Subgroups — C₅×#23017 #11945737

Order 1280.

864 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3035	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#444	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#443	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2935	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2906	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1963	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1950	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1938	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1937	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1876	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1876	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1866	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1866	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1768	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1759	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×#135	C₂²	1	1	yes	characteristic
17	C₂×C₅×#135	C₂²	1	1	yes	characteristic
18	C₂×C₅×#131	C₂²	1	1	yes	characteristic
19	C₂×C₅×#131	C₂²	1	1	yes	characteristic
20	C₂×C₅×#131	C₂²	1	1	yes	characteristic
21	C₂×C₅×#131	C₂²	1	1	yes	characteristic
22	C₅×#532	C₂²	1	1	yes	characteristic
23	C₄×C₅×#41	C₂²	1	1	yes	characteristic
24	C₅×#464	C₄	1	1	yes	characteristic, complemented
25	C₅×#464	C₄	1	1	yes	characteristic, complemented
26	C₅×#463	C₄	1	1	yes	characteristic, complemented
27	C₅×#463	C₄	1	1	yes	characteristic, complemented
28	C₅×#462	C₄	1	1	yes	characteristic, complemented
29	C₅×#461	C₄	1	1	yes	characteristic, complemented
30	C₅×#460	C₄	1	1	yes	characteristic, complemented
31	C₅×#459	C₄	1	1	yes	characteristic, complemented
32	C₅×#444	—	2	4	no	—
33	C₅×#443	—	2	4	no	—
34	C₅×#436	—	2	1	no	—
35	C₅×#435	—	2	1	no	—
36	C₅×#435	—	2	1	no	—
37	C₅×C₈×D₄	—	2	1	no	—
38	C₂×C₅×#108	C₂²	1	1	yes	characteristic
39	C₂×C₅×#108	C₂²	1	1	yes	characteristic
40	C₅×#424	—	2	1	no	—
41	C₅×#424	—	2	1	no	—
42	C₅×#424	C₂²	1	1	yes	characteristic
43	C₅×#424	C₂²	1	1	yes	characteristic
44	C₅×#423	—	2	1	no	—
45	C₅×#423	C₂²	1	1	yes	characteristic
46	C₂×C₅×C₄⋊C₈	—	2	1	no	—
47	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
48	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
49	C₂×C₅×#104	C₂²	1	1	yes	characteristic
50	C₂×C₅×#104	C₂²	1	1	yes	characteristic
51	C₂×C₅×#104	C₂²	1	1	yes	characteristic
52	C₂×C₅×#104	C₂²	1	1	yes	characteristic
53	C₂×C₅×#104	C₂²	1	1	yes	characteristic
54	C₂×C₅×#104	C₂²	1	1	yes	characteristic
55	C₅×#416	C₂²	1	1	yes	characteristic
56	C₅×#416	C₂²	1	1	yes	characteristic
57	C₅×#408	C₂²	1	1	yes	characteristic
58	C₅×#408	C₂²	1	1	yes	characteristic
59	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
60	C₂×C₅×#97	C₂²	1	1	yes	characteristic
61	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
62	C₅×#376	C₂²	1	1	yes	characteristic
63	C₅×#341	C₂²	1	1	yes	characteristic
64	C₅×#341	C₂²	1	1	yes	characteristic
65	C₅×#339	C₂²	1	1	yes	characteristic
66	C₅×#339	C₂²	1	1	yes	characteristic
67	C₅×#336	C₂²	1	1	yes	characteristic
68	C₅×#336	C₂²	1	1	yes	characteristic
69	#23017	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
70	C₂×C₅×#41	C₂³	1	1	yes	characteristic
71	C₂×C₅×#41	C₂³	1	1	yes	characteristic
72	C₂×C₅×#41	C₂³	1	1	yes	characteristic
