Subgroups — C₅×#23012 #11945732

Order 1280.

982 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#461	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#440	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₅×SD₁₆	C₂	1	1	yes	maximal, characteristic
4	C₅×#2365	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2349	C₂	1	1	yes	maximal, characteristic
6	C₅×#1960	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1949	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1935	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1933	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1877	C₂	1	1	yes	maximal, characteristic
11	C₅×#1877	C₂	1	1	yes	maximal, characteristic
12	C₅×#1865	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1863	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1771	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1762	C₂	1	1	yes	maximal, characteristic
16	C₂²×C₅×SD₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₅×SD₁₆	C₂²	1	1	yes	characteristic
18	C₂×C₅×C₄⋊Q₈	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×D₄	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
24	C₅×#461	C₄	1	8	yes	complemented
25	C₅×#440	—	2	4	no	—
26	C₄×C₅×SD₁₆	—	2	4	no	—
27	C₂×C₅×#107	C₂²	1	1	yes	characteristic
28	C₂×C₅×#106	C₂²	1	1	yes	characteristic
29	C₂×C₅×C₄⋊C₈	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×#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×#97	C₂²	1	1	yes	characteristic
39	C₂×C₅×#97	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
41	C₅×#391	C₂²	1	1	yes	characteristic
42	C₅×#391	C₂²	1	1	yes	characteristic
43	C₅×#389	—	2	1	no	—
44	C₅×#389	C₂²	1	1	yes	characteristic
45	C₅×#389	C₂²	1	1	yes	characteristic
46	C₅×#387	—	2	1	no	—
47	C₅×#387	—	2	1	no	—
48	C₅×#385	—	2	1	no	—
49	C₅×#385	—	2	1	no	—
50	C₅×#382	C₂²	1	1	yes	characteristic
51	C₅×#380	—	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	C₂×C₅×#95	—	2	1	no	—
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	#23012	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
63	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
64	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
69	C₂×C₅×SD₁₆	—	2	2	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	C₂×C₄	1	4	yes	—
74	C₂×C₅×SD₁₆	C₂×C₄	1	4	yes	—
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×C₄⋊Q₈	—	2	2	no	—
80	C₅×C₄⋊Q₈	C₂×C₄	1	4	yes	complemented
81	C₄×C₅×Q₈	—	2	2	no	—
82	C₄×C₅×Q₈	—	2	2	no	—
83	C₄×C₅×Q₈	—	4	1	no	—
84	C₄×C₅×Q₈	—	4	1	no	—
85	C₄×C₅×D₄	—	2	2	no	—
86	C₄×C₅×D₄	—	2	2	no	—
87	C₄×C₅×D₄	—	2	2	no	—
88	C₄×C₅×D₄	—	4	1	no	—
89	C₄×C₅×D₄	—	4	1	no	—
90	C₄×C₅×D₄	C₂×C₄	1	4	yes	—
91	C₂×C₅×C₄⋊C₄	—	2	1	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	—	2	1	no	—
97	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
98	C₂×C₅×C₄⋊C₄	D₄	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×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₄²×C₅	—	2	1	no	—
108	C₂×C₄²×C₅	—	2	1	no	—
109	C₂×C₄²×C₅	—	2	1	no	—
110	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
113	C₅×#107	—	2	2	no	—
114	C₅×#106	—	2	2	no	—
115	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
