Subgroups — C₅×#22951 #11945671

Order 1280.

730 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3091	C₂	1	1	yes	maximal, characteristic
2	C₅×#2933	C₂	1	1	yes	maximal, characteristic
3	C₅×#2924	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1946	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1937	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1929	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1922	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1922	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1897	C₂	1	1	yes	maximal, characteristic
10	C₅×#1866	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1855	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1772	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1765	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1750	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1733	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×#131	C₂²	1	1	yes	characteristic
17	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
18	C₅×#525	C₂²	1	1	yes	characteristic
19	C₂×C₅×#117	C₂²	1	1	yes	characteristic
20	C₂×C₅×#117	C₂²	1	1	yes	characteristic
21	C₅×#485	C₄	1	1	yes	characteristic, complemented
22	C₅×#485	C₄	1	1	yes	characteristic, complemented
23	C₅×#484	C₄	1	1	yes	characteristic, complemented
24	C₅×#483	C₄	1	1	yes	characteristic, complemented
25	C₅×#482	C₄	1	1	yes	characteristic, complemented
26	C₅×#482	C₄	1	1	yes	characteristic, complemented
27	C₅×#481	C₄	1	1	yes	characteristic, complemented
28	C₅×#480	C₄	1	1	yes	characteristic, complemented
29	C₅×#436	—	2	1	no	—
30	C₅×#435	—	2	1	no	—
31	C₅×#435	—	2	1	no	—
32	C₅×C₈×D₄	—	2	1	no	—
33	C₅×#433	—	2	1	no	—
34	C₅×#433	—	2	1	no	—
35	C₅×#432	—	2	1	no	—
36	C₅×#431	—	2	1	no	—
37	C₂×C₅×#108	C₂²	1	1	yes	characteristic
38	C₂×C₅×#108	C₂²	1	1	yes	characteristic
39	C₅×#427	C₂²	1	1	yes	characteristic
40	C₅×#427	C₂²	1	1	yes	characteristic
41	C₅×#424	C₂²	1	1	yes	characteristic
42	C₅×#424	C₂²	1	1	yes	characteristic
43	C₅×#424	C₂²	1	1	yes	characteristic
44	C₂×C₅×#104	C₂²	1	1	yes	characteristic
45	C₂×C₅×#104	C₂²	1	1	yes	characteristic
46	C₅×#416	C₂²	1	1	yes	characteristic
47	C₅×#416	C₂²	1	1	yes	characteristic
48	C₅×#408	C₂²	1	1	yes	characteristic
49	C₅×#407	C₂²	1	1	yes	characteristic
50	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
51	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
52	C₅×#405	C₂²	1	1	yes	characteristic
53	C₅×#405	C₂²	1	1	yes	characteristic
54	C₅×#405	C₂²	1	1	yes	characteristic
55	C₂×C₅×#97	C₂²	1	1	yes	characteristic
56	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
57	C₅×#341	C₂²	1	1	yes	characteristic
58	C₅×#341	C₂²	1	1	yes	characteristic
59	C₅×#339	C₂²	1	1	yes	characteristic
60	C₅×#339	C₂²	1	1	yes	characteristic
61	C₅×#339	C₂²	1	1	yes	characteristic
62	C₅×#339	C₂²	1	1	yes	characteristic
63	C₅×#339	C₂²	1	1	yes	characteristic
64	C₅×#339	C₂²	1	1	yes	characteristic
