Subgroups — C₅×#23681 #11946401

Order 1280.

880 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×C₅×SD₁₆	C₂	1	1	yes	maximal, characteristic
3	C₄×C₅×#124	C₂	1	1	yes	maximal, characteristic
4	C₅×#2295	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2085	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2074	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2067	C₂	1	1	yes	maximal, characteristic
8	C₅×#2066	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2056	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#2055	C₂	1	1	yes	maximal, characteristic
11	C₅×#2042	C₂	1	1	yes	maximal, characteristic
12	C₅×#2015	C₂	1	1	yes	maximal, characteristic
13	C₄×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₅×#103	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₅×#102	C₂	1	1	yes	maximal, characteristic
16	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₅×SD₁₆	C₂²	1	1	yes	characteristic
18	C₂×C₅×#124	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
22	C₄×C₅×Q₁₆	—	2	4	no	—
23	C₄×C₅×SD₁₆	—	2	4	no	—
24	C₂×C₅×#107	C₂²	1	1	yes	characteristic
25	C₂×C₅×#106	C₂²	1	1	yes	characteristic
26	C₂×C₅×C₄⋊C₈	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×#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×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
38	C₅×#391	C₂²	1	1	yes	characteristic
39	C₅×#391	C₂²	1	1	yes	characteristic
40	C₅×#391	C₂²	1	1	yes	characteristic
41	C₅×#390	C₂²	1	1	yes	characteristic
42	C₅×#389	C₂²	1	1	yes	characteristic
43	C₅×#389	C₂²	1	1	yes	characteristic
44	C₅×#388	—	2	1	no	—
45	C₅×#388	—	2	1	no	—
46	C₅×#387	—	2	1	no	—
47	C₅×#387	—	2	1	no	—
48	C₅×#382	C₂²	1	1	yes	characteristic
49	C₄×C₅×C₄⋊C₄	—	2	1	no	—
50	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
51	C₄×C₅×C₂²⋊C₄	—	2	1	no	—
52	C₄×C₅×C₂²⋊C₄	—	2	1	no	—
53	C₅×#376	—	2	1	no	—
54	C₄³×C₅	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	#23681	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
62	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
63	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
64	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₅	—	2	1	no	—
66	C₂×C₅×Q₁₆	—	2	2	no	—
67	C₂×C₅×Q₁₆	—	2	2	no	—
68	C₂×C₅×Q₁₆	—	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	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
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	C₅×#124	—	2	2	no	—
77	C₅×#124	—	2	2	no	—
78	C₄×C₅×Q₈	—	2	2	no	—
79	C₄×C₅×Q₈	—	2	2	no	—
80	C₄×C₅×Q₈	—	2	2	no	—
81	C₄×C₅×Q₈	D₄	1	4	yes	—
82	C₄×C₅×D₄	—	2	2	no	—
83	C₄×C₅×D₄	—	2	2	no	—
84	C₂×C₅×C₄⋊C₄	—	2	1	no	—
85	C₂×C₅×C₄⋊C₄	—	2	1	no	—
86	C₂×C₅×C₄⋊C₄	—	2	1	no	—
87	C₂×C₅×C₄⋊C₄	—	2	1	no	—
88	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
89	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
90	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
91	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
92	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
93	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
