Subgroups — C₅×#23034 #11945754

Order 1280.

1026 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#468	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₅×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#428	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2362	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2361	C₂	1	1	yes	maximal, characteristic
6	C₅×#1973	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1942	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1928	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1926	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1875	C₂	1	1	yes	maximal, characteristic
11	C₅×#1872	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1865	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1862	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1776	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1753	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₅×SD₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
18	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₅×#121	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₅×D₄	—	2	1	no	—
22	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
23	C₂×C₅×#117	C₂²	1	1	yes	characteristic
24	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₅×#468	C₄	1	8	yes	complemented
26	C₄×C₅×SD₁₆	—	2	4	no	—
27	C₅×#428	—	2	4	no	—
28	C₂×C₅×#107	C₂²	1	1	yes	characteristic
29	C₂×C₅×#107	C₂²	1	1	yes	characteristic
30	C₂×C₅×#107	C₂²	1	1	yes	characteristic
31	C₂×C₅×#106	C₂²	1	1	yes	characteristic
32	C₂×C₅×#106	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×#103	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×C₂²⋊C₈	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×#391	C₂²	1	1	yes	characteristic
43	C₅×#390	C₂²	1	1	yes	characteristic
44	C₅×#389	C₂²	1	1	yes	characteristic
45	C₅×#389	C₂²	1	1	yes	characteristic
46	C₅×#388	—	2	1	no	—
47	C₅×#388	—	2	1	no	—
48	C₅×#388	—	2	1	no	—
49	C₅×#387	—	2	1	no	—
50	C₅×#386	—	2	1	no	—
51	C₅×#385	—	2	1	no	—
52	C₄×C₅×C₄⋊C₄	—	2	1	no	—
53	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
54	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
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	#23034	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	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₅	—	2	1	no	—
67	C₂³×C₄×C₅	—	2	1	no	—
68	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
69	C₂×C₅×SD₁₆	—	2	2	no	—
70	C₂×C₅×SD₁₆	—	2	2	no	—
71	C₂×C₅×SD₁₆	C₂×C₄	1	4	yes	complemented
72	C₂×C₅×M₁₆	—	2	2	no	—
73	C₂×C₅×M₁₆	—	2	2	no	—
74	C₂×C₅×M₁₆	C₂×C₄	1	4	yes	complemented
75	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
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	C₅×C₂²⋊Q₈	—	2	2	no	—
80	C₅×C₂²⋊Q₈	C₂×C₄	1	4	yes	complemented
81	C₅×#121	—	2	2	no	—
82	C₅×#121	C₂×C₄	1	4	yes	—
83	C₄×C₅×Q₈	—	2	2	no	—
84	C₄×C₅×Q₈	—	4	1	no	—
85	C₄×C₅×D₄	—	2	2	no	—
86	C₄×C₅×D₄	—	4	1	no	—
87	C₄×C₅×D₄	—	4	4	no	—
88	C₅×#117	—	2	2	no	—
