Subgroups — C₅×#22871 #11945591

Order 1280.

1098 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#451	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₅×#103	C₂	1	1	yes	maximal, characteristic
4	C₅×#2360	C₂	1	1	yes	maximal, characteristic
5	C₅×Q₈×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
6	C₅×#1969	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1933	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1928	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1892	C₂	1	1	yes	maximal, characteristic
10	C₅×#1878	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1878	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1863	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1852	C₂	1	1	yes	maximal, characteristic
14	C₄×C₅×#103	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×C₈×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
16	C₂³×C₅×Q₈	C₂²	1	1	yes	characteristic
17	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
19	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
20	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
24	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₅×#451	C₄	1	8	yes	complemented
26	C₄×C₅×Q₁₆	—	2	4	no	—
27	C₂×C₅×#107	C₂²	1	1	yes	characteristic
28	C₂×C₅×#107	C₂²	1	1	yes	characteristic
29	C₂×C₅×#103	—	2	4	no	—
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×#103	C₂²	1	1	yes	characteristic
37	C₂×C₅×#103	C₂²	1	1	yes	characteristic
38	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
41	C₅×#391	—	2	1	no	—
42	C₅×#391	—	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×#389	—	2	1	no	—
47	C₅×#389	C₂²	1	1	yes	characteristic
48	C₅×#387	—	2	1	no	—
49	C₅×#385	—	2	1	no	—
50	C₅×#380	—	2	1	no	—
51	C₅×#380	C₂²	1	1	yes	characteristic
52	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
53	C₄×C₅×C₂²⋊C₄	—	2	1	no	—
54	C₄×C₅×C₂²⋊C₄	—	2	1	no	—
55	C₄×C₅×C₂²⋊C₄	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×#340	C₂²	1	1	yes	characteristic
60	C₅×#336	C₂²	1	1	yes	characteristic
61	C₅×#336	C₂²	1	1	yes	characteristic
62	#22871	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
63	C₂²×C₅×Q₈	—	2	1	no	—
64	C₂²×C₅×Q₈	—	2	2	no	—
65	C₂²×C₅×Q₈	—	2	2	no	—
66	C₂²×C₅×Q₈	—	2	2	no	—
67	C₂²×C₅×Q₈	—	4	1	no	—
68	C₂²×C₅×Q₈	—	4	1	no	—
69	C₂²×C₅×Q₈	C₂×C₄	1	4	yes	—
70	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
71	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
72	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₅	—	2	1	no	—
74	C₂³×C₄×C₅	—	2	1	no	—
75	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
76	C₂×C₅×Q₁₆	—	2	2	no	—
77	C₂×C₅×Q₁₆	—	2	2	no	—
78	C₂×C₅×Q₁₆	—	4	1	no	—
79	C₂×C₅×Q₁₆	—	4	1	no	—
80	C₂×C₅×Q₁₆	C₂×C₄	1	4	yes	complemented
81	C₂×C₅×Q₁₆	C₂×C₄	1	4	yes	complemented
82	C₂²×C₅×C₈	—	2	2	no	—
83	C₂²×C₅×C₈	—	2	2	no	—
84	C₂²×C₅×C₈	—	4	1	no	—
85	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
86	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
87	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
88	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
89	C₅×C₂²⋊Q₈	—	2	2	no	—
