Subgroups — C₅×#26836 #11949556

Order 1280.

842 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#487	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#440	C₂	1	1	yes	maximal, characteristic
3	C₅×#2452	C₂	1	1	yes	maximal, characteristic
4	C₅×#2446	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2068	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2057	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2055	C₂	1	1	yes	maximal, characteristic
8	C₅×#2013	C₂	1	1	yes	maximal, characteristic
9	C₅×#1973	C₂	1	1	yes	maximal, characteristic
10	C₅×#1935	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1935	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1934	C₂	1	1	yes	maximal, characteristic
13	C₅×#1877	C₂	1	1	yes	maximal, characteristic
14	C₅×#1863	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1771	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	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₅×C₂²⋊Q₈	—	2	1	no	—
21	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
23	C₅×#487	—	2	4	no	—
24	C₅×#440	—	2	4	no	—
25	C₂×C₅×#107	C₂²	1	1	yes	characteristic
26	C₂×C₅×#107	C₂²	1	1	yes	characteristic
27	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₅×#103	C₂²	1	1	yes	characteristic
29	C₂×C₅×#103	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×#102	C₂²	1	1	yes	characteristic
35	C₂×C₅×#102	C₂²	1	1	yes	characteristic
36	C₂×C₅×#97	C₂²	1	1	yes	characteristic
37	C₂×C₅×#97	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
39	C₅×#400	—	2	1	no	—
40	C₅×#398	—	2	1	no	—
41	C₅×#396	—	2	1	no	—
42	C₅×#393	—	2	1	no	—
43	C₅×#391	C₂²	1	1	yes	characteristic
44	C₅×#391	C₂²	1	1	yes	characteristic
45	C₅×#391	C₂²	1	1	yes	characteristic
46	C₅×#390	C₂²	1	1	yes	characteristic
47	C₅×#390	C₂²	1	1	yes	characteristic
48	C₅×#389	C₂²	1	1	yes	characteristic
49	C₅×#389	C₂²	1	1	yes	characteristic
50	C₅×#389	C₂²	1	1	yes	characteristic
51	C₅×#387	—	2	1	no	—
52	C₅×#387	—	2	1	no	—
53	C₅×#385	—	2	1	no	—
54	C₄×C₅×C₄⋊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	#26836	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
62	C₂²×C₅×Q₈	—	2	1	no	—
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	C₂×C₅×SD₁₆	—	2	2	no	—
68	C₂×C₅×SD₁₆	—	2	2	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	—	4	1	no	—
73	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
74	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
75	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
76	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
77	C₅×C₄⋊Q₈	—	2	2	no	—
78	C₅×C₄⋊Q₈	—	2	2	no	—
79	C₅×C₄⋊Q₈	—	4	1	no	—
80	C₅×C₄⋊Q₈	—	4	1	no	—
81	C₅×C₂²⋊Q₈	—	4	4	no	—
82	C₄×C₅×Q₈	—	2	2	no	—
