Subgroups — C₅×#17682 #11940402

Order 1280.

876 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3515	C₂	1	1	yes	maximal, characteristic
2	C₅×#2971	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2923	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1535	C₂	1	2	yes	maximal, complemented
5	C₅×#1534	C₂	1	2	yes	maximal, complemented
6	C₅×#1531	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1529	C₂	1	2	yes	maximal, complemented
8	C₅×#1529	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1528	C₂	1	2	yes	maximal, complemented
10	C₅×#1526	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1524	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#557	C₄	1	1	yes	characteristic
13	C₅×#554	C₄	1	1	yes	characteristic
14	C₅×#554	C₄	1	1	yes	characteristic
15	C₅×#553	C₄	1	2	yes	—
16	C₅×#552	—	2	2	no	—
17	C₅×#552	—	2	1	no	—
18	C₅×#552	C₄	1	2	yes	—
19	C₅×#547	—	2	1	no	—
20	C₅×#547	C₄	1	1	yes	characteristic
21	C₅×#541	—	2	1	no	—
22	C₅×#539	—	2	2	no	—
23	C₅×#533	C₂²	1	1	yes	characteristic
24	C₅×#529	C₂²	1	1	yes	characteristic
25	C₅×#529	C₂²	1	2	yes	—
26	C₂×C₅×#125	C₂²	1	2	yes	—
27	C₅×#520	—	2	1	no	—
28	C₄×C₅×#41	C₂²	1	1	yes	characteristic
29	C₅×C₈×Q₈	—	2	1	no	—
30	C₅×#436	—	2	1	no	—
31	C₅×#436	—	2	2	no	—
32	C₅×#433	—	2	2	no	—
33	C₅×#432	C₂²	1	2	yes	—
34	C₅×#432	C₂²	1	1	yes	characteristic
35	C₅×#432	C₂²	1	2	yes	—
36	C₅×#432	C₂²	1	2	yes	—
37	C₅×#424	—	2	1	no	—
38	C₅×#408	—	2	1	no	—
39	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
40	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
41	C₄×C₅×M₁₆	C₂²	1	2	yes	—
42	C₂×C₅×#97	C₂²	1	1	yes	characteristic
43	C₅×#330	C₂²	1	1	yes	characteristic
44	C₅×#330	C₂²	1	1	yes	characteristic
45	C₅×#330	C₂²	1	2	yes	—
46	C₅×#330	C₂²	1	2	yes	—
47	C₅×#330	C₂²	1	2	yes	—
48	C₅×#330	C₂²	1	2	yes	—
49	C₅×#330	C₂²	1	2	yes	—
50	C₅×#329	C₂²	1	1	yes	characteristic
51	C₅×#329	C₂²	1	1	yes	characteristic
52	C₅×#329	C₂²	1	2	yes	—
53	#17682	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
54	C₂×C₅×#41	—	2	1	no	—
55	C₂×C₅×#41	D₄	1	1	yes	characteristic
56	C₂×C₅×M₁₆	—	2	1	no	—
57	C₂×C₅×M₁₆	—	2	2	no	—
58	C₂×C₅×M₁₆	—	2	1	no	—
59	C₂²×C₅×C₈	—	2	1	no	—
60	C₅×C₄⋊Q₈	—	2	1	no	—
61	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
62	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
63	C₅×#126	—	2	2	no	—
64	C₅×#126	—	2	2	no	—
65	C₅×#126	—	2	2	no	—
66	C₅×#126	—	2	1	no	—
67	C₅×#125	—	2	2	no	—
68	C₅×#125	—	2	2	no	—
69	C₅×#125	—	2	1	no	—
70	C₅×#125	—	2	2	no	—
71	C₅×#125	—	2	2	no	—
72	C₅×#125	C₂×C₄	1	2	yes	—
73	C₅×#125	C₂×C₄	1	2	yes	—
74	C₅×#125	C₂³	1	1	yes	characteristic
75	C₅×#125	C₂³	1	2	yes	—
76	C₅×#124	C₂³	1	1	yes	characteristic
77	C₅×#123	—	2	2	no	—
78	C₅×#123	—	2	1	no	—
79	C₅×#123	—	2	2	no	—
80	C₅×#123	—	2	2	no	—
