Subgroups — C₅×#19409 #11942129

Order 1280.

704 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3208	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3076	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3038	C₂	1	1	yes	maximal, characteristic
4	C₅×#2988	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1678	C₂	1	2	yes	maximal, complemented
6	C₅×#1677	C₂	1	2	yes	maximal, complemented
7	C₅×#1666	C₂	1	2	yes	maximal, complemented
8	C₅×#1665	C₂	1	2	yes	maximal, complemented
9	C₅×#1570	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1550	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×#331	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×AGL(1,ℤ/8)	—	2	1	no	—
13	C₅×#533	C₂²	1	1	yes	characteristic
14	C₂×C₅×#127	C₂²	1	1	yes	characteristic
15	C₄×C₅×#41	C₂²	1	1	yes	characteristic
16	C₅×#492	C₂²	1	2	yes	—
17	C₅×#486	C₂²	1	2	yes	—
18	C₅×#479	—	2	1	no	—
19	C₅×#478	—	2	1	no	—
20	C₅×#477	C₂²	1	1	yes	characteristic, complemented
21	C₅×#476	C₂²	1	1	yes	characteristic, complemented
22	C₅×#475	C₂²	1	1	yes	characteristic, complemented
23	C₅×#474	C₂²	1	1	yes	characteristic, complemented
24	C₅×#460	—	2	1	no	—
25	C₅×#460	—	2	1	no	—
26	C₅×#460	—	2	1	no	—
27	C₅×#460	C₂²	1	2	yes	—
28	C₅×#459	—	2	1	no	—
29	C₅×#459	C₂²	1	2	yes	—
30	C₅×#450	—	2	2	no	—
31	C₅×C₈×Q₈	C₂²	1	2	yes	complemented
32	C₅×C₈×D₄	—	2	2	no	—
33	C₅×C₈×D₄	C₂²	1	2	yes	complemented
34	C₅×#431	—	2	1	no	—
35	C₅×#431	C₂²	1	1	yes	characteristic
36	C₅×#427	—	2	1	no	—
37	C₅×#423	C₂²	1	1	yes	characteristic
38	C₂×C₅×C₄⋊C₈	—	2	1	no	—
39	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
41	C₅×#418	—	2	1	no	—
42	C₅×#416	—	2	1	no	—
43	C₅×#334	C₂²	1	2	yes	complemented
44	C₅×#334	C₂²	1	2	yes	complemented
45	C₅×#333	C₂²	1	2	yes	complemented
46	C₅×#332	C₂²	1	2	yes	complemented
47	C₅×#331	C₂²	1	2	yes	—
48	C₅×#331	C₂²	1	2	yes	—
49	#19409	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₂×C₅×#41	D₄	1	1	yes	characteristic
51	C₂²×C₅×D₄	—	2	1	no	—
52	C₂²×C₅×D₄	—	2	1	no	—
53	C₂²×C₅×D₄	—	2	1	no	—
54	C₅×AGL(1,ℤ/8)	—	4	4	no	—
55	C₂×C₅×SD₁₆	—	2	2	no	—
56	C₂×C₅×SD₁₆	—	2	2	no	—
57	C₂×C₅×SD₁₆	—	2	2	no	—
58	C₂×C₅×D₈	—	2	2	no	—
59	C₂×C₅×M₁₆	—	2	1	no	—
60	C₂²×C₅×C₈	—	2	1	no	—
61	C₂²×C₅×C₈	—	2	1	no	—
62	C₂²×C₅×C₈	—	2	2	no	—
63	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
64	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
65	C₅×#127	—	2	1	no	—
66	C₅×#127	—	2	1	no	—
67	C₅×#127	—	2	1	no	—
68	C₅×#127	C₂³	1	2	yes	—
69	C₅×#125	—	2	1	no	—
70	C₅×C₂²⋊Q₈	—	2	1	no	—
71	C₅×C₂²⋊Q₈	—	2	1	no	—
72	C₄×C₅×Q₈	—	2	1	no	—
73	C₄×C₅×Q₈	—	2	1	no	—
74	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
75	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
76	C₄×C₅×D₄	—	2	1	no	—
77	C₄×C₅×D₄	—	2	1	no	—
78	C₄×C₅×D₄	D₄	1	1	yes	characteristic
79	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
80	C₅×#117	—	2	1	no	—
81	C₅×#117	—	2	1	no	—
82	C₅×#117	D₄	1	1	yes	characteristic
83	C₂×C₄²×C₅	—	2	1	no	—
84	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
85	C₅×#107	—	2	1	no	—
86	C₅×#107	—	2	1	no	—
87	C₅×#106	—	2	1	no	—
88	C₅×#106	—	2	1	no	—
89	C₅×C₄⋊C₈	—	2	2	no	—
90	C₅×C₄⋊C₈	—	2	1	no	—
91	C₅×C₄⋊C₈	—	2	1	no	—
92	C₅×C₄⋊C₈	—	2	1	no	—
93	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
94	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
95	C₅×C₄⋊C₈	C₂³	1	2	yes	—
96	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
97	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
98	C₅×C₄⋊C₈	C₂³	1	2	yes	—
99	C₅×#103	—	2	1	no	—
100	C₅×#103	—	2	1	no	—
101	C₅×#102	—	2	1	no	—
102	C₅×#102	—	2	1	no	—
103	C₅×#102	—	2	2	no	—
104	C₅×#102	—	2	2	no	—
105	C₅×#102	—	2	2	no	—
106	C₅×#102	—	2	2	no	—
107	C₅×C₂²⋊C₈	—	2	2	no	—
108	C₅×C₂²⋊C₈	D₄	1	2	yes	—
109	C₄×C₅×C₈	—	2	2	no	—
110	C₄×C₅×C₈	C₂³	1	2	yes	—
111	#3208	C₂×C₅	1	1	yes	characteristic, complemented
112	#3076	C₂×C₅	1	1	yes	characteristic, complemented
113	#3038	C₂×C₅	1	1	yes	characteristic
114	#2988	C₂×C₅	1	1	yes	characteristic, complemented
115	#1678	C₂×C₅	1	2	yes	complemented
116	#1677	C₂×C₅	1	2	yes	complemented
117	#1666	C₂×C₅	1	2	yes	complemented
118	#1665	C₂×C₅	1	2	yes	complemented
119	#1570	C₂×C₅	1	1	yes	characteristic, complemented
120	#1550	C₂×C₅	1	1	yes	characteristic, complemented
121	C₂×#331	C₂×C₅	1	1	yes	characteristic, complemented
122	C₂⁴×C₅	—	4	1	no	—
123	C₅×#41	—	2	2	no	—
124	C₅×#41	SD₁₆	1	4	yes	complemented
125	C₂×C₅×Q₈	—	2	1	no	—
126	C₂×C₅×Q₈	—	2	1	no	—
127	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
128	C₂×C₅×D₄	—	2	1	no	—
129	C₂×C₅×D₄	—	2	2	no	—
130	C₂×C₅×D₄	—	2	2	no	—
131	C₂×C₅×D₄	—	2	2	no	—
132	C₂×C₅×D₄	—	4	1	no	—
133	C₂×C₅×D₄	—	4	1	no	—
134	C₂×C₅×D₄	—	4	1	no	—
135	C₂×C₅×D₄	—	4	2	no	—
136	C₂×C₅×D₄	—	4	2	no	—
137	C₂×C₅×D₄	—	8	1	no	—
138	C₂×C₅×D₄	—	8	1	no	—
139	C₂×C₅×D₄	—	8	2	no	—
140	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₅	—	2	1	no	—
142	C₂²×C₄×C₅	—	2	1	no	—
143	C₂²×C₄×C₅	—	2	1	no	—
144	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₅	#41	1	1	yes	characteristic
147	C₅×SD₁₆	—	4	4	no	—
148	C₅×SD₁₆	—	8	2	no	—
149	C₅×SD₁₆	—	8	2	no	—
150	C₅×D₈	—	4	4	no	—
151	C₅×M₁₆	—	4	2	no	—
152	C₂×C₅×C₈	—	2	2	no	—
153	C₂×C₅×C₈	—	2	1	no	—
154	C₂×C₅×C₈	—	2	1	no	—
155	C₂×C₅×C₈	—	2	2	no	—
156	C₂×C₅×C₈	—	4	2	no	—
157	C₂×C₅×C₈	—	8	2	no	—
158	C₂×C₅×C₈	—	8	1	no	—
159	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
160	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
161	C₅×C₄⋊C₄	—	2	1	no	—
162	C₅×C₄⋊C₄	—	2	1	no	—
163	C₅×C₄⋊C₄	—	2	1	no	—
164	C₅×C₄⋊C₄	—	2	1	no	—
165	C₅×C₄⋊C₄	—	2	1	no	—
166	C₅×C₄⋊C₄	—	2	1	no	—
167	C₅×C₄⋊C₄	—	4	1	no	—
168	C₅×C₄⋊C₄	—	4	1	no	—
169	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
170	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
171	C₅×C₂²⋊C₄	—	2	1	no	—
172	C₅×C₂²⋊C₄	—	2	1	no	—
173	C₅×C₂²⋊C₄	—	2	1	no	—
174	C₅×C₂²⋊C₄	—	4	1	no	—
175	C₄²×C₅	—	2	1	no	—
176	C₄²×C₅	—	2	1	no	—
177	C₄²×C₅	—	2	1	no	—
178	C₄²×C₅	—	4	1	no	—
179	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
181	C₄²×C₅	#41	1	1	yes	characteristic
182	C₄²×C₅	C₂⁴	1	1	yes	characteristic
183	C₂×AGL(1,ℤ/8)	—	2	1	no	—
184	#533	C₂²×C₅	1	1	yes	characteristic
185	C₂×#127	C₂²×C₅	1	1	yes	characteristic
186	C₄×#41	C₂²×C₅	1	1	yes	characteristic
187	#492	C₂²×C₅	1	2	yes	—
188	#486	C₂²×C₅	1	2	yes	—
189	#479	—	2	1	no	—
190	#478	—	2	1	no	—
191	#477	C₂²×C₅	1	1	yes	characteristic, complemented
192	#476	C₂²×C₅	1	1	yes	characteristic, complemented
193	#475	C₂²×C₅	1	1	yes	characteristic, complemented
194	#474	C₂²×C₅	1	1	yes	characteristic, complemented
195	#460	—	2	1	no	—
196	#460	—	2	1	no	—
197	#460	—	2	1	no	—
198	#460	C₂²×C₅	1	2	yes	—
199	#459	—	2	1	no	—
200	#459	C₂²×C₅	1	2	yes	—
201	#450	—	2	2	no	—
202	C₈×Q₈	C₂²×C₅	1	2	yes	complemented
203	C₈×D₄	—	2	2	no	—
204	C₈×D₄	C₂²×C₅	1	2	yes	complemented
205	#431	—	2	1	no	—
206	#431	C₂²×C₅	1	1	yes	characteristic
207	#427	—	2	1	no	—
208	#423	C₂²×C₅	1	1	yes	characteristic
209	C₂×C₄⋊C₈	—	2	1	no	—
210	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
211	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
212	#418	—	2	1	no	—
213	#416	—	2	1	no	—
214	#334	C₂²×C₅	1	2	yes	complemented
215	#334	C₂²×C₅	1	2	yes	complemented
216	#333	C₂²×C₅	1	2	yes	complemented
217	#332	C₂²×C₅	1	2	yes	complemented
218	#331	C₂²×C₅	1	2	yes	—
219	#331	C₂²×C₅	1	2	yes	—
220	C₂³×C₅	—	2	1	no	—
221	C₂³×C₅	—	4	2	no	—
222	C₂³×C₅	—	8	2	no	—
223	C₂³×C₅	—	8	2	no	—
224	C₂³×C₅	—	8	2	no	—
225	C₂³×C₅	#121	1	1	yes	characteristic
226	C₅×Q₈	—	2	1	no	—
227	C₅×Q₈	—	4	1	no	—
228	C₅×Q₈	—	4	1	no	—
229	C₅×Q₈	—	8	1	no	—
230	C₅×Q₈	C₂×SD₁₆	1	2	yes	—
231	C₅×D₄	—	2	4	no	—
232	C₅×D₄	—	2	1	no	—
233	C₅×D₄	—	4	2	no	—
234	C₅×D₄	—	4	2	no	—
235	C₅×D₄	—	4	2	no	—
236	C₅×D₄	—	4	2	no	—
237	C₅×D₄	—	8	2	no	—
238	C₅×D₄	—	8	2	no	—
239	C₅×D₄	—	8	2	no	—
240	C₅×D₄	—	8	2	no	—
241	C₅×D₄	C₂×SD₁₆	1	2	yes	—
242	C₂×C₄×C₅	—	2	1	no	—
243	C₂×C₄×C₅	—	2	1	no	—
244	C₂×C₄×C₅	—	2	1	no	—
245	C₂×C₄×C₅	—	2	4	no	—
246	C₂×C₄×C₅	—	2	1	no	—
247	C₂×C₄×C₅	—	2	1	no	—
248	C₂×C₄×C₅	—	4	1	no	—
249	C₂×C₄×C₅	—	4	1	no	—
250	C₂×C₄×C₅	—	4	1	no	—
251	C₂×C₄×C₅	—	4	1	no	—
252	C₂×C₄×C₅	—	4	1	no	—
253	C₂×C₄×C₅	—	8	1	no	—
254	C₂×C₄×C₅	#121	1	1	yes	characteristic
255	C₂×C₄×C₅	#121	1	1	yes	characteristic
256	C₂×C₄×C₅	#121	1	1	yes	characteristic
257	C₂×C₄×C₅	C₂×SD₁₆	1	2	yes	—
258	C₂×C₄×C₅	#135	1	2	yes	—
259	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
260	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
261	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
262	C₅×C₈	—	2	2	no	—
263	C₅×C₈	—	2	2	no	—
264	C₅×C₈	—	4	2	no	—
265	C₅×C₈	—	4	1	no	—
266	C₅×C₈	—	4	1	no	—
267	C₅×C₈	—	4	2	no	—
268	C₂×#41	C₅×D₄	1	1	yes	characteristic
269	C₂²×D₄	—	2	1	no	—
270	C₂²×D₄	—	2	1	no	—
271	C₂²×D₄	—	2	1	no	—
272	AGL(1,ℤ/8)	—	4	4	no	—
273	C₂×SD₁₆	—	2	2	no	—
274	C₂×SD₁₆	—	2	2	no	—
275	C₂×SD₁₆	—	2	2	no	—
276	C₂×D₈	—	2	2	no	—
277	C₂×M₁₆	—	2	1	no	—
278	C₂²×C₈	—	2	1	no	—
279	C₂²×C₈	—	2	1	no	—
280	C₂²×C₈	—	2	2	no	—
281	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
282	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
283	#127	—	2	1	no	—
284	#127	—	2	1	no	—
285	#127	—	2	1	no	—
286	#127	C₂³×C₅	1	2	yes	—
287	#125	—	2	1	no	—
288	C₂²⋊Q₈	—	2	1	no	—
289	C₂²⋊Q₈	—	2	1	no	—
290	C₄×Q₈	—	2	1	no	—
291	C₄×Q₈	—	2	1	no	—
292	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
293	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
294	C₄×D₄	—	2	1	no	—
295	C₄×D₄	—	2	1	no	—
296	C₄×D₄	C₅×D₄	1	1	yes	characteristic
297	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
298	#117	—	2	1	no	—
299	#117	—	2	1	no	—
300	#117	C₅×D₄	1	1	yes	characteristic
301	C₂×C₄²	—	2	1	no	—
302	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
303	#107	—	2	1	no	—
304	#107	—	2	1	no	—
305	#106	—	2	1	no	—
306	#106	—	2	1	no	—
307	C₄⋊C₈	—	2	2	no	—
308	C₄⋊C₈	—	2	1	no	—
309	C₄⋊C₈	—	2	1	no	—
310	C₄⋊C₈	—	2	1	no	—
311	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
312	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
313	C₄⋊C₈	C₂³×C₅	1	2	yes	—
314	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
315	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
316	C₄⋊C₈	C₂³×C₅	1	2	yes	—
317	#103	—	2	1	no	—
318	#103	—	2	1	no	—
319	#102	—	2	1	no	—
320	#102	—	2	1	no	—
321	#102	—	2	2	no	—
322	#102	—	2	2	no	—
323	#102	—	2	2	no	—
324	#102	—	2	2	no	—
325	C₂²⋊C₈	—	2	2	no	—
326	C₂²⋊C₈	C₅×D₄	1	2	yes	—
327	C₄×C₈	—	2	2	no	—
328	C₄×C₈	C₂³×C₅	1	2	yes	—
329	C₂²×C₅	—	2	1	no	—
330	C₂²×C₅	—	2	1	no	—
331	C₂²×C₅	—	2	2	no	—
332	C₂²×C₅	—	4	1	no	—
333	C₂²×C₅	—	4	1	no	—
334	C₂²×C₅	—	8	2	no	—
335	C₂²×C₅	—	8	2	no	—
336	C₂²×C₅	—	8	2	no	—
337	C₂²×C₅	—	16	4	no	—
338	C₂²×C₅	#465	1	2	yes	—
339	C₂²×C₅	C₂×#121	1	1	yes	characteristic
340	C₄×C₅	—	2	1	no	—
341	C₄×C₅	—	2	2	no	—
342	C₄×C₅	—	2	1	no	—
343	C₄×C₅	—	2	1	no	—
344	C₄×C₅	—	4	1	no	—
345	C₄×C₅	—	4	1	no	—
346	C₄×C₅	—	8	1	no	—
347	C₄×C₅	—	8	1	no	—
348	C₄×C₅	#465	1	2	yes	—
349	C₄×C₅	C₂²×SD₁₆	1	1	yes	characteristic
350	C₄×C₅	C₂×#135	1	1	yes	characteristic
351	C₄×C₅	#576	1	1	yes	characteristic
352	C₄×C₅	#577	1	1	yes	characteristic
353	C₂⁴	—	4	1	no	—
354	#41	—	2	2	no	—
355	#41	C₅×SD₁₆	1	4	yes	complemented
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	2	1	no	—
358	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
359	C₂×D₄	—	2	1	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	4	1	no	—
364	C₂×D₄	—	4	1	no	—
365	C₂×D₄	—	4	1	no	—
366	C₂×D₄	—	4	2	no	—
367	C₂×D₄	—	4	2	no	—
368	C₂×D₄	—	8	1	no	—
369	C₂×D₄	—	8	1	no	—
370	C₂×D₄	—	8	2	no	—
371	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
376	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
377	C₂²×C₄	C₅×#41	1	1	yes	characteristic
378	SD₁₆	—	4	4	no	—
379	SD₁₆	—	8	2	no	—
380	SD₁₆	—	8	2	no	—
381	D₈	—	4	4	no	—
382	M₁₆	—	4	2	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	2	1	no	—
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	4	2	no	—
388	C₂×C₈	—	8	2	no	—
389	C₂×C₈	—	8	1	no	—
390	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
391	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	4	1	no	—
399	C₄⋊C₄	—	4	1	no	—
400	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
401	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
402	C₂²⋊C₄	—	2	1	no	—
403	C₂²⋊C₄	—	2	1	no	—
404	C₂²⋊C₄	—	2	1	no	—
405	C₂²⋊C₄	—	4	1	no	—
406	C₄²	—	2	1	no	—
407	C₄²	—	2	1	no	—
408	C₄²	—	2	1	no	—
409	C₄²	—	4	1	no	—
410	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
411	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
412	C₄²	C₅×#41	1	1	yes	characteristic
413	C₄²	C₂⁴×C₅	1	1	yes	characteristic
414	C₂×C₅	—	2	2	no	—
415	C₂×C₅	—	4	2	no	—
416	C₂×C₅	—	16	2	no	—
417	C₂×C₅	#3045	1	1	yes	characteristic
418	C₂×C₅	C₂×#465	1	1	yes	characteristic
419	C₂×C₅	#3068	1	1	yes	characteristic
420	C₂³	—	2	1	no	—
421	C₂³	—	4	2	no	—
422	C₂³	—	8	2	no	—
423	C₂³	—	8	2	no	—
424	C₂³	—	8	2	no	—
425	C₂³	C₅×#121	1	1	yes	characteristic
426	Q₈	—	2	1	no	—
427	Q₈	—	4	1	no	—
428	Q₈	—	4	1	no	—
429	Q₈	—	8	1	no	—
430	Q₈	C₂×C₅×SD₁₆	1	2	yes	—
431	D₄	—	2	4	no	—
432	D₄	—	2	1	no	—
433	D₄	—	4	2	no	—
434	D₄	—	4	2	no	—
435	D₄	—	4	2	no	—
436	D₄	—	4	2	no	—
437	D₄	—	8	2	no	—
438	D₄	—	8	2	no	—
439	D₄	—	8	2	no	—
440	D₄	—	8	2	no	—
441	D₄	C₂×C₅×SD₁₆	1	2	yes	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	8	1	no	—
454	C₂×C₄	C₅×#121	1	1	yes	characteristic
455	C₂×C₄	C₅×#121	1	1	yes	characteristic
456	C₂×C₄	C₅×#121	1	1	yes	characteristic
457	C₂×C₄	C₂×C₅×SD₁₆	1	2	yes	—
458	C₂×C₄	C₅×#135	1	2	yes	—
459	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
460	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
461	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
462	C₈	—	2	2	no	—
463	C₈	—	2	2	no	—
464	C₈	—	4	2	no	—
465	C₈	—	4	1	no	—
466	C₈	—	4	1	no	—
467	C₈	—	4	2	no	—
468	C₅	#19409	1	1	yes	characteristic, direct product factor, Sylow
469	C₂²	—	2	1	no	—
470	C₂²	—	2	1	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	4	1	no	—
473	C₂²	—	4	1	no	—
474	C₂²	—	8	2	no	—
475	C₂²	—	8	2	no	—
476	C₂²	—	8	2	no	—
477	C₂²	—	16	4	no	—
478	C₂²	C₅×#465	1	2	yes	—
479	C₂²	C₂×C₅×#121	1	1	yes	characteristic
480	C₄	—	2	1	no	—
481	C₄	—	2	2	no	—
482	C₄	—	2	1	no	—
483	C₄	—	2	1	no	—
484	C₄	—	4	1	no	—
485	C₄	—	4	1	no	—
486	C₄	—	8	1	no	—
487	C₄	—	8	1	no	—
488	C₄	C₅×#465	1	2	yes	—
489	C₄	C₂²×C₅×SD₁₆	1	1	yes	characteristic
490	C₄	C₂×C₅×#135	1	1	yes	characteristic
491	C₄	C₅×#576	1	1	yes	characteristic
492	C₄	C₅×#577	1	1	yes	characteristic
493	C₂	—	2	2	no	—
494	C₂	—	4	2	no	—
495	C₂	—	16	2	no	—
496	C₂	C₅×#3045	1	1	yes	characteristic
497	C₂	C₂×C₅×#465	1	1	yes	characteristic
498	C₂	C₅×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₅×#3038	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#3208	C₂	semidirect
2. C₅×#3076	C₂	semidirect
4. C₅×#2988	C₂	semidirect
5. C₅×#1678	C₂	semidirect
6. C₅×#1677	C₂	semidirect
7. C₅×#1666	C₂	semidirect
8. C₅×#1665	C₂	semidirect
9. C₅×#1570	C₂	semidirect
10. C₅×#1550	C₂	semidirect
11. C₂×C₅×#331	C₂	semidirect
20. C₅×#477	C₂²	semidirect
21. C₅×#476	C₂²	semidirect
22. C₅×#475	C₂²	semidirect
23. C₅×#474	C₂²	semidirect
31. C₅×C₈×Q₈	C₂²	semidirect
33. C₅×C₈×D₄	C₂²	semidirect
43. C₅×#334	C₂²	semidirect
44. C₅×#334	C₂²	semidirect
45. C₅×#333	C₂²	semidirect
46. C₅×#332	C₂²	semidirect
49. #19409	C₅	direct (N × H)
111. #3208	C₂×C₅	semidirect
112. #3076	C₂×C₅	semidirect
114. #2988	C₂×C₅	semidirect
115. #1678	C₂×C₅	semidirect
116. #1677	C₂×C₅	semidirect
117. #1666	C₂×C₅	semidirect
118. #1665	C₂×C₅	semidirect
119. #1570	C₂×C₅	semidirect
120. #1550	C₂×C₅	semidirect
121. C₂×#331	C₂×C₅	semidirect
124. C₅×#41	SD₁₆	semidirect
191. #477	C₂²×C₅	semidirect
192. #476	C₂²×C₅	semidirect
193. #475	C₂²×C₅	semidirect
194. #474	C₂²×C₅	semidirect
202. C₈×Q₈	C₂²×C₅	semidirect
204. C₈×D₄	C₂²×C₅	semidirect
214. #334	C₂²×C₅	semidirect
215. #334	C₂²×C₅	semidirect
216. #333	C₂²×C₅	semidirect
217. #332	C₂²×C₅	semidirect
355. #41	C₅×SD₁₆	semidirect
468. C₅	#19409	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×#3208	2
C₅×#3076	2
C₅×#3038	2
C₅×#2988	2
C₅×#1678	2
C₅×#1677	2
C₅×#1666	2
C₅×#1665	2
C₅×#1570	2
C₅×#1550	2
C₂×C₅×#331	2
#19409	5

Subgroups — C5×#19409 #11942129

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19409 #11942129