemented
429	#102	—	2	2	no	—
430	#102	—	2	2	no	—
431	#102	—	4	1	no	—
432	#102	—	4	1	no	—
433	#102	C₂×C₄×C₅	1	4	yes	complemented
434	#102	C₂×C₄×C₅	1	4	yes	complemented
435	#97	—	2	2	no	—
436	#97	—	2	2	no	—
437	C₄×C₈	—	2	2	no	—
438	#95	—	2	1	no	—
439	#95	—	2	1	no	—
440	#95	—	2	1	no	—
441	#95	—	2	1	no	—
442	#95	—	2	1	no	—
443	#95	C₅×D₄	1	1	yes	characteristic
444	#95	C₅×D₄	1	1	yes	characteristic
445	C₂²×C₅	—	4	2	no	—
446	C₂²×C₅	—	4	2	no	—
447	C₂²×C₅	—	4	2	no	—
448	C₂²×C₅	—	4	2	no	—
449	C₂²×C₅	—	4	2	no	—
450	C₂²×C₅	—	4	2	no	—
451	C₂²×C₅	—	8	1	no	—
452	C₂²×C₅	—	8	1	no	—
453	C₂²×C₅	—	8	1	no	—
454	C₂²×C₅	—	8	1	no	—
455	C₂²×C₅	—	8	1	no	—
456	C₂²×C₅	—	8	1	no	—
457	C₂²×C₅	—	8	1	no	—
458	C₂²×C₅	—	8	1	no	—
459	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
460	C₂²×C₅	D₄²	1	1	yes	characteristic
461	C₂²×C₅	#548	1	1	yes	characteristic
462	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
463	C₂²×C₅	#575	1	1	yes	characteristic
464	C₂²×C₅	#577	1	1	yes	characteristic
465	C₂²×C₅	#577	1	1	yes	characteristic
466	C₄×C₅	—	2	4	no	—
467	C₄×C₅	—	2	2	no	—
468	C₄×C₅	—	2	2	no	—
469	C₄×C₅	—	2	2	no	—
470	C₄×C₅	—	4	2	no	—
471	C₄×C₅	—	4	1	no	—
472	C₄×C₅	—	4	2	no	—
473	C₄×C₅	—	4	1	no	—
474	C₄×C₅	—	4	1	no	—
475	C₄×C₅	—	8	1	no	—
476	C₄×C₅	—	8	1	no	—
477	C₄×C₅	—	8	1	no	—
478	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
479	C₄×C₅	#520	1	1	yes	characteristic
480	C₄×C₅	#547	1	1	yes	characteristic
481	C₄×C₅	#553	1	1	yes	characteristic
482	C₂⁴	—	2	1	no	—
483	C₂⁴	—	2	1	no	—
484	C₂×Q₈	—	2	1	no	—
485	C₂×Q₈	—	2	1	no	—
486	C₂×Q₈	—	2	1	no	—
487	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
488	C₂×Q₈	C₂×C₅×D₄	1	2	yes	—
489	C₂×Q₈	C₅×#41	1	2	yes	—
490	C₂×D₄	—	2	4	no	—
491	C₂×D₄	—	2	4	no	—
492	C₂×D₄	—	2	1	no	—
493	C₂×D₄	—	2	1	no	—
494	C₂×D₄	—	2	1	no	—
495	C₂×D₄	—	2	1	no	—
496	C₂×D₄	—	2	1	no	—
497	C₂×D₄	—	2	1	no	—
498	C₂×D₄	—	2	1	no	—
499	C₂×D₄	—	2	1	no	—
500	C₂×D₄	—	2	1	no	—
501	C₂×D₄	—	2	1	no	—
502	C₂×D₄	—	4	2	no	—
503	C₂×D₄	—	4	2	no	—
504	C₂×D₄	—	8	1	no	—
505	C₂×D₄	—	8	1	no	—
506	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
507	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	—	2	1	no	—
510	C₂²×C₄	—	2	1	no	—
511	C₂²×C₄	—	2	1	no	—
512	C₂²×C₄	—	2	1	no	—
513	C₂²×C₄	—	2	1	no	—
514	C₂²×C₄	—	4	2	no	—
515	C₂²×C₄	—	4	2	no	—
516	C₂²×C₄	—	4	2	no	—
517	C₂²×C₄	—	4	2	no	—
518	C₂²×C₄	—	8	1	no	—
519	C₂²×C₄	—	8	1	no	—
520	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
521	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
522	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
523	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
524	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
525	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
526	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
527	SD₁₆	—	2	8	no	—
528	SD₁₆	—	2	8	no	—
529	C₂×C₈	—	2	1	no	—
530	C₂×C₈	—	2	1	no	—
531	C₂×C₈	—	2	1	no	—
532	C₂×C₈	—	2	1	no	—
533	C₂×C₈	—	2	1	no	—
534	C₂×C₈	—	2	1	no	—
535	C₂×C₈	—	2	1	no	—
536	C₂×C₈	—	2	1	no	—
537	C₂×C₈	—	2	1	no	—