94	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
95	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
96	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
97	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
98	C₂×C₄²×C₅	—	2	1	no	—
99	C₂×C₄²×C₅	—	2	1	no	—
100	C₂×C₄²×C₅	—	2	1	no	—
101	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
102	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
103	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
104	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
105	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
108	C₅×#107	—	2	2	no	—
109	C₅×#106	—	2	2	no	—
110	C₅×C₄⋊C₈	—	2	2	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×#102	—	2	2	no	—
118	C₅×#102	—	2	2	no	—
119	C₅×#102	—	2	2	no	—
120	C₄×C₅×C₈	—	2	2	no	—
121	C₄×C₅×C₈	—	2	2	no	—
122	C₅×#95	—	2	1	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	—	2	1	no	—
133	C₂×C₄×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
134	C₂×C₄×SD₁₆	C₂×C₅	1	1	yes	characteristic
135	C₄×#124	C₂×C₅	1	1	yes	characteristic
136	#2295	C₂×C₅	1	1	yes	characteristic, complemented
137	#2085	C₂×C₅	1	1	yes	characteristic, complemented
138	#2074	C₂×C₅	1	1	yes	characteristic, complemented
139	#2067	C₂×C₅	1	1	yes	characteristic
140	#2066	C₂×C₅	1	1	yes	characteristic, complemented
141	#2056	C₂×C₅	1	1	yes	characteristic, complemented
142	#2055	C₂×C₅	1	1	yes	characteristic
143	#2042	C₂×C₅	1	1	yes	characteristic
144	#2015	C₂×C₅	1	1	yes	characteristic
145	C₄×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
146	C₄×#103	C₂×C₅	1	1	yes	characteristic, complemented
147	C₄×#102	C₂×C₅	1	1	yes	characteristic
148	C₂⁴×C₅	—	2	1	no	—
149	C₂×C₅×Q₈	—	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	C₂×D₄	1	2	yes	—
160	C₂×C₅×Q₈	#41	1	2	yes	—
161	C₂×C₅×D₄	—	2	1	no	—
162	C₂×C₅×D₄	—	2	1	no	—
163	C₂×C₅×D₄	—	2	1	no	—
164	C₂×C₅×D₄	—	2	1	no	—
165	C₂×C₅×D₄	—	2	1	no	—
166	C₂×C₅×D₄	#41	1	2	yes	—
167	C₂²×C₄×C₅	—	2	1	no	—
168	C₂²×C₄×C₅	—	2	1	no	—
169	C₂²×C₄×C₅	—	2	1	no	—
170	C₂²×C₄×C₅	—	2	1	no	—
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	—	4	2	no	—
175	C₂²×C₄×C₅	—	4	2	no	—
176	C₂²×C₄×C₅	—	4	2	no	—
177	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
184	C₅×Q₁₆	—	2	8	no	—
185	C₅×SD₁₆	—	2	8	no	—
186	C₂×C₅×C₈	—	2	1	no	—
187	C₂×C₅×C₈	—	2	1	no	—
188	C₂×C₅×C₈	—	2	1	no	—
189	C₂×C₅×C₈	—	2	1	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	#41	1	2	yes	—
197	C₂×C₅×C₈	#41	1	2	yes	—
198	C₅×C₄⋊C₄	—	2	4	no	—
199	C₅×C₄⋊C₄	—	2	1	no	—
200	C₅×C₄⋊C₄	—	2	1	no	—
201	C₅×C₄⋊C₄	—	2	1	no	—
202	C₅×C₄⋊C₄	—	2	1	no	—
203	C₅×C₄⋊C₄	—	2	1	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	—	4	2	no	—
209	C₅×C₄⋊C₄	—	4	2	no	—
210	C₅×C₄⋊C₄	—	4	2	no	—
211	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
212	C₅×C₂²⋊C₄	—	2	4	no	—
213	C₅×C₂²⋊C₄	—	2	4	no	—
214	C₅×C₂²⋊C₄	—	4	2	no	—
215	C₅×C₂²⋊C₄	—	4	2	no	—
216	C₅×C₂²⋊C₄	—	4	2	no	—
217	C₄²×C₅	—	2	4	no	—
218	C₄²×C₅	—	2	2	no	—
219	C₄²×C₅	—	2	2	no	—
220	C₄²×C₅	—	2	2	no	—
221	C₄²×C₅	—	2	1	no	—
222	C₄²×C₅	—	2	1	no	—