83	C₄×C₅×Q₈	—	4	1	no	—
84	C₄×C₅×D₄	—	2	2	no	—
85	C₄×C₅×D₄	—	4	1	no	—
86	C₂×C₅×C₄⋊C₄	—	2	1	no	—
87	C₂×C₅×C₄⋊C₄	—	2	1	no	—
88	C₂×C₅×C₄⋊C₄	—	2	1	no	—
89	C₂×C₅×C₄⋊C₄	—	2	1	no	—
90	C₂×C₅×C₄⋊C₄	—	2	1	no	—
91	C₂×C₅×C₄⋊C₄	—	2	1	no	—
92	C₂×C₅×C₄⋊C₄	—	2	1	no	—
93	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
94	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
95	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
96	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄	—	2	1	no	—
101	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
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×C₄²×C₅	—	2	1	no	—
106	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
109	C₅×#107	—	2	2	no	—
110	C₅×#107	—	4	1	no	—
111	C₅×C₄⋊C₈	—	2	2	no	—
112	C₅×#103	—	2	2	no	—
113	C₅×#103	—	2	2	no	—
114	C₅×#103	—	2	2	no	—
115	C₅×#103	—	2	2	no	—
116	C₅×#103	—	2	2	no	—
117	C₅×#103	D₄	1	4	yes	—
118	C₅×#102	—	2	2	no	—
119	C₅×#102	—	2	2	no	—
120	C₅×#97	—	2	2	no	—
121	C₅×#97	—	2	2	no	—
122	C₄×C₅×C₈	—	2	2	no	—
123	C₅×#95	—	2	1	no	—
124	C₅×#95	—	2	1	no	—
125	C₅×#95	—	2	1	no	—
126	C₅×#95	—	2	1	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	D₄	1	1	yes	characteristic
133	C₅×#95	D₄	1	1	yes	characteristic
134	C₂×#487	C₂×C₅	1	1	yes	characteristic, complemented
135	C₂×#440	C₂×C₅	1	1	yes	characteristic
136	#2452	C₂×C₅	1	1	yes	characteristic
137	#2446	C₂×C₅	1	1	yes	characteristic, complemented
138	#2068	C₂×C₅	1	1	yes	characteristic, complemented
139	#2057	C₂×C₅	1	1	yes	characteristic, complemented
140	#2055	C₂×C₅	1	1	yes	characteristic
141	#2013	C₂×C₅	1	1	yes	characteristic
142	#1973	C₂×C₅	1	1	yes	characteristic
143	#1935	C₂×C₅	1	1	yes	characteristic, complemented
144	#1935	C₂×C₅	1	1	yes	characteristic, complemented
145	#1934	C₂×C₅	1	1	yes	characteristic
146	#1877	C₂×C₅	1	1	yes	characteristic
147	#1863	C₂×C₅	1	1	yes	characteristic, complemented
148	#1771	C₂×C₅	1	1	yes	characteristic, complemented
149	C₂⁴×C₅	—	2	1	no	—
150	C₂×C₅×Q₈	—	2	1	no	—
151	C₂×C₅×Q₈	—	2	1	no	—
152	C₂×C₅×Q₈	—	2	1	no	—
153	C₂×C₅×Q₈	—	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	—	4	2	no	—
162	C₂×C₅×Q₈	—	4	2	no	—
163	C₂×C₅×Q₈	—	8	1	no	—
164	C₂×C₅×Q₈	C₂×D₄	1	2	yes	—
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	#41	1	2	yes	—
171	C₂²×C₄×C₅	—	2	1	no	—
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	1	no	—
177	C₂²×C₄×C₅	—	2	1	no	—
178	C₂²×C₄×C₅	—	4	2	no	—
179	C₂²×C₄×C₅	—	4	2	no	—
180	C₂²×C₄×C₅	—	8	1	no	—
181	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
188	C₅×SD₁₆	—	2	8	no	—
189	C₅×SD₁₆	—	4	4	no	—
190	C₂×C₅×C₈	—	2	1	no	—
191	C₂×C₅×C₈	—	2	1	no	—
192	C₂×C₅×C₈	—	2	1	no	—
193	C₂×C₅×C₈	—	2	1	no	—
