Subgroups — C₅×#19301 #11942021

Order 1280.

732 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#486	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3039	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×#1702	C₂	1	4	yes	maximal, complemented
6	C₅×#1701	C₂	1	4	yes	maximal, complemented
7	C₅×#1566	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1546	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1545	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×#137	—	2	1	no	—
11	C₂×C₅×AGL(1,ℤ/8)	—	2	1	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×#486	—	2	1	no	—
16	C₅×#486	—	2	1	no	—
17	C₅×#486	C₂²	1	4	yes	—
18	C₅×#462	—	2	1	no	—
19	C₅×#462	C₂²	1	2	yes	complemented
20	C₅×#461	—	2	1	no	—
21	C₅×#461	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×#423	C₂²	1	1	yes	characteristic
32	C₅×#423	C₂²	1	1	yes	characteristic
33	C₅×#419	—	2	1	no	—
34	C₅×#418	—	2	1	no	—
35	C₂×C₅×#102	—	2	2	no	—
36	C₄×C₅×M₁₆	—	2	1	no	—
37	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
38	C₅×#334	C₂²	1	4	yes	complemented
39	C₅×#332	C₂²	1	4	yes	complemented
40	C₅×#331	C₂²	1	4	yes	—
41	#19301	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×#137	—	4	4	no	—
48	C₅×AGL(1,ℤ/8)	—	4	4	no	—
49	C₂×C₅×Q₁₆	—	2	2	no	—
50	C₂×C₅×SD₁₆	—	2	2	no	—
51	C₂×C₅×SD₁₆	—	2	2	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×C₄⋊C₈	—	2	2	no	—
78	C₅×C₄⋊C₈	—	2	1	no	—
79	C₅×C₄⋊C₈	—	2	1	no	—
80	C₅×C₄⋊C₈	C₂³	1	2	yes	—
81	C₅×C₄⋊C₈	C₂³	1	2	yes	—
82	C₅×C₄⋊C₈	C₂³	1	2	yes	—
83	C₅×#103	—	2	2	no	—
84	C₅×#103	—	2	2	no	—
85	C₅×#102	—	2	4	no	—
86	C₅×#102	—	2	4	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×#486	C₂×C₅	1	1	yes	characteristic, complemented
97	#3039	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	#1702	C₂×C₅	1	4	yes	complemented
101	#1701	C₂×C₅	1	4	yes	complemented
102	#1566	C₂×C₅	1	1	yes	characteristic, complemented
103	#1546	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	1	no	—
110	C₂×C₅×Q₈	—	4	2	no	—
111	C₂×C₅×Q₈	—	4	2	no	—
112	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
113	C₂×C₅×D₄	—	2	1	no	—
114	C₂×C₅×D₄	—	2	2	no	—
115	C₂×C₅×D₄	—	2	2	no	—
116	C₂×C₅×D₄	—	2	2	no	—
117	C₂×C₅×D₄	—	4	4	no	—
118	C₂×C₅×D₄	—	4	1	no	—
119	C₂×C₅×D₄	—	4	1	no	—
120	C₂×C₅×D₄	—	4	1	no	—
121	C₂×C₅×D₄	—	4	2	no	—
122	C₂×C₅×D₄	—	4	2	no	—
123	C₂×C₅×D₄	—	8	2	no	—
124	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₅	—	2	1	no	—
126	C₂²×C₄×C₅	—	2	1	no	—
127	C₂²×C₄×C₅	—	2	1	no	—
128	C₂²×C₄×C₅	—	4	1	no	—
129	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₅	#41	1	1	yes	characteristic
132	C₅×Q₁₆	—	4	4	no	—
133	C₅×SD₁₆	—	4	4	no	—
134	C₅×SD₁₆	—	4	4	no	—
135	C₅×D₈	—	4	4	no	—
136	C₅×M₁₆	—	4	4	no	—
137	C₅×M₁₆	—	4	2	no	—
138	C₅×M₁₆	—	4	2	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	—	4	2	no	—
143	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
144	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
145	C₅×C₄⋊C₄	—	2	1	no	—
