Subgroups — C₅×#17772 #11940492

Order 1280.

924 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3511	C₂	1	1	yes	maximal, characteristic
2	C₅×#2991	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2990	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1560	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1557	C₂	1	2	yes	maximal, complemented
6	C₅×#1554	C₂	1	2	yes	maximal, complemented
7	C₅×#1550	C₂	1	2	yes	maximal, complemented
8	C₅×#1549	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1546	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1543	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1540	C₂	1	2	yes	maximal, complemented
12	C₅×#556	—	2	1	no	—
13	C₅×#555	—	2	1	no	—
14	C₅×#554	—	2	1	no	—
15	C₅×#553	—	2	2	no	—
16	C₅×#548	—	2	2	no	—
17	C₅×#547	—	2	1	no	—
18	C₅×#542	C₄	1	4	yes	—
19	C₅×#537	C₄	1	2	yes	—
20	C₅×#533	C₂²	1	2	yes	—
21	C₅×#532	C₂²	1	1	yes	characteristic
22	C₅×#532	C₂²	1	2	yes	—
23	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₅×#520	C₄	1	2	yes	—
25	C₄×C₅×#41	C₂²	1	1	yes	characteristic
26	C₅×#446	—	2	1	no	—
27	C₅×C₈×Q₈	—	2	1	no	—
28	C₅×#436	—	2	2	no	—
29	C₅×#436	—	2	1	no	—
30	C₅×#435	—	2	2	no	—
31	C₅×C₈×D₄	—	2	1	no	—
32	C₅×#432	C₂²	1	2	yes	—
33	C₅×#431	C₂²	1	1	yes	characteristic
34	C₅×#431	C₂²	1	2	yes	—
35	C₅×#431	C₂²	1	1	yes	characteristic
36	C₅×#423	C₂²	1	1	yes	characteristic
37	C₅×#423	C₂²	1	1	yes	characteristic
38	C₅×#423	C₂²	1	2	yes	—
39	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
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	2	yes	—
46	C₅×#332	C₂²	1	2	yes	—
47	C₅×#331	C₂²	1	1	yes	characteristic
48	C₅×#331	C₂²	1	2	yes	—
49	C₅×#331	C₂²	1	1	yes	characteristic
50	#17772	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
51	C₂×C₅×#41	—	2	2	no	—
52	C₂×C₅×#41	C₂×C₄	1	2	yes	—
53	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
54	C₂²×C₅×Q₈	—	2	1	no	—
55	C₂×C₅×M₁₆	—	2	1	no	—
56	C₂×C₅×M₁₆	—	2	1	no	—
57	C₂×C₅×M₁₆	—	2	2	no	—
58	C₂²×C₅×C₈	—	2	2	no	—
59	C₅×C₄⋊Q₈	—	2	1	no	—
60	C₅×C₄⋊Q₈	—	2	1	no	—
61	C₅×C₄⋊Q₈	C₂×C₄	1	2	yes	—
62	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
63	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
64	C₅×#127	C₂³	1	1	yes	characteristic
65	C₅×#126	—	2	4	no	—
66	C₅×#125	—	2	2	no	—
67	C₅×#124	—	2	4	no	—
68	C₅×#124	—	2	2	no	—
69	C₅×#124	C₂×C₄	1	2	yes	—
70	C₅×#123	—	2	4	no	—
71	C₅×C₂²⋊Q₈	—	2	2	no	—
72	C₅×C₂²⋊Q₈	—	2	2	no	—
73	C₅×C₂²⋊Q₈	—	2	4	no	—
74	C₅×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
75	C₅×#121	—	2	2	no	—
76	C₅×#121	—	2	4	no	—
77	C₅×#121	—	2	1	no	—
78	C₅×#121	—	2	1	no	—
79	C₅×#121	—	2	2	no	—
80	C₅×#121	C₂×C₄	1	4	yes	—
81	C₄×C₅×Q₈	—	2	2	no	—
82	C₄×C₅×Q₈	C₂×C₄	1	4	yes	—
83	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
84	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