116	C₅×#103	—	2	2	no	—
117	C₅×#103	—	2	2	no	—
118	C₅×#103	—	4	1	no	—
119	C₅×#103	—	4	1	no	—
120	C₅×#103	C₂×C₄	1	4	yes	complemented
121	C₅×#103	C₂×C₄	1	4	yes	complemented
122	C₅×#102	—	2	2	no	—
123	C₅×#102	D₄	1	4	yes	—
124	C₅×#97	—	2	2	no	—
125	C₅×#97	—	2	2	no	—
126	C₄×C₅×C₈	—	2	2	no	—
127	C₅×#95	—	2	1	no	—
128	C₅×#95	—	2	1	no	—
129	C₅×#95	—	2	1	no	—
130	C₅×#95	—	2	1	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	D₄	1	1	yes	characteristic
137	C₅×#95	D₄	1	1	yes	characteristic
138	C₂×#461	C₂×C₅	1	1	yes	characteristic
139	C₂×#440	C₂×C₅	1	1	yes	characteristic
140	C₂×C₄×SD₁₆	C₂×C₅	1	1	yes	characteristic
141	#2365	C₂×C₅	1	1	yes	characteristic, complemented
142	#2349	C₂×C₅	1	1	yes	characteristic
143	#1960	C₂×C₅	1	1	yes	characteristic, complemented
144	#1949	C₂×C₅	1	1	yes	characteristic, complemented
145	#1935	C₂×C₅	1	1	yes	characteristic, complemented
146	#1933	C₂×C₅	1	1	yes	characteristic, complemented
147	#1877	C₂×C₅	1	1	yes	characteristic
148	#1877	C₂×C₅	1	1	yes	characteristic
149	#1865	C₂×C₅	1	1	yes	characteristic, complemented
150	#1863	C₂×C₅	1	1	yes	characteristic, complemented
151	#1771	C₂×C₅	1	1	yes	characteristic, complemented
152	#1762	C₂×C₅	1	1	yes	characteristic
153	C₂⁴×C₅	—	2	1	no	—
154	C₂×C₅×Q₈	—	2	1	no	—
155	C₂×C₅×Q₈	—	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	—	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	C₂²×C₄	1	2	yes	—
165	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
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	C₂²×C₄	1	2	yes	—
170	C₂×C₅×D₄	C₂×D₄	1	2	yes	—
171	C₂×C₅×D₄	#41	1	2	yes	—
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	4	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	—	4	2	no	—
181	C₂²×C₄×C₅	—	4	2	no	—
182	C₂²×C₄×C₅	—	4	2	no	—
183	C₂²×C₄×C₅	—	4	2	no	—
184	C₂²×C₄×C₅	—	8	1	no	—
185	C₂²×C₄×C₅	—	8	1	no	—
186	C₂²×C₄×C₅	—	8	1	no	—
187	C₂²×C₄×C₅	—	8	1	no	—
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	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
195	C₅×SD₁₆	—	2	8	no	—
196	C₅×SD₁₆	—	2	8	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	—	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	C₅×C₄⋊C₄	—	2	4	no	—
210	C₅×C₄⋊C₄	—	2	4	no	—
211	C₅×C₄⋊C₄	—	2	2	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	—	2	1	no	—
220	C₅×C₄⋊C₄	—	4	1	no	—
221	C₅×C₄⋊C₄	—	4	2	no	—
222	C₅×C₄⋊C₄	—	4	2	no	—
223	C₅×C₄⋊C₄	—	8	1	no	—
224	C₅×C₄⋊C₄	—	8	1	no	—
225	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
226	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
227	C₅×C₂²⋊C₄	—	2	4	no	—
228	C₅×C₂²⋊C₄	—	4	2	no	—
229	C₅×C₂²⋊C₄	—	4	2	no	—
230	C₄²×C₅	—	2	1	no	—
231	C₄²×C₅	—	2	1	no	—
232	C₄²×C₅	—	2	1	no	—
233	C₄²×C₅	—	2	1	no	—
234	C₄²×C₅	—	4	2	no	—
235	C₄²×C₅	—	4	2	no	—
236	C₄²×C₅	—	4	2	no	—
237	C₄²×C₅	C₂²×C₄	1	2	yes	—
238	C₄²×C₅	#41	1	2	yes	—
239	C₂²×SD₁₆	C₂²×C₅	1	1	yes	characteristic
240	C₂²×SD₁₆	C₂²×C₅	1	1	yes	characteristic
241	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
242	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
243	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
244	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