81	C₅×#123	—	2	2	no	—
82	C₅×C₂²⋊Q₈	—	2	1	no	—
83	C₅×C₂²⋊Q₈	—	2	1	no	—
84	C₅×C₂²⋊Q₈	—	2	1	no	—
85	C₅×C₂²⋊Q₈	—	2	2	no	—
86	C₅×C₂²⋊Q₈	—	2	1	no	—
87	C₅×C₂²⋊Q₈	—	2	2	no	—
88	C₅×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
89	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
90	C₅×#121	—	2	2	no	—
91	C₅×#121	C₂×C₄	1	2	yes	—
92	C₅×#121	C₂×C₄	1	1	yes	characteristic
93	C₄×C₅×Q₈	—	2	1	no	—
94	C₄×C₅×Q₈	—	2	1	no	—
95	C₄×C₅×Q₈	—	2	1	no	—
96	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
97	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
98	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
99	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
100	C₄×C₅×D₄	—	2	1	no	—
101	C₄×C₅×D₄	—	2	2	no	—
102	C₄×C₅×D₄	—	2	1	no	—
103	C₄×C₅×D₄	—	2	2	no	—
104	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
105	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
106	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
107	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
108	C₄×C₅×D₄	D₄	1	1	yes	characteristic
109	C₄×C₅×D₄	D₄	1	2	yes	—
110	C₅×#117	—	2	2	no	—
111	C₅×#117	—	2	1	no	—
112	C₅×#117	—	2	2	no	—
113	C₅×#117	C₂×C₄	1	2	yes	—
114	C₅×#117	D₄	1	1	yes	characteristic
115	C₅×#117	D₄	1	2	yes	—
116	C₂×C₅×C₄⋊C₄	—	2	2	no	—
117	C₂×C₅×C₄⋊C₄	—	2	2	no	—
118	C₂×C₅×C₄⋊C₄	—	2	1	no	—
119	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
120	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
121	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
122	C₂×C₄²×C₅	C₂³	1	2	yes	—
123	C₅×C₄⋊C₈	—	2	2	no	—
124	C₅×C₄⋊C₈	—	2	2	no	—
125	C₅×C₄⋊C₈	—	2	1	no	—
126	C₅×C₄⋊C₈	—	2	2	no	—
127	C₅×C₂²⋊C₈	—	2	2	no	—
128	C₅×C₂²⋊C₈	—	2	2	no	—
129	C₅×C₂²⋊C₈	—	2	2	no	—
130	C₅×C₂²⋊C₈	—	2	1	no	—
131	C₅×#97	—	2	1	no	—
132	C₅×#97	C₂³	1	1	yes	characteristic
133	C₅×#97	C₂³	1	1	yes	characteristic
134	C₅×#97	C₂³	1	1	yes	characteristic
135	C₅×#97	C₂³	1	1	yes	characteristic
136	C₅×#97	C₂³	1	2	yes	—
137	C₅×#97	C₂³	1	2	yes	—
138	C₄×C₅×C₈	—	2	1	no	—
139	C₄×C₅×C₈	—	2	1	no	—
140	C₄×C₅×C₈	—	2	2	no	—
141	#3515	C₂×C₅	1	1	yes	characteristic
142	#2971	C₂×C₅	1	1	yes	characteristic, complemented
143	#2923	C₂×C₅	1	1	yes	characteristic, complemented
144	#1535	C₂×C₅	1	2	yes	complemented
145	#1534	C₂×C₅	1	2	yes	complemented
146	#1531	C₂×C₅	1	1	yes	characteristic, complemented
147	#1529	C₂×C₅	1	1	yes	characteristic, complemented
148	#1529	C₂×C₅	1	2	yes	complemented
149	#1528	C₂×C₅	1	2	yes	complemented
150	#1526	C₂×C₅	1	1	yes	characteristic, complemented
151	#1524	C₂×C₅	1	1	yes	characteristic, complemented
152	C₅×#41	—	4	2	no	—
153	C₅×#41	—	4	4	no	—
154	C₂×C₅×Q₈	—	2	1	no	—
155	C₂×C₅×Q₈	—	2	1	no	—
156	C₂×C₅×Q₈	C₂²⋊C₄	1	1	yes	characteristic
157	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₅×D₄	—	2	2	no	—