73	C₅×#135	—	2	2	no	—
74	C₅×#135	—	2	2	no	—
75	C₅×#135	—	2	2	no	—
76	C₅×#135	—	2	2	no	—
77	C₂×C₅×Q₁₆	C₂×C₄	1	1	yes	characteristic
78	C₂×C₅×Q₁₆	C₂×C₄	1	1	yes	characteristic
79	C₂×C₅×SD₁₆	C₂×C₄	1	1	yes	characteristic
80	C₂×C₅×SD₁₆	C₂×C₄	1	1	yes	characteristic
81	C₂×C₅×SD₁₆	C₂×C₄	1	1	yes	characteristic
82	C₂×C₅×SD₁₆	C₂×C₄	1	1	yes	characteristic
83	C₂×C₅×D₈	C₂×C₄	1	1	yes	characteristic
84	C₂×C₅×D₈	C₂×C₄	1	1	yes	characteristic
85	C₅×#131	—	2	2	no	—
86	C₅×#131	—	2	2	no	—
87	C₅×#131	—	2	2	no	—
88	C₅×#131	—	2	2	no	—
89	C₅×#131	—	4	1	no	—
90	C₅×#131	—	4	1	no	—
91	C₅×#131	—	4	1	no	—
92	C₅×#131	—	4	1	no	—
93	C₂×C₅×M₁₆	—	2	1	no	—
94	C₂×C₅×M₁₆	—	2	1	no	—
95	C₂×C₅×M₁₆	—	2	1	no	—
96	C₂×C₅×M₁₆	—	2	1	no	—
97	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
98	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
99	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
100	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
101	C₂²×C₅×C₈	—	2	1	no	—
102	C₂²×C₅×C₈	—	2	1	no	—
103	C₂²×C₅×C₈	—	2	1	no	—
104	C₂²×C₅×C₈	—	2	1	no	—
105	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
106	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
107	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
108	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
109	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
110	C₅×#127	C₂×C₄	1	1	yes	characteristic
111	C₅×#124	C₂×C₄	1	1	yes	characteristic
112	C₅×#124	C₂×C₄	1	1	yes	characteristic
113	C₅×#121	—	2	1	no	—
114	C₅×#121	—	2	1	no	—
115	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
116	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
117	C₄×C₅×D₄	—	2	1	no	—
118	C₄×C₅×D₄	—	2	1	no	—
119	C₄×C₅×D₄	—	2	1	no	—
120	C₄×C₅×D₄	—	2	1	no	—
121	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
122	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
123	C₅×#117	—	2	1	no	—
124	C₅×#117	C₂³	1	1	yes	characteristic
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×#108	—	2	2	no	—
130	C₅×#108	—	2	2	no	—
131	C₅×C₄⋊C₈	—	2	1	no	—
132	C₅×C₄⋊C₈	—	2	1	no	—
133	C₅×C₄⋊C₈	—	2	1	no	—
134	C₅×C₄⋊C₈	—	2	1	no	—
135	C₅×C₄⋊C₈	—	2	1	no	—
136	C₅×C₄⋊C₈	—	2	1	no	—
137	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
138	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
139	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
140	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
141	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
142	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
143	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
144	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
145	C₅×#104	—	2	2	no	—
146	C₅×#104	—	2	2	no	—
147	C₅×#104	—	2	2	no	—
148	C₅×#104	—	4	1	no	—
149	C₅×#104	—	4	1	no	—
150	C₅×#104	D₄	1	4	yes	complemented
151	C₅×#103	C₂×C₄	1	1	yes	characteristic
152	C₅×#103	C₂×C₄	1	1	yes	characteristic
153	C₅×#103	C₂×C₄	1	1	yes	characteristic
154	C₅×#103	C₂×C₄	1	1	yes	characteristic
155	C₅×#102	C₂×C₄	1	1	yes	characteristic
156	C₅×#102	C₂×C₄	1	1	yes	characteristic
157	C₅×#102	C₂×C₄	1	1	yes	characteristic
158	C₅×#102	C₂×C₄	1	1	yes	characteristic
159	C₅×C₂²⋊C₈	—	2	1	no	—
160	C₅×C₂²⋊C₈	—	2	1	no	—
161	C₅×C₂²⋊C₈	—	2	1	no	—
162	C₅×C₂²⋊C₈	—	2	1	no	—
163	C₅×#97	—	2	2	no	—
164	C₅×#97	—	2	1	no	—
165	C₄×C₅×C₈	—	2	2	no	—
166	C₄×C₅×C₈	—	2	1	no	—
