Subgroups — C₅×#24346 #11947066

Order 1280.

1064 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#557	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#478	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#440	C₂	1	1	yes	maximal, characteristic
4	C₅×#2538	C₂	1	1	yes	maximal, characteristic
5	C₅×#2059	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2057	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2025	C₂	1	1	yes	maximal, characteristic
8	C₅×#2023	C₂	1	1	yes	maximal, characteristic
9	C₅×#1992	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1985	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1880	C₂	1	1	yes	maximal, characteristic
12	C₅×#1880	C₂	1	1	yes	maximal, characteristic
13	C₅×#1865	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1863	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1803	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₅×SD₁₆	C₂²	1	1	yes	characteristic
17	C₅×#557	—	2	4	no	—
18	C₅×#557	—	2	4	no	—
19	C₂×C₅×C₄⋊Q₈	—	2	1	no	—
20	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₅×#125	—	2	1	no	—
22	C₂×C₅×#125	—	2	1	no	—
23	C₂×C₅×#125	C₂²	1	1	yes	characteristic
24	C₂×C₅×#125	C₂²	1	1	yes	characteristic
25	C₂×C₅×C₂²⋊Q₈	—	2	1	no	—
26	C₂×C₄×C₅×Q₈	—	2	1	no	—
27	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
32	C₅×#478	—	2	4	no	—
33	C₅×#440	—	2	4	no	—
34	C₂×C₅×#107	C₂²	1	1	yes	characteristic
35	C₂×C₅×#107	C₂²	1	1	yes	characteristic
36	C₂×C₅×#106	C₂²	1	1	yes	characteristic
37	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×C₅×#103	C₂²	1	1	yes	characteristic
39	C₂×C₅×#103	C₂²	1	1	yes	characteristic
40	C₂×C₅×#103	C₂²	1	1	yes	characteristic
41	C₂×C₅×#102	C₂²	1	1	yes	characteristic
42	C₂×C₅×#102	C₂²	1	1	yes	characteristic
43	C₂×C₅×#102	C₂²	1	1	yes	characteristic
44	C₂×C₅×#97	C₂²	1	1	yes	characteristic
45	C₅×#396	—	2	1	no	—
46	C₅×#396	—	2	1	no	—
47	C₅×#390	C₂²	1	1	yes	characteristic
48	C₅×#390	C₂²	1	1	yes	characteristic
49	C₅×#389	C₂²	1	1	yes	characteristic
50	C₅×#389	C₂²	1	1	yes	characteristic
51	C₅×#384	C₂²	1	1	yes	characteristic
52	C₅×#380	—	2	1	no	—
53	C₅×#340	C₂²	1	1	yes	characteristic
54	C₅×#340	C₂²	1	1	yes	characteristic
55	C₅×#340	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×#336	C₂²	1	1	yes	characteristic
60	C₅×#336	C₂²	1	1	yes	characteristic
61	C₅×#336	C₂²	1	1	yes	characteristic
62	C₅×#336	C₂²	1	1	yes	characteristic
63	#24346	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
64	C₂²×C₅×Q₈	—	2	1	no	—
65	C₂²×C₅×Q₈	D₄	1	1	yes	characteristic
66	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
67	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₅	—	2	1	no	—
69	C₂×C₅×SD₁₆	—	2	2	no	—
70	C₂×C₅×SD₁₆	—	2	2	no	—
71	C₂×C₅×SD₁₆	Q₈	1	4	yes	complemented
72	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