159	C₂×C₅×D₄	—	2	1	no	—
160	C₂×C₅×D₄	C₂²⋊C₄	1	1	yes	characteristic
161	C₂×C₅×D₄	C₂²⋊C₄	1	2	yes	—
162	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
163	C₂²×C₄×C₅	—	2	2	no	—
164	C₂²×C₄×C₅	—	2	2	no	—
165	C₂²×C₄×C₅	—	2	1	no	—
166	C₂²×C₄×C₅	—	2	2	no	—
167	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
168	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
169	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
171	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
172	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
173	C₅×M₁₆	—	4	4	no	—
174	C₅×M₁₆	—	4	2	no	—
175	C₅×M₁₆	—	4	2	no	—
176	C₂×C₅×C₈	—	2	1	no	—
177	C₂×C₅×C₈	—	2	1	no	—
178	C₂×C₅×C₈	—	2	1	no	—
179	C₂×C₅×C₈	—	2	2	no	—
180	C₂×C₅×C₈	—	2	2	no	—
181	C₂×C₅×C₈	—	2	1	no	—
182	C₂×C₅×C₈	—	4	2	no	—
183	C₅×C₄⋊C₄	—	2	2	no	—
184	C₅×C₄⋊C₄	—	2	1	no	—
185	C₅×C₄⋊C₄	—	2	2	no	—
186	C₅×C₄⋊C₄	—	2	2	no	—
187	C₅×C₄⋊C₄	—	2	2	no	—
188	C₅×C₄⋊C₄	—	2	2	no	—
189	C₅×C₄⋊C₄	—	2	2	no	—
190	C₅×C₄⋊C₄	—	2	1	no	—
191	C₅×C₄⋊C₄	—	2	2	no	—
192	C₅×C₄⋊C₄	—	2	1	no	—
193	C₅×C₄⋊C₄	—	2	1	no	—
194	C₅×C₄⋊C₄	—	2	2	no	—
195	C₅×C₄⋊C₄	—	2	1	no	—
196	C₅×C₄⋊C₄	—	2	1	no	—
197	C₅×C₄⋊C₄	—	2	2	no	—
198	C₅×C₄⋊C₄	—	2	2	no	—
199	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
200	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
201	C₅×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
202	C₅×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
203	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
204	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
205	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
206	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
207	C₅×C₂²⋊C₄	—	2	2	no	—
208	C₅×C₂²⋊C₄	—	2	2	no	—
209	C₅×C₂²⋊C₄	—	2	1	no	—
210	C₅×C₂²⋊C₄	—	2	1	no	—
211	C₅×C₂²⋊C₄	—	2	2	no	—
212	C₅×C₂²⋊C₄	—	2	2	no	—
213	C₅×C₂²⋊C₄	—	2	1	no	—
214	C₅×C₂²⋊C₄	—	2	1	no	—
215	C₅×C₂²⋊C₄	—	2	1	no	—
216	C₅×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
217	C₅×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
218	C₅×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
219	C₄²×C₅	—	2	2	no	—
220	C₄²×C₅	—	2	2	no	—
221	C₄²×C₅	—	2	1	no	—
222	C₄²×C₅	C₂²×C₄	1	2	yes	—
223	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
224	C₄²×C₅	C₂×D₄	1	2	yes	—
225	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
226	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
227	C₄²×C₅	C₂×D₄	1	2	yes	—
228	C₄²×C₅	C₂⁴	1	1	yes	characteristic
229	#557	C₄×C₅	1	1	yes	characteristic
230	#554	C₄×C₅	1	1	yes	characteristic
231	#554	C₄×C₅	1	1	yes	characteristic
232	#553	C₄×C₅	1	2	yes	—
233	#552	—	2	2	no	—
234	#552	—	2	1	no	—
235	#552	C₄×C₅	1	2	yes	—
236	#547	—	2	1	no	—
237	#547	C₄×C₅	1	1	yes	characteristic
238	#541	—	2	1	no	—
239	#539	—	2	2	no	—
240	#533	C₂²×C₅	1	1	yes	characteristic
241	#529	C₂²×C₅	1	1	yes	characteristic
242	#529	C₂²×C₅	1	2	yes	—
243	C₂×#125	C₂²×C₅	1	2	yes	—
244	#520	—	2	1	no	—
245	C₄×#41	C₂²×C₅	1	1	yes	characteristic
246	C₈×Q₈	—	2	1	no	—
247	#436	—	2	1	no	—
248	#436	—	2	2	no	—
249	#433	—	2	2	no	—
250	#432	C₂²×C₅	1	2	yes	—
251	#432	C₂²×C₅	1	2	yes	—
252	#432	C₂²×C₅	1	1	yes	characteristic
253	#432	C₂²×C₅	1	2	yes	—
254	#424	—	2	1	no	—
255	#408	—	2	1	no	—
256	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
257	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
258	C₄×M₁₆	C₂²×C₅	1	2	yes	—
259	C₂×#97	C₂²×C₅	1	1	yes	characteristic
260	#330	C₂²×C₅	1	1	yes	characteristic
261	#330	C₂²×C₅	1	1	yes	characteristic
262	#330	C₂²×C₅	1	2	yes	—
263	#330	C₂²×C₅	1	2	yes	—
264	#330	C₂²×C₅	1	2	yes	—
265	#330	C₂²×C₅	1	2	yes	—
266	#330	C₂²×C₅	1	2	yes	—
267	#329	C₂²×C₅	1	1	yes	characteristic
268	#329	C₂²×C₅	1	1	yes	characteristic
269	#329	C₂²×C₅	1	2	yes	—
270	C₂³×C₅	—	2	1	no	—
271	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
272	C₂³×C₅	C₂×C₂²⋊C₄	1	2	yes	—
273	C₅×Q₈	—	2	2	no	—
274	C₅×Q₈	—	4	1	no	—
275	C₅×Q₈	—	4	2	no	—
276	C₅×Q₈	—	8	1	no	—
277	C₅×D₄	—	2	2	no	—
278	C₅×D₄	—	4	2	no	—
279	C₅×D₄	—	4	1	no	—
280	C₅×D₄	—	4	4	no	—
281	C₅×D₄	—	8	1	no	—
282	C₂×C₄×C₅	—	2	2	no	—
283	C₂×C₄×C₅	—	2	1	no	—
284	C₂×C₄×C₅	—	2	2	no	—
285	C₂×C₄×C₅	—	2	2	no	—
286	C₂×C₄×C₅	—	2	1	no	—
287	C₂×C₄×C₅	—	2	1	no	—
288	C₂×C₄×C₅	—	4	2	no	—
289	C₂×C₄×C₅	—	4	1	no	—
290	C₂×C₄×C₅	—	4	2	no	—
291	C₂×C₄×C₅	—	4	1	no	—
292	C₂×C₄×C₅	—	4	2	no	—
293	C₂×C₄×C₅	—	4	4	no	—
294	C₂×C₄×C₅	—	4	2	no	—
295	C₂×C₄×C₅	—	8	2	no	—
296	C₂×C₄×C₅	—	8	2	no	—
297	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
298	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
299	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
300	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
301	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
302	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
303	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
304	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
305	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
306	C₅×C₈	—	2	2	no	—
307	C₅×C₈	—	4	1	no	—
308	C₅×C₈	—	4	1	no	—
309	C₅×C₈	—	4	2	no	—
310	C₅×C₈	—	4	2	no	—
311	C₅×C₈	—	4	1	no	—
312	C₂×#41	—	2	1	no	—
313	C₂×#41	C₅×D₄	1	1	yes	characteristic
314	C₂×M₁₆	—	2	1	no	—
315	C₂×M₁₆	—	2	2	no	—
316	C₂×M₁₆	—	2	1	no	—
317	C₂²×C₈	—	2	1	no	—
318	C₄⋊Q₈	—	2	1	no	—
319	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
320	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
321	#126	—	2	2	no	—
322	#126	—	2	2	no	—
323	#126	—	2	2	no	—
324	#126	—	2	1	no	—
325	#125	—	2	2	no	—
326	#125	—	2	2	no	—
327	#125	—	2	1	no	—
328	#125	—	2	2	no	—
329	#125	—	2	2	no	—
330	#125	C₂×C₄×C₅	1	2	yes	—
331	#125	C₂×C₄×C₅	1	2	yes	—
332	#125	C₂³×C₅	1	1	yes	characteristic
333	#125	C₂³×C₅	1	2	yes	—
334	#124	C₂³×C₅	1	1	yes	characteristic
335	#123	—	2	2	no	—
336	#123	—	2	1	no	—
337	#123	—	2	2	no	—
338	#123	—	2	2	no	—
339	#123	—	2	2	no	—
340	C₂²⋊Q₈	—	2	1	no	—
341	C₂²⋊Q₈	—	2	1	no	—
342	C₂²⋊Q₈	—	2	1	no	—
343	C₂²⋊Q₈	—	2	2	no	—
344	C₂²⋊Q₈	—	2	1	no	—
345	C₂²⋊Q₈	—	2	2	no	—
346	C₂²⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
347	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
348	#121	—	2	2	no	—
349	#121	C₂×C₄×C₅	1	2	yes	—
350	#121	C₂×C₄×C₅	1	1	yes	characteristic
351	C₄×Q₈	—	2	1	no	—
352	C₄×Q₈	—	2	1	no	—
353	C₄×Q₈	—	2	1	no	—
354	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
355	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
356	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
357	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
358	C₄×D₄	—	2	1	no	—
359	C₄×D₄	—	2	2	no	—
360	C₄×D₄	—	2	1	no	—
361	C₄×D₄	—	2	2	no	—
362	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
363	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
364	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
365	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
366	C₄×D₄	C₅×D₄	1	1	yes	characteristic
367	C₄×D₄	C₅×D₄	1	2	yes	—
368	#117	—	2	2	no	—
369	#117	—	2	1	no	—
370	#117	—	2	2	no	—
371	#117	C₂×C₄×C₅	1	2	yes	—
372	#117	C₅×D₄	1	1	yes	characteristic
373	#117	C₅×D₄	1	2	yes	—
374	C₂×C₄⋊C₄	—	2	2	no	—
375	C₂×C₄⋊C₄	—	2	2	no	—
376	C₂×C₄⋊C₄	—	2	1	no	—
377	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
378	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
379	C₂×C₄²	C₂³×C₅	1	2	yes	—
380	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
381	C₄⋊C₈	—	2	2	no	—
382	C₄⋊C₈	—	2	2	no	—
383	C₄⋊C₈	—	2	1	no	—
384	C₄⋊C₈	—	2	2	no	—
385	C₂²⋊C₈	—	2	2	no	—
386	C₂²⋊C₈	—	2	2	no	—
387	C₂²⋊C₈	—	2	2	no	—
388	C₂²⋊C₈	—	2	1	no	—
389	#97	—	2	1	no	—
390	#97	C₂³×C₅	1	1	yes	characteristic
391	#97	C₂³×C₅	1	1	yes	characteristic
392	#97	C₂³×C₅	1	1	yes	characteristic
393	#97	C₂³×C₅	1	1	yes	characteristic
394	#97	C₂³×C₅	1	2	yes	—
395	#97	C₂³×C₅	1	2	yes	—
396	C₄×C₈	—	2	1	no	—
397	C₄×C₈	—	2	1	no	—
398	C₄×C₈	—	2	2	no	—
399	C₂²×C₅	—	2	1	no	—
400	C₂²×C₅	—	2	2	no	—
401	C₂²×C₅	—	2	1	no	—
402	C₂²×C₅	—	2	2	no	—
403	C₂²×C₅	—	2	2	no	—
404	C₂²×C₅	—	2	1	no	—
405	C₂²×C₅	—	4	1	no	—
406	C₂²×C₅	—	4	1	no	—
407	C₂²×C₅	—	4	1	no	—
408	C₂²×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
409	C₄×C₅	—	2	1	no	—
410	C₄×C₅	—	2	1	no	—
411	C₄×C₅	—	2	2	no	—
412	C₄×C₅	—	2	1	no	—
413	C₄×C₅	—	2	2	no	—
414	C₄×C₅	—	2	1	no	—
415	C₄×C₅	—	2	2	no	—
416	C₄×C₅	—	2	1	no	—
417	C₄×C₅	—	4	1	no	—
418	C₄×C₅	—	4	1	no	—
419	C₄×C₅	—	4	2	no	—
420	C₄×C₅	—	4	1	no	—
421	C₄×C₅	—	4	2	no	—
422	C₄×C₅	#421	1	2	yes	—
423	#41	—	4	2	no	—
424	#41	—	4	4	no	—
425	C₂×Q₈	—	2	1	no	—
426	C₂×Q₈	—	2	1	no	—
427	C₂×Q₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
428	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
429	C₂×D₄	—	2	2	no	—
430	C₂×D₄	—	2	1	no	—
431	C₂×D₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
432	C₂×D₄	C₅×C₂²⋊C₄	1	2	yes	—
433	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
439	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
440	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
441	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
442	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
443	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
444	M₁₆	—	4	4	no	—
445	M₁₆	—	4	2	no	—
446	M₁₆	—	4	2	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	2	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	2	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	4	2	no	—
454	C₄⋊C₄	—	2	2	no	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	2	no	—
457	C₄⋊C₄	—	2	2	no	—
458	C₄⋊C₄	—	2	2	no	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	—	2	2	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	2	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	2	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	2	no	—
469	C₄⋊C₄	—	2	2	no	—
470	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
471	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
472	C₄⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
473	C₄⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
474	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
475	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
476	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
477	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
478	C₂²⋊C₄	—	2	2	no	—
479	C₂²⋊C₄	—	2	2	no	—
480	C₂²⋊C₄	—	2	1	no	—
481	C₂²⋊C₄	—	2	1	no	—
482	C₂²⋊C₄	—	2	2	no	—
483	C₂²⋊C₄	—	2	2	no	—
484	C₂²⋊C₄	—	2	1	no	—
485	C₂²⋊C₄	—	2	1	no	—
486	C₂²⋊C₄	—	2	1	no	—
487	C₂²⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
488	C₂²⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
489	C₂²⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
490	C₄²	—	2	2	no	—
491	C₄²	—	2	2	no	—
492	C₄²	—	2	1	no	—
493	C₄²	C₂²×C₄×C₅	1	2	yes	—
494	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
495	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
496	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
497	C₄²	C₂×C₅×D₄	1	2	yes	—
498	C₄²	C₂×C₅×D₄	1	2	yes	—
499	C₄²	C₂⁴×C₅	1	1	yes	characteristic
500	C₂×C₅	—	4	1	no	—
501	C₂×C₅	—	4	2	no	—
502	C₂×C₅	—	8	1	no	—
503	C₂×C₅	#2889	1	1	yes	characteristic
504	C₂×C₅	C₂×#421	1	1	yes	characteristic
505	C₂×C₅	#2901	1	1	yes	characteristic
506	C₂³	—	2	1	no	—
507	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
508	C₂³	C₂×C₅×C₂²⋊C₄	1	2	yes	—
509	Q₈	—	2	2	no	—
510	Q₈	—	4	1	no	—
511	Q₈	—	4	2	no	—
512	Q₈	—	8	1	no	—
513	D₄	—	2	2	no	—
514	D₄	—	4	2	no	—
515	D₄	—	4	1	no	—
516	D₄	—	4	4	no	—
517	D₄	—	8	1	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	4	4	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	8	2	no	—
532	C₂×C₄	—	8	2	no	—
533	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
534	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
535	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
536	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
537	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
538	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
539	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
540	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
541	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
542	C₈	—	2	2	no	—
543	C₈	—	4	1	no	—
544	C₈	—	4	1	no	—
545	C₈	—	4	2	no	—
546	C₈	—	4	1	no	—
547	C₈	—	4	2	no	—
548	C₅	#17682	1	1	yes	characteristic, direct product factor, Sylow
549	C₂²	—	2	1	no	—
550	C₂²	—	2	2	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	2	1	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	1	no	—
558	C₂²	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
559	C₄	—	2	1	no	—
560	C₄	—	2	1	no	—
561	C₄	—	2	2	no	—
562	C₄	—	2	1	no	—
563	C₄	—	2	2	no	—
564	C₄	—	2	1	no	—
565	C₄	—	2	2	no	—
566	C₄	—	2	1	no	—
567	C₄	—	4	1	no	—
568	C₄	—	4	1	no	—
569	C₄	—	4	2	no	—
570	C₄	—	4	1	no	—
571	C₄	—	4	2	no	—
572	C₄	C₅×#421	1	2	yes	—
573	C₂	—	4	1	no	—
574	C₂	—	4	2	no	—
575	C₂	—	8	1	no	—
576	C₂	C₅×#2889	1	1	yes	characteristic
577	C₂	C₂×C₅×#421	1	1	yes	characteristic
578	C₂	C₅×#2901	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×#3515	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×#2971	C₂	semidirect
3. C₅×#2923	C₂	semidirect
4. C₅×#1535	C₂	semidirect
5. C₅×#1534	C₂	semidirect
6. C₅×#1531	C₂	semidirect
7. C₅×#1529	C₂	semidirect
8. C₅×#1529	C₂	semidirect
9. C₅×#1528	C₂	semidirect
10. C₅×#1526	C₂	semidirect
11. C₅×#1524	C₂	semidirect
53. #17682	C₅	direct (N × H)
142. #2971	C₂×C₅	semidirect
143. #2923	C₂×C₅	semidirect
144. #1535	C₂×C₅	semidirect
145. #1534	C₂×C₅	semidirect
146. #1531	C₂×C₅	semidirect
147. #1529	C₂×C₅	semidirect
148. #1529	C₂×C₅	semidirect
149. #1528	C₂×C₅	semidirect
150. #1526	C₂×C₅	semidirect
151. #1524	C₂×C₅	semidirect
548. C₅	#17682	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×#3515	2
C₅×#2971	2
C₅×#2923	2
C₅×#1535	2
C₅×#1534	2
C₅×#1531	2
C₅×#1529	2
C₅×#1528	2
C₅×#1526	2
C₅×#1524	2
#17682	5

Subgroups — C5×#17682 #11940402

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#17682 #11940402