65	C₅×#336	C₂²	1	1	yes	characteristic
66	C₅×#336	C₂²	1	1	yes	characteristic
67	#22951	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂×C₅×#41	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
70	C₅×#131	—	2	2	no	—
71	C₅×#131	—	4	1	no	—
72	C₂×C₅×M₁₆	—	2	1	no	—
73	C₂×C₅×M₁₆	—	2	1	no	—
74	C₂×C₅×M₁₆	—	2	2	no	—
75	C₂×C₅×M₁₆	—	4	1	no	—
76	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
77	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
78	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
79	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
80	C₂²×C₅×C₈	—	2	1	no	—
81	C₂²×C₅×C₈	—	2	1	no	—
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	—	2	1	no	—
87	C₅×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
88	C₅×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
89	C₅×#121	C₂×C₄	1	1	yes	characteristic
90	C₅×#121	C₂×C₄	1	1	yes	characteristic
91	C₅×#120	—	2	1	no	—
92	C₄×C₅×D₄	—	2	1	no	—
93	C₄×C₅×D₄	—	2	1	no	—
94	C₅×#117	—	2	1	no	—
95	C₅×#117	—	2	1	no	—
96	C₅×#117	—	2	2	no	—
97	C₅×#117	—	4	1	no	—
98	C₅×#117	C₂×C₄	1	1	yes	characteristic
99	C₅×#117	C₂×C₄	1	1	yes	characteristic
100	C₅×#117	C₂³	1	1	yes	characteristic
101	C₅×#117	C₂³	1	1	yes	characteristic
102	C₅×#117	C₂³	1	1	yes	characteristic
103	C₂×C₅×C₄⋊C₄	—	2	1	no	—
104	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
105	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
106	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
107	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
108	C₂×C₄²×C₅	—	2	1	no	—
109	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
111	C₅×#108	—	2	2	no	—
112	C₅×#108	—	4	1	no	—
113	C₅×#107	C₂×C₄	1	1	yes	characteristic
114	C₅×#107	C₂×C₄	1	1	yes	characteristic
115	C₅×#107	C₂×C₄	1	1	yes	characteristic
116	C₅×#107	C₂×C₄	1	1	yes	characteristic
117	C₅×#106	C₂×C₄	1	1	yes	characteristic
118	C₅×#106	C₂×C₄	1	1	yes	characteristic
119	C₅×#106	C₂×C₄	1	1	yes	characteristic
120	C₅×#106	C₂×C₄	1	1	yes	characteristic
121	C₅×C₄⋊C₈	—	2	1	no	—
122	C₅×C₄⋊C₈	—	2	1	no	—
123	C₅×C₄⋊C₈	—	2	1	no	—
124	C₅×C₄⋊C₈	—	2	1	no	—
125	C₅×C₄⋊C₈	—	2	1	no	—
126	C₅×C₄⋊C₈	—	2	1	no	—
127	C₅×#104	—	2	2	no	—
128	C₅×#104	—	4	1	no	—
129	C₅×#103	C₂×C₄	1	1	yes	characteristic
130	C₅×#103	C₂×C₄	1	1	yes	characteristic
131	C₅×#103	C₂×C₄	1	1	yes	characteristic
132	C₅×#103	C₂×C₄	1	1	yes	characteristic
133	C₅×#102	C₂×C₄	1	1	yes	characteristic
134	C₅×#102	C₂×C₄	1	1	yes	characteristic
135	C₅×#102	C₂×C₄	1	1	yes	characteristic
136	C₅×#102	C₂×C₄	1	1	yes	characteristic
137	C₅×C₂²⋊C₈	—	2	1	no	—
138	C₅×C₂²⋊C₈	—	2	1	no	—
139	C₅×C₂²⋊C₈	—	2	1	no	—
140	C₅×C₂²⋊C₈	—	2	1	no	—
141	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
142	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
143	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
144	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
145	C₅×C₂²⋊C₈	D₄	1	1	yes	characteristic
146	C₅×C₂²⋊C₈	D₄	1	1	yes	characteristic