73	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
74	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
75	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
76	C₅×C₄⋊Q₈	—	2	8	no	—
77	C₅×C₄⋊Q₈	—	2	2	no	—
78	C₅×C₄⋊Q₈	—	2	2	no	—
79	C₅×#125	—	2	8	no	—
80	C₅×#125	—	2	8	no	—
81	C₅×#125	—	2	2	no	—
82	C₅×#125	—	2	2	no	—
83	C₅×#125	—	2	2	no	—
84	C₅×#125	D₄	1	4	yes	—
85	C₅×C₂²⋊Q₈	—	4	4	no	—
86	C₄×C₅×Q₈	—	2	8	no	—
87	C₄×C₅×Q₈	—	2	2	no	—
88	C₄×C₅×Q₈	—	2	2	no	—
89	C₄×C₅×Q₈	—	2	2	no	—
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	—	2	2	no	—
94	C₄×C₅×Q₈	D₄	1	4	yes	—
95	C₄×C₅×D₄	—	2	2	no	—
96	C₄×C₅×D₄	—	2	2	no	—
97	C₂×C₅×C₄⋊C₄	—	2	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	—	2	1	no	—
104	C₂×C₅×C₄⋊C₄	—	2	1	no	—
105	C₂×C₅×C₄⋊C₄	—	2	1	no	—
106	C₂×C₅×C₄⋊C₄	—	2	1	no	—
107	C₂×C₅×C₄⋊C₄	—	2	1	no	—
108	C₂×C₅×C₄⋊C₄	—	2	1	no	—
109	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
110	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
111	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
112	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
113	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
114	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
115	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
116	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
117	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
118	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
119	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
120	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
121	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
122	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
123	C₂×C₄²×C₅	—	2	1	no	—
124	C₂×C₄²×C₅	—	2	1	no	—
125	C₂×C₄²×C₅	—	2	1	no	—
126	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
129	C₅×#107	—	2	2	no	—
130	C₅×#107	—	2	2	no	—
131	C₅×#106	—	2	2	no	—
132	C₅×C₄⋊C₈	—	2	2	no	—
133	C₅×#103	—	2	2	no	—
134	C₅×#103	—	2	2	no	—
135	C₅×#103	—	2	2	no	—
136	C₅×#102	—	2	2	no	—
137	C₅×#102	—	2	2	no	—
138	C₅×#102	—	2	2	no	—
139	C₅×#97	—	2	2	no	—
140	C₅×#95	—	2	1	no	—
141	C₅×#95	—	2	1	no	—
142	C₂×#557	C₂×C₅	1	1	yes	characteristic, complemented
143	C₂×#478	C₂×C₅	1	1	yes	characteristic
144	C₂×#440	C₂×C₅	1	1	yes	characteristic
145	#2538	C₂×C₅	1	1	yes	characteristic
146	#2059	C₂×C₅	1	1	yes	characteristic, complemented
147	#2057	C₂×C₅	1	1	yes	characteristic, complemented
148	#2025	C₂×C₅	1	1	yes	characteristic
149	#2023	C₂×C₅	1	1	yes	characteristic
150	#1992	C₂×C₅	1	1	yes	characteristic, complemented
151	#1985	C₂×C₅	1	1	yes	characteristic, complemented
152	#1880	C₂×C₅	1	1	yes	characteristic
153	#1880	C₂×C₅	1	1	yes	characteristic
154	#1865	C₂×C₅	1	1	yes	characteristic, complemented
155	#1863	C₂×C₅	1	1	yes	characteristic, complemented
