Subgroups — C₅×#19157 #11941877

Order 1280.

704 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3169	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3035	C₂	1	2	yes	maximal, complemented
3	C₅×#2965	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1702	C₂	1	2	yes	maximal, complemented
5	C₅×#1701	C₂	1	2	yes	maximal, complemented
6	C₅×#1694	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1693	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1688	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1687	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×#334	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1540	C₂	1	2	yes	maximal, complemented
12	C₂×C₅×#135	—	2	2	no	—
13	C₅×#532	C₂²	1	2	yes	—
14	C₄×C₅×#41	C₂²	1	1	yes	characteristic
15	C₅×#500	C₂²	1	1	yes	characteristic
16	C₅×#493	C₂²	1	1	yes	characteristic
17	C₅×#486	C₂²	1	2	yes	—
18	C₅×#466	—	2	1	no	—
19	C₅×#466	—	2	1	no	—
20	C₅×#464	—	2	2	no	—
21	C₅×#463	—	2	2	no	—
22	C₅×#462	C₂²	1	2	yes	—
23	C₅×#461	C₂²	1	2	yes	—
24	C₅×#460	C₂²	1	2	yes	—
25	C₅×#459	C₂²	1	2	yes	—
26	C₅×#446	C₂²	1	1	yes	characteristic
27	C₅×#446	C₂²	1	1	yes	characteristic
28	C₄×C₅×D₈	—	2	1	no	—
29	C₄×C₅×D₈	—	2	1	no	—
30	C₅×#436	C₂²	1	1	yes	characteristic
31	C₅×#436	C₂²	1	1	yes	characteristic
32	C₅×#435	—	2	1	no	—
33	C₅×#435	—	2	1	no	—
34	C₅×#431	—	2	1	no	—
35	C₅×#431	C₂²	1	1	yes	characteristic
36	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
37	C₅×#416	—	2	2	no	—
38	C₄×C₅×M₁₆	—	2	1	no	—
39	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
40	C₅×#334	C₂²	1	1	yes	characteristic
41	C₅×#334	C₂²	1	1	yes	characteristic
42	C₅×#334	C₂²	1	2	yes	—
43	C₅×#332	C₂²	1	2	yes	—
44	C₅×#332	C₂²	1	2	yes	—
45	C₅×#331	C₂²	1	2	yes	—
46	C₅×#331	C₂²	1	2	yes	—
47	#19157	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂×C₅×#41	—	2	2	no	—
49	C₂×C₅×#41	D₄	1	1	yes	characteristic
50	C₅×#135	—	4	8	no	—
51	C₂×C₅×Q₁₆	—	2	2	no	—
52	C₂×C₅×SD₁₆	—	2	2	no	—
53	C₂×C₅×SD₁₆	—	2	2	no	—
54	C₂×C₅×D₈	—	2	2	no	—
55	C₂×C₅×D₈	—	2	1	no	—
56	C₂×C₅×D₈	—	2	1	no	—
57	C₂×C₅×M₁₆	—	2	1	no	—
58	C₂×C₅×M₁₆	—	2	1	no	—
59	C₂²×C₅×C₈	—	2	2	no	—
60	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
61	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
62	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
63	C₅×#127	C₂³	1	2	yes	—
64	C₅×#124	—	2	2	no	—
65	C₅×#121	—	2	2	no	—
66	C₅×#121	—	2	2	no	—
67	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
68	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
69	C₄×C₅×D₄	—	2	1	no	—
70	C₄×C₅×D₄	—	2	1	no	—
71	C₄×C₅×D₄	—	2	2	no	—
72	C₄×C₅×D₄	—	2	2	no	—
73	C₄×C₅×D₄	D₄	1	1	yes	characteristic
74	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
75	C₅×#117	—	2	1	no	—
76	C₅×#117	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₅	—	2	1	no	—
78	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