89	C₅×#117	—	4	1	no	—
90	C₂×C₅×C₄⋊C₄	—	2	1	no	—
91	C₂×C₅×C₄⋊C₄	—	2	2	no	—
92	C₂×C₅×C₄⋊C₄	—	2	1	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	—	4	1	no	—
97	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
98	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
99	C₂×C₅×C₄⋊C₄	C₂³	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×C₂²⋊C₄	—	2	1	no	—
104	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
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	D₄	1	1	yes	characteristic
110	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
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	C₅×#107	—	2	2	no	—
118	C₅×#107	—	2	2	no	—
119	C₅×#107	C₂×C₄	1	4	yes	complemented
120	C₅×#106	—	2	2	no	—
121	C₅×#106	D₄	1	4	yes	complemented
122	C₅×#103	—	2	2	no	—
123	C₅×#103	—	4	1	no	—
124	C₅×#103	C₂×C₄	1	4	yes	complemented
125	C₅×#102	—	2	2	no	—
126	C₅×#102	—	4	1	no	—
127	C₅×#102	C₂×C₄	1	4	yes	complemented
128	C₅×C₂²⋊C₈	—	2	2	no	—
129	C₅×#97	—	2	2	no	—
130	C₄×C₅×C₈	—	2	2	no	—
131	C₅×#95	—	2	1	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×#468	C₂×C₅	1	1	yes	characteristic
140	C₂×C₄×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
141	C₂×#428	C₂×C₅	1	1	yes	characteristic, complemented
142	#2362	C₂×C₅	1	1	yes	characteristic, complemented
143	#2361	C₂×C₅	1	1	yes	characteristic
144	#1973	C₂×C₅	1	1	yes	characteristic, complemented
145	#1942	C₂×C₅	1	1	yes	characteristic, complemented
146	#1928	C₂×C₅	1	1	yes	characteristic, complemented
147	#1926	C₂×C₅	1	1	yes	characteristic, complemented
148	#1875	C₂×C₅	1	1	yes	characteristic
149	#1872	C₂×C₅	1	1	yes	characteristic, complemented
150	#1865	C₂×C₅	1	1	yes	characteristic, complemented
151	#1862	C₂×C₅	1	1	yes	characteristic, complemented
152	#1776	C₂×C₅	1	1	yes	characteristic, complemented
153	#1753	C₂×C₅	1	1	yes	characteristic, complemented
154	C₂⁴×C₅	—	2	1	no	—
155	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
160	C₂×C₅×Q₈	—	2	1	no	—
161	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
162	C₂×C₅×D₄	—	2	4	no	—
163	C₂×C₅×D₄	—	2	1	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	—	4	2	no	—
169	C₂×C₅×D₄	—	4	2	no	—
170	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
171	C₂²×C₄×C₅	—	2	1	no	—
172	C₂²×C₄×C₅	—	2	1	no	—
173	C₂²×C₄×C₅	—	2	1	no	—
174	C₂²×C₄×C₅	—	2	1	no	—
175	C₂²×C₄×C₅	—	2	1	no	—
176	C₂²×C₄×C₅	—	2	1	no	—
177	C₂²×C₄×C₅	—	2	1	no	—
178	C₂²×C₄×C₅	—	2	1	no	—
179	C₂²×C₄×C₅	—	2	1	no	—
180	C₂²×C₄×C₅	—	2	1	no	—
181	C₂²×C₄×C₅	—	2	1	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	—	8	1	no	—
187	C₂²×C₄×C₅	—	8	1	no	—
188	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
189	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
191	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₅	#41	1	2	yes	—
195	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
196	C₅×SD₁₆	—	2	8	no	—
197	C₅×M₁₆	—	2	8	no	—
198	C₂×C₅×C₈	—	2	1	no	—
199	C₂×C₅×C₈	—	2	1	no	—
200	C₂×C₅×C₈	—	2	1	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	C₂²×C₄	1	2	yes	—