156	#1803	C₂×C₅	1	1	yes	characteristic, complemented
157	C₂⁴×C₅	—	2	1	no	—
158	C₂×C₅×Q₈	—	2	4	no	—
159	C₂×C₅×Q₈	—	2	2	no	—
160	C₂×C₅×Q₈	—	2	2	no	—
161	C₂×C₅×Q₈	—	2	1	no	—
162	C₂×C₅×Q₈	—	2	1	no	—
163	C₂×C₅×Q₈	—	2	1	no	—
164	C₂×C₅×Q₈	—	4	1	no	—
165	C₂×C₅×Q₈	—	4	2	no	—
166	C₂×C₅×Q₈	—	4	2	no	—
167	C₂×C₅×Q₈	C₂×D₄	1	2	yes	—
168	C₂×C₅×Q₈	C₂×Q₈	1	2	yes	—
169	C₂×C₅×Q₈	#41	1	2	yes	—
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	—	2	1	no	—
175	C₂×C₅×D₄	C₂×Q₈	1	2	yes	—
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	—	2	1	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	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
188	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
193	C₅×SD₁₆	—	2	8	no	—
194	C₂×C₅×C₈	—	2	1	no	—
195	C₂×C₅×C₈	—	2	1	no	—
196	C₂×C₅×C₈	—	2	1	no	—
197	C₂×C₅×C₈	—	2	1	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	C₂×Q₈	1	2	yes	—
206	C₅×C₄⋊C₄	—	2	4	no	—
207	C₅×C₄⋊C₄	—	2	4	no	—
208	C₅×C₄⋊C₄	—	2	4	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	—	2	4	no	—
214	C₅×C₄⋊C₄	—	2	2	no	—
215	C₅×C₄⋊C₄	—	2	2	no	—
216	C₅×C₄⋊C₄	—	2	2	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	—	2	1	no	—
224	C₅×C₄⋊C₄	—	2	1	no	—
225	C₅×C₄⋊C₄	—	2	1	no	—
226	C₅×C₄⋊C₄	—	4	2	no	—
227	C₅×C₄⋊C₄	—	4	2	no	—
228	C₅×C₄⋊C₄	—	4	2	no	—
229	C₅×C₄⋊C₄	—	8	1	no	—
230	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
231	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
232	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
233	C₅×C₂²⋊C₄	—	4	2	no	—
234	C₅×C₂²⋊C₄	—	4	2	no	—
235	C₅×C₂²⋊C₄	—	4	2	no	—
236	C₅×C₂²⋊C₄	—	8	1	no	—
237	C₅×C₂²⋊C₄	—	8	1	no	—
238	C₄²×C₅	—	2	4	no	—
239	C₄²×C₅	—	2	4	no	—
240	C₄²×C₅	—	2	4	no	—
241	C₄²×C₅	—	2	1	no	—
242	C₄²×C₅	—	2	1	no	—
243	C₄²×C₅	—	2	1	no	—
244	C₄²×C₅	—	2	1	no	—
245	C₄²×C₅	C₂×D₄	1	2	yes	—
246	C₄²×C₅	C₂×D₄	1	2	yes	—
247	C₂²×SD₁₆	C₂²×C₅	1	1	yes	characteristic
248	#557	—	2	4	no	—
249	#557	—	2	4	no	—
250	C₂×C₄⋊Q₈	—	2	1	no	—
251	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
252	C₂×#125	—	2	1	no	—
253	C₂×#125	—	2	1	no	—
254	C₂×#125	C₂²×C₅	1	1	yes	characteristic
255	C₂×#125	C₂²×C₅	1	1	yes	characteristic
256	C₂×C₂²⋊Q₈	—	2	1	no	—
257	C₂×C₄×Q₈	—	2	1	no	—
258	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
259	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
260	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
261	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
262	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
263	#478	—	2	4	no	—
264	#440	—	2	4	no	—
265	C₂×#107	C₂²×C₅	1	1	yes	characteristic
266	C₂×#107	C₂²×C₅	1	1	yes	characteristic
267	C₂×#106	C₂²×C₅	1	1	yes	characteristic
268	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
269	C₂×#103	C₂²×C₅	1	1	yes	characteristic
270	C₂×#103	C₂²×C₅	1	1	yes	characteristic