146	C₅×C₄⋊C₄	—	2	1	no	—
147	C₅×C₄⋊C₄	—	2	2	no	—
148	C₅×C₄⋊C₄	—	2	2	no	—
149	C₅×C₄⋊C₄	—	4	1	no	—
150	C₅×C₄⋊C₄	—	4	1	no	—
151	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
152	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
153	C₅×C₂²⋊C₄	—	2	1	no	—
154	C₅×C₂²⋊C₄	—	2	1	no	—
155	C₅×C₂²⋊C₄	—	2	1	no	—
156	C₄²×C₅	—	2	1	no	—
157	C₄²×C₅	—	2	1	no	—
158	C₄²×C₅	—	2	1	no	—
159	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
160	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
161	C₄²×C₅	#41	1	1	yes	characteristic
162	C₄²×C₅	C₂⁴	1	1	yes	characteristic
163	C₂×#137	—	2	1	no	—
164	C₂×AGL(1,ℤ/8)	—	2	1	no	—
165	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
166	C₂×#127	C₂²×C₅	1	1	yes	characteristic
167	C₄×#41	C₂²×C₅	1	1	yes	characteristic
168	#486	—	2	1	no	—
169	#486	—	2	1	no	—
170	#486	C₂²×C₅	1	4	yes	—
171	#462	—	2	1	no	—
172	#462	C₂²×C₅	1	2	yes	complemented
173	#461	—	2	1	no	—
174	#461	C₂²×C₅	1	2	yes	complemented
175	#460	—	2	1	no	—
176	#460	C₂²×C₅	1	2	yes	—
177	#459	—	2	1	no	—
178	#459	C₂²×C₅	1	2	yes	—
179	#446	C₂²×C₅	1	2	yes	complemented
180	#436	C₂²×C₅	1	2	yes	complemented
181	#435	—	2	2	no	—
182	#431	—	2	1	no	—
183	#431	C₂²×C₅	1	1	yes	characteristic
184	#423	C₂²×C₅	1	1	yes	characteristic
185	#423	C₂²×C₅	1	1	yes	characteristic
186	#419	—	2	1	no	—
187	#418	—	2	1	no	—
188	C₂×#102	—	2	2	no	—
189	C₄×M₁₆	—	2	1	no	—
190	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
191	#334	C₂²×C₅	1	4	yes	complemented
192	#332	C₂²×C₅	1	4	yes	complemented
193	#331	C₂²×C₅	1	4	yes	—
194	C₂³×C₅	—	2	1	no	—
195	C₂³×C₅	—	4	2	no	—
196	C₂³×C₅	—	8	2	no	—
197	C₂³×C₅	—	8	2	no	—
198	C₂³×C₅	—	8	2	no	—
199	C₂³×C₅	#121	1	1	yes	characteristic
200	C₅×Q₈	—	2	1	no	—
201	C₅×Q₈	—	2	1	no	—
202	C₅×Q₈	—	4	2	no	—
203	C₅×Q₈	—	4	2	no	—
204	C₅×Q₈	—	8	2	no	—
205	C₅×D₄	—	2	1	no	—
206	C₅×D₄	—	2	1	no	—
207	C₅×D₄	—	4	2	no	—
208	C₅×D₄	—	4	2	no	—
209	C₅×D₄	—	4	2	no	—
210	C₅×D₄	—	4	4	no	—
211	C₅×D₄	—	8	2	no	—
212	C₅×D₄	—	8	2	no	—
213	C₅×D₄	—	8	2	no	—
214	C₅×D₄	—	8	2	no	—
215	C₂×C₄×C₅	—	2	2	no	—
216	C₂×C₄×C₅	—	2	2	no	—
217	C₂×C₄×C₅	—	2	1	no	—
218	C₂×C₄×C₅	—	2	1	no	—
219	C₂×C₄×C₅	—	2	1	no	—
220	C₂×C₄×C₅	—	4	2	no	—
221	C₂×C₄×C₅	—	4	2	no	—
222	C₂×C₄×C₅	—	4	2	no	—
223	C₂×C₄×C₅	—	4	2	no	—
224	C₂×C₄×C₅	—	8	2	no	—
225	C₂×C₄×C₅	#121	1	1	yes	characteristic
226	C₂×C₄×C₅	#121	1	1	yes	characteristic
227	C₂×C₄×C₅	#121	1	1	yes	characteristic
228	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
229	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
230	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
233	C₅×C₈	—	2	2	no	—
234	C₅×C₈	—	2	2	no	—
235	C₅×C₈	—	4	2	no	—
236	C₅×C₈	—	4	2	no	—
237	C₅×C₈	—	4	2	no	—
238	C₂×#41	C₅×D₄	1	1	yes	characteristic
239	C₂²×Q₈	—	2	1	no	—
240	C₂²×D₄	—	2	1	no	—
241	C₂²×D₄	—	2	1	no	—
242	C₂²×D₄	—	2	1	no	—
243	#137	—	4	4	no	—
244	AGL(1,ℤ/8)	—	4	4	no	—
245	C₂×Q₁₆	—	2	2	no	—
246	C₂×SD₁₆	—	2	2	no	—
247	C₂×SD₁₆	—	2	2	no	—