167	C₅×#95	—	2	1	no	—
168	C₅×#95	—	2	1	no	—
169	#3035	C₂×C₅	1	1	yes	characteristic
170	C₂×#444	C₂×C₅	1	1	yes	characteristic, complemented
171	C₂×#443	C₂×C₅	1	1	yes	characteristic, complemented
172	#2935	C₂×C₅	1	1	yes	characteristic, complemented
173	#2906	C₂×C₅	1	1	yes	characteristic, complemented
174	#1963	C₂×C₅	1	1	yes	characteristic, complemented
175	#1950	C₂×C₅	1	1	yes	characteristic, complemented
176	#1938	C₂×C₅	1	1	yes	characteristic, complemented
177	#1937	C₂×C₅	1	1	yes	characteristic, complemented
178	#1876	C₂×C₅	1	1	yes	characteristic, complemented
179	#1876	C₂×C₅	1	1	yes	characteristic, complemented
180	#1866	C₂×C₅	1	1	yes	characteristic, complemented
181	#1866	C₂×C₅	1	1	yes	characteristic, complemented
182	#1768	C₂×C₅	1	1	yes	characteristic, complemented
183	#1759	C₂×C₅	1	1	yes	characteristic, complemented
184	C₅×#41	—	2	1	no	—
185	C₅×#41	—	2	1	no	—
186	C₅×#41	—	2	1	no	—
187	C₅×#41	—	2	1	no	—
188	C₅×#41	—	2	1	no	—
189	C₅×#41	—	2	1	no	—
190	C₅×#41	—	2	1	no	—
191	C₅×#41	—	2	1	no	—
192	C₅×#41	—	2	1	no	—
193	C₅×#41	—	2	1	no	—
194	C₅×#41	C₂×D₄	1	2	yes	—
195	C₅×#41	#41	1	2	yes	—
196	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
197	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
198	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
199	C₂×C₅×D₄	—	2	1	no	—
200	C₂×C₅×D₄	—	2	1	no	—
201	C₂×C₅×D₄	—	2	1	no	—
202	C₂×C₅×D₄	—	2	1	no	—
203	C₂×C₅×D₄	—	2	1	no	—
204	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
205	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
206	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
207	C₂²×C₄×C₅	—	2	1	no	—
208	C₂²×C₄×C₅	—	2	1	no	—
209	C₂²×C₄×C₅	—	2	1	no	—
210	C₂²×C₄×C₅	—	2	1	no	—
211	C₂²×C₄×C₅	—	2	1	no	—
212	C₂²×C₄×C₅	—	2	1	no	—
213	C₂²×C₄×C₅	—	2	1	no	—
214	C₂²×C₄×C₅	#41	1	1	yes	characteristic
215	C₂²×C₄×C₅	#41	1	1	yes	characteristic
216	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
217	C₅×Q₁₆	—	2	2	no	—
218	C₅×Q₁₆	—	2	2	no	—
219	C₅×SD₁₆	—	2	2	no	—
220	C₅×SD₁₆	—	2	2	no	—
221	C₅×SD₁₆	—	2	2	no	—
222	C₅×SD₁₆	—	2	2	no	—
223	C₅×D₈	—	2	2	no	—
224	C₅×D₈	—	2	2	no	—
225	C₅×M₁₆	—	2	1	no	—
226	C₅×M₁₆	—	2	1	no	—
227	C₅×M₁₆	—	2	1	no	—
228	C₅×M₁₆	—	2	1	no	—
229	C₅×M₁₆	—	2	1	no	—
230	C₅×M₁₆	—	2	1	no	—
231	C₅×M₁₆	—	2	1	no	—
232	C₅×M₁₆	—	4	2	no	—
233	C₅×M₁₆	—	4	2	no	—
234	C₅×M₁₆	—	4	2	no	—
235	C₅×M₁₆	—	4	2	no	—
236	C₅×M₁₆	C₂×D₄	1	2	yes	—
237	C₂×C₅×C₈	—	2	1	no	—
238	C₂×C₅×C₈	—	2	1	no	—
239	C₂×C₅×C₈	—	2	1	no	—
240	C₂×C₅×C₈	—	2	1	no	—
241	C₂×C₅×C₈	—	2	1	no	—
242	C₂×C₅×C₈	—	2	1	no	—
243	C₂×C₅×C₈	—	2	1	no	—
244	C₂×C₅×C₈	—	2	1	no	—
245	C₂×C₅×C₈	—	2	1	no	—
246	C₂×C₅×C₈	—	2	1	no	—
247	C₂×C₅×C₈	—	2	1	no	—
248	C₂×C₅×C₈	—	2	1	no	—
249	C₂×C₅×C₈	—	4	2	no	—
250	C₂×C₅×C₈	—	4	2	no	—
251	C₂×C₅×C₈	—	4	2	no	—
252	C₂×C₅×C₈	—	4	2	no	—
253	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
254	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
255	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
256	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
257	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
258	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
259	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
260	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
261	C₅×C₄⋊C₄	—	2	1	no	—
262	C₅×C₄⋊C₄	—	2	1	no	—
