Subgroups — C₅×#17449 #11940169

Order 1280.

1214 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₅×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×#1491	C₂	1	4	yes	maximal, complemented
5	C₅×#1487	C₂	1	4	yes	maximal, complemented
6	C₅×#1479	C₂	1	4	yes	maximal, complemented
7	C₂³×C₅×Q₈	C₄	1	1	yes	characteristic
8	C₂×C₄×C₅×Q₈	—	2	1	no	—
9	C₂×C₄×C₅×Q₈	—	2	1	no	—
10	C₂×C₄×C₅×Q₈	—	2	1	no	—
11	C₂×C₄×C₅×Q₈	—	2	1	no	—
12	C₂×C₄×C₅×Q₈	—	2	1	no	—
13	C₂×C₄×C₅×Q₈	—	2	1	no	—
14	C₂×C₄×C₅×Q₈	C₄	1	2	yes	—
15	C₂×C₄×C₅×Q₈	C₄	1	2	yes	—
16	C₂×C₄×C₅×Q₈	C₄	1	2	yes	—
17	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
18	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
19	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
20	C₂²×C₅×C₄⋊C₄	—	2	1	no	—
21	C₂²×C₅×C₄⋊C₄	C₄	1	1	yes	characteristic
22	C₂²×C₄²×C₅	—	2	1	no	—
23	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
24	C₅×#432	—	2	1	no	—
25	C₅×#432	—	2	1	no	—
26	C₅×#432	—	2	1	no	—
27	C₅×#432	C₂²	1	2	yes	—
28	C₅×#431	—	2	1	no	—
29	C₅×#431	C₂²	1	2	yes	—
30	C₅×#431	C₂²	1	2	yes	—
31	C₅×#431	C₂²	1	2	yes	—
32	C₅×#423	—	2	1	no	—
33	C₅×#423	C₂²	1	2	yes	—
34	C₅×#407	—	2	1	no	—
35	C₅×#407	—	2	1	no	—
36	C₄×C₅×M₁₆	—	2	1	no	—
37	C₄×C₅×M₁₆	C₂²	1	2	yes	—
38	C₅×Q₈⋊C₈	C₂²	1	16	yes	complemented
39	#17449	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
40	C₂²×C₅×Q₈	—	2	8	no	—
41	C₂²×C₅×Q₈	—	2	1	no	—
42	C₂²×C₅×Q₈	—	2	1	no	—
43	C₂²×C₅×Q₈	—	2	1	no	—
44	C₂²×C₅×Q₈	C₂×C₄	1	2	yes	—
45	C₂²×C₅×Q₈	C₂×C₄	1	2	yes	—
46	C₂²×C₅×Q₈	C₂×C₄	1	2	yes	—
47	C₂³×C₄×C₅	—	2	1	no	—
48	C₂³×C₄×C₅	—	2	1	no	—
49	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
50	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
52	C₂×C₅×M₁₆	—	2	2	no	—
53	C₂×C₅×M₁₆	—	2	2	no	—
54	C₄×C₅×Q₈	—	2	2	no	—
55	C₄×C₅×Q₈	—	2	2	no	—
56	C₄×C₅×Q₈	—	2	2	no	—
57	C₄×C₅×Q₈	—	2	2	no	—
58	C₄×C₅×Q₈	—	2	2	no	—
59	C₄×C₅×Q₈	—	2	2	no	—
60	C₄×C₅×Q₈	—	2	2	no	—
61	C₄×C₅×Q₈	—	2	2	no	—
62	C₄×C₅×Q₈	—	2	2	no	—
63	C₄×C₅×Q₈	—	2	2	no	—
64	C₄×C₅×Q₈	—	2	2	no	—
65	C₄×C₅×Q₈	—	2	2	no	—
66	C₄×C₅×Q₈	C₂×C₄	1	4	yes	—
67	C₄×C₅×Q₈	C₂×C₄	1	4	yes	—
68	C₄×C₅×Q₈	C₂×C₄	1	4	yes	—
69	C₄×C₅×Q₈	C₂³	1	4	yes	—
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	1	no	—
74	C₂×C₅×C₄⋊C₄	—	2	1	no	—
75	C₂×C₅×C₄⋊C₄	—	2	1	no	—
76	C₂×C₅×C₄⋊C₄	—	2	2	no	—
77	C₂×C₅×C₄⋊C₄	—	2	2	no	—
78	C₂×C₅×C₄⋊C₄	—	2	2	no	—
79	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
80	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
81	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
82	C₂×C₄²×C₅	—	2	2	no	—
83	C₂×C₄²×C₅	—	2	2	no	—
84	C₂×C₄²×C₅	—	2	2	no	—
85	C₂×C₄²×C₅	—	2	2	no	—
86	C₂×C₄²×C₅	—	2	2	no	—
87	C₂×C₄²×C₅	—	2	2	no	—
88	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
89	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
92	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
93	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
94	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
96	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
97	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
100	C₅×C₄⋊C₈	—	2	2	no	—
101	C₅×C₄⋊C₈	—	2	2	no	—
102	C₅×C₄⋊C₈	—	2	2	no	—
103	C₅×C₄⋊C₈	C₂³	1	4	yes	—
104	C₅×C₂²⋊C₈	—	2	2	no	—
105	C₅×C₂²⋊C₈	—	2	2	no	—
106	C₅×C₂²⋊C₈	—	2	2	no	—
107	C₅×C₂²⋊C₈	—	2	2	no	—
108	C₅×#97	—	2	2	no	—
109	C₅×#97	—	2	2	no	—
110	C₄×C₅×C₈	—	2	2	no	—
111	C₄×C₅×C₈	C₂³	1	4	yes	—
112	C₂²×C₄×Q₈	C₂×C₅	1	1	yes	characteristic
113	#2920	C₂×C₅	1	1	yes	characteristic
114	#2920	C₂×C₅	1	1	yes	characteristic
115	#1491	C₂×C₅	1	4	yes	complemented
116	#1487	C₂×C₅	1	4	yes	complemented