271	C₂×#103	C₂²×C₅	1	1	yes	characteristic
272	C₂×#102	C₂²×C₅	1	1	yes	characteristic
273	C₂×#102	C₂²×C₅	1	1	yes	characteristic
274	C₂×#102	C₂²×C₅	1	1	yes	characteristic
275	C₂×#97	C₂²×C₅	1	1	yes	characteristic
276	#396	—	2	1	no	—
277	#396	—	2	1	no	—
278	#390	C₂²×C₅	1	1	yes	characteristic
279	#390	C₂²×C₅	1	1	yes	characteristic
280	#389	C₂²×C₅	1	1	yes	characteristic
281	#389	C₂²×C₅	1	1	yes	characteristic
282	#384	C₂²×C₅	1	1	yes	characteristic
283	#380	—	2	1	no	—
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	#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	#336	C₂²×C₅	1	1	yes	characteristic
293	#336	C₂²×C₅	1	1	yes	characteristic
294	C₂³×C₅	—	2	2	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	C₂²×D₄	1	1	yes	characteristic
302	C₅×Q₈	—	2	2	no	—
303	C₅×Q₈	—	2	2	no	—
304	C₅×Q₈	—	2	2	no	—
305	C₅×Q₈	—	4	4	no	—
306	C₅×Q₈	—	4	8	no	—
307	C₅×Q₈	C₂²⋊Q₈	1	4	yes	complemented
308	C₅×D₄	—	2	2	no	—
309	C₅×D₄	—	2	2	no	—
310	C₅×D₄	—	4	1	no	—
311	C₅×D₄	—	4	1	no	—
312	C₂×C₄×C₅	—	2	2	no	—
313	C₂×C₄×C₅	—	2	1	no	—
314	C₂×C₄×C₅	—	2	2	no	—
315	C₂×C₄×C₅	—	2	2	no	—
316	C₂×C₄×C₅	—	2	1	no	—
317	C₂×C₄×C₅	—	2	1	no	—
318	C₂×C₄×C₅	—	2	1	no	—
319	C₂×C₄×C₅	—	2	1	no	—
320	C₂×C₄×C₅	—	2	1	no	—
321	C₂×C₄×C₅	—	2	1	no	—
322	C₂×C₄×C₅	—	2	1	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	—	4	1	no	—
334	C₂×C₄×C₅	—	4	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	—	8	4	no	—
349	C₂×C₄×C₅	#120	1	2	yes	—
350	C₂×C₄×C₅	#120	1	2	yes	—
351	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
352	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
353	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
354	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
355	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
356	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
357	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
358	C₅×C₈	—	2	2	no	—
359	C₅×C₈	—	4	1	no	—
360	C₅×C₈	—	4	1	no	—
361	C₅×C₈	—	4	1	no	—
362	C₂²×Q₈	—	2	1	no	—
363	C₂²×Q₈	C₅×D₄	1	1	yes	characteristic
364	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
365	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
366	C₂³×C₄	—	2	1	no	—
367	C₂×SD₁₆	—	2	2	no	—
368	C₂×SD₁₆	—	2	2	no	—
369	C₂×SD₁₆	C₅×Q₈	1	4	yes	complemented
370	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
371	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
372	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
373	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
374	C₄⋊Q₈	—	2	8	no	—
375	C₄⋊Q₈	—	2	2	no	—
376	C₄⋊Q₈	—	2	2	no	—
377	#125	—	2	8	no	—
378	#125	—	2	8	no	—
379	#125	—	2	2	no	—
380	#125	—	2	2	no	—
381	#125	—	2	2	no	—
382	#125	C₅×D₄	1	4	yes	—
383	C₂²⋊Q₈	—	4	4	no	—
384	C₄×Q₈	—	2	8	no	—
385	C₄×Q₈	—	2	2	no	—
386	C₄×Q₈	—	2	2	no	—
387	C₄×Q₈	—	2	2	no	—
