Subgroups — C₅×#19352 #11942072

Order 1280.

712 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3239	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3217	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#492	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2966	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1686	C₂	1	2	yes	maximal, complemented
6	C₅×#1685	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×#1568	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1556	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1555	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₅×SD₁₆	—	2	1	no	—
13	C₂²×C₅×SD₁₆	—	2	1	no	—
14	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₅×#127	C₂²	1	1	yes	characteristic
16	C₅×#529	C₂²	1	1	yes	characteristic
17	C₅×#501	—	2	1	no	—
18	C₅×#496	—	2	1	no	—
19	C₅×#492	—	2	1	no	—
20	C₅×#492	—	2	1	no	—
21	C₅×#492	C₂²	1	2	yes	—
22	C₅×#492	C₂²	1	2	yes	—
23	C₅×#490	—	2	1	no	—
24	C₅×#489	—	2	1	no	—
25	C₅×#484	—	2	1	no	—
26	C₅×#481	—	2	1	no	—
27	C₅×#475	C₂²	1	2	yes	complemented
28	C₅×#474	C₂²	1	2	yes	complemented
29	C₅×#460	C₂²	1	2	yes	—
30	C₅×#459	C₂²	1	2	yes	—
31	C₅×#450	—	2	1	no	—
32	C₅×#447	—	2	1	no	—
33	C₅×#446	C₂²	1	1	yes	characteristic, complemented
34	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₅×#436	C₂²	1	1	yes	characteristic, complemented
36	C₅×#435	—	2	1	no	—
37	C₅×C₈×D₄	—	2	1	no	—
38	C₅×C₈×D₄	C₂²	1	1	yes	characteristic, complemented
39	C₅×#433	—	2	1	no	—
40	C₅×#432	C₂²	1	1	yes	characteristic
41	C₅×#432	C₂²	1	1	yes	characteristic
42	C₅×#432	C₂²	1	1	yes	characteristic
43	C₅×#405	—	2	1	no	—
44	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
45	C₅×#335	C₂²	1	2	yes	complemented
46	C₅×#334	C₂²	1	2	yes	complemented
47	C₅×#332	C₂²	1	2	yes	complemented
48	C₅×#332	C₂²	1	2	yes	complemented
49	C₅×#331	C₂²	1	2	yes	—
50	C₅×#331	C₂²	1	2	yes	—
51	#19352	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
52	C₂²×C₅×Q₈	—	2	1	no	—
53	C₂²×C₅×D₄	—	2	1	no	—
54	C₂²×C₅×D₄	—	2	1	no	—
55	C₂²×C₅×D₄	—	2	1	no	—
56	C₂×C₅×SD₁₆	—	2	2	no	—
57	C₂×C₅×SD₁₆	—	2	2	no	—
58	C₂×C₅×SD₁₆	—	2	2	no	—
59	C₂×C₅×SD₁₆	—	2	2	no	—
60	C₂×C₅×SD₁₆	—	2	2	no	—
61	C₂×C₅×SD₁₆	—	4	4	no	—
62	C₂×C₅×SD₁₆	—	4	4	no	—
63	C₂×C₅×D₈	—	2	2	no	—
64	C₂×C₅×M₁₆	—	2	1	no	—
65	C₂²×C₅×C₈	—	2	1	no	—
66	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
67	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
68	C₅×C₄⋊Q₈	—	2	1	no	—
69	C₅×C₄⋊Q₈	—	2	1	no	—
70	C₅×C₄⋊Q₈	—	2	1	no	—
71	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
72	C₅×#127	—	2	1	no	—
73	C₅×#127	—	2	1	no	—
74	C₅×#127	—	2	1	no	—
75	C₅×#127	C₂³	1	2	yes	—
76	C₅×#126	—	2	1	no	—