245	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
246	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
247	#461	C₄×C₅	1	8	yes	complemented
248	#440	—	2	4	no	—
249	C₄×SD₁₆	—	2	4	no	—
250	C₂×#107	C₂²×C₅	1	1	yes	characteristic
251	C₂×#106	C₂²×C₅	1	1	yes	characteristic
252	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
253	C₂×#103	C₂²×C₅	1	1	yes	characteristic
254	C₂×#103	C₂²×C₅	1	1	yes	characteristic
255	C₂×#103	C₂²×C₅	1	1	yes	characteristic
256	C₂×#103	C₂²×C₅	1	1	yes	characteristic
257	C₂×#103	C₂²×C₅	1	1	yes	characteristic
258	C₂×#103	C₂²×C₅	1	1	yes	characteristic
259	C₂×#102	C₂²×C₅	1	1	yes	characteristic
260	C₂×#102	C₂²×C₅	1	1	yes	characteristic
261	C₂×#97	C₂²×C₅	1	1	yes	characteristic
262	C₂×#97	C₂²×C₅	1	1	yes	characteristic
263	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
264	#391	C₂²×C₅	1	1	yes	characteristic
265	#391	C₂²×C₅	1	1	yes	characteristic
266	#389	—	2	1	no	—
267	#389	C₂²×C₅	1	1	yes	characteristic
268	#389	C₂²×C₅	1	1	yes	characteristic
269	#387	—	2	1	no	—
270	#387	—	2	1	no	—
271	#385	—	2	1	no	—
272	#385	—	2	1	no	—
273	#382	C₂²×C₅	1	1	yes	characteristic
274	#380	—	2	1	no	—
275	C₄×C₄⋊C₄	—	2	1	no	—
276	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
277	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
278	C₂×#95	—	2	1	no	—
279	#340	C₂²×C₅	1	1	yes	characteristic
280	#340	C₂²×C₅	1	1	yes	characteristic
281	#340	C₂²×C₅	1	1	yes	characteristic
282	#340	C₂²×C₅	1	1	yes	characteristic
283	#336	C₂²×C₅	1	1	yes	characteristic
284	#336	C₂²×C₅	1	1	yes	characteristic
285	C₂³×C₅	—	2	2	no	—
286	C₂³×C₅	—	2	2	no	—
287	C₂³×C₅	—	2	2	no	—
288	C₂³×C₅	—	4	1	no	—
289	C₂³×C₅	—	4	1	no	—
290	C₂³×C₅	—	4	1	no	—
291	C₂³×C₅	—	4	1	no	—
292	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
293	C₅×Q₈	—	2	2	no	—
294	C₅×Q₈	—	2	2	no	—
295	C₅×Q₈	—	2	2	no	—
296	C₅×Q₈	—	2	2	no	—
297	C₅×Q₈	—	4	1	no	—
298	C₅×Q₈	—	4	1	no	—
299	C₅×Q₈	—	4	1	no	—
300	C₅×Q₈	—	4	1	no	—
301	C₅×D₄	—	2	2	no	—
302	C₅×D₄	—	2	2	no	—
303	C₅×D₄	—	2	2	no	—
304	C₅×D₄	C₄×D₄	1	4	yes	—
305	C₂×C₄×C₅	—	2	1	no	—
306	C₂×C₄×C₅	—	2	1	no	—
307	C₂×C₄×C₅	—	2	1	no	—
308	C₂×C₄×C₅	—	2	1	no	—
309	C₂×C₄×C₅	—	2	1	no	—
310	C₂×C₄×C₅	—	2	1	no	—
311	C₂×C₄×C₅	—	2	2	no	—
312	C₂×C₄×C₅	—	2	2	no	—
313	C₂×C₄×C₅	—	2	2	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	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	1	no	—
324	C₂×C₄×C₅	—	4	1	no	—
325	C₂×C₄×C₅	—	4	1	no	—
326	C₂×C₄×C₅	—	4	1	no	—
327	C₂×C₄×C₅	—	4	1	no	—
328	C₂×C₄×C₅	—	4	1	no	—
329	C₂×C₄×C₅	—	4	1	no	—
330	C₂×C₄×C₅	—	4	1	no	—
331	C₂×C₄×C₅	—	4	1	no	—
332	C₂×C₄×C₅	—	4	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	—	8	4	no	—
342	C₂×C₄×C₅	—	8	4	no	—
343	C₂×C₄×C₅	—	8	4	no	—
344	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
345	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
346	C₂×C₄×C₅	#137	1	2	yes	—
347	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
348	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
349	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
350	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
351	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