194	C₂×C₅×C₈	—	2	1	no	—
195	C₂×C₅×C₈	—	2	1	no	—
196	C₂×C₅×C₈	—	2	1	no	—
197	C₂×C₅×C₈	—	2	1	no	—
198	C₂×C₅×C₈	—	2	1	no	—
199	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
200	C₂×C₅×C₈	#41	1	2	yes	—
201	C₂×C₅×C₈	#41	1	2	yes	—
202	C₅×C₄⋊C₄	—	2	2	no	—
203	C₅×C₄⋊C₄	—	2	2	no	—
204	C₅×C₄⋊C₄	—	2	1	no	—
205	C₅×C₄⋊C₄	—	2	1	no	—
206	C₅×C₄⋊C₄	—	2	1	no	—
207	C₅×C₄⋊C₄	—	2	1	no	—
208	C₅×C₄⋊C₄	—	2	1	no	—
209	C₅×C₄⋊C₄	—	2	1	no	—
210	C₅×C₄⋊C₄	—	2	1	no	—
211	C₅×C₄⋊C₄	—	2	1	no	—
212	C₅×C₄⋊C₄	—	2	1	no	—
213	C₅×C₄⋊C₄	—	4	2	no	—
214	C₅×C₄⋊C₄	—	4	2	no	—
215	C₅×C₄⋊C₄	—	4	2	no	—
216	C₅×C₄⋊C₄	—	4	2	no	—
217	C₅×C₄⋊C₄	—	4	2	no	—
218	C₅×C₄⋊C₄	—	4	2	no	—
219	C₅×C₄⋊C₄	—	4	2	no	—
220	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
221	C₅×C₂²⋊C₄	—	4	2	no	—
222	C₅×C₂²⋊C₄	—	4	2	no	—
223	C₅×C₂²⋊C₄	—	4	2	no	—
224	C₅×C₂²⋊C₄	—	4	2	no	—
225	C₅×C₂²⋊C₄	—	8	1	no	—
226	C₄²×C₅	—	2	1	no	—
227	C₄²×C₅	—	2	1	no	—
228	C₄²×C₅	—	2	1	no	—
229	C₄²×C₅	—	2	1	no	—
230	C₄²×C₅	—	2	1	no	—
231	C₄²×C₅	—	2	1	no	—
232	C₄²×C₅	—	4	2	no	—
233	C₂²×SD₁₆	C₂²×C₅	1	1	yes	characteristic
234	C₂²×SD₁₆	C₂²×C₅	1	1	yes	characteristic
235	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
236	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
237	C₂×C₂²⋊Q₈	—	2	1	no	—
238	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
239	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
240	#487	—	2	4	no	—
241	#440	—	2	4	no	—
242	C₂×#107	C₂²×C₅	1	1	yes	characteristic
243	C₂×#107	C₂²×C₅	1	1	yes	characteristic
244	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
245	C₂×#103	C₂²×C₅	1	1	yes	characteristic
246	C₂×#103	C₂²×C₅	1	1	yes	characteristic
247	C₂×#103	C₂²×C₅	1	1	yes	characteristic
248	C₂×#103	C₂²×C₅	1	1	yes	characteristic
249	C₂×#103	C₂²×C₅	1	1	yes	characteristic
250	C₂×#103	C₂²×C₅	1	1	yes	characteristic
251	C₂×#102	C₂²×C₅	1	1	yes	characteristic
252	C₂×#102	C₂²×C₅	1	1	yes	characteristic
253	C₂×#97	C₂²×C₅	1	1	yes	characteristic
254	C₂×#97	C₂²×C₅	1	1	yes	characteristic
255	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
256	#400	—	2	1	no	—
257	#398	—	2	1	no	—
258	#396	—	2	1	no	—
259	#393	—	2	1	no	—
260	#391	C₂²×C₅	1	1	yes	characteristic
261	#391	C₂²×C₅	1	1	yes	characteristic
262	#391	C₂²×C₅	1	1	yes	characteristic
263	#390	C₂²×C₅	1	1	yes	characteristic
264	#390	C₂²×C₅	1	1	yes	characteristic
265	#389	C₂²×C₅	1	1	yes	characteristic
266	#389	C₂²×C₅	1	1	yes	characteristic
267	#389	C₂²×C₅	1	1	yes	characteristic
268	#387	—	2	1	no	—
269	#387	—	2	1	no	—
270	#385	—	2	1	no	—
271	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
272	#340	C₂²×C₅	1	1	yes	characteristic
273	#340	C₂²×C₅	1	1	yes	characteristic
274	#340	C₂²×C₅	1	1	yes	characteristic