207	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
208	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
209	C₂×C₅×C₈	#41	1	2	yes	—
210	C₅×C₄⋊C₄	—	2	4	no	—
211	C₅×C₄⋊C₄	—	2	1	no	—
212	C₅×C₄⋊C₄	—	2	1	no	—
213	C₅×C₄⋊C₄	—	2	1	no	—
214	C₅×C₄⋊C₄	—	2	1	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	—	4	2	no	—
220	C₅×C₄⋊C₄	—	4	2	no	—
221	C₅×C₄⋊C₄	—	4	2	no	—
222	C₅×C₄⋊C₄	—	4	2	no	—
223	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
224	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
225	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
226	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
227	C₅×C₂²⋊C₄	—	2	4	no	—
228	C₅×C₂²⋊C₄	—	2	4	no	—
229	C₅×C₂²⋊C₄	—	2	2	no	—
230	C₅×C₂²⋊C₄	—	4	1	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	C₄²×C₅	—	2	1	no	—
236	C₄²×C₅	—	2	1	no	—
237	C₄²×C₅	—	2	1	no	—
238	C₄²×C₅	—	2	1	no	—
239	C₄²×C₅	—	4	2	no	—
240	C₄²×C₅	—	4	2	no	—
241	C₄²×C₅	—	4	2	no	—
242	C₄²×C₅	—	4	2	no	—
243	C₂²×SD₁₆	C₂²×C₅	1	1	yes	characteristic
244	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
245	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
246	C₂×#121	C₂²×C₅	1	1	yes	characteristic
247	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
248	C₂×C₄×D₄	—	2	1	no	—
249	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
250	C₂×#117	C₂²×C₅	1	1	yes	characteristic
251	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
252	#468	C₄×C₅	1	8	yes	complemented
253	C₄×SD₁₆	—	2	4	no	—
254	#428	—	2	4	no	—
255	C₂×#107	C₂²×C₅	1	1	yes	characteristic
256	C₂×#107	C₂²×C₅	1	1	yes	characteristic
257	C₂×#107	C₂²×C₅	1	1	yes	characteristic
258	C₂×#106	C₂²×C₅	1	1	yes	characteristic
259	C₂×#106	C₂²×C₅	1	1	yes	characteristic
260	C₂×#103	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×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
267	C₂×#97	C₂²×C₅	1	1	yes	characteristic
268	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
269	#391	C₂²×C₅	1	1	yes	characteristic
270	#390	C₂²×C₅	1	1	yes	characteristic
271	#389	C₂²×C₅	1	1	yes	characteristic
272	#389	C₂²×C₅	1	1	yes	characteristic
273	#388	—	2	1	no	—
274	#388	—	2	1	no	—
275	#388	—	2	1	no	—
276	#387	—	2	1	no	—
277	#386	—	2	1	no	—
278	#385	—	2	1	no	—
279	C₄×C₄⋊C₄	—	2	1	no	—
280	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
281	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
282	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
283	#340	C₂²×C₅	1	1	yes	characteristic
284	#340	C₂²×C₅	1	1	yes	characteristic
285	#340	C₂²×C₅	1	1	yes	characteristic
286	#340	C₂²×C₅	1	1	yes	characteristic
287	#336	C₂²×C₅	1	1	yes	characteristic
288	#336	C₂²×C₅	1	1	yes	characteristic
289	C₂³×C₅	—	2	1	no	—
290	C₂³×C₅	—	2	1	no	—
291	C₂³×C₅	—	2	1	no	—
292	C₂³×C₅	—	2	1	no	—
293	C₂³×C₅	—	2	1	no	—
294	C₂³×C₅	—	2	1	no	—
295	C₂³×C₅	—	2	2	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	C₄×D₄	1	2	yes	—
303	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
304	C₅×Q₈	—	2	2	no	—
305	C₅×Q₈	—	2	2	no	—
306	C₅×Q₈	—	4	1	no	—