90	C₅×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
91	C₄×C₅×Q₈	—	2	2	no	—
92	C₄×C₅×Q₈	—	2	2	no	—
93	C₄×C₅×Q₈	—	2	2	no	—
94	C₄×C₅×Q₈	—	4	1	no	—
95	C₄×C₅×Q₈	—	4	1	no	—
96	C₄×C₅×Q₈	—	4	1	no	—
97	C₂×C₅×C₄⋊C₄	—	2	1	no	—
98	C₂×C₅×C₄⋊C₄	—	2	2	no	—
99	C₂×C₅×C₄⋊C₄	—	2	1	no	—
100	C₂×C₅×C₄⋊C₄	—	2	1	no	—
101	C₂×C₅×C₄⋊C₄	—	2	1	no	—
102	C₂×C₅×C₄⋊C₄	—	2	1	no	—
103	C₂×C₅×C₄⋊C₄	—	2	1	no	—
104	C₂×C₅×C₄⋊C₄	—	4	1	no	—
105	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
106	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
107	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
109	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
117	C₂×C₄²×C₅	—	2	1	no	—
118	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
119	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
120	C₅×#107	—	2	2	no	—
121	C₅×#107	—	4	1	no	—
122	C₅×#103	—	2	2	no	—
123	C₅×#103	—	2	2	no	—
124	C₅×#103	—	2	2	no	—
125	C₅×#103	—	2	2	no	—
126	C₅×#103	—	4	1	no	—
127	C₅×#103	C₂×C₄	1	4	yes	complemented
128	C₅×#103	C₂×C₄	1	4	yes	complemented
129	C₅×#103	D₄	1	4	yes	—
130	C₅×C₂²⋊C₈	C₂×C₄	1	4	yes	—
131	C₄×C₅×C₈	—	2	2	no	—
132	C₄×C₅×C₈	—	4	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	—	2	1	no	—
138	C₅×#95	—	2	1	no	—
139	C₅×#95	—	2	1	no	—
140	C₅×#95	—	2	1	no	—
141	C₅×#95	—	2	1	no	—
142	C₅×#95	D₄	1	1	yes	characteristic
143	C₅×#95	D₄	1	1	yes	characteristic
144	C₂×#451	C₂×C₅	1	1	yes	characteristic
145	C₂×C₄×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
146	C₂²×#103	C₂×C₅	1	1	yes	characteristic
147	#2360	C₂×C₅	1	1	yes	characteristic
148	Q₈×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic
149	#1969	C₂×C₅	1	1	yes	characteristic, complemented
150	#1933	C₂×C₅	1	1	yes	characteristic, complemented
151	#1928	C₂×C₅	1	1	yes	characteristic, complemented
152	#1892	C₂×C₅	1	1	yes	characteristic
153	#1878	C₂×C₅	1	1	yes	characteristic, complemented
154	#1878	C₂×C₅	1	1	yes	characteristic, complemented
155	#1863	C₂×C₅	1	1	yes	characteristic, complemented
156	#1852	C₂×C₅	1	1	yes	characteristic
157	C₄×#103	C₂×C₅	1	1	yes	characteristic, complemented
158	C₈×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic
159	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
160	C₂×C₅×Q₈	—	2	4	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	—	2	1	no	—
165	C₂×C₅×Q₈	—	2	1	no	—
166	C₂×C₅×Q₈	—	2	8	no	—
167	C₂×C₅×Q₈	—	2	1	no	—
168	C₂×C₅×Q₈	—	2	1	no	—
169	C₂×C₅×Q₈	—	2	1	no	—
170	C₂×C₅×Q₈	—	2	1	no	—
171	C₂×C₅×Q₈	—	2	1	no	—
172	C₂×C₅×Q₈	—	2	1	no	—
173	C₂×C₅×Q₈	—	2	1	no	—
174	C₂×C₅×Q₈	—	2	1	no	—
175	C₂×C₅×Q₈	—	4	2	no	—
176	C₂×C₅×Q₈	—	4	2	no	—
177	C₂×C₅×Q₈	—	4	4	no	—
178	C₂×C₅×Q₈	—	4	4	no	—
179	C₂×C₅×Q₈	—	4	4	no	—
180	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
181	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
182	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
183	C₂×C₅×Q₈	C₂×D₄	1	2	yes	—
184	C₂×C₅×Q₈	#41	1	2	yes	—
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	4	no	—
191	C₂²×C₄×C₅	—	2	1	no	—
192	C₂²×C₄×C₅	—	2	1	no	—
193	C₂²×C₄×C₅	—	2	1	no	—
194	C₂²×C₄×C₅	—	2	1	no	—
195	C₂²×C₄×C₅	—	2	1	no	—