538	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
539	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
540	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
541	C₄⋊C₄	—	2	4	no	—
542	C₄⋊C₄	—	2	2	no	—
543	C₄⋊C₄	—	2	1	no	—
544	C₄⋊C₄	—	2	1	no	—
545	C₄⋊C₄	—	2	1	no	—
546	C₄⋊C₄	—	2	1	no	—
547	C₄⋊C₄	—	2	1	no	—
548	C₄⋊C₄	—	2	1	no	—
549	C₄⋊C₄	—	2	1	no	—
550	C₄⋊C₄	—	2	1	no	—
551	C₄⋊C₄	—	4	1	no	—
552	C₄⋊C₄	—	4	2	no	—
553	C₄⋊C₄	—	4	2	no	—
554	C₄⋊C₄	—	4	2	no	—
555	C₄⋊C₄	—	4	2	no	—
556	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
557	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
558	C₂²⋊C₄	—	4	2	no	—
559	C₂²⋊C₄	—	4	2	no	—
560	C₂²⋊C₄	—	4	2	no	—
561	C₂²⋊C₄	—	4	2	no	—
562	C₂²⋊C₄	—	8	1	no	—
563	C₂²⋊C₄	—	8	1	no	—
564	C₄²	—	2	4	no	—
565	C₄²	—	2	1	no	—
566	C₄²	—	2	1	no	—
567	C₄²	—	2	1	no	—
568	C₄²	—	2	1	no	—
569	C₄²	—	4	2	no	—
570	C₄²	—	4	2	no	—
571	C₄²	—	4	2	no	—
572	C₄²	C₂²×C₄×C₅	1	2	yes	—
573	C₄²	C₅×#41	1	2	yes	—
574	C₂×C₅	—	8	2	no	—
575	C₂×C₅	—	8	2	no	—
576	C₂×C₅	#2361	1	1	yes	characteristic
577	C₂×C₅	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
578	C₂×C₅	#2949	1	1	yes	characteristic
579	C₂×C₅	#3265	1	1	yes	characteristic
580	C₂×C₅	#3271	1	1	yes	characteristic
581	C₂×C₅	#3368	1	1	yes	characteristic
582	C₂×C₅	#3371	1	1	yes	characteristic
583	C₂³	—	2	2	no	—
584	C₂³	—	2	2	no	—
585	C₂³	—	4	1	no	—
586	C₂³	—	4	1	no	—
587	C₂³	—	4	1	no	—
588	C₂³	—	4	1	no	—
589	C₂³	—	4	1	no	—
590	C₂³	—	4	1	no	—
591	C₂³	—	4	1	no	—
592	C₂³	—	4	1	no	—
593	C₂³	—	4	1	no	—
594	C₂³	—	4	1	no	—
595	C₂³	—	4	1	no	—
596	C₂³	—	4	1	no	—
597	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
598	Q₈	—	2	2	no	—
599	Q₈	—	2	2	no	—
600	Q₈	—	2	2	no	—
601	Q₈	C₄×C₅×D₄	1	4	yes	complemented
602	D₄	—	2	2	no	—
603	D₄	—	2	2	no	—
604	D₄	—	2	2	no	—
605	D₄	—	2	2	no	—
606	D₄	—	4	8	no	—
607	D₄	—	4	1	no	—
608	D₄	—	4	1	no	—
609	D₄	—	4	1	no	—
610	D₄	—	4	1	no	—
611	D₄	—	8	4	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	4	1	no	—
633	C₂×C₄	—	4	1	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	4	1	no	—
636	C₂×C₄	—	4	1	no	—
637	C₂×C₄	—	4	1	no	—
638	C₂×C₄	—	4	1	no	—
639	C₂×C₄	—	4	1	no	—
640	C₂×C₄	—	4	1	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	4	1	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	8	4	no	—
646	C₂×C₄	—	8	4	no	—
647	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
648	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
649	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
650	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
651	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
652	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
653	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
654	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
655	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
656	C₈	—	2	2	no	—
657	C₈	—	2	2	no	—
658	C₈	—	2	2	no	—
659	C₈	—	4	1	no	—
660	C₅	#23010	1	1	yes	characteristic, direct product factor, Sylow
661	C₂²	—	4	2	no	—
662	C₂²	—	4	2	no	—
663	C₂²	—	4	2	no	—