307	C₅×Q₈	—	4	1	no	—
308	C₅×D₄	—	2	2	no	—
309	C₅×D₄	—	2	2	no	—
310	C₅×D₄	—	4	8	no	—
311	C₅×D₄	—	4	1	no	—
312	C₅×D₄	—	4	1	no	—
313	C₂×C₄×C₅	—	2	1	no	—
314	C₂×C₄×C₅	—	2	1	no	—
315	C₂×C₄×C₅	—	2	1	no	—
316	C₂×C₄×C₅	—	2	1	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	1	no	—
325	C₂×C₄×C₅	—	2	2	no	—
326	C₂×C₄×C₅	—	2	2	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	1	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	1	no	—
335	C₂×C₄×C₅	—	4	1	no	—
336	C₂×C₄×C₅	—	4	1	no	—
337	C₂×C₄×C₅	—	4	1	no	—
338	C₂×C₄×C₅	—	4	1	no	—
339	C₂×C₄×C₅	—	4	1	no	—
340	C₂×C₄×C₅	—	4	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	—	8	4	no	—
352	C₂×C₄×C₅	—	8	4	no	—
353	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
354	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
355	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
356	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
357	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
358	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
359	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
360	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
361	C₅×C₈	—	2	2	no	—
362	C₅×C₈	—	4	1	no	—
363	C₅×C₈	—	4	1	no	—
364	C₅×C₈	C₄×D₄	1	4	yes	complemented
365	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
366	C₂²×D₄	—	2	1	no	—
367	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
368	C₂³×C₄	—	2	1	no	—
369	C₂³×C₄	—	2	1	no	—
370	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
371	C₂×SD₁₆	—	2	2	no	—
372	C₂×SD₁₆	—	2	2	no	—
373	C₂×SD₁₆	C₂×C₄×C₅	1	4	yes	complemented
374	C₂×M₁₆	—	2	2	no	—
375	C₂×M₁₆	—	2	2	no	—
376	C₂×M₁₆	C₂×C₄×C₅	1	4	yes	complemented
377	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
378	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
379	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
380	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
381	C₂²⋊Q₈	—	2	2	no	—
382	C₂²⋊Q₈	C₂×C₄×C₅	1	4	yes	complemented
383	#121	—	2	2	no	—
384	#121	C₂×C₄×C₅	1	4	yes	—
385	C₄×Q₈	—	2	2	no	—
386	C₄×Q₈	—	4	1	no	—
387	C₄×D₄	—	2	2	no	—
388	C₄×D₄	—	4	1	no	—
389	C₄×D₄	—	4	4	no	—
390	#117	—	2	2	no	—
391	#117	—	4	1	no	—
392	C₂×C₄⋊C₄	—	2	1	no	—
393	C₂×C₄⋊C₄	—	2	2	no	—
394	C₂×C₄⋊C₄	—	2	1	no	—
395	C₂×C₄⋊C₄	—	2	1	no	—
396	C₂×C₄⋊C₄	—	2	1	no	—
397	C₂×C₄⋊C₄	—	2	1	no	—
398	C₂×C₄⋊C₄	—	4	1	no	—
399	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
400	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
401	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
402	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
403	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
404	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
405	C₂×C₂²⋊C₄	—	2	1	no	—
406	C₂×C₂²⋊C₄	—	2	1	no	—
407	C₂×C₂²⋊C₄	—	2	1	no	—
408	C₂×C₂²⋊C₄	—	2	1	no	—
409	C₂×C₂²⋊C₄	—	2	1	no	—
410	C₂×C₂²⋊C₄	—	2	1	no	—
411	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
412	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
413	C₂×C₄²	—	2	1	no	—
414	C₂×C₄²	—	2	1	no	—
