Subgroups — C₅×#19291 #11942011

Order 1280.

764 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#492	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3079	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3038	C₂	1	1	yes	maximal, characteristic
4	C₅×#2965	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1686	C₂	1	4	yes	maximal, complemented
6	C₅×#1685	C₂	1	4	yes	maximal, complemented
7	C₅×#1567	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1549	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1545	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×AGL(1,ℤ/8)	—	2	1	no	—
11	C₂²×C₅×SD₁₆	—	2	2	no	—
12	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₅×#127	C₂²	1	1	yes	characteristic
14	C₄×C₅×#41	C₂²	1	1	yes	characteristic
15	C₅×#492	—	2	1	no	—
16	C₅×#492	—	2	1	no	—
17	C₅×#492	C₂²	1	4	yes	—
18	C₅×#477	—	2	1	no	—
19	C₅×#476	—	2	1	no	—
20	C₅×#475	C₂²	1	2	yes	complemented
21	C₅×#474	C₂²	1	2	yes	complemented
22	C₅×#460	—	2	1	no	—
23	C₅×#460	C₂²	1	2	yes	—
24	C₅×#459	—	2	1	no	—
25	C₅×#459	C₂²	1	2	yes	—
26	C₅×#446	C₂²	1	2	yes	complemented
27	C₅×#436	C₂²	1	2	yes	complemented
28	C₅×#435	—	2	2	no	—
29	C₅×#431	—	2	1	no	—
30	C₅×#431	C₂²	1	1	yes	characteristic
31	C₅×#428	—	2	1	no	—
32	C₅×#423	C₂²	1	1	yes	characteristic
33	C₅×#423	C₂²	1	1	yes	characteristic
34	C₅×#418	—	2	1	no	—
35	C₅×#417	—	2	1	no	—
36	C₄×C₅×M₁₆	—	2	1	no	—
37	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
38	C₅×#335	C₂²	1	4	yes	complemented
39	C₅×#332	C₂²	1	4	yes	complemented
40	C₅×#331	C₂²	1	4	yes	—
41	#19291	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂×C₅×#41	D₄	1	1	yes	characteristic
43	C₂²×C₅×Q₈	—	2	1	no	—
44	C₂²×C₅×D₄	—	2	1	no	—
45	C₂²×C₅×D₄	—	2	1	no	—
46	C₂²×C₅×D₄	—	2	1	no	—
47	C₅×AGL(1,ℤ/8)	—	4	4	no	—
48	C₂×C₅×SD₁₆	—	2	2	no	—
49	C₂×C₅×SD₁₆	—	2	4	no	—
50	C₂×C₅×SD₁₆	—	2	4	no	—
51	C₂×C₅×SD₁₆	—	4	8	no	—
52	C₂×C₅×D₈	—	2	2	no	—
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	D₄	1	2	yes	—
57	C₅×C₄⋊Q₈	—	2	1	no	—
58	C₅×C₄⋊Q₈	—	2	1	no	—
59	C₅×C₄⋊Q₈	—	2	1	no	—
60	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
61	C₅×#127	—	2	1	no	—
62	C₅×#127	—	2	1	no	—
63	C₅×#127	—	2	1	no	—
64	C₅×#127	C₂³	1	2	yes	—
65	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
66	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
67	C₄×C₅×D₄	—	2	1	no	—
68	C₄×C₅×D₄	—	2	1	no	—
69	C₄×C₅×D₄	D₄	1	1	yes	characteristic
70	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
71	C₅×#117	—	2	1	no	—
72	C₅×#117	D₄	1	1	yes	characteristic
73	C₂×C₅×C₄⋊C₄	—	2	1	no	—
74	C₂×C₅×C₄⋊C₄	—	2	1	no	—
75	C₂×C₄²×C₅	—	2	1	no	—
76	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
77	C₅×#107	—	2	2	no	—
78	C₅×#106	—	2	2	no	—
79	C₅×C₄⋊C₈	—	2	2	no	—
80	C₅×C₄⋊C₈	—	2	1	no	—
81	C₅×C₄⋊C₈	—	2	1	no	—
82	C₅×C₄⋊C₈	C₂³	1	2	yes	—
