Subgroups — C₅×#19316 #11942036

Order 1280.

682 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3138	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3116	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3038	C₂	1	1	yes	maximal, characteristic
4	C₅×#2970	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1702	C₂	1	2	yes	maximal, complemented
6	C₅×#1698	C₂	1	2	yes	maximal, complemented
7	C₅×#1681	C₂	1	2	yes	maximal, complemented
8	C₅×#1677	C₂	1	2	yes	maximal, complemented
9	C₅×#1569	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1559	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1555	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×#490	—	2	1	no	—
17	C₅×#490	—	2	1	no	—
18	C₅×#486	C₂²	1	2	yes	—
19	C₅×#486	C₂²	1	2	yes	—
20	C₅×#485	—	2	1	no	—
21	C₅×#477	C₂²	1	1	yes	characteristic, complemented
22	C₅×#476	C₂²	1	1	yes	characteristic, complemented
23	C₅×#462	C₂²	1	1	yes	characteristic, complemented
24	C₅×#461	C₂²	1	1	yes	characteristic, complemented
25	C₅×#460	—	2	1	no	—
26	C₅×#460	C₂²	1	2	yes	—
27	C₅×#459	—	2	1	no	—
28	C₅×#459	C₂²	1	2	yes	—
29	C₅×#452	—	2	1	no	—
30	C₅×#446	C₂²	1	2	yes	complemented
31	C₅×#441	—	2	1	no	—
32	C₅×#440	—	2	1	no	—
33	C₅×#435	—	2	2	no	—
34	C₅×C₈×D₄	C₂²	1	2	yes	complemented
35	C₅×#432	—	2	1	no	—
36	C₅×#432	C₂²	1	1	yes	characteristic
37	C₅×#432	C₂²	1	1	yes	characteristic
38	C₅×#423	C₂²	1	1	yes	characteristic
39	C₅×#418	—	2	2	no	—
40	C₅×#418	—	2	1	no	—
41	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
42	C₂×C₅×#97	—	2	1	no	—
43	C₅×#335	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	#19316	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×Q₁₆	—	2	1	no	—
56	C₂×C₅×SD₁₆	—	2	2	no	—
57	C₂×C₅×SD₁₆	—	2	1	no	—
58	C₂×C₅×D₈	—	2	2	no	—
59	C₂×C₅×M₁₆	—	2	1	no	—
60	C₂×C₅×M₁₆	D₄	1	2	yes	—
61	C₂²×C₅×C₈	—	2	2	no	—
62	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
63	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
64	C₅×#127	—	2	1	no	—
65	C₅×#127	—	2	1	no	—
66	C₅×#127	—	2	1	no	—
67	C₅×#127	C₂³	1	2	yes	—
68	C₅×#125	—	2	1	no	—
69	C₅×C₂²⋊Q₈	—	2	1	no	—
70	C₅×C₂²⋊Q₈	—	2	1	no	—
71	C₄×C₅×Q₈	—	2	1	no	—
72	C₄×C₅×Q₈	—	2	1	no	—
73	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
74	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
75	C₄×C₅×D₄	—	2	1	no	—
76	C₄×C₅×D₄	—	2	1	no	—
77	C₄×C₅×D₄	D₄	1	1	yes	characteristic
78	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
79	C₅×#117	—	2	1	no	—
80	C₅×#117	—	2	1	no	—
81	C₅×#117	D₄	1	1	yes	characteristic
82	C₂×C₄²×C₅	—	2	1	no	—
83	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
84	C₅×#107	—	2	1	no	—
85	C₅×#106	—	2	1	no	—
86	C₅×C₄⋊C₈	—	2	2	no	—
87	C₅×C₄⋊C₈	—	2	1	no	—
88	C₅×C₄⋊C₈	C₂³	1	2	yes	—
89	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
90	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
91	C₅×C₄⋊C₈	C₂³	1	2	yes	—
92	C₅×#103	—	2	1	no	—
93	C₅×#103	—	2	1	no	—