196	C₂²×C₄×C₅	—	2	1	no	—
197	C₂²×C₄×C₅	—	2	1	no	—
198	C₂²×C₄×C₅	—	4	2	no	—
199	C₂²×C₄×C₅	—	4	2	no	—
200	C₂²×C₄×C₅	—	4	2	no	—
201	C₂²×C₄×C₅	—	4	2	no	—
202	C₂²×C₄×C₅	—	8	1	no	—
203	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
204	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₅	#41	1	2	yes	—
210	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
211	C₅×Q₁₆	—	2	8	no	—
212	C₅×Q₁₆	—	4	4	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	—	2	1	no	—
220	C₂×C₅×C₈	—	2	1	no	—
221	C₂×C₅×C₈	—	2	1	no	—
222	C₂×C₅×C₈	—	4	4	no	—
223	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
224	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
225	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
226	C₅×C₄⋊C₄	—	2	4	no	—
227	C₅×C₄⋊C₄	—	2	1	no	—
228	C₅×C₄⋊C₄	—	2	1	no	—
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	—	2	1	no	—
234	C₅×C₄⋊C₄	—	2	1	no	—
235	C₅×C₄⋊C₄	—	4	2	no	—
236	C₅×C₄⋊C₄	—	4	2	no	—
237	C₅×C₄⋊C₄	—	4	2	no	—
238	C₅×C₄⋊C₄	—	4	2	no	—
239	C₅×C₄⋊C₄	—	8	1	no	—
240	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
241	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
242	C₅×C₂²⋊C₄	—	2	4	no	—
243	C₅×C₂²⋊C₄	—	2	2	no	—
244	C₅×C₂²⋊C₄	—	4	2	no	—
245	C₅×C₂²⋊C₄	Q₁₆	1	4	yes	complemented
246	C₄²×C₅	—	2	1	no	—
247	C₄²×C₅	—	2	1	no	—
248	C₄²×C₅	—	2	1	no	—
249	C₄²×C₅	—	2	1	no	—
250	C₄²×C₅	—	4	2	no	—
251	C₄²×C₅	—	4	2	no	—
252	C₄²×C₅	—	4	2	no	—
253	C₄²×C₅	—	8	1	no	—
254	C₂³×Q₈	C₂²×C₅	1	1	yes	characteristic
255	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
256	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
257	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
258	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
259	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
260	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
261	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
262	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
263	#451	C₄×C₅	1	8	yes	complemented
264	C₄×Q₁₆	—	2	4	no	—
265	C₂×#107	C₂²×C₅	1	1	yes	characteristic
266	C₂×#107	C₂²×C₅	1	1	yes	characteristic
267	C₂×#103	—	2	4	no	—
268	C₂×#103	C₂²×C₅	1	1	yes	characteristic
269	C₂×#103	C₂²×C₅	1	1	yes	characteristic
270	C₂×#103	C₂²×C₅	1	1	yes	characteristic
271	C₂×#103	C₂²×C₅	1	1	yes	characteristic
272	C₂×#103	C₂²×C₅	1	1	yes	characteristic
273	C₂×#103	C₂²×C₅	1	1	yes	characteristic
274	C₂×#103	C₂²×C₅	1	1	yes	characteristic
275	C₂×#103	C₂²×C₅	1	1	yes	characteristic
276	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
277	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
278	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
279	#391	—	2	1	no	—
280	#391	—	2	1	no	—
281	#391	C₂²×C₅	1	1	yes	characteristic
282	#391	C₂²×C₅	1	1	yes	characteristic
283	#391	C₂²×C₅	1	1	yes	characteristic
284	#389	—	2	1	no	—
285	#389	C₂²×C₅	1	1	yes	characteristic
286	#387	—	2	1	no	—
287	#385	—	2	1	no	—
288	#380	—	2	1	no	—
289	#380	C₂²×C₅	1	1	yes	characteristic
290	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
291	C₄×C₂²⋊C₄	—	2	1	no	—
292	C₄×C₂²⋊C₄	—	2	1	no	—
293	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