263	C₅×C₄⋊C₄	—	2	1	no	—
264	C₅×C₄⋊C₄	—	2	1	no	—
265	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
266	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
267	C₅×C₂²⋊C₄	—	2	1	no	—
268	C₅×C₂²⋊C₄	—	2	1	no	—
269	C₅×C₂²⋊C₄	—	2	1	no	—
270	C₅×C₂²⋊C₄	—	2	1	no	—
271	C₅×C₂²⋊C₄	—	2	1	no	—
272	C₅×C₂²⋊C₄	—	2	1	no	—
273	C₅×C₂²⋊C₄	—	2	1	no	—
274	C₄²×C₅	—	2	1	no	—
275	C₄²×C₅	—	2	1	no	—
276	C₄²×C₅	—	2	1	no	—
277	C₄²×C₅	—	2	1	no	—
278	C₄²×C₅	—	2	1	no	—
279	C₄²×C₅	—	2	1	no	—
280	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
281	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
282	C₄²×C₅	C₂×D₄	1	2	yes	—
283	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
284	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
285	C₂×#135	C₂²×C₅	1	1	yes	characteristic
286	C₂×#135	C₂²×C₅	1	1	yes	characteristic
287	C₂×#131	C₂²×C₅	1	1	yes	characteristic
288	C₂×#131	C₂²×C₅	1	1	yes	characteristic
289	C₂×#131	C₂²×C₅	1	1	yes	characteristic
290	C₂×#131	C₂²×C₅	1	1	yes	characteristic
291	#532	C₂²×C₅	1	1	yes	characteristic
292	C₄×#41	C₂²×C₅	1	1	yes	characteristic
293	#464	C₄×C₅	1	1	yes	characteristic, complemented
294	#464	C₄×C₅	1	1	yes	characteristic, complemented
295	#463	C₄×C₅	1	1	yes	characteristic, complemented
296	#463	C₄×C₅	1	1	yes	characteristic, complemented
297	#462	C₄×C₅	1	1	yes	characteristic, complemented
298	#461	C₄×C₅	1	1	yes	characteristic, complemented
299	#460	C₄×C₅	1	1	yes	characteristic, complemented
300	#459	C₄×C₅	1	1	yes	characteristic, complemented
301	#444	—	2	4	no	—
302	#443	—	2	4	no	—
303	#436	—	2	1	no	—
304	#435	—	2	1	no	—
305	#435	—	2	1	no	—
306	C₈×D₄	—	2	1	no	—
307	C₂×#108	C₂²×C₅	1	1	yes	characteristic
308	C₂×#108	C₂²×C₅	1	1	yes	characteristic
309	#424	—	2	1	no	—
310	#424	—	2	1	no	—
311	#424	C₂²×C₅	1	1	yes	characteristic
312	#424	C₂²×C₅	1	1	yes	characteristic
313	#423	—	2	1	no	—
314	#423	C₂²×C₅	1	1	yes	characteristic
315	C₂×C₄⋊C₈	—	2	1	no	—
316	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
317	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
318	C₂×#104	C₂²×C₅	1	1	yes	characteristic
319	C₂×#104	C₂²×C₅	1	1	yes	characteristic
320	C₂×#104	C₂²×C₅	1	1	yes	characteristic
321	C₂×#104	C₂²×C₅	1	1	yes	characteristic
322	C₂×#104	C₂²×C₅	1	1	yes	characteristic
323	C₂×#104	C₂²×C₅	1	1	yes	characteristic
324	#416	C₂²×C₅	1	1	yes	characteristic
325	#416	C₂²×C₅	1	1	yes	characteristic
326	#408	C₂²×C₅	1	1	yes	characteristic
327	#408	C₂²×C₅	1	1	yes	characteristic
328	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
329	C₂×#97	C₂²×C₅	1	1	yes	characteristic
330	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
331	#376	C₂²×C₅	1	1	yes	characteristic
332	#341	C₂²×C₅	1	1	yes	characteristic
333	#341	C₂²×C₅	1	1	yes	characteristic
334	#339	C₂²×C₅	1	1	yes	characteristic
335	#339	C₂²×C₅	1	1	yes	characteristic
336	#336	C₂²×C₅	1	1	yes	characteristic
337	#336	C₂²×C₅	1	1	yes	characteristic
338	C₂³×C₅	—	2	1	no	—
339	C₂³×C₅	—	2	1	no	—
340	C₂³×C₅	—	2	1	no	—
341	C₂³×C₅	C₂×#41	1	1	yes	characteristic
342	C₅×Q₈	—	2	1	no	—
343	C₅×Q₈	—	2	1	no	—
344	C₅×Q₈	—	2	1	no	—
345	C₅×Q₈	—	2	1	no	—
346	C₅×Q₈	—	2	1	no	—
347	C₅×Q₈	C₄×D₄	1	2	yes	—
348	C₅×D₄	—	2	2	no	—
349	C₅×D₄	—	2	2	no	—
350	C₅×D₄	—	2	1	no	—
351	C₅×D₄	—	2	1	no	—
352	C₅×D₄	—	2	1	no	—
353	C₅×D₄	—	2	1	no	—
354	C₅×D₄	—	2	1	no	—
355	C₅×D₄	—	4	2	no	—