79	C₅×#107	—	2	1	no	—
80	C₅×#107	—	2	1	no	—
81	C₅×C₄⋊C₈	—	2	1	no	—
82	C₅×C₄⋊C₈	—	2	1	no	—
83	C₅×C₄⋊C₈	—	2	2	no	—
84	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
85	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
86	C₅×C₄⋊C₈	C₂³	1	2	yes	—
87	C₅×C₄⋊C₈	C₂³	1	2	yes	—
88	C₅×#103	—	2	2	no	—
89	C₅×#103	—	2	2	no	—
90	C₅×#102	—	2	2	no	—
91	C₅×#102	—	2	2	no	—
92	C₅×#102	—	2	2	no	—
93	C₅×#102	—	2	2	no	—
94	C₅×C₂²⋊C₈	—	2	1	no	—
95	C₅×C₂²⋊C₈	—	2	1	no	—
96	C₅×C₂²⋊C₈	—	2	1	no	—
97	C₅×#97	—	2	1	no	—
98	C₅×#97	—	2	1	no	—
99	C₄×C₅×C₈	—	2	1	no	—
100	C₄×C₅×C₈	D₄	1	1	yes	characteristic
101	C₄×C₅×C₈	D₄	1	1	yes	characteristic
102	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
103	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
104	#3169	C₂×C₅	1	1	yes	characteristic, complemented
105	#3035	C₂×C₅	1	2	yes	complemented
106	#2965	C₂×C₅	1	1	yes	characteristic, complemented
107	#1702	C₂×C₅	1	2	yes	complemented
108	#1701	C₂×C₅	1	2	yes	complemented
109	#1694	C₂×C₅	1	1	yes	characteristic, complemented
110	#1693	C₂×C₅	1	1	yes	characteristic, complemented
111	#1688	C₂×C₅	1	1	yes	characteristic, complemented
112	#1687	C₂×C₅	1	1	yes	characteristic, complemented
113	C₂×#334	C₂×C₅	1	1	yes	characteristic, complemented
114	#1540	C₂×C₅	1	2	yes	complemented
115	C₅×#41	—	2	4	no	—
116	C₅×#41	—	4	4	no	—
117	C₅×#41	—	4	4	no	—
118	C₂×C₅×Q₈	—	2	2	no	—
119	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
120	C₂×C₅×D₄	—	2	1	no	—
121	C₂×C₅×D₄	—	2	2	no	—
122	C₂×C₅×D₄	—	2	2	no	—
123	C₂×C₅×D₄	—	2	2	no	—
124	C₂×C₅×D₄	—	4	2	no	—
125	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₅	—	2	1	no	—
127	C₂²×C₄×C₅	—	2	1	no	—
128	C₂²×C₄×C₅	—	2	1	no	—
129	C₂²×C₄×C₅	—	4	2	no	—
130	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₅	#41	1	1	yes	characteristic
133	C₅×Q₁₆	—	4	4	no	—
134	C₅×SD₁₆	—	4	4	no	—
135	C₅×SD₁₆	—	4	4	no	—
136	C₅×D₈	—	4	2	no	—
137	C₅×D₈	—	4	4	no	—
138	C₅×D₈	—	4	2	no	—
139	C₅×M₁₆	—	4	2	no	—
140	C₅×M₁₆	—	4	2	no	—
141	C₂×C₅×C₈	—	2	2	no	—
142	C₂×C₅×C₈	—	2	2	no	—
143	C₂×C₅×C₈	—	2	2	no	—
144	C₂×C₅×C₈	—	2	1	no	—
145	C₂×C₅×C₈	—	2	1	no	—
146	C₂×C₅×C₈	—	4	1	no	—
147	C₂×C₅×C₈	—	4	4	no	—
148	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
149	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
150	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
151	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
152	C₅×C₄⋊C₄	—	2	1	no	—
153	C₅×C₄⋊C₄	—	2	1	no	—
154	C₅×C₄⋊C₄	—	2	2	no	—
155	C₅×C₄⋊C₄	—	2	2	no	—
156	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
157	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
158	C₅×C₂²⋊C₄	—	2	1	no	—
159	C₅×C₂²⋊C₄	—	2	1	no	—
160	C₅×C₂²⋊C₄	—	2	1	no	—
161	C₅×C₂²⋊C₄	—	4	2	no	—
162	C₅×C₂²⋊C₄	—	4	2	no	—
163	C₄²×C₅	—	2	1	no	—
164	C₄²×C₅	—	2	1	no	—
165	C₄²×C₅	—	2	1	no	—
166	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
