Subgroups — C₅×#17761 #11940481

Order 1280.

896 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3503	C₂	1	1	yes	maximal, characteristic
2	C₅×#2989	C₂	1	1	yes	maximal, characteristic
3	C₅×#2925	C₂	1	1	yes	maximal, characteristic
4	C₅×#1559	C₂	1	2	yes	maximal, complemented
5	C₅×#1556	C₂	1	2	yes	maximal, complemented
6	C₅×#1554	C₂	1	2	yes	maximal, complemented
7	C₅×#1550	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1549	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1546	C₂	1	2	yes	maximal, complemented
10	C₅×#1542	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×#332	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×Q₈²	C₄	1	2	yes	—
13	C₅×#557	—	2	1	no	—
14	C₅×#554	C₄	1	4	yes	—
15	C₅×#554	C₄	1	2	yes	—
16	C₅×D₄×Q₈	—	2	2	no	—
17	C₅×D₄×Q₈	—	2	1	no	—
18	C₅×#544	—	2	1	no	—
19	C₅×#544	—	2	2	no	—
20	C₅×#533	C₂²	1	1	yes	characteristic
21	C₅×#533	C₂²	1	2	yes	—
22	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
24	C₅×#520	—	2	1	no	—
25	C₄×C₅×#41	C₂²	1	1	yes	characteristic
26	C₅×#446	—	2	1	no	—
27	C₅×#436	—	2	1	no	—
28	C₅×#435	—	2	2	no	—
29	C₅×#433	—	2	2	no	—
30	C₅×#432	C₂²	1	2	yes	—
31	C₅×#432	C₂²	1	2	yes	—
32	C₅×#431	C₂²	1	1	yes	characteristic
33	C₅×#431	C₂²	1	2	yes	—
34	C₅×#423	C₂²	1	2	yes	—
35	C₅×#423	C₂²	1	1	yes	characteristic
36	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
38	C₅×#408	—	2	1	no	—
39	C₅×#405	—	2	1	no	—
40	C₅×#333	C₂²	1	1	yes	characteristic
41	C₅×#333	C₂²	1	1	yes	characteristic
42	C₅×#333	C₂²	1	2	yes	—
43	C₅×#332	C₂²	1	2	yes	—
44	C₅×#332	C₂²	1	2	yes	—
45	C₅×#332	C₂²	1	1	yes	characteristic
46	C₅×#332	C₂²	1	1	yes	characteristic
47	C₅×#332	C₂²	1	2	yes	—
48	C₅×#332	C₂²	1	2	yes	—
49	C₅×#332	C₂²	1	2	yes	—
50	#17761	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
51	C₂×C₅×#41	D₄	1	1	yes	characteristic
52	C₂²×C₅×Q₈	—	2	1	no	—
53	C₂²×C₅×Q₈	—	2	2	no	—
54	C₂×C₅×M₁₆	—	2	1	no	—
55	C₂×C₅×M₁₆	—	2	2	no	—
56	C₂²×C₅×C₈	—	2	1	no	—
57	C₂²×C₅×C₈	—	2	1	no	—
58	C₅×C₄⋊Q₈	—	2	4	no	—
59	C₅×C₄⋊Q₈	—	2	2	no	—
60	C₅×C₄⋊Q₈	—	2	2	no	—
61	C₅×C₄⋊Q₈	—	2	1	no	—
62	C₅×C₄⋊Q₈	—	2	1	no	—
63	C₅×C₄⋊Q₈	—	2	2	no	—
64	C₅×C₄⋊Q₈	C₂×C₄	1	2	yes	—
65	C₅×C₄⋊Q₈	C₂×C₄	1	4	yes	—
66	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
67	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
68	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
69	C₅×#125	—	2	4	no	—
70	C₅×#125	—	2	2	no	—
71	C₅×#125	—	2	2	no	—
72	C₅×#125	—	2	1	no	—
73	C₅×C₂²⋊Q₈	—	2	1	no	—
74	C₅×C₂²⋊Q₈	—	2	2	no	—
75	C₅×C₂²⋊Q₈	—	2	4	no	—
76	C₅×C₂²⋊Q₈	—	2	4	no	—
77	C₅×C₂²⋊Q₈	—	2	4	no	—
78	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
79	C₅×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
80	C₄×C₅×Q₈	—	2	2	no	—
81	C₄×C₅×Q₈	—	2	1	no	—
82	C₄×C₅×Q₈	—	2	2	no	—
83	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
84	C₄×C₅×Q₈	C₂×C₄	1	4	yes	—