83	C₅×C₄⋊C₈	C₂³	1	2	yes	—
84	C₅×C₄⋊C₈	C₂³	1	2	yes	—
85	C₅×#103	—	2	2	no	—
86	C₅×#102	—	2	2	no	—
87	C₅×#102	—	2	2	no	—
88	C₅×#102	—	2	2	no	—
89	C₅×C₂²⋊C₈	—	2	1	no	—
90	C₅×C₂²⋊C₈	—	2	2	no	—
91	C₅×#97	—	2	2	no	—
92	C₄×C₅×C₈	—	2	1	no	—
93	C₄×C₅×C₈	D₄	1	1	yes	characteristic
94	C₄×C₅×C₈	D₄	1	1	yes	characteristic
95	C₄×C₅×C₈	C₂³	1	2	yes	—
96	C₂×#492	C₂×C₅	1	1	yes	characteristic, complemented
97	#3079	C₂×C₅	1	1	yes	characteristic, complemented
98	#3038	C₂×C₅	1	1	yes	characteristic
99	#2965	C₂×C₅	1	1	yes	characteristic, complemented
100	#1686	C₂×C₅	1	4	yes	complemented
101	#1685	C₂×C₅	1	4	yes	complemented
102	#1567	C₂×C₅	1	1	yes	characteristic, complemented
103	#1549	C₂×C₅	1	1	yes	characteristic, complemented
104	#1545	C₂×C₅	1	1	yes	characteristic, complemented
105	C₂⁴×C₅	—	4	1	no	—
106	C₅×#41	—	2	2	no	—
107	C₅×#41	—	2	2	no	—
108	C₂×C₅×Q₈	—	2	2	no	—
109	C₂×C₅×Q₈	—	4	4	no	—
110	C₂×C₅×Q₈	—	4	1	no	—
111	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
112	C₂×C₅×D₄	—	2	1	no	—
113	C₂×C₅×D₄	—	2	2	no	—
114	C₂×C₅×D₄	—	2	2	no	—
115	C₂×C₅×D₄	—	2	2	no	—
116	C₂×C₅×D₄	—	4	4	no	—
117	C₂×C₅×D₄	—	4	1	no	—
118	C₂×C₅×D₄	—	4	1	no	—
119	C₂×C₅×D₄	—	4	1	no	—
120	C₂×C₅×D₄	—	4	2	no	—
121	C₂×C₅×D₄	—	4	2	no	—
122	C₂×C₅×D₄	—	8	2	no	—
123	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₅	—	2	1	no	—
125	C₂²×C₄×C₅	—	2	1	no	—
126	C₂²×C₄×C₅	—	2	1	no	—
127	C₂²×C₄×C₅	—	4	1	no	—
128	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₅	#41	1	1	yes	characteristic
131	C₅×SD₁₆	—	4	8	no	—
132	C₅×SD₁₆	—	4	4	no	—
133	C₅×SD₁₆	—	4	8	no	—
134	C₅×D₈	—	4	4	no	—
135	C₅×M₁₆	—	4	2	no	—
136	C₅×M₁₆	—	4	2	no	—
137	C₅×M₁₆	—	4	4	no	—
138	C₂×C₅×C₈	—	2	4	no	—
139	C₂×C₅×C₈	—	2	2	no	—
140	C₂×C₅×C₈	—	2	2	no	—
141	C₂×C₅×C₈	—	2	2	no	—
142	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
143	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
144	C₅×C₄⋊C₄	—	2	1	no	—
145	C₅×C₄⋊C₄	—	2	1	no	—
146	C₅×C₄⋊C₄	—	2	2	no	—
147	C₅×C₄⋊C₄	—	2	2	no	—
148	C₅×C₄⋊C₄	—	4	1	no	—
149	C₅×C₄⋊C₄	—	4	1	no	—
150	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
151	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
152	C₅×C₂²⋊C₄	—	2	1	no	—
153	C₅×C₂²⋊C₄	—	2	1	no	—
154	C₅×C₂²⋊C₄	—	2	1	no	—
155	C₄²×C₅	—	2	1	no	—
156	C₄²×C₅	—	2	1	no	—
157	C₄²×C₅	—	2	1	no	—
158	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
159	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
160	C₄²×C₅	#41	1	1	yes	characteristic
161	C₄²×C₅	C₂⁴	1	1	yes	characteristic
162	C₂×AGL(1,ℤ/8)	—	2	1	no	—
163	C₂²×SD₁₆	—	2	2	no	—
164	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
165	C₂×#127	C₂²×C₅	1	1	yes	characteristic
166	C₄×#41	C₂²×C₅	1	1	yes	characteristic
167	#492	—	2	1	no	—
168	#492	—	2	1	no	—
169	#492	C₂²×C₅	1	4	yes	—
170	#477	—	2	1	no	—
171	#476	—	2	1	no	—