388	C₄×Q₈	—	2	2	no	—
389	C₄×Q₈	—	2	2	no	—
390	C₄×Q₈	—	2	2	no	—
391	C₄×Q₈	—	2	2	no	—
392	C₄×Q₈	C₅×D₄	1	4	yes	—
393	C₄×D₄	—	2	2	no	—
394	C₄×D₄	—	2	2	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	—	2	1	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	—	2	1	no	—
405	C₂×C₄⋊C₄	—	2	1	no	—
406	C₂×C₄⋊C₄	—	2	1	no	—
407	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
408	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
409	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
410	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
411	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
412	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
413	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
414	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
415	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
416	C₂×C₂²⋊C₄	—	2	1	no	—
417	C₂×C₂²⋊C₄	—	2	1	no	—
418	C₂×C₂²⋊C₄	—	2	1	no	—
419	C₂×C₂²⋊C₄	—	2	1	no	—
420	C₂×C₂²⋊C₄	—	2	1	no	—
421	C₂×C₄²	—	2	1	no	—
422	C₂×C₄²	—	2	1	no	—
423	C₂×C₄²	—	2	1	no	—
424	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
425	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
426	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
427	#107	—	2	2	no	—
428	#107	—	2	2	no	—
429	#106	—	2	2	no	—
430	C₄⋊C₈	—	2	2	no	—
431	#103	—	2	2	no	—
432	#103	—	2	2	no	—
433	#103	—	2	2	no	—
434	#102	—	2	2	no	—
435	#102	—	2	2	no	—
436	#102	—	2	2	no	—
437	#97	—	2	2	no	—
438	#95	—	2	1	no	—
439	#95	—	2	1	no	—
440	C₂²×C₅	—	4	2	no	—
441	C₂²×C₅	—	4	2	no	—
442	C₂²×C₅	—	4	2	no	—
443	C₂²×C₅	—	8	1	no	—
444	C₂²×C₅	—	8	1	no	—
445	C₂²×C₅	—	8	1	no	—
446	C₂²×C₅	—	8	1	no	—
447	C₂²×C₅	C₂×#120	1	1	yes	characteristic
448	C₂²×C₅	#548	1	1	yes	characteristic
449	C₂²×C₅	D₄×Q₈	1	1	yes	characteristic
450	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
451	C₂²×C₅	#575	1	1	yes	characteristic
452	C₂²×C₅	#577	1	1	yes	characteristic
453	C₂²×C₅	#578	1	1	yes	characteristic
454	C₄×C₅	—	2	4	no	—
455	C₄×C₅	—	2	2	no	—
456	C₄×C₅	—	2	2	no	—
457	C₄×C₅	—	2	2	no	—
458	C₄×C₅	—	4	1	no	—
459	C₄×C₅	—	4	2	no	—
460	C₄×C₅	—	4	2	no	—
461	C₄×C₅	—	4	1	no	—
462	C₄×C₅	—	4	1	no	—
463	C₄×C₅	—	4	2	no	—
464	C₄×C₅	—	8	1	no	—
465	C₄×C₅	—	8	1	no	—
466	C₄×C₅	—	8	1	no	—
467	C₄×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
468	C₄×C₅	#536	1	1	yes	characteristic
469	C₄×C₅	#548	1	1	yes	characteristic
470	C₄×C₅	D₄×Q₈	1	1	yes	characteristic
471	C₂⁴	—	2	1	no	—
472	C₂×Q₈	—	2	4	no	—
473	C₂×Q₈	—	2	2	no	—
474	C₂×Q₈	—	2	2	no	—
475	C₂×Q₈	—	2	1	no	—
476	C₂×Q₈	—	2	1	no	—
477	C₂×Q₈	—	2	1	no	—
478	C₂×Q₈	—	4	1	no	—
479	C₂×Q₈	—	4	2	no	—
480	C₂×Q₈	—	4	2	no	—
481	C₂×Q₈	C₂×C₅×D₄	1	2	yes	—
482	C₂×Q₈	C₂×C₅×Q₈	1	2	yes	—
483	C₂×Q₈	C₅×#41	1	2	yes	—
484	C₂×D₄	—	2	1	no	—
485	C₂×D₄	—	2	1	no	—
486	C₂×D₄	—	2	1	no	—
487	C₂×D₄	—	2	1	no	—