85	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
86	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
87	C₄×C₅×D₄	—	2	4	no	—
88	C₄×C₅×D₄	—	2	2	no	—
89	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
90	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
91	C₄×C₅×D₄	D₄	1	2	yes	—
92	C₄×C₅×D₄	D₄	1	1	yes	characteristic
93	C₅×#117	—	2	2	no	—
94	C₅×#117	—	2	1	no	—
95	C₅×#117	D₄	1	1	yes	characteristic
96	C₅×#117	D₄	1	2	yes	—
97	C₂×C₅×C₄⋊C₄	—	2	2	no	—
98	C₂×C₅×C₄⋊C₄	—	2	1	no	—
99	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
100	C₂×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
101	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₅	C₂³	1	2	yes	—
103	C₅×C₄⋊C₈	—	2	1	no	—
104	C₅×C₄⋊C₈	—	2	1	no	—
105	C₅×C₄⋊C₈	—	2	1	no	—
106	C₅×C₄⋊C₈	—	2	2	no	—
107	C₅×C₄⋊C₈	C₂³	1	2	yes	—
108	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
109	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
110	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
111	C₅×C₄⋊C₈	C₂³	1	2	yes	—
112	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
113	C₅×C₂²⋊C₈	—	2	2	no	—
114	C₅×C₂²⋊C₈	—	2	2	no	—
115	C₅×C₂²⋊C₈	—	2	1	no	—
116	C₅×C₂²⋊C₈	—	2	2	no	—
117	C₅×#97	—	2	2	no	—
118	C₅×#97	—	2	2	no	—
119	C₄×C₅×C₈	—	2	2	no	—
120	C₄×C₅×C₈	—	2	1	no	—
121	#3503	C₂×C₅	1	1	yes	characteristic
122	#2989	C₂×C₅	1	1	yes	characteristic
123	#2925	C₂×C₅	1	1	yes	characteristic
124	#1559	C₂×C₅	1	2	yes	complemented
125	#1556	C₂×C₅	1	2	yes	complemented
126	#1554	C₂×C₅	1	2	yes	complemented
127	#1550	C₂×C₅	1	1	yes	characteristic, complemented
128	#1549	C₂×C₅	1	1	yes	characteristic, complemented
129	#1546	C₂×C₅	1	2	yes	complemented
130	#1542	C₂×C₅	1	1	yes	characteristic, complemented
131	C₂×#332	C₂×C₅	1	1	yes	characteristic, complemented
132	C₅×#41	—	2	2	no	—
133	C₅×#41	—	2	2	no	—
134	C₂×C₅×Q₈	—	2	4	no	—
135	C₂×C₅×Q₈	—	2	2	no	—
136	C₂×C₅×Q₈	—	2	1	no	—
137	C₂×C₅×Q₈	—	2	2	no	—
138	C₂×C₅×Q₈	—	8	1	no	—
139	C₂×C₅×Q₈	—	8	2	no	—
140	C₂×C₅×Q₈	—	8	1	no	—
141	C₂×C₅×Q₈	—	8	2	no	—
142	C₂×C₅×Q₈	C₂²⋊C₄	1	1	yes	characteristic
143	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
144	C₂×C₅×D₄	C₂²⋊C₄	1	2	yes	—
145	C₂×C₅×D₄	C₂²⋊C₄	1	1	yes	characteristic
146	C₂²×C₄×C₅	—	2	4	no	—
147	C₂²×C₄×C₅	—	2	2	no	—
148	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
149	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
150	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
151	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
153	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
154	C₅×M₁₆	—	4	2	no	—
155	C₅×M₁₆	—	8	2	no	—
156	C₂×C₅×C₈	—	2	2	no	—
157	C₂×C₅×C₈	—	2	1	no	—
158	C₂×C₅×C₈	—	2	1	no	—
159	C₂×C₅×C₈	—	2	1	no	—
160	C₂×C₅×C₈	—	2	2	no	—
161	C₂×C₅×C₈	—	2	1	no	—
162	C₂×C₅×C₈	—	4	2	no	—
163	C₂×C₅×C₈	—	8	1	no	—
164	C₅×C₄⋊C₄	—	2	4	no	—
165	C₅×C₄⋊C₄	—	2	2	no	—
166	C₅×C₄⋊C₄	—	2	4	no	—
167	C₅×C₄⋊C₄	—	2	2	no	—