147	C₅×C₂²⋊C₈	D₄	1	1	yes	characteristic
148	C₅×C₂²⋊C₈	D₄	1	1	yes	characteristic
149	C₅×#97	—	2	1	no	—
150	C₅×#97	—	2	1	no	—
151	C₅×#97	—	2	1	no	—
152	C₅×#97	—	4	1	no	—
153	C₄×C₅×C₈	—	2	1	no	—
154	C₄×C₅×C₈	—	2	1	no	—
155	C₄×C₅×C₈	—	2	1	no	—
156	C₄×C₅×C₈	—	2	2	no	—
157	#3091	C₂×C₅	1	1	yes	characteristic
158	#2933	C₂×C₅	1	1	yes	characteristic
159	#2924	C₂×C₅	1	1	yes	characteristic, complemented
160	#1946	C₂×C₅	1	1	yes	characteristic, complemented
161	#1937	C₂×C₅	1	1	yes	characteristic, complemented
162	#1929	C₂×C₅	1	1	yes	characteristic, complemented
163	#1922	C₂×C₅	1	1	yes	characteristic, complemented
164	#1922	C₂×C₅	1	1	yes	characteristic, complemented
165	#1897	C₂×C₅	1	1	yes	characteristic
166	#1866	C₂×C₅	1	1	yes	characteristic, complemented
167	#1855	C₂×C₅	1	1	yes	characteristic, complemented
168	#1772	C₂×C₅	1	1	yes	characteristic, complemented
169	#1765	C₂×C₅	1	1	yes	characteristic, complemented
170	#1750	C₂×C₅	1	1	yes	characteristic, complemented
171	#1733	C₂×C₅	1	1	yes	characteristic, complemented
172	C₂⁴×C₅	#41	1	1	yes	characteristic
173	C₅×#41	—	2	1	no	—
174	C₅×#41	—	2	1	no	—
175	C₅×#41	—	2	1	no	—
176	C₅×#41	—	2	1	no	—
177	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
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	C₂²×C₄	1	1	yes	characteristic
182	C₂²×C₄×C₅	—	2	1	no	—
183	C₂²×C₄×C₅	—	2	1	no	—
184	C₂²×C₄×C₅	—	2	1	no	—
185	C₂²×C₄×C₅	—	2	1	no	—
186	C₂²×C₄×C₅	—	2	1	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	C₂²×C₄	1	1	yes	characteristic
192	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
193	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₅	#41	1	1	yes	characteristic
196	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
197	C₅×M₁₆	—	2	1	no	—
198	C₅×M₁₆	—	2	1	no	—
199	C₅×M₁₆	—	2	1	no	—
200	C₅×M₁₆	—	2	1	no	—
201	C₅×M₁₆	—	2	1	no	—
202	C₅×M₁₆	—	2	1	no	—
203	C₅×M₁₆	—	2	1	no	—
204	C₅×M₁₆	—	4	2	no	—
205	C₅×M₁₆	—	4	2	no	—
206	C₅×M₁₆	#41	1	2	yes	—
207	C₂×C₅×C₈	—	2	1	no	—
208	C₂×C₅×C₈	—	2	1	no	—
209	C₂×C₅×C₈	—	2	1	no	—
210	C₂×C₅×C₈	—	2	1	no	—
211	C₂×C₅×C₈	—	2	1	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	—	4	2	no	—
220	C₂×C₅×C₈	—	4	2	no	—
221	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
222	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
223	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
224	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
225	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
226	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
227	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
228	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
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	—	4	2	no	—
234	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
235	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
236	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
237	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