85	C₄×C₅×D₄	—	2	4	no	—
86	C₄×C₅×D₄	—	2	1	no	—
87	C₄×C₅×D₄	—	2	2	no	—
88	C₄×C₅×D₄	—	2	1	no	—
89	C₄×C₅×D₄	C₂×C₄	1	4	yes	—
90	C₄×C₅×D₄	D₄	1	1	yes	characteristic
91	C₄×C₅×D₄	D₄	1	2	yes	—
92	C₄×C₅×D₄	D₄	1	2	yes	—
93	C₄×C₅×D₄	D₄	1	1	yes	characteristic
94	C₅×#117	—	2	2	no	—
95	C₅×#117	—	2	2	no	—
96	C₅×#117	C₂×C₄	1	1	yes	characteristic
97	C₅×#117	C₂×C₄	1	2	yes	—
98	C₂×C₅×C₄⋊C₄	—	2	1	no	—
99	C₂×C₅×C₄⋊C₄	—	2	2	no	—
100	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
101	C₂×C₄²×C₅	C₂³	1	2	yes	—
102	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
103	C₅×C₄⋊C₈	—	2	2	no	—
104	C₅×C₄⋊C₈	—	2	1	no	—
105	C₅×C₄⋊C₈	—	2	2	no	—
106	C₅×C₄⋊C₈	—	2	1	no	—
107	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
108	C₅×C₄⋊C₈	C₂³	1	2	yes	—
109	C₅×C₄⋊C₈	C₂³	1	2	yes	—
110	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
111	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
112	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
113	C₅×C₂²⋊C₈	—	2	1	no	—
114	C₅×C₂²⋊C₈	—	2	1	no	—
115	C₅×C₂²⋊C₈	—	2	2	no	—
116	C₅×C₂²⋊C₈	—	2	2	no	—
117	C₅×#97	—	2	2	no	—
118	C₄×C₅×C₈	—	2	1	no	—
119	C₄×C₅×C₈	—	2	2	no	—
120	C₄×C₅×C₈	—	2	1	no	—
121	#3511	C₂×C₅	1	1	yes	characteristic
122	#2991	C₂×C₅	1	1	yes	characteristic, complemented
123	#2990	C₂×C₅	1	1	yes	characteristic, complemented
124	#1560	C₂×C₅	1	1	yes	characteristic, complemented
125	#1557	C₂×C₅	1	2	yes	complemented
126	#1554	C₂×C₅	1	2	yes	complemented
127	#1550	C₂×C₅	1	2	yes	complemented
128	#1549	C₂×C₅	1	1	yes	characteristic, complemented
129	#1546	C₂×C₅	1	1	yes	characteristic, complemented
130	#1543	C₂×C₅	1	1	yes	characteristic, complemented
131	#1540	C₂×C₅	1	2	yes	complemented
132	C₅×#41	—	4	2	no	—
133	C₅×#41	—	4	4	no	—
134	C₅×#41	—	8	2	no	—
135	C₅×#41	—	8	2	no	—
136	C₂×C₅×Q₈	—	2	2	no	—
137	C₂×C₅×Q₈	—	2	2	no	—
138	C₂×C₅×Q₈	—	8	1	no	—
139	C₂×C₅×Q₈	—	8	1	no	—
140	C₂×C₅×Q₈	C₂²⋊C₄	1	1	yes	characteristic
141	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
142	C₂×C₅×D₄	—	2	2	no	—
143	C₂×C₅×D₄	—	2	4	no	—
144	C₂×C₅×D₄	—	2	1	no	—
145	C₂×C₅×D₄	—	2	1	no	—
146	C₂×C₅×D₄	C₂²⋊C₄	1	1	yes	characteristic
147	C₂×C₅×D₄	C₂²⋊C₄	1	2	yes	—
148	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
149	C₂²×C₄×C₅	—	2	2	no	—
150	C₂²×C₄×C₅	—	2	2	no	—
151	C₂²×C₄×C₅	—	2	4	no	—
152	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
154	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
156	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
158	C₅×M₁₆	—	8	1	no	—
159	C₅×M₁₆	—	8	1	no	—
160	C₅×M₁₆	—	8	2	no	—
161	C₂×C₅×C₈	—	2	1	no	—
162	C₂×C₅×C₈	—	2	2	no	—
163	C₂×C₅×C₈	—	2	2	no	—
164	C₂×C₅×C₈	—	2	1	no	—
165	C₂×C₅×C₈	—	2	1	no	—
166	C₂×C₅×C₈	—	2	1	no	—
167	C₂×C₅×C₈	—	8	2	no	—
168	C₅×C₄⋊C₄	—	2	2	no	—
169	C₅×C₄⋊C₄	—	2	4	no	—
170	C₅×C₄⋊C₄	—	2	2	no	—
171	C₅×C₄⋊C₄	—	2	4	no	—
172	C₅×C₄⋊C₄	—	2	2	no	—