352	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
353	C₅×C₈	—	2	2	no	—
354	C₅×C₈	—	2	2	no	—
355	C₅×C₈	—	2	2	no	—
356	C₅×C₈	—	4	1	no	—
357	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
358	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
359	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
360	C₂³×C₄	—	2	1	no	—
361	C₂³×C₄	—	2	1	no	—
362	C₂³×C₄	—	2	1	no	—
363	C₂×SD₁₆	—	2	2	no	—
364	C₂×SD₁₆	—	2	2	no	—
365	C₂×SD₁₆	—	2	2	no	—
366	C₂×SD₁₆	—	2	2	no	—
367	C₂×SD₁₆	C₂×C₄×C₅	1	4	yes	—
368	C₂×SD₁₆	C₂×C₄×C₅	1	4	yes	—
369	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
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	C₄⋊Q₈	—	2	2	no	—
374	C₄⋊Q₈	C₂×C₄×C₅	1	4	yes	complemented
375	C₄×Q₈	—	2	2	no	—
376	C₄×Q₈	—	2	2	no	—
377	C₄×Q₈	—	4	1	no	—
378	C₄×Q₈	—	4	1	no	—
379	C₄×D₄	—	2	2	no	—
380	C₄×D₄	—	2	2	no	—
381	C₄×D₄	—	2	2	no	—
382	C₄×D₄	—	4	1	no	—
383	C₄×D₄	—	4	1	no	—
384	C₄×D₄	C₂×C₄×C₅	1	4	yes	—
385	C₂×C₄⋊C₄	—	2	1	no	—
386	C₂×C₄⋊C₄	—	2	1	no	—
387	C₂×C₄⋊C₄	—	2	1	no	—
388	C₂×C₄⋊C₄	—	2	1	no	—
389	C₂×C₄⋊C₄	—	2	1	no	—
390	C₂×C₄⋊C₄	—	2	1	no	—
391	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
392	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
393	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
394	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
395	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
396	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
397	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
398	C₂×C₂²⋊C₄	—	2	1	no	—
399	C₂×C₂²⋊C₄	—	2	1	no	—
400	C₂×C₂²⋊C₄	—	2	1	no	—
401	C₂×C₄²	—	2	1	no	—
402	C₂×C₄²	—	2	1	no	—
403	C₂×C₄²	—	2	1	no	—
404	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
405	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
406	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
407	#107	—	2	2	no	—
408	#106	—	2	2	no	—
409	C₄⋊C₈	C₂×C₄×C₅	1	4	yes	complemented
410	#103	—	2	2	no	—
411	#103	—	2	2	no	—
412	#103	—	4	1	no	—
413	#103	—	4	1	no	—
414	#103	C₂×C₄×C₅	1	4	yes	complemented
415	#103	C₂×C₄×C₅	1	4	yes	complemented
416	#102	—	2	2	no	—
417	#102	C₅×D₄	1	4	yes	—
418	#97	—	2	2	no	—
419	#97	—	2	2	no	—
420	C₄×C₈	—	2	2	no	—
421	#95	—	2	1	no	—
422	#95	—	2	1	no	—
423	#95	—	2	1	no	—
424	#95	—	2	1	no	—
425	#95	—	2	1	no	—
426	#95	—	2	1	no	—
427	#95	—	2	1	no	—
428	#95	—	2	1	no	—
429	#95	—	2	1	no	—
430	#95	C₅×D₄	1	1	yes	characteristic
431	#95	C₅×D₄	1	1	yes	characteristic
432	C₂²×C₅	—	2	4	no	—
433	C₂²×C₅	—	4	2	no	—
434	C₂²×C₅	—	4	2	no	—
435	C₂²×C₅	—	4	2	no	—
436	C₂²×C₅	—	4	2	no	—
437	C₂²×C₅	—	4	2	no	—
438	C₂²×C₅	—	4	2	no	—
439	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
440	C₂²×C₅	D₄²	1	1	yes	characteristic
441	C₂²×C₅	#548	1	1	yes	characteristic
442	C₂²×C₅	C₂×#137	1	1	yes	characteristic
443	C₂²×C₅	#575	1	1	yes	characteristic
444	C₂²×C₅	#577	1	1	yes	characteristic
445	C₂²×C₅	#577	1	1	yes	characteristic
446	C₄×C₅	—	2	2	no	—
447	C₄×C₅	—	2	2	no	—
448	C₄×C₅	—	2	2	no	—
449	C₄×C₅	—	4	2	no	—
450	C₄×C₅	—	4	2	no	—
451	C₄×C₅	—	4	2	no	—
452	C₄×C₅	—	4	1	no	—
453	C₄×C₅	—	4	1	no	—
454	C₄×C₅	—	4	1	no	—
455	C₄×C₅	—	4	2	no	—
456	C₄×C₅	—	8	1	no	—
457	C₄×C₅	—	8	1	no	—