294	#340	C₂²×C₅	1	1	yes	characteristic
295	#340	C₂²×C₅	1	1	yes	characteristic
296	#340	C₂²×C₅	1	1	yes	characteristic
297	#340	C₂²×C₅	1	1	yes	characteristic
298	#336	C₂²×C₅	1	1	yes	characteristic
299	#336	C₂²×C₅	1	1	yes	characteristic
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	C₄×D₄	1	2	yes	—
305	C₂³×C₅	C₂×Q₁₆	1	2	yes	—
306	C₂³×C₅	#135	1	2	yes	—
307	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
308	C₅×Q₈	—	2	2	no	—
309	C₅×Q₈	—	2	2	no	—
310	C₅×Q₈	—	2	2	no	—
311	C₅×Q₈	—	2	2	no	—
312	C₅×Q₈	—	2	2	no	—
313	C₅×Q₈	—	2	2	no	—
314	C₅×Q₈	—	2	2	no	—
315	C₅×Q₈	—	4	8	no	—
316	C₅×Q₈	—	4	1	no	—
317	C₅×Q₈	—	4	1	no	—
318	C₅×Q₈	—	4	1	no	—
319	C₅×Q₈	—	4	1	no	—
320	C₅×Q₈	C₄×D₄	1	4	yes	—
321	C₂×C₄×C₅	—	2	2	no	—
322	C₂×C₄×C₅	—	2	1	no	—
323	C₂×C₄×C₅	—	2	2	no	—
324	C₂×C₄×C₅	—	2	1	no	—
325	C₂×C₄×C₅	—	2	1	no	—
326	C₂×C₄×C₅	—	2	2	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	2	no	—
331	C₂×C₄×C₅	—	2	2	no	—
332	C₂×C₄×C₅	—	2	2	no	—
333	C₂×C₄×C₅	—	2	2	no	—
334	C₂×C₄×C₅	—	2	2	no	—
335	C₂×C₄×C₅	—	2	2	no	—
336	C₂×C₄×C₅	—	2	2	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	1	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	—	4	8	no	—
345	C₂×C₄×C₅	—	4	1	no	—
346	C₂×C₄×C₅	—	4	1	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	—	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	—	8	4	no	—
363	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
364	C₂×C₄×C₅	C₂×Q₁₆	1	2	yes	—
365	C₂×C₄×C₅	C₂×Q₁₆	1	2	yes	—
366	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
367	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
368	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
369	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
370	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
371	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
372	C₅×C₈	—	2	2	no	—
373	C₅×C₈	—	2	2	no	—
374	C₅×C₈	—	2	2	no	—
375	C₅×C₈	—	4	1	no	—
376	C₂²×Q₈	—	2	1	no	—
377	C₂²×Q₈	—	2	2	no	—
378	C₂²×Q₈	—	2	2	no	—
379	C₂²×Q₈	—	2	2	no	—
380	C₂²×Q₈	—	4	1	no	—
381	C₂²×Q₈	—	4	1	no	—
382	C₂²×Q₈	C₂×C₄×C₅	1	4	yes	—
383	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
384	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
385	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
386	C₂³×C₄	—	2	1	no	—
387	C₂³×C₄	—	2	1	no	—
388	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
389	C₂×Q₁₆	—	2	2	no	—
390	C₂×Q₁₆	—	2	2	no	—
391	C₂×Q₁₆	—	4	1	no	—
392	C₂×Q₁₆	—	4	1	no	—
393	C₂×Q₁₆	C₂×C₄×C₅	1	4	yes	complemented
394	C₂×Q₁₆	C₂×C₄×C₅	1	4	yes	complemented
395	C₂²×C₈	—	2	2	no	—
396	C₂²×C₈	—	2	2	no	—
397	C₂²×C₈	—	4	1	no	—
398	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
399	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
400	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
401	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
402	C₂²⋊Q₈	—	2	2	no	—
403	C₂²⋊Q₈	C₂×C₄×C₅	1	4	yes	—
404	C₄×Q₈	—	2	2	no	—
405	C₄×Q₈	—	2	2	no	—
406	C₄×Q₈	—	2	2	no	—
407	C₄×Q₈	—	4	1	no	—
408	C₄×Q₈	—	4	1	no	—
409	C₄×Q₈	—	4	1	no	—
410	C₂×C₄⋊C₄	—	2	1	no	—