173	C₅×C₄⋊C₄	—	2	1	no	—
174	C₅×C₄⋊C₄	—	2	1	no	—
175	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
176	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
177	C₅×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
178	C₅×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
179	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
180	C₅×C₂²⋊C₄	—	2	4	no	—
181	C₅×C₂²⋊C₄	—	2	4	no	—
182	C₅×C₂²⋊C₄	—	2	4	no	—
183	C₅×C₂²⋊C₄	—	2	2	no	—
184	C₅×C₂²⋊C₄	—	2	2	no	—
185	C₅×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
186	C₅×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
187	C₅×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
188	C₄²×C₅	—	2	4	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	#556	—	2	1	no	—
197	#555	—	2	1	no	—
198	#554	—	2	1	no	—
199	#553	—	2	2	no	—
200	#548	—	2	2	no	—
201	#547	—	2	1	no	—
202	#542	C₄×C₅	1	4	yes	—
203	#537	C₄×C₅	1	2	yes	—
204	#533	C₂²×C₅	1	2	yes	—
205	#532	C₂²×C₅	1	1	yes	characteristic
206	#532	C₂²×C₅	1	2	yes	—
207	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
208	#520	C₄×C₅	1	2	yes	—
209	C₄×#41	C₂²×C₅	1	1	yes	characteristic
210	#446	—	2	1	no	—
211	C₈×Q₈	—	2	1	no	—
212	#436	—	2	2	no	—
213	#436	—	2	1	no	—
214	#435	—	2	2	no	—
215	C₈×D₄	—	2	1	no	—
216	#432	C₂²×C₅	1	2	yes	—
217	#431	C₂²×C₅	1	2	yes	—
218	#431	C₂²×C₅	1	1	yes	characteristic
219	#431	C₂²×C₅	1	1	yes	characteristic
220	#423	C₂²×C₅	1	1	yes	characteristic
221	#423	C₂²×C₅	1	1	yes	characteristic
222	#423	C₂²×C₅	1	2	yes	—
223	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
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	2	yes	—
230	#332	C₂²×C₅	1	2	yes	—
231	#331	C₂²×C₅	1	1	yes	characteristic
232	#331	C₂²×C₅	1	2	yes	—
233	#331	C₂²×C₅	1	1	yes	characteristic
234	C₂³×C₅	—	2	2	no	—
235	C₂³×C₅	C₂×C₂²⋊C₄	1	2	yes	—
236	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
237	C₅×Q₈	—	2	2	no	—
238	C₅×Q₈	—	4	2	no	—
239	C₅×Q₈	—	4	2	no	—
240	C₅×Q₈	—	4	2	no	—
241	C₅×Q₈	—	8	2	no	—
242	C₅×D₄	—	2	2	no	—
243	C₅×D₄	—	4	2	no	—
244	C₅×D₄	—	4	2	no	—
245	C₅×D₄	—	4	4	no	—
246	C₅×D₄	—	4	1	no	—
247	C₅×D₄	—	4	1	no	—
248	C₅×D₄	—	4	1	no	—
249	C₅×D₄	—	4	1	no	—
250	C₅×D₄	—	8	4	no	—
251	C₂×C₄×C₅	—	2	2	no	—
252	C₂×C₄×C₅	—	2	1	no	—
253	C₂×C₄×C₅	—	2	1	no	—
254	C₂×C₄×C₅	—	2	2	no	—
255	C₂×C₄×C₅	—	2	1	no	—
256	C₂×C₄×C₅	—	2	2	no	—
257	C₂×C₄×C₅	—	2	1	no	—
258	C₂×C₄×C₅	—	2	2	no	—
259	C₂×C₄×C₅	—	2	2	no	—
260	C₂×C₄×C₅	—	2	2	no	—
261	C₂×C₄×C₅	—	2	4	no	—
262	C₂×C₄×C₅	—	4	2	no	—
263	C₂×C₄×C₅	—	4	4	no	—
264	C₂×C₄×C₅	—	8	4	no	—
265	C₂×C₄×C₅	—	8	2	no	—
266	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
267	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
268	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
269	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
270	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