168	C₅×C₄⋊C₄	—	2	4	no	—
169	C₅×C₄⋊C₄	—	2	2	no	—
170	C₅×C₄⋊C₄	—	2	4	no	—
171	C₅×C₄⋊C₄	—	2	2	no	—
172	C₅×C₄⋊C₄	—	2	1	no	—
173	C₅×C₄⋊C₄	—	2	2	no	—
174	C₅×C₄⋊C₄	—	2	1	no	—
175	C₅×C₄⋊C₄	—	2	1	no	—
176	C₅×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
177	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
178	C₅×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
179	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
180	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
181	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
182	C₅×C₂²⋊C₄	—	2	4	no	—
183	C₅×C₂²⋊C₄	—	2	2	no	—
184	C₅×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
185	C₅×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
186	C₅×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
187	C₄²×C₅	—	2	4	no	—
188	C₄²×C₅	—	2	2	no	—
189	C₄²×C₅	C₂²×C₄	1	2	yes	—
190	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
191	C₄²×C₅	C₂×D₄	1	2	yes	—
192	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
193	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
194	C₄²×C₅	C₂×D₄	1	2	yes	—
195	C₄²×C₅	C₂⁴	1	1	yes	characteristic
196	Q₈²	C₄×C₅	1	2	yes	—
197	#557	—	2	1	no	—
198	#554	C₄×C₅	1	4	yes	—
199	#554	C₄×C₅	1	2	yes	—
200	D₄×Q₈	—	2	2	no	—
201	D₄×Q₈	—	2	1	no	—
202	#544	—	2	1	no	—
203	#544	—	2	2	no	—
204	#533	C₂²×C₅	1	1	yes	characteristic
205	#533	C₂²×C₅	1	2	yes	—
206	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
207	C₂×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
208	#520	—	2	1	no	—
209	C₄×#41	C₂²×C₅	1	1	yes	characteristic
210	#446	—	2	1	no	—
211	#436	—	2	1	no	—
212	#435	—	2	2	no	—
213	#433	—	2	2	no	—
214	#432	C₂²×C₅	1	2	yes	—
215	#432	C₂²×C₅	1	2	yes	—
216	#431	C₂²×C₅	1	1	yes	characteristic
217	#431	C₂²×C₅	1	2	yes	—
218	#423	C₂²×C₅	1	2	yes	—
219	#423	C₂²×C₅	1	1	yes	characteristic
220	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
221	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
222	#408	—	2	1	no	—
223	#405	—	2	1	no	—
224	#333	C₂²×C₅	1	1	yes	characteristic
225	#333	C₂²×C₅	1	1	yes	characteristic
226	#333	C₂²×C₅	1	2	yes	—
227	#332	C₂²×C₅	1	2	yes	—
228	#332	C₂²×C₅	1	2	yes	—
229	#332	C₂²×C₅	1	1	yes	characteristic
230	#332	C₂²×C₅	1	1	yes	characteristic
231	#332	C₂²×C₅	1	2	yes	—
232	#332	C₂²×C₅	1	2	yes	—
233	#332	C₂²×C₅	1	2	yes	—
234	C₂³×C₅	C₂×C₂²⋊C₄	1	2	yes	—
235	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
236	C₅×Q₈	—	2	2	no	—
237	C₅×Q₈	—	4	2	no	—
238	C₅×Q₈	—	4	2	no	—
239	C₅×Q₈	—	4	1	no	—
240	C₅×Q₈	—	4	2	no	—
241	C₅×Q₈	—	4	1	no	—
242	C₅×Q₈	—	8	2	no	—
243	C₅×Q₈	—	8	4	no	—
244	C₅×D₄	—	2	4	no	—
245	C₅×D₄	—	2	2	no	—
246	C₂×C₄×C₅	—	2	2	no	—
247	C₂×C₄×C₅	—	2	2	no	—
248	C₂×C₄×C₅	—	2	1	no	—
249	C₂×C₄×C₅	—	2	2	no	—
250	C₂×C₄×C₅	—	2	1	no	—
251	C₂×C₄×C₅	—	2	2	no	—
252	C₂×C₄×C₅	—	2	2	no	—
253	C₂×C₄×C₅	—	2	4	no	—
254	C₂×C₄×C₅	—	2	2	no	—