167	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
168	C₄²×C₅	#41	1	1	yes	characteristic
169	C₄²×C₅	C₂⁴	1	1	yes	characteristic
170	C₂×#135	—	2	2	no	—
171	#532	C₂²×C₅	1	2	yes	—
172	C₄×#41	C₂²×C₅	1	1	yes	characteristic
173	#500	C₂²×C₅	1	1	yes	characteristic
174	#493	C₂²×C₅	1	1	yes	characteristic
175	#486	C₂²×C₅	1	2	yes	—
176	#466	—	2	1	no	—
177	#466	—	2	1	no	—
178	#464	—	2	2	no	—
179	#463	—	2	2	no	—
180	#462	C₂²×C₅	1	2	yes	—
181	#461	C₂²×C₅	1	2	yes	—
182	#460	C₂²×C₅	1	2	yes	—
183	#459	C₂²×C₅	1	2	yes	—
184	#446	C₂²×C₅	1	1	yes	characteristic
185	#446	C₂²×C₅	1	1	yes	characteristic
186	C₄×D₈	—	2	1	no	—
187	C₄×D₈	—	2	1	no	—
188	#436	C₂²×C₅	1	1	yes	characteristic
189	#436	C₂²×C₅	1	1	yes	characteristic
190	#435	—	2	1	no	—
191	#435	—	2	1	no	—
192	#431	—	2	1	no	—
193	#431	C₂²×C₅	1	1	yes	characteristic
194	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
195	#416	—	2	2	no	—
196	C₄×M₁₆	—	2	1	no	—
197	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
198	#334	C₂²×C₅	1	1	yes	characteristic
199	#334	C₂²×C₅	1	1	yes	characteristic
200	#334	C₂²×C₅	1	2	yes	—
201	#332	C₂²×C₅	1	2	yes	—
202	#332	C₂²×C₅	1	2	yes	—
203	#331	C₂²×C₅	1	2	yes	—
204	#331	C₂²×C₅	1	2	yes	—
205	C₂³×C₅	—	2	1	no	—
206	C₂³×C₅	—	4	2	no	—
207	C₂³×C₅	#121	1	1	yes	characteristic
208	C₅×Q₈	—	2	2	no	—
209	C₅×Q₈	—	4	2	no	—
210	C₅×Q₈	—	4	2	no	—
211	C₅×D₄	—	2	2	no	—
212	C₅×D₄	—	4	2	no	—
213	C₅×D₄	—	4	2	no	—
214	C₅×D₄	—	4	2	no	—
215	C₅×D₄	—	4	2	no	—
216	C₅×D₄	—	4	2	no	—
217	C₅×D₄	—	8	2	no	—
218	C₅×D₄	—	8	4	no	—
219	C₂×C₄×C₅	—	2	1	no	—
220	C₂×C₄×C₅	—	2	1	no	—
221	C₂×C₄×C₅	—	2	1	no	—
222	C₂×C₄×C₅	—	2	1	no	—
223	C₂×C₄×C₅	—	2	1	no	—
224	C₂×C₄×C₅	—	4	1	no	—
225	C₂×C₄×C₅	—	4	2	no	—
226	C₂×C₄×C₅	—	4	1	no	—
227	C₂×C₄×C₅	—	4	1	no	—
228	C₂×C₄×C₅	—	4	2	no	—
229	C₂×C₄×C₅	—	4	2	no	—
230	C₂×C₄×C₅	—	8	4	no	—
231	C₂×C₄×C₅	#121	1	1	yes	characteristic
232	C₂×C₄×C₅	#121	1	1	yes	characteristic
233	C₂×C₄×C₅	#121	1	1	yes	characteristic
234	C₂×C₄×C₅	AGL(1,ℤ/8)	1	4	yes	—
235	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
238	C₅×C₈	—	2	1	no	—
239	C₅×C₈	—	2	1	no	—
240	C₅×C₈	—	2	1	no	—
241	C₅×C₈	—	4	1	no	—
242	C₅×C₈	—	4	2	no	—
243	C₅×C₈	—	4	2	no	—
244	C₅×C₈	—	4	1	no	—
245	C₅×C₈	#135	1	2	yes	complemented
246	C₂×#41	—	2	2	no	—
247	C₂×#41	C₅×D₄	1	1	yes	characteristic
248	#135	—	4	8	no	—
249	C₂×Q₁₆	—	2	2	no	—
250	C₂×SD₁₆	—	2	2	no	—
251	C₂×SD₁₆	—	2	2	no	—
252	C₂×D₈	—	2	2	no	—
253	C₂×D₈	—	2	1	no	—
254	C₂×D₈	—	2	1	no	—
255	C₂×M₁₆	—	2	1	no	—
256	C₂×M₁₆	—	2	1	no	—
257	C₂²×C₈	—	2	2	no	—
258	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
259	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
260	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
261	#127	C₂³×C₅	1	2	yes	—
262	#124	—	2	2	no	—
263	#121	—	2	2	no	—
264	#121	—	2	2	no	—
265	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
266	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