415	C₂×C₄²	—	2	1	no	—
416	C₂×C₄²	—	2	1	no	—
417	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
418	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
419	#107	—	2	2	no	—
420	#107	—	2	2	no	—
421	#107	C₂×C₄×C₅	1	4	yes	complemented
422	#106	—	2	2	no	—
423	#106	C₅×D₄	1	4	yes	complemented
424	#103	—	2	2	no	—
425	#103	—	4	1	no	—
426	#103	C₂×C₄×C₅	1	4	yes	complemented
427	#102	—	2	2	no	—
428	#102	—	4	1	no	—
429	#102	C₂×C₄×C₅	1	4	yes	complemented
430	C₂²⋊C₈	—	2	2	no	—
431	#97	—	2	2	no	—
432	C₄×C₈	—	2	2	no	—
433	#95	—	2	1	no	—
434	#95	—	2	1	no	—
435	#95	—	2	1	no	—
436	#95	—	2	1	no	—
437	#95	—	2	1	no	—
438	#95	—	2	1	no	—
439	#95	C₅×D₄	1	1	yes	characteristic
440	#95	C₅×D₄	1	1	yes	characteristic
441	C₂²×C₅	—	2	2	no	—
442	C₂²×C₅	—	2	2	no	—
443	C₂²×C₅	—	2	2	no	—
444	C₂²×C₅	—	4	1	no	—
445	C₂²×C₅	—	4	1	no	—
446	C₂²×C₅	—	4	1	no	—
447	C₂²×C₅	—	4	1	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	C₂×C₄×D₄	1	1	yes	characteristic
456	C₂²×C₅	D₄²	1	1	yes	characteristic
457	C₂²×C₅	#547	1	1	yes	characteristic
458	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
459	C₂²×C₅	#575	1	1	yes	characteristic
460	C₂²×C₅	#577	1	1	yes	characteristic
461	C₂²×C₅	#578	1	1	yes	characteristic
462	C₄×C₅	—	2	2	no	—
463	C₄×C₅	—	2	2	no	—
464	C₄×C₅	—	4	1	no	—
465	C₄×C₅	—	4	1	no	—
466	C₄×C₅	—	4	2	no	—
467	C₄×C₅	—	4	2	no	—
468	C₄×C₅	—	4	2	no	—
469	C₄×C₅	—	4	2	no	—
470	C₄×C₅	—	4	1	no	—
471	C₄×C₅	—	4	2	no	—
472	C₄×C₅	—	8	1	no	—
473	C₄×C₅	—	8	1	no	—
474	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
475	C₄×C₅	#520	1	1	yes	characteristic
476	C₄×C₅	#548	1	1	yes	characteristic
477	C₄×C₅	#553	1	1	yes	characteristic
478	C₂⁴	—	2	1	no	—
479	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
480	C₂×Q₈	—	2	1	no	—
481	C₂×Q₈	—	2	1	no	—
482	C₂×Q₈	—	2	1	no	—
483	C₂×Q₈	—	2	1	no	—
484	C₂×Q₈	—	2	1	no	—
485	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
486	C₂×D₄	—	2	4	no	—
487	C₂×D₄	—	2	1	no	—
488	C₂×D₄	—	2	1	no	—
489	C₂×D₄	—	2	1	no	—
490	C₂×D₄	—	2	1	no	—
491	C₂×D₄	—	2	1	no	—
492	C₂×D₄	—	4	2	no	—
493	C₂×D₄	—	4	2	no	—
494	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	2	1	no	—
501	C₂²×C₄	—	2	1	no	—
502	C₂²×C₄	—	2	1	no	—
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	2	1	no	—
505	C₂²×C₄	—	2	1	no	—
506	C₂²×C₄	—	4	2	no	—
507	C₂²×C₄	—	4	2	no	—
508	C₂²×C₄	—	4	2	no	—
509	C₂²×C₄	—	4	2	no	—
510	C₂²×C₄	—	8	1	no	—
511	C₂²×C₄	—	8	1	no	—
512	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
513	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
514	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
515	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
516	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
517	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
518	C₂²×C₄	C₅×#41	1	2	yes	—
519	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
520	SD₁₆	—	2	8	no	—
521	M₁₆	—	2	8	no	—
522	C₂×C₈	—	2	1	no	—
523	C₂×C₈	—	2	1	no	—
524	C₂×C₈	—	2	1	no	—
525	C₂×C₈	—	2	1	no	—
526	C₂×C₈	—	2	1	no	—
527	C₂×C₈	—	2	1	no	—
