Subgroups — C₅×#24910 #11947630

Order 1280.

1010 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#448	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#440	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2422	C₂	1	1	yes	maximal, characteristic
4	C₅×Q₈×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2095	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2075	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2055	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2033	C₂	1	1	yes	maximal, characteristic
9	C₅×#1935	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1924	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1880	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1877	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1863	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1803	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1787	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×C₅×Q₈	C₂²	1	1	yes	characteristic
17	C₂²×C₅×SD₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₅×SD₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₅×#123	—	2	1	no	—
20	C₂×C₅×#121	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×D₄	C₂²	1	1	yes	characteristic
24	C₅×#448	—	2	4	no	—
25	C₅×#440	—	2	4	no	—
26	C₂×C₅×#107	C₂²	1	1	yes	characteristic
27	C₂×C₅×#107	C₂²	1	1	yes	characteristic
28	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₅×#103	C₂²	1	1	yes	characteristic
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×C₂²⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
39	C₂×C₅×#97	C₂²	1	1	yes	characteristic
40	C₅×#397	—	2	1	no	—
41	C₅×#394	—	2	1	no	—
42	C₅×#391	—	2	1	no	—
43	C₅×#391	—	2	1	no	—
44	C₅×#391	C₂²	1	1	yes	characteristic
45	C₅×#391	C₂²	1	1	yes	characteristic
46	C₅×#390	C₂²	1	1	yes	characteristic
47	C₅×#389	C₂²	1	1	yes	characteristic
48	C₅×#385	—	2	1	no	—
49	C₅×#384	C₂²	1	1	yes	characteristic
50	C₅×#380	—	2	1	no	—
51	C₅×#380	C₂²	1	1	yes	characteristic
52	C₅×#380	C₂²	1	1	yes	characteristic
53	C₄×C₅×C₂²⋊C₄	—	2	1	no	—
54	C₄×C₅×C₂²⋊C₄	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	#24910	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
62	C₂²×C₅×Q₈	—	2	2	no	—
63	C₂²×C₅×Q₈	—	2	2	no	—
64	C₂²×C₅×Q₈	—	2	1	no	—
65	C₂²×C₅×Q₈	—	2	2	no	—
66	C₂²×C₅×Q₈	—	2	2	no	—
67	C₂²×C₅×Q₈	—	4	1	no	—
68	C₂²×C₅×Q₈	—	4	1	no	—
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	—	2	1	no	—
75	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
76	C₂×C₅×SD₁₆	—	2	2	no	—
77	C₂×C₅×SD₁₆	—	2	2	no	—
78	C₂×C₅×SD₁₆	—	2	2	no	—
79	C₂×C₅×SD₁₆	—	2	2	no	—
80	C₂×C₅×SD₁₆	—	4	1	no	—
81	C₂×C₅×SD₁₆	D₄	1	4	yes	—
82	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