117	#1479	C₂×C₅	1	4	yes	complemented
118	C₂⁴×C₅	C₂²⋊C₄	1	1	yes	characteristic
119	C₂×C₅×Q₈	—	2	8	no	—
120	C₂×C₅×Q₈	—	2	8	no	—
121	C₂×C₅×Q₈	—	2	8	no	—
122	C₂×C₅×Q₈	—	2	8	no	—
123	C₂×C₅×Q₈	—	2	8	no	—
124	C₂×C₅×Q₈	—	2	2	no	—
125	C₂×C₅×Q₈	—	2	2	no	—
126	C₂×C₅×Q₈	—	2	2	no	—
127	C₂×C₅×Q₈	—	2	4	no	—
128	C₂×C₅×Q₈	M₁₆	1	8	yes	complemented
129	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	—
130	C₂²×C₄×C₅	—	2	8	no	—
131	C₂²×C₄×C₅	—	2	2	no	—
132	C₂²×C₄×C₅	—	2	2	no	—
133	C₂²×C₄×C₅	—	2	2	no	—
134	C₂²×C₄×C₅	—	2	4	no	—
135	C₂²×C₄×C₅	—	2	4	no	—
136	C₂²×C₄×C₅	—	2	2	no	—
137	C₂²×C₄×C₅	—	2	2	no	—
138	C₂²×C₄×C₅	—	2	2	no	—
139	C₂²×C₄×C₅	—	4	2	no	—
140	C₂²×C₄×C₅	—	4	4	no	—
141	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
142	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
143	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
144	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
145	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
146	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
147	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
148	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
149	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
150	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
152	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
159	C₅×M₁₆	—	4	4	no	—
160	C₅×M₁₆	—	4	4	no	—
161	C₂×C₅×C₈	—	2	4	no	—
162	C₂×C₅×C₈	—	2	4	no	—
163	C₅×C₄⋊C₄	—	2	4	no	—
164	C₅×C₄⋊C₄	—	2	4	no	—
165	C₅×C₄⋊C₄	—	2	4	no	—
166	C₅×C₄⋊C₄	—	2	2	no	—
167	C₅×C₄⋊C₄	—	2	2	no	—
168	C₅×C₄⋊C₄	—	2	2	no	—
169	C₅×C₄⋊C₄	—	2	4	no	—
170	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
171	C₄²×C₅	—	2	4	no	—
172	C₄²×C₅	—	2	4	no	—
173	C₄²×C₅	—	2	4	no	—
174	C₄²×C₅	—	2	4	no	—
175	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
176	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
177	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
178	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
179	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
180	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
181	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
182	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
183	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
184	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
185	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
186	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
187	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
188	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
189	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
190	C₄²×C₅	C₂⁴	1	1	yes	characteristic
191	C₂³×Q₈	C₄×C₅	1	1	yes	characteristic
192	C₂×C₄×Q₈	—	2	1	no	—
193	C₂×C₄×Q₈	—	2	1	no	—
194	C₂×C₄×Q₈	—	2	1	no	—
195	C₂×C₄×Q₈	—	2	1	no	—
196	C₂×C₄×Q₈	—	2	1	no	—
197	C₂×C₄×Q₈	—	2	1	no	—
198	C₂×C₄×Q₈	C₄×C₅	1	2	yes	—
199	C₂×C₄×Q₈	C₄×C₅	1	2	yes	—
200	C₂×C₄×Q₈	C₄×C₅	1	2	yes	—
201	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
202	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
203	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
204	C₂²×C₄⋊C₄	—	2	1	no	—
205	C₂²×C₄⋊C₄	C₄×C₅	1	1	yes	characteristic
206	C₂²×C₄²	—	2	1	no	—
207	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
208	#432	—	2	1	no	—
209	#432	—	2	1	no	—
210	#432	—	2	1	no	—
211	#432	C₂²×C₅	1	2	yes	—
212	#431	—	2	1	no	—
213	#431	C₂²×C₅	1	2	yes	—
214	#431	C₂²×C₅	1	2	yes	—
215	#431	C₂²×C₅	1	2	yes	—
216	#423	—	2	1	no	—
217	#423	C₂²×C₅	1	2	yes	—
218	#407	—	2	1	no	—
219	#407	—	2	1	no	—
220	C₄×M₁₆	—	2	1	no	—