94	C₅×#103	—	2	1	no	—
95	C₅×#102	—	2	1	no	—
96	C₅×#102	—	2	2	no	—
97	C₅×#102	—	2	2	no	—
98	C₅×#102	—	2	2	no	—
99	C₅×#102	—	2	2	no	—
100	C₅×#102	—	2	2	no	—
101	C₅×#102	—	2	2	no	—
102	C₅×C₂²⋊C₈	—	2	1	no	—
103	C₅×C₂²⋊C₈	—	2	1	no	—
104	C₅×C₂²⋊C₈	—	2	2	no	—
105	C₅×#97	—	2	2	no	—
106	C₅×#97	—	2	1	no	—
107	C₅×#97	—	2	1	no	—
108	C₅×#97	D₄	1	1	yes	characteristic
109	C₅×#97	D₄	1	1	yes	characteristic
110	C₄×C₅×C₈	C₂³	1	2	yes	—
111	#3138	C₂×C₅	1	1	yes	characteristic, complemented
112	#3116	C₂×C₅	1	1	yes	characteristic, complemented
113	#3038	C₂×C₅	1	1	yes	characteristic
114	#2970	C₂×C₅	1	1	yes	characteristic, complemented
115	#1702	C₂×C₅	1	2	yes	complemented
116	#1698	C₂×C₅	1	2	yes	complemented
117	#1681	C₂×C₅	1	2	yes	complemented
118	#1677	C₂×C₅	1	2	yes	complemented
119	#1569	C₂×C₅	1	1	yes	characteristic, complemented
120	#1559	C₂×C₅	1	1	yes	characteristic, complemented
121	#1555	C₂×C₅	1	1	yes	characteristic, complemented
122	C₂⁴×C₅	—	4	1	no	—
123	C₅×#41	—	2	2	no	—
124	C₅×#41	—	4	1	no	—
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	2	no	—
133	C₂×C₅×D₄	—	4	4	no	—
134	C₂×C₅×D₄	—	4	2	no	—
135	C₂×C₅×D₄	—	4	1	no	—
136	C₂×C₅×D₄	—	4	1	no	—
137	C₂×C₅×D₄	—	4	1	no	—
138	C₂×C₅×D₄	—	8	2	no	—
139	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₅	—	2	1	no	—
141	C₂²×C₄×C₅	—	2	1	no	—
142	C₂²×C₄×C₅	—	2	1	no	—
143	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₅	#41	1	1	yes	characteristic
146	C₅×Q₁₆	—	4	2	no	—
147	C₅×SD₁₆	—	4	4	no	—
148	C₅×SD₁₆	—	4	2	no	—
149	C₅×D₈	—	4	4	no	—
150	C₅×M₁₆	—	4	2	no	—
151	C₅×M₁₆	—	4	2	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	—	4	4	no	—
157	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
158	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
159	C₅×C₄⋊C₄	—	2	1	no	—
160	C₅×C₄⋊C₄	—	2	1	no	—
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	—	4	1	no	—
166	C₅×C₄⋊C₄	—	4	1	no	—
167	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
168	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
169	C₅×C₂²⋊C₄	—	2	1	no	—
170	C₅×C₂²⋊C₄	—	2	1	no	—
171	C₅×C₂²⋊C₄	—	2	1	no	—
172	C₅×C₂²⋊C₄	—	4	1	no	—
173	C₄²×C₅	—	2	1	no	—
174	C₄²×C₅	—	2	1	no	—
175	C₄²×C₅	—	2	1	no	—
176	C₄²×C₅	—	4	1	no	—
177	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
178	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
179	C₄²×C₅	#41	1	1	yes	characteristic
180	C₄²×C₅	C₂⁴	1	1	yes	characteristic
181	C₂×AGL(1,ℤ/8)	—	2	1	no	—
182	#533	C₂²×C₅	1	1	yes	characteristic
183	C₂×#127	C₂²×C₅	1	1	yes	characteristic
184	C₄×#41	C₂²×C₅	1	1	yes	characteristic
185	#490	—	2	1	no	—
186	#490	—	2	1	no	—
187	#486	C₂²×C₅	1	2	yes	—
188	#486	C₂²×C₅	1	2	yes	—
189	#485	—	2	1	no	—
190	#477	C₂²×C₅	1	1	yes	characteristic, complemented
191	#476	C₂²×C₅	1	1	yes	characteristic, complemented
192	#462	C₂²×C₅	1	1	yes	characteristic, complemented
193	#461	C₂²×C₅	1	1	yes	characteristic, complemented
194	#460	—	2	1	no	—
195	#460	C₂²×C₅	1	2	yes	—