83	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
84	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
85	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
86	C₅×#123	—	4	4	no	—
87	C₅×#121	—	2	2	no	—
88	C₅×#121	—	4	1	no	—
89	C₄×C₅×Q₈	—	2	2	no	—
90	C₄×C₅×Q₈	—	2	2	no	—
91	C₄×C₅×Q₈	—	4	1	no	—
92	C₄×C₅×Q₈	—	4	1	no	—
93	C₄×C₅×D₄	—	2	2	no	—
94	C₄×C₅×D₄	—	4	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	—	2	1	no	—
99	C₂×C₅×C₄⋊C₄	—	2	1	no	—
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×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
112	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
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	—	4	1	no	—
119	C₅×C₄⋊C₈	—	4	1	no	—
120	C₅×#103	—	2	2	no	—
121	C₅×#103	—	2	2	no	—
122	C₅×#103	—	2	2	no	—
123	C₅×#103	—	2	2	no	—
124	C₅×#103	—	2	2	no	—
125	C₅×#103	—	4	1	no	—
126	C₅×#102	—	2	2	no	—
127	C₅×#102	—	4	1	no	—
128	C₅×C₂²⋊C₈	—	2	2	no	—
129	C₅×C₂²⋊C₈	—	4	1	no	—
130	C₅×#97	—	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	—	2	1	no	—
138	C₅×#95	D₄	1	1	yes	characteristic
139	C₅×#95	D₄	1	1	yes	characteristic
140	C₂×#448	C₂×C₅	1	1	yes	characteristic
141	C₂×#440	C₂×C₅	1	1	yes	characteristic, complemented
142	#2422	C₂×C₅	1	1	yes	characteristic
143	Q₈×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
144	#2095	C₂×C₅	1	1	yes	characteristic, complemented
145	#2075	C₂×C₅	1	1	yes	characteristic, complemented
146	#2055	C₂×C₅	1	1	yes	characteristic, complemented
147	#2033	C₂×C₅	1	1	yes	characteristic
148	#1935	C₂×C₅	1	1	yes	characteristic, complemented
149	#1924	C₂×C₅	1	1	yes	characteristic, complemented
150	#1880	C₂×C₅	1	1	yes	characteristic, complemented
151	#1877	C₂×C₅	1	1	yes	characteristic, complemented
152	#1863	C₂×C₅	1	1	yes	characteristic, complemented
153	#1803	C₂×C₅	1	1	yes	characteristic, complemented
154	#1787	C₂×C₅	1	1	yes	characteristic, complemented
155	C₂⁴×C₅	—	2	1	no	—
156	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
157	C₂×C₅×Q₈	—	2	4	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	—	2	1	no	—
162	C₂×C₅×Q₈	—	2	1	no	—
163	C₂×C₅×Q₈	—	2	1	no	—
164	C₂×C₅×Q₈	—	2	1	no	—
165	C₂×C₅×Q₈	—	2	1	no	—
166	C₂×C₅×Q₈	—	4	2	no	—
167	C₂×C₅×Q₈	—	4	2	no	—
168	C₂×C₅×Q₈	—	4	4	no	—
169	C₂×C₅×Q₈	—	4	4	no	—
170	C₂×C₅×Q₈	—	4	4	no	—
171	C₂×C₅×Q₈	—	4	4	no	—
172	C₂×C₅×Q₈	C₂×D₄	1	2	yes	—
173	C₂×C₅×Q₈	#41	1	2	yes	—
174	C₂×C₅×Q₈	#41	1	2	yes	—
175	C₂×C₅×Q₈	#41	1	2	yes	—
176	C₂×C₅×D₄	—	2	1	no	—
177	C₂×C₅×D₄	—	2	1	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	—	4	2	no	—
182	C₂×C₅×D₄	—	4	2	no	—
183	C₂×C₅×D₄	—	8	1	no	—
184	C₂×C₅×D₄	C₂×D₄	1	2	yes	—
185	C₂²×C₄×C₅	—	2	1	no	—
186	C₂²×C₄×C₅	—	2	4	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	1	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	—	2	1	no	—