458	C₄×C₅	—	8	1	no	—
459	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
460	C₄×C₅	#520	1	1	yes	characteristic
461	C₄×C₅	#547	1	1	yes	characteristic
462	C₄×C₅	#553	1	1	yes	characteristic
463	C₂⁴	—	2	1	no	—
464	C₂×Q₈	—	2	1	no	—
465	C₂×Q₈	—	2	1	no	—
466	C₂×Q₈	—	2	1	no	—
467	C₂×Q₈	—	2	1	no	—
468	C₂×Q₈	—	2	1	no	—
469	C₂×Q₈	—	2	1	no	—
470	C₂×Q₈	—	2	1	no	—
471	C₂×Q₈	—	2	1	no	—
472	C₂×Q₈	—	2	1	no	—
473	C₂×Q₈	—	2	1	no	—
474	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
475	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
476	C₂×D₄	—	2	1	no	—
477	C₂×D₄	—	2	1	no	—
478	C₂×D₄	—	2	1	no	—
479	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
480	C₂×D₄	C₂×C₅×D₄	1	2	yes	—
481	C₂×D₄	C₅×#41	1	2	yes	—
482	C₂²×C₄	—	2	1	no	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	2	1	no	—
486	C₂²×C₄	—	2	4	no	—
487	C₂²×C₄	—	2	1	no	—
488	C₂²×C₄	—	2	1	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	4	2	no	—
491	C₂²×C₄	—	4	2	no	—
492	C₂²×C₄	—	4	2	no	—
493	C₂²×C₄	—	4	2	no	—
494	C₂²×C₄	—	8	1	no	—
495	C₂²×C₄	—	8	1	no	—
496	C₂²×C₄	—	8	1	no	—
497	C₂²×C₄	—	8	1	no	—
498	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
499	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
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	C₂⁴×C₅	1	1	yes	characteristic
505	SD₁₆	—	2	8	no	—
506	SD₁₆	—	2	8	no	—
507	C₂×C₈	—	2	1	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	C₂²×C₄×C₅	1	2	yes	—
517	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
518	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
519	C₄⋊C₄	—	2	4	no	—
520	C₄⋊C₄	—	2	4	no	—
521	C₄⋊C₄	—	2	2	no	—
522	C₄⋊C₄	—	2	1	no	—
523	C₄⋊C₄	—	2	1	no	—
524	C₄⋊C₄	—	2	1	no	—
525	C₄⋊C₄	—	2	1	no	—
526	C₄⋊C₄	—	2	1	no	—
527	C₄⋊C₄	—	2	1	no	—
528	C₄⋊C₄	—	2	1	no	—
529	C₄⋊C₄	—	2	1	no	—
530	C₄⋊C₄	—	4	1	no	—
531	C₄⋊C₄	—	4	2	no	—
532	C₄⋊C₄	—	4	2	no	—
533	C₄⋊C₄	—	8	1	no	—
534	C₄⋊C₄	—	8	1	no	—
535	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
536	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
537	C₂²⋊C₄	—	2	4	no	—
538	C₂²⋊C₄	—	4	2	no	—
539	C₂²⋊C₄	—	4	2	no	—
540	C₄²	—	2	1	no	—
541	C₄²	—	2	1	no	—
542	C₄²	—	2	1	no	—
543	C₄²	—	2	1	no	—
544	C₄²	—	4	2	no	—
545	C₄²	—	4	2	no	—
546	C₄²	—	4	2	no	—
547	C₄²	C₂²×C₄×C₅	1	2	yes	—
548	C₄²	C₅×#41	1	2	yes	—
549	C₂×C₅	—	4	4	no	—
550	C₂×C₅	#2361	1	1	yes	characteristic
551	C₂×C₅	C₄×#137	1	1	yes	characteristic
552	C₂×C₅	#2949	1	1	yes	characteristic
553	C₂×C₅	#3266	1	1	yes	characteristic
554	C₂×C₅	#3267	1	1	yes	characteristic
555	C₂×C₅	#3372	1	1	yes	characteristic
556	C₂×C₅	#3376	1	1	yes	characteristic
557	C₂³	—	2	2	no	—
558	C₂³	—	2	2	no	—
559	C₂³	—	2	2	no	—
560	C₂³	—	4	1	no	—
561	C₂³	—	4	1	no	—
562	C₂³	—	4	1	no	—
563	C₂³	—	4	1	no	—
564	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
565	Q₈	—	2	2	no	—
566	Q₈	—	2	2	no	—
567	Q₈	—	2	2	no	—
568	Q₈	—	2	2	no	—
569	Q₈	—	4	1	no	—
570	Q₈	—	4	1	no	—
571	Q₈	—	4	1	no	—
572	Q₈	—	4	1	no	—
573	D₄	—	2	2	no	—
574	D₄	—	2	2	no	—
575	D₄	—	2	2	no	—
576	D₄	C₄×C₅×D₄	1	4	yes	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	1	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	—	4	1	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	4	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	—	8	4	no	—