271	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
272	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
273	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
274	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
275	C₅×C₈	—	4	1	no	—
276	C₅×C₈	—	4	2	no	—
277	C₅×C₈	—	4	1	no	—
278	C₅×C₈	—	4	2	no	—
279	C₅×C₈	—	4	1	no	—
280	C₅×C₈	—	4	1	no	—
281	C₂×#41	—	2	2	no	—
282	C₂×#41	C₂×C₄×C₅	1	2	yes	—
283	C₂×#41	C₂×C₄×C₅	1	1	yes	characteristic
284	C₂²×Q₈	—	2	1	no	—
285	C₂×M₁₆	—	2	1	no	—
286	C₂×M₁₆	—	2	1	no	—
287	C₂×M₁₆	—	2	2	no	—
288	C₂²×C₈	—	2	2	no	—
289	C₄⋊Q₈	—	2	1	no	—
290	C₄⋊Q₈	—	2	1	no	—
291	C₄⋊Q₈	C₂×C₄×C₅	1	2	yes	—
292	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
293	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
294	#127	C₂³×C₅	1	1	yes	characteristic
295	#126	—	2	4	no	—
296	#125	—	2	2	no	—
297	#124	—	2	4	no	—
298	#124	—	2	2	no	—
299	#124	C₂×C₄×C₅	1	2	yes	—
300	#123	—	2	4	no	—
301	C₂²⋊Q₈	—	2	2	no	—
302	C₂²⋊Q₈	—	2	2	no	—
303	C₂²⋊Q₈	—	2	4	no	—
304	C₂²⋊Q₈	C₂×C₄×C₅	1	4	yes	—
305	#121	—	2	2	no	—
306	#121	—	2	4	no	—
307	#121	—	2	1	no	—
308	#121	—	2	1	no	—
309	#121	—	2	2	no	—
310	#121	C₂×C₄×C₅	1	4	yes	—
311	C₄×Q₈	—	2	2	no	—
312	C₄×Q₈	C₂×C₄×C₅	1	4	yes	—
313	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
314	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
315	C₄×D₄	—	2	4	no	—
316	C₄×D₄	—	2	1	no	—
317	C₄×D₄	—	2	2	no	—
318	C₄×D₄	—	2	1	no	—
319	C₄×D₄	C₂×C₄×C₅	1	4	yes	—
320	C₄×D₄	C₅×D₄	1	1	yes	characteristic
321	C₄×D₄	C₅×D₄	1	2	yes	—
322	C₄×D₄	C₅×D₄	1	2	yes	—
323	C₄×D₄	C₅×D₄	1	1	yes	characteristic
324	#117	—	2	2	no	—
325	#117	—	2	2	no	—
326	#117	C₂×C₄×C₅	1	1	yes	characteristic
327	#117	C₂×C₄×C₅	1	2	yes	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	—	2	2	no	—
330	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
331	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
332	C₂×C₄²	C₂³×C₅	1	2	yes	—
333	C₄⋊C₈	—	2	2	no	—
334	C₄⋊C₈	—	2	1	no	—
335	C₄⋊C₈	—	2	2	no	—
336	C₄⋊C₈	—	2	1	no	—
337	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
338	C₄⋊C₈	C₂³×C₅	1	2	yes	—
339	C₄⋊C₈	C₂³×C₅	1	2	yes	—
340	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
341	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
342	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
343	C₂²⋊C₈	—	2	1	no	—
344	C₂²⋊C₈	—	2	1	no	—
345	C₂²⋊C₈	—	2	2	no	—
346	C₂²⋊C₈	—	2	2	no	—
347	#97	—	2	2	no	—
348	C₄×C₈	—	2	1	no	—
349	C₄×C₈	—	2	2	no	—
350	C₄×C₈	—	2	1	no	—
351	C₂²×C₅	—	2	1	no	—
352	C₂²×C₅	—	2	2	no	—
353	C₂²×C₅	—	2	1	no	—
354	C₂²×C₅	—	2	2	no	—
355	C₂²×C₅	—	2	2	no	—
356	C₂²×C₅	—	2	1	no	—
357	C₂²×C₅	—	4	2	no	—
358	C₂²×C₅	—	4	2	no	—
359	C₂²×C₅	—	4	2	no	—
360	C₂²×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
361	C₄×C₅	—	2	1	no	—
362	C₄×C₅	—	2	2	no	—
363	C₄×C₅	—	2	2	no	—
