Subgroups — C₅×#26938 #11949658

Order 1280.

946 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×#482	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#463	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2427	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2363	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2088	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2042	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2000	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1999	C₂	1	1	yes	maximal, characteristic
9	C₅×#1968	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1928	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1923	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1879	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1873	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1862	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₅×#102	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₅×SD₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₅×D₈	C₂²	1	1	yes	characteristic
18	C₂×C₅×#124	C₂²	1	1	yes	characteristic
19	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₅×#121	C₂²	1	1	yes	characteristic
21	C₂×C₅×#121	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	C₂×C₅×#117	C₂²	1	1	yes	characteristic
25	C₅×#482	—	2	4	no	—
26	C₅×#463	—	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×#102	C₂²	1	1	yes	characteristic
34	C₂×C₅×#102	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×#102	C₂²	1	1	yes	characteristic
38	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
39	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
41	C₅×#397	—	2	1	no	—
42	C₅×#394	—	2	1	no	—
43	C₅×#391	C₂²	1	1	yes	characteristic
44	C₅×#390	—	2	1	no	—
45	C₅×#390	C₂²	1	1	yes	characteristic
46	C₅×#389	C₂²	1	1	yes	characteristic
47	C₅×#389	C₂²	1	1	yes	characteristic
48	C₅×#388	—	2	1	no	—
49	C₅×#386	—	2	1	no	—
50	C₅×#386	—	2	1	no	—
51	C₅×#380	—	2	1	no	—
52	C₄×C₅×C₄⋊C₄	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	#26938	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
62	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
63	C₂²×C₅×D₄	—	2	1	no	—
64	C₂²×C₅×D₄	—	2	1	no	—
65	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
66	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₅	—	2	1	no	—
68	C₂³×C₄×C₅	—	2	1	no	—
69	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
70	C₂×C₅×SD₁₆	—	2	2	no	—
71	C₂×C₅×SD₁₆	—	2	2	no	—
72	C₂×C₅×SD₁₆	—	4	1	no	—
73	C₂×C₅×D₈	—	2	2	no	—
74	C₂×C₅×D₈	—	2	2	no	—
75	C₂×C₅×D₈	—	4	1	no	—
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	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
80	C₅×#124	—	2	2	no	—
81	C₅×#124	—	4	1	no	—
82	C₅×C₂²⋊Q₈	—	2	2	no	—
83	C₅×C₂²⋊Q₈	—	4	1	no	—
84	C₅×#121	—	2	2	no	—
85	C₅×#121	—	2	2	no	—
86	C₅×#121	—	2	2	no	—
87	C₅×#121	—	4	1	no	—
88	C₄×C₅×D₄	—	2	2	no	—
89	C₄×C₅×D₄	—	2	2	no	—
90	C₄×C₅×D₄	—	4	1	no	—
91	C₄×C₅×D₄	—	4	1	no	—
92	C₅×#117	—	2	2	no	—
93	C₅×#117	—	4	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	C₂³	1	1	yes	characteristic
