Subgroups — C₅×#24193 #11946913

Order 1280.

1122 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#463	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₅×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2580	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2043	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2042	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2013	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2012	C₂	1	1	yes	maximal, characteristic
9	C₅×#1984	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1958	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1880	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1879	C₂	1	1	yes	maximal, characteristic
13	C₅×#1865	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1864	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1805	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	C₂²×C₅×D₈	C₂²	1	1	yes	characteristic
19	C₅×#556	—	2	4	no	—
20	C₅×#556	—	2	4	no	—
21	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₅×#126	—	2	1	no	—
23	C₂×C₅×#126	—	2	1	no	—
24	C₂×C₅×#124	C₂²	1	1	yes	characteristic
25	C₂×C₅×#124	C₂²	1	1	yes	characteristic
26	C₂×C₅×C₂²⋊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×D₄	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
32	C₂×C₅×#117	—	2	1	no	—
33	C₅×#463	—	2	4	no	—
34	C₄×C₅×SD₁₆	—	2	4	no	—
35	C₂×C₅×#106	C₂²	1	1	yes	characteristic
36	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₅×#103	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×#103	C₂²	1	1	yes	characteristic
42	C₂×C₅×#103	C₂²	1	1	yes	characteristic
43	C₂×C₅×#102	C₂²	1	1	yes	characteristic
44	C₂×C₅×#102	C₂²	1	1	yes	characteristic
45	C₂×C₅×#102	C₂²	1	1	yes	characteristic
46	C₂×C₅×#102	C₂²	1	1	yes	characteristic
47	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
48	C₅×#399	—	2	1	no	—
49	C₅×#393	—	2	1	no	—
50	C₅×#390	C₂²	1	1	yes	characteristic
51	C₅×#390	C₂²	1	1	yes	characteristic
52	C₅×#389	C₂²	1	1	yes	characteristic
53	C₅×#389	C₂²	1	1	yes	characteristic
54	C₅×#385	—	2	1	no	—
55	C₅×#385	—	2	1	no	—
56	C₅×#382	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	#24193	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
64	C₂²×C₅×Q₈	D₄	1	1	yes	characteristic
65	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
66	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
67	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
68	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₅	—	2	1	no	—
70	C₂³×C₄×C₅	—	2	1	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	—	2	2	no	—
75	C₂×C₅×SD₁₆	—	2	2	no	—
76	C₂×C₅×SD₁₆	—	4	1	no	—
77	C₂×C₅×D₈	—	2	2	no	—
78	C₂×C₅×D₈	—	2	2	no	—