528	C₂×C₈	—	2	1	no	—
529	C₂×C₈	—	2	1	no	—
530	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
531	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
532	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
533	C₂×C₈	C₅×#41	1	2	yes	—
534	C₄⋊C₄	—	2	4	no	—
535	C₄⋊C₄	—	2	1	no	—
536	C₄⋊C₄	—	2	1	no	—
537	C₄⋊C₄	—	2	1	no	—
538	C₄⋊C₄	—	2	1	no	—
539	C₄⋊C₄	—	2	1	no	—
540	C₄⋊C₄	—	2	1	no	—
541	C₄⋊C₄	—	2	1	no	—
542	C₄⋊C₄	—	2	1	no	—
543	C₄⋊C₄	—	4	2	no	—
544	C₄⋊C₄	—	4	2	no	—
545	C₄⋊C₄	—	4	2	no	—
546	C₄⋊C₄	—	4	2	no	—
547	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
548	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
549	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
550	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
551	C₂²⋊C₄	—	2	4	no	—
552	C₂²⋊C₄	—	2	4	no	—
553	C₂²⋊C₄	—	2	2	no	—
554	C₂²⋊C₄	—	4	1	no	—
555	C₂²⋊C₄	—	4	2	no	—
556	C₂²⋊C₄	—	4	2	no	—
557	C₂²⋊C₄	—	4	2	no	—
558	C₂²⋊C₄	—	8	1	no	—
559	C₄²	—	2	1	no	—
560	C₄²	—	2	1	no	—
561	C₄²	—	2	1	no	—
562	C₄²	—	2	1	no	—
563	C₄²	—	4	2	no	—
564	C₄²	—	4	2	no	—
565	C₄²	—	4	2	no	—
566	C₄²	—	4	2	no	—
567	C₂×C₅	—	4	2	no	—
568	C₂×C₅	—	8	2	no	—
569	C₂×C₅	#2361	1	1	yes	characteristic
570	C₂×C₅	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
571	C₂×C₅	#2947	1	1	yes	characteristic
572	C₂×C₅	#3265	1	1	yes	characteristic
573	C₂×C₅	#3269	1	1	yes	characteristic
574	C₂×C₅	#3351	1	1	yes	characteristic
575	C₂×C₅	#3353	1	1	yes	characteristic
576	C₂³	—	2	1	no	—
577	C₂³	—	2	1	no	—
578	C₂³	—	2	1	no	—
579	C₂³	—	2	1	no	—
580	C₂³	—	2	1	no	—
581	C₂³	—	2	1	no	—
582	C₂³	—	2	2	no	—
583	C₂³	—	4	1	no	—
584	C₂³	—	4	1	no	—
585	C₂³	—	4	1	no	—
586	C₂³	—	4	1	no	—
587	C₂³	—	4	1	no	—
588	C₂³	—	4	1	no	—
589	C₂³	C₄×C₅×D₄	1	2	yes	—
590	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
591	Q₈	—	2	2	no	—
592	Q₈	—	2	2	no	—
593	Q₈	—	4	1	no	—
594	Q₈	—	4	1	no	—
595	D₄	—	2	2	no	—
596	D₄	—	2	2	no	—
597	D₄	—	4	8	no	—
598	D₄	—	4	1	no	—
599	D₄	—	4	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	1	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	1	no	—
622	C₂×C₄	—	4	1	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	4	1	no	—
625	C₂×C₄	—	4	1	no	—
626	C₂×C₄	—	4	1	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	4	1	no	—
630	C₂×C₄	—	4	1	no	—
631	C₂×C₄	—	4	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	—	8	4	no	—
639	C₂×C₄	—	8	4	no	—
640	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
641	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
642	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
643	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
644	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
645	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
646	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
647	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
648	C₈	—	2	2	no	—
649	C₈	—	4	1	no	—
650	C₈	—	4	1	no	—
651	C₈	C₄×C₅×D₄	1	4	yes	complemented
652	C₅	#23034	1	1	yes	characteristic, direct product factor, Sylow