98	C₂×C₅×C₄⋊C₄	C₂³	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×C₂²⋊C₄	—	2	1	no	—
103	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
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×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	—	2	1	no	—
112	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
113	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
114	C₂×C₄²×C₅	—	2	1	no	—
115	C₂×C₄²×C₅	—	2	1	no	—
116	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
118	C₅×#107	—	2	2	no	—
119	C₅×#106	—	2	2	no	—
120	C₅×C₄⋊C₈	—	2	2	no	—
121	C₅×#103	—	2	2	no	—
122	C₅×#103	—	2	2	no	—
123	C₅×#103	—	4	1	no	—
124	C₅×#102	—	2	2	no	—
125	C₅×#102	—	2	2	no	—
126	C₅×#102	—	2	2	no	—
127	C₅×#102	—	4	1	no	—
128	C₅×#102	D₄	1	4	yes	complemented
129	C₅×C₂²⋊C₈	—	2	2	no	—
130	C₅×C₂²⋊C₈	—	4	1	no	—
131	C₄×C₅×C₈	—	4	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	D₄	1	1	yes	characteristic
138	C₅×#95	D₄	1	1	yes	characteristic
139	C₂×#482	C₂×C₅	1	1	yes	characteristic, complemented
140	C₂×#463	C₂×C₅	1	1	yes	characteristic, complemented
141	#2427	C₂×C₅	1	1	yes	characteristic, complemented
142	#2363	C₂×C₅	1	1	yes	characteristic, complemented
143	#2088	C₂×C₅	1	1	yes	characteristic, complemented
144	#2042	C₂×C₅	1	1	yes	characteristic, complemented
145	#2000	C₂×C₅	1	1	yes	characteristic, complemented
146	#1999	C₂×C₅	1	1	yes	characteristic
147	#1968	C₂×C₅	1	1	yes	characteristic, complemented
148	#1928	C₂×C₅	1	1	yes	characteristic, complemented
149	#1923	C₂×C₅	1	1	yes	characteristic, complemented
150	#1879	C₂×C₅	1	1	yes	characteristic, complemented
151	#1873	C₂×C₅	1	1	yes	characteristic, complemented
152	#1862	C₂×C₅	1	1	yes	characteristic, complemented
153	C₄×#102	C₂×C₅	1	1	yes	characteristic, complemented
154	C₂⁴×C₅	—	2	1	no	—
155	C₂⁴×C₅	—	2	1	no	—
156	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
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×D₄	—	2	4	no	—
164	C₂×C₅×D₄	—	2	1	no	—
165	C₂×C₅×D₄	—	2	1	no	—
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	—	2	1	no	—
170	C₂×C₅×D₄	—	2	1	no	—
171	C₂×C₅×D₄	—	2	1	no	—
172	C₂×C₅×D₄	—	2	1	no	—
173	C₂×C₅×D₄	—	2	1	no	—
174	C₂×C₅×D₄	—	4	2	no	—
175	C₂×C₅×D₄	—	4	2	no	—
176	C₂×C₅×D₄	—	8	1	no	—
177	C₂×C₅×D₄	—	8	1	no	—
178	C₂×C₅×D₄	—	8	1	no	—
179	C₂×C₅×D₄	C₂×D₄	1	2	yes	—
180	C₂×C₅×D₄	#41	1	2	yes	—
181	C₂²×C₄×C₅	—	2	1	no	—
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	—	2	1	no	—
192	C₂²×C₄×C₅	—	2	1	no	—
193	C₂²×C₄×C₅	—	4	2	no	—
194	C₂²×C₄×C₅	—	4	2	no	—
195	C₂²×C₄×C₅	—	4	2	no	—
196	C₂²×C₄×C₅	—	4	2	no	—
197	C₂²×C₄×C₅	—	8	1	no	—
198	C₂²×C₄×C₅	—	8	1	no	—
199	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
205	C₅×SD₁₆	—	4	4	no	—
206	C₅×D₈	—	4	4	no	—
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	C₂×D₄	1	2	yes	—
219	C₅×C₄⋊C₄	—	2	1	no	—
220	C₅×C₄⋊C₄	—	2	1	no	—
221	C₅×C₄⋊C₄	—	2	1	no	—
222	C₅×C₄⋊C₄	—	2	1	no	—
223	C₅×C₄⋊C₄	—	2	1	no	—
224	C₅×C₄⋊C₄	—	2	1	no	—
225	C₅×C₄⋊C₄	—	2	1	no	—
226	C₅×C₄⋊C₄	—	4	2	no	—
227	C₅×C₄⋊C₄	—	8	1	no	—
228	C₅×C₄⋊C₄	—	8	1	no	—
229	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
230	C₅×C₄⋊C₄	#41	1	2	yes	—
231	C₅×C₄⋊C₄	#41	1	2	yes	—
232	C₅×C₂²⋊C₄	—	2	4	no	—