77	C₅×#125	D₄	1	1	yes	characteristic
78	C₅×#124	D₄	1	1	yes	characteristic
79	C₅×#123	—	2	1	no	—
80	C₅×C₂²⋊Q₈	D₄	1	1	yes	characteristic
81	C₅×#121	D₄	1	1	yes	characteristic
82	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
83	C₄×C₅×D₄	—	2	1	no	—
84	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
85	C₅×#117	—	2	1	no	—
86	C₂×C₅×C₄⋊C₄	—	2	1	no	—
87	C₂×C₅×C₄⋊C₄	—	2	1	no	—
88	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
89	C₅×#107	—	2	2	no	—
90	C₅×#106	—	2	2	no	—
91	C₅×C₄⋊C₈	—	2	1	no	—
92	C₅×C₄⋊C₈	—	2	1	no	—
93	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
94	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
95	C₅×C₄⋊C₈	C₂³	1	2	yes	—
96	C₅×C₄⋊C₈	C₂³	1	2	yes	—
97	C₅×#103	—	2	2	no	—
98	C₅×#102	—	2	2	no	—
99	C₅×#102	—	2	2	no	—
100	C₅×#102	—	2	2	no	—
101	C₅×C₂²⋊C₈	—	2	1	no	—
102	C₅×C₂²⋊C₈	—	2	1	no	—
103	C₅×C₂²⋊C₈	—	2	1	no	—
104	C₅×C₂²⋊C₈	—	2	1	no	—
105	C₅×C₂²⋊C₈	—	2	1	no	—
106	C₅×#97	—	2	1	no	—
107	C₅×#97	—	2	1	no	—
108	C₅×#97	—	2	1	no	—
109	C₅×#97	—	2	1	no	—
110	C₄×C₅×C₈	—	2	1	no	—
111	C₄×C₅×C₈	D₄	1	1	yes	characteristic
112	C₄×C₅×C₈	D₄	1	1	yes	characteristic
113	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
114	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
115	#3239	C₂×C₅	1	1	yes	characteristic, complemented
116	#3217	C₂×C₅	1	1	yes	characteristic
117	C₂×#492	C₂×C₅	1	1	yes	characteristic, complemented
118	#2966	C₂×C₅	1	1	yes	characteristic, complemented
119	#1686	C₂×C₅	1	2	yes	complemented
120	#1685	C₂×C₅	1	2	yes	complemented
121	#1666	C₂×C₅	1	2	yes	complemented
122	#1665	C₂×C₅	1	2	yes	complemented
123	#1568	C₂×C₅	1	1	yes	characteristic, complemented
124	#1556	C₂×C₅	1	1	yes	characteristic, complemented
125	#1555	C₂×C₅	1	1	yes	characteristic, complemented
126	C₂⁴×C₅	—	4	1	no	—
127	C₂×C₅×Q₈	—	2	2	no	—
128	C₂×C₅×Q₈	—	4	2	no	—
129	C₂×C₅×Q₈	—	4	2	no	—
130	C₂×C₅×Q₈	—	4	1	no	—
131	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
132	C₂×C₅×D₄	—	2	1	no	—
133	C₂×C₅×D₄	—	2	2	no	—
134	C₂×C₅×D₄	—	2	2	no	—
135	C₂×C₅×D₄	—	2	2	no	—
136	C₂×C₅×D₄	—	4	2	no	—
137	C₂×C₅×D₄	—	4	2	no	—
138	C₂×C₅×D₄	—	4	1	no	—
139	C₂×C₅×D₄	—	4	1	no	—
140	C₂×C₅×D₄	—	4	1	no	—
141	C₂×C₅×D₄	—	8	2	no	—
142	C₂×C₅×D₄	—	8	2	no	—
143	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₅	—	2	1	no	—
145	C₂²×C₄×C₅	—	4	1	no	—
146	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₅	#41	1	1	yes	characteristic
149	C₅×SD₁₆	—	4	4	no	—
150	C₅×SD₁₆	—	4	4	no	—
151	C₅×SD₁₆	—	4	4	no	—
152	C₅×SD₁₆	—	4	4	no	—
153	C₅×SD₁₆	—	8	2	no	—
154	C₅×D₈	—	8	2	no	—
155	C₅×M₁₆	—	4	2	no	—
156	C₂×C₅×C₈	—	2	2	no	—
157	C₂×C₅×C₈	—	2	2	no	—
158	C₂×C₅×C₈	—	2	1	no	—
159	C₂×C₅×C₈	—	2	1	no	—
160	C₂×C₅×C₈	—	2	2	no	—
161	C₂×C₅×C₈	—	2	2	no	—
162	C₂×C₅×C₈	—	4	2	no	—
163	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
164	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
165	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
166	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
167	C₅×C₄⋊C₄	—	2	1	no	—
168	C₅×C₄⋊C₄	—	2	1	no	—
169	C₅×C₄⋊C₄	—	2	1	no	—
170	C₅×C₄⋊C₄	—	2	1	no	—
171	C₅×C₄⋊C₄	—	2	2	no	—
172	C₅×C₄⋊C₄	—	2	2	no	—
173	C₅×C₄⋊C₄	—	4	1	no	—
174	C₅×C₄⋊C₄	—	4	1	no	—
175	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
176	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
177	C₅×C₂²⋊C₄	—	2	1	no	—
178	C₅×C₂²⋊C₄	—	2	1	no	—
179	C₅×C₂²⋊C₄	—	2	1	no	—
180	C₅×C₂²⋊C₄	—	2	1	no	—
181	C₅×C₂²⋊C₄	—	2	1	no	—
182	C₄²×C₅	—	2	1	no	—
183	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
184	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
185	C₄²×C₅	#41	1	1	yes	characteristic
186	C₄²×C₅	C₂⁴	1	1	yes	characteristic
187	C₂²×SD₁₆	—	2	1	no	—
188	C₂²×SD₁₆	—	2	1	no	—
189	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
190	C₂×#127	C₂²×C₅	1	1	yes	characteristic
191	#529	C₂²×C₅	1	1	yes	characteristic
192	#501	—	2	1	no	—
193	#496	—	2	1	no	—
194	#492	—	2	1	no	—
195	#492	—	2	1	no	—
196	#492	C₂²×C₅	1	2	yes	—
197	#492	C₂²×C₅	1	2	yes	—
198	#490	—	2	1	no	—
199	#489	—	2	1	no	—
200	#484	—	2	1	no	—
201	#481	—	2	1	no	—
202	#475	C₂²×C₅	1	2	yes	complemented
203	#474	C₂²×C₅	1	2	yes	complemented
204	#460	C₂²×C₅	1	2	yes	—
205	#459	C₂²×C₅	1	2	yes	—
206	#450	—	2	1	no	—
207	#447	—	2	1	no	—
208	#446	C₂²×C₅	1	1	yes	characteristic, complemented
209	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
210	#436	C₂²×C₅	1	1	yes	characteristic, complemented
211	#435	—	2	1	no	—
212	C₈×D₄	—	2	1	no	—
213	C₈×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
214	#433	—	2	1	no	—
215	#432	C₂²×C₅	1	1	yes	characteristic
216	#432	C₂²×C₅	1	1	yes	characteristic
217	#432	C₂²×C₅	1	1	yes	characteristic
218	#405	—	2	1	no	—
219	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
220	#335	C₂²×C₅	1	2	yes	complemented
221	#334	C₂²×C₅	1	2	yes	complemented
222	#332	C₂²×C₅	1	2	yes	complemented
223	#332	C₂²×C₅	1	2	yes	complemented
224	#331	C₂²×C₅	1	2	yes	—
225	#331	C₂²×C₅	1	2	yes	—
226	C₂³×C₅	—	2	1	no	—
227	C₂³×C₅	—	4	2	no	—
228	C₂³×C₅	—	8	2	no	—
229	C₂³×C₅	—	8	2	no	—
230	C₂³×C₅	—	8	2	no	—
231	C₂³×C₅	#121	1	1	yes	characteristic
232	C₅×Q₈	—	2	2	no	—
233	C₅×Q₈	—	4	2	no	—
234	C₅×Q₈	—	4	2	no	—
235	C₅×Q₈	—	8	2	no	—
236	C₅×D₄	—	2	2	no	—
237	C₅×D₄	—	4	2	no	—
238	C₅×D₄	—	4	2	no	—
239	C₅×D₄	—	4	2	no	—
240	C₅×D₄	—	4	2	no	—
241	C₅×D₄	—	4	2	no	—
242	C₅×D₄	—	8	2	no	—
243	C₅×D₄	—	8	2	no	—
244	C₅×D₄	—	8	2	no	—
245	C₅×D₄	—	8	2	no	—
246	C₂×C₄×C₅	—	2	2	no	—
