Subgroups — C₅×#17767 #11940487

Order 1280.

862 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3509	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×#1561	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1559	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1559	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1556	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1554	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1554	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1552	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1552	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1550	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1549	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1544	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1542	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#557	—	2	1	no	—
17	C₅×#557	C₄	1	2	yes	—
18	C₅×#556	—	2	1	no	—
19	C₅×#556	C₄	1	2	yes	—
20	C₅×#552	—	2	1	no	—
21	C₅×#552	—	2	1	no	—
22	C₅×#552	C₄	1	2	yes	—
23	C₅×#552	C₄	1	2	yes	—
24	C₅×#541	—	2	1	no	—
25	C₅×#541	—	2	1	no	—
26	C₅×#536	—	2	1	no	—
27	C₅×#533	C₂²	1	1	yes	characteristic
28	C₅×#533	C₂²	1	1	yes	characteristic
29	C₅×#533	C₂²	1	1	yes	characteristic
30	C₅×#533	C₂²	1	1	yes	characteristic
31	C₅×#533	C₂²	1	1	yes	characteristic
32	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
33	C₅×#519	—	2	1	no	—
34	C₄×C₅×#41	C₂²	1	1	yes	characteristic
35	C₅×#446	—	2	1	no	—
36	C₅×#436	—	2	1	no	—
37	C₅×#435	—	2	1	no	—
38	C₅×#435	—	2	1	no	—
39	C₅×#433	—	2	1	no	—
40	C₅×#433	—	2	1	no	—
41	C₅×#432	C₂²	1	1	yes	characteristic
42	C₅×#432	C₂²	1	1	yes	characteristic
43	C₅×#432	C₂²	1	1	yes	characteristic
44	C₅×#432	C₂²	1	1	yes	characteristic
45	C₅×#431	C₂²	1	1	yes	characteristic
46	C₅×#431	C₂²	1	1	yes	characteristic
47	C₅×#431	C₂²	1	1	yes	characteristic
48	C₅×#423	C₂²	1	1	yes	characteristic
49	C₅×#423	C₂²	1	1	yes	characteristic
50	C₅×#423	C₂²	1	1	yes	characteristic
51	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
52	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
53	C₅×#408	—	2	1	no	—
54	C₅×#405	—	2	1	no	—
55	C₅×#333	C₂²	1	1	yes	characteristic
56	C₅×#333	C₂²	1	1	yes	characteristic
57	C₅×#333	C₂²	1	1	yes	characteristic
58	C₅×#333	C₂²	1	1	yes	characteristic
59	C₅×#332	C₂²	1	1	yes	characteristic
60	C₅×#332	C₂²	1	1	yes	characteristic
61	C₅×#332	C₂²	1	1	yes	characteristic
62	C₅×#332	C₂²	1	1	yes	characteristic
63	C₅×#332	C₂²	1	1	yes	characteristic
64	C₅×#332	C₂²	1	1	yes	characteristic
65	C₅×#332	C₂²	1	1	yes	characteristic
66	C₅×#332	C₂²	1	1	yes	characteristic
67	C₅×#332	C₂²	1	1	yes	characteristic
68	C₅×#332	C₂²	1	1	yes	characteristic
69	C₅×#332	C₂²	1	1	yes	characteristic
70	C₅×#332	C₂²	1	1	yes	characteristic
71	#17767	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
72	C₂×C₅×#41	D₄	1	1	yes	characteristic
73	C₂²×C₅×Q₈	—	2	1	no	—
74	C₂×C₅×M₁₆	—	2	1	no	—
75	C₂×C₅×M₁₆	—	2	1	no	—
76	C₂×C₅×M₁₆	—	2	1	no	—
77	C₂²×C₅×C₈	—	2	1	no	—
78	C₂²×C₅×C₈	—	2	1	no	—
79	C₅×C₄⋊Q₈	—	2	2	no	—
80	C₅×C₄⋊Q₈	—	2	1	no	—
81	C₅×C₄⋊Q₈	—	2	1	no	—
82	C₅×C₄⋊Q₈	C₂×C₄	1	2	yes	—
83	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
84	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
85	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
86	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
87	C₅×#126	—	2	2	no	—
88	C₅×#126	—	2	2	no	—
89	C₅×#126	—	2	2	no	—
90	C₅×#126	—	2	2	no	—
91	C₅×#125	—	2	2	no	—
92	C₅×#125	—	2	2	no	—
93	C₅×#125	—	2	2	no	—
94	C₅×#125	—	2	2	no	—
95	C₅×#125	—	2	1	no	—
96	C₅×#125	—	2	1	no	—
97	C₅×#125	—	2	1	no	—
98	C₅×#125	C₂×C₄	1	2	yes	—
99	C₅×#125	C₂×C₄	1	2	yes	—
100	C₅×#124	—	2	2	no	—
101	C₅×#123	—	2	2	no	—
102	C₅×#123	—	2	2	no	—
103	C₅×C₂²⋊Q₈	—	2	1	no	—
104	C₅×C₂²⋊Q₈	—	2	1	no	—
105	C₅×C₂²⋊Q₈	—	2	1	no	—
106	C₅×C₂²⋊Q₈	—	2	1	no	—
107	C₅×C₂²⋊Q₈	—	2	1	no	—
108	C₅×C₂²⋊Q₈	—	2	1	no	—
109	C₅×C₂²⋊Q₈	—	2	1	no	—
110	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
111	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
112	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
113	C₄×C₅×Q₈	—	2	2	no	—
114	C₄×C₅×Q₈	—	2	2	no	—
115	C₄×C₅×Q₈	—	2	1	no	—
116	C₄×C₅×Q₈	—	2	1	no	—
117	C₄×C₅×Q₈	—	2	1	no	—
118	C₄×C₅×Q₈	—	2	1	no	—
119	C₄×C₅×Q₈	—	2	1	no	—
120	C₄×C₅×Q₈	—	2	1	no	—
121	C₄×C₅×Q₈	—	2	1	no	—
122	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
123	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
124	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
125	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
126	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
127	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
128	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
129	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
130	C₄×C₅×D₄	D₄	1	1	yes	characteristic
131	C₄×C₅×D₄	D₄	1	1	yes	characteristic
132	C₄×C₅×D₄	D₄	1	1	yes	characteristic
133	C₅×#117	—	2	1	no	—
134	C₅×#117	—	2	1	no	—
135	C₅×#117	—	2	1	no	—
136	C₅×#117	—	2	2	no	—
137	C₅×#117	—	2	2	no	—
138	C₅×#117	C₂×C₄	1	2	yes	—
139	C₅×#117	C₂×C₄	1	2	yes	—
140	C₅×#117	D₄	1	1	yes	characteristic
141	C₅×#117	D₄	1	1	yes	characteristic
142	C₅×#117	D₄	1	1	yes	characteristic
143	C₂×C₅×C₄⋊C₄	—	2	1	no	—
144	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
145	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
146	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
147	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
148	C₅×C₄⋊C₈	—	2	1	no	—
149	C₅×C₄⋊C₈	—	2	1	no	—
150	C₅×C₄⋊C₈	—	2	1	no	—
151	C₅×C₄⋊C₈	—	2	1	no	—
152	C₅×C₄⋊C₈	—	2	1	no	—
153	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
154	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
155	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
156	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
157	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
158	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
159	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
160	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
161	C₅×C₂²⋊C₈	—	2	1	no	—
162	C₅×C₂²⋊C₈	—	2	1	no	—
163	C₅×C₂²⋊C₈	—	2	1	no	—
164	C₅×C₂²⋊C₈	—	2	1	no	—
165	C₅×C₂²⋊C₈	—	2	1	no	—
166	C₅×C₂²⋊C₈	—	2	1	no	—
167	C₅×C₂²⋊C₈	—	2	1	no	—
168	C₅×#97	—	2	1	no	—
169	C₅×#97	—	2	1	no	—
170	C₅×#97	—	2	1	no	—
171	C₅×#97	—	2	1	no	—
172	C₄×C₅×C₈	—	2	1	no	—
173	C₄×C₅×C₈	—	2	1	no	—
174	C₄×C₅×C₈	—	2	1	no	—
175	#3509	C₂×C₅	1	1	yes	characteristic
176	#2989	C₂×C₅	1	1	yes	characteristic
177	#2925	C₂×C₅	1	1	yes	characteristic
178	#1561	C₂×C₅	1	1	yes	characteristic, complemented
179	#1559	C₂×C₅	1	1	yes	characteristic, complemented
180	#1559	C₂×C₅	1	1	yes	characteristic, complemented
181	#1556	C₂×C₅	1	1	yes	characteristic, complemented
182	#1554	C₂×C₅	1	1	yes	characteristic, complemented
183	#1554	C₂×C₅	1	1	yes	characteristic, complemented
184	#1552	C₂×C₅	1	1	yes	characteristic, complemented
185	#1552	C₂×C₅	1	1	yes	characteristic, complemented
186	#1550	C₂×C₅	1	1	yes	characteristic, complemented
187	#1549	C₂×C₅	1	1	yes	characteristic, complemented
188	#1544	C₂×C₅	1	1	yes	characteristic, complemented
189	#1542	C₂×C₅	1	1	yes	characteristic, complemented
190	C₅×#41	—	4	1	no	—
191	C₅×#41	—	4	1	no	—
192	C₂×C₅×Q₈	—	2	2	no	—
193	C₂×C₅×Q₈	—	2	1	no	—
194	C₂×C₅×Q₈	—	2	1	no	—
195	C₂×C₅×Q₈	—	2	1	no	—
196	C₂×C₅×Q₈	—	4	2	no	—
197	C₂×C₅×Q₈	—	4	2	no	—
198	C₂×C₅×Q₈	C₂²⋊C₄	1	1	yes	characteristic
199	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
200	C₂×C₅×D₄	C₂²⋊C₄	1	1	yes	characteristic
201	C₂×C₅×D₄	C₂²⋊C₄	1	1	yes	characteristic
202	C₂×C₅×D₄	C₂²⋊C₄	1	1	yes	characteristic
203	C₂²×C₄×C₅	—	2	2	no	—
204	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
205	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
206	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
207	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
210	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
211	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
212	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
213	C₅×M₁₆	—	4	2	no	—
214	C₅×M₁₆	—	8	1	no	—
215	C₅×M₁₆	—	8	1	no	—
216	C₂×C₅×C₈	—	2	1	no	—
217	C₂×C₅×C₈	—	2	1	no	—
218	C₂×C₅×C₈	—	2	1	no	—
219	C₂×C₅×C₈	—	2	1	no	—
220	C₂×C₅×C₈	—	2	1	no	—
221	C₂×C₅×C₈	—	2	1	no	—
222	C₂×C₅×C₈	—	2	1	no	—
223	C₂×C₅×C₈	—	2	1	no	—
224	C₂×C₅×C₈	—	4	2	no	—
225	C₂×C₅×C₈	—	8	1	no	—
226	C₅×C₄⋊C₄	—	2	2	no	—
227	C₅×C₄⋊C₄	—	2	2	no	—
228	C₅×C₄⋊C₄	—	2	2	no	—
229	C₅×C₄⋊C₄	—	2	2	no	—
230	C₅×C₄⋊C₄	—	2	2	no	—
231	C₅×C₄⋊C₄	—	2	2	no	—
232	C₅×C₄⋊C₄	—	2	2	no	—
233	C₅×C₄⋊C₄	—	2	2	no	—
234	C₅×C₄⋊C₄	—	2	2	no	—
235	C₅×C₄⋊C₄	—	2	2	no	—
236	C₅×C₄⋊C₄	—	2	2	no	—
237	C₅×C₄⋊C₄	—	2	2	no	—
238	C₅×C₄⋊C₄	—	2	1	no	—
239	C₅×C₄⋊C₄	—	2	1	no	—
240	C₅×C₄⋊C₄	—	2	1	no	—
241	C₅×C₄⋊C₄	—	2	1	no	—
242	C₅×C₄⋊C₄	—	2	1	no	—
243	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
244	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
245	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
246	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
247	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
248	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
249	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
250	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
251	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
252	C₅×C₂²⋊C₄	—	2	2	no	—
253	C₅×C₂²⋊C₄	—	2	2	no	—
254	C₅×C₂²⋊C₄	—	2	2	no	—
255	C₅×C₂²⋊C₄	—	2	2	no	—
256	C₅×C₂²⋊C₄	—	2	2	no	—
257	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
258	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
259	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
260	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
261	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
262	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
263	C₄²×C₅	—	2	2	no	—
264	C₄²×C₅	—	2	2	no	—
265	C₄²×C₅	—	2	2	no	—
266	C₄²×C₅	—	2	2	no	—
267	C₄²×C₅	—	2	2	no	—
268	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
269	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
270	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
271	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
272	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
273	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
274	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
275	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
276	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
277	C₄²×C₅	C₂⁴	1	1	yes	characteristic
278	#557	—	2	1	no	—
279	#557	C₄×C₅	1	2	yes	—
280	#556	—	2	1	no	—
281	#556	C₄×C₅	1	2	yes	—
282	#552	—	2	1	no	—
283	#552	—	2	1	no	—
284	#552	C₄×C₅	1	2	yes	—
285	#552	C₄×C₅	1	2	yes	—
286	#541	—	2	1	no	—
287	#541	—	2	1	no	—
288	#536	—	2	1	no	—
289	#533	C₂²×C₅	1	1	yes	characteristic
290	#533	C₂²×C₅	1	1	yes	characteristic
291	#533	C₂²×C₅	1	1	yes	characteristic
292	#533	C₂²×C₅	1	1	yes	characteristic
293	#533	C₂²×C₅	1	1	yes	characteristic
294	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
295	#519	—	2	1	no	—
296	C₄×#41	C₂²×C₅	1	1	yes	characteristic
297	#446	—	2	1	no	—
298	#436	—	2	1	no	—
299	#435	—	2	1	no	—
300	#435	—	2	1	no	—
301	#433	—	2	1	no	—
302	#433	—	2	1	no	—
303	#432	C₂²×C₅	1	1	yes	characteristic
304	#432	C₂²×C₅	1	1	yes	characteristic
305	#432	C₂²×C₅	1	1	yes	characteristic
306	#432	C₂²×C₅	1	1	yes	characteristic
307	#431	C₂²×C₅	1	1	yes	characteristic
308	#431	C₂²×C₅	1	1	yes	characteristic
309	#431	C₂²×C₅	1	1	yes	characteristic
310	#423	C₂²×C₅	1	1	yes	characteristic
311	#423	C₂²×C₅	1	1	yes	characteristic
312	#423	C₂²×C₅	1	1	yes	characteristic
313	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
314	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
315	#408	—	2	1	no	—
316	#405	—	2	1	no	—
317	#333	C₂²×C₅	1	1	yes	characteristic
318	#333	C₂²×C₅	1	1	yes	characteristic
319	#333	C₂²×C₅	1	1	yes	characteristic
320	#333	C₂²×C₅	1	1	yes	characteristic
321	#332	C₂²×C₅	1	1	yes	characteristic
322	#332	C₂²×C₅	1	1	yes	characteristic
323	#332	C₂²×C₅	1	1	yes	characteristic
324	#332	C₂²×C₅	1	1	yes	characteristic
325	#332	C₂²×C₅	1	1	yes	characteristic
326	#332	C₂²×C₅	1	1	yes	characteristic
327	#332	C₂²×C₅	1	1	yes	characteristic
328	#332	C₂²×C₅	1	1	yes	characteristic
329	#332	C₂²×C₅	1	1	yes	characteristic
330	#332	C₂²×C₅	1	1	yes	characteristic
331	#332	C₂²×C₅	1	1	yes	characteristic
332	#332	C₂²×C₅	1	1	yes	characteristic
333	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
334	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
335	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
336	C₅×Q₈	—	4	1	no	—
337	C₅×Q₈	—	4	2	no	—
338	C₅×Q₈	—	4	4	no	—
339	C₅×Q₈	—	4	1	no	—
340	C₅×Q₈	—	4	1	no	—
341	C₅×Q₈	—	4	1	no	—
342	C₅×Q₈	—	4	1	no	—
343	C₅×Q₈	—	4	1	no	—
344	C₅×Q₈	—	4	1	no	—
345	C₅×D₄	—	4	1	no	—
346	C₅×D₄	—	4	1	no	—
347	C₅×D₄	—	4	1	no	—
348	C₂×C₄×C₅	—	2	1	no	—
349	C₂×C₄×C₅	—	2	1	no	—
350	C₂×C₄×C₅	—	2	1	no	—
351	C₂×C₄×C₅	—	2	1	no	—
352	C₂×C₄×C₅	—	2	1	no	—
353	C₂×C₄×C₅	—	2	1	no	—
354	C₂×C₄×C₅	—	2	1	no	—
355	C₂×C₄×C₅	—	2	1	no	—
356	C₂×C₄×C₅	—	2	1	no	—
357	C₂×C₄×C₅	—	2	1	no	—
358	C₂×C₄×C₅	—	2	1	no	—
359	C₂×C₄×C₅	—	2	1	no	—
360	C₂×C₄×C₅	—	2	2	no	—
361	C₂×C₄×C₅	—	2	2	no	—
362	C₂×C₄×C₅	—	2	2	no	—
363	C₂×C₄×C₅	—	2	2	no	—
364	C₂×C₄×C₅	—	4	1	no	—
365	C₂×C₄×C₅	—	4	1	no	—
366	C₂×C₄×C₅	—	4	1	no	—
367	C₂×C₄×C₅	—	4	4	no	—
368	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
369	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
370	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
371	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
372	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
373	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
374	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
375	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
376	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
377	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
378	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
379	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
380	C₅×C₈	—	4	1	no	—
381	C₅×C₈	—	4	1	no	—
382	C₅×C₈	—	4	1	no	—
383	C₅×C₈	—	4	1	no	—
384	C₅×C₈	—	4	1	no	—
385	C₅×C₈	—	4	1	no	—
386	C₅×C₈	—	4	1	no	—
387	C₅×C₈	—	4	1	no	—
388	C₂×#41	C₅×D₄	1	1	yes	characteristic
389	C₂²×Q₈	—	2	1	no	—
390	C₂×M₁₆	—	2	1	no	—
391	C₂×M₁₆	—	2	1	no	—
392	C₂×M₁₆	—	2	1	no	—
393	C₂²×C₈	—	2	1	no	—
394	C₂²×C₈	—	2	1	no	—
395	C₄⋊Q₈	—	2	2	no	—
396	C₄⋊Q₈	—	2	1	no	—
397	C₄⋊Q₈	—	2	1	no	—
398	C₄⋊Q₈	C₂×C₄×C₅	1	2	yes	—
399	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
400	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
401	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
402	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
403	#126	—	2	2	no	—
404	#126	—	2	2	no	—
405	#126	—	2	2	no	—
406	#126	—	2	2	no	—
407	#125	—	2	2	no	—
408	#125	—	2	2	no	—
409	#125	—	2	2	no	—
410	#125	—	2	2	no	—
411	#125	—	2	1	no	—
412	#125	—	2	1	no	—
413	#125	—	2	1	no	—
414	#125	C₂×C₄×C₅	1	2	yes	—
415	#125	C₂×C₄×C₅	1	2	yes	—
416	#124	—	2	2	no	—
417	#123	—	2	2	no	—
418	#123	—	2	2	no	—
419	C₂²⋊Q₈	—	2	1	no	—
420	C₂²⋊Q₈	—	2	1	no	—
421	C₂²⋊Q₈	—	2	1	no	—
422	C₂²⋊Q₈	—	2	1	no	—
423	C₂²⋊Q₈	—	2	1	no	—
424	C₂²⋊Q₈	—	2	1	no	—
425	C₂²⋊Q₈	—	2	1	no	—
426	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
427	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
428	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
429	C₄×Q₈	—	2	2	no	—
430	C₄×Q₈	—	2	2	no	—
431	C₄×Q₈	—	2	1	no	—
432	C₄×Q₈	—	2	1	no	—
433	C₄×Q₈	—	2	1	no	—
434	C₄×Q₈	—	2	1	no	—
435	C₄×Q₈	—	2	1	no	—
436	C₄×Q₈	—	2	1	no	—
437	C₄×Q₈	—	2	1	no	—
438	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
439	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
440	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
441	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
442	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
443	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
444	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
445	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
446	C₄×D₄	C₅×D₄	1	1	yes	characteristic
447	C₄×D₄	C₅×D₄	1	1	yes	characteristic
448	C₄×D₄	C₅×D₄	1	1	yes	characteristic
449	#117	—	2	1	no	—
450	#117	—	2	1	no	—
451	#117	—	2	1	no	—
452	#117	—	2	2	no	—
453	#117	—	2	2	no	—
454	#117	C₂×C₄×C₅	1	2	yes	—
455	#117	C₂×C₄×C₅	1	2	yes	—
456	#117	C₅×D₄	1	1	yes	characteristic
457	#117	C₅×D₄	1	1	yes	characteristic
458	#117	C₅×D₄	1	1	yes	characteristic
459	C₂×C₄⋊C₄	—	2	1	no	—
460	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
461	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
462	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
463	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
464	C₄⋊C₈	—	2	1	no	—
465	C₄⋊C₈	—	2	1	no	—
466	C₄⋊C₈	—	2	1	no	—
467	C₄⋊C₈	—	2	1	no	—
468	C₄⋊C₈	—	2	1	no	—
469	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
470	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
471	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
472	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
473	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
474	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
475	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
476	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
477	C₂²⋊C₈	—	2	1	no	—
478	C₂²⋊C₈	—	2	1	no	—
479	C₂²⋊C₈	—	2	1	no	—
480	C₂²⋊C₈	—	2	1	no	—
481	C₂²⋊C₈	—	2	1	no	—
482	C₂²⋊C₈	—	2	1	no	—
483	C₂²⋊C₈	—	2	1	no	—
484	#97	—	2	1	no	—
485	#97	—	2	1	no	—
486	#97	—	2	1	no	—
487	#97	—	2	1	no	—
488	C₄×C₈	—	2	1	no	—
489	C₄×C₈	—	2	1	no	—
490	C₄×C₈	—	2	1	no	—
491	C₂²×C₅	—	2	1	no	—
492	C₂²×C₅	—	2	1	no	—
493	C₂²×C₅	—	2	1	no	—
494	C₂²×C₅	—	2	1	no	—
495	C₂²×C₅	—	2	1	no	—
496	C₂²×C₅	—	2	1	no	—
497	C₂²×C₅	—	2	1	no	—
498	C₂²×C₅	—	2	1	no	—
499	C₂²×C₅	—	2	1	no	—
500	C₂²×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
501	C₄×C₅	—	2	1	no	—
502	C₄×C₅	—	2	1	no	—
503	C₄×C₅	—	2	1	no	—
504	C₄×C₅	—	2	1	no	—
505	C₄×C₅	—	2	1	no	—
506	C₄×C₅	—	2	1	no	—
507	C₄×C₅	—	2	1	no	—
508	C₄×C₅	—	2	1	no	—
509	C₄×C₅	—	2	1	no	—
510	C₄×C₅	—	2	1	no	—
511	C₄×C₅	—	4	2	no	—
512	C₄×C₅	—	4	2	no	—
513	C₄×C₅	—	4	2	no	—
514	C₄×C₅	—	4	2	no	—
515	C₄×C₅	#575	1	1	yes	characteristic
516	C₄×C₅	#575	1	1	yes	characteristic
517	C₄×C₅	#577	1	1	yes	characteristic
518	C₄×C₅	#578	1	1	yes	characteristic
519	#41	—	4	1	no	—
520	#41	—	4	1	no	—
521	C₂×Q₈	—	2	2	no	—
522	C₂×Q₈	—	2	1	no	—
523	C₂×Q₈	—	2	1	no	—
524	C₂×Q₈	—	2	1	no	—
525	C₂×Q₈	—	4	2	no	—
526	C₂×Q₈	—	4	2	no	—
527	C₂×Q₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
528	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
529	C₂×D₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
530	C₂×D₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
531	C₂×D₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
532	C₂²×C₄	—	2	2	no	—
533	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
534	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
535	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
536	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
537	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
538	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
539	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
540	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
541	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
542	M₁₆	—	4	2	no	—
543	M₁₆	—	8	1	no	—
544	M₁₆	—	8	1	no	—
545	C₂×C₈	—	2	1	no	—
546	C₂×C₈	—	2	1	no	—
547	C₂×C₈	—	2	1	no	—
548	C₂×C₈	—	2	1	no	—
549	C₂×C₈	—	2	1	no	—
550	C₂×C₈	—	2	1	no	—
551	C₂×C₈	—	2	1	no	—
552	C₂×C₈	—	2	1	no	—
553	C₂×C₈	—	4	2	no	—
554	C₂×C₈	—	8	1	no	—
555	C₄⋊C₄	—	2	2	no	—
556	C₄⋊C₄	—	2	2	no	—
557	C₄⋊C₄	—	2	2	no	—
558	C₄⋊C₄	—	2	2	no	—
559	C₄⋊C₄	—	2	2	no	—
560	C₄⋊C₄	—	2	2	no	—
561	C₄⋊C₄	—	2	2	no	—
562	C₄⋊C₄	—	2	2	no	—
563	C₄⋊C₄	—	2	2	no	—
564	C₄⋊C₄	—	2	2	no	—
565	C₄⋊C₄	—	2	2	no	—
566	C₄⋊C₄	—	2	2	no	—
567	C₄⋊C₄	—	2	1	no	—
568	C₄⋊C₄	—	2	1	no	—
569	C₄⋊C₄	—	2	1	no	—
570	C₄⋊C₄	—	2	1	no	—
571	C₄⋊C₄	—	2	1	no	—
572	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
573	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
574	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
575	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
576	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
577	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
578	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
579	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
580	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
581	C₂²⋊C₄	—	2	2	no	—
582	C₂²⋊C₄	—	2	2	no	—
583	C₂²⋊C₄	—	2	2	no	—
584	C₂²⋊C₄	—	2	2	no	—
585	C₂²⋊C₄	—	2	2	no	—
586	C₂²⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
587	C₂²⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
588	C₂²⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
589	C₂²⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
590	C₂²⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
591	C₂²⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
592	C₄²	—	2	2	no	—
593	C₄²	—	2	2	no	—
594	C₄²	—	2	2	no	—
595	C₄²	—	2	2	no	—
596	C₄²	—	2	2	no	—
597	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
598	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
599	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
600	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
601	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
602	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
603	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
604	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
605	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
606	C₄²	C₂⁴×C₅	1	1	yes	characteristic
607	C₂×C₅	—	4	1	no	—
608	C₂×C₅	—	4	1	no	—
609	C₂×C₅	—	4	1	no	—
610	C₂×C₅	#2889	1	1	yes	characteristic
611	C₂×C₅	#2896	1	1	yes	characteristic
612	C₂×C₅	#2898	1	1	yes	characteristic
613	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
614	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
615	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
616	Q₈	—	4	1	no	—
617	Q₈	—	4	2	no	—
618	Q₈	—	4	4	no	—
619	Q₈	—	4	1	no	—
620	Q₈	—	4	1	no	—
621	Q₈	—	4	1	no	—
622	Q₈	—	4	1	no	—
623	Q₈	—	4	1	no	—
624	Q₈	—	4	1	no	—
625	D₄	—	4	1	no	—
626	D₄	—	4	1	no	—
627	D₄	—	4	1	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	4	no	—
648	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
649	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
650	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
651	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
652	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
653	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
654	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
655	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
656	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
657	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
658	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
659	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
660	C₈	—	4	1	no	—
661	C₈	—	4	1	no	—
662	C₈	—	4	1	no	—
663	C₈	—	4	1	no	—
664	C₈	—	4	1	no	—
665	C₈	—	4	1	no	—
666	C₈	—	4	1	no	—
667	C₈	—	4	1	no	—
668	C₅	#17767	1	1	yes	characteristic, direct product factor, Sylow
669	C₂²	—	2	1	no	—
670	C₂²	—	2	1	no	—
671	C₂²	—	2	1	no	—
672	C₂²	—	2	1	no	—
673	C₂²	—	2	1	no	—
674	C₂²	—	2	1	no	—
675	C₂²	—	2	1	no	—
676	C₂²	—	2	1	no	—
677	C₂²	—	2	1	no	—
678	C₂²	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
679	C₄	—	2	1	no	—
680	C₄	—	2	1	no	—
681	C₄	—	2	1	no	—
682	C₄	—	2	1	no	—
683	C₄	—	2	1	no	—
684	C₄	—	2	1	no	—
685	C₄	—	2	1	no	—
686	C₄	—	2	1	no	—
687	C₄	—	2	1	no	—
688	C₄	—	2	1	no	—
689	C₄	—	4	2	no	—
690	C₄	—	4	2	no	—
691	C₄	—	4	2	no	—
692	C₄	—	4	2	no	—
693	C₄	C₅×#575	1	1	yes	characteristic
694	C₄	C₅×#575	1	1	yes	characteristic
695	C₄	C₅×#577	1	1	yes	characteristic
696	C₄	C₅×#578	1	1	yes	characteristic
697	C₂	—	4	1	no	—
698	C₂	—	4	1	no	—
699	C₂	—	4	1	no	—
700	C₂	C₅×#2889	1	1	yes	characteristic
701	C₂	C₅×#2896	1	1	yes	characteristic
702	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	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×#1561	C₂	semidirect
5. C₅×#1559	C₂	semidirect
6. C₅×#1559	C₂	semidirect
7. C₅×#1556	C₂	semidirect
8. C₅×#1554	C₂	semidirect
9. C₅×#1554	C₂	semidirect
10. C₅×#1552	C₂	semidirect
11. C₅×#1552	C₂	semidirect
12. C₅×#1550	C₂	semidirect
13. C₅×#1549	C₂	semidirect
14. C₅×#1544	C₂	semidirect
15. C₅×#1542	C₂	semidirect
71. #17767	C₅	direct (N × H)
178. #1561	C₂×C₅	semidirect
179. #1559	C₂×C₅	semidirect
180. #1559	C₂×C₅	semidirect
181. #1556	C₂×C₅	semidirect
182. #1554	C₂×C₅	semidirect
183. #1554	C₂×C₅	semidirect
184. #1552	C₂×C₅	semidirect
185. #1552	C₂×C₅	semidirect
186. #1550	C₂×C₅	semidirect
187. #1549	C₂×C₅	semidirect
188. #1544	C₂×C₅	semidirect
189. #1542	C₂×C₅	semidirect
668. C₅	#17767	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×#3509	2
C₅×#2989	2
C₅×#2925	2
C₅×#1561	2
C₅×#1559	2
C₅×#1556	2
C₅×#1554	2
C₅×#1552	2
C₅×#1550	2
C₅×#1549	2
C₅×#1544	2
C₅×#1542	2
#17767	5

Subgroups — C5×#17767 #11940487

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#17767 #11940487