238	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
239	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
240	C₅×C₂²⋊C₄	—	2	1	no	—
241	C₅×C₂²⋊C₄	—	2	1	no	—
242	C₅×C₂²⋊C₄	—	2	1	no	—
243	C₅×C₂²⋊C₄	—	2	1	no	—
244	C₅×C₂²⋊C₄	—	2	1	no	—
245	C₅×C₂²⋊C₄	—	2	1	no	—
246	C₅×C₂²⋊C₄	—	2	1	no	—
247	C₅×C₂²⋊C₄	—	2	1	no	—
248	C₅×C₂²⋊C₄	—	2	1	no	—
249	C₅×C₂²⋊C₄	—	4	2	no	—
250	C₄²×C₅	—	2	1	no	—
251	C₄²×C₅	—	2	1	no	—
252	C₄²×C₅	—	2	1	no	—
253	C₄²×C₅	—	2	1	no	—
254	C₄²×C₅	—	2	1	no	—
255	C₄²×C₅	—	2	1	no	—
256	C₄²×C₅	—	2	1	no	—
257	C₄²×C₅	—	2	1	no	—
258	C₄²×C₅	#41	1	2	yes	—
259	C₂×#131	C₂²×C₅	1	1	yes	characteristic
260	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
261	#525	C₂²×C₅	1	1	yes	characteristic
262	C₂×#117	C₂²×C₅	1	1	yes	characteristic
263	C₂×#117	C₂²×C₅	1	1	yes	characteristic
264	#485	C₄×C₅	1	1	yes	characteristic, complemented
265	#485	C₄×C₅	1	1	yes	characteristic, complemented
266	#484	C₄×C₅	1	1	yes	characteristic, complemented
267	#483	C₄×C₅	1	1	yes	characteristic, complemented
268	#482	C₄×C₅	1	1	yes	characteristic, complemented
269	#482	C₄×C₅	1	1	yes	characteristic, complemented
270	#481	C₄×C₅	1	1	yes	characteristic, complemented
271	#480	C₄×C₅	1	1	yes	characteristic, complemented
272	#436	—	2	1	no	—
273	#435	—	2	1	no	—
274	#435	—	2	1	no	—
275	C₈×D₄	—	2	1	no	—
276	#433	—	2	1	no	—
277	#433	—	2	1	no	—
278	#432	—	2	1	no	—
279	#431	—	2	1	no	—
280	C₂×#108	C₂²×C₅	1	1	yes	characteristic
281	C₂×#108	C₂²×C₅	1	1	yes	characteristic
282	#427	C₂²×C₅	1	1	yes	characteristic
283	#427	C₂²×C₅	1	1	yes	characteristic
284	#424	C₂²×C₅	1	1	yes	characteristic
285	#424	C₂²×C₅	1	1	yes	characteristic
286	#424	C₂²×C₅	1	1	yes	characteristic
287	C₂×#104	C₂²×C₅	1	1	yes	characteristic
288	C₂×#104	C₂²×C₅	1	1	yes	characteristic
289	#416	C₂²×C₅	1	1	yes	characteristic
290	#416	C₂²×C₅	1	1	yes	characteristic
291	#408	C₂²×C₅	1	1	yes	characteristic
292	#407	C₂²×C₅	1	1	yes	characteristic
293	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
294	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
295	#405	C₂²×C₅	1	1	yes	characteristic
296	#405	C₂²×C₅	1	1	yes	characteristic
297	#405	C₂²×C₅	1	1	yes	characteristic
298	C₂×#97	C₂²×C₅	1	1	yes	characteristic
299	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
300	#341	C₂²×C₅	1	1	yes	characteristic
301	#341	C₂²×C₅	1	1	yes	characteristic
302	#339	C₂²×C₅	1	1	yes	characteristic
303	#339	C₂²×C₅	1	1	yes	characteristic
304	#339	C₂²×C₅	1	1	yes	characteristic
305	#339	C₂²×C₅	1	1	yes	characteristic
306	#339	C₂²×C₅	1	1	yes	characteristic
307	#339	C₂²×C₅	1	1	yes	characteristic
308	#336	C₂²×C₅	1	1	yes	characteristic
309	#336	C₂²×C₅	1	1	yes	characteristic
310	C₂³×C₅	—	2	1	no	—
311	C₂³×C₅	—	2	1	no	—
312	C₂³×C₅	—	2	1	no	—
313	C₂³×C₅	—	4	1	no	—
314	C₂³×C₅	—	4	1	no	—
315	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
316	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