411	C₂×C₄⋊C₄	—	2	2	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	—	2	1	no	—
416	C₂×C₄⋊C₄	—	2	1	no	—
417	C₂×C₄⋊C₄	—	4	1	no	—
418	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
419	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
420	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
421	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
422	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
423	C₂×C₂²⋊C₄	—	2	1	no	—
424	C₂×C₂²⋊C₄	—	2	1	no	—
425	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
426	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
427	C₂×C₄²	—	2	1	no	—
428	C₂×C₄²	—	2	1	no	—
429	C₂×C₄²	—	2	1	no	—
430	C₂×C₄²	—	2	1	no	—
431	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
432	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
433	#107	—	2	2	no	—
434	#107	—	4	1	no	—
435	#103	—	2	2	no	—
436	#103	—	2	2	no	—
437	#103	—	2	2	no	—
438	#103	—	2	2	no	—
439	#103	—	4	1	no	—
440	#103	C₂×C₄×C₅	1	4	yes	complemented
441	#103	C₂×C₄×C₅	1	4	yes	complemented
442	#103	C₅×D₄	1	4	yes	—
443	C₂²⋊C₈	C₂×C₄×C₅	1	4	yes	—
444	C₄×C₈	—	2	2	no	—
445	C₄×C₈	—	4	1	no	—
446	#95	—	2	1	no	—
447	#95	—	2	1	no	—
448	#95	—	2	1	no	—
449	#95	—	2	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	—	2	2	no	—
458	C₂²×C₅	—	2	2	no	—
459	C₂²×C₅	—	2	2	no	—
460	C₂²×C₅	—	2	2	no	—
461	C₂²×C₅	—	2	2	no	—
462	C₂²×C₅	—	2	2	no	—
463	C₂²×C₅	C₄×Q₁₆	1	4	yes	complemented
464	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
465	C₂²×C₅	D₄²	1	1	yes	characteristic
466	C₂²×C₅	#546	1	1	yes	characteristic
467	C₂²×C₅	C₂²×Q₁₆	1	1	yes	characteristic
468	C₂²×C₅	C₂×#135	1	1	yes	characteristic
469	C₂²×C₅	#577	1	1	yes	characteristic
470	C₂²×C₅	#578	1	1	yes	characteristic
471	C₄×C₅	—	2	2	no	—
472	C₄×C₅	—	2	4	no	—
473	C₄×C₅	—	2	2	no	—
474	C₄×C₅	—	2	2	no	—
475	C₄×C₅	—	4	2	no	—
476	C₄×C₅	—	4	2	no	—
477	C₄×C₅	—	4	2	no	—
478	C₄×C₅	—	4	1	no	—
479	C₄×C₅	—	4	2	no	—
480	C₄×C₅	—	4	1	no	—
481	C₄×C₅	—	8	1	no	—
482	C₄×C₅	—	8	1	no	—
483	C₄×C₅	—	8	1	no	—
484	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
485	C₄×C₅	#518	1	1	yes	characteristic
486	C₄×C₅	#546	1	1	yes	characteristic
487	C₄×C₅	#551	1	1	yes	characteristic
488	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
489	C₂×Q₈	—	2	4	no	—
490	C₂×Q₈	—	2	1	no	—
491	C₂×Q₈	—	2	1	no	—
492	C₂×Q₈	—	2	1	no	—
493	C₂×Q₈	—	2	1	no	—
494	C₂×Q₈	—	2	1	no	—
495	C₂×Q₈	—	2	8	no	—
496	C₂×Q₈	—	2	1	no	—
497	C₂×Q₈	—	2	1	no	—
498	C₂×Q₈	—	2	1	no	—
499	C₂×Q₈	—	2	1	no	—
500	C₂×Q₈	—	2	1	no	—
501	C₂×Q₈	—	2	1	no	—
502	C₂×Q₈	—	2	1	no	—
503	C₂×Q₈	—	2	1	no	—
504	C₂×Q₈	—	4	2	no	—
505	C₂×Q₈	—	4	2	no	—
506	C₂×Q₈	—	4	4	no	—
507	C₂×Q₈	—	4	4	no	—
508	C₂×Q₈	—	4	4	no	—
509	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
510	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
511	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
512	C₂×Q₈	C₂×C₅×D₄	1	2	yes	—
513	C₂×Q₈	C₅×#41	1	2	yes	—
514	C₂²×C₄	—	2	1	no	—
515	C₂²×C₄	—	2	1	no	—
516	C₂²×C₄	—	2	1	no	—
517	C₂²×C₄	—	2	1	no	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	2	4	no	—
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	—	2	1	no	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	2	1	no	—