199	C₂²×C₄×C₅	—	4	2	no	—
200	C₂²×C₄×C₅	—	4	2	no	—
201	C₂²×C₄×C₅	—	4	2	no	—
202	C₂²×C₄×C₅	—	4	2	no	—
203	C₂²×C₄×C₅	—	8	1	no	—
204	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
210	C₅×SD₁₆	—	2	8	no	—
211	C₅×SD₁₆	—	4	4	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	—	2	1	no	—
220	C₂×C₅×C₈	—	2	1	no	—
221	C₂×C₅×C₈	—	2	1	no	—
222	C₂×C₅×C₈	—	2	1	no	—
223	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
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	—	2	1	no	—
233	C₅×C₄⋊C₄	—	2	1	no	—
234	C₅×C₄⋊C₄	—	4	2	no	—
235	C₅×C₄⋊C₄	—	4	2	no	—
236	C₅×C₄⋊C₄	—	4	2	no	—
237	C₅×C₄⋊C₄	—	4	2	no	—
238	C₅×C₄⋊C₄	—	8	1	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	—	4	2	no	—
245	C₅×C₂²⋊C₄	—	4	2	no	—
246	C₅×C₂²⋊C₄	—	4	2	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	C₂³×Q₈	C₂²×C₅	1	1	yes	characteristic
254	C₂²×SD₁₆	C₂²×C₅	1	1	yes	characteristic
255	C₂²×SD₁₆	C₂²×C₅	1	1	yes	characteristic
256	C₂×#123	—	2	1	no	—
257	C₂×#121	C₂²×C₅	1	1	yes	characteristic
258	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
259	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
260	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
261	#448	—	2	4	no	—
262	#440	—	2	4	no	—
263	C₂×#107	C₂²×C₅	1	1	yes	characteristic
264	C₂×#107	C₂²×C₅	1	1	yes	characteristic
265	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
266	C₂×#103	C₂²×C₅	1	1	yes	characteristic
267	C₂×#103	C₂²×C₅	1	1	yes	characteristic
268	C₂×#103	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×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
275	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
276	C₂×#97	C₂²×C₅	1	1	yes	characteristic
277	#397	—	2	1	no	—
278	#394	—	2	1	no	—
279	#391	—	2	1	no	—
280	#391	—	2	1	no	—
281	#391	C₂²×C₅	1	1	yes	characteristic
282	#391	C₂²×C₅	1	1	yes	characteristic
283	#390	C₂²×C₅	1	1	yes	characteristic
284	#389	C₂²×C₅	1	1	yes	characteristic
285	#385	—	2	1	no	—
286	#384	C₂²×C₅	1	1	yes	characteristic
287	#380	—	2	1	no	—
288	#380	C₂²×C₅	1	1	yes	characteristic
289	#380	C₂²×C₅	1	1	yes	characteristic
290	C₄×C₂²⋊C₄	—	2	1	no	—
291	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
292	#340	C₂²×C₅	1	1	yes	characteristic
293	#340	C₂²×C₅	1	1	yes	characteristic
294	#340	C₂²×C₅	1	1	yes	characteristic
295	#340	C₂²×C₅	1	1	yes	characteristic
296	#336	C₂²×C₅	1	1	yes	characteristic
297	#336	C₂²×C₅	1	1	yes	characteristic
298	C₂³×C₅	—	2	1	no	—
299	C₂³×C₅	—	2	1	no	—
300	C₂³×C₅	—	2	1	no	—
301	C₂³×C₅	—	2	1	no	—
302	C₂³×C₅	—	2	1	no	—
303	C₂³×C₅	—	2	1	no	—
304	C₂³×C₅	—	2	2	no	—
305	C₂³×C₅	—	4	1	no	—
306	C₂³×C₅	—	4	1	no	—
307	C₂³×C₅	—	4	1	no	—
308	C₂³×C₅	—	4	1	no	—