172	#475	C₂²×C₅	1	2	yes	complemented
173	#474	C₂²×C₅	1	2	yes	complemented
174	#460	—	2	1	no	—
175	#460	C₂²×C₅	1	2	yes	—
176	#459	—	2	1	no	—
177	#459	C₂²×C₅	1	2	yes	—
178	#446	C₂²×C₅	1	2	yes	complemented
179	#436	C₂²×C₅	1	2	yes	complemented
180	#435	—	2	2	no	—
181	#431	—	2	1	no	—
182	#431	C₂²×C₅	1	1	yes	characteristic
183	#428	—	2	1	no	—
184	#423	C₂²×C₅	1	1	yes	characteristic
185	#423	C₂²×C₅	1	1	yes	characteristic
186	#418	—	2	1	no	—
187	#417	—	2	1	no	—
188	C₄×M₁₆	—	2	1	no	—
189	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
190	#335	C₂²×C₅	1	4	yes	complemented
191	#332	C₂²×C₅	1	4	yes	complemented
192	#331	C₂²×C₅	1	4	yes	—
193	C₂³×C₅	—	2	1	no	—
194	C₂³×C₅	—	4	2	no	—
195	C₂³×C₅	—	8	2	no	—
196	C₂³×C₅	—	8	2	no	—
197	C₂³×C₅	—	8	2	no	—
198	C₂³×C₅	#121	1	1	yes	characteristic
199	C₅×Q₈	—	2	1	no	—
200	C₅×Q₈	—	2	1	no	—
201	C₅×Q₈	—	4	4	no	—
202	C₅×Q₈	—	8	2	no	—
203	C₅×D₄	—	2	1	no	—
204	C₅×D₄	—	2	1	no	—
205	C₅×D₄	—	4	2	no	—
206	C₅×D₄	—	4	2	no	—
207	C₅×D₄	—	4	4	no	—
208	C₅×D₄	—	4	2	no	—
209	C₅×D₄	—	8	2	no	—
210	C₅×D₄	—	8	2	no	—
211	C₅×D₄	—	8	2	no	—
212	C₅×D₄	—	8	2	no	—
213	C₂×C₄×C₅	—	2	2	no	—
214	C₂×C₄×C₅	—	2	2	no	—
215	C₂×C₄×C₅	—	2	1	no	—
216	C₂×C₄×C₅	—	2	1	no	—
217	C₂×C₄×C₅	—	2	1	no	—
218	C₂×C₄×C₅	—	4	2	no	—
219	C₂×C₄×C₅	—	4	2	no	—
220	C₂×C₄×C₅	—	4	2	no	—
221	C₂×C₄×C₅	—	4	2	no	—
222	C₂×C₄×C₅	—	8	2	no	—
223	C₂×C₄×C₅	#121	1	1	yes	characteristic
224	C₂×C₄×C₅	#121	1	1	yes	characteristic
225	C₂×C₄×C₅	#121	1	1	yes	characteristic
226	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
227	C₂×C₄×C₅	#137	1	2	yes	—
228	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
231	C₅×C₈	—	2	2	no	—
232	C₅×C₈	—	4	2	no	—
233	C₅×C₈	—	4	2	no	—
234	C₅×C₈	—	4	2	no	—
235	C₅×C₈	AGL(1,ℤ/8)	1	4	yes	complemented
236	C₂×#41	C₅×D₄	1	1	yes	characteristic
237	C₂²×Q₈	—	2	1	no	—
238	C₂²×D₄	—	2	1	no	—
239	C₂²×D₄	—	2	1	no	—
240	C₂²×D₄	—	2	1	no	—
241	AGL(1,ℤ/8)	—	4	4	no	—
242	C₂×SD₁₆	—	2	2	no	—
243	C₂×SD₁₆	—	2	4	no	—
244	C₂×SD₁₆	—	2	4	no	—
245	C₂×SD₁₆	—	4	8	no	—
246	C₂×D₈	—	2	2	no	—
247	C₂×M₁₆	—	2	1	no	—
248	C₂×M₁₆	—	2	1	no	—
249	C₂×M₁₆	—	2	2	no	—
250	C₂²×C₈	C₅×D₄	1	2	yes	—
251	C₄⋊Q₈	—	2	1	no	—
252	C₄⋊Q₈	—	2	1	no	—
253	C₄⋊Q₈	—	2	1	no	—
254	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
255	#127	—	2	1	no	—
256	#127	—	2	1	no	—
257	#127	—	2	1	no	—
258	#127	C₂³×C₅	1	2	yes	—
259	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
260	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
261	C₄×D₄	—	2	1	no	—
262	C₄×D₄	—	2	1	no	—
263	C₄×D₄	C₅×D₄	1	1	yes	characteristic
264	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
265	#117	—	2	1	no	—
266	#117	C₅×D₄	1	1	yes	characteristic
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄²	—	2	1	no	—
270	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