79	C₂×C₅×D₈	—	4	1	no	—
80	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
81	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
82	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
83	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
84	C₅×C₄⋊Q₈	—	2	2	no	—
85	C₅×C₄⋊Q₈	—	2	2	no	—
86	C₅×#126	—	2	8	no	—
87	C₅×#126	—	2	8	no	—
88	C₅×#124	—	2	2	no	—
89	C₅×#124	—	2	2	no	—
90	C₅×#124	—	2	2	no	—
91	C₅×#124	D₄	1	4	yes	—
92	C₅×C₂²⋊Q₈	—	2	8	no	—
93	C₄×C₅×Q₈	—	2	2	no	—
94	C₄×C₅×Q₈	—	2	2	no	—
95	C₄×C₅×Q₈	—	2	2	no	—
96	C₄×C₅×Q₈	—	2	2	no	—
97	C₄×C₅×Q₈	—	2	2	no	—
98	C₄×C₅×Q₈	D₄	1	4	yes	—
99	C₄×C₅×D₄	—	2	2	no	—
100	C₄×C₅×D₄	—	2	2	no	—
101	C₄×C₅×D₄	—	2	2	no	—
102	C₄×C₅×D₄	—	2	2	no	—
103	C₅×#117	—	2	8	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	—	2	1	no	—
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	D₄	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×C₂²⋊C₄	—	2	1	no	—
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×C₅×C₂²⋊C₄	—	2	1	no	—
124	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
125	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
126	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
127	C₂×C₄²×C₅	—	2	1	no	—
128	C₂×C₄²×C₅	—	2	1	no	—
129	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
130	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
131	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
132	C₅×#106	—	2	2	no	—
133	C₅×C₄⋊C₈	—	2	2	no	—
134	C₅×#103	—	2	2	no	—
135	C₅×#103	—	2	2	no	—
136	C₅×#103	—	2	2	no	—
137	C₅×#103	—	4	1	no	—
138	C₅×#103	—	4	1	no	—
139	C₅×#103	—	4	1	no	—
140	C₅×#102	—	2	2	no	—
141	C₅×#102	—	2	2	no	—
142	C₅×#102	—	2	2	no	—
143	C₅×#102	—	4	1	no	—
144	C₄×C₅×C₈	—	2	2	no	—
145	C₅×#95	—	2	1	no	—
146	C₅×#95	—	2	1	no	—
147	C₅×#95	—	2	1	no	—
148	C₅×#95	—	2	1	no	—
149	C₂×#556	C₂×C₅	1	1	yes	characteristic, complemented
150	C₂×#463	C₂×C₅	1	1	yes	characteristic
151	C₂×C₄×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
152	#2580	C₂×C₅	1	1	yes	characteristic, complemented
153	#2043	C₂×C₅	1	1	yes	characteristic, complemented
154	#2042	C₂×C₅	1	1	yes	characteristic, complemented
155	#2013	C₂×C₅	1	1	yes	characteristic, complemented
156	#2012	C₂×C₅	1	1	yes	characteristic
157	#1984	C₂×C₅	1	1	yes	characteristic, complemented
158	#1958	C₂×C₅	1	1	yes	characteristic, complemented
159	#1880	C₂×C₅	1	1	yes	characteristic, complemented
160	#1879	C₂×C₅	1	1	yes	characteristic
161	#1865	C₂×C₅	1	1	yes	characteristic, complemented
162	#1864	C₂×C₅	1	1	yes	characteristic, complemented
163	#1805	C₂×C₅	1	1	yes	characteristic, complemented
164	C₂⁴×C₅	—	2	1	no	—
165	C₂⁴×C₅	—	2	1	no	—
166	C₂×C₅×Q₈	—	2	2	no	—