267	C₄×D₄	—	2	1	no	—
268	C₄×D₄	—	2	1	no	—
269	C₄×D₄	—	2	2	no	—
270	C₄×D₄	—	2	2	no	—
271	C₄×D₄	C₅×D₄	1	1	yes	characteristic
272	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
273	#117	—	2	1	no	—
274	#117	C₅×D₄	1	1	yes	characteristic
275	C₂×C₄²	—	2	1	no	—
276	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
277	#107	—	2	1	no	—
278	#107	—	2	1	no	—
279	C₄⋊C₈	—	2	1	no	—
280	C₄⋊C₈	—	2	1	no	—
281	C₄⋊C₈	—	2	2	no	—
282	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
283	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
284	C₄⋊C₈	C₂³×C₅	1	2	yes	—
285	C₄⋊C₈	C₂³×C₅	1	2	yes	—
286	#103	—	2	2	no	—
287	#103	—	2	2	no	—
288	#102	—	2	2	no	—
289	#102	—	2	2	no	—
290	#102	—	2	2	no	—
291	#102	—	2	2	no	—
292	C₂²⋊C₈	—	2	1	no	—
293	C₂²⋊C₈	—	2	1	no	—
294	C₂²⋊C₈	—	2	1	no	—
295	#97	—	2	1	no	—
296	#97	—	2	1	no	—
297	C₄×C₈	—	2	1	no	—
298	C₄×C₈	C₅×D₄	1	1	yes	characteristic
299	C₄×C₈	C₅×D₄	1	1	yes	characteristic
300	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
301	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
302	C₂²×C₅	—	2	1	no	—
303	C₂²×C₅	—	2	1	no	—
304	C₂²×C₅	—	4	1	no	—
305	C₂²×C₅	—	4	1	no	—
306	C₂²×C₅	—	4	1	no	—
307	C₂²×C₅	—	8	2	no	—
308	C₂²×C₅	—	8	2	no	—
309	C₂²×C₅	—	8	2	no	—
310	C₂²×C₅	#469	1	2	yes	—
311	C₂²×C₅	C₂×#121	1	1	yes	characteristic
312	C₄×C₅	—	2	1	no	—
313	C₄×C₅	—	2	1	no	—
314	C₄×C₅	—	2	1	no	—
315	C₄×C₅	—	4	1	no	—
316	C₄×C₅	—	4	1	no	—
317	C₄×C₅	—	4	1	no	—
318	C₄×C₅	—	8	2	no	—
319	C₄×C₅	#469	1	2	yes	—
320	C₄×C₅	C₂×#135	1	1	yes	characteristic
321	C₄×C₅	C₂×AGL(1,ℤ/8)	1	2	yes	—
322	C₄×C₅	#575	1	1	yes	characteristic
323	#41	—	2	4	no	—
324	#41	—	4	4	no	—
325	#41	—	4	4	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	4	2	no	—
333	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	4	2	no	—
338	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
339	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
340	C₂²×C₄	C₅×#41	1	1	yes	characteristic
341	Q₁₆	—	4	4	no	—
342	SD₁₆	—	4	4	no	—
343	SD₁₆	—	4	4	no	—
344	D₈	—	4	2	no	—
345	D₈	—	4	4	no	—
346	D₈	—	4	2	no	—
347	M₁₆	—	4	2	no	—
348	M₁₆	—	4	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	4	1	no	—
355	C₂×C₈	—	4	4	no	—
356	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
357	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
358	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
359	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
365	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
366	C₂²⋊C₄	—	2	1	no	—
367	C₂²⋊C₄	—	2	1	no	—
368	C₂²⋊C₄	—	2	1	no	—
369	C₂²⋊C₄	—	4	2	no	—
370	C₂²⋊C₄	—	4	2	no	—
371	C₄²	—	2	1	no	—
372	C₄²	—	2	1	no	—
373	C₄²	—	2	1	no	—
374	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
375	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
376	C₄²	C₅×#41	1	1	yes	characteristic
377	C₄²	C₂⁴×C₅	1	1	yes	characteristic
378	C₂×C₅	—	2	2	no	—
379	C₂×C₅	—	8	1	no	—