356	C₅×D₄	—	4	1	no	—
357	C₅×D₄	—	4	1	no	—
358	C₅×D₄	—	4	1	no	—
359	C₅×D₄	—	4	1	no	—
360	C₅×D₄	—	8	1	no	—
361	C₅×D₄	C₄×D₄	1	2	yes	—
362	C₂×C₄×C₅	—	2	1	no	—
363	C₂×C₄×C₅	—	2	2	no	—
364	C₂×C₄×C₅	—	2	2	no	—
365	C₂×C₄×C₅	—	2	1	no	—
366	C₂×C₄×C₅	—	2	1	no	—
367	C₂×C₄×C₅	—	2	1	no	—
368	C₂×C₄×C₅	—	2	1	no	—
369	C₂×C₄×C₅	—	2	2	no	—
370	C₂×C₄×C₅	—	4	1	no	—
371	C₂×C₄×C₅	—	4	1	no	—
372	C₂×C₄×C₅	—	4	2	no	—
373	C₂×C₄×C₅	—	4	1	no	—
374	C₂×C₄×C₅	—	4	1	no	—
375	C₂×C₄×C₅	—	4	1	no	—
376	C₂×C₄×C₅	—	4	1	no	—
377	C₂×C₄×C₅	—	4	1	no	—
378	C₂×C₄×C₅	—	4	1	no	—
379	C₂×C₄×C₅	—	4	1	no	—
380	C₂×C₄×C₅	—	4	1	no	—
381	C₂×C₄×C₅	—	4	1	no	—
382	C₂×C₄×C₅	—	8	1	no	—
383	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
384	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
385	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
386	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
387	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
388	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
390	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
391	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
392	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
393	C₅×C₈	—	2	1	no	—
394	C₅×C₈	—	2	1	no	—
395	C₅×C₈	—	2	1	no	—
396	C₅×C₈	—	2	1	no	—
397	C₅×C₈	—	2	1	no	—
398	C₅×C₈	—	2	1	no	—
399	C₅×C₈	—	2	1	no	—
400	C₅×C₈	—	2	1	no	—
401	C₅×C₈	—	2	2	no	—
402	C₅×C₈	—	4	1	no	—
403	C₅×C₈	—	4	1	no	—
404	C₅×C₈	—	4	1	no	—
405	C₂×#41	C₂³×C₅	1	1	yes	characteristic
406	C₂×#41	C₂³×C₅	1	1	yes	characteristic
407	C₂×#41	C₂³×C₅	1	1	yes	characteristic
408	#135	—	2	2	no	—
409	#135	—	2	2	no	—
410	#135	—	2	2	no	—
411	#135	—	2	2	no	—
412	C₂×Q₁₆	C₂×C₄×C₅	1	1	yes	characteristic
413	C₂×Q₁₆	C₂×C₄×C₅	1	1	yes	characteristic
414	C₂×SD₁₆	C₂×C₄×C₅	1	1	yes	characteristic
415	C₂×SD₁₆	C₂×C₄×C₅	1	1	yes	characteristic
416	C₂×SD₁₆	C₂×C₄×C₅	1	1	yes	characteristic
417	C₂×SD₁₆	C₂×C₄×C₅	1	1	yes	characteristic
418	C₂×D₈	C₂×C₄×C₅	1	1	yes	characteristic
419	C₂×D₈	C₂×C₄×C₅	1	1	yes	characteristic
420	#131	—	2	2	no	—
421	#131	—	2	2	no	—
422	#131	—	2	2	no	—
423	#131	—	2	2	no	—
424	#131	—	4	1	no	—
425	#131	—	4	1	no	—
426	#131	—	4	1	no	—
427	#131	—	4	1	no	—
428	C₂×M₁₆	—	2	1	no	—
429	C₂×M₁₆	—	2	1	no	—
430	C₂×M₁₆	—	2	1	no	—
431	C₂×M₁₆	—	2	1	no	—
432	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
433	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
434	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
435	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
436	C₂²×C₈	—	2	1	no	—
437	C₂²×C₈	—	2	1	no	—
438	C₂²×C₈	—	2	1	no	—
439	C₂²×C₈	—	2	1	no	—
440	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
441	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
442	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
443	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
444	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
445	#127	C₂×C₄×C₅	1	1	yes	characteristic
446	#124	C₂×C₄×C₅	1	1	yes	characteristic
447	#124	C₂×C₄×C₅	1	1	yes	characteristic
448	#121	—	2	1	no	—
449	#121	—	2	1	no	—
450	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
451	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
452	C₄×D₄	—	2	1	no	—
453	C₄×D₄	—	2	1	no	—
454	C₄×D₄	—	2	1	no	—
455	C₄×D₄	—	2	1	no	—
456	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