275	#340	C₂²×C₅	1	1	yes	characteristic
276	#336	C₂²×C₅	1	1	yes	characteristic
277	#336	C₂²×C₅	1	1	yes	characteristic
278	C₂³×C₅	—	2	2	no	—
279	C₂³×C₅	—	4	1	no	—
280	C₂³×C₅	—	4	1	no	—
281	C₂³×C₅	—	4	1	no	—
282	C₂³×C₅	—	4	1	no	—
283	C₂³×C₅	—	4	1	no	—
284	C₂³×C₅	—	4	1	no	—
285	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
286	C₅×Q₈	—	2	2	no	—
287	C₅×Q₈	—	2	2	no	—
288	C₅×Q₈	—	4	1	no	—
289	C₅×Q₈	—	4	1	no	—
290	C₅×Q₈	—	4	1	no	—
291	C₅×Q₈	—	4	1	no	—
292	C₅×Q₈	—	4	1	no	—
293	C₅×Q₈	—	4	1	no	—
294	C₅×Q₈	—	8	4	no	—
295	C₅×D₄	—	2	2	no	—
296	C₅×D₄	—	2	2	no	—
297	C₅×D₄	—	4	1	no	—
298	C₅×D₄	—	4	1	no	—
299	C₂×C₄×C₅	—	2	1	no	—
300	C₂×C₄×C₅	—	2	1	no	—
301	C₂×C₄×C₅	—	2	1	no	—
302	C₂×C₄×C₅	—	2	1	no	—
303	C₂×C₄×C₅	—	2	1	no	—
304	C₂×C₄×C₅	—	2	1	no	—
305	C₂×C₄×C₅	—	2	1	no	—
306	C₂×C₄×C₅	—	2	1	no	—
307	C₂×C₄×C₅	—	2	2	no	—
308	C₂×C₄×C₅	—	2	2	no	—
309	C₂×C₄×C₅	—	2	1	no	—
310	C₂×C₄×C₅	—	2	1	no	—
311	C₂×C₄×C₅	—	2	1	no	—
312	C₂×C₄×C₅	—	2	1	no	—
313	C₂×C₄×C₅	—	2	1	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	—	4	1	no	—
318	C₂×C₄×C₅	—	4	1	no	—
319	C₂×C₄×C₅	—	4	1	no	—
320	C₂×C₄×C₅	—	4	1	no	—
321	C₂×C₄×C₅	—	4	1	no	—
322	C₂×C₄×C₅	—	4	1	no	—
323	C₂×C₄×C₅	—	4	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	—	8	4	no	—
337	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
338	C₂×C₄×C₅	#137	1	2	yes	—
339	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
340	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
341	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
342	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
343	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
344	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
345	C₅×C₈	—	2	2	no	—
346	C₅×C₈	—	2	2	no	—
347	C₅×C₈	—	2	2	no	—
348	C₅×C₈	—	4	1	no	—
349	C₂²×Q₈	—	2	1	no	—
350	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
351	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
352	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
353	C₂³×C₄	—	2	1	no	—
354	C₂×SD₁₆	—	2	2	no	—
355	C₂×SD₁₆	—	2	2	no	—
356	C₂×SD₁₆	—	2	2	no	—
357	C₂×SD₁₆	—	2	2	no	—
358	C₂×SD₁₆	—	2	2	no	—
359	C₂×SD₁₆	—	4	1	no	—
360	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
361	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
362	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
363	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
364	C₄⋊Q₈	—	2	2	no	—
365	C₄⋊Q₈	—	2	2	no	—
366	C₄⋊Q₈	—	4	1	no	—
367	C₄⋊Q₈	—	4	1	no	—
368	C₂²⋊Q₈	—	4	4	no	—
369	C₄×Q₈	—	2	2	no	—
370	C₄×Q₈	—	4	1	no	—
371	C₄×D₄	—	2	2	no	—
372	C₄×D₄	—	4	1	no	—
373	C₂×C₄⋊C₄	—	2	1	no	—
374	C₂×C₄⋊C₄	—	2	1	no	—
375	C₂×C₄⋊C₄	—	2	1	no	—
376	C₂×C₄⋊C₄	—	2	1	no	—