614	C₂×C₄	—	8	4	no	—
615	C₂×C₄	—	8	4	no	—
616	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
617	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
618	C₂×C₄	C₅×#137	1	2	yes	—
619	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
620	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
621	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
622	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
623	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
624	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
625	C₈	—	2	2	no	—
626	C₈	—	2	2	no	—
627	C₈	—	2	2	no	—
628	C₈	—	4	1	no	—
629	C₅	#23012	1	1	yes	characteristic, direct product factor, Sylow
630	C₂²	—	2	4	no	—
631	C₂²	—	4	2	no	—
632	C₂²	—	4	2	no	—
633	C₂²	—	4	2	no	—
634	C₂²	—	4	2	no	—
635	C₂²	—	4	2	no	—
636	C₂²	—	4	2	no	—
637	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
638	C₂²	C₅×D₄²	1	1	yes	characteristic
639	C₂²	C₅×#548	1	1	yes	characteristic
640	C₂²	C₂×C₅×#137	1	1	yes	characteristic
641	C₂²	C₅×#575	1	1	yes	characteristic
642	C₂²	C₅×#577	1	1	yes	characteristic
643	C₂²	C₅×#577	1	1	yes	characteristic
644	C₄	—	2	2	no	—
645	C₄	—	2	2	no	—
646	C₄	—	2	2	no	—
647	C₄	—	4	1	no	—
648	C₄	—	4	1	no	—
649	C₄	—	4	1	no	—
650	C₄	—	4	2	no	—
651	C₄	—	4	2	no	—
652	C₄	—	4	2	no	—
653	C₄	—	4	2	no	—
654	C₄	—	8	1	no	—
655	C₄	—	8	1	no	—
656	C₄	—	8	1	no	—
657	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
658	C₄	C₅×#520	1	1	yes	characteristic
659	C₄	C₅×#547	1	1	yes	characteristic
660	C₄	C₅×#553	1	1	yes	characteristic
661	C₂	—	4	4	no	—
662	C₂	C₅×#2361	1	1	yes	characteristic
663	C₂	C₄×C₅×#137	1	1	yes	characteristic
664	C₂	C₅×#2949	1	1	yes	characteristic
665	C₂	C₅×#3266	1	1	yes	characteristic
666	C₂	C₅×#3267	1	1	yes	characteristic
667	C₂	C₅×#3372	1	1	yes	characteristic
668	C₂	C₅×#3376	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	C₂²×C₅×D₄	C₂³
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
4. C₅×#2365	C₂	semidirect
6. C₅×#1960	C₂	semidirect
7. C₅×#1949	C₂	semidirect
8. C₅×#1935	C₂	semidirect
9. C₅×#1933	C₂	semidirect
12. C₅×#1865	C₂	semidirect
13. C₅×#1863	C₂	semidirect
14. C₅×#1771	C₂	semidirect
24. C₅×#461	C₄	semidirect
62. #23012	C₅	direct (N × H)
80. C₅×C₄⋊Q₈	C₂×C₄	semidirect
115. C₅×C₄⋊C₈	C₂×C₄	semidirect
120. C₅×#103	C₂×C₄	semidirect
121. C₅×#103	C₂×C₄	semidirect
141. #2365	C₂×C₅	semidirect
143. #1960	C₂×C₅	semidirect
144. #1949	C₂×C₅	semidirect
145. #1935	C₂×C₅	semidirect
146. #1933	C₂×C₅	semidirect
149. #1865	C₂×C₅	semidirect
150. #1863	C₂×C₅	semidirect
151. #1771	C₂×C₅	semidirect
247. #461	C₄×C₅	semidirect
374. C₄⋊Q₈	C₂×C₄×C₅	semidirect
409. C₄⋊C₈	C₂×C₄×C₅	semidirect
414. #103	C₂×C₄×C₅	semidirect
415. #103	C₂×C₄×C₅	semidirect
629. C₅	#23012	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×#461	2
C₂×C₅×#440	2
C₂×C₄×C₅×SD₁₆	2
C₅×#2365	2
C₅×#2349	2
C₅×#1960	2
C₅×#1949	2
C₅×#1935	2
C₅×#1933	2
C₅×#1877	2
C₅×#1865	2
C₅×#1863	2
C₅×#1771	2
C₅×#1762	2
#23012	5

Subgroups — C5×#23012 #11945732

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#23012 #11945732