317	C₂³×C₅	C₂×#41	1	1	yes	characteristic
318	C₅×Q₈	—	2	1	no	—
319	C₅×Q₈	—	2	1	no	—
320	C₅×D₄	—	2	1	no	—
321	C₅×D₄	—	2	1	no	—
322	C₅×D₄	—	4	2	no	—
323	C₅×D₄	—	4	1	no	—
324	C₅×D₄	—	4	1	no	—
325	C₅×D₄	—	8	1	no	—
326	C₂×C₄×C₅	—	2	1	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	—	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	2	no	—
344	C₂×C₄×C₅	—	4	1	no	—
345	C₂×C₄×C₅	—	4	1	no	—
346	C₂×C₄×C₅	—	4	2	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	—	8	1	no	—
353	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
354	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
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	1	no	—
362	C₅×C₈	—	2	1	no	—
363	C₅×C₈	—	2	1	no	—
364	C₅×C₈	—	2	1	no	—
365	C₅×C₈	—	2	1	no	—
366	C₅×C₈	—	2	1	no	—
367	C₅×C₈	—	2	2	no	—
368	C₅×C₈	—	2	1	no	—
369	C₅×C₈	—	2	1	no	—
370	C₅×C₈	—	4	1	no	—
371	C₅×C₈	—	4	1	no	—
372	C₅×C₈	—	4	1	no	—
373	C₂×#41	C₂³×C₅	1	1	yes	characteristic
374	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
375	#131	—	2	2	no	—
376	#131	—	4	1	no	—
377	C₂×M₁₆	—	2	1	no	—
378	C₂×M₁₆	—	2	1	no	—
379	C₂×M₁₆	—	2	2	no	—
380	C₂×M₁₆	—	4	1	no	—
381	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
382	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
383	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
384	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
385	C₂²×C₈	—	2	1	no	—
386	C₂²×C₈	—	2	1	no	—
387	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
388	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
389	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
390	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
391	#123	—	2	1	no	—
392	C₂²⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
393	C₂²⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
394	#121	C₂×C₄×C₅	1	1	yes	characteristic
395	#121	C₂×C₄×C₅	1	1	yes	characteristic
396	#120	—	2	1	no	—
397	C₄×D₄	—	2	1	no	—
398	C₄×D₄	—	2	1	no	—
399	#117	—	2	1	no	—
400	#117	—	2	1	no	—
401	#117	—	2	2	no	—
402	#117	—	4	1	no	—
403	#117	C₂×C₄×C₅	1	1	yes	characteristic
404	#117	C₂×C₄×C₅	1	1	yes	characteristic
405	#117	C₂³×C₅	1	1	yes	characteristic
406	#117	C₂³×C₅	1	1	yes	characteristic
407	#117	C₂³×C₅	1	1	yes	characteristic
408	C₂×C₄⋊C₄	—	2	1	no	—
409	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
410	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
411	C₂×C₂²⋊C₄	—	2	1	no	—
412	C₂×C₂²⋊C₄	—	2	1	no	—
413	C₂×C₄²	—	2	1	no	—
414	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
415	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
416	#108	—	2	2	no	—
417	#108	—	4	1	no	—
418	#107	C₂×C₄×C₅	1	1	yes	characteristic
419	#107	C₂×C₄×C₅	1	1	yes	characteristic
420	#107	C₂×C₄×C₅	1	1	yes	characteristic
421	#107	C₂×C₄×C₅	1	1	yes	characteristic
422	#106	C₂×C₄×C₅	1	1	yes	characteristic
423	#106	C₂×C₄×C₅	1	1	yes	characteristic
424	#106	C₂×C₄×C₅	1	1	yes	characteristic
425	#106	C₂×C₄×C₅	1	1	yes	characteristic