309	C₂³×C₅	—	4	1	no	—
310	C₂³×C₅	—	4	1	no	—
311	C₂³×C₅	AGL(1,ℤ/8)	1	2	yes	—
312	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
313	C₅×Q₈	—	2	2	no	—
314	C₅×Q₈	—	2	2	no	—
315	C₅×Q₈	—	2	2	no	—
316	C₅×Q₈	—	2	2	no	—
317	C₅×Q₈	—	2	2	no	—
318	C₅×Q₈	—	4	8	no	—
319	C₅×Q₈	—	4	1	no	—
320	C₅×Q₈	—	4	1	no	—
321	C₅×Q₈	#123	1	4	yes	complemented
322	C₅×D₄	—	2	2	no	—
323	C₅×D₄	—	2	2	no	—
324	C₅×D₄	—	4	1	no	—
325	C₅×D₄	—	4	1	no	—
326	C₅×D₄	—	8	4	no	—
327	C₂×C₄×C₅	—	2	2	no	—
328	C₂×C₄×C₅	—	2	2	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	2	no	—
333	C₂×C₄×C₅	—	2	1	no	—
334	C₂×C₄×C₅	—	2	1	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	—	2	1	no	—
342	C₂×C₄×C₅	—	2	1	no	—
343	C₂×C₄×C₅	—	2	1	no	—
344	C₂×C₄×C₅	—	2	1	no	—
345	C₂×C₄×C₅	—	4	8	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	—	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	—	8	4	no	—
368	C₂×C₄×C₅	#137	1	2	yes	—
369	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
370	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
371	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
372	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
373	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
374	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
375	C₅×C₈	—	2	2	no	—
376	C₅×C₈	—	4	1	no	—
377	C₅×C₈	—	4	1	no	—
378	C₅×C₈	—	4	1	no	—
379	C₂²×Q₈	—	2	2	no	—
380	C₂²×Q₈	—	2	2	no	—
381	C₂²×Q₈	—	2	1	no	—
382	C₂²×Q₈	—	2	2	no	—
383	C₂²×Q₈	—	2	2	no	—
384	C₂²×Q₈	—	4	1	no	—
385	C₂²×Q₈	—	4	1	no	—
386	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
387	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
388	C₂²×D₄	—	2	1	no	—
389	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
390	C₂³×C₄	—	2	1	no	—
391	C₂³×C₄	—	2	1	no	—
392	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
393	C₂×SD₁₆	—	2	2	no	—
394	C₂×SD₁₆	—	2	2	no	—
395	C₂×SD₁₆	—	2	2	no	—
396	C₂×SD₁₆	—	2	2	no	—
397	C₂×SD₁₆	—	4	1	no	—
398	C₂×SD₁₆	C₅×D₄	1	4	yes	—
399	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
400	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
401	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
402	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
403	#123	—	4	4	no	—
404	#121	—	2	2	no	—
405	#121	—	4	1	no	—
406	C₄×Q₈	—	2	2	no	—
407	C₄×Q₈	—	2	2	no	—
408	C₄×Q₈	—	4	1	no	—
409	C₄×Q₈	—	4	1	no	—
410	C₄×D₄	—	2	2	no	—
411	C₄×D₄	—	4	1	no	—
412	C₂×C₄⋊C₄	—	2	1	no	—
413	C₂×C₄⋊C₄	—	2	1	no	—
414	C₂×C₄⋊C₄	—	2	1	no	—
415	C₂×C₄⋊C₄	—	2	1	no	—
416	C₂×C₄⋊C₄	—	2	1	no	—
417	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
418	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
419	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