377	C₂×C₄⋊C₄	—	2	1	no	—
378	C₂×C₄⋊C₄	—	2	1	no	—
379	C₂×C₄⋊C₄	—	2	1	no	—
380	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
381	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
382	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
383	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
384	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
385	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
386	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
387	C₂×C₂²⋊C₄	—	2	1	no	—
388	C₂×C₂²⋊C₄	—	2	1	no	—
389	C₂×C₂²⋊C₄	—	2	1	no	—
390	C₂×C₂²⋊C₄	—	2	1	no	—
391	C₂×C₂²⋊C₄	—	2	1	no	—
392	C₂×C₄²	—	2	1	no	—
393	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
394	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
395	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
396	#107	—	2	2	no	—
397	#107	—	4	1	no	—
398	C₄⋊C₈	—	2	2	no	—
399	#103	—	2	2	no	—
400	#103	—	2	2	no	—
401	#103	—	2	2	no	—
402	#103	—	2	2	no	—
403	#103	—	2	2	no	—
404	#103	C₅×D₄	1	4	yes	—
405	#102	—	2	2	no	—
406	#102	—	2	2	no	—
407	#97	—	2	2	no	—
408	#97	—	2	2	no	—
409	C₄×C₈	—	2	2	no	—
410	#95	—	2	1	no	—
411	#95	—	2	1	no	—
412	#95	—	2	1	no	—
413	#95	—	2	1	no	—
414	#95	—	2	1	no	—
415	#95	—	2	1	no	—
416	#95	—	2	1	no	—
417	#95	—	2	1	no	—
418	#95	—	2	1	no	—
419	#95	C₅×D₄	1	1	yes	characteristic
420	#95	C₅×D₄	1	1	yes	characteristic
421	C₂²×C₅	—	4	2	no	—
422	C₂²×C₅	—	4	2	no	—
423	C₂²×C₅	—	4	2	no	—
424	C₂²×C₅	—	8	1	no	—
425	C₂²×C₅	—	8	1	no	—
426	C₂²×C₅	—	8	1	no	—
427	C₂²×C₅	—	8	1	no	—
428	C₂²×C₅	#532	1	1	yes	characteristic
429	C₂²×C₅	D₄²	1	1	yes	characteristic
430	C₂²×C₅	#548	1	1	yes	characteristic
431	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
432	C₂²×C₅	C₂×#137	1	1	yes	characteristic
433	C₂²×C₅	#577	1	1	yes	characteristic
434	C₂²×C₅	#578	1	1	yes	characteristic
435	C₄×C₅	—	2	2	no	—
436	C₄×C₅	—	2	2	no	—
437	C₄×C₅	—	4	1	no	—
438	C₄×C₅	—	4	1	no	—
439	C₄×C₅	—	4	2	no	—
440	C₄×C₅	—	4	1	no	—
441	C₄×C₅	—	4	2	no	—
442	C₄×C₅	—	4	1	no	—
443	C₄×C₅	—	8	1	no	—
444	C₄×C₅	—	8	1	no	—
445	C₄×C₅	—	8	1	no	—
446	C₄×C₅	—	8	1	no	—
447	C₄×C₅	—	8	1	no	—
448	C₄×C₅	#525	1	1	yes	characteristic
449	C₄×C₅	#542	1	1	yes	characteristic
450	C₄×C₅	#547	1	1	yes	characteristic
451	C₄×C₅	#551	1	1	yes	characteristic
452	C₂⁴	—	2	1	no	—
453	C₂×Q₈	—	2	1	no	—
454	C₂×Q₈	—	2	1	no	—
455	C₂×Q₈	—	2	1	no	—
456	C₂×Q₈	—	2	1	no	—
457	C₂×Q₈	—	2	1	no	—
458	C₂×Q₈	—	2	1	no	—
459	C₂×Q₈	—	2	1	no	—
460	C₂×Q₈	—	2	1	no	—
461	C₂×Q₈	—	2	1	no	—
462	C₂×Q₈	—	2	1	no	—
463	C₂×Q₈	—	2	1	no	—
464	C₂×Q₈	—	4	2	no	—
465	C₂×Q₈	—	4	2	no	—
466	C₂×Q₈	—	8	1	no	—
467	C₂×Q₈	C₂×C₅×D₄	1	2	yes	—
468	C₂×D₄	—	2	1	no	—
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	—	2	1	no	—