223	C₄²×C₅	—	2	1	no	—
224	C₄²×C₅	—	2	1	no	—
225	C₄²×C₅	—	4	1	no	—
226	C₄²×C₅	—	4	2	no	—
227	C₄²×C₅	—	4	2	no	—
228	C₄²×C₅	C₂×D₄	1	2	yes	—
229	C₄²×C₅	#41	1	2	yes	—
230	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
231	C₂²×SD₁₆	C₂²×C₅	1	1	yes	characteristic
232	C₂×#124	C₂²×C₅	1	1	yes	characteristic
233	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
234	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
235	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
236	C₄×Q₁₆	—	2	4	no	—
237	C₄×SD₁₆	—	2	4	no	—
238	C₂×#107	C₂²×C₅	1	1	yes	characteristic
239	C₂×#106	C₂²×C₅	1	1	yes	characteristic
240	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
241	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
242	C₂×#103	C₂²×C₅	1	1	yes	characteristic
243	C₂×#103	C₂²×C₅	1	1	yes	characteristic
244	C₂×#103	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×#102	C₂²×C₅	1	1	yes	characteristic
248	C₂×#102	C₂²×C₅	1	1	yes	characteristic
249	C₂×#102	C₂²×C₅	1	1	yes	characteristic
250	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
251	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
252	#391	C₂²×C₅	1	1	yes	characteristic
253	#391	C₂²×C₅	1	1	yes	characteristic
254	#391	C₂²×C₅	1	1	yes	characteristic
255	#390	C₂²×C₅	1	1	yes	characteristic
256	#389	C₂²×C₅	1	1	yes	characteristic
257	#389	C₂²×C₅	1	1	yes	characteristic
258	#388	—	2	1	no	—
259	#388	—	2	1	no	—
260	#387	—	2	1	no	—
261	#387	—	2	1	no	—
262	#382	C₂²×C₅	1	1	yes	characteristic
263	C₄×C₄⋊C₄	—	2	1	no	—
264	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
265	C₄×C₂²⋊C₄	—	2	1	no	—
266	C₄×C₂²⋊C₄	—	2	1	no	—
267	#376	—	2	1	no	—
268	C₄³	C₂²×C₅	1	1	yes	characteristic
269	#340	C₂²×C₅	1	1	yes	characteristic
270	#340	C₂²×C₅	1	1	yes	characteristic
271	#340	C₂²×C₅	1	1	yes	characteristic
272	#340	C₂²×C₅	1	1	yes	characteristic
273	#336	C₂²×C₅	1	1	yes	characteristic
274	#336	C₂²×C₅	1	1	yes	characteristic
275	C₂³×C₅	—	2	2	no	—
276	C₂³×C₅	—	4	1	no	—
277	C₂³×C₅	—	4	1	no	—
278	C₂³×C₅	—	4	1	no	—
279	C₂³×C₅	—	4	1	no	—
280	C₂³×C₅	—	4	1	no	—
281	C₂³×C₅	—	4	1	no	—
282	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
283	C₅×Q₈	—	2	2	no	—
284	C₅×Q₈	—	2	2	no	—
285	C₅×Q₈	—	2	2	no	—
286	C₅×Q₈	—	2	2	no	—
287	C₅×Q₈	—	4	1	no	—
288	C₅×Q₈	—	4	1	no	—
289	C₅×Q₈	—	4	1	no	—
290	C₅×Q₈	—	4	1	no	—
291	C₅×D₄	—	2	2	no	—
292	C₅×D₄	—	2	2	no	—
293	C₅×D₄	—	4	1	no	—
294	C₅×D₄	—	4	1	no	—
295	C₂×C₄×C₅	—	2	1	no	—
296	C₂×C₄×C₅	—	2	1	no	—
297	C₂×C₄×C₅	—	2	1	no	—
298	C₂×C₄×C₅	—	2	1	no	—
299	C₂×C₄×C₅	—	2	2	no	—
300	C₂×C₄×C₅	—	2	2	no	—
301	C₂×C₄×C₅	—	2	1	no	—
302	C₂×C₄×C₅	—	2	1	no	—
303	C₂×C₄×C₅	—	2	2	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	1	no	—
308	C₂×C₄×C₅	—	2	1	no	—
309	C₂×C₄×C₅	—	2	1	no	—
310	C₂×C₄×C₅	—	2	1	no	—
311	C₂×C₄×C₅	—	4	1	no	—
312	C₂×C₄×C₅	—	4	1	no	—
313	C₂×C₄×C₅	—	4	1	no	—
314	C₂×C₄×C₅	—	4	1	no	—
315	C₂×C₄×C₅	—	4	1	no	—
316	C₂×C₄×C₅	—	4	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	—	8	4	no	—
330	C₂×C₄×C₅	#121	1	2	yes	—
331	C₂×C₄×C₅	#121	1	2	yes	—
332	C₂×C₄×C₅	#135	1	2	yes	—