420	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
421	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
422	C₂×C₂²⋊C₄	—	2	1	no	—
423	C₂×C₂²⋊C₄	—	2	1	no	—
424	C₂×C₂²⋊C₄	—	2	1	no	—
425	C₂×C₂²⋊C₄	—	2	1	no	—
426	C₂×C₂²⋊C₄	—	2	1	no	—
427	C₂×C₂²⋊C₄	—	2	1	no	—
428	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
429	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
430	C₂×C₄²	—	2	1	no	—
431	C₂×C₄²	—	2	1	no	—
432	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
433	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
434	#107	—	2	2	no	—
435	#107	—	4	1	no	—
436	C₄⋊C₈	—	4	1	no	—
437	#103	—	2	2	no	—
438	#103	—	2	2	no	—
439	#103	—	2	2	no	—
440	#103	—	2	2	no	—
441	#103	—	2	2	no	—
442	#103	—	4	1	no	—
443	#102	—	2	2	no	—
444	#102	—	4	1	no	—
445	C₂²⋊C₈	—	2	2	no	—
446	C₂²⋊C₈	—	4	1	no	—
447	#97	—	2	2	no	—
448	#95	—	2	1	no	—
449	#95	—	2	1	no	—
450	#95	—	2	1	no	—
451	#95	—	2	1	no	—
452	#95	—	2	1	no	—
453	#95	—	2	1	no	—
454	#95	—	2	1	no	—
455	#95	C₅×D₄	1	1	yes	characteristic
456	#95	C₅×D₄	1	1	yes	characteristic
457	C₂²×C₅	—	2	2	no	—
458	C₂²×C₅	—	2	2	no	—
459	C₂²×C₅	—	2	2	no	—
460	C₂²×C₅	—	4	1	no	—
461	C₂²×C₅	—	4	1	no	—
462	C₂²×C₅	—	4	1	no	—
463	C₂²×C₅	—	4	1	no	—
464	C₂²×C₅	—	4	2	no	—
465	C₂²×C₅	—	4	2	no	—
466	C₂²×C₅	—	4	2	no	—
467	C₂²×C₅	—	8	1	no	—
468	C₂²×C₅	—	8	1	no	—
469	C₂²×C₅	—	8	1	no	—
470	C₂²×C₅	—	8	1	no	—
471	C₂²×C₅	#525	1	1	yes	characteristic
472	C₂²×C₅	D₄²	1	1	yes	characteristic
473	C₂²×C₅	#546	1	1	yes	characteristic
474	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
475	C₂²×C₅	C₂×#137	1	1	yes	characteristic
476	C₂²×C₅	#577	1	1	yes	characteristic
477	C₂²×C₅	#578	1	1	yes	characteristic
478	C₄×C₅	—	2	4	no	—
479	C₄×C₅	—	2	2	no	—
480	C₄×C₅	—	4	1	no	—
481	C₄×C₅	—	4	2	no	—
482	C₄×C₅	—	4	1	no	—
483	C₄×C₅	—	4	1	no	—
484	C₄×C₅	—	4	1	no	—
485	C₄×C₅	—	8	1	no	—
486	C₄×C₅	—	8	1	no	—
487	C₄×C₅	—	8	1	no	—
488	C₄×C₅	—	8	1	no	—
489	C₄×C₅	—	8	1	no	—
490	C₄×C₅	C₂×#123	1	1	yes	characteristic
491	C₄×C₅	#538	1	1	yes	characteristic
492	C₄×C₅	#546	1	1	yes	characteristic
493	C₄×C₅	#551	1	1	yes	characteristic
494	C₂⁴	—	2	1	no	—
495	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
496	C₂×Q₈	—	2	4	no	—
497	C₂×Q₈	—	2	1	no	—
498	C₂×Q₈	—	2	1	no	—
499	C₂×Q₈	—	2	1	no	—
500	C₂×Q₈	—	2	1	no	—
501	C₂×Q₈	—	2	1	no	—
502	C₂×Q₈	—	2	1	no	—
503	C₂×Q₈	—	2	1	no	—
504	C₂×Q₈	—	2	1	no	—
505	C₂×Q₈	—	4	2	no	—
506	C₂×Q₈	—	4	2	no	—
507	C₂×Q₈	—	4	4	no	—
508	C₂×Q₈	—	4	4	no	—
509	C₂×Q₈	—	4	4	no	—
510	C₂×Q₈	—	4	4	no	—
511	C₂×Q₈	C₂×C₅×D₄	1	2	yes	—
512	C₂×Q₈	C₅×#41	1	2	yes	—
513	C₂×Q₈	C₅×#41	1	2	yes	—
514	C₂×Q₈	C₅×#41	1	2	yes	—
515	C₂×D₄	—	2	1	no	—
516	C₂×D₄	—	2	1	no	—
517	C₂×D₄	—	2	1	no	—
518	C₂×D₄	—	2	1	no	—
519	C₂×D₄	—	2	1	no	—
520	C₂×D₄	—	4	2	no	—