167	C₂×C₅×Q₈	—	2	2	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	—	2	1	no	—
174	C₂×C₅×Q₈	—	2	1	no	—
175	C₂×C₅×Q₈	—	2	1	no	—
176	C₂×C₅×Q₈	—	2	1	no	—
177	C₂×C₅×Q₈	—	2	1	no	—
178	C₂×C₅×Q₈	—	4	1	no	—
179	C₂×C₅×Q₈	C₂×D₄	1	2	yes	—
180	C₂×C₅×Q₈	C₂×D₄	1	2	yes	—
181	C₂×C₅×D₄	—	2	1	no	—
182	C₂×C₅×D₄	—	2	1	no	—
183	C₂×C₅×D₄	—	2	1	no	—
184	C₂×C₅×D₄	—	2	1	no	—
185	C₂×C₅×D₄	—	2	1	no	—
186	C₂×C₅×D₄	—	2	1	no	—
187	C₂×C₅×D₄	—	2	1	no	—
188	C₂×C₅×D₄	—	2	1	no	—
189	C₂×C₅×D₄	—	2	1	no	—
190	C₂×C₅×D₄	—	2	1	no	—
191	C₂×C₅×D₄	C₂×D₄	1	2	yes	—
192	C₂×C₅×D₄	#41	1	2	yes	—
193	C₂²×C₄×C₅	—	2	4	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	—	2	1	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	—	8	1	no	—
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	C₂×D₄	1	1	yes	characteristic
210	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
211	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
212	C₅×SD₁₆	—	2	8	no	—
213	C₅×SD₁₆	—	4	4	no	—
214	C₅×D₈	—	4	4	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	—	2	1	no	—
224	C₂×C₅×C₈	—	2	1	no	—
225	C₂×C₅×C₈	—	2	1	no	—
226	C₂×C₅×C₈	#41	1	2	yes	—
227	C₅×C₄⋊C₄	—	2	4	no	—
228	C₅×C₄⋊C₄	—	2	4	no	—
229	C₅×C₄⋊C₄	—	2	4	no	—
230	C₅×C₄⋊C₄	—	2	4	no	—
231	C₅×C₄⋊C₄	—	2	2	no	—
232	C₅×C₄⋊C₄	—	2	2	no	—
233	C₅×C₄⋊C₄	—	2	2	no	—
234	C₅×C₄⋊C₄	—	2	1	no	—
235	C₅×C₄⋊C₄	—	2	1	no	—
236	C₅×C₄⋊C₄	—	2	1	no	—
237	C₅×C₄⋊C₄	—	2	1	no	—
238	C₅×C₄⋊C₄	—	2	1	no	—
239	C₅×C₄⋊C₄	—	2	1	no	—
240	C₅×C₄⋊C₄	—	2	1	no	—
241	C₅×C₄⋊C₄	—	8	1	no	—
242	C₅×C₄⋊C₄	—	8	1	no	—
243	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
244	C₅×C₂²⋊C₄	—	2	4	no	—
245	C₅×C₂²⋊C₄	—	2	4	no	—
246	C₅×C₂²⋊C₄	—	2	4	no	—
247	C₅×C₂²⋊C₄	—	2	4	no	—
248	C₅×C₂²⋊C₄	—	2	4	no	—
249	C₅×C₂²⋊C₄	—	4	2	no	—
250	C₅×C₂²⋊C₄	—	4	2	no	—
251	C₅×C₂²⋊C₄	—	4	2	no	—
252	C₅×C₂²⋊C₄	—	8	1	no	—
253	C₅×C₂²⋊C₄	—	8	1	no	—
254	C₄²×C₅	—	2	4	no	—
255	C₄²×C₅	—	2	4	no	—
256	C₄²×C₅	—	2	1	no	—
257	C₄²×C₅	—	2	1	no	—
258	C₄²×C₅	—	2	1	no	—
259	C₄²×C₅	—	2	1	no	—
260	C₄²×C₅	C₂×D₄	1	2	yes	—
261	C₄²×C₅	C₂×D₄	1	2	yes	—
262	C₂²×SD₁₆	C₂²×C₅	1	1	yes	characteristic
263	C₂²×SD₁₆	C₂²×C₅	1	1	yes	characteristic
264	C₂²×D₈	C₂²×C₅	1	1	yes	characteristic
265	#556	—	2	4	no	—
266	#556	—	2	4	no	—
267	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
268	C₂×#126	—	2	1	no	—
269	C₂×#126	—	2	1	no	—
270	C₂×#124	C₂²×C₅	1	1	yes	characteristic
271	C₂×#124	C₂²×C₅	1	1	yes	characteristic
272	C₂×C₂²⋊Q₈	—	2	1	no	—
273	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
274	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
275	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
276	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
277	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