271	#107	—	2	2	no	—
272	#106	—	2	2	no	—
273	C₄⋊C₈	—	2	2	no	—
274	C₄⋊C₈	—	2	1	no	—
275	C₄⋊C₈	—	2	1	no	—
276	C₄⋊C₈	C₂³×C₅	1	2	yes	—
277	C₄⋊C₈	C₂³×C₅	1	2	yes	—
278	C₄⋊C₈	C₂³×C₅	1	2	yes	—
279	#103	—	2	2	no	—
280	#102	—	2	2	no	—
281	#102	—	2	2	no	—
282	#102	—	2	2	no	—
283	C₂²⋊C₈	—	2	1	no	—
284	C₂²⋊C₈	—	2	2	no	—
285	#97	—	2	2	no	—
286	C₄×C₈	—	2	1	no	—
287	C₄×C₈	C₅×D₄	1	1	yes	characteristic
288	C₄×C₈	C₅×D₄	1	1	yes	characteristic
289	C₄×C₈	C₂³×C₅	1	2	yes	—
290	C₂²×C₅	—	2	1	no	—
291	C₂²×C₅	—	2	1	no	—
292	C₂²×C₅	—	4	1	no	—
293	C₂²×C₅	—	4	1	no	—
294	C₂²×C₅	—	4	1	no	—
295	C₂²×C₅	—	8	2	no	—
296	C₂²×C₅	—	8	2	no	—
297	C₂²×C₅	—	8	2	no	—
298	C₂²×C₅	—	16	4	no	—
299	C₂²×C₅	#468	1	2	yes	—
300	C₂²×C₅	C₂×#121	1	1	yes	characteristic
301	C₄×C₅	—	2	1	no	—
302	C₄×C₅	—	2	1	no	—
303	C₄×C₅	—	4	1	no	—
304	C₄×C₅	—	4	1	no	—
305	C₄×C₅	—	4	1	no	—
306	C₄×C₅	—	8	2	no	—
307	C₄×C₅	#468	1	2	yes	—
308	C₄×C₅	#471	1	2	yes	—
309	C₄×C₅	C₂×AGL(1,ℤ/8)	1	2	yes	—
310	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
311	C₄×C₅	C₂×#137	1	1	yes	characteristic
312	C₂⁴	—	4	1	no	—
313	#41	—	2	2	no	—
314	#41	—	2	2	no	—
315	C₂×Q₈	—	2	2	no	—
316	C₂×Q₈	—	4	4	no	—
317	C₂×Q₈	—	4	1	no	—
318	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	—	2	2	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	4	4	no	—
324	C₂×D₄	—	4	1	no	—
325	C₂×D₄	—	4	1	no	—
326	C₂×D₄	—	4	1	no	—
327	C₂×D₄	—	4	2	no	—
328	C₂×D₄	—	4	2	no	—
329	C₂×D₄	—	8	2	no	—
330	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	4	1	no	—
335	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
336	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
337	C₂²×C₄	C₅×#41	1	1	yes	characteristic
338	SD₁₆	—	4	8	no	—
339	SD₁₆	—	4	4	no	—
340	SD₁₆	—	4	8	no	—
341	D₈	—	4	4	no	—
342	M₁₆	—	4	2	no	—
343	M₁₆	—	4	2	no	—
344	M₁₆	—	4	4	no	—
345	C₂×C₈	—	2	4	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
350	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	4	1	no	—
356	C₄⋊C₄	—	4	1	no	—
357	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
358	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
359	C₂²⋊C₄	—	2	1	no	—
360	C₂²⋊C₄	—	2	1	no	—
361	C₂²⋊C₄	—	2	1	no	—
362	C₄²	—	2	1	no	—
363	C₄²	—	2	1	no	—
364	C₄²	—	2	1	no	—
365	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
366	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
367	C₄²	C₅×#41	1	1	yes	characteristic
368	C₄²	C₂⁴×C₅	1	1	yes	characteristic
369	C₂×C₅	—	2	2	no	—
370	C₂×C₅	—	8	1	no	—
371	C₂×C₅	—	16	2	no	—
372	C₂×C₅	#3038	1	1	yes	characteristic
373	C₂×C₅	C₂×#468	1	1	yes	characteristic
374	C₂×C₅	C₂×#471	1	1	yes	characteristic
375	C₂³	—	2	1	no	—
376	C₂³	—	4	2	no	—
377	C₂³	—	8	2	no	—
378	C₂³	—	8	2	no	—
379	C₂³	—	8	2	no	—
380	C₂³	C₅×#121	1	1	yes	characteristic
381	Q₈	—	2	1	no	—
382	Q₈	—	2	1	no	—
383	Q₈	—	4	4	no	—
384	Q₈	—	8	2	no	—