333	C₂×C₄×C₅	#135	1	2	yes	—
334	C₂×C₄×C₅	#137	1	2	yes	—
335	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
336	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
337	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
338	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
339	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
340	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
341	C₅×C₈	—	2	2	no	—
342	C₅×C₈	—	2	2	no	—
343	C₅×C₈	—	4	1	no	—
344	C₅×C₈	—	4	1	no	—
345	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
346	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
347	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
348	C₂³×C₄	—	2	1	no	—
349	C₂×Q₁₆	—	2	2	no	—
350	C₂×Q₁₆	—	2	2	no	—
351	C₂×Q₁₆	—	2	2	no	—
352	C₂×SD₁₆	—	2	2	no	—
353	C₂×SD₁₆	—	2	2	no	—
354	C₂×SD₁₆	—	2	2	no	—
355	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
356	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
357	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
358	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
359	#124	—	2	2	no	—
360	#124	—	2	2	no	—
361	C₄×Q₈	—	2	2	no	—
362	C₄×Q₈	—	2	2	no	—
363	C₄×Q₈	—	2	2	no	—
364	C₄×Q₈	C₅×D₄	1	4	yes	—
365	C₄×D₄	—	2	2	no	—
366	C₄×D₄	—	2	2	no	—
367	C₂×C₄⋊C₄	—	2	1	no	—
368	C₂×C₄⋊C₄	—	2	1	no	—
369	C₂×C₄⋊C₄	—	2	1	no	—
370	C₂×C₄⋊C₄	—	2	1	no	—
371	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
372	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
373	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
374	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
375	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
376	C₂×C₂²⋊C₄	—	2	1	no	—
377	C₂×C₂²⋊C₄	—	2	1	no	—
378	C₂×C₂²⋊C₄	—	2	1	no	—
379	C₂×C₂²⋊C₄	—	2	1	no	—
380	C₂×C₂²⋊C₄	—	2	1	no	—
381	C₂×C₄²	—	2	1	no	—
382	C₂×C₄²	—	2	1	no	—
383	C₂×C₄²	—	2	1	no	—
384	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
385	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
386	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
387	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
388	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
389	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
390	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
391	#107	—	2	2	no	—
392	#106	—	2	2	no	—
393	C₄⋊C₈	—	2	2	no	—
394	C₄⋊C₈	—	2	2	no	—
395	#103	—	2	2	no	—
396	#103	—	2	2	no	—
397	#103	—	2	2	no	—
398	#103	—	2	2	no	—
399	#103	—	2	2	no	—
400	#102	—	2	2	no	—
401	#102	—	2	2	no	—
402	#102	—	2	2	no	—
403	C₄×C₈	—	2	2	no	—
404	C₄×C₈	—	2	2	no	—
405	#95	—	2	1	no	—
406	#95	—	2	1	no	—
407	#95	—	2	1	no	—
408	#95	—	2	1	no	—
409	#95	—	2	1	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	C₂²×C₅	—	4	2	no	—
417	C₂²×C₅	—	4	2	no	—
418	C₂²×C₅	—	4	2	no	—
419	C₂²×C₅	—	8	1	no	—
420	C₂²×C₅	—	8	1	no	—
421	C₂²×C₅	—	8	1	no	—
422	C₂²×C₅	—	8	1	no	—
423	C₂²×C₅	C₂×#121	1	1	yes	characteristic
424	C₂²×C₅	#525	1	1	yes	characteristic
425	C₂²×C₅	#532	1	1	yes	characteristic
426	C₂²×C₅	C₂×#135	1	1	yes	characteristic
427	C₂²×C₅	C₂×#135	1	1	yes	characteristic