653	C₂²	—	2	2	no	—
654	C₂²	—	2	2	no	—
655	C₂²	—	2	2	no	—
656	C₂²	—	4	1	no	—
657	C₂²	—	4	1	no	—
658	C₂²	—	4	1	no	—
659	C₂²	—	4	1	no	—
660	C₂²	—	4	2	no	—
661	C₂²	—	4	2	no	—
662	C₂²	—	4	2	no	—
663	C₂²	—	8	1	no	—
664	C₂²	—	8	1	no	—
665	C₂²	—	8	1	no	—
666	C₂²	—	8	1	no	—
667	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
668	C₂²	C₅×D₄²	1	1	yes	characteristic
669	C₂²	C₅×#547	1	1	yes	characteristic
670	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
671	C₂²	C₅×#575	1	1	yes	characteristic
672	C₂²	C₅×#577	1	1	yes	characteristic
673	C₂²	C₅×#578	1	1	yes	characteristic
674	C₄	—	2	2	no	—
675	C₄	—	2	2	no	—
676	C₄	—	4	2	no	—
677	C₄	—	4	1	no	—
678	C₄	—	4	2	no	—
679	C₄	—	4	1	no	—
680	C₄	—	4	1	no	—
681	C₄	—	4	2	no	—
682	C₄	—	4	2	no	—
683	C₄	—	4	2	no	—
684	C₄	—	8	1	no	—
685	C₄	—	8	1	no	—
686	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
687	C₄	C₅×#520	1	1	yes	characteristic
688	C₄	C₅×#548	1	1	yes	characteristic
689	C₄	C₅×#553	1	1	yes	characteristic
690	C₂	—	4	2	no	—
691	C₂	—	8	2	no	—
692	C₂	C₅×#2361	1	1	yes	characteristic
693	C₂	C₄×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
694	C₂	C₅×#2947	1	1	yes	characteristic
695	C₂	C₅×#3265	1	1	yes	characteristic
696	C₂	C₅×#3269	1	1	yes	characteristic
697	C₂	C₅×#3351	1	1	yes	characteristic
698	C₂	C₅×#3353	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×#121	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×SD₁₆	C₂	semidirect
3. C₂×C₅×#428	C₂	semidirect
4. C₅×#2362	C₂	semidirect
6. C₅×#1973	C₂	semidirect
7. C₅×#1942	C₂	semidirect
8. C₅×#1928	C₂	semidirect
9. C₅×#1926	C₂	semidirect
11. C₅×#1872	C₂	semidirect
12. C₅×#1865	C₂	semidirect
13. C₅×#1862	C₂	semidirect
14. C₅×#1776	C₂	semidirect
15. C₅×#1753	C₂	semidirect
25. C₅×#468	C₄	semidirect
62. #23034	C₅	direct (N × H)
71. C₂×C₅×SD₁₆	C₂×C₄	semidirect
74. C₂×C₅×M₁₆	C₂×C₄	semidirect
80. C₅×C₂²⋊Q₈	C₂×C₄	semidirect
119. C₅×#107	C₂×C₄	semidirect
121. C₅×#106	D₄	semidirect
124. C₅×#103	C₂×C₄	semidirect
127. C₅×#102	C₂×C₄	semidirect
140. C₂×C₄×SD₁₆	C₂×C₅	semidirect
141. C₂×#428	C₂×C₅	semidirect
142. #2362	C₂×C₅	semidirect
144. #1973	C₂×C₅	semidirect
145. #1942	C₂×C₅	semidirect
146. #1928	C₂×C₅	semidirect
147. #1926	C₂×C₅	semidirect
149. #1872	C₂×C₅	semidirect
150. #1865	C₂×C₅	semidirect
151. #1862	C₂×C₅	semidirect
152. #1776	C₂×C₅	semidirect
153. #1753	C₂×C₅	semidirect
252. #468	C₄×C₅	semidirect
364. C₅×C₈	C₄×D₄	semidirect
373. C₂×SD₁₆	C₂×C₄×C₅	semidirect
376. C₂×M₁₆	C₂×C₄×C₅	semidirect
382. C₂²⋊Q₈	C₂×C₄×C₅	semidirect
421. #107	C₂×C₄×C₅	semidirect
423. #106	C₅×D₄	semidirect
426. #103	C₂×C₄×C₅	semidirect
429. #102	C₂×C₄×C₅	semidirect
651. C₈	C₄×C₅×D₄	semidirect
652. C₅	#23034	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×#468	2
C₂×C₄×C₅×SD₁₆	2
C₂×C₅×#428	2
C₅×#2362	2
C₅×#2361	2
C₅×#1973	2
C₅×#1942	2
C₅×#1928	2
C₅×#1926	2
C₅×#1875	2
C₅×#1872	2
C₅×#1865	2
C₅×#1862	2
C₅×#1776	2
C₅×#1753	2
#23034	5

Subgroups — C5×#23034 #11945754

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#23034 #11945754