278	C₂×#117	—	2	1	no	—
279	#463	—	2	4	no	—
280	C₄×SD₁₆	—	2	4	no	—
281	C₂×#106	C₂²×C₅	1	1	yes	characteristic
282	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
283	C₂×#103	C₂²×C₅	1	1	yes	characteristic
284	C₂×#103	C₂²×C₅	1	1	yes	characteristic
285	C₂×#103	C₂²×C₅	1	1	yes	characteristic
286	C₂×#103	C₂²×C₅	1	1	yes	characteristic
287	C₂×#103	C₂²×C₅	1	1	yes	characteristic
288	C₂×#103	C₂²×C₅	1	1	yes	characteristic
289	C₂×#102	C₂²×C₅	1	1	yes	characteristic
290	C₂×#102	C₂²×C₅	1	1	yes	characteristic
291	C₂×#102	C₂²×C₅	1	1	yes	characteristic
292	C₂×#102	C₂²×C₅	1	1	yes	characteristic
293	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
294	#399	—	2	1	no	—
295	#393	—	2	1	no	—
296	#390	C₂²×C₅	1	1	yes	characteristic
297	#390	C₂²×C₅	1	1	yes	characteristic
298	#389	C₂²×C₅	1	1	yes	characteristic
299	#389	C₂²×C₅	1	1	yes	characteristic
300	#385	—	2	1	no	—
301	#385	—	2	1	no	—
302	#382	C₂²×C₅	1	1	yes	characteristic
303	#340	C₂²×C₅	1	1	yes	characteristic
304	#340	C₂²×C₅	1	1	yes	characteristic
305	#336	C₂²×C₅	1	1	yes	characteristic
306	#336	C₂²×C₅	1	1	yes	characteristic
307	#336	C₂²×C₅	1	1	yes	characteristic
308	#336	C₂²×C₅	1	1	yes	characteristic
309	C₂³×C₅	—	2	2	no	—
310	C₂³×C₅	—	2	2	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	—	4	1	no	—
316	C₂³×C₅	—	4	1	no	—
317	C₂³×C₅	—	4	1	no	—
318	C₂³×C₅	—	4	1	no	—
319	C₂³×C₅	—	4	1	no	—
320	C₂³×C₅	—	4	1	no	—
321	C₂³×C₅	—	4	1	no	—
322	C₂³×C₅	—	4	1	no	—
323	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
324	C₅×Q₈	—	2	2	no	—
325	C₅×Q₈	—	2	2	no	—
326	C₅×Q₈	—	2	2	no	—
327	C₅×Q₈	—	2	2	no	—
328	C₅×Q₈	—	4	4	no	—
329	C₅×Q₈	—	4	1	no	—
330	C₅×Q₈	—	4	1	no	—
331	C₅×Q₈	—	4	1	no	—
332	C₅×Q₈	—	4	1	no	—
333	C₅×D₄	—	2	2	no	—
334	C₅×D₄	—	2	2	no	—
335	C₅×D₄	—	2	2	no	—
336	C₅×D₄	—	2	2	no	—
337	C₅×D₄	—	4	1	no	—
338	C₅×D₄	—	4	1	no	—
339	C₅×D₄	—	4	1	no	—
340	C₅×D₄	—	4	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	—	2	1	no	—
346	C₂×C₄×C₅	—	2	1	no	—
347	C₂×C₄×C₅	—	2	1	no	—
348	C₂×C₄×C₅	—	2	2	no	—
349	C₂×C₄×C₅	—	2	1	no	—
350	C₂×C₄×C₅	—	2	2	no	—
351	C₂×C₄×C₅	—	2	2	no	—
352	C₂×C₄×C₅	—	2	1	no	—
353	C₂×C₄×C₅	—	2	1	no	—
354	C₂×C₄×C₅	—	2	1	no	—
355	C₂×C₄×C₅	—	2	1	no	—
356	C₂×C₄×C₅	—	2	1	no	—
357	C₂×C₄×C₅	—	2	1	no	—
358	C₂×C₄×C₅	—	2	1	no	—
359	C₂×C₄×C₅	—	4	8	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	—	4	1	no	—
369	C₂×C₄×C₅	—	4	1	no	—
370	C₂×C₄×C₅	—	4	1	no	—
371	C₂×C₄×C₅	—	4	1	no	—
372	C₂×C₄×C₅	—	4	1	no	—
373	C₂×C₄×C₅	—	4	1	no	—
374	C₂×C₄×C₅	—	4	1	no	—
375	C₂×C₄×C₅	—	8	4	no	—
376	C₂×C₄×C₅	#120	1	2	yes	—
377	C₂×C₄×C₅	#120	1	2	yes	—
378	C₂×C₄×C₅	#135	1	2	yes	—
379	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