221	C₄×M₁₆	C₂²×C₅	1	2	yes	—
222	Q₈⋊C₈	C₂²×C₅	1	16	yes	complemented
223	C₂³×C₅	—	2	2	no	—
224	C₂³×C₅	—	2	2	no	—
225	C₂³×C₅	—	2	2	no	—
226	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
227	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
228	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
229	C₅×Q₈	—	2	8	no	—
230	C₅×Q₈	—	2	8	no	—
231	C₅×Q₈	—	2	4	no	—
232	C₅×Q₈	—	2	8	no	—
233	C₅×Q₈	C₂×M₁₆	1	8	yes	—
234	C₂×C₄×C₅	—	2	8	no	—
235	C₂×C₄×C₅	—	2	8	no	—
236	C₂×C₄×C₅	—	2	4	no	—
237	C₂×C₄×C₅	—	2	8	no	—
238	C₂×C₄×C₅	—	2	2	no	—
239	C₂×C₄×C₅	—	2	2	no	—
240	C₂×C₄×C₅	—	2	2	no	—
241	C₂×C₄×C₅	—	2	2	no	—
242	C₂×C₄×C₅	—	2	2	no	—
243	C₂×C₄×C₅	—	2	2	no	—
244	C₂×C₄×C₅	—	2	2	no	—
245	C₂×C₄×C₅	—	2	2	no	—
246	C₂×C₄×C₅	—	2	2	no	—
247	C₂×C₄×C₅	—	2	2	no	—
248	C₂×C₄×C₅	—	2	2	no	—
249	C₂×C₄×C₅	—	2	2	no	—
250	C₂×C₄×C₅	—	2	4	no	—
251	C₂×C₄×C₅	—	4	1	no	—
252	C₂×C₄×C₅	—	4	1	no	—
253	C₂×C₄×C₅	—	4	1	no	—
254	C₂×C₄×C₅	—	4	1	no	—
255	C₂×C₄×C₅	—	4	4	no	—
256	C₂×C₄×C₅	—	4	4	no	—
257	C₂×C₄×C₅	—	4	4	no	—
258	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
259	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
260	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
261	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
262	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
263	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
264	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
265	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
266	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
267	C₂×C₄×C₅	C₂×M₁₆	1	4	yes	—
268	C₂×C₄×C₅	#137	1	4	yes	—
269	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
270	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
271	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
272	C₅×C₈	—	4	4	no	—
273	C₅×C₈	—	4	4	no	—
274	C₂²×Q₈	—	2	8	no	—
275	C₂²×Q₈	—	2	1	no	—
276	C₂²×Q₈	—	2	1	no	—
277	C₂²×Q₈	—	2	1	no	—
278	C₂²×Q₈	C₂×C₄×C₅	1	2	yes	—
279	C₂²×Q₈	C₂×C₄×C₅	1	2	yes	—
280	C₂²×Q₈	C₂×C₄×C₅	1	2	yes	—
281	C₂³×C₄	—	2	1	no	—
282	C₂³×C₄	—	2	1	no	—
283	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
284	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
285	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
286	C₂×M₁₆	—	2	2	no	—
287	C₂×M₁₆	—	2	2	no	—
288	C₄×Q₈	—	2	2	no	—
289	C₄×Q₈	—	2	2	no	—
290	C₄×Q₈	—	2	2	no	—
291	C₄×Q₈	—	2	2	no	—
292	C₄×Q₈	—	2	2	no	—
293	C₄×Q₈	—	2	2	no	—
294	C₄×Q₈	—	2	2	no	—
295	C₄×Q₈	—	2	2	no	—
296	C₄×Q₈	—	2	2	no	—
297	C₄×Q₈	—	2	2	no	—
298	C₄×Q₈	—	2	2	no	—
299	C₄×Q₈	—	2	2	no	—
300	C₄×Q₈	C₂×C₄×C₅	1	4	yes	—
301	C₄×Q₈	C₂×C₄×C₅	1	4	yes	—
302	C₄×Q₈	C₂×C₄×C₅	1	4	yes	—
303	C₄×Q₈	C₂³×C₅	1	4	yes	—
304	C₂×C₄⋊C₄	—	2	2	no	—
305	C₂×C₄⋊C₄	—	2	2	no	—
306	C₂×C₄⋊C₄	—	2	2	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	—	2	1	no	—
309	C₂×C₄⋊C₄	—	2	1	no	—
310	C₂×C₄⋊C₄	—	2	2	no	—
311	C₂×C₄⋊C₄	—	2	2	no	—
312	C₂×C₄⋊C₄	—	2	2	no	—
313	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
314	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
315	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
316	C₂×C₄²	—	2	2	no	—
317	C₂×C₄²	—	2	2	no	—
318	C₂×C₄²	—	2	2	no	—
319	C₂×C₄²	—	2	2	no	—
320	C₂×C₄²	—	2	2	no	—
321	C₂×C₄²	—	2	2	no	—
322	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
323	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
324	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
325	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
326	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
327	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