196	#459	—	2	1	no	—
197	#459	C₂²×C₅	1	2	yes	—
198	#452	—	2	1	no	—
199	#446	C₂²×C₅	1	2	yes	complemented
200	#441	—	2	1	no	—
201	#440	—	2	1	no	—
202	#435	—	2	2	no	—
203	C₈×D₄	C₂²×C₅	1	2	yes	complemented
204	#432	—	2	1	no	—
205	#432	C₂²×C₅	1	1	yes	characteristic
206	#432	C₂²×C₅	1	1	yes	characteristic
207	#423	C₂²×C₅	1	1	yes	characteristic
208	#418	—	2	2	no	—
209	#418	—	2	1	no	—
210	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
211	C₂×#97	—	2	1	no	—
212	#335	C₂²×C₅	1	2	yes	complemented
213	#334	C₂²×C₅	1	2	yes	complemented
214	#333	C₂²×C₅	1	2	yes	complemented
215	#332	C₂²×C₅	1	2	yes	complemented
216	#331	C₂²×C₅	1	2	yes	—
217	#331	C₂²×C₅	1	2	yes	—
218	C₂³×C₅	—	2	1	no	—
219	C₂³×C₅	—	4	2	no	—
220	C₂³×C₅	—	8	2	no	—
221	C₂³×C₅	—	8	2	no	—
222	C₂³×C₅	—	8	2	no	—
223	C₂³×C₅	#121	1	1	yes	characteristic
224	C₅×Q₈	—	2	1	no	—
225	C₅×Q₈	—	2	1	no	—
226	C₅×Q₈	—	4	1	no	—
227	C₅×Q₈	—	4	1	no	—
228	C₅×Q₈	—	8	1	no	—
229	C₅×D₄	—	2	1	no	—
230	C₅×D₄	—	4	2	no	—
231	C₅×D₄	—	4	2	no	—
232	C₅×D₄	—	4	4	no	—
233	C₅×D₄	—	4	2	no	—
234	C₅×D₄	—	8	2	no	—
235	C₅×D₄	—	8	2	no	—
236	C₅×D₄	—	8	2	no	—
237	C₅×D₄	—	8	2	no	—
238	C₅×D₄	AGL(1,ℤ/8)	1	2	yes	—
239	C₂×C₄×C₅	—	2	1	no	—
240	C₂×C₄×C₅	—	2	2	no	—
241	C₂×C₄×C₅	—	2	1	no	—
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	—	4	1	no	—
246	C₂×C₄×C₅	—	4	2	no	—
247	C₂×C₄×C₅	—	4	2	no	—
248	C₂×C₄×C₅	—	4	1	no	—
249	C₂×C₄×C₅	—	4	1	no	—
250	C₂×C₄×C₅	—	8	1	no	—
251	C₂×C₄×C₅	#121	1	1	yes	characteristic
252	C₂×C₄×C₅	#121	1	1	yes	characteristic
253	C₂×C₄×C₅	#121	1	1	yes	characteristic
254	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
255	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
257	C₅×C₈	—	2	2	no	—
258	C₅×C₈	—	2	2	no	—
259	C₅×C₈	—	4	2	no	—
260	C₅×C₈	—	4	1	no	—
261	C₅×C₈	—	4	2	no	—
262	C₅×C₈	—	4	1	no	—
263	C₂×#41	C₅×D₄	1	1	yes	characteristic
264	C₂²×D₄	—	2	1	no	—
265	C₂²×D₄	—	2	1	no	—
266	C₂²×D₄	—	2	1	no	—
267	AGL(1,ℤ/8)	—	4	4	no	—
268	C₂×Q₁₆	—	2	1	no	—
269	C₂×SD₁₆	—	2	2	no	—
270	C₂×SD₁₆	—	2	1	no	—
271	C₂×D₈	—	2	2	no	—
272	C₂×M₁₆	—	2	1	no	—
273	C₂×M₁₆	C₅×D₄	1	2	yes	—
274	C₂²×C₈	—	2	2	no	—
275	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
276	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
277	#127	—	2	1	no	—
278	#127	—	2	1	no	—
279	#127	—	2	1	no	—
280	#127	C₂³×C₅	1	2	yes	—
281	#125	—	2	1	no	—
282	C₂²⋊Q₈	—	2	1	no	—
283	C₂²⋊Q₈	—	2	1	no	—
284	C₄×Q₈	—	2	1	no	—
285	C₄×Q₈	—	2	1	no	—
286	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
287	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
288	C₄×D₄	—	2	1	no	—
289	C₄×D₄	—	2	1	no	—
290	C₄×D₄	C₅×D₄	1	1	yes	characteristic
291	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
292	#117	—	2	1	no	—
293	#117	—	2	1	no	—
294	#117	C₅×D₄	1	1	yes	characteristic
295	C₂×C₄²	—	2	1	no	—
296	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
297	#107	—	2	1	no	—
298	#106	—	2	1	no	—
299	C₄⋊C₈	—	2	2	no	—