457	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
458	#117	—	2	1	no	—
459	#117	C₂³×C₅	1	1	yes	characteristic
460	C₂×C₄²	—	2	1	no	—
461	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
462	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
463	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
464	#108	—	2	2	no	—
465	#108	—	2	2	no	—
466	C₄⋊C₈	—	2	1	no	—
467	C₄⋊C₈	—	2	1	no	—
468	C₄⋊C₈	—	2	1	no	—
469	C₄⋊C₈	—	2	1	no	—
470	C₄⋊C₈	—	2	1	no	—
471	C₄⋊C₈	—	2	1	no	—
472	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
473	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
474	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
475	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
476	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
477	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
478	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
479	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
480	#104	—	2	2	no	—
481	#104	—	2	2	no	—
482	#104	—	2	2	no	—
483	#104	—	4	1	no	—
484	#104	—	4	1	no	—
485	#104	C₅×D₄	1	4	yes	complemented
486	#103	C₂×C₄×C₅	1	1	yes	characteristic
487	#103	C₂×C₄×C₅	1	1	yes	characteristic
488	#103	C₂×C₄×C₅	1	1	yes	characteristic
489	#103	C₂×C₄×C₅	1	1	yes	characteristic
490	#102	C₂×C₄×C₅	1	1	yes	characteristic
491	#102	C₂×C₄×C₅	1	1	yes	characteristic
492	#102	C₂×C₄×C₅	1	1	yes	characteristic
493	#102	C₂×C₄×C₅	1	1	yes	characteristic
494	C₂²⋊C₈	—	2	1	no	—
495	C₂²⋊C₈	—	2	1	no	—
496	C₂²⋊C₈	—	2	1	no	—
497	C₂²⋊C₈	—	2	1	no	—
498	#97	—	2	2	no	—
499	#97	—	2	1	no	—
500	C₄×C₈	—	2	2	no	—
501	C₄×C₈	—	2	1	no	—
502	#95	—	2	1	no	—
503	#95	—	2	1	no	—
504	C₂²×C₅	—	2	1	no	—
505	C₂²×C₅	—	2	1	no	—
506	C₂²×C₅	—	2	2	no	—
507	C₂²×C₅	—	4	1	no	—
508	C₂²×C₅	—	4	1	no	—
509	C₂²×C₅	—	4	1	no	—
510	C₂²×C₅	—	4	1	no	—
511	C₂²×C₅	—	4	1	no	—
512	C₂²×C₅	—	4	1	no	—
513	C₂²×C₅	—	4	1	no	—
514	C₂²×C₅	—	4	1	no	—
515	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
516	C₂²×C₅	#547	1	1	yes	characteristic
517	C₂²×C₅	#553	1	1	yes	characteristic
518	C₄×C₅	—	2	2	no	—
519	C₄×C₅	—	2	1	no	—
520	C₄×C₅	—	2	1	no	—
521	C₄×C₅	—	2	1	no	—
522	C₄×C₅	—	2	1	no	—
523	C₄×C₅	—	4	2	no	—
524	C₄×C₅	—	4	1	no	—
525	C₄×C₅	—	4	1	no	—
526	C₄×C₅	—	4	1	no	—
527	C₄×C₅	—	4	1	no	—
528	C₄×C₅	—	8	1	no	—
529	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
530	C₄×C₅	#520	1	1	yes	characteristic
531	C₄×C₅	D₄²	1	1	yes	characteristic
532	C₄×C₅	#548	1	1	yes	characteristic
533	#41	—	2	1	no	—
534	#41	—	2	1	no	—
535	#41	—	2	1	no	—
536	#41	—	2	1	no	—
537	#41	—	2	1	no	—
538	#41	—	2	1	no	—
539	#41	—	2	1	no	—
540	#41	—	2	1	no	—
541	#41	—	2	1	no	—
542	#41	—	2	1	no	—
543	#41	C₂×C₅×D₄	1	2	yes	—
544	#41	C₅×#41	1	2	yes	—
545	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
546	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
547	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
548	C₂×D₄	—	2	1	no	—
549	C₂×D₄	—	2	1	no	—
550	C₂×D₄	—	2	1	no	—
551	C₂×D₄	—	2	1	no	—
552	C₂×D₄	—	2	1	no	—
553	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
554	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
555	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
556	C₂²×C₄	—	2	1	no	—
557	C₂²×C₄	—	2	1	no	—
558	C₂²×C₄	—	2	1	no	—
559	C₂²×C₄	—	2	1	no	—
560	C₂²×C₄	—	2	1	no	—
561	C₂²×C₄	—	2	1	no	—
562	C₂²×C₄	—	2	1	no	—