385	D₄	—	2	1	no	—
386	D₄	—	2	1	no	—
387	D₄	—	4	2	no	—
388	D₄	—	4	2	no	—
389	D₄	—	4	4	no	—
390	D₄	—	4	2	no	—
391	D₄	—	8	2	no	—
392	D₄	—	8	2	no	—
393	D₄	—	8	2	no	—
394	D₄	—	8	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	8	2	no	—
405	C₂×C₄	C₅×#121	1	1	yes	characteristic
406	C₂×C₄	C₅×#121	1	1	yes	characteristic
407	C₂×C₄	C₅×#121	1	1	yes	characteristic
408	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
409	C₂×C₄	C₅×#137	1	2	yes	—
410	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
411	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
412	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
413	C₈	—	2	2	no	—
414	C₈	—	4	2	no	—
415	C₈	—	4	2	no	—
416	C₈	—	4	2	no	—
417	C₈	C₅×AGL(1,ℤ/8)	1	4	yes	complemented
418	C₅	#19291	1	1	yes	characteristic, direct product factor, Sylow
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	4	1	no	—
422	C₂²	—	4	1	no	—
423	C₂²	—	4	1	no	—
424	C₂²	—	8	2	no	—
425	C₂²	—	8	2	no	—
426	C₂²	—	8	2	no	—
427	C₂²	—	16	4	no	—
428	C₂²	C₅×#468	1	2	yes	—
429	C₂²	C₂×C₅×#121	1	1	yes	characteristic
430	C₄	—	2	1	no	—
431	C₄	—	2	1	no	—
432	C₄	—	4	1	no	—
433	C₄	—	4	1	no	—
434	C₄	—	4	1	no	—
435	C₄	—	8	2	no	—
436	C₄	C₅×#468	1	2	yes	—
437	C₄	C₅×#471	1	2	yes	—
438	C₄	C₂×C₅×AGL(1,ℤ/8)	1	2	yes	—
439	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
440	C₄	C₂×C₅×#137	1	1	yes	characteristic
441	C₂	—	2	2	no	—
442	C₂	—	8	1	no	—
443	C₂	—	16	2	no	—
444	C₂	C₅×#3038	1	1	yes	characteristic
445	C₂	C₂×C₅×#468	1	1	yes	characteristic
446	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×#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. C₂×C₅×#492	C₂	semidirect
2. C₅×#3079	C₂	semidirect
4. C₅×#2965	C₂	semidirect
5. C₅×#1686	C₂	semidirect
6. C₅×#1685	C₂	semidirect
7. C₅×#1567	C₂	semidirect
8. C₅×#1549	C₂	semidirect
9. C₅×#1545	C₂	semidirect
20. C₅×#475	C₂²	semidirect
21. C₅×#474	C₂²	semidirect
26. C₅×#446	C₂²	semidirect
27. C₅×#436	C₂²	semidirect
38. C₅×#335	C₂²	semidirect
39. C₅×#332	C₂²	semidirect
41. #19291	C₅	direct (N × H)
96. C₂×#492	C₂×C₅	semidirect
97. #3079	C₂×C₅	semidirect
99. #2965	C₂×C₅	semidirect
100. #1686	C₂×C₅	semidirect
101. #1685	C₂×C₅	semidirect
102. #1567	C₂×C₅	semidirect
103. #1549	C₂×C₅	semidirect
104. #1545	C₂×C₅	semidirect
172. #475	C₂²×C₅	semidirect
173. #474	C₂²×C₅	semidirect
178. #446	C₂²×C₅	semidirect
179. #436	C₂²×C₅	semidirect
190. #335	C₂²×C₅	semidirect
191. #332	C₂²×C₅	semidirect
235. C₅×C₈	AGL(1,ℤ/8)	semidirect
417. C₈	C₅×AGL(1,ℤ/8)	semidirect
418. C₅	#19291	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₅×#492	2
C₅×#3079	2
C₅×#3038	2
C₅×#2965	2
C₅×#1686	2
C₅×#1685	2
C₅×#1567	2
C₅×#1549	2
C₅×#1545	2
#19291	5

Subgroups — C5×#19291 #11942011

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19291 #11942011