521	C₂×D₄	—	4	2	no	—
522	C₂×D₄	—	8	1	no	—
523	C₂×D₄	C₂×C₅×D₄	1	2	yes	—
524	C₂²×C₄	—	2	1	no	—
525	C₂²×C₄	—	2	4	no	—
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	1	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	—	4	2	no	—
541	C₂²×C₄	—	4	2	no	—
542	C₂²×C₄	—	8	1	no	—
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	C₂×C₅×D₄	1	1	yes	characteristic
547	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
548	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
549	SD₁₆	—	2	8	no	—
550	SD₁₆	—	4	4	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	—	2	1	no	—
560	C₂×C₈	—	2	1	no	—
561	C₂×C₈	—	2	1	no	—
562	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
563	C₄⋊C₄	—	2	1	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	—	2	1	no	—
573	C₄⋊C₄	—	4	2	no	—
574	C₄⋊C₄	—	4	2	no	—
575	C₄⋊C₄	—	4	2	no	—
576	C₄⋊C₄	—	4	2	no	—
577	C₄⋊C₄	—	8	1	no	—
578	C₂²⋊C₄	—	2	2	no	—
579	C₂²⋊C₄	—	2	2	no	—
580	C₂²⋊C₄	—	4	2	no	—
581	C₂²⋊C₄	—	4	2	no	—
582	C₂²⋊C₄	—	4	2	no	—
583	C₂²⋊C₄	—	4	2	no	—
584	C₂²⋊C₄	—	4	2	no	—
585	C₂²⋊C₄	—	4	2	no	—
586	C₄²	—	2	1	no	—
587	C₄²	—	2	1	no	—
588	C₄²	—	2	1	no	—
589	C₄²	—	2	1	no	—
590	C₄²	—	4	2	no	—
591	C₄²	—	4	2	no	—
592	C₂×C₅	—	4	2	no	—
593	C₂×C₅	—	8	2	no	—
594	C₂×C₅	#2418	1	1	yes	characteristic
595	C₂×C₅	#3112	1	1	yes	characteristic
596	C₂×C₅	#3121	1	1	yes	characteristic
597	C₂×C₅	#3265	1	1	yes	characteristic
598	C₂×C₅	#3276	1	1	yes	characteristic
599	C₂×C₅	#3308	1	1	yes	characteristic
600	C₂×C₅	#3320	1	1	yes	characteristic
601	C₂³	—	2	1	no	—
602	C₂³	—	2	1	no	—
603	C₂³	—	2	1	no	—
604	C₂³	—	2	1	no	—
605	C₂³	—	2	1	no	—
606	C₂³	—	2	1	no	—
607	C₂³	—	2	2	no	—
608	C₂³	—	4	1	no	—
609	C₂³	—	4	1	no	—
610	C₂³	—	4	1	no	—
611	C₂³	—	4	1	no	—
612	C₂³	—	4	1	no	—
613	C₂³	—	4	1	no	—
614	C₂³	C₅×AGL(1,ℤ/8)	1	2	yes	—
615	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
616	Q₈	—	2	2	no	—
617	Q₈	—	2	2	no	—
618	Q₈	—	2	2	no	—
619	Q₈	—	2	2	no	—
620	Q₈	—	2	2	no	—
621	Q₈	—	4	8	no	—
622	Q₈	—	4	1	no	—
623	Q₈	—	4	1	no	—
624	Q₈	C₅×#123	1	4	yes	complemented
625	D₄	—	2	2	no	—
626	D₄	—	2	2	no	—
627	D₄	—	4	1	no	—
628	D₄	—	4	1	no	—
629	D₄	—	8	4	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	4	8	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	4	1	no	—
652	C₂×C₄	—	4	1	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	—	4	1	no	—
655	C₂×C₄	—	4	1	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	—	8	4	no	—
671	C₂×C₄	C₅×#137	1	2	yes	—
672	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
673	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
674	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
675	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
676	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