563	C₂²×C₄	C₅×#41	1	1	yes	characteristic
564	C₂²×C₄	C₅×#41	1	1	yes	characteristic
565	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
566	Q₁₆	—	2	2	no	—
567	Q₁₆	—	2	2	no	—
568	SD₁₆	—	2	2	no	—
569	SD₁₆	—	2	2	no	—
570	SD₁₆	—	2	2	no	—
571	SD₁₆	—	2	2	no	—
572	D₈	—	2	2	no	—
573	D₈	—	2	2	no	—
574	M₁₆	—	2	1	no	—
575	M₁₆	—	2	1	no	—
576	M₁₆	—	2	1	no	—
577	M₁₆	—	2	1	no	—
578	M₁₆	—	2	1	no	—
579	M₁₆	—	2	1	no	—
580	M₁₆	—	2	1	no	—
581	M₁₆	—	4	2	no	—
582	M₁₆	—	4	2	no	—
583	M₁₆	—	4	2	no	—
584	M₁₆	—	4	2	no	—
585	M₁₆	C₂×C₅×D₄	1	2	yes	—
586	C₂×C₈	—	2	1	no	—
587	C₂×C₈	—	2	1	no	—
588	C₂×C₈	—	2	1	no	—
589	C₂×C₈	—	2	1	no	—
590	C₂×C₈	—	2	1	no	—
591	C₂×C₈	—	2	1	no	—
592	C₂×C₈	—	2	1	no	—
593	C₂×C₈	—	2	1	no	—
594	C₂×C₈	—	2	1	no	—
595	C₂×C₈	—	2	1	no	—
596	C₂×C₈	—	2	1	no	—
597	C₂×C₈	—	2	1	no	—
598	C₂×C₈	—	4	2	no	—
599	C₂×C₈	—	4	2	no	—
600	C₂×C₈	—	4	2	no	—
601	C₂×C₈	—	4	2	no	—
602	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
603	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
604	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
605	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
606	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
607	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
608	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
609	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
610	C₄⋊C₄	—	2	1	no	—
611	C₄⋊C₄	—	2	1	no	—
612	C₄⋊C₄	—	2	1	no	—
613	C₄⋊C₄	—	2	1	no	—
614	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
615	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
616	C₂²⋊C₄	—	2	1	no	—
617	C₂²⋊C₄	—	2	1	no	—
618	C₂²⋊C₄	—	2	1	no	—
619	C₂²⋊C₄	—	2	1	no	—
620	C₂²⋊C₄	—	2	1	no	—
621	C₂²⋊C₄	—	2	1	no	—
622	C₂²⋊C₄	—	2	1	no	—
623	C₄²	—	2	1	no	—
624	C₄²	—	2	1	no	—
625	C₄²	—	2	1	no	—
626	C₄²	—	2	1	no	—
627	C₄²	—	2	1	no	—
628	C₄²	—	2	1	no	—
629	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
630	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
631	C₄²	C₂×C₅×D₄	1	2	yes	—
632	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
633	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
634	C₂×C₅	—	2	1	no	—
635	C₂×C₅	—	2	1	no	—
636	C₂×C₅	—	4	2	no	—
637	C₂×C₅	—	8	1	no	—
638	C₂×C₅	—	8	1	no	—
639	C₂×C₅	#2361	1	1	yes	characteristic
640	C₂×C₅	#2955	1	1	yes	characteristic
641	C₂×C₅	#2957	1	1	yes	characteristic
642	C₂³	—	2	1	no	—
643	C₂³	—	2	1	no	—
644	C₂³	—	2	1	no	—
645	C₂³	C₂×C₅×#41	1	1	yes	characteristic
646	Q₈	—	2	1	no	—
647	Q₈	—	2	1	no	—
648	Q₈	—	2	1	no	—
649	Q₈	—	2	1	no	—
650	Q₈	—	2	1	no	—
651	Q₈	C₄×C₅×D₄	1	2	yes	—
652	D₄	—	2	2	no	—
653	D₄	—	2	2	no	—
654	D₄	—	2	1	no	—
655	D₄	—	2	1	no	—
656	D₄	—	2	1	no	—
657	D₄	—	2	1	no	—
658	D₄	—	2	1	no	—
659	D₄	—	4	2	no	—
660	D₄	—	4	1	no	—
661	D₄	—	4	1	no	—
662	D₄	—	4	1	no	—
663	D₄	—	4	1	no	—
664	D₄	—	8	1	no	—
665	D₄	C₄×C₅×D₄	1	2	yes	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	4	1	no	—
675	C₂×C₄	—	4	1	no	—
676	C₂×C₄	—	4	2	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	—	4	1	no	—
685	C₂×C₄	—	4	1	no	—
686	C₂×C₄	—	8	1	no	—
687	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
688	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
689	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
690	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
691	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