426	C₄⋊C₈	—	2	1	no	—
427	C₄⋊C₈	—	2	1	no	—
428	C₄⋊C₈	—	2	1	no	—
429	C₄⋊C₈	—	2	1	no	—
430	C₄⋊C₈	—	2	1	no	—
431	C₄⋊C₈	—	2	1	no	—
432	#104	—	2	2	no	—
433	#104	—	4	1	no	—
434	#103	C₂×C₄×C₅	1	1	yes	characteristic
435	#103	C₂×C₄×C₅	1	1	yes	characteristic
436	#103	C₂×C₄×C₅	1	1	yes	characteristic
437	#103	C₂×C₄×C₅	1	1	yes	characteristic
438	#102	C₂×C₄×C₅	1	1	yes	characteristic
439	#102	C₂×C₄×C₅	1	1	yes	characteristic
440	#102	C₂×C₄×C₅	1	1	yes	characteristic
441	#102	C₂×C₄×C₅	1	1	yes	characteristic
442	C₂²⋊C₈	—	2	1	no	—
443	C₂²⋊C₈	—	2	1	no	—
444	C₂²⋊C₈	—	2	1	no	—
445	C₂²⋊C₈	—	2	1	no	—
446	C₂²⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
447	C₂²⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
448	C₂²⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
449	C₂²⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
450	C₂²⋊C₈	C₅×D₄	1	1	yes	characteristic
451	C₂²⋊C₈	C₅×D₄	1	1	yes	characteristic
452	C₂²⋊C₈	C₅×D₄	1	1	yes	characteristic
453	C₂²⋊C₈	C₅×D₄	1	1	yes	characteristic
454	#97	—	2	1	no	—
455	#97	—	2	1	no	—
456	#97	—	2	1	no	—
457	#97	—	4	1	no	—
458	C₄×C₈	—	2	1	no	—
459	C₄×C₈	—	2	1	no	—
460	C₄×C₈	—	2	1	no	—
461	C₄×C₈	—	2	2	no	—
462	C₂²×C₅	—	2	1	no	—
463	C₂²×C₅	—	2	1	no	—
464	C₂²×C₅	—	2	1	no	—
465	C₂²×C₅	—	2	1	no	—
466	C₂²×C₅	—	2	1	no	—
467	C₂²×C₅	—	2	1	no	—
468	C₂²×C₅	—	2	1	no	—
469	C₂²×C₅	—	2	1	no	—
470	C₂²×C₅	—	4	1	no	—
471	C₂²×C₅	—	4	1	no	—
472	C₂²×C₅	—	4	1	no	—
473	C₂²×C₅	—	8	1	no	—
474	C₂²×C₅	—	8	1	no	—
475	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
476	C₂²×C₅	#551	1	1	yes	characteristic
477	C₂²×C₅	#552	1	1	yes	characteristic
478	C₄×C₅	—	2	1	no	—
479	C₄×C₅	—	2	1	no	—
480	C₄×C₅	—	4	2	no	—
481	C₄×C₅	—	4	1	no	—
482	C₄×C₅	—	4	1	no	—
483	C₄×C₅	—	4	1	no	—
484	C₄×C₅	—	4	1	no	—
485	C₄×C₅	—	4	1	no	—
486	C₄×C₅	—	4	1	no	—
487	C₄×C₅	—	4	1	no	—
488	C₄×C₅	—	8	1	no	—
489	C₄×C₅	C₄×#41	1	1	yes	characteristic
490	C₄×C₅	#520	1	1	yes	characteristic
491	C₄×C₅	#546	1	1	yes	characteristic
492	C₄×C₅	#547	1	1	yes	characteristic
493	C₂⁴	C₅×#41	1	1	yes	characteristic
494	#41	—	2	1	no	—
495	#41	—	2	1	no	—
496	#41	—	2	1	no	—
497	#41	—	2	1	no	—
498	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
499	C₂×D₄	—	2	1	no	—
500	C₂×D₄	—	2	1	no	—
501	C₂×D₄	—	2	1	no	—
502	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	2	1	no	—
505	C₂²×C₄	—	2	1	no	—
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	—	2	1	no	—
510	C₂²×C₄	—	2	1	no	—
511	C₂²×C₄	—	2	1	no	—
512	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
513	C₂²×C₄	C₂²×C₄×C₅	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	C₅×#41	1	1	yes	characteristic
517	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
518	M₁₆	—	2	1	no	—
519	M₁₆	—	2	1	no	—
520	M₁₆	—	2	1	no	—
521	M₁₆	—	2	1	no	—
522	M₁₆	—	2	1	no	—
523	M₁₆	—	2	1	no	—
524	M₁₆	—	2	1	no	—
525	M₁₆	—	4	2	no	—
526	M₁₆	—	4	2	no	—
527	M₁₆	C₅×#41	1	2	yes	—
528	C₂×C₈	—	2	1	no	—
529	C₂×C₈	—	2	1	no	—
530	C₂×C₈	—	2	1	no	—