364	C₄×C₅	—	2	1	no	—
365	C₄×C₅	—	2	2	no	—
366	C₄×C₅	—	2	1	no	—
367	C₄×C₅	—	4	2	no	—
368	C₄×C₅	—	4	4	no	—
369	C₄×C₅	#413	1	2	yes	—
370	C₄×C₅	#576	1	1	yes	characteristic
371	C₄×C₅	#577	1	1	yes	characteristic
372	C₄×C₅	#577	1	1	yes	characteristic
373	C₄×C₅	#578	1	1	yes	characteristic
374	#41	—	4	2	no	—
375	#41	—	4	4	no	—
376	#41	—	8	2	no	—
377	#41	—	8	2	no	—
378	C₂×Q₈	—	2	2	no	—
379	C₂×Q₈	—	2	2	no	—
380	C₂×Q₈	—	8	1	no	—
381	C₂×Q₈	—	8	1	no	—
382	C₂×Q₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
383	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
384	C₂×D₄	—	2	2	no	—
385	C₂×D₄	—	2	4	no	—
386	C₂×D₄	—	2	1	no	—
387	C₂×D₄	—	2	1	no	—
388	C₂×D₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
389	C₂×D₄	C₅×C₂²⋊C₄	1	2	yes	—
390	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	4	no	—
394	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
395	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
396	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
397	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
398	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
399	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
400	M₁₆	—	8	1	no	—
401	M₁₆	—	8	1	no	—
402	M₁₆	—	8	2	no	—
403	C₂×C₈	—	2	1	no	—
404	C₂×C₈	—	2	1	no	—
405	C₂×C₈	—	2	1	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	—	2	1	no	—
408	C₂×C₈	—	2	2	no	—
409	C₂×C₈	—	8	2	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	4	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	4	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	2	1	no	—
416	C₄⋊C₄	—	2	1	no	—
417	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
418	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
419	C₄⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
420	C₄⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
421	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
422	C₂²⋊C₄	—	2	4	no	—
423	C₂²⋊C₄	—	2	4	no	—
424	C₂²⋊C₄	—	2	4	no	—
425	C₂²⋊C₄	—	2	2	no	—
426	C₂²⋊C₄	—	2	2	no	—
427	C₂²⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
428	C₂²⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
429	C₂²⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
430	C₄²	—	2	4	no	—
431	C₄²	C₂²×C₄×C₅	1	2	yes	—
432	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
433	C₄²	C₂×C₅×D₄	1	2	yes	—
434	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
435	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
436	C₄²	C₂×C₅×D₄	1	2	yes	—
437	C₄²	C₂⁴×C₅	1	1	yes	characteristic
438	C₂×C₅	—	4	1	no	—
439	C₂×C₅	—	4	2	no	—
440	C₂×C₅	—	8	2	no	—
441	C₂×C₅	C₂×#413	1	1	yes	characteristic
442	C₂×C₅	#2897	1	1	yes	characteristic
443	C₂×C₅	#2898	1	1	yes	characteristic
444	C₂³	—	2	2	no	—
445	C₂³	C₂×C₅×C₂²⋊C₄	1	2	yes	—
446	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