255	C₂×C₄×C₅	—	4	1	no	—
256	C₂×C₄×C₅	—	4	2	no	—
257	C₂×C₄×C₅	—	8	2	no	—
258	C₂×C₄×C₅	—	8	4	no	—
259	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
260	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
261	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
262	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
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	#137	1	2	yes	—
266	C₂×C₄×C₅	#137	1	2	yes	—
267	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
268	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
269	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
270	C₅×C₈	—	4	1	no	—
271	C₅×C₈	—	4	1	no	—
272	C₅×C₈	—	4	2	no	—
273	C₅×C₈	—	4	2	no	—
274	C₅×C₈	—	4	1	no	—
275	C₅×C₈	—	4	1	no	—
276	C₂×#41	C₅×D₄	1	1	yes	characteristic
277	C₂²×Q₈	—	2	1	no	—
278	C₂²×Q₈	—	2	2	no	—
279	C₂×M₁₆	—	2	1	no	—
280	C₂×M₁₆	—	2	2	no	—
281	C₂²×C₈	—	2	1	no	—
282	C₂²×C₈	—	2	1	no	—
283	C₄⋊Q₈	—	2	4	no	—
284	C₄⋊Q₈	—	2	2	no	—
285	C₄⋊Q₈	—	2	2	no	—
286	C₄⋊Q₈	—	2	1	no	—
287	C₄⋊Q₈	—	2	1	no	—
288	C₄⋊Q₈	—	2	2	no	—
289	C₄⋊Q₈	C₂×C₄×C₅	1	2	yes	—
290	C₄⋊Q₈	C₂×C₄×C₅	1	4	yes	—
291	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
292	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
293	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
294	#125	—	2	4	no	—
295	#125	—	2	2	no	—
296	#125	—	2	2	no	—
297	#125	—	2	1	no	—
298	C₂²⋊Q₈	—	2	1	no	—
299	C₂²⋊Q₈	—	2	2	no	—
300	C₂²⋊Q₈	—	2	4	no	—
301	C₂²⋊Q₈	—	2	4	no	—
302	C₂²⋊Q₈	—	2	4	no	—
303	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
304	C₂²⋊Q₈	C₂×C₄×C₅	1	4	yes	—
305	C₄×Q₈	—	2	2	no	—
306	C₄×Q₈	—	2	1	no	—
307	C₄×Q₈	—	2	2	no	—
308	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
309	C₄×Q₈	C₂×C₄×C₅	1	4	yes	—
310	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
311	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
312	C₄×D₄	—	2	4	no	—
313	C₄×D₄	—	2	2	no	—
314	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
315	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
316	C₄×D₄	C₅×D₄	1	2	yes	—
317	C₄×D₄	C₅×D₄	1	1	yes	characteristic
318	#117	—	2	2	no	—
319	#117	—	2	1	no	—
320	#117	C₅×D₄	1	1	yes	characteristic
321	#117	C₅×D₄	1	2	yes	—
322	C₂×C₄⋊C₄	—	2	2	no	—
323	C₂×C₄⋊C₄	—	2	1	no	—
324	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
325	C₂×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
326	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
327	C₂×C₄²	C₂³×C₅	1	2	yes	—
328	C₄⋊C₈	—	2	1	no	—
329	C₄⋊C₈	—	2	1	no	—
330	C₄⋊C₈	—	2	1	no	—
331	C₄⋊C₈	—	2	2	no	—
332	C₄⋊C₈	C₂³×C₅	1	2	yes	—
333	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
334	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
335	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
336	C₄⋊C₈	C₂³×C₅	1	2	yes	—
337	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
338	C₂²⋊C₈	—	2	2	no	—
339	C₂²⋊C₈	—	2	2	no	—