428	C₂²×C₅	C₂×#137	1	1	yes	characteristic
429	C₂²×C₅	#575	1	1	yes	characteristic
430	C₄×C₅	—	2	2	no	—
431	C₄×C₅	—	2	2	no	—
432	C₄×C₅	—	4	1	no	—
433	C₄×C₅	—	4	1	no	—
434	C₄×C₅	—	4	2	no	—
435	C₄×C₅	—	4	2	no	—
436	C₄×C₅	—	4	1	no	—
437	C₄×C₅	—	4	2	no	—
438	C₄×C₅	—	8	1	no	—
439	C₄×C₅	—	8	1	no	—
440	C₄×C₅	—	8	1	no	—
441	C₄×C₅	—	8	1	no	—
442	C₄×C₅	#464	1	4	yes	—
443	C₄×C₅	#525	1	1	yes	characteristic
444	C₄×C₅	#525	1	1	yes	characteristic
445	C₄×C₅	#529	1	1	yes	characteristic
446	C₄×C₅	#529	1	1	yes	characteristic
447	C₂⁴	—	2	1	no	—
448	C₂×Q₈	—	2	1	no	—
449	C₂×Q₈	—	2	1	no	—
450	C₂×Q₈	—	2	1	no	—
451	C₂×Q₈	—	2	1	no	—
452	C₂×Q₈	—	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	C₂×C₅×D₄	1	2	yes	—
459	C₂×Q₈	C₅×#41	1	2	yes	—
460	C₂×D₄	—	2	1	no	—
461	C₂×D₄	—	2	1	no	—
462	C₂×D₄	—	2	1	no	—
463	C₂×D₄	—	2	1	no	—
464	C₂×D₄	—	2	1	no	—
465	C₂×D₄	C₅×#41	1	2	yes	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	4	2	no	—
474	C₂²×C₄	—	4	2	no	—
475	C₂²×C₄	—	4	2	no	—
476	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
477	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
478	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
479	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
480	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
481	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
482	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
483	Q₁₆	—	2	8	no	—
484	SD₁₆	—	2	8	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	—	2	1	no	—
489	C₂×C₈	—	2	1	no	—
490	C₂×C₈	—	2	1	no	—
491	C₂×C₈	—	2	1	no	—
492	C₂×C₈	—	2	1	no	—
493	C₂×C₈	—	2	1	no	—
494	C₂×C₈	—	2	1	no	—
495	C₂×C₈	C₅×#41	1	2	yes	—
496	C₂×C₈	C₅×#41	1	2	yes	—
497	C₄⋊C₄	—	2	4	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	—	2	1	no	—
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	4	2	no	—
508	C₄⋊C₄	—	4	2	no	—
509	C₄⋊C₄	—	4	2	no	—
510	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
511	C₂²⋊C₄	—	2	4	no	—
512	C₂²⋊C₄	—	2	4	no	—
513	C₂²⋊C₄	—	4	2	no	—
514	C₂²⋊C₄	—	4	2	no	—
515	C₂²⋊C₄	—	4	2	no	—
516	C₄²	—	2	4	no	—
517	C₄²	—	2	2	no	—
518	C₄²	—	2	2	no	—
519	C₄²	—	2	2	no	—
520	C₄²	—	2	1	no	—
521	C₄²	—	2	1	no	—
522	C₄²	—	2	1	no	—
523	C₄²	—	2	1	no	—
524	C₄²	—	4	1	no	—
525	C₄²	—	4	2	no	—
526	C₄²	—	4	2	no	—
527	C₄²	C₂×C₅×D₄	1	2	yes	—
528	C₄²	C₅×#41	1	2	yes	—
529	C₂×C₅	—	8	2	no	—
530	C₂×C₅	#2392	1	1	yes	characteristic
531	C₂×C₅	C₂×#464	1	1	yes	characteristic
532	C₂×C₅	#3035	1	1	yes	characteristic
533	C₂×C₅	#3102	1	1	yes	characteristic
534	C₂×C₅	#3107	1	1	yes	characteristic
535	C₂×C₅	#3168	1	1	yes	characteristic
536	C₂×C₅	#3172	1	1	yes	characteristic
537	C₂³	—	2	2	no	—
538	C₂³	—	4	1	no	—
539	C₂³	—	4	1	no	—
540	C₂³	—	4	1	no	—
541	C₂³	—	4	1	no	—
542	C₂³	—	4	1	no	—
543	C₂³	—	4	1	no	—
544	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
545	Q₈	—	2	2	no	—
546	Q₈	—	2	2	no	—
547	Q₈	—	2	2	no	—
548	Q₈	—	2	2	no	—
549	Q₈	—	4	1	no	—
550	Q₈	—	4	1	no	—
551	Q₈	—	4	1	no	—
552	Q₈	—	4	1	no	—
553	D₄	—	2	2	no	—
554	D₄	—	2	2	no	—
555	D₄	—	4	1	no	—
556	D₄	—	4	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	2	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	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	4	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	—	8	4	no	—
592	C₂×C₄	C₅×#121	1	2	yes	—
593	C₂×C₄	C₅×#121	1	2	yes	—
594	C₂×C₄	C₅×#135	1	2	yes	—
595	C₂×C₄	C₅×#135	1	2	yes	—
596	C₂×C₄	C₅×#137	1	2	yes	—
597	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
598	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
599	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
600	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
601	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
602	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
603	C₈	—	2	2	no	—
604	C₈	—	2	2	no	—
605	C₈	—	4	1	no	—
606	C₈	—	4	1	no	—
607	C₅	#23681	1	1	yes	characteristic, direct product factor, Sylow
608	C₂²	—	4	2	no	—
609	C₂²	—	4	2	no	—
610	C₂²	—	4	2	no	—
611	C₂²	—	8	1	no	—
612	C₂²	—	8	1	no	—
613	C₂²	—	8	1	no	—
614	C₂²	—	8	1	no	—
615	C₂²	C₂×C₅×#121	1	1	yes	characteristic
616	C₂²	C₅×#525	1	1	yes	characteristic
617	C₂²	C₅×#532	1	1	yes	characteristic
618	C₂²	C₂×C₅×#135	1	1	yes	characteristic
619	C₂²	C₂×C₅×#135	1	1	yes	characteristic
620	C₂²	C₂×C₅×#137	1	1	yes	characteristic
621	C₂²	C₅×#575	1	1	yes	characteristic
622	C₄	—	2	2	no	—
623	C₄	—	2	2	no	—
624	C₄	—	4	2	no	—
625	C₄	—	4	1	no	—
626	C₄	—	4	1	no	—
627	C₄	—	4	2	no	—
628	C₄	—	4	2	no	—
629	C₄	—	4	1	no	—
630	C₄	—	8	1	no	—
631	C₄	—	8	1	no	—
632	C₄	—	8	1	no	—
633	C₄	—	8	1	no	—
634	C₄	C₅×#464	1	4	yes	—
635	C₄	C₅×#525	1	1	yes	characteristic
636	C₄	C₅×#525	1	1	yes	characteristic
637	C₄	C₅×#529	1	1	yes	characteristic
638	C₄	C₅×#529	1	1	yes	characteristic
639	C₂	—	8	2	no	—
640	C₂	C₅×#2392	1	1	yes	characteristic
641	C₂	C₂×C₅×#464	1	1	yes	characteristic
642	C₂	C₅×#3035	1	1	yes	characteristic
643	C₂	C₅×#3102	1	1	yes	characteristic
644	C₂	C₅×#3107	1	1	yes	characteristic
645	C₂	C₅×#3168	1	1	yes	characteristic
646	C₂	C₅×#3172	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂³×C₅	C₂²×D₄
prime radical	C₂²×C₅×D₄	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₄³×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄×C₅×Q₁₆	C₂	semidirect
4. C₅×#2295	C₂	semidirect
5. C₅×#2085	C₂	semidirect
6. C₅×#2074	C₂	semidirect
8. C₅×#2066	C₂	semidirect
9. C₅×#2056	C₂	semidirect
13. C₄×C₅×C₄⋊C₈	C₂	semidirect
14. C₄×C₅×#103	C₂	semidirect
61. #23681	C₅	direct (N × H)
133. C₂×C₄×Q₁₆	C₂×C₅	semidirect
136. #2295	C₂×C₅	semidirect
137. #2085	C₂×C₅	semidirect
138. #2074	C₂×C₅	semidirect
140. #2066	C₂×C₅	semidirect
141. #2056	C₂×C₅	semidirect
145. C₄×C₄⋊C₈	C₂×C₅	semidirect
146. C₄×#103	C₂×C₅	semidirect
607. C₅	#23681	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×C₄×C₅×Q₁₆	2
C₂×C₄×C₅×SD₁₆	2
C₄×C₅×#124	2
C₅×#2295	2
C₅×#2085	2
C₅×#2074	2
C₅×#2067	2
C₅×#2066	2
C₅×#2056	2
C₅×#2055	2
C₅×#2042	2
C₅×#2015	2
C₄×C₅×C₄⋊C₈	2
C₄×C₅×#103	2
C₄×C₅×#102	2
#23681	5

Subgroups — C5×#23681 #11946401

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#23681 #11946401