524	C₂²×C₄	—	2	1	no	—
525	C₂²×C₄	—	2	1	no	—
526	C₂²×C₄	—	2	1	no	—
527	C₂²×C₄	—	4	2	no	—
528	C₂²×C₄	—	4	2	no	—
529	C₂²×C₄	—	4	2	no	—
530	C₂²×C₄	—	4	2	no	—
531	C₂²×C₄	—	8	1	no	—
532	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
533	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
534	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
535	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
536	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
537	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
538	C₂²×C₄	C₅×#41	1	2	yes	—
539	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
540	Q₁₆	—	2	8	no	—
541	Q₁₆	—	4	4	no	—
542	C₂×C₈	—	2	1	no	—
543	C₂×C₈	—	2	1	no	—
544	C₂×C₈	—	2	1	no	—
545	C₂×C₈	—	2	1	no	—
546	C₂×C₈	—	2	1	no	—
547	C₂×C₈	—	2	1	no	—
548	C₂×C₈	—	2	1	no	—
549	C₂×C₈	—	2	1	no	—
550	C₂×C₈	—	2	1	no	—
551	C₂×C₈	—	4	4	no	—
552	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
553	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
554	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
555	C₄⋊C₄	—	2	4	no	—
556	C₄⋊C₄	—	2	1	no	—
557	C₄⋊C₄	—	2	1	no	—
558	C₄⋊C₄	—	2	1	no	—
559	C₄⋊C₄	—	2	1	no	—
560	C₄⋊C₄	—	2	1	no	—
561	C₄⋊C₄	—	2	1	no	—
562	C₄⋊C₄	—	2	1	no	—
563	C₄⋊C₄	—	2	1	no	—
564	C₄⋊C₄	—	4	2	no	—
565	C₄⋊C₄	—	4	2	no	—
566	C₄⋊C₄	—	4	2	no	—
567	C₄⋊C₄	—	4	2	no	—
568	C₄⋊C₄	—	8	1	no	—
569	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
570	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
571	C₂²⋊C₄	—	2	4	no	—
572	C₂²⋊C₄	—	2	2	no	—
573	C₂²⋊C₄	—	4	2	no	—
574	C₂²⋊C₄	C₅×Q₁₆	1	4	yes	complemented
575	C₄²	—	2	1	no	—
576	C₄²	—	2	1	no	—
577	C₄²	—	2	1	no	—
578	C₄²	—	2	1	no	—
579	C₄²	—	4	2	no	—
580	C₄²	—	4	2	no	—
581	C₄²	—	4	2	no	—
582	C₄²	—	8	1	no	—
583	C₂×C₅	—	2	4	no	—
584	C₂×C₅	#2358	1	1	yes	characteristic
585	C₂×C₅	C₂×C₄×Q₁₆	1	1	yes	characteristic
586	C₂×C₅	#2947	1	1	yes	characteristic
587	C₂×C₅	#3282	1	1	yes	characteristic
588	C₂×C₅	D₄×Q₁₆	1	1	yes	characteristic
589	C₂×C₅	#3299	1	1	yes	characteristic
590	C₂×C₅	#3300	1	1	yes	characteristic
591	C₂³	—	2	1	no	—
592	C₂³	—	2	1	no	—
593	C₂³	—	2	1	no	—
594	C₂³	—	2	1	no	—
595	C₂³	C₄×C₅×D₄	1	2	yes	—
596	C₂³	C₂×C₅×Q₁₆	1	2	yes	—
597	C₂³	C₅×#135	1	2	yes	—
598	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
599	Q₈	—	2	2	no	—
600	Q₈	—	2	2	no	—
601	Q₈	—	2	2	no	—
602	Q₈	—	2	2	no	—
603	Q₈	—	2	2	no	—
604	Q₈	—	2	2	no	—
605	Q₈	—	2	2	no	—
606	Q₈	—	4	8	no	—
607	Q₈	—	4	1	no	—
608	Q₈	—	4	1	no	—
609	Q₈	—	4	1	no	—
610	Q₈	—	4	1	no	—
611	Q₈	C₄×C₅×D₄	1	4	yes	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	2	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	—	2	2	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	4	8	no	—
636	C₂×C₄	—	4	1	no	—
637	C₂×C₄	—	4	1	no	—
638	C₂×C₄	—	4	1	no	—
639	C₂×C₄	—	4	1	no	—
640	C₂×C₄	—	4	1	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	4	1	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	4	1	no	—
652	C₂×C₄	—	4	1	no	—
653	C₂×C₄	—	8	4	no	—
654	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
655	C₂×C₄	C₂×C₅×Q₁₆	1	2	yes	—