340	C₂²⋊C₈	—	2	1	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	—	2	1	no	—
346	C₂²×C₅	—	2	1	no	—
347	C₂²×C₅	—	2	1	no	—
348	C₂²×C₅	—	2	2	no	—
349	C₂²×C₅	—	2	2	no	—
350	C₂²×C₅	—	2	2	no	—
351	C₂²×C₅	#419	1	2	yes	—
352	C₂²×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
353	C₄×C₅	—	2	1	no	—
354	C₄×C₅	—	2	1	no	—
355	C₄×C₅	—	2	2	no	—
356	C₄×C₅	—	2	2	no	—
357	C₄×C₅	—	2	1	no	—
358	C₄×C₅	—	2	2	no	—
359	C₄×C₅	—	4	2	no	—
360	C₄×C₅	—	4	4	no	—
361	C₄×C₅	—	4	2	no	—
362	C₄×C₅	#419	1	2	yes	—
363	C₄×C₅	C₂×#137	1	1	yes	characteristic
364	C₄×C₅	C₂×#137	1	1	yes	characteristic
365	C₄×C₅	#576	1	1	yes	characteristic
366	C₄×C₅	#577	1	1	yes	characteristic
367	#41	—	2	2	no	—
368	#41	—	2	2	no	—
369	C₂×Q₈	—	2	4	no	—
370	C₂×Q₈	—	2	2	no	—
371	C₂×Q₈	—	2	1	no	—
372	C₂×Q₈	—	2	2	no	—
373	C₂×Q₈	—	8	1	no	—
374	C₂×Q₈	—	8	2	no	—
375	C₂×Q₈	—	8	1	no	—
376	C₂×Q₈	—	8	2	no	—
377	C₂×Q₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
378	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
379	C₂×D₄	C₅×C₂²⋊C₄	1	2	yes	—
380	C₂×D₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
384	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
385	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
386	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
387	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
388	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
389	M₁₆	—	4	2	no	—
390	M₁₆	—	8	2	no	—
391	C₂×C₈	—	2	1	no	—
392	C₂×C₈	—	2	1	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	2	1	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	4	2	no	—
398	C₂×C₈	—	8	1	no	—
399	C₄⋊C₄	—	2	4	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	4	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	4	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	4	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
412	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
413	C₄⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
414	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
415	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
416	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
417	C₂²⋊C₄	—	2	4	no	—
418	C₂²⋊C₄	—	2	2	no	—
419	C₂²⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
420	C₂²⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
421	C₂²⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
422	C₄²	—	2	4	no	—
423	C₄²	—	2	2	no	—
424	C₄²	C₂²×C₄×C₅	1	2	yes	—
425	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
426	C₄²	C₂×C₅×D₄	1	2	yes	—
427	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
428	C₄²	C₂×C₅×D₄	1	2	yes	—
429	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
430	C₄²	C₂⁴×C₅	1	1	yes	characteristic
431	C₂×C₅	—	2	2	no	—
432	C₂×C₅	—	4	2	no	—
433	C₂×C₅	#2889	1	1	yes	characteristic
434	C₂×C₅	C₂×#419	1	1	yes	characteristic