692	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
693	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
694	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
695	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
696	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
697	C₈	—	2	1	no	—
698	C₈	—	2	1	no	—
699	C₈	—	2	1	no	—
700	C₈	—	2	1	no	—
701	C₈	—	2	1	no	—
702	C₈	—	2	1	no	—
703	C₈	—	2	1	no	—
704	C₈	—	2	1	no	—
705	C₈	—	2	2	no	—
706	C₈	—	4	1	no	—
707	C₈	—	4	1	no	—
708	C₈	—	4	1	no	—
709	C₅	#23017	1	1	yes	characteristic, direct product factor, Sylow
710	C₂²	—	2	1	no	—
711	C₂²	—	2	1	no	—
712	C₂²	—	2	2	no	—
713	C₂²	—	4	1	no	—
714	C₂²	—	4	1	no	—
715	C₂²	—	4	1	no	—
716	C₂²	—	4	1	no	—
717	C₂²	—	4	1	no	—
718	C₂²	—	4	1	no	—
719	C₂²	—	4	1	no	—
720	C₂²	—	4	1	no	—
721	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
722	C₂²	C₅×#547	1	1	yes	characteristic
723	C₂²	C₅×#553	1	1	yes	characteristic
724	C₄	—	2	2	no	—
725	C₄	—	2	1	no	—
726	C₄	—	2	1	no	—
727	C₄	—	2	1	no	—
728	C₄	—	2	1	no	—
729	C₄	—	4	2	no	—
730	C₄	—	4	1	no	—
731	C₄	—	4	1	no	—
732	C₄	—	4	1	no	—
733	C₄	—	4	1	no	—
734	C₄	—	8	1	no	—
735	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
736	C₄	C₅×#520	1	1	yes	characteristic
737	C₄	C₅×D₄²	1	1	yes	characteristic
738	C₄	C₅×#548	1	1	yes	characteristic
739	C₂	—	2	1	no	—
740	C₂	—	2	1	no	—
741	C₂	—	4	2	no	—
742	C₂	—	8	1	no	—
743	C₂	—	8	1	no	—
744	C₂	C₅×#2361	1	1	yes	characteristic
745	C₂	C₅×#2955	1	1	yes	characteristic
746	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×#3035	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₅×C₄⋊C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#444	C₂	semidirect
3. C₂×C₅×#443	C₂	semidirect
4. C₅×#2935	C₂	semidirect
5. C₅×#2906	C₂	semidirect
6. C₅×#1963	C₂	semidirect
7. C₅×#1950	C₂	semidirect
8. C₅×#1938	C₂	semidirect
9. C₅×#1937	C₂	semidirect
10. C₅×#1876	C₂	semidirect
11. C₅×#1876	C₂	semidirect
12. C₅×#1866	C₂	semidirect
13. C₅×#1866	C₂	semidirect
14. C₅×#1768	C₂	semidirect
15. C₅×#1759	C₂	semidirect
24. C₅×#464	C₄	semidirect
25. C₅×#464	C₄	semidirect
26. C₅×#463	C₄	semidirect
27. C₅×#463	C₄	semidirect
28. C₅×#462	C₄	semidirect
29. C₅×#461	C₄	semidirect
30. C₅×#460	C₄	semidirect
31. C₅×#459	C₄	semidirect
69. #23017	C₅	direct (N × H)
150. C₅×#104	D₄	semidirect
170. C₂×#444	C₂×C₅	semidirect
171. C₂×#443	C₂×C₅	semidirect
172. #2935	C₂×C₅	semidirect
173. #2906	C₂×C₅	semidirect
174. #1963	C₂×C₅	semidirect
175. #1950	C₂×C₅	semidirect
176. #1938	C₂×C₅	semidirect
177. #1937	C₂×C₅	semidirect
178. #1876	C₂×C₅	semidirect
179. #1876	C₂×C₅	semidirect
180. #1866	C₂×C₅	semidirect
181. #1866	C₂×C₅	semidirect
182. #1768	C₂×C₅	semidirect
183. #1759	C₂×C₅	semidirect
293. #464	C₄×C₅	semidirect
294. #464	C₄×C₅	semidirect
295. #463	C₄×C₅	semidirect
296. #463	C₄×C₅	semidirect
297. #462	C₄×C₅	semidirect
298. #461	C₄×C₅	semidirect
299. #460	C₄×C₅	semidirect
300. #459	C₄×C₅	semidirect
485. #104	C₅×D₄	semidirect
709. C₅	#23017	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×#3035	2
C₂×C₅×#444	2
C₂×C₅×#443	2
C₅×#2935	2
C₅×#2906	2
C₅×#1963	2
C₅×#1950	2
C₅×#1938	2
C₅×#1937	2
C₅×#1876	2
C₅×#1866	2
C₅×#1768	2
C₅×#1759	2
#23017	5

Subgroups — C5×#23017 #11945737

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#23017 #11945737