248	C₂×D₈	—	2	2	no	—
249	C₂×M₁₆	—	2	1	no	—
250	C₂×M₁₆	—	2	1	no	—
251	C₂×M₁₆	—	2	2	no	—
252	C₂²×C₈	C₅×D₄	1	2	yes	—
253	C₄⋊Q₈	—	2	1	no	—
254	C₄⋊Q₈	—	2	1	no	—
255	C₄⋊Q₈	—	2	1	no	—
256	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
257	#127	—	2	1	no	—
258	#127	—	2	1	no	—
259	#127	—	2	1	no	—
260	#127	C₂³×C₅	1	2	yes	—
261	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
262	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
263	C₄×D₄	—	2	1	no	—
264	C₄×D₄	—	2	1	no	—
265	C₄×D₄	C₅×D₄	1	1	yes	characteristic
266	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
267	#117	—	2	1	no	—
268	#117	C₅×D₄	1	1	yes	characteristic
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄²	—	2	1	no	—
272	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
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	#103	—	2	2	no	—
281	#102	—	2	4	no	—
282	#102	—	2	4	no	—
283	#102	—	2	2	no	—
284	#102	—	2	2	no	—
285	C₂²⋊C₈	—	2	1	no	—
286	C₂²⋊C₈	—	2	2	no	—
287	#97	—	2	2	no	—
288	C₄×C₈	—	2	1	no	—
289	C₄×C₈	C₅×D₄	1	1	yes	characteristic
290	C₄×C₈	C₅×D₄	1	1	yes	characteristic
291	C₄×C₈	C₂³×C₅	1	2	yes	—
292	C₂²×C₅	—	2	1	no	—
293	C₂²×C₅	—	2	1	no	—
294	C₂²×C₅	—	4	1	no	—
295	C₂²×C₅	—	4	1	no	—
296	C₂²×C₅	—	4	1	no	—
297	C₂²×C₅	—	8	2	no	—
298	C₂²×C₅	—	8	2	no	—
299	C₂²×C₅	—	8	2	no	—
300	C₂²×C₅	—	16	4	no	—
301	C₂²×C₅	#469	1	2	yes	—
302	C₂²×C₅	C₂×#121	1	1	yes	characteristic
303	C₄×C₅	—	2	1	no	—
304	C₄×C₅	—	2	1	no	—
305	C₄×C₅	—	4	1	no	—
306	C₄×C₅	—	4	1	no	—
307	C₄×C₅	—	4	1	no	—
308	C₄×C₅	—	8	2	no	—
309	C₄×C₅	#469	1	2	yes	—
310	C₄×C₅	#471	1	2	yes	—
311	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
312	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
313	C₄×C₅	#575	1	2	yes	—
314	C₂⁴	—	4	1	no	—
315	#41	—	2	2	no	—
316	#41	—	2	2	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	4	1	no	—
319	C₂×Q₈	—	4	2	no	—
320	C₂×Q₈	—	4	2	no	—
321	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	4	4	no	—
327	C₂×D₄	—	4	1	no	—
328	C₂×D₄	—	4	1	no	—
329	C₂×D₄	—	4	1	no	—
330	C₂×D₄	—	4	2	no	—
331	C₂×D₄	—	4	2	no	—
332	C₂×D₄	—	8	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	1	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	4	no	—
345	M₁₆	—	4	4	no	—
346	M₁₆	—	4	2	no	—
347	M₁₆	—	4	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	4	2	no	—
352	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
353	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	4	1	no	—
359	C₄⋊C₄	—	4	1	no	—
360	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
361	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
362	C₂²⋊C₄	—	2	1	no	—
363	C₂²⋊C₄	—	2	1	no	—
364	C₂²⋊C₄	—	2	1	no	—
365	C₄²	—	2	1	no	—
366	C₄²	—	2	1	no	—
367	C₄²	—	2	1	no	—
368	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
369	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
370	C₄²	C₅×#41	1	1	yes	characteristic
371	C₄²	C₂⁴×C₅	1	1	yes	characteristic
372	C₂×C₅	—	2	2	no	—
373	C₂×C₅	—	8	1	no	—