531	C₂×C₈	—	2	1	no	—
532	C₂×C₈	—	2	1	no	—
533	C₂×C₈	—	2	1	no	—
534	C₂×C₈	—	2	1	no	—
535	C₂×C₈	—	2	1	no	—
536	C₂×C₈	—	2	1	no	—
537	C₂×C₈	—	2	1	no	—
538	C₂×C₈	—	2	1	no	—
539	C₂×C₈	—	2	1	no	—
540	C₂×C₈	—	4	2	no	—
541	C₂×C₈	—	4	2	no	—
542	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
543	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
544	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
545	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
546	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
547	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
548	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
549	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
550	C₄⋊C₄	—	2	1	no	—
551	C₄⋊C₄	—	2	1	no	—
552	C₄⋊C₄	—	2	1	no	—
553	C₄⋊C₄	—	2	1	no	—
554	C₄⋊C₄	—	4	2	no	—
555	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
556	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
557	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
558	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
559	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
560	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
561	C₂²⋊C₄	—	2	1	no	—
562	C₂²⋊C₄	—	2	1	no	—
563	C₂²⋊C₄	—	2	1	no	—
564	C₂²⋊C₄	—	2	1	no	—
565	C₂²⋊C₄	—	2	1	no	—
566	C₂²⋊C₄	—	2	1	no	—
567	C₂²⋊C₄	—	2	1	no	—
568	C₂²⋊C₄	—	2	1	no	—
569	C₂²⋊C₄	—	2	1	no	—
570	C₂²⋊C₄	—	4	2	no	—
571	C₄²	—	2	1	no	—
572	C₄²	—	2	1	no	—
573	C₄²	—	2	1	no	—
574	C₄²	—	2	1	no	—
575	C₄²	—	2	1	no	—
576	C₄²	—	2	1	no	—
577	C₄²	—	2	1	no	—
578	C₄²	—	2	1	no	—
579	C₄²	C₅×#41	1	2	yes	—
580	C₂×C₅	—	2	1	no	—
581	C₂×C₅	—	2	1	no	—
582	C₂×C₅	—	4	1	no	—
583	C₂×C₅	—	4	1	no	—
584	C₂×C₅	—	8	1	no	—
585	C₂×C₅	#2359	1	1	yes	characteristic
586	C₂×C₅	#2955	1	1	yes	characteristic
587	C₂×C₅	#2957	1	1	yes	characteristic
588	C₂³	—	2	1	no	—
589	C₂³	—	2	1	no	—
590	C₂³	—	2	1	no	—
591	C₂³	—	4	1	no	—
592	C₂³	—	4	1	no	—
593	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
594	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
595	C₂³	C₂×C₅×#41	1	1	yes	characteristic
596	Q₈	—	2	1	no	—
597	Q₈	—	2	1	no	—
598	D₄	—	2	1	no	—
599	D₄	—	2	1	no	—
600	D₄	—	4	2	no	—
601	D₄	—	4	1	no	—
602	D₄	—	4	1	no	—
603	D₄	—	8	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	—	2	1	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	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	2	no	—
622	C₂×C₄	—	4	1	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	4	2	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	—	8	1	no	—
631	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
632	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
633	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
634	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
635	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
636	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
637	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