656	C₂×C₄	C₂×C₅×Q₁₆	1	2	yes	—
657	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
658	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
659	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
660	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
661	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
662	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
663	C₈	—	2	2	no	—
664	C₈	—	2	2	no	—
665	C₈	—	2	2	no	—
666	C₈	—	4	1	no	—
667	C₅	#22871	1	1	yes	characteristic, direct product factor, Sylow
668	C₂²	—	2	2	no	—
669	C₂²	—	2	2	no	—
670	C₂²	—	2	2	no	—
671	C₂²	—	2	2	no	—
672	C₂²	—	2	2	no	—
673	C₂²	—	2	2	no	—
674	C₂²	C₄×C₅×Q₁₆	1	4	yes	complemented
675	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
676	C₂²	C₅×D₄²	1	1	yes	characteristic
677	C₂²	C₅×#546	1	1	yes	characteristic
678	C₂²	C₂²×C₅×Q₁₆	1	1	yes	characteristic
679	C₂²	C₂×C₅×#135	1	1	yes	characteristic
680	C₂²	C₅×#577	1	1	yes	characteristic
681	C₂²	C₅×#578	1	1	yes	characteristic
682	C₄	—	2	2	no	—
683	C₄	—	2	2	no	—
684	C₄	—	2	2	no	—
685	C₄	—	2	4	no	—
686	C₄	—	4	1	no	—
687	C₄	—	4	2	no	—
688	C₄	—	4	1	no	—
689	C₄	—	4	2	no	—
690	C₄	—	4	2	no	—
691	C₄	—	4	2	no	—
692	C₄	—	8	1	no	—
693	C₄	—	8	1	no	—
694	C₄	—	8	1	no	—
695	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
696	C₄	C₅×#518	1	1	yes	characteristic
697	C₄	C₅×#546	1	1	yes	characteristic
698	C₄	C₅×#551	1	1	yes	characteristic
699	C₂	—	2	4	no	—
700	C₂	C₅×#2358	1	1	yes	characteristic
701	C₂	C₂×C₄×C₅×Q₁₆	1	1	yes	characteristic
702	C₂	C₅×#2947	1	1	yes	characteristic
703	C₂	C₅×#3282	1	1	yes	characteristic
704	C₂	C₅×D₄×Q₁₆	1	1	yes	characteristic
705	C₂	C₅×#3299	1	1	yes	characteristic
706	C₂	C₅×#3300	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	C₂⁴×C₅	C₂×D₄
LCS	G ▷ C₂×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
2. C₂×C₄×C₅×Q₁₆	C₂	semidirect
6. C₅×#1969	C₂	semidirect
7. C₅×#1933	C₂	semidirect
8. C₅×#1928	C₂	semidirect
10. C₅×#1878	C₂	semidirect
11. C₅×#1878	C₂	semidirect
12. C₅×#1863	C₂	semidirect
14. C₄×C₅×#103	C₂	semidirect
25. C₅×#451	C₄	semidirect
62. #22871	C₅	direct (N × H)
80. C₂×C₅×Q₁₆	C₂×C₄	semidirect
81. C₂×C₅×Q₁₆	C₂×C₄	semidirect
127. C₅×#103	C₂×C₄	semidirect
128. C₅×#103	C₂×C₄	semidirect
145. C₂×C₄×Q₁₆	C₂×C₅	semidirect
149. #1969	C₂×C₅	semidirect
150. #1933	C₂×C₅	semidirect
151. #1928	C₂×C₅	semidirect
153. #1878	C₂×C₅	semidirect
154. #1878	C₂×C₅	semidirect
155. #1863	C₂×C₅	semidirect
157. C₄×#103	C₂×C₅	semidirect
245. C₅×C₂²⋊C₄	Q₁₆	semidirect
263. #451	C₄×C₅	semidirect
393. C₂×Q₁₆	C₂×C₄×C₅	semidirect
394. C₂×Q₁₆	C₂×C₄×C₅	semidirect
440. #103	C₂×C₄×C₅	semidirect
441. #103	C₂×C₄×C₅	semidirect
463. C₂²×C₅	C₄×Q₁₆	semidirect
574. C₂²⋊C₄	C₅×Q₁₆	semidirect
667. C₅	#22871	direct (N × H)
674. C₂²	C₄×C₅×Q₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#451	2
C₂×C₄×C₅×Q₁₆	2
C₂²×C₅×#103	2
C₅×#2360	2
C₅×Q₈×C₂²⋊C₄	2
C₅×#1969	2
C₅×#1933	2
C₅×#1928	2
C₅×#1892	2
C₅×#1878	2
C₅×#1863	2
C₅×#1852	2
C₄×C₅×#103	2
C₅×C₈×C₂²⋊C₄	2
#22871	5

Subgroups — C5×#22871 #11945591

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22871 #11945591