435	C₂×C₅	#2897	1	1	yes	characteristic
436	C₂³	C₂×C₅×C₂²⋊C₄	1	2	yes	—
437	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
438	Q₈	—	2	2	no	—
439	Q₈	—	4	2	no	—
440	Q₈	—	4	2	no	—
441	Q₈	—	4	1	no	—
442	Q₈	—	4	2	no	—
443	Q₈	—	4	1	no	—
444	Q₈	—	8	2	no	—
445	Q₈	—	8	4	no	—
446	D₄	—	2	4	no	—
447	D₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	8	2	no	—
460	C₂×C₄	—	8	4	no	—
461	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
462	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
463	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
464	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
465	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
466	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
467	C₂×C₄	C₅×#137	1	2	yes	—
468	C₂×C₄	C₅×#137	1	2	yes	—
469	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
470	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
471	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
472	C₈	—	4	1	no	—
473	C₈	—	4	1	no	—
474	C₈	—	4	2	no	—
475	C₈	—	4	2	no	—
476	C₈	—	4	1	no	—
477	C₈	—	4	1	no	—
478	C₅	#17761	1	1	yes	characteristic, direct product factor, Sylow
479	C₂²	—	2	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	2	no	—
482	C₂²	—	2	2	no	—
483	C₂²	—	2	2	no	—
484	C₂²	C₅×#419	1	2	yes	—
485	C₂²	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
486	C₄	—	2	1	no	—
487	C₄	—	2	1	no	—
488	C₄	—	2	2	no	—
489	C₄	—	2	2	no	—
490	C₄	—	2	1	no	—
491	C₄	—	2	2	no	—
492	C₄	—	4	2	no	—
493	C₄	—	4	4	no	—
494	C₄	—	4	2	no	—
495	C₄	C₅×#419	1	2	yes	—
496	C₄	C₂×C₅×#137	1	1	yes	characteristic
497	C₄	C₂×C₅×#137	1	1	yes	characteristic
498	C₄	C₅×#576	1	1	yes	characteristic
499	C₄	C₅×#577	1	1	yes	characteristic
500	C₂	—	2	2	no	—
501	C₂	—	4	2	no	—
502	C₂	C₅×#2889	1	1	yes	characteristic
503	C₂	C₂×C₅×#419	1	1	yes	characteristic
504	C₂	C₅×#2897	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	C₂×C₅×#41	D₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₄×C₅×#41 ◁ G

Complements

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

N	H ≅ G/N	type
4. C₅×#1559	C₂	semidirect
5. C₅×#1556	C₂	semidirect
6. C₅×#1554	C₂	semidirect
7. C₅×#1550	C₂	semidirect
8. C₅×#1549	C₂	semidirect
9. C₅×#1546	C₂	semidirect
10. C₅×#1542	C₂	semidirect
11. C₂×C₅×#332	C₂	semidirect
50. #17761	C₅	direct (N × H)
124. #1559	C₂×C₅	semidirect
125. #1556	C₂×C₅	semidirect
126. #1554	C₂×C₅	semidirect
127. #1550	C₂×C₅	semidirect
128. #1549	C₂×C₅	semidirect
129. #1546	C₂×C₅	semidirect
130. #1542	C₂×C₅	semidirect
131. C₂×#332	C₂×C₅	semidirect
478. C₅	#17761	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#3503	2
C₅×#2989	2
C₅×#2925	2
C₅×#1559	2
C₅×#1556	2
C₅×#1554	2
C₅×#1550	2
C₅×#1549	2
C₅×#1546	2
C₅×#1542	2
C₂×C₅×#332	2
#17761	5

Subgroups — C5×#17761 #11940481

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#17761 #11940481