Subgroups — C₅×#17778 #11940498

Order 1280.

868 conjugacy classes of subgroups.

The subgroup lattice has 494 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×#2991	C₂	1	1	yes	maximal, characteristic
3	C₅×#2990	C₂	1	1	yes	maximal, characteristic
4	C₅×#1561	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1559	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×#1548	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1548	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1544	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1542	C₂	1	2	yes	maximal, complemented
12	C₅×#557	—	2	1	no	—
13	C₅×#557	—	2	1	no	—
14	C₅×#556	—	2	1	no	—
15	C₅×#556	—	2	1	no	—
16	C₅×#552	—	2	2	no	—
17	C₅×#552	—	2	2	no	—
18	C₅×#541	C₄	1	4	yes	—
19	C₅×#536	C₄	1	2	yes	—
20	C₅×#533	C₂²	1	2	yes	—
21	C₅×#533	C₂²	1	2	yes	—
22	C₅×#533	C₂²	1	1	yes	characteristic
23	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₅×#519	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	2	yes	—
41	C₅×#333	C₂²	1	2	yes	—
42	C₅×#333	C₂²	1	2	yes	—
43	C₅×#333	C₂²	1	2	yes	—
44	C₅×#332	C₂²	1	1	yes	characteristic
45	C₅×#332	C₂²	1	2	yes	—
46	C₅×#332	C₂²	1	1	yes	characteristic
47	C₅×#332	C₂²	1	1	yes	characteristic
48	C₅×#332	C₂²	1	1	yes	characteristic
49	C₅×#332	C₂²	1	2	yes	—
50	#17778	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
51	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₅×Q₈	C₂×C₄	1	2	yes	—
53	C₂×C₅×M₁₆	—	2	1	no	—
54	C₂×C₅×M₁₆	—	2	1	no	—
55	C₂×C₅×M₁₆	—	2	2	no	—
56	C₂²×C₅×C₈	—	2	2	no	—
57	C₅×C₄⋊Q₈	—	2	2	no	—
58	C₅×C₄⋊Q₈	—	2	1	no	—
59	C₅×C₄⋊Q₈	—	2	1	no	—
60	C₅×C₄⋊Q₈	C₂×C₄	1	2	yes	—
61	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
62	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
63	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
64	C₅×#126	—	2	4	no	—
65	C₅×#126	—	2	4	no	—
66	C₅×#125	—	2	4	no	—
67	C₅×#125	—	2	4	no	—
68	C₅×#125	—	2	2	no	—
69	C₅×#125	—	2	2	no	—
70	C₅×#125	C₂×C₄	1	2	yes	—
71	C₅×#124	—	2	2	no	—
72	C₅×#123	—	2	4	no	—
73	C₅×C₂²⋊Q₈	—	2	1	no	—
74	C₅×C₂²⋊Q₈	—	2	1	no	—
75	C₅×C₂²⋊Q₈	—	2	2	no	—
76	C₅×C₂²⋊Q₈	—	2	2	no	—
77	C₅×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
78	C₅×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
79	C₄×C₅×Q₈	—	2	2	no	—
80	C₄×C₅×Q₈	—	2	2	no	—
81	C₄×C₅×Q₈	—	2	2	no	—
82	C₄×C₅×Q₈	—	2	2	no	—
83	C₄×C₅×Q₈	—	2	1	no	—
84	C₄×C₅×Q₈	—	2	1	no	—
85	C₄×C₅×Q₈	C₂×C₄	1	4	yes	—
86	C₄×C₅×Q₈	C₂×C₄	1	4	yes	—
87	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
88	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
89	C₄×C₅×D₄	D₄	1	1	yes	characteristic
90	C₄×C₅×D₄	D₄	1	2	yes	—
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	2	no	—
95	C₅×#117	—	2	4	no	—
96	C₅×#117	C₂×C₄	1	2	yes	—
97	C₅×#117	C₂×C₄	1	1	yes	characteristic
98	C₅×#117	C₂×C₄	1	2	yes	—
99	C₂×C₅×C₄⋊C₄	—	2	1	no	—
100	C₂×C₅×C₄⋊C₄	—	2	1	no	—
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	#3509	C₂×C₅	1	1	yes	characteristic
122	#2991	C₂×C₅	1	1	yes	characteristic
123	#2990	C₂×C₅	1	1	yes	characteristic
124	#1561	C₂×C₅	1	1	yes	characteristic, complemented
125	#1559	C₂×C₅	1	2	yes	complemented
126	#1554	C₂×C₅	1	2	yes	complemented
127	#1550	C₂×C₅	1	2	yes	complemented
128	#1548	C₂×C₅	1	1	yes	characteristic, complemented
129	#1548	C₂×C₅	1	1	yes	characteristic, complemented
130	#1544	C₂×C₅	1	1	yes	characteristic, complemented
131	#1542	C₂×C₅	1	2	yes	complemented
132	C₅×#41	—	4	2	no	—
133	C₂×C₅×Q₈	—	2	2	no	—
134	C₂×C₅×Q₈	—	2	1	no	—
135	C₂×C₅×Q₈	—	2	1	no	—
136	C₂×C₅×Q₈	—	4	4	no	—
137	C₂×C₅×Q₈	C₂²⋊C₄	1	1	yes	characteristic
138	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	—
139	C₂×C₅×D₄	C₂²⋊C₄	1	1	yes	characteristic
140	C₂×C₅×D₄	C₂²⋊C₄	1	2	yes	—
141	C₂²×C₄×C₅	—	2	2	no	—
142	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
144	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
148	C₅×M₁₆	—	8	1	no	—
149	C₅×M₁₆	—	8	1	no	—
150	C₅×M₁₆	—	8	2	no	—
151	C₂×C₅×C₈	—	2	1	no	—
152	C₂×C₅×C₈	—	2	2	no	—
153	C₂×C₅×C₈	—	2	2	no	—
154	C₂×C₅×C₈	—	2	1	no	—
155	C₂×C₅×C₈	—	2	1	no	—
156	C₂×C₅×C₈	—	2	1	no	—
157	C₂×C₅×C₈	—	8	2	no	—
158	C₅×C₄⋊C₄	—	2	2	no	—
159	C₅×C₄⋊C₄	—	2	2	no	—
160	C₅×C₄⋊C₄	—	2	4	no	—
161	C₅×C₄⋊C₄	—	2	4	no	—
162	C₅×C₄⋊C₄	—	2	2	no	—
163	C₅×C₄⋊C₄	—	2	2	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	1	no	—
169	C₅×C₄⋊C₄	—	2	1	no	—
170	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
171	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
172	C₅×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
173	C₅×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
174	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
175	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
176	C₅×C₂²⋊C₄	—	2	2	no	—
177	C₅×C₂²⋊C₄	—	2	4	no	—
178	C₅×C₂²⋊C₄	—	2	4	no	—
179	C₅×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
180	C₅×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
181	C₅×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
182	C₄²×C₅	—	2	4	no	—
183	C₄²×C₅	—	2	4	no	—
184	C₄²×C₅	—	2	2	no	—
185	C₄²×C₅	C₂²×C₄	1	2	yes	—
186	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
187	C₄²×C₅	C₂×D₄	1	2	yes	—
188	C₄²×C₅	C₂×D₄	1	2	yes	—
189	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
190	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
191	C₄²×C₅	C₂⁴	1	1	yes	characteristic
192	#557	—	2	1	no	—
193	#557	—	2	1	no	—
194	#556	—	2	1	no	—
195	#556	—	2	1	no	—
196	#552	—	2	2	no	—
197	#552	—	2	2	no	—
198	#541	C₄×C₅	1	4	yes	—
199	#536	C₄×C₅	1	2	yes	—
200	#533	C₂²×C₅	1	2	yes	—
201	#533	C₂²×C₅	1	2	yes	—
202	#533	C₂²×C₅	1	1	yes	characteristic
203	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
204	#519	C₄×C₅	1	2	yes	—
205	C₄×#41	C₂²×C₅	1	1	yes	characteristic
206	#446	—	2	1	no	—
207	C₈×Q₈	—	2	1	no	—
208	#436	—	2	2	no	—
209	#436	—	2	1	no	—
210	#435	—	2	2	no	—
211	C₈×D₄	—	2	1	no	—
212	#432	C₂²×C₅	1	2	yes	—
213	#431	C₂²×C₅	1	2	yes	—
214	#431	C₂²×C₅	1	1	yes	characteristic
215	#431	C₂²×C₅	1	1	yes	characteristic
216	#423	C₂²×C₅	1	1	yes	characteristic
217	#423	C₂²×C₅	1	1	yes	characteristic
218	#423	C₂²×C₅	1	2	yes	—
219	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
220	#333	C₂²×C₅	1	2	yes	—
221	#333	C₂²×C₅	1	2	yes	—
222	#333	C₂²×C₅	1	2	yes	—
223	#333	C₂²×C₅	1	2	yes	—
224	#332	C₂²×C₅	1	1	yes	characteristic
225	#332	C₂²×C₅	1	2	yes	—
226	#332	C₂²×C₅	1	1	yes	characteristic
227	#332	C₂²×C₅	1	1	yes	characteristic
228	#332	C₂²×C₅	1	1	yes	characteristic
229	#332	C₂²×C₅	1	2	yes	—
230	C₂³×C₅	C₂×C₂²⋊C₄	1	2	yes	—
231	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
232	C₅×Q₈	—	2	2	no	—
233	C₅×Q₈	—	4	4	no	—
234	C₅×Q₈	—	4	1	no	—
235	C₅×Q₈	—	4	1	no	—
236	C₅×Q₈	—	4	1	no	—
237	C₅×Q₈	—	4	1	no	—
238	C₅×Q₈	—	4	4	no	—
239	C₅×D₄	—	2	2	no	—
240	C₅×D₄	—	4	2	no	—
241	C₂×C₄×C₅	—	2	2	no	—
242	C₂×C₄×C₅	—	2	1	no	—
243	C₂×C₄×C₅	—	2	1	no	—
244	C₂×C₄×C₅	—	2	2	no	—
245	C₂×C₄×C₅	—	2	1	no	—
246	C₂×C₄×C₅	—	2	1	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	2	no	—
251	C₂×C₄×C₅	—	2	2	no	—
252	C₂×C₄×C₅	—	2	4	no	—
253	C₂×C₄×C₅	—	4	2	no	—
254	C₂×C₄×C₅	—	4	4	no	—
255	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
256	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
257	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
258	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
259	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
260	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
261	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
262	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
263	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
264	C₅×C₈	—	4	1	no	—
265	C₅×C₈	—	4	2	no	—
266	C₅×C₈	—	4	2	no	—
267	C₅×C₈	—	4	1	no	—
268	C₅×C₈	—	4	1	no	—
269	C₅×C₈	—	4	1	no	—
270	C₂×#41	C₂×C₄×C₅	1	1	yes	characteristic
271	C₂²×Q₈	C₂×C₄×C₅	1	2	yes	—
272	C₂×M₁₆	—	2	1	no	—
273	C₂×M₁₆	—	2	1	no	—
274	C₂×M₁₆	—	2	2	no	—
275	C₂²×C₈	—	2	2	no	—
276	C₄⋊Q₈	—	2	2	no	—
277	C₄⋊Q₈	—	2	1	no	—
278	C₄⋊Q₈	—	2	1	no	—
279	C₄⋊Q₈	C₂×C₄×C₅	1	2	yes	—
280	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
281	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
282	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
283	#126	—	2	4	no	—
284	#126	—	2	4	no	—
285	#125	—	2	4	no	—
286	#125	—	2	4	no	—
287	#125	—	2	2	no	—
288	#125	—	2	2	no	—
289	#125	C₂×C₄×C₅	1	2	yes	—
290	#124	—	2	2	no	—
291	#123	—	2	4	no	—
292	C₂²⋊Q₈	—	2	1	no	—
293	C₂²⋊Q₈	—	2	1	no	—
294	C₂²⋊Q₈	—	2	2	no	—
295	C₂²⋊Q₈	—	2	2	no	—
296	C₂²⋊Q₈	C₂×C₄×C₅	1	4	yes	—
297	C₂²⋊Q₈	C₂×C₄×C₅	1	4	yes	—
298	C₄×Q₈	—	2	2	no	—
299	C₄×Q₈	—	2	2	no	—
300	C₄×Q₈	—	2	2	no	—
301	C₄×Q₈	—	2	2	no	—
302	C₄×Q₈	—	2	1	no	—
303	C₄×Q₈	—	2	1	no	—
304	C₄×Q₈	C₂×C₄×C₅	1	4	yes	—
305	C₄×Q₈	C₂×C₄×C₅	1	4	yes	—
306	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
307	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
308	C₄×D₄	C₅×D₄	1	2	yes	—
309	C₄×D₄	C₅×D₄	1	2	yes	—
310	C₄×D₄	C₅×D₄	1	1	yes	characteristic
311	C₄×D₄	C₅×D₄	1	1	yes	characteristic
312	#117	—	2	2	no	—
313	#117	—	2	2	no	—
314	#117	—	2	4	no	—
315	#117	C₂×C₄×C₅	1	2	yes	—
316	#117	C₂×C₄×C₅	1	1	yes	characteristic
317	#117	C₂×C₄×C₅	1	2	yes	—
318	C₂×C₄⋊C₄	—	2	1	no	—
319	C₂×C₄⋊C₄	—	2	1	no	—
320	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
321	C₂×C₄²	C₂³×C₅	1	2	yes	—
322	C₄⋊C₈	—	2	2	no	—
323	C₄⋊C₈	—	2	1	no	—
324	C₄⋊C₈	—	2	2	no	—
325	C₄⋊C₈	—	2	1	no	—
326	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
327	C₄⋊C₈	C₂³×C₅	1	2	yes	—
328	C₄⋊C₈	C₂³×C₅	1	2	yes	—
329	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
330	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
331	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
332	C₂²⋊C₈	—	2	1	no	—
333	C₂²⋊C₈	—	2	1	no	—
334	C₂²⋊C₈	—	2	2	no	—
335	C₂²⋊C₈	—	2	2	no	—
336	#97	—	2	2	no	—
337	C₄×C₈	—	2	1	no	—
338	C₄×C₈	—	2	2	no	—
339	C₄×C₈	—	2	1	no	—
340	C₂²×C₅	—	2	1	no	—
341	C₂²×C₅	—	2	2	no	—
342	C₂²×C₅	—	2	2	no	—
343	C₂²×C₅	—	2	2	no	—
344	C₂²×C₅	—	2	1	no	—
345	C₂²×C₅	—	2	1	no	—
346	C₂²×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
347	C₄×C₅	—	2	1	no	—
348	C₄×C₅	—	2	2	no	—
349	C₄×C₅	—	2	2	no	—
350	C₄×C₅	—	2	2	no	—
351	C₄×C₅	—	2	1	no	—
352	C₄×C₅	—	2	1	no	—
353	C₄×C₅	—	4	4	no	—
354	C₄×C₅	—	4	2	no	—
355	C₄×C₅	—	4	2	no	—
356	C₄×C₅	#413	1	2	yes	—
357	C₄×C₅	#577	1	1	yes	characteristic
358	C₄×C₅	#577	1	1	yes	characteristic
359	C₄×C₅	#578	1	1	yes	characteristic
360	C₄×C₅	#578	1	1	yes	characteristic
361	#41	—	4	2	no	—
362	C₂×Q₈	—	2	2	no	—
363	C₂×Q₈	—	2	1	no	—
364	C₂×Q₈	—	2	1	no	—
365	C₂×Q₈	—	4	4	no	—
366	C₂×Q₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
367	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	—
368	C₂×D₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
369	C₂×D₄	C₅×C₂²⋊C₄	1	2	yes	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
372	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
373	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
374	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
375	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
376	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
377	M₁₆	—	8	1	no	—
378	M₁₆	—	8	1	no	—
379	M₁₆	—	8	2	no	—
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	2	1	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	2	1	no	—
385	C₂×C₈	—	2	2	no	—
386	C₂×C₈	—	8	2	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	4	no	—
390	C₄⋊C₄	—	2	4	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	2	4	no	—
394	C₄⋊C₄	—	2	4	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
400	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
401	C₄⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
402	C₄⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
403	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
404	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
405	C₂²⋊C₄	—	2	2	no	—
406	C₂²⋊C₄	—	2	4	no	—
407	C₂²⋊C₄	—	2	4	no	—
408	C₂²⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
409	C₂²⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
410	C₂²⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
411	C₄²	—	2	4	no	—
412	C₄²	—	2	4	no	—
413	C₄²	—	2	2	no	—
414	C₄²	C₂²×C₄×C₅	1	2	yes	—
415	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
416	C₄²	C₂×C₅×D₄	1	2	yes	—
417	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
418	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
419	C₄²	C₂×C₅×D₄	1	2	yes	—
420	C₄²	C₂⁴×C₅	1	1	yes	characteristic
421	C₂×C₅	—	4	1	no	—
422	C₂×C₅	—	4	2	no	—
423	C₂×C₅	C₂×#413	1	1	yes	characteristic
424	C₂×C₅	#2898	1	1	yes	characteristic
425	C₂×C₅	#2898	1	1	yes	characteristic
426	C₂³	C₂×C₅×C₂²⋊C₄	1	2	yes	—
427	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
428	Q₈	—	2	2	no	—
429	Q₈	—	4	4	no	—
430	Q₈	—	4	4	no	—
431	Q₈	—	4	1	no	—
432	Q₈	—	4	1	no	—
433	Q₈	—	4	1	no	—
434	Q₈	—	4	1	no	—
435	D₄	—	2	2	no	—
436	D₄	—	4	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	4	no	—
451	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
452	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
453	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
454	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
455	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
456	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
457	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
458	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
459	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
460	C₈	—	4	1	no	—
461	C₈	—	4	2	no	—
462	C₈	—	4	2	no	—
463	C₈	—	4	1	no	—
464	C₈	—	4	1	no	—
465	C₈	—	4	1	no	—
466	C₅	#17778	1	1	yes	characteristic, direct product factor, Sylow
467	C₂²	—	2	1	no	—
468	C₂²	—	2	2	no	—
469	C₂²	—	2	2	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	2	1	no	—
472	C₂²	—	2	1	no	—
473	C₂²	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
474	C₄	—	2	1	no	—
475	C₄	—	2	2	no	—
476	C₄	—	2	2	no	—
477	C₄	—	2	2	no	—
478	C₄	—	2	1	no	—
479	C₄	—	2	1	no	—
480	C₄	—	4	4	no	—
481	C₄	—	4	2	no	—
482	C₄	—	4	2	no	—
483	C₄	C₅×#413	1	2	yes	—
484	C₄	C₅×#577	1	1	yes	characteristic
485	C₄	C₅×#577	1	1	yes	characteristic
486	C₄	C₅×#578	1	1	yes	characteristic
487	C₄	C₅×#578	1	1	yes	characteristic
488	C₂	—	4	1	no	—
489	C₂	—	4	2	no	—
490	C₂	C₂×C₅×#413	1	1	yes	characteristic
491	C₂	C₅×#2898	1	1	yes	characteristic
492	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	C₂×C₄
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×#1554	C₂	semidirect
7. C₅×#1550	C₂	semidirect
8. C₅×#1548	C₂	semidirect
9. C₅×#1548	C₂	semidirect
10. C₅×#1544	C₂	semidirect
11. C₅×#1542	C₂	semidirect
50. #17778	C₅	direct (N × H)
124. #1561	C₂×C₅	semidirect
125. #1559	C₂×C₅	semidirect
126. #1554	C₂×C₅	semidirect
127. #1550	C₂×C₅	semidirect
128. #1548	C₂×C₅	semidirect
129. #1548	C₂×C₅	semidirect
130. #1544	C₂×C₅	semidirect
131. #1542	C₂×C₅	semidirect
466. C₅	#17778	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×#2991	2
C₅×#2990	2
C₅×#1561	2
C₅×#1559	2
C₅×#1554	2
C₅×#1550	2
C₅×#1548	2
C₅×#1544	2
C₅×#1542	2
#17778	5

Subgroups — C5×#17778 #11940498

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#17778 #11940498