380	C₂×C₅	—	16	2	no	—
381	C₂×C₅	#3035	1	1	yes	characteristic
382	C₂×C₅	C₂×#469	1	1	yes	characteristic
383	C₂×C₅	#3067	1	1	yes	characteristic
384	C₂³	—	2	1	no	—
385	C₂³	—	4	2	no	—
386	C₂³	C₅×#121	1	1	yes	characteristic
387	Q₈	—	2	2	no	—
388	Q₈	—	4	2	no	—
389	Q₈	—	4	2	no	—
390	D₄	—	2	2	no	—
391	D₄	—	4	2	no	—
392	D₄	—	4	2	no	—
393	D₄	—	4	2	no	—
394	D₄	—	4	2	no	—
395	D₄	—	4	2	no	—
396	D₄	—	8	2	no	—
397	D₄	—	8	4	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	8	4	no	—
410	C₂×C₄	C₅×#121	1	1	yes	characteristic
411	C₂×C₄	C₅×#121	1	1	yes	characteristic
412	C₂×C₄	C₅×#121	1	1	yes	characteristic
413	C₂×C₄	C₅×AGL(1,ℤ/8)	1	4	yes	—
414	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
415	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
416	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
417	C₈	—	2	1	no	—
418	C₈	—	2	1	no	—
419	C₈	—	2	1	no	—
420	C₈	—	4	1	no	—
421	C₈	—	4	2	no	—
422	C₈	—	4	2	no	—
423	C₈	—	4	1	no	—
424	C₈	C₅×#135	1	2	yes	complemented
425	C₅	#19157	1	1	yes	characteristic, direct product factor, Sylow
426	C₂²	—	2	1	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	4	1	no	—
429	C₂²	—	4	1	no	—
430	C₂²	—	4	1	no	—
431	C₂²	—	8	2	no	—
432	C₂²	—	8	2	no	—
433	C₂²	—	8	2	no	—
434	C₂²	C₅×#469	1	2	yes	—
435	C₂²	C₂×C₅×#121	1	1	yes	characteristic
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	2	1	no	—
439	C₄	—	4	1	no	—
440	C₄	—	4	1	no	—
441	C₄	—	4	1	no	—
442	C₄	—	8	2	no	—
443	C₄	C₅×#469	1	2	yes	—
444	C₄	C₂×C₅×#135	1	1	yes	characteristic
445	C₄	C₂×C₅×AGL(1,ℤ/8)	1	2	yes	—
446	C₄	C₅×#575	1	1	yes	characteristic
447	C₂	—	2	2	no	—
448	C₂	—	8	1	no	—
449	C₂	—	16	2	no	—
450	C₂	C₅×#3035	1	1	yes	characteristic
451	C₂	C₂×C₅×#469	1	1	yes	characteristic
452	C₂	C₅×#3067	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
socle	C₂²×C₅	C₂×#121
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#3169	C₂	semidirect
2. C₅×#3035	C₂	semidirect
3. C₅×#2965	C₂	semidirect
4. C₅×#1702	C₂	semidirect
5. C₅×#1701	C₂	semidirect
6. C₅×#1694	C₂	semidirect
7. C₅×#1693	C₂	semidirect
8. C₅×#1688	C₂	semidirect
9. C₅×#1687	C₂	semidirect
10. C₂×C₅×#334	C₂	semidirect
11. C₅×#1540	C₂	semidirect
47. #19157	C₅	direct (N × H)
104. #3169	C₂×C₅	semidirect
105. #3035	C₂×C₅	semidirect
106. #2965	C₂×C₅	semidirect
107. #1702	C₂×C₅	semidirect
108. #1701	C₂×C₅	semidirect
109. #1694	C₂×C₅	semidirect
110. #1693	C₂×C₅	semidirect
111. #1688	C₂×C₅	semidirect
112. #1687	C₂×C₅	semidirect
113. C₂×#334	C₂×C₅	semidirect
114. #1540	C₂×C₅	semidirect
245. C₅×C₈	#135	semidirect
424. C₈	C₅×#135	semidirect
425. C₅	#19157	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×#3169	2
C₅×#3035	2
C₅×#2965	2
C₅×#1702	2
C₅×#1701	2
C₅×#1694	2
C₅×#1693	2
C₅×#1688	2
C₅×#1687	2
C₂×C₅×#334	2
C₅×#1540	2
#19157	5

Subgroups — C5×#19157 #11941877

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19157 #11941877