471	C₂×D₄	—	2	1	no	—
472	C₂×D₄	—	2	1	no	—
473	C₂×D₄	C₅×#41	1	2	yes	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	4	2	no	—
482	C₂²×C₄	—	4	2	no	—
483	C₂²×C₄	—	8	1	no	—
484	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
485	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
486	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
487	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
488	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
489	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
490	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
491	SD₁₆	—	2	8	no	—
492	SD₁₆	—	4	4	no	—
493	C₂×C₈	—	2	1	no	—
494	C₂×C₈	—	2	1	no	—
495	C₂×C₈	—	2	1	no	—
496	C₂×C₈	—	2	1	no	—
497	C₂×C₈	—	2	1	no	—
498	C₂×C₈	—	2	1	no	—
499	C₂×C₈	—	2	1	no	—
500	C₂×C₈	—	2	1	no	—
501	C₂×C₈	—	2	1	no	—
502	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
503	C₂×C₈	C₅×#41	1	2	yes	—
504	C₂×C₈	C₅×#41	1	2	yes	—
505	C₄⋊C₄	—	2	2	no	—
506	C₄⋊C₄	—	2	2	no	—
507	C₄⋊C₄	—	2	1	no	—
508	C₄⋊C₄	—	2	1	no	—
509	C₄⋊C₄	—	2	1	no	—
510	C₄⋊C₄	—	2	1	no	—
511	C₄⋊C₄	—	2	1	no	—
512	C₄⋊C₄	—	2	1	no	—
513	C₄⋊C₄	—	2	1	no	—
514	C₄⋊C₄	—	2	1	no	—
515	C₄⋊C₄	—	2	1	no	—
516	C₄⋊C₄	—	4	2	no	—
517	C₄⋊C₄	—	4	2	no	—
518	C₄⋊C₄	—	4	2	no	—
519	C₄⋊C₄	—	4	2	no	—
520	C₄⋊C₄	—	4	2	no	—
521	C₄⋊C₄	—	4	2	no	—
522	C₄⋊C₄	—	4	2	no	—
523	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
524	C₂²⋊C₄	—	4	2	no	—
525	C₂²⋊C₄	—	4	2	no	—
526	C₂²⋊C₄	—	4	2	no	—
527	C₂²⋊C₄	—	4	2	no	—
528	C₂²⋊C₄	—	8	1	no	—
529	C₄²	—	2	1	no	—
530	C₄²	—	2	1	no	—
531	C₄²	—	2	1	no	—
532	C₄²	—	2	1	no	—
533	C₄²	—	2	1	no	—
534	C₄²	—	2	1	no	—
535	C₄²	—	4	2	no	—
536	C₂×C₅	—	8	2	no	—
537	C₂×C₅	#2461	1	1	yes	characteristic
538	C₂×C₅	#3178	1	1	yes	characteristic
539	C₂×C₅	#3182	1	1	yes	characteristic
540	C₂×C₅	#3265	1	1	yes	characteristic
541	C₂×C₅	#3270	1	1	yes	characteristic
542	C₂×C₅	#3367	1	1	yes	characteristic
543	C₂×C₅	#3372	1	1	yes	characteristic
544	C₂³	—	2	2	no	—
545	C₂³	—	4	1	no	—
546	C₂³	—	4	1	no	—
547	C₂³	—	4	1	no	—
548	C₂³	—	4	1	no	—
549	C₂³	—	4	1	no	—
550	C₂³	—	4	1	no	—
551	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
552	Q₈	—	2	2	no	—
553	Q₈	—	2	2	no	—
554	Q₈	—	4	1	no	—
555	Q₈	—	4	1	no	—
556	Q₈	—	4	1	no	—
557	Q₈	—	4	1	no	—
558	Q₈	—	4	1	no	—
559	Q₈	—	4	1	no	—
560	Q₈	—	8	4	no	—
561	D₄	—	2	2	no	—
562	D₄	—	2	2	no	—
563	D₄	—	4	1	no	—
564	D₄	—	4	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
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	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	4	1	no	—
590	C₂×C₄	—	4	1	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	4	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	—	8	4	no	—
