Subgroups — C₅×#17742 #11940462

Order 1280.

1178 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₅×#2920	C₂	1	1	yes	maximal, characteristic
3	C₅×#2920	C₂	1	1	yes	maximal, characteristic
4	C₅×#1556	C₂	1	4	yes	maximal, complemented
5	C₅×#1549	C₂	1	4	yes	maximal, complemented
6	C₅×#1546	C₂	1	4	yes	maximal, complemented
7	C₂³×C₅×Q₈	—	2	1	no	—
8	C₂×C₅×C₄⋊Q₈	—	2	1	no	—
9	C₂×C₅×C₄⋊Q₈	—	2	1	no	—
10	C₂×C₅×C₄⋊Q₈	—	2	1	no	—
11	C₂×C₅×C₄⋊Q₈	—	2	1	no	—
12	C₂×C₅×C₄⋊Q₈	—	2	1	no	—
13	C₂×C₅×C₄⋊Q₈	—	2	1	no	—
14	C₂×C₅×C₄⋊Q₈	C₄	1	2	yes	—
15	C₂×C₅×C₄⋊Q₈	C₄	1	2	yes	—
16	C₂×C₅×C₄⋊Q₈	C₄	1	2	yes	—
17	C₂×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
18	C₂×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
19	C₂×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
20	C₂²×C₅×C₄⋊C₄	—	2	1	no	—
21	C₂²×C₅×C₄⋊C₄	C₄	1	2	yes	—
22	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
23	C₅×#432	—	2	1	no	—
24	C₅×#432	—	2	1	no	—
25	C₅×#432	C₂²	1	2	yes	—
26	C₅×#432	C₂²	1	2	yes	—
27	C₅×#431	—	2	1	no	—
28	C₅×#431	—	2	1	no	—
29	C₅×#431	C₂²	1	2	yes	—
30	C₅×#431	C₂²	1	2	yes	—
31	C₅×#423	C₂²	1	2	yes	—
32	C₅×#423	C₂²	1	2	yes	—
33	C₅×#407	—	2	1	no	—
34	C₅×#407	—	2	1	no	—
35	C₄×C₅×M₁₆	—	2	1	no	—
36	C₄×C₅×M₁₆	—	2	1	no	—
37	C₅×#332	C₂²	1	16	yes	complemented
38	#17742	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
39	C₂²×C₅×Q₈	—	2	2	no	—
40	C₂²×C₅×Q₈	—	2	2	no	—
41	C₂²×C₅×Q₈	—	2	2	no	—
42	C₂²×C₅×Q₈	—	2	2	no	—
43	C₂²×C₅×Q₈	—	2	2	no	—
44	C₂²×C₅×Q₈	—	2	2	no	—
45	C₂²×C₅×Q₈	—	4	8	no	—
46	C₂³×C₄×C₅	—	2	2	no	—
47	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
50	C₂×C₅×M₁₆	—	2	2	no	—
51	C₂×C₅×M₁₆	—	2	2	no	—
52	C₅×C₄⋊Q₈	—	2	2	no	—
53	C₅×C₄⋊Q₈	—	2	2	no	—
54	C₅×C₄⋊Q₈	—	2	2	no	—
55	C₅×C₄⋊Q₈	—	2	2	no	—
56	C₅×C₄⋊Q₈	—	2	2	no	—
57	C₅×C₄⋊Q₈	—	2	2	no	—
58	C₅×C₄⋊Q₈	—	2	2	no	—
59	C₅×C₄⋊Q₈	—	2	2	no	—
60	C₅×C₄⋊Q₈	—	2	2	no	—
61	C₅×C₄⋊Q₈	—	2	2	no	—
62	C₅×C₄⋊Q₈	—	2	2	no	—
63	C₅×C₄⋊Q₈	—	2	2	no	—
64	C₅×C₄⋊Q₈	C₂×C₄	1	4	yes	—
65	C₅×C₄⋊Q₈	C₂×C₄	1	4	yes	—
66	C₅×C₄⋊Q₈	C₂×C₄	1	4	yes	—
67	C₅×C₄⋊Q₈	C₂³	1	4	yes	—
68	C₂×C₅×C₄⋊C₄	—	2	2	no	—
69	C₂×C₅×C₄⋊C₄	—	2	2	no	—
70	C₂×C₅×C₄⋊C₄	—	2	2	no	—
71	C₂×C₅×C₄⋊C₄	—	2	2	no	—
72	C₂×C₅×C₄⋊C₄	—	2	2	no	—
73	C₂×C₅×C₄⋊C₄	—	2	2	no	—
74	C₂×C₅×C₄⋊C₄	—	2	2	no	—
75	C₂×C₅×C₄⋊C₄	—	2	2	no	—
76	C₂×C₅×C₄⋊C₄	—	2	2	no	—
77	C₂×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
78	C₂×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
79	C₂×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
80	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
83	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
84	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
85	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
86	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
87	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
88	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
89	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
92	C₅×C₄⋊C₈	—	2	2	no	—
93	C₅×C₄⋊C₈	—	2	2	no	—
94	C₅×C₄⋊C₈	C₂³	1	4	yes	—
95	C₅×C₄⋊C₈	C₂³	1	4	yes	—
96	C₅×C₂²⋊C₈	—	2	2	no	—
97	C₅×C₂²⋊C₈	—	2	2	no	—
98	C₅×C₂²⋊C₈	—	2	2	no	—
99	C₅×C₂²⋊C₈	—	2	2	no	—
100	C₅×#97	—	2	2	no	—
101	C₅×#97	—	2	2	no	—
102	C₄×C₅×C₈	—	2	2	no	—
103	C₄×C₅×C₈	—	2	2	no	—
104	C₂²×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic
105	#2920	C₂×C₅	1	1	yes	characteristic
106	#2920	C₂×C₅	1	1	yes	characteristic
107	#1556	C₂×C₅	1	4	yes	complemented
108	#1549	C₂×C₅	1	4	yes	complemented
109	#1546	C₂×C₅	1	4	yes	complemented
110	C₂⁴×C₅	C₂²⋊C₄	1	1	yes	characteristic
111	C₂×C₅×Q₈	—	2	4	no	—
112	C₂×C₅×Q₈	—	2	4	no	—
113	C₂×C₅×Q₈	—	2	4	no	—
114	C₂×C₅×Q₈	—	2	4	no	—
115	C₂×C₅×Q₈	—	4	8	no	—
116	C₂×C₅×Q₈	—	4	8	no	—
117	C₂×C₅×Q₈	—	4	8	no	—
118	C₂×C₅×Q₈	—	4	8	no	—
119	C₂×C₅×Q₈	—	4	8	no	—
120	C₂×C₅×Q₈	—	4	8	no	—
121	C₂²×C₄×C₅	—	2	4	no	—
122	C₂²×C₄×C₅	—	2	4	no	—
123	C₂²×C₄×C₅	—	2	4	no	—
124	C₂²×C₄×C₅	—	2	4	no	—
125	C₂²×C₄×C₅	—	2	4	no	—
126	C₂²×C₄×C₅	—	2	4	no	—
127	C₂²×C₄×C₅	—	4	8	no	—
128	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
129	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
130	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
131	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
132	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
133	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
134	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
135	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
136	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
137	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
146	C₅×M₁₆	—	4	4	no	—
147	C₅×M₁₆	—	4	4	no	—
148	C₂×C₅×C₈	—	2	4	no	—
149	C₂×C₅×C₈	—	2	4	no	—
150	C₅×C₄⋊C₄	—	2	4	no	—
151	C₅×C₄⋊C₄	—	2	4	no	—
152	C₅×C₄⋊C₄	—	2	4	no	—
153	C₅×C₄⋊C₄	—	2	4	no	—
154	C₅×C₄⋊C₄	—	2	4	no	—
155	C₅×C₄⋊C₄	—	2	4	no	—
156	C₅×C₄⋊C₄	—	2	4	no	—
157	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
158	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
159	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
160	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
161	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
162	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
163	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
164	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
165	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
166	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
167	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
168	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
171	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₅	C₂⁴	1	1	yes	characteristic
174	C₂³×Q₈	—	2	1	no	—
175	C₂×C₄⋊Q₈	—	2	1	no	—
176	C₂×C₄⋊Q₈	—	2	1	no	—
177	C₂×C₄⋊Q₈	—	2	1	no	—
178	C₂×C₄⋊Q₈	—	2	1	no	—
179	C₂×C₄⋊Q₈	—	2	1	no	—
180	C₂×C₄⋊Q₈	—	2	1	no	—
181	C₂×C₄⋊Q₈	C₄×C₅	1	2	yes	—
182	C₂×C₄⋊Q₈	C₄×C₅	1	2	yes	—
183	C₂×C₄⋊Q₈	C₄×C₅	1	2	yes	—
184	C₂×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
185	C₂×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
186	C₂×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
187	C₂²×C₄⋊C₄	—	2	1	no	—
188	C₂²×C₄⋊C₄	C₄×C₅	1	2	yes	—
189	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
190	#432	—	2	1	no	—
191	#432	—	2	1	no	—
192	#432	C₂²×C₅	1	2	yes	—
193	#432	C₂²×C₅	1	2	yes	—
194	#431	—	2	1	no	—
195	#431	—	2	1	no	—
196	#431	C₂²×C₅	1	2	yes	—
197	#431	C₂²×C₅	1	2	yes	—
198	#423	C₂²×C₅	1	2	yes	—
199	#423	C₂²×C₅	1	2	yes	—
200	#407	—	2	1	no	—
201	#407	—	2	1	no	—
202	C₄×M₁₆	—	2	1	no	—
203	C₄×M₁₆	—	2	1	no	—
204	#332	C₂²×C₅	1	16	yes	complemented
205	C₂³×C₅	—	2	2	no	—
206	C₂³×C₅	—	2	2	no	—
207	C₂³×C₅	—	2	2	no	—