300	C₄⋊C₈	—	2	1	no	—
301	C₄⋊C₈	C₂³×C₅	1	2	yes	—
302	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
303	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
304	C₄⋊C₈	C₂³×C₅	1	2	yes	—
305	#103	—	2	1	no	—
306	#103	—	2	1	no	—
307	#103	—	2	1	no	—
308	#102	—	2	1	no	—
309	#102	—	2	2	no	—
310	#102	—	2	2	no	—
311	#102	—	2	2	no	—
312	#102	—	2	2	no	—
313	#102	—	2	2	no	—
314	#102	—	2	2	no	—
315	C₂²⋊C₈	—	2	1	no	—
316	C₂²⋊C₈	—	2	1	no	—
317	C₂²⋊C₈	—	2	2	no	—
318	#97	—	2	2	no	—
319	#97	—	2	1	no	—
320	#97	—	2	1	no	—
321	#97	C₅×D₄	1	1	yes	characteristic
322	#97	C₅×D₄	1	1	yes	characteristic
323	C₄×C₈	C₂³×C₅	1	2	yes	—
324	C₂²×C₅	—	2	1	no	—
325	C₂²×C₅	—	2	1	no	—
326	C₂²×C₅	—	2	2	no	—
327	C₂²×C₅	—	2	1	no	—
328	C₂²×C₅	—	4	1	no	—
329	C₂²×C₅	—	4	1	no	—
330	C₂²×C₅	—	8	2	no	—
331	C₂²×C₅	—	8	2	no	—
332	C₂²×C₅	—	8	2	no	—
333	C₂²×C₅	—	16	4	no	—
334	C₂²×C₅	C₂×#121	1	1	yes	characteristic
335	C₄×C₅	—	2	1	no	—
336	C₄×C₅	—	2	1	no	—
337	C₄×C₅	—	2	1	no	—
338	C₄×C₅	—	2	1	no	—
339	C₄×C₅	—	4	1	no	—
340	C₄×C₅	—	4	1	no	—
341	C₄×C₅	—	4	1	no	—
342	C₄×C₅	—	8	1	no	—
343	C₄×C₅	—	8	1	no	—
344	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
345	C₄×C₅	#575	1	2	yes	—
346	C₄×C₅	#575	1	1	yes	characteristic
347	C₂⁴	—	4	1	no	—
348	#41	—	2	2	no	—
349	#41	—	4	1	no	—
350	C₂×Q₈	—	2	1	no	—
351	C₂×Q₈	—	2	1	no	—
352	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	4	2	no	—
358	C₂×D₄	—	4	4	no	—
359	C₂×D₄	—	4	2	no	—
360	C₂×D₄	—	4	1	no	—
361	C₂×D₄	—	4	1	no	—
362	C₂×D₄	—	4	1	no	—
363	C₂×D₄	—	8	2	no	—
364	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
369	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
370	C₂²×C₄	C₅×#41	1	1	yes	characteristic
371	Q₁₆	—	4	2	no	—
372	SD₁₆	—	4	4	no	—
373	SD₁₆	—	4	2	no	—
374	D₈	—	4	4	no	—
375	M₁₆	—	4	2	no	—
376	M₁₆	—	4	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	4	4	no	—
382	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
383	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	4	1	no	—
391	C₄⋊C₄	—	4	1	no	—
392	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
393	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
394	C₂²⋊C₄	—	2	1	no	—
395	C₂²⋊C₄	—	2	1	no	—
396	C₂²⋊C₄	—	2	1	no	—
397	C₂²⋊C₄	—	4	1	no	—
398	C₄²	—	2	1	no	—
399	C₄²	—	2	1	no	—
400	C₄²	—	2	1	no	—
401	C₄²	—	4	1	no	—
402	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
403	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
404	C₄²	C₅×#41	1	1	yes	characteristic
405	C₄²	C₂⁴×C₅	1	1	yes	characteristic
406	C₂×C₅	—	4	1	no	—
407	C₂×C₅	—	4	2	no	—
408	C₂×C₅	—	16	2	no	—
409	C₂×C₅	#3040	1	1	yes	characteristic
410	C₂×C₅	#3055	1	1	yes	characteristic
411	C₂×C₅	#3068	1	1	yes	characteristic
412	C₂³	—	2	1	no	—
413	C₂³	—	4	2	no	—
414	C₂³	—	8	2	no	—
415	C₂³	—	8	2	no	—
416	C₂³	—	8	2	no	—
417	C₂³	C₅×#121	1	1	yes	characteristic
418	Q₈	—	2	1	no	—
419	Q₈	—	2	1	no	—
420	Q₈	—	4	1	no	—
421	Q₈	—	4	1	no	—
422	Q₈	—	8	1	no	—
423	D₄	—	2	1	no	—