328	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
329	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
330	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
331	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
332	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
333	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
334	C₄⋊C₈	—	2	2	no	—
335	C₄⋊C₈	—	2	2	no	—
336	C₄⋊C₈	—	2	2	no	—
337	C₄⋊C₈	C₂³×C₅	1	4	yes	—
338	C₂²⋊C₈	—	2	2	no	—
339	C₂²⋊C₈	—	2	2	no	—
340	C₂²⋊C₈	—	2	2	no	—
341	C₂²⋊C₈	—	2	2	no	—
342	#97	—	2	2	no	—
343	#97	—	2	2	no	—
344	C₄×C₈	—	2	2	no	—
345	C₄×C₈	C₂³×C₅	1	4	yes	—
346	C₂²×C₅	—	2	8	no	—
347	C₂²×C₅	—	2	1	no	—
348	C₂²×C₅	—	2	1	no	—
349	C₂²×C₅	—	2	1	no	—
350	C₂²×C₅	—	2	1	no	—
351	C₂²×C₅	—	2	1	no	—
352	C₂²×C₅	—	2	1	no	—
353	C₂²×C₅	#407	1	2	yes	—
354	C₂²×C₅	#419	1	2	yes	—
355	C₂²×C₅	#421	1	2	yes	—
356	C₂²×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
357	C₄×C₅	—	2	8	no	—
358	C₄×C₅	—	2	1	no	—
359	C₄×C₅	—	2	1	no	—
360	C₄×C₅	—	2	1	no	—
361	C₄×C₅	—	2	1	no	—
362	C₄×C₅	—	2	1	no	—
363	C₄×C₅	—	2	1	no	—
364	C₄×C₅	—	2	1	no	—
365	C₄×C₅	—	2	1	no	—
366	C₄×C₅	—	4	4	no	—
367	C₄×C₅	#407	1	2	yes	—
368	C₄×C₅	#419	1	2	yes	—
369	C₄×C₅	C₂²×M₁₆	1	2	yes	—
370	C₄×C₅	C₂×#137	1	2	yes	—
371	C₂⁴	C₅×C₂²⋊C₄	1	1	yes	characteristic
372	C₂×Q₈	—	2	8	no	—
373	C₂×Q₈	—	2	8	no	—
374	C₂×Q₈	—	2	8	no	—
375	C₂×Q₈	—	2	8	no	—
376	C₂×Q₈	—	2	8	no	—
377	C₂×Q₈	—	2	2	no	—
378	C₂×Q₈	—	2	2	no	—
379	C₂×Q₈	—	2	2	no	—
380	C₂×Q₈	—	2	4	no	—
381	C₂×Q₈	C₅×M₁₆	1	8	yes	complemented
382	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	—
383	C₂²×C₄	—	2	8	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	4	no	—
388	C₂²×C₄	—	2	4	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	4	2	no	—
393	C₂²×C₄	—	4	4	no	—
394	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
395	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
396	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
397	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
398	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
399	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
400	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
401	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
402	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
403	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
404	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
405	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
406	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
407	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
408	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
409	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
410	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
411	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
412	M₁₆	—	4	4	no	—
413	M₁₆	—	4	4	no	—
414	C₂×C₈	—	2	4	no	—
415	C₂×C₈	—	2	4	no	—
416	C₄⋊C₄	—	2	4	no	—
417	C₄⋊C₄	—	2	4	no	—
418	C₄⋊C₄	—	2	4	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	4	no	—
423	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
424	C₄²	—	2	4	no	—
425	C₄²	—	2	4	no	—
426	C₄²	—	2	4	no	—
427	C₄²	—	2	4	no	—
428	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
429	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
430	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
431	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
432	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
433	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
434	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