488	C₂×D₄	—	2	1	no	—
489	C₂×D₄	C₂×C₅×Q₈	1	2	yes	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	2	1	no	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	2	1	no	—
494	C₂²×C₄	—	2	1	no	—
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	4	2	no	—
498	C₂²×C₄	—	4	2	no	—
499	C₂²×C₄	—	4	2	no	—
500	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
501	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
502	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
503	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
504	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
505	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
506	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
507	SD₁₆	—	2	8	no	—
508	C₂×C₈	—	2	1	no	—
509	C₂×C₈	—	2	1	no	—
510	C₂×C₈	—	2	1	no	—
511	C₂×C₈	—	2	1	no	—
512	C₂×C₈	—	2	1	no	—
513	C₂×C₈	—	2	1	no	—
514	C₂×C₈	—	2	1	no	—
515	C₂×C₈	—	2	1	no	—
516	C₂×C₈	—	2	1	no	—
517	C₂×C₈	—	2	1	no	—
518	C₂×C₈	—	2	1	no	—
519	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
520	C₄⋊C₄	—	2	4	no	—
521	C₄⋊C₄	—	2	4	no	—
522	C₄⋊C₄	—	2	4	no	—
523	C₄⋊C₄	—	2	4	no	—
524	C₄⋊C₄	—	2	4	no	—
525	C₄⋊C₄	—	2	4	no	—
526	C₄⋊C₄	—	2	4	no	—
527	C₄⋊C₄	—	2	4	no	—
528	C₄⋊C₄	—	2	2	no	—
529	C₄⋊C₄	—	2	2	no	—
530	C₄⋊C₄	—	2	2	no	—
531	C₄⋊C₄	—	2	1	no	—
532	C₄⋊C₄	—	2	1	no	—
533	C₄⋊C₄	—	2	1	no	—
534	C₄⋊C₄	—	2	1	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	—	4	2	no	—
541	C₄⋊C₄	—	4	2	no	—
542	C₄⋊C₄	—	4	2	no	—
543	C₄⋊C₄	—	8	1	no	—
544	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
545	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
546	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
547	C₂²⋊C₄	—	4	2	no	—
548	C₂²⋊C₄	—	4	2	no	—
549	C₂²⋊C₄	—	4	2	no	—
550	C₂²⋊C₄	—	8	1	no	—
551	C₂²⋊C₄	—	8	1	no	—
552	C₄²	—	2	4	no	—
553	C₄²	—	2	4	no	—
554	C₄²	—	2	4	no	—
555	C₄²	—	2	1	no	—
556	C₄²	—	2	1	no	—
557	C₄²	—	2	1	no	—
558	C₄²	—	2	1	no	—
559	C₄²	C₂×C₅×D₄	1	2	yes	—
560	C₄²	C₂×C₅×D₄	1	2	yes	—
561	C₂×C₅	—	8	2	no	—
562	C₂×C₅	#2409	1	1	yes	characteristic
563	C₂×C₅	#3006	1	1	yes	characteristic
564	C₂×C₅	#3013	1	1	yes	characteristic
565	C₂×C₅	#3368	1	1	yes	characteristic
566	C₂×C₅	#3377	1	1	yes	characteristic
567	C₂×C₅	#3386	1	1	yes	characteristic
568	C₂×C₅	#3388	1	1	yes	characteristic
569	C₂³	—	2	2	no	—
570	C₂³	—	4	1	no	—
571	C₂³	—	4	1	no	—
572	C₂³	—	4	1	no	—
573	C₂³	—	4	1	no	—
574	C₂³	—	4	1	no	—
575	C₂³	—	4	1	no	—
576	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
577	Q₈	—	2	2	no	—
578	Q₈	—	2	2	no	—
579	Q₈	—	2	2	no	—
580	Q₈	—	4	4	no	—
581	Q₈	—	4	8	no	—
582	Q₈	C₅×C₂²⋊Q₈	1	4	yes	complemented
583	D₄	—	2	2	no	—
584	D₄	—	2	2	no	—
585	D₄	—	4	1	no	—
586	D₄	—	4	1	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	—	4	1	no	—
623	C₂×C₄	—	8	4	no	—
624	C₂×C₄	C₅×#120	1	2	yes	—
625	C₂×C₄	C₅×#120	1	2	yes	—