638	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
639	C₈	—	2	1	no	—
640	C₈	—	2	1	no	—
641	C₈	—	2	1	no	—
642	C₈	—	2	1	no	—
643	C₈	—	2	1	no	—
644	C₈	—	2	1	no	—
645	C₈	—	2	2	no	—
646	C₈	—	2	1	no	—
647	C₈	—	2	1	no	—
648	C₈	—	4	1	no	—
649	C₈	—	4	1	no	—
650	C₈	—	4	1	no	—
651	C₅	#22951	1	1	yes	characteristic, direct product factor, Sylow
652	C₂²	—	2	1	no	—
653	C₂²	—	2	1	no	—
654	C₂²	—	2	1	no	—
655	C₂²	—	2	1	no	—
656	C₂²	—	2	1	no	—
657	C₂²	—	2	1	no	—
658	C₂²	—	2	1	no	—
659	C₂²	—	2	1	no	—
660	C₂²	—	4	1	no	—
661	C₂²	—	4	1	no	—
662	C₂²	—	4	1	no	—
663	C₂²	—	8	1	no	—
664	C₂²	—	8	1	no	—
665	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
666	C₂²	C₅×#551	1	1	yes	characteristic
667	C₂²	C₅×#552	1	1	yes	characteristic
668	C₄	—	2	1	no	—
669	C₄	—	2	1	no	—
670	C₄	—	4	2	no	—
671	C₄	—	4	1	no	—
672	C₄	—	4	1	no	—
673	C₄	—	4	1	no	—
674	C₄	—	4	1	no	—
675	C₄	—	4	1	no	—
676	C₄	—	4	1	no	—
677	C₄	—	4	1	no	—
678	C₄	—	8	1	no	—
679	C₄	C₄×C₅×#41	1	1	yes	characteristic
680	C₄	C₅×#520	1	1	yes	characteristic
681	C₄	C₅×#546	1	1	yes	characteristic
682	C₄	C₅×#547	1	1	yes	characteristic
683	C₂	—	2	1	no	—
684	C₂	—	2	1	no	—
685	C₂	—	4	1	no	—
686	C₂	—	4	1	no	—
687	C₂	—	8	1	no	—
688	C₂	C₅×#2359	1	1	yes	characteristic
689	C₂	C₅×#2955	1	1	yes	characteristic
690	C₂	C₅×#2957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₅×#525	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₅×C₂²⋊C₈ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₅×#2924	C₂	semidirect
4. C₅×#1946	C₂	semidirect
5. C₅×#1937	C₂	semidirect
6. C₅×#1929	C₂	semidirect
7. C₅×#1922	C₂	semidirect
8. C₅×#1922	C₂	semidirect
10. C₅×#1866	C₂	semidirect
11. C₅×#1855	C₂	semidirect
12. C₅×#1772	C₂	semidirect
13. C₅×#1765	C₂	semidirect
14. C₅×#1750	C₂	semidirect
15. C₅×#1733	C₂	semidirect
21. C₅×#485	C₄	semidirect
22. C₅×#485	C₄	semidirect
23. C₅×#484	C₄	semidirect
24. C₅×#483	C₄	semidirect
25. C₅×#482	C₄	semidirect
26. C₅×#482	C₄	semidirect
27. C₅×#481	C₄	semidirect
28. C₅×#480	C₄	semidirect
67. #22951	C₅	direct (N × H)
159. #2924	C₂×C₅	semidirect
160. #1946	C₂×C₅	semidirect
161. #1937	C₂×C₅	semidirect
162. #1929	C₂×C₅	semidirect
163. #1922	C₂×C₅	semidirect
164. #1922	C₂×C₅	semidirect
166. #1866	C₂×C₅	semidirect
167. #1855	C₂×C₅	semidirect
168. #1772	C₂×C₅	semidirect
169. #1765	C₂×C₅	semidirect
170. #1750	C₂×C₅	semidirect
171. #1733	C₂×C₅	semidirect
264. #485	C₄×C₅	semidirect
265. #485	C₄×C₅	semidirect
266. #484	C₄×C₅	semidirect
267. #483	C₄×C₅	semidirect
268. #482	C₄×C₅	semidirect
269. #482	C₄×C₅	semidirect
270. #481	C₄×C₅	semidirect
271. #480	C₄×C₅	semidirect
651. C₅	#22951	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅×#3091	2
C₅×#2933	2
C₅×#2924	2
C₅×#1946	2
C₅×#1937	2
C₅×#1929	2
C₅×#1922	2
C₅×#1897	2
C₅×#1866	2
C₅×#1855	2
C₅×#1772	2
C₅×#1765	2
C₅×#1750	2
C₅×#1733	2
#22951	5

Subgroups — C5×#22951 #11945671

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22951 #11945671