677	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
678	C₈	—	2	2	no	—
679	C₈	—	4	1	no	—
680	C₈	—	4	1	no	—
681	C₈	—	4	1	no	—
682	C₅	#24910	1	1	yes	characteristic, direct product factor, Sylow
683	C₂²	—	2	2	no	—
684	C₂²	—	2	2	no	—
685	C₂²	—	2	2	no	—
686	C₂²	—	4	1	no	—
687	C₂²	—	4	1	no	—
688	C₂²	—	4	1	no	—
689	C₂²	—	4	1	no	—
690	C₂²	—	4	2	no	—
691	C₂²	—	4	2	no	—
692	C₂²	—	4	2	no	—
693	C₂²	—	8	1	no	—
694	C₂²	—	8	1	no	—
695	C₂²	—	8	1	no	—
696	C₂²	—	8	1	no	—
697	C₂²	C₅×#525	1	1	yes	characteristic
698	C₂²	C₅×D₄²	1	1	yes	characteristic
699	C₂²	C₅×#546	1	1	yes	characteristic
700	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
701	C₂²	C₂×C₅×#137	1	1	yes	characteristic
702	C₂²	C₅×#577	1	1	yes	characteristic
703	C₂²	C₅×#578	1	1	yes	characteristic
704	C₄	—	2	2	no	—
705	C₄	—	2	4	no	—
706	C₄	—	4	1	no	—
707	C₄	—	4	1	no	—
708	C₄	—	4	1	no	—
709	C₄	—	4	1	no	—
710	C₄	—	4	2	no	—
711	C₄	—	8	1	no	—
712	C₄	—	8	1	no	—
713	C₄	—	8	1	no	—
714	C₄	—	8	1	no	—
715	C₄	—	8	1	no	—
716	C₄	C₂×C₅×#123	1	1	yes	characteristic
717	C₄	C₅×#538	1	1	yes	characteristic
718	C₄	C₅×#546	1	1	yes	characteristic
719	C₄	C₅×#551	1	1	yes	characteristic
720	C₂	—	4	2	no	—
721	C₂	—	8	2	no	—
722	C₂	C₅×#2418	1	1	yes	characteristic
723	C₂	C₅×#3112	1	1	yes	characteristic
724	C₂	C₅×#3121	1	1	yes	characteristic
725	C₂	C₅×#3265	1	1	yes	characteristic
726	C₂	C₅×#3276	1	1	yes	characteristic
727	C₂	C₅×#3308	1	1	yes	characteristic
728	C₂	C₅×#3320	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂×C₅×#121	C₂²
LCS	G ▷ C₂²×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×C₅×#440	C₂	semidirect
4. C₅×Q₈×C₂²⋊C₄	C₂	semidirect
5. C₅×#2095	C₂	semidirect
6. C₅×#2075	C₂	semidirect
7. C₅×#2055	C₂	semidirect
9. C₅×#1935	C₂	semidirect
10. C₅×#1924	C₂	semidirect
11. C₅×#1880	C₂	semidirect
12. C₅×#1877	C₂	semidirect
13. C₅×#1863	C₂	semidirect
14. C₅×#1803	C₂	semidirect
15. C₅×#1787	C₂	semidirect
61. #24910	C₅	direct (N × H)
141. C₂×#440	C₂×C₅	semidirect
143. Q₈×C₂²⋊C₄	C₂×C₅	semidirect
144. #2095	C₂×C₅	semidirect
145. #2075	C₂×C₅	semidirect
146. #2055	C₂×C₅	semidirect
148. #1935	C₂×C₅	semidirect
149. #1924	C₂×C₅	semidirect
150. #1880	C₂×C₅	semidirect
151. #1877	C₂×C₅	semidirect
152. #1863	C₂×C₅	semidirect
153. #1803	C₂×C₅	semidirect
154. #1787	C₂×C₅	semidirect
321. C₅×Q₈	#123	semidirect
624. Q₈	C₅×#123	semidirect
682. C₅	#24910	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×#448	2
C₂×C₅×#440	2
C₅×#2422	2
C₅×Q₈×C₂²⋊C₄	2
C₅×#2095	2
C₅×#2075	2
C₅×#2055	2
C₅×#2033	2
C₅×#1935	2
C₅×#1924	2
C₅×#1880	2
C₅×#1877	2
C₅×#1863	2
C₅×#1803	2
C₅×#1787	2
#24910	5

Subgroups — C5×#24910 #11947630

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#24910 #11947630