664	C₂²	—	4	2	no	—
665	C₂²	—	4	2	no	—
666	C₂²	—	4	2	no	—
667	C₂²	—	8	1	no	—
668	C₂²	—	8	1	no	—
669	C₂²	—	8	1	no	—
670	C₂²	—	8	1	no	—
671	C₂²	—	8	1	no	—
672	C₂²	—	8	1	no	—
673	C₂²	—	8	1	no	—
674	C₂²	—	8	1	no	—
675	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
676	C₂²	C₅×D₄²	1	1	yes	characteristic
677	C₂²	C₅×#548	1	1	yes	characteristic
678	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
679	C₂²	C₅×#575	1	1	yes	characteristic
680	C₂²	C₅×#577	1	1	yes	characteristic
681	C₂²	C₅×#577	1	1	yes	characteristic
682	C₄	—	2	2	no	—
683	C₄	—	2	4	no	—
684	C₄	—	2	2	no	—
685	C₄	—	2	2	no	—
686	C₄	—	4	1	no	—
687	C₄	—	4	2	no	—
688	C₄	—	4	1	no	—
689	C₄	—	4	1	no	—
690	C₄	—	4	2	no	—
691	C₄	—	8	1	no	—
692	C₄	—	8	1	no	—
693	C₄	—	8	1	no	—
694	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
695	C₄	C₅×#520	1	1	yes	characteristic
696	C₄	C₅×#547	1	1	yes	characteristic
697	C₄	C₅×#553	1	1	yes	characteristic
698	C₂	—	8	2	no	—
699	C₂	—	8	2	no	—
700	C₂	C₅×#2361	1	1	yes	characteristic
701	C₂	C₄×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
702	C₂	C₅×#2949	1	1	yes	characteristic
703	C₂	C₅×#3265	1	1	yes	characteristic
704	C₂	C₅×#3271	1	1	yes	characteristic
705	C₂	C₅×#3368	1	1	yes	characteristic
706	C₂	C₅×#3371	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	C₂×C₅×#127	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₄×C₅×C₄⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#440	C₂	semidirect
3. C₂×C₄×C₅×SD₁₆	C₂	semidirect
5. C₅×#2351	C₂	semidirect
7. C₅×#1949	C₂	semidirect
8. C₅×#1936	C₂	semidirect
9. C₅×#1934	C₂	semidirect
10. C₅×#1880	C₂	semidirect
11. C₅×#1880	C₂	semidirect
12. C₅×#1864	C₂	semidirect
13. C₅×#1862	C₂	semidirect
14. C₅×#1771	C₂	semidirect
15. C₅×#1763	C₂	semidirect
25. C₅×#460	C₄	semidirect
62. #23010	C₅	direct (N × H)
74. C₂×C₅×SD₁₆	C₂×C₄	semidirect
75. C₂×C₅×SD₁₆	C₂×C₄	semidirect
87. C₄×C₅×Q₈	C₂×C₄	semidirect
120. C₅×C₄⋊C₈	C₂×C₄	semidirect
122. C₅×#103	D₄	semidirect
127. C₅×#102	C₂×C₄	semidirect
128. C₅×#102	C₂×C₄	semidirect
140. C₂×#440	C₂×C₅	semidirect
141. C₂×C₄×SD₁₆	C₂×C₅	semidirect
143. #2351	C₂×C₅	semidirect
145. #1949	C₂×C₅	semidirect
146. #1936	C₂×C₅	semidirect
147. #1934	C₂×C₅	semidirect
148. #1880	C₂×C₅	semidirect
149. #1880	C₂×C₅	semidirect
150. #1864	C₂×C₅	semidirect
151. #1862	C₂×C₅	semidirect
152. #1771	C₂×C₅	semidirect
153. #1763	C₂×C₅	semidirect
255. #460	C₄×C₅	semidirect
310. C₅×Q₈	C₄×D₄	semidirect
380. C₂×SD₁₆	C₂×C₄×C₅	semidirect
381. C₂×SD₁₆	C₂×C₄×C₅	semidirect
393. C₄×Q₈	C₂×C₄×C₅	semidirect
426. C₄⋊C₈	C₂×C₄×C₅	semidirect
428. #103	C₅×D₄	semidirect
433. #102	C₂×C₄×C₅	semidirect
434. #102	C₂×C₄×C₅	semidirect
601. Q₈	C₄×C₅×D₄	semidirect
660. C₅	#23010	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×#460	2
C₂×C₅×#440	2
C₂×C₄×C₅×SD₁₆	2
C₅×#2366	2
C₅×#2351	2
C₅×#1961	2
C₅×#1949	2
C₅×#1936	2
C₅×#1934	2
C₅×#1880	2
C₅×#1864	2
C₅×#1862	2
C₅×#1771	2
C₅×#1763	2
#23010	5

Subgroups — C5×#23010 #11945730

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#23010 #11945730