247	C₂×C₄×C₅	—	2	1	no	—
248	C₂×C₄×C₅	—	2	1	no	—
249	C₂×C₄×C₅	—	2	2	no	—
250	C₂×C₄×C₅	—	2	1	no	—
251	C₂×C₄×C₅	—	2	1	no	—
252	C₂×C₄×C₅	—	2	1	no	—
253	C₂×C₄×C₅	—	4	1	no	—
254	C₂×C₄×C₅	—	4	1	no	—
255	C₂×C₄×C₅	—	4	2	no	—
256	C₂×C₄×C₅	—	8	2	no	—
257	C₂×C₄×C₅	#121	1	1	yes	characteristic
258	C₂×C₄×C₅	#121	1	1	yes	characteristic
259	C₂×C₄×C₅	#121	1	1	yes	characteristic
260	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
261	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
262	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
263	C₅×C₈	—	2	1	no	—
264	C₅×C₈	—	2	1	no	—
265	C₅×C₈	—	4	1	no	—
266	C₅×C₈	—	4	1	no	—
267	C₅×C₈	—	4	2	no	—
268	C₅×C₈	—	4	2	no	—
269	C₅×C₈	AGL(1,ℤ/8)	1	2	yes	—
270	C₅×C₈	AGL(1,ℤ/8)	1	2	yes	—
271	C₂²×Q₈	—	2	1	no	—
272	C₂²×D₄	—	2	1	no	—
273	C₂²×D₄	—	2	1	no	—
274	C₂²×D₄	—	2	1	no	—
275	C₂×SD₁₆	—	2	2	no	—
276	C₂×SD₁₆	—	2	2	no	—
277	C₂×SD₁₆	—	2	2	no	—
278	C₂×SD₁₆	—	2	2	no	—
279	C₂×SD₁₆	—	2	2	no	—
280	C₂×SD₁₆	—	4	4	no	—
281	C₂×SD₁₆	—	4	4	no	—
282	C₂×D₈	—	2	2	no	—
283	C₂×M₁₆	—	2	1	no	—
284	C₂²×C₈	—	2	1	no	—
285	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
286	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
287	C₄⋊Q₈	—	2	1	no	—
288	C₄⋊Q₈	—	2	1	no	—
289	C₄⋊Q₈	—	2	1	no	—
290	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
291	#127	—	2	1	no	—
292	#127	—	2	1	no	—
293	#127	—	2	1	no	—
294	#127	C₂³×C₅	1	2	yes	—
295	#126	—	2	1	no	—
296	#125	C₅×D₄	1	1	yes	characteristic
297	#124	C₅×D₄	1	1	yes	characteristic
298	#123	—	2	1	no	—
299	C₂²⋊Q₈	C₅×D₄	1	1	yes	characteristic
300	#121	C₅×D₄	1	1	yes	characteristic
301	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
302	C₄×D₄	—	2	1	no	—
303	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
304	#117	—	2	1	no	—
305	C₂×C₄⋊C₄	—	2	1	no	—
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
308	#107	—	2	2	no	—
309	#106	—	2	2	no	—
310	C₄⋊C₈	—	2	1	no	—
311	C₄⋊C₈	—	2	1	no	—
312	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
313	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
314	C₄⋊C₈	C₂³×C₅	1	2	yes	—
315	C₄⋊C₈	C₂³×C₅	1	2	yes	—
316	#103	—	2	2	no	—
317	#102	—	2	2	no	—
318	#102	—	2	2	no	—
319	#102	—	2	2	no	—
320	C₂²⋊C₈	—	2	1	no	—
321	C₂²⋊C₈	—	2	1	no	—
322	C₂²⋊C₈	—	2	1	no	—
323	C₂²⋊C₈	—	2	1	no	—
324	C₂²⋊C₈	—	2	1	no	—
325	#97	—	2	1	no	—
326	#97	—	2	1	no	—
327	#97	—	2	1	no	—
328	#97	—	2	1	no	—
329	C₄×C₈	—	2	1	no	—
330	C₄×C₈	C₅×D₄	1	1	yes	characteristic
331	C₄×C₈	C₅×D₄	1	1	yes	characteristic
332	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
333	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
334	C₂²×C₅	—	2	1	no	—
335	C₂²×C₅	—	2	1	no	—
336	C₂²×C₅	—	4	1	no	—
337	C₂²×C₅	—	4	1	no	—
338	C₂²×C₅	—	4	1	no	—
339	C₂²×C₅	—	8	2	no	—
340	C₂²×C₅	—	8	2	no	—
341	C₂²×C₅	—	8	2	no	—
342	C₂²×C₅	—	16	4	no	—
343	C₂²×C₅	#471	1	2	yes	—
344	C₂²×C₅	C₂×#121	1	1	yes	characteristic
345	C₄×C₅	—	2	1	no	—
346	C₄×C₅	—	2	1	no	—
347	C₄×C₅	—	2	1	no	—
348	C₄×C₅	—	2	1	no	—
349	C₄×C₅	—	4	1	no	—
350	C₄×C₅	—	4	1	no	—
351	C₄×C₅	—	4	1	no	—
352	C₄×C₅	—	8	2	no	—
353	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
354	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
355	C₄×C₅	#577	1	2	yes	—
356	C₂⁴	—	4	1	no	—
357	C₂×Q₈	—	2	2	no	—
358	C₂×Q₈	—	4	2	no	—
359	C₂×Q₈	—	4	2	no	—
360	C₂×Q₈	—	4	1	no	—
361	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
362	C₂×D₄	—	2	1	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	—	4	2	no	—
367	C₂×D₄	—	4	2	no	—
368	C₂×D₄	—	4	1	no	—
369	C₂×D₄	—	4	1	no	—
370	C₂×D₄	—	4	1	no	—
371	C₂×D₄	—	8	2	no	—
372	C₂×D₄	—	8	2	no	—
373	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	4	1	no	—
376	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
377	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
378	C₂²×C₄	C₅×#41	1	1	yes	characteristic
379	SD₁₆	—	4	4	no	—
380	SD₁₆	—	4	4	no	—
381	SD₁₆	—	4	4	no	—
382	SD₁₆	—	4	4	no	—
383	SD₁₆	—	8	2	no	—
384	D₈	—	8	2	no	—
385	M₁₆	—	4	2	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	—	2	1	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	4	2	no	—
393	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
394	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
395	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
396	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	4	1	no	—
404	C₄⋊C₄	—	4	1	no	—
405	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
406	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
407	C₂²⋊C₄	—	2	1	no	—
408	C₂²⋊C₄	—	2	1	no	—
409	C₂²⋊C₄	—	2	1	no	—
410	C₂²⋊C₄	—	2	1	no	—
411	C₂²⋊C₄	—	2	1	no	—
412	C₄²	—	2	1	no	—
413	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
414	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
415	C₄²	C₅×#41	1	1	yes	characteristic
416	C₄²	C₂⁴×C₅	1	1	yes	characteristic
417	C₂×C₅	—	2	2	no	—
418	C₂×C₅	—	8	1	no	—
419	C₂×C₅	—	16	2	no	—
420	C₂×C₅	#3038	1	1	yes	characteristic
421	C₂×C₅	#3057	1	1	yes	characteristic
422	C₂×C₅	C₂×#471	1	1	yes	characteristic
423	C₂³	—	2	1	no	—
424	C₂³	—	4	2	no	—
425	C₂³	—	8	2	no	—
426	C₂³	—	8	2	no	—
427	C₂³	—	8	2	no	—
428	C₂³	C₅×#121	1	1	yes	characteristic
429	Q₈	—	2	2	no	—
430	Q₈	—	4	2	no	—
431	Q₈	—	4	2	no	—
432	Q₈	—	8	2	no	—
433	D₄	—	2	2	no	—
434	D₄	—	4	2	no	—
435	D₄	—	4	2	no	—
436	D₄	—	4	2	no	—
437	D₄	—	4	2	no	—
438	D₄	—	4	2	no	—
439	D₄	—	8	2	no	—
440	D₄	—	8	2	no	—
441	D₄	—	8	2	no	—
442	D₄	—	8	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	8	2	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	C₂²×C₅×D₄	1	1	yes	characteristic
458	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
459	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
460	C₈	—	2	1	no	—
461	C₈	—	2	1	no	—
462	C₈	—	4	1	no	—
463	C₈	—	4	1	no	—
464	C₈	—	4	2	no	—
465	C₈	—	4	2	no	—
466	C₈	C₅×AGL(1,ℤ/8)	1	2	yes	—
467	C₈	C₅×AGL(1,ℤ/8)	1	2	yes	—
468	C₅	#19352	1	1	yes	characteristic, direct product factor, Sylow
469	C₂²	—	2	1	no	—
470	C₂²	—	2	1	no	—
471	C₂²	—	4	1	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×#471	1	2	yes	—
479	C₂²	C₂×C₅×#121	1	1	yes	characteristic
480	C₄	—	2	1	no	—
481	C₄	—	2	1	no	—
482	C₄	—	2	1	no	—
483	C₄	—	2	1	no	—
484	C₄	—	4	1	no	—
485	C₄	—	4	1	no	—
486	C₄	—	4	1	no	—
487	C₄	—	8	2	no	—
488	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
489	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
490	C₄	C₅×#577	1	2	yes	—
491	C₂	—	2	2	no	—
492	C₂	—	8	1	no	—
493	C₂	—	16	2	no	—
494	C₂	C₅×#3038	1	1	yes	characteristic
495	C₂	C₅×#3057	1	1	yes	characteristic
496	C₂	C₂×C₅×#471	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₅×#3217	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×#3239	C₂	semidirect
3. C₂×C₅×#492	C₂	semidirect
4. C₅×#2966	C₂	semidirect
5. C₅×#1686	C₂	semidirect
6. C₅×#1685	C₂	semidirect
7. C₅×#1666	C₂	semidirect
8. C₅×#1665	C₂	semidirect
9. C₅×#1568	C₂	semidirect
10. C₅×#1556	C₂	semidirect
11. C₅×#1555	C₂	semidirect
27. C₅×#475	C₂²	semidirect
28. C₅×#474	C₂²	semidirect
33. C₅×#446	C₂²	semidirect
34. C₅×C₈×Q₈	C₂²	semidirect
35. C₅×#436	C₂²	semidirect
38. C₅×C₈×D₄	C₂²	semidirect
45. C₅×#335	C₂²	semidirect
46. C₅×#334	C₂²	semidirect
47. C₅×#332	C₂²	semidirect
48. C₅×#332	C₂²	semidirect
51. #19352	C₅	direct (N × H)
115. #3239	C₂×C₅	semidirect
117. C₂×#492	C₂×C₅	semidirect
118. #2966	C₂×C₅	semidirect
119. #1686	C₂×C₅	semidirect
120. #1685	C₂×C₅	semidirect
121. #1666	C₂×C₅	semidirect
122. #1665	C₂×C₅	semidirect
123. #1568	C₂×C₅	semidirect
124. #1556	C₂×C₅	semidirect
125. #1555	C₂×C₅	semidirect
202. #475	C₂²×C₅	semidirect
203. #474	C₂²×C₅	semidirect
208. #446	C₂²×C₅	semidirect
209. C₈×Q₈	C₂²×C₅	semidirect
210. #436	C₂²×C₅	semidirect
213. C₈×D₄	C₂²×C₅	semidirect
220. #335	C₂²×C₅	semidirect
221. #334	C₂²×C₅	semidirect
222. #332	C₂²×C₅	semidirect
223. #332	C₂²×C₅	semidirect
468. C₅	#19352	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×#3239	2
C₅×#3217	2
C₂×C₅×#492	2
C₅×#2966	2
C₅×#1686	2
C₅×#1685	2
C₅×#1666	2
C₅×#1665	2
C₅×#1568	2
C₅×#1556	2
C₅×#1555	2
#19352	5

Subgroups — C5×#19352 #11942072

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19352 #11942072