603	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
604	C₂×C₄	C₅×#137	1	2	yes	—
605	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
606	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
607	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
608	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
609	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
610	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
611	C₈	—	2	2	no	—
612	C₈	—	2	2	no	—
613	C₈	—	2	2	no	—
614	C₈	—	4	1	no	—
615	C₅	#26836	1	1	yes	characteristic, direct product factor, Sylow
616	C₂²	—	4	2	no	—
617	C₂²	—	4	2	no	—
618	C₂²	—	4	2	no	—
619	C₂²	—	8	1	no	—
620	C₂²	—	8	1	no	—
621	C₂²	—	8	1	no	—
622	C₂²	—	8	1	no	—
623	C₂²	C₅×#532	1	1	yes	characteristic
624	C₂²	C₅×D₄²	1	1	yes	characteristic
625	C₂²	C₅×#548	1	1	yes	characteristic
626	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
627	C₂²	C₂×C₅×#137	1	1	yes	characteristic
628	C₂²	C₅×#577	1	1	yes	characteristic
629	C₂²	C₅×#578	1	1	yes	characteristic
630	C₄	—	2	2	no	—
631	C₄	—	2	2	no	—
632	C₄	—	4	1	no	—
633	C₄	—	4	2	no	—
634	C₄	—	4	1	no	—
635	C₄	—	4	1	no	—
636	C₄	—	4	1	no	—
637	C₄	—	4	2	no	—
638	C₄	—	8	1	no	—
639	C₄	—	8	1	no	—
640	C₄	—	8	1	no	—
641	C₄	—	8	1	no	—
642	C₄	—	8	1	no	—
643	C₄	C₅×#525	1	1	yes	characteristic
644	C₄	C₅×#542	1	1	yes	characteristic
645	C₄	C₅×#547	1	1	yes	characteristic
646	C₄	C₅×#551	1	1	yes	characteristic
647	C₂	—	8	2	no	—
648	C₂	C₅×#2461	1	1	yes	characteristic
649	C₂	C₅×#3178	1	1	yes	characteristic
650	C₂	C₅×#3182	1	1	yes	characteristic
651	C₂	C₅×#3265	1	1	yes	characteristic
652	C₂	C₅×#3270	1	1	yes	characteristic
653	C₂	C₅×#3367	1	1	yes	characteristic
654	C₂	C₅×#3372	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂²×C₅×D₄	C₂³
LCS	G ▷ C₂²×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
1. C₂×C₅×#487	C₂	semidirect
4. C₅×#2446	C₂	semidirect
5. C₅×#2068	C₂	semidirect
6. C₅×#2057	C₂	semidirect
10. C₅×#1935	C₂	semidirect
11. C₅×#1935	C₂	semidirect
14. C₅×#1863	C₂	semidirect
15. C₅×#1771	C₂	semidirect
61. #26836	C₅	direct (N × H)
134. C₂×#487	C₂×C₅	semidirect
137. #2446	C₂×C₅	semidirect
138. #2068	C₂×C₅	semidirect
139. #2057	C₂×C₅	semidirect
143. #1935	C₂×C₅	semidirect
144. #1935	C₂×C₅	semidirect
147. #1863	C₂×C₅	semidirect
148. #1771	C₂×C₅	semidirect
615. C₅	#26836	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×#487	2
C₂×C₅×#440	2
C₅×#2452	2
C₅×#2446	2
C₅×#2068	2
C₅×#2057	2
C₅×#2055	2
C₅×#2013	2
C₅×#1973	2
C₅×#1935	2
C₅×#1934	2
C₅×#1877	2
C₅×#1863	2
C₅×#1771	2
#26836	5

Subgroups — C5×#26836 #11949556

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#26836 #11949556