Subgroups — C₅×#81761 #14439123

Order 1920.

1312 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#914	C₂	1	4	yes	maximal, complemented
2	C₅×#5725	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₃×#127	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#492	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5176	C₂	1	4	yes	maximal, complemented
6	C₅×#5085	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5073	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4695	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₅×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#3151	—	3	1	no	maximal, Hall
11	C₂×C₅×#239	C₂²	1	2	yes	—
12	C₂×C₅×D₃×D₄	—	2	2	no	—
13	C₂×C₅×D₃×D₄	C₂²	1	2	yes	—
14	C₂×C₃×C₅×SD₁₆	C₂²	1	4	yes	complemented
15	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
16	C₃×C₅×#127	C₂²	1	1	yes	characteristic
17	C₅×#947	C₂²	1	2	yes	complemented
18	C₂×C₅×#215	C₂²	1	4	yes	complemented
19	C₅×#940	—	2	2	no	—
20	C₅×#940	C₂²	1	2	yes	—
21	C₂×C₅×#213	C₂²	1	4	yes	complemented
22	C₅×#914	—	2	16	no	—
23	C₂×C₅×D₂₄	C₂²	1	4	yes	complemented
24	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
25	C₅×#895	—	2	2	no	—
26	C₅×#893	—	2	2	no	—
27	C₅×#874	C₂²	1	1	yes	characteristic
28	C₅×#874	C₂²	1	1	yes	characteristic, complemented
29	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
30	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
31	C₅×#815	C₂²	1	2	yes	complemented
32	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
33	#81761	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
34	C₂×C₅×AGL(1,ℤ/8)	—	3	4	no	—
35	C₅×#532	—	3	1	no	—
36	C₂×C₅×#127	—	3	1	no	—
37	C₅×#496	—	3	4	no	—
38	C₅×#493	—	3	1	no	—
39	C₅×#493	—	3	1	no	—
40	C₅×#492	—	3	1	no	—
41	C₅×#492	D₃	1	1	yes	characteristic, complemented
42	C₄×C₅×M₁₆	—	3	1	no	—
43	C₂³×C₅×D₃	—	2	2	no	—
44	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
45	C₂×C₃×C₅×D₄	—	2	2	no	—
46	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
47	C₂×C₅×#67	—	2	2	no	—
48	C₂×C₅×#67	—	2	4	no	—
49	C₅×#239	—	2	8	no	—
50	C₅×D₃×D₄	—	2	8	no	—
51	C₅×D₃×D₄	—	4	8	no	—
52	C₂×C₅×D₁₂	—	2	2	no	—
53	C₂×C₅×D₁₂	—	2	2	no	—
54	C₂×C₅×D₁₂	—	2	2	no	—
55	C₂×C₅×D₁₂	C₂³	1	2	yes	—
56	C₂×C₅×D₁₂	C₂³	1	2	yes	—
57	C₂×C₄×C₅×D₃	—	2	2	no	—
58	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
59	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
60	C₃×C₅×SD₁₆	—	2	8	no	—
61	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
62	C₃×C₅×C₄⋊C₄	—	2	2	no	—
63	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
64	C₅×#215	—	2	8	no	—
65	C₅×#213	—	2	8	no	—
66	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
67	C₄×C₅×Dic₃	D₄	1	2	yes	—
68	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
69	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
70	C₅×D₂₄	—	2	8	no	—
71	C₅×ΓL(1,𝔽₂₅)	D₄	1	8	yes	complemented
72	C₂×#914	C₂×C₅	1	4	yes	complemented
73	#5725	C₂×C₅	1	1	yes	characteristic, complemented
74	D₃×#127	C₂×C₅	1	1	yes	characteristic, complemented
75	C₃×#492	C₂×C₅	1	1	yes	characteristic, complemented
76	#5176	C₂×C₅	1	4	yes	complemented
77	#5085	C₂×C₅	1	1	yes	characteristic, complemented
78	#5073	C₂×C₅	1	1	yes	characteristic, complemented
79	#4695	C₂×C₅	1	1	yes	characteristic, complemented
80	C₄×ΓL(1,𝔽₂₅)	C₂×C₅	1	1	yes	characteristic, complemented
81	C₂×C₅×#41	—	3	2	no	—
82	C₂²×C₅×D₄	—	3	2	no	—
83	C₂²×C₅×D₄	—	6	2	no	—
84	C₅×AGL(1,ℤ/8)	—	6	16	no	—
85	C₂×C₅×SD₁₆	—	3	4	no	—
86	C₂×C₅×SD₁₆	C₂×D₃	1	4	yes	complemented
87	C₂×C₅×D₈	—	3	4	no	—
88	C₂×C₅×D₈	—	3	4	no	—
89	C₂×C₅×M₁₆	—	3	2	no	—
90	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
91	C₅×#127	—	3	2	no	—
92	C₅×#127	—	3	1	no	—
93	C₅×#127	—	3	1	no	—
94	C₅×#127	—	6	2	no	—
95	C₅×#127	C₂×D₃	1	1	yes	characteristic
96	C₅×#124	—	3	2	no	—
97	C₅×#121	—	6	2	no	—
98	C₄×C₅×D₄	—	6	2	no	—
99	C₂×C₄²×C₅	—	3	1	no	—
100	C₅×#97	—	3	2	no	—
101	C₄×C₅×C₈	—	3	1	no	—
102	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic, complemented
103	#3151	—	3	1	no	Sylow
104	C₂³×C₃×C₅	—	2	2	no	—
105	C₂²×C₅×D₃	—	2	2	no	—
106	C₂²×C₅×D₃	—	2	2	no	—
107	C₂²×C₅×D₃	—	4	8	no	—
108	C₂²×C₅×D₃	—	4	4	no	—
109	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
110	C₃×C₅×Q₈	—	2	4	no	—
111	C₃×C₅×D₄	—	2	4	no	—
112	C₃×C₅×D₄	—	4	4	no	—
113	C₂×C₃×C₄×C₅	—	2	2	no	—
114	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
115	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
116	C₅×#67	—	4	8	no	—
117	C₅×#67	—	4	4	no	—
118	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
119	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
120	C₅×D₁₂	—	2	4	no	—
121	C₅×D₁₂	—	2	4	no	—
122	C₅×D₁₂	—	4	4	no	—
123	C₅×D₁₂	—	4	4	no	—
124	C₅×D₁₂	—	4	4	no	—
125	C₄×C₅×D₃	—	2	4	no	—
126	C₄×C₅×D₃	—	4	4	no	—
127	C₄×C₅×D₃	C₂×D₄	1	4	yes	—
128	C₃×C₅×C₈	C₂×D₄	1	4	yes	complemented
129	C₅×C₃⋊C₈	C₂×D₄	1	4	yes	complemented
130	C₂×#239	C₂²×C₅	1	2	yes	—
131	C₂×D₃×D₄	—	2	2	no	—
132	C₂×D₃×D₄	C₂²×C₅	1	2	yes	—
133	C₂×C₃×SD₁₆	C₂²×C₅	1	4	yes	complemented
134	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
135	C₃×#127	C₂²×C₅	1	1	yes	characteristic
136	#947	C₂²×C₅	1	2	yes	complemented
137	C₂×#215	C₂²×C₅	1	4	yes	complemented
138	#940	—	2	2	no	—
139	#940	C₂²×C₅	1	2	yes	—
140	C₂×#213	C₂²×C₅	1	4	yes	complemented
141	#914	—	2	16	no	—
142	C₂×D₂₄	C₂²×C₅	1	4	yes	complemented
143	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	2	yes	—
144	#895	—	2	2	no	—
145	#893	—	2	2	no	—
146	#874	C₂²×C₅	1	1	yes	characteristic
147	#874	C₂²×C₅	1	1	yes	characteristic, complemented
148	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
149	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
150	#815	C₂²×C₅	1	2	yes	complemented
151	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
152	C₂⁴×C₅	—	6	2	no	—
153	C₅×#41	—	6	8	no	—
154	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
155	C₂×C₅×D₄	—	2	2	no	—
156	C₂×C₅×D₄	—	3	2	no	—
157	C₂×C₅×D₄	—	3	2	no	—
158	C₂×C₅×D₄	—	6	2	no	—
159	C₂×C₅×D₄	—	6	8	no	—
160	C₂×C₅×D₄	—	6	4	no	—
161	C₂×C₅×D₄	—	6	2	no	—
162	C₂×C₅×D₄	—	6	2	no	—
163	C₂×C₅×D₄	—	6	2	no	—
164	C₂×C₅×D₄	—	12	8	no	—
165	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
166	C₂²×C₄×C₅	—	3	1	no	—
167	C₂²×C₄×C₅	—	3	2	no	—
168	C₂²×C₄×C₅	—	6	2	no	—
169	C₅×SD₁₆	—	2	8	no	—
170	C₅×SD₁₆	—	6	8	no	—
171	C₅×D₈	—	6	8	no	—
172	C₅×D₈	—	6	8	no	—
173	C₅×M₁₆	—	3	8	no	—
174	C₂×C₅×C₈	—	3	2	no	—
175	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
176	C₅×C₄⋊C₄	—	2	2	no	—
177	C₅×C₂²⋊C₄	—	6	4	no	—
178	C₄²×C₅	—	3	2	no	—
179	C₄²×C₅	—	3	1	no	—
180	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
181	C₂×AGL(1,ℤ/8)	—	3	4	no	—
182	#532	—	3	1	no	—
183	C₂×#127	—	3	1	no	—
184	#496	—	3	4	no	—
185	#493	—	3	1	no	—
186	#493	—	3	1	no	—
187	#492	—	3	1	no	—
188	#492	C₅×D₃	1	1	yes	characteristic, complemented
189	C₄×M₁₆	—	3	1	no	—
190	C₂²×C₃×C₅	—	4	2	no	—
191	C₂²×C₃×C₅	—	4	4	no	—
192	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₅×D₃	—	2	2	no	—
194	C₂×C₅×D₃	—	4	2	no	—
195	C₂×C₅×D₃	—	4	2	no	—
196	C₂×C₅×D₃	—	4	4	no	—
197	C₂×C₅×D₃	—	4	4	no	—
198	C₂×C₅×D₃	—	8	8	no	—
199	C₂×C₅×D₃	#127	1	2	yes	—
200	C₃×C₄×C₅	—	4	2	no	—
201	C₃×C₄×C₅	AGL(1,ℤ/8)	1	4	yes	complemented
202	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
203	C₅×Dic₃	—	2	2	no	—
204	C₅×Dic₃	#127	1	2	yes	—
205	C₂³×D₃	—	2	2	no	—
206	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
207	C₂×C₃×D₄	—	2	2	no	—
208	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
209	C₂×#67	—	2	2	no	—
210	C₂×#67	—	2	4	no	—
211	#239	—	2	8	no	—
212	D₃×D₄	—	2	8	no	—
213	D₃×D₄	—	4	8	no	—
214	C₂×D₁₂	—	2	2	no	—
215	C₂×D₁₂	—	2	2	no	—
216	C₂×D₁₂	—	2	2	no	—
217	C₂×D₁₂	C₂³×C₅	1	2	yes	—
218	C₂×D₁₂	C₂³×C₅	1	2	yes	—
219	C₂×C₄×D₃	—	2	2	no	—
220	C₂×C₄×D₃	C₅×D₄	1	2	yes	—
221	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
222	C₃×SD₁₆	—	2	8	no	—
223	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
224	C₃×C₄⋊C₄	—	2	2	no	—
225	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
226	#215	—	2	8	no	—
227	#213	—	2	8	no	—
228	(C₂×D₃)⋊C₄	—	2	4	no	—
229	C₄×Dic₃	C₅×D₄	1	2	yes	—
230	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