233	C₅×C₂²⋊C₄	—	2	2	no	—
234	C₅×C₂²⋊C₄	—	4	1	no	—
235	C₅×C₂²⋊C₄	—	4	2	no	—
236	C₅×C₂²⋊C₄	—	4	2	no	—
237	C₅×C₂²⋊C₄	—	4	2	no	—
238	C₅×C₂²⋊C₄	—	4	2	no	—
239	C₅×C₂²⋊C₄	—	4	2	no	—
240	C₅×C₂²⋊C₄	—	4	2	no	—
241	C₅×C₂²⋊C₄	—	4	2	no	—
242	C₅×C₂²⋊C₄	—	4	2	no	—
243	C₅×C₂²⋊C₄	—	8	1	no	—
244	C₄²×C₅	—	2	1	no	—
245	C₄²×C₅	—	2	1	no	—
246	C₄²×C₅	—	2	1	no	—
247	C₄²×C₅	—	2	1	no	—
248	C₄²×C₅	—	4	2	no	—
249	C₄²×C₅	—	8	1	no	—
250	C₂²×SD₁₆	C₂²×C₅	1	1	yes	characteristic
251	C₂²×D₈	C₂²×C₅	1	1	yes	characteristic
252	C₂×#124	C₂²×C₅	1	1	yes	characteristic
253	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
254	C₂×#121	C₂²×C₅	1	1	yes	characteristic
255	C₂×#121	C₂²×C₅	1	1	yes	characteristic
256	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
257	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
258	C₂×#117	C₂²×C₅	1	1	yes	characteristic
259	#482	—	2	4	no	—
260	#463	—	2	4	no	—
261	C₂×#107	C₂²×C₅	1	1	yes	characteristic
262	C₂×#106	C₂²×C₅	1	1	yes	characteristic
263	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
264	C₂×#103	C₂²×C₅	1	1	yes	characteristic
265	C₂×#103	C₂²×C₅	1	1	yes	characteristic
266	C₂×#103	C₂²×C₅	1	1	yes	characteristic
267	C₂×#102	C₂²×C₅	1	1	yes	characteristic
268	C₂×#102	C₂²×C₅	1	1	yes	characteristic
269	C₂×#102	C₂²×C₅	1	1	yes	characteristic
270	C₂×#102	C₂²×C₅	1	1	yes	characteristic
271	C₂×#102	C₂²×C₅	1	1	yes	characteristic
272	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
273	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
274	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
275	#397	—	2	1	no	—
276	#394	—	2	1	no	—
277	#391	C₂²×C₅	1	1	yes	characteristic
278	#390	—	2	1	no	—
279	#390	C₂²×C₅	1	1	yes	characteristic
280	#389	C₂²×C₅	1	1	yes	characteristic
281	#389	C₂²×C₅	1	1	yes	characteristic
282	#388	—	2	1	no	—
283	#386	—	2	1	no	—
284	#386	—	2	1	no	—
285	#380	—	2	1	no	—
286	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
287	C₄×C₂²⋊C₄	—	2	1	no	—
288	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
289	#340	C₂²×C₅	1	1	yes	characteristic
290	#340	C₂²×C₅	1	1	yes	characteristic
291	#340	C₂²×C₅	1	1	yes	characteristic
292	#340	C₂²×C₅	1	1	yes	characteristic
293	#336	C₂²×C₅	1	1	yes	characteristic
294	#336	C₂²×C₅	1	1	yes	characteristic
295	C₂³×C₅	—	2	2	no	—
296	C₂³×C₅	—	2	1	no	—
297	C₂³×C₅	—	2	2	no	—
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	—	4	1	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	—	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	C₂²×D₄	1	1	yes	characteristic
317	C₅×Q₈	—	4	1	no	—
318	C₅×Q₈	—	4	1	no	—
319	C₅×Q₈	—	4	1	no	—
320	C₅×Q₈	—	4	1	no	—
321	C₅×D₄	—	2	2	no	—
322	C₅×D₄	—	2	2	no	—
323	C₅×D₄	—	2	2	no	—
324	C₅×D₄	—	2	2	no	—
325	C₅×D₄	—	4	1	no	—
326	C₅×D₄	—	4	1	no	—
327	C₅×D₄	—	4	1	no	—
328	C₅×D₄	—	4	1	no	—
329	C₅×D₄	—	8	4	no	—
330	C₅×D₄	—	8	4	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	2	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	2	no	—
339	C₂×C₄×C₅	—	2	1	no	—
340	C₂×C₄×C₅	—	2	2	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	—	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	—	8	4	no	—