380	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
382	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
383	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
384	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
385	C₅×C₈	—	2	2	no	—
386	C₅×C₈	—	4	1	no	—
387	C₅×C₈	—	4	1	no	—
388	C₅×C₈	—	4	1	no	—
389	C₂²×Q₈	C₅×D₄	1	1	yes	characteristic
390	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
391	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
392	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
393	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
394	C₂³×C₄	—	2	1	no	—
395	C₂³×C₄	—	2	1	no	—
396	C₂×SD₁₆	—	2	2	no	—
397	C₂×SD₁₆	—	2	2	no	—
398	C₂×SD₁₆	—	2	2	no	—
399	C₂×SD₁₆	—	2	2	no	—
400	C₂×SD₁₆	—	2	2	no	—
401	C₂×SD₁₆	—	4	1	no	—
402	C₂×D₈	—	2	2	no	—
403	C₂×D₈	—	2	2	no	—
404	C₂×D₈	—	4	1	no	—
405	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
406	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
407	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
408	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
409	C₄⋊Q₈	—	2	2	no	—
410	C₄⋊Q₈	—	2	2	no	—
411	#126	—	2	8	no	—
412	#126	—	2	8	no	—
413	#124	—	2	2	no	—
414	#124	—	2	2	no	—
415	#124	—	2	2	no	—
416	#124	C₅×D₄	1	4	yes	—
417	C₂²⋊Q₈	—	2	8	no	—
418	C₄×Q₈	—	2	2	no	—
419	C₄×Q₈	—	2	2	no	—
420	C₄×Q₈	—	2	2	no	—
421	C₄×Q₈	—	2	2	no	—
422	C₄×Q₈	—	2	2	no	—
423	C₄×Q₈	C₅×D₄	1	4	yes	—
424	C₄×D₄	—	2	2	no	—
425	C₄×D₄	—	2	2	no	—
426	C₄×D₄	—	2	2	no	—
427	C₄×D₄	—	2	2	no	—
428	#117	—	2	8	no	—
429	C₂×C₄⋊C₄	—	2	1	no	—
430	C₂×C₄⋊C₄	—	2	1	no	—
431	C₂×C₄⋊C₄	—	2	1	no	—
432	C₂×C₄⋊C₄	—	2	1	no	—
433	C₂×C₄⋊C₄	—	2	1	no	—
434	C₂×C₄⋊C₄	—	2	1	no	—
435	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
436	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
437	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
438	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
439	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
440	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
441	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
442	C₂×C₂²⋊C₄	—	2	1	no	—
443	C₂×C₂²⋊C₄	—	2	1	no	—
444	C₂×C₂²⋊C₄	—	2	1	no	—
445	C₂×C₂²⋊C₄	—	2	1	no	—
446	C₂×C₂²⋊C₄	—	2	1	no	—
447	C₂×C₂²⋊C₄	—	2	1	no	—
448	C₂×C₂²⋊C₄	—	2	1	no	—
449	C₂×C₂²⋊C₄	—	2	1	no	—
450	C₂×C₂²⋊C₄	—	2	1	no	—
451	C₂×C₂²⋊C₄	—	2	1	no	—
452	C₂×C₄²	—	2	1	no	—
453	C₂×C₄²	—	2	1	no	—
454	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
455	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
456	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
457	#106	—	2	2	no	—
458	C₄⋊C₈	—	2	2	no	—
459	#103	—	2	2	no	—
460	#103	—	2	2	no	—
461	#103	—	2	2	no	—
462	#103	—	4	1	no	—
463	#103	—	4	1	no	—