435	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
436	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
437	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
438	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
439	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
440	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
441	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
442	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
443	C₄²	C₂⁴×C₅	1	1	yes	characteristic
444	C₂×C₅	—	2	2	no	—
445	C₂×C₅	—	2	2	no	—
446	C₂×C₅	—	2	2	no	—
447	C₂×C₅	C₂×#407	1	1	yes	characteristic
448	C₂×C₅	C₂×#419	1	1	yes	characteristic
449	C₂×C₅	C₂×#421	1	1	yes	characteristic
450	C₂³	—	2	2	no	—
451	C₂³	—	2	2	no	—
452	C₂³	—	2	2	no	—
453	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
454	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
455	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
456	Q₈	—	2	8	no	—
457	Q₈	—	2	8	no	—
458	Q₈	—	2	8	no	—
459	Q₈	—	2	4	no	—
460	Q₈	C₂×C₅×M₁₆	1	8	yes	—
461	C₂×C₄	—	2	8	no	—
462	C₂×C₄	—	2	8	no	—
463	C₂×C₄	—	2	8	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	4	no	—
483	C₂×C₄	—	4	4	no	—
484	C₂×C₄	—	4	4	no	—
485	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
486	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
487	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
488	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
489	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
490	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
491	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
492	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
493	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
494	C₂×C₄	C₂×C₅×M₁₆	1	4	yes	—
495	C₂×C₄	C₅×#137	1	4	yes	—
496	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
497	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
498	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
499	C₈	—	4	4	no	—
500	C₈	—	4	4	no	—
501	C₅	#17449	1	1	yes	characteristic, direct product factor, Sylow
502	C₂²	—	2	8	no	—
503	C₂²	—	2	1	no	—
504	C₂²	—	2	1	no	—
505	C₂²	—	2	1	no	—
506	C₂²	—	2	1	no	—
507	C₂²	—	2	1	no	—
508	C₂²	—	2	1	no	—
509	C₂²	C₅×#407	1	2	yes	—
510	C₂²	C₅×#419	1	2	yes	—
511	C₂²	C₅×#421	1	2	yes	—
512	C₂²	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
513	C₄	—	2	8	no	—
514	C₄	—	2	1	no	—
515	C₄	—	2	1	no	—
516	C₄	—	2	1	no	—
517	C₄	—	2	1	no	—
518	C₄	—	2	1	no	—
519	C₄	—	2	1	no	—
520	C₄	—	2	1	no	—
521	C₄	—	2	1	no	—
522	C₄	—	4	4	no	—
523	C₄	C₅×#407	1	2	yes	—
524	C₄	C₅×#419	1	2	yes	—
525	C₄	C₂²×C₅×M₁₆	1	2	yes	—
526	C₄	C₂×C₅×#137	1	2	yes	—
527	C₂	—	2	2	no	—
528	C₂	—	2	2	no	—
529	C₂	—	2	2	no	—
530	C₂	C₂×C₅×#407	1	1	yes	characteristic
531	C₂	C₂×C₅×#419	1	1	yes	characteristic
532	C₂	C₂×C₅×#421	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₄²	C₂⁴×C₅
socle	C₂²×C₅	C₂²×C₂²⋊C₄
prime radical	C₂⁴×C₅	C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂²×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₅×#1491	C₂	semidirect
5. C₅×#1487	C₂	semidirect
6. C₅×#1479	C₂	semidirect
38. C₅×Q₈⋊C₈	C₂²	semidirect
39. #17449	C₅	direct (N × H)
115. #1491	C₂×C₅	semidirect
116. #1487	C₂×C₅	semidirect
117. #1479	C₂×C₅	semidirect
128. C₂×C₅×Q₈	M₁₆	semidirect
222. Q₈⋊C₈	C₂²×C₅	semidirect
381. C₂×Q₈	C₅×M₁₆	semidirect
501. C₅	#17449	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×C₄×C₅×Q₈	2
C₅×#2920	2
C₅×#1491	2
C₅×#1487	2
C₅×#1479	2
#17449	5

Subgroups — C5×#17449 #11940169

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#17449 #11940169