369	C₂×C₄×C₅	#135	1	2	yes	—
370	C₂×C₄×C₅	C₂²×D₄	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	C₂×#41	1	1	yes	characteristic
374	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
375	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
376	C₅×C₈	—	2	2	no	—
377	C₅×C₈	—	4	1	no	—
378	C₅×C₈	—	4	1	no	—
379	C₅×C₈	—	4	1	no	—
380	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
381	C₂²×D₄	—	2	1	no	—
382	C₂²×D₄	—	2	1	no	—
383	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
384	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
385	C₂³×C₄	—	2	1	no	—
386	C₂³×C₄	—	2	1	no	—
387	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
388	C₂×SD₁₆	—	2	2	no	—
389	C₂×SD₁₆	—	2	2	no	—
390	C₂×SD₁₆	—	4	1	no	—
391	C₂×D₈	—	2	2	no	—
392	C₂×D₈	—	2	2	no	—
393	C₂×D₈	—	4	1	no	—
394	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
395	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
396	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
397	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
398	#124	—	2	2	no	—
399	#124	—	4	1	no	—
400	C₂²⋊Q₈	—	2	2	no	—
401	C₂²⋊Q₈	—	4	1	no	—
402	#121	—	2	2	no	—
403	#121	—	2	2	no	—
404	#121	—	2	2	no	—
405	#121	—	4	1	no	—
406	C₄×D₄	—	2	2	no	—
407	C₄×D₄	—	2	2	no	—
408	C₄×D₄	—	4	1	no	—
409	C₄×D₄	—	4	1	no	—
410	#117	—	2	2	no	—
411	#117	—	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	C₂³×C₅	1	1	yes	characteristic
416	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
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×C₂²⋊C₄	—	2	1	no	—
421	C₂×C₂²⋊C₄	—	2	1	no	—
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	—	2	1	no	—
429	C₂×C₂²⋊C₄	—	2	1	no	—
430	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
431	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
432	C₂×C₄²	—	2	1	no	—
433	C₂×C₄²	—	2	1	no	—
434	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
435	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
436	#107	—	2	2	no	—
437	#106	—	2	2	no	—
438	C₄⋊C₈	—	2	2	no	—
439	#103	—	2	2	no	—
440	#103	—	2	2	no	—
441	#103	—	4	1	no	—
442	#102	—	2	2	no	—
443	#102	—	2	2	no	—
444	#102	—	2	2	no	—
445	#102	—	4	1	no	—
446	#102	C₅×D₄	1	4	yes	complemented
447	C₂²⋊C₈	—	2	2	no	—
448	C₂²⋊C₈	—	4	1	no	—
449	C₄×C₈	—	4	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	—	4	1	no	—
458	C₂²×C₅	—	4	2	no	—
459	C₂²×C₅	—	4	1	no	—
460	C₂²×C₅	—	4	2	no	—
461	C₂²×C₅	—	4	1	no	—
462	C₂²×C₅	—	4	2	no	—
463	C₂²×C₅	—	4	2	no	—
464	C₂²×C₅	—	4	1	no	—
465	C₂²×C₅	—	4	2	no	—
466	C₂²×C₅	—	4	1	no	—
467	C₂²×C₅	—	4	2	no	—
468	C₂²×C₅	—	4	1	no	—
469	C₂²×C₅	—	4	1	no	—
470	C₂²×C₅	—	8	1	no	—
471	C₂²×C₅	—	8	1	no	—
472	C₂²×C₅	—	8	1	no	—
473	C₂²×C₅	—	8	1	no	—
474	C₂²×C₅	—	8	1	no	—
475	C₂²×C₅	—	8	1	no	—
476	C₂²×C₅	—	8	1	no	—
477	C₂²×C₅	—	8	1	no	—
478	C₂²×C₅	#525	1	1	yes	characteristic
479	C₂²×C₅	D₄²	1	1	yes	characteristic
480	C₂²×C₅	#546	1	1	yes	characteristic
481	C₂²×C₅	C₂×#135	1	1	yes	characteristic
482	C₂²×C₅	#575	1	1	yes	characteristic
483	C₂²×C₅	#576	1	1	yes	characteristic
484	C₂²×C₅	#577	1	1	yes	characteristic
485	C₄×C₅	—	2	2	no	—
486	C₄×C₅	—	4	2	no	—
487	C₄×C₅	—	4	1	no	—
488	C₄×C₅	—	4	1	no	—