464	#103	—	4	1	no	—
465	#102	—	2	2	no	—
466	#102	—	2	2	no	—
467	#102	—	2	2	no	—
468	#102	—	4	1	no	—
469	C₄×C₈	—	2	2	no	—
470	#95	—	2	1	no	—
471	#95	—	2	1	no	—
472	#95	—	2	1	no	—
473	#95	—	2	1	no	—
474	C₂²×C₅	—	4	2	no	—
475	C₂²×C₅	—	4	2	no	—
476	C₂²×C₅	—	4	2	no	—
477	C₂²×C₅	—	4	2	no	—
478	C₂²×C₅	—	4	2	no	—
479	C₂²×C₅	—	4	2	no	—
480	C₂²×C₅	—	8	1	no	—
481	C₂²×C₅	—	8	1	no	—
482	C₂²×C₅	—	8	1	no	—
483	C₂²×C₅	—	8	1	no	—
484	C₂²×C₅	—	8	1	no	—
485	C₂²×C₅	—	8	1	no	—
486	C₂²×C₅	—	8	1	no	—
487	C₂²×C₅	—	8	1	no	—
488	C₂²×C₅	C₂×#120	1	1	yes	characteristic
489	C₂²×C₅	#548	1	1	yes	characteristic
490	C₂²×C₅	#550	1	1	yes	characteristic
491	C₂²×C₅	C₂×#135	1	1	yes	characteristic
492	C₂²×C₅	#575	1	1	yes	characteristic
493	C₂²×C₅	#577	1	1	yes	characteristic
494	C₂²×C₅	#577	1	1	yes	characteristic
495	C₄×C₅	—	2	2	no	—
496	C₄×C₅	—	2	2	no	—
497	C₄×C₅	—	2	2	no	—
498	C₄×C₅	—	4	2	no	—
499	C₄×C₅	—	4	2	no	—
500	C₄×C₅	—	4	1	no	—
501	C₄×C₅	—	4	2	no	—
502	C₄×C₅	—	4	1	no	—
503	C₄×C₅	—	4	1	no	—
504	C₄×C₅	—	8	1	no	—
505	C₄×C₅	—	8	1	no	—
506	C₄×C₅	—	8	1	no	—
507	C₄×C₅	#525	1	1	yes	characteristic
508	C₄×C₅	#537	1	1	yes	characteristic
509	C₄×C₅	#546	1	1	yes	characteristic
510	C₄×C₅	#547	1	1	yes	characteristic
511	C₂⁴	—	2	1	no	—
512	C₂⁴	—	2	1	no	—
513	C₂×Q₈	—	2	2	no	—
514	C₂×Q₈	—	2	2	no	—
515	C₂×Q₈	—	2	1	no	—
516	C₂×Q₈	—	2	1	no	—
517	C₂×Q₈	—	2	1	no	—
518	C₂×Q₈	—	2	1	no	—
519	C₂×Q₈	—	2	1	no	—
520	C₂×Q₈	—	2	1	no	—
521	C₂×Q₈	—	2	1	no	—
522	C₂×Q₈	—	2	1	no	—
523	C₂×Q₈	—	2	1	no	—
524	C₂×Q₈	—	2	1	no	—
525	C₂×Q₈	—	4	1	no	—
526	C₂×Q₈	C₂×C₅×D₄	1	2	yes	—
527	C₂×Q₈	C₂×C₅×D₄	1	2	yes	—
528	C₂×D₄	—	2	1	no	—
529	C₂×D₄	—	2	1	no	—
530	C₂×D₄	—	2	1	no	—
531	C₂×D₄	—	2	1	no	—
532	C₂×D₄	—	2	1	no	—
533	C₂×D₄	—	2	1	no	—
534	C₂×D₄	—	2	1	no	—
535	C₂×D₄	—	2	1	no	—
536	C₂×D₄	—	2	1	no	—
537	C₂×D₄	—	2	1	no	—
538	C₂×D₄	C₂×C₅×D₄	1	2	yes	—
539	C₂×D₄	C₅×#41	1	2	yes	—
540	C₂²×C₄	—	2	4	no	—
541	C₂²×C₄	—	2	1	no	—
542	C₂²×C₄	—	2	1	no	—
543	C₂²×C₄	—	2	1	no	—
544	C₂²×C₄	—	2	1	no	—
545	C₂²×C₄	—	2	1	no	—
546	C₂²×C₄	—	2	1	no	—
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	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
553	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
554	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
555	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
556	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
557	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
558	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
559	SD₁₆	—	2	8	no	—
560	SD₁₆	—	4	4	no	—
561	D₈	—	4	4	no	—
562	C₂×C₈	—	2	1	no	—
563	C₂×C₈	—	2	1	no	—
564	C₂×C₈	—	2	1	no	—
565	C₂×C₈	—	2	1	no	—
566	C₂×C₈	—	2	1	no	—
567	C₂×C₈	—	2	1	no	—
568	C₂×C₈	—	2	1	no	—
569	C₂×C₈	—	2	1	no	—
570	C₂×C₈	—	2	1	no	—
571	C₂×C₈	—	2	1	no	—
572	C₂×C₈	—	2	1	no	—
573	C₂×C₈	C₅×#41	1	2	yes	—
574	C₄⋊C₄	—	2	4	no	—
575	C₄⋊C₄	—	2	4	no	—
576	C₄⋊C₄	—	2	4	no	—
577	C₄⋊C₄	—	2	4	no	—
578	C₄⋊C₄	—	2	2	no	—
579	C₄⋊C₄	—	2	2	no	—
580	C₄⋊C₄	—	2	2	no	—
581	C₄⋊C₄	—	2	1	no	—
582	C₄⋊C₄	—	2	1	no	—
583	C₄⋊C₄	—	2	1	no	—
584	C₄⋊C₄	—	2	1	no	—
585	C₄⋊C₄	—	2	1	no	—
586	C₄⋊C₄	—	2	1	no	—
587	C₄⋊C₄	—	2	1	no	—
588	C₄⋊C₄	—	8	1	no	—
589	C₄⋊C₄	—	8	1	no	—
590	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
591	C₂²⋊C₄	—	2	4	no	—
592	C₂²⋊C₄	—	2	4	no	—
593	C₂²⋊C₄	—	2	4	no	—
594	C₂²⋊C₄	—	2	4	no	—
595	C₂²⋊C₄	—	2	4	no	—
596	C₂²⋊C₄	—	4	2	no	—
597	C₂²⋊C₄	—	4	2	no	—
598	C₂²⋊C₄	—	4	2	no	—
599	C₂²⋊C₄	—	8	1	no	—
600	C₂²⋊C₄	—	8	1	no	—
601	C₄²	—	2	4	no	—
602	C₄²	—	2	4	no	—
603	C₄²	—	2	1	no	—
604	C₄²	—	2	1	no	—
605	C₄²	—	2	1	no	—
606	C₄²	—	2	1	no	—
607	C₄²	C₂×C₅×D₄	1	2	yes	—
608	C₄²	C₂×C₅×D₄	1	2	yes	—
609	C₂×C₅	—	8	2	no	—
610	C₂×C₅	—	8	2	no	—
611	C₂×C₅	#2407	1	1	yes	characteristic
612	C₂×C₅	#3002	1	1	yes	characteristic
613	C₂×C₅	#3010	1	1	yes	characteristic
614	C₂×C₅	#3360	1	1	yes	characteristic
615	C₂×C₅	#3376	1	1	yes	characteristic
616	C₂×C₅	#3394	1	1	yes	characteristic
617	C₂×C₅	#3401	1	1	yes	characteristic
618	C₂³	—	2	2	no	—
619	C₂³	—	2	2	no	—
620	C₂³	—	4	1	no	—
621	C₂³	—	4	1	no	—
622	C₂³	—	4	1	no	—
623	C₂³	—	4	1	no	—
624	C₂³	—	4	1	no	—
625	C₂³	—	4	1	no	—
626	C₂³	—	4	1	no	—
627	C₂³	—	4	1	no	—
628	C₂³	—	4	1	no	—
629	C₂³	—	4	1	no	—
630	C₂³	—	4	1	no	—
631	C₂³	—	4	1	no	—
632	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
633	Q₈	—	2	2	no	—
634	Q₈	—	2	2	no	—
635	Q₈	—	2	2	no	—
636	Q₈	—	2	2	no	—
637	Q₈	—	4	4	no	—
638	Q₈	—	4	1	no	—
639	Q₈	—	4	1	no	—
640	Q₈	—	4	1	no	—
641	Q₈	—	4	1	no	—
642	D₄	—	2	2	no	—
643	D₄	—	2	2	no	—
644	D₄	—	2	2	no	—
645	D₄	—	2	2	no	—
646	D₄	—	4	1	no	—
647	D₄	—	4	1	no	—
648	D₄	—	4	1	no	—
649	D₄	—	4	1	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	—	2	1	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	4	8	no	—
669	C₂×C₄	—	4	1	no	—
670	C₂×C₄	—	4	1	no	—
671	C₂×C₄	—	4	1	no	—
672	C₂×C₄	—	4	1	no	—
673	C₂×C₄	—	4	1	no	—
674	C₂×C₄	—	4	1	no	—
675	C₂×C₄	—	4	1	no	—
676	C₂×C₄	—	4	1	no	—
677	C₂×C₄	—	4	1	no	—
678	C₂×C₄	—	4	1	no	—
679	C₂×C₄	—	4	1	no	—
680	C₂×C₄	—	4	1	no	—
681	C₂×C₄	—	4	1	no	—
682	C₂×C₄	—	4	1	no	—
683	C₂×C₄	—	4	1	no	—
684	C₂×C₄	—	8	4	no	—
685	C₂×C₄	C₅×#120	1	2	yes	—
686	C₂×C₄	C₅×#120	1	2	yes	—
687	C₂×C₄	C₅×#135	1	2	yes	—
688	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
689	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
690	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
691	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
692	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
693	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
694	C₈	—	2	2	no	—
695	C₈	—	4	1	no	—
696	C₈	—	4	1	no	—
697	C₈	—	4	1	no	—
698	C₅	#24193	1	1	yes	characteristic, direct product factor, Sylow
699	C₂²	—	4	2	no	—
700	C₂²	—	4	2	no	—
701	C₂²	—	4	2	no	—
702	C₂²	—	4	2	no	—
703	C₂²	—	4	2	no	—
704	C₂²	—	4	2	no	—
705	C₂²	—	8	1	no	—
706	C₂²	—	8	1	no	—
707	C₂²	—	8	1	no	—
708	C₂²	—	8	1	no	—
709	C₂²	—	8	1	no	—
710	C₂²	—	8	1	no	—
711	C₂²	—	8	1	no	—
712	C₂²	—	8	1	no	—
713	C₂²	C₂×C₅×#120	1	1	yes	characteristic
714	C₂²	C₅×#548	1	1	yes	characteristic
715	C₂²	C₅×#550	1	1	yes	characteristic
716	C₂²	C₂×C₅×#135	1	1	yes	characteristic
717	C₂²	C₅×#575	1	1	yes	characteristic
718	C₂²	C₅×#577	1	1	yes	characteristic
719	C₂²	C₅×#577	1	1	yes	characteristic
720	C₄	—	2	2	no	—
721	C₄	—	2	2	no	—
722	C₄	—	2	2	no	—
723	C₄	—	4	1	no	—
724	C₄	—	4	2	no	—
725	C₄	—	4	1	no	—
726	C₄	—	4	1	no	—
727	C₄	—	4	2	no	—
728	C₄	—	4	2	no	—
729	C₄	—	8	1	no	—
730	C₄	—	8	1	no	—
731	C₄	—	8	1	no	—
732	C₄	C₅×#525	1	1	yes	characteristic
733	C₄	C₅×#537	1	1	yes	characteristic
734	C₄	C₅×#546	1	1	yes	characteristic
735	C₄	C₅×#547	1	1	yes	characteristic
736	C₂	—	8	2	no	—
737	C₂	—	8	2	no	—
738	C₂	C₅×#2407	1	1	yes	characteristic
739	C₂	C₅×#3002	1	1	yes	characteristic
740	C₂	C₅×#3010	1	1	yes	characteristic
741	C₂	C₅×#3360	1	1	yes	characteristic
742	C₂	C₅×#3376	1	1	yes	characteristic
743	C₂	C₅×#3394	1	1	yes	characteristic
744	C₂	C₅×#3401	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂²×C₅×D₈	C₂²
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×#556	C₂	semidirect
3. C₂×C₄×C₅×SD₁₆	C₂	semidirect
4. C₅×#2580	C₂	semidirect
5. C₅×#2043	C₂	semidirect
6. C₅×#2042	C₂	semidirect
7. C₅×#2013	C₂	semidirect
9. C₅×#1984	C₂	semidirect
10. C₅×#1958	C₂	semidirect
11. C₅×#1880	C₂	semidirect
13. C₅×#1865	C₂	semidirect
14. C₅×#1864	C₂	semidirect
15. C₅×#1805	C₂	semidirect
63. #24193	C₅	direct (N × H)
149. C₂×#556	C₂×C₅	semidirect
151. C₂×C₄×SD₁₆	C₂×C₅	semidirect
152. #2580	C₂×C₅	semidirect
153. #2043	C₂×C₅	semidirect
154. #2042	C₂×C₅	semidirect
155. #2013	C₂×C₅	semidirect
157. #1984	C₂×C₅	semidirect
158. #1958	C₂×C₅	semidirect
159. #1880	C₂×C₅	semidirect
161. #1865	C₂×C₅	semidirect
162. #1864	C₂×C₅	semidirect
163. #1805	C₂×C₅	semidirect
698. C₅	#24193	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×#556	2
C₂×C₅×#463	2
C₂×C₄×C₅×SD₁₆	2
C₅×#2580	2
C₅×#2043	2
C₅×#2042	2
C₅×#2013	2
C₅×#2012	2
C₅×#1984	2
C₅×#1958	2
C₅×#1880	2
C₅×#1879	2
C₅×#1865	2
C₅×#1864	2
C₅×#1805	2
#24193	5

Subgroups — C5×#24193 #11946913

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#24193 #11946913