374	C₂×C₅	—	16	2	no	—
375	C₂×C₅	#3040	1	1	yes	characteristic
376	C₂×C₅	C₂×#469	1	1	yes	characteristic
377	C₂×C₅	C₂×#471	1	1	yes	characteristic
378	C₂³	—	2	1	no	—
379	C₂³	—	4	2	no	—
380	C₂³	—	8	2	no	—
381	C₂³	—	8	2	no	—
382	C₂³	—	8	2	no	—
383	C₂³	C₅×#121	1	1	yes	characteristic
384	Q₈	—	2	1	no	—
385	Q₈	—	2	1	no	—
386	Q₈	—	4	2	no	—
387	Q₈	—	4	2	no	—
388	Q₈	—	8	2	no	—
389	D₄	—	2	1	no	—
390	D₄	—	2	1	no	—
391	D₄	—	4	2	no	—
392	D₄	—	4	2	no	—
393	D₄	—	4	2	no	—
394	D₄	—	4	4	no	—
395	D₄	—	8	2	no	—
396	D₄	—	8	2	no	—
397	D₄	—	8	2	no	—
398	D₄	—	8	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	8	2	no	—
409	C₂×C₄	C₅×#121	1	1	yes	characteristic
410	C₂×C₄	C₅×#121	1	1	yes	characteristic
411	C₂×C₄	C₅×#121	1	1	yes	characteristic
412	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
413	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	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	2	no	—
418	C₈	—	2	2	no	—
419	C₈	—	4	2	no	—
420	C₈	—	4	2	no	—
421	C₈	—	4	2	no	—
422	C₅	#19301	1	1	yes	characteristic, direct product factor, Sylow
423	C₂²	—	2	1	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	4	1	no	—
426	C₂²	—	4	1	no	—
427	C₂²	—	4	1	no	—
428	C₂²	—	8	2	no	—
429	C₂²	—	8	2	no	—
430	C₂²	—	8	2	no	—
431	C₂²	—	16	4	no	—
432	C₂²	C₅×#469	1	2	yes	—
433	C₂²	C₂×C₅×#121	1	1	yes	characteristic
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	4	1	no	—
437	C₄	—	4	1	no	—
438	C₄	—	4	1	no	—
439	C₄	—	8	2	no	—
440	C₄	C₅×#469	1	2	yes	—
441	C₄	C₅×#471	1	2	yes	—
442	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
443	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
444	C₄	C₅×#575	1	2	yes	—
445	C₂	—	2	2	no	—
446	C₂	—	8	1	no	—
447	C₂	—	16	2	no	—
448	C₂	C₅×#3040	1	1	yes	characteristic
449	C₂	C₂×C₅×#469	1	1	yes	characteristic
450	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×#486	C₂	semidirect
2. C₅×#3039	C₂	semidirect
4. C₅×#2965	C₂	semidirect
5. C₅×#1702	C₂	semidirect
6. C₅×#1701	C₂	semidirect
7. C₅×#1566	C₂	semidirect
8. C₅×#1546	C₂	semidirect
9. C₅×#1545	C₂	semidirect
19. C₅×#462	C₂²	semidirect
21. C₅×#461	C₂²	semidirect
26. C₅×#446	C₂²	semidirect
27. C₅×#436	C₂²	semidirect
38. C₅×#334	C₂²	semidirect
39. C₅×#332	C₂²	semidirect
41. #19301	C₅	direct (N × H)
96. C₂×#486	C₂×C₅	semidirect
97. #3039	C₂×C₅	semidirect
99. #2965	C₂×C₅	semidirect
100. #1702	C₂×C₅	semidirect
101. #1701	C₂×C₅	semidirect
102. #1566	C₂×C₅	semidirect
103. #1546	C₂×C₅	semidirect
104. #1545	C₂×C₅	semidirect
172. #462	C₂²×C₅	semidirect
174. #461	C₂²×C₅	semidirect
179. #446	C₂²×C₅	semidirect
180. #436	C₂²×C₅	semidirect
191. #334	C₂²×C₅	semidirect
192. #332	C₂²×C₅	semidirect
422. C₅	#19301	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×#486	2
C₅×#3039	2
C₅×#3038	2
C₅×#2965	2
C₅×#1702	2
C₅×#1701	2
C₅×#1566	2
C₅×#1546	2
C₅×#1545	2
#19301	5

Subgroups — C5×#19301 #11942021

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19301 #11942021