626	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
627	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
628	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
629	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
630	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
631	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
632	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
633	C₈	—	2	2	no	—
634	C₈	—	4	1	no	—
635	C₈	—	4	1	no	—
636	C₈	—	4	1	no	—
637	C₅	#24346	1	1	yes	characteristic, direct product factor, Sylow
638	C₂²	—	4	2	no	—
639	C₂²	—	4	2	no	—
640	C₂²	—	4	2	no	—
641	C₂²	—	8	1	no	—
642	C₂²	—	8	1	no	—
643	C₂²	—	8	1	no	—
644	C₂²	—	8	1	no	—
645	C₂²	C₂×C₅×#120	1	1	yes	characteristic
646	C₂²	C₅×#548	1	1	yes	characteristic
647	C₂²	C₅×D₄×Q₈	1	1	yes	characteristic
648	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
649	C₂²	C₅×#575	1	1	yes	characteristic
650	C₂²	C₅×#577	1	1	yes	characteristic
651	C₂²	C₅×#578	1	1	yes	characteristic
652	C₄	—	2	2	no	—
653	C₄	—	2	2	no	—
654	C₄	—	2	2	no	—
655	C₄	—	2	4	no	—
656	C₄	—	4	1	no	—
657	C₄	—	4	2	no	—
658	C₄	—	4	2	no	—
659	C₄	—	4	1	no	—
660	C₄	—	4	1	no	—
661	C₄	—	4	2	no	—
662	C₄	—	8	1	no	—
663	C₄	—	8	1	no	—
664	C₄	—	8	1	no	—
665	C₄	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
666	C₄	C₅×#536	1	1	yes	characteristic
667	C₄	C₅×#548	1	1	yes	characteristic
668	C₄	C₅×D₄×Q₈	1	1	yes	characteristic
669	C₂	—	8	2	no	—
670	C₂	C₅×#2409	1	1	yes	characteristic
671	C₂	C₅×#3006	1	1	yes	characteristic
672	C₂	C₅×#3013	1	1	yes	characteristic
673	C₂	C₅×#3368	1	1	yes	characteristic
674	C₂	C₅×#3377	1	1	yes	characteristic
675	C₂	C₅×#3386	1	1	yes	characteristic
676	C₂	C₅×#3388	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂²×C₅×D₄	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄×C₅×Q₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#557	C₂	semidirect
5. C₅×#2059	C₂	semidirect
6. C₅×#2057	C₂	semidirect
9. C₅×#1992	C₂	semidirect
10. C₅×#1985	C₂	semidirect
13. C₅×#1865	C₂	semidirect
14. C₅×#1863	C₂	semidirect
15. C₅×#1803	C₂	semidirect
63. #24346	C₅	direct (N × H)
71. C₂×C₅×SD₁₆	Q₈	semidirect
142. C₂×#557	C₂×C₅	semidirect
146. #2059	C₂×C₅	semidirect
147. #2057	C₂×C₅	semidirect
150. #1992	C₂×C₅	semidirect
151. #1985	C₂×C₅	semidirect
154. #1865	C₂×C₅	semidirect
155. #1863	C₂×C₅	semidirect
156. #1803	C₂×C₅	semidirect
307. C₅×Q₈	C₂²⋊Q₈	semidirect
369. C₂×SD₁₆	C₅×Q₈	semidirect
582. Q₈	C₅×C₂²⋊Q₈	semidirect
637. C₅	#24346	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×#557	2
C₂×C₅×#478	2
C₂×C₅×#440	2
C₅×#2538	2
C₅×#2059	2
C₅×#2057	2
C₅×#2025	2
C₅×#2023	2
C₅×#1992	2
C₅×#1985	2
C₅×#1880	2
C₅×#1865	2
C₅×#1863	2
C₅×#1803	2
#24346	5

Subgroups — C5×#24346 #11947066

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#24346 #11947066