447	Q₈	—	2	2	no	—
448	Q₈	—	4	2	no	—
449	Q₈	—	4	2	no	—
450	Q₈	—	4	2	no	—
451	Q₈	—	8	2	no	—
452	D₄	—	2	2	no	—
453	D₄	—	4	2	no	—
454	D₄	—	4	2	no	—
455	D₄	—	4	4	no	—
456	D₄	—	4	1	no	—
457	D₄	—	4	1	no	—
458	D₄	—	4	1	no	—
459	D₄	—	4	1	no	—
460	D₄	—	8	4	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	4	no	—
474	C₂×C₄	—	8	4	no	—
475	C₂×C₄	—	8	2	no	—
476	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
477	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
478	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
479	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
480	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
481	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
482	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
483	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
484	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
485	C₈	—	4	1	no	—
486	C₈	—	4	2	no	—
487	C₈	—	4	2	no	—
488	C₈	—	4	1	no	—
489	C₈	—	4	1	no	—
490	C₈	—	4	1	no	—
491	C₅	#17772	1	1	yes	characteristic, direct product factor, Sylow
492	C₂²	—	2	1	no	—
493	C₂²	—	2	2	no	—
494	C₂²	—	2	1	no	—
495	C₂²	—	2	2	no	—
496	C₂²	—	2	2	no	—
497	C₂²	—	2	1	no	—
498	C₂²	—	4	2	no	—
499	C₂²	—	4	2	no	—
500	C₂²	—	4	2	no	—
501	C₂²	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
502	C₄	—	2	1	no	—
503	C₄	—	2	2	no	—
504	C₄	—	2	2	no	—
505	C₄	—	2	1	no	—
506	C₄	—	2	2	no	—
507	C₄	—	2	1	no	—
508	C₄	—	4	2	no	—
509	C₄	—	4	4	no	—
510	C₄	C₅×#413	1	2	yes	—
511	C₄	C₅×#576	1	1	yes	characteristic
512	C₄	C₅×#577	1	1	yes	characteristic
513	C₄	C₅×#577	1	1	yes	characteristic
514	C₄	C₅×#578	1	1	yes	characteristic
515	C₂	—	4	1	no	—
516	C₂	—	4	2	no	—
517	C₂	—	8	2	no	—
518	C₂	C₂×C₅×#413	1	1	yes	characteristic
519	C₂	C₅×#2897	1	1	yes	characteristic
520	C₂	C₅×#2898	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	C₅×#3511	C₂
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
2. C₅×#2991	C₂	semidirect
3. C₅×#2990	C₂	semidirect
4. C₅×#1560	C₂	semidirect
5. C₅×#1557	C₂	semidirect
6. C₅×#1554	C₂	semidirect
7. C₅×#1550	C₂	semidirect
8. C₅×#1549	C₂	semidirect
9. C₅×#1546	C₂	semidirect
10. C₅×#1543	C₂	semidirect
11. C₅×#1540	C₂	semidirect
50. #17772	C₅	direct (N × H)
122. #2991	C₂×C₅	semidirect
123. #2990	C₂×C₅	semidirect
124. #1560	C₂×C₅	semidirect
125. #1557	C₂×C₅	semidirect
126. #1554	C₂×C₅	semidirect
127. #1550	C₂×C₅	semidirect
128. #1549	C₂×C₅	semidirect
129. #1546	C₂×C₅	semidirect
130. #1543	C₂×C₅	semidirect
131. #1540	C₂×C₅	semidirect
491. C₅	#17772	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×#3511	2
C₅×#2991	2
C₅×#2990	2
C₅×#1560	2
C₅×#1557	2
C₅×#1554	2
C₅×#1550	2
C₅×#1549	2
C₅×#1546	2
C₅×#1543	2
C₅×#1540	2
#17772	5

Subgroups — C5×#17772 #11940492

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#17772 #11940492