424	D₄	—	4	2	no	—
425	D₄	—	4	2	no	—
426	D₄	—	4	4	no	—
427	D₄	—	4	2	no	—
428	D₄	—	8	2	no	—
429	D₄	—	8	2	no	—
430	D₄	—	8	2	no	—
431	D₄	—	8	2	no	—
432	D₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	8	1	no	—
445	C₂×C₄	C₅×#121	1	1	yes	characteristic
446	C₂×C₄	C₅×#121	1	1	yes	characteristic
447	C₂×C₄	C₅×#121	1	1	yes	characteristic
448	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
449	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
450	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
451	C₈	—	2	2	no	—
452	C₈	—	2	2	no	—
453	C₈	—	4	2	no	—
454	C₈	—	4	1	no	—
455	C₈	—	4	2	no	—
456	C₈	—	4	1	no	—
457	C₅	#19316	1	1	yes	characteristic, direct product factor, Sylow
458	C₂²	—	2	1	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	2	2	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	4	1	no	—
463	C₂²	—	4	1	no	—
464	C₂²	—	8	2	no	—
465	C₂²	—	8	2	no	—
466	C₂²	—	8	2	no	—
467	C₂²	—	16	4	no	—
468	C₂²	C₂×C₅×#121	1	1	yes	characteristic
469	C₄	—	2	1	no	—
470	C₄	—	2	1	no	—
471	C₄	—	2	1	no	—
472	C₄	—	2	1	no	—
473	C₄	—	4	1	no	—
474	C₄	—	4	1	no	—
475	C₄	—	4	1	no	—
476	C₄	—	8	1	no	—
477	C₄	—	8	1	no	—
478	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
479	C₄	C₅×#575	1	2	yes	—
480	C₄	C₅×#575	1	1	yes	characteristic
481	C₂	—	4	1	no	—
482	C₂	—	4	2	no	—
483	C₂	—	16	2	no	—
484	C₂	C₅×#3040	1	1	yes	characteristic
485	C₂	C₅×#3055	1	1	yes	characteristic
486	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×#3138	C₂	semidirect
2. C₅×#3116	C₂	semidirect
4. C₅×#2970	C₂	semidirect
5. C₅×#1702	C₂	semidirect
6. C₅×#1698	C₂	semidirect
7. C₅×#1681	C₂	semidirect
8. C₅×#1677	C₂	semidirect
9. C₅×#1569	C₂	semidirect
10. C₅×#1559	C₂	semidirect
11. C₅×#1555	C₂	semidirect
21. C₅×#477	C₂²	semidirect
22. C₅×#476	C₂²	semidirect
23. C₅×#462	C₂²	semidirect
24. C₅×#461	C₂²	semidirect
30. C₅×#446	C₂²	semidirect
34. C₅×C₈×D₄	C₂²	semidirect
43. C₅×#335	C₂²	semidirect
44. C₅×#334	C₂²	semidirect
45. C₅×#333	C₂²	semidirect
46. C₅×#332	C₂²	semidirect
49. #19316	C₅	direct (N × H)
111. #3138	C₂×C₅	semidirect
112. #3116	C₂×C₅	semidirect
114. #2970	C₂×C₅	semidirect
115. #1702	C₂×C₅	semidirect
116. #1698	C₂×C₅	semidirect
117. #1681	C₂×C₅	semidirect
118. #1677	C₂×C₅	semidirect
119. #1569	C₂×C₅	semidirect
120. #1559	C₂×C₅	semidirect
121. #1555	C₂×C₅	semidirect
190. #477	C₂²×C₅	semidirect
191. #476	C₂²×C₅	semidirect
192. #462	C₂²×C₅	semidirect
193. #461	C₂²×C₅	semidirect
199. #446	C₂²×C₅	semidirect
203. C₈×D₄	C₂²×C₅	semidirect
212. #335	C₂²×C₅	semidirect
213. #334	C₂²×C₅	semidirect
214. #333	C₂²×C₅	semidirect
215. #332	C₂²×C₅	semidirect
457. C₅	#19316	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×#3138	2
C₅×#3116	2
C₅×#3038	2
C₅×#2970	2
C₅×#1702	2
C₅×#1698	2
C₅×#1681	2
C₅×#1677	2
C₅×#1569	2
C₅×#1559	2
C₅×#1555	2
#19316	5

Subgroups — C5×#19316 #11942036

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19316 #11942036