489	C₄×C₅	—	4	2	no	—
490	C₄×C₅	—	4	1	no	—
491	C₄×C₅	—	4	2	no	—
492	C₄×C₅	—	4	1	no	—
493	C₄×C₅	—	8	1	no	—
494	C₄×C₅	—	8	1	no	—
495	C₄×C₅	—	8	1	no	—
496	C₄×C₅	#532	1	1	yes	characteristic
497	C₄×C₅	#540	1	1	yes	characteristic
498	C₄×C₅	#546	1	1	yes	characteristic
499	C₄×C₅	#553	1	1	yes	characteristic
500	C₂⁴	—	2	1	no	—
501	C₂⁴	—	2	1	no	—
502	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
503	C₂×Q₈	—	2	1	no	—
504	C₂×Q₈	—	2	1	no	—
505	C₂×Q₈	—	2	1	no	—
506	C₂×Q₈	—	2	1	no	—
507	C₂×Q₈	—	2	1	no	—
508	C₂×Q₈	—	2	1	no	—
509	C₂×D₄	—	2	4	no	—
510	C₂×D₄	—	2	1	no	—
511	C₂×D₄	—	2	1	no	—
512	C₂×D₄	—	2	1	no	—
513	C₂×D₄	—	2	1	no	—
514	C₂×D₄	—	2	1	no	—
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	—	8	1	no	—
524	C₂×D₄	—	8	1	no	—
525	C₂×D₄	C₂×C₅×D₄	1	2	yes	—
526	C₂×D₄	C₅×#41	1	2	yes	—
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	—	2	1	no	—
539	C₂²×C₄	—	4	2	no	—
540	C₂²×C₄	—	4	2	no	—
541	C₂²×C₄	—	4	2	no	—
542	C₂²×C₄	—	4	2	no	—
543	C₂²×C₄	—	8	1	no	—
544	C₂²×C₄	—	8	1	no	—
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	C₂×C₅×D₄	1	1	yes	characteristic
549	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
550	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
551	SD₁₆	—	4	4	no	—
552	D₈	—	4	4	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	—	2	1	no	—
563	C₂×C₈	—	2	1	no	—
564	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
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	—	4	2	no	—
573	C₄⋊C₄	—	8	1	no	—
574	C₄⋊C₄	—	8	1	no	—
575	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
576	C₄⋊C₄	C₅×#41	1	2	yes	—
577	C₄⋊C₄	C₅×#41	1	2	yes	—
578	C₂²⋊C₄	—	2	4	no	—
579	C₂²⋊C₄	—	2	2	no	—
580	C₂²⋊C₄	—	4	1	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	C₂²⋊C₄	—	4	2	no	—
587	C₂²⋊C₄	—	4	2	no	—
588	C₂²⋊C₄	—	4	2	no	—
589	C₂²⋊C₄	—	8	1	no	—
590	C₄²	—	2	1	no	—
591	C₄²	—	2	1	no	—
592	C₄²	—	2	1	no	—
593	C₄²	—	2	1	no	—
594	C₄²	—	4	2	no	—
595	C₄²	—	8	1	no	—
596	C₂×C₅	—	8	1	no	—
597	C₂×C₅	—	8	2	no	—
598	C₂×C₅	—	8	2	no	—
599	C₂×C₅	#2464	1	1	yes	characteristic
600	C₂×C₅	#3102	1	1	yes	characteristic
601	C₂×C₅	#3118	1	1	yes	characteristic
602	C₂×C₅	#3273	1	1	yes	characteristic
603	C₂×C₅	#3284	1	1	yes	characteristic
604	C₂×C₅	#3297	1	1	yes	characteristic
605	C₂×C₅	#3321	1	1	yes	characteristic
606	C₂³	—	2	2	no	—
607	C₂³	—	2	1	no	—
608	C₂³	—	2	2	no	—
609	C₂³	—	2	1	no	—
610	C₂³	—	2	1	no	—
611	C₂³	—	2	1	no	—
612	C₂³	—	2	1	no	—
613	C₂³	—	2	1	no	—
614	C₂³	—	2	1	no	—
615	C₂³	—	4	1	no	—
616	C₂³	—	4	1	no	—
617	C₂³	—	4	1	no	—
618	C₂³	—	4	1	no	—
619	C₂³	—	4	1	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	C₂²×C₅×D₄	1	1	yes	characteristic
628	Q₈	—	4	1	no	—
629	Q₈	—	4	1	no	—
630	Q₈	—	4	1	no	—
631	Q₈	—	4	1	no	—
632	D₄	—	2	2	no	—
633	D₄	—	2	2	no	—
634	D₄	—	2	2	no	—
635	D₄	—	2	2	no	—
636	D₄	—	4	1	no	—
637	D₄	—	4	1	no	—
638	D₄	—	4	1	no	—
639	D₄	—	4	1	no	—
640	D₄	—	8	4	no	—
641	D₄	—	8	4	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	2	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	1	no	—
658	C₂×C₄	—	2	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	—	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	—	8	4	no	—
679	C₂×C₄	—	8	4	no	—
680	C₂×C₄	C₅×#135	1	2	yes	—
681	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
682	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
683	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
684	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
685	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
686	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
687	C₈	—	2	2	no	—
688	C₈	—	4	1	no	—
689	C₈	—	4	1	no	—
690	C₈	—	4	1	no	—
691	C₅	#26938	1	1	yes	characteristic, direct product factor, Sylow
692	C₂²	—	4	1	no	—
693	C₂²	—	4	2	no	—
694	C₂²	—	4	1	no	—
695	C₂²	—	4	2	no	—
696	C₂²	—	4	1	no	—
697	C₂²	—	4	1	no	—
698	C₂²	—	4	1	no	—
699	C₂²	—	4	2	no	—
700	C₂²	—	4	1	no	—
701	C₂²	—	4	2	no	—
702	C₂²	—	4	1	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	C₅×#525	1	1	yes	characteristic
714	C₂²	C₅×D₄²	1	1	yes	characteristic
715	C₂²	C₅×#546	1	1	yes	characteristic
716	C₂²	C₂×C₅×#135	1	1	yes	characteristic
717	C₂²	C₅×#575	1	1	yes	characteristic
718	C₂²	C₅×#576	1	1	yes	characteristic
719	C₂²	C₅×#577	1	1	yes	characteristic
720	C₄	—	2	2	no	—
721	C₄	—	4	1	no	—
722	C₄	—	4	2	no	—
723	C₄	—	4	1	no	—
724	C₄	—	4	2	no	—
725	C₄	—	4	1	no	—
726	C₄	—	4	2	no	—
727	C₄	—	4	1	no	—
728	C₄	—	8	1	no	—
729	C₄	—	8	1	no	—
730	C₄	—	8	1	no	—
731	C₄	C₅×#532	1	1	yes	characteristic
732	C₄	C₅×#540	1	1	yes	characteristic
733	C₄	C₅×#546	1	1	yes	characteristic
734	C₄	C₅×#553	1	1	yes	characteristic
735	C₂	—	8	1	no	—
736	C₂	—	8	2	no	—
737	C₂	—	8	2	no	—
738	C₂	C₅×#2464	1	1	yes	characteristic
739	C₂	C₅×#3102	1	1	yes	characteristic
740	C₂	C₅×#3118	1	1	yes	characteristic
741	C₂	C₅×#3273	1	1	yes	characteristic
742	C₂	C₅×#3284	1	1	yes	characteristic
743	C₂	C₅×#3297	1	1	yes	characteristic
744	C₂	C₅×#3321	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₅×#1999	C₂
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
1. C₂×C₅×#482	C₂	semidirect
2. C₂×C₅×#463	C₂	semidirect
3. C₅×#2427	C₂	semidirect
4. C₅×#2363	C₂	semidirect
5. C₅×#2088	C₂	semidirect
6. C₅×#2042	C₂	semidirect
7. C₅×#2000	C₂	semidirect
9. C₅×#1968	C₂	semidirect
10. C₅×#1928	C₂	semidirect
11. C₅×#1923	C₂	semidirect
12. C₅×#1879	C₂	semidirect
13. C₅×#1873	C₂	semidirect
14. C₅×#1862	C₂	semidirect
15. C₄×C₅×#102	C₂	semidirect
61. #26938	C₅	direct (N × H)
128. C₅×#102	D₄	semidirect
139. C₂×#482	C₂×C₅	semidirect
140. C₂×#463	C₂×C₅	semidirect
141. #2427	C₂×C₅	semidirect
142. #2363	C₂×C₅	semidirect
143. #2088	C₂×C₅	semidirect
144. #2042	C₂×C₅	semidirect
145. #2000	C₂×C₅	semidirect
147. #1968	C₂×C₅	semidirect
148. #1928	C₂×C₅	semidirect
149. #1923	C₂×C₅	semidirect
150. #1879	C₂×C₅	semidirect
151. #1873	C₂×C₅	semidirect
152. #1862	C₂×C₅	semidirect
153. C₄×#102	C₂×C₅	semidirect
446. #102	C₅×D₄	semidirect
691. C₅	#26938	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×#482	2
C₂×C₅×#463	2
C₅×#2427	2
C₅×#2363	2
C₅×#2088	2
C₅×#2042	2
C₅×#2000	2
C₅×#1999	2
C₅×#1968	2
C₅×#1928	2
C₅×#1923	2
C₅×#1879	2
C₅×#1873	2
C₅×#1862	2
C₄×C₅×#102	2
#26938	5

Subgroups — C5×#26938 #11949658

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#26938 #11949658