208	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
209	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
210	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
211	C₅×Q₈	—	4	8	no	—
212	C₅×Q₈	—	4	8	no	—
213	C₅×Q₈	—	4	8	no	—
214	C₅×Q₈	—	4	8	no	—
215	C₂×C₄×C₅	—	2	2	no	—
216	C₂×C₄×C₅	—	2	2	no	—
217	C₂×C₄×C₅	—	2	2	no	—
218	C₂×C₄×C₅	—	2	2	no	—
219	C₂×C₄×C₅	—	2	2	no	—
220	C₂×C₄×C₅	—	2	2	no	—
221	C₂×C₄×C₅	—	2	2	no	—
222	C₂×C₄×C₅	—	2	2	no	—
223	C₂×C₄×C₅	—	2	2	no	—
224	C₂×C₄×C₅	—	2	2	no	—
225	C₂×C₄×C₅	—	2	2	no	—
226	C₂×C₄×C₅	—	2	2	no	—
227	C₂×C₄×C₅	—	2	2	no	—
228	C₂×C₄×C₅	—	2	2	no	—
229	C₂×C₄×C₅	—	2	2	no	—
230	C₂×C₄×C₅	—	2	8	no	—
231	C₂×C₄×C₅	—	4	8	no	—
232	C₂×C₄×C₅	—	4	8	no	—
233	C₂×C₄×C₅	—	4	8	no	—
234	C₂×C₄×C₅	#101	1	4	yes	—
235	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
236	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
237	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
238	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
239	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
240	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
241	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
242	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
243	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
244	C₂×C₄×C₅	AGL(1,ℤ/8)	1	4	yes	—
245	C₂×C₄×C₅	#137	1	4	yes	—
246	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
247	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
249	C₅×C₈	—	4	4	no	—
250	C₅×C₈	—	4	4	no	—
251	C₂²×Q₈	—	2	2	no	—
252	C₂²×Q₈	—	2	2	no	—
253	C₂²×Q₈	—	2	2	no	—
254	C₂²×Q₈	—	2	2	no	—
255	C₂²×Q₈	—	2	2	no	—
256	C₂²×Q₈	—	2	2	no	—
257	C₂²×Q₈	—	4	8	no	—
258	C₂³×C₄	—	2	2	no	—
259	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
260	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
261	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
262	C₂×M₁₆	—	2	2	no	—
263	C₂×M₁₆	—	2	2	no	—
264	C₄⋊Q₈	—	2	2	no	—
265	C₄⋊Q₈	—	2	2	no	—
266	C₄⋊Q₈	—	2	2	no	—
267	C₄⋊Q₈	—	2	2	no	—
268	C₄⋊Q₈	—	2	2	no	—
269	C₄⋊Q₈	—	2	2	no	—
270	C₄⋊Q₈	—	2	2	no	—
271	C₄⋊Q₈	—	2	2	no	—
272	C₄⋊Q₈	—	2	2	no	—
273	C₄⋊Q₈	—	2	2	no	—
274	C₄⋊Q₈	—	2	2	no	—
275	C₄⋊Q₈	—	2	2	no	—
276	C₄⋊Q₈	C₂×C₄×C₅	1	4	yes	—
277	C₄⋊Q₈	C₂×C₄×C₅	1	4	yes	—
278	C₄⋊Q₈	C₂×C₄×C₅	1	4	yes	—
279	C₄⋊Q₈	C₂³×C₅	1	4	yes	—
280	C₂×C₄⋊C₄	—	2	2	no	—
281	C₂×C₄⋊C₄	—	2	2	no	—
282	C₂×C₄⋊C₄	—	2	2	no	—
283	C₂×C₄⋊C₄	—	2	2	no	—
284	C₂×C₄⋊C₄	—	2	2	no	—
285	C₂×C₄⋊C₄	—	2	2	no	—
286	C₂×C₄⋊C₄	—	2	2	no	—
287	C₂×C₄⋊C₄	—	2	2	no	—
288	C₂×C₄⋊C₄	—	2	2	no	—
289	C₂×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
290	C₂×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
291	C₂×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
292	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
293	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
294	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
295	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
296	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
297	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
298	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
299	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
300	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
301	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
302	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
303	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
304	C₄⋊C₈	—	2	2	no	—
305	C₄⋊C₈	—	2	2	no	—
306	C₄⋊C₈	C₂³×C₅	1	4	yes	—
307	C₄⋊C₈	C₂³×C₅	1	4	yes	—
308	C₂²⋊C₈	—	2	2	no	—
309	C₂²⋊C₈	—	2	2	no	—
310	C₂²⋊C₈	—	2	2	no	—
311	C₂²⋊C₈	—	2	2	no	—
312	#97	—	2	2	no	—
313	#97	—	2	2	no	—
314	C₄×C₈	—	2	2	no	—
315	C₄×C₈	—	2	2	no	—
316	C₂²×C₅	—	2	8	no	—
317	C₂²×C₅	—	2	1	no	—
318	C₂²×C₅	—	2	1	no	—
319	C₂²×C₅	—	2	1	no	—
320	C₂²×C₅	—	2	1	no	—
321	C₂²×C₅	—	2	1	no	—
322	C₂²×C₅	—	2	1	no	—
323	C₂²×C₅	C₂×#101	1	2	yes	—
324	C₂²×C₅	#418	1	2	yes	—
325	C₂²×C₅	#419	1	2	yes	—
326	C₂²×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
327	C₄×C₅	—	2	1	no	—
328	C₄×C₅	—	2	1	no	—
329	C₄×C₅	—	2	1	no	—
330	C₄×C₅	—	2	1	no	—
331	C₄×C₅	—	2	1	no	—
332	C₄×C₅	—	2	1	no	—
333	C₄×C₅	—	4	8	no	—
334	C₄×C₅	C₂×#101	1	2	yes	—
335	C₄×C₅	C₂×#101	1	2	yes	—
336	C₄×C₅	#418	1	2	yes	—
337	C₄×C₅	#419	1	2	yes	—
338	C₄×C₅	C₂×AGL(1,ℤ/8)	1	2	yes	—
339	C₄×C₅	C₂×#137	1	2	yes	—
340	C₂⁴	C₅×C₂²⋊C₄	1	1	yes	characteristic
341	C₂×Q₈	—	2	4	no	—
342	C₂×Q₈	—	2	4	no	—
343	C₂×Q₈	—	2	4	no	—
344	C₂×Q₈	—	2	4	no	—
345	C₂×Q₈	—	4	8	no	—
346	C₂×Q₈	—	4	8	no	—
347	C₂×Q₈	—	4	8	no	—
348	C₂×Q₈	—	4	8	no	—
349	C₂×Q₈	—	4	8	no	—
350	C₂×Q₈	—	4	8	no	—
351	C₂²×C₄	—	2	4	no	—
352	C₂²×C₄	—	2	4	no	—
353	C₂²×C₄	—	2	4	no	—
354	C₂²×C₄	—	2	4	no	—
355	C₂²×C₄	—	2	4	no	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	4	8	no	—
358	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
359	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
360	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
361	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
362	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
363	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
364	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
365	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
366	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
367	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
368	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
369	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
370	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
371	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
372	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
373	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
374	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
375	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
376	M₁₆	—	4	4	no	—
377	M₁₆	—	4	4	no	—
378	C₂×C₈	—	2	4	no	—
379	C₂×C₈	—	2	4	no	—
380	C₄⋊C₄	—	2	4	no	—
381	C₄⋊C₄	—	2	4	no	—
382	C₄⋊C₄	—	2	4	no	—
383	C₄⋊C₄	—	2	4	no	—
384	C₄⋊C₄	—	2	4	no	—
385	C₄⋊C₄	—	2	4	no	—
386	C₄⋊C₄	—	2	4	no	—
387	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
388	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
389	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
390	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
391	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
392	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
393	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
394	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
395	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
396	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
397	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
398	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
399	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
400	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
401	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
402	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
403	C₄²	C₂⁴×C₅	1	1	yes	characteristic
404	C₂×C₅	—	2	2	no	—
405	C₂×C₅	—	2	2	no	—
406	C₂×C₅	—	2	2	no	—
407	C₂×C₅	C₂²×#101	1	1	yes	characteristic
408	C₂×C₅	C₂×#418	1	1	yes	characteristic
409	C₂×C₅	C₂×#419	1	1	yes	characteristic
410	C₂³	—	2	2	no	—
411	C₂³	—	2	2	no	—
412	C₂³	—	2	2	no	—
413	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
414	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
415	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
416	Q₈	—	4	8	no	—
417	Q₈	—	4	8	no	—
418	Q₈	—	4	8	no	—
419	Q₈	—	4	8	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	8	no	—
436	C₂×C₄	—	4	8	no	—
437	C₂×C₄	—	4	8	no	—
438	C₂×C₄	—	4	8	no	—
439	C₂×C₄	C₅×#101	1	4	yes	—
440	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
441	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
442	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
443	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
444	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
445	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
446	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
447	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
448	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
449	C₂×C₄	C₅×AGL(1,ℤ/8)	1	4	yes	—
450	C₂×C₄	C₅×#137	1	4	yes	—
451	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
452	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
453	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
454	C₈	—	4	4	no	—
455	C₈	—	4	4	no	—
456	C₅	#17742	1	1	yes	characteristic, direct product factor, Sylow
457	C₂²	—	2	8	no	—
458	C₂²	—	2	1	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	2	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	2	1	no	—
464	C₂²	C₂×C₅×#101	1	2	yes	—
465	C₂²	C₅×#418	1	2	yes	—
466	C₂²	C₅×#419	1	2	yes	—
467	C₂²	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
468	C₄	—	2	1	no	—
469	C₄	—	2	1	no	—
470	C₄	—	2	1	no	—
471	C₄	—	2	1	no	—
472	C₄	—	2	1	no	—
473	C₄	—	2	1	no	—
474	C₄	—	4	8	no	—
475	C₄	C₂×C₅×#101	1	2	yes	—
476	C₄	C₂×C₅×#101	1	2	yes	—
477	C₄	C₅×#418	1	2	yes	—
478	C₄	C₅×#419	1	2	yes	—
479	C₄	C₂×C₅×AGL(1,ℤ/8)	1	2	yes	—
480	C₄	C₂×C₅×#137	1	2	yes	—
481	C₂	—	2	2	no	—
482	C₂	—	2	2	no	—
483	C₂	—	2	2	no	—
484	C₂	C₂²×C₅×#101	1	1	yes	characteristic
485	C₂	C₂×C₅×#418	1	1	yes	characteristic
486	C₂	C₂×C₅×#419	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₂⁴×C₅	C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₅×#1556	C₂	semidirect
5. C₅×#1549	C₂	semidirect
6. C₅×#1546	C₂	semidirect
37. C₅×#332	C₂²	semidirect
38. #17742	C₅	direct (N × H)
107. #1556	C₂×C₅	semidirect
108. #1549	C₂×C₅	semidirect
109. #1546	C₂×C₅	semidirect
204. #332	C₂²×C₅	semidirect
456. C₅	#17742	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₅×C₄⋊Q₈	2
C₅×#2920	2
C₅×#1556	2
C₅×#1549	2
C₅×#1546	2
#17742	5

Subgroups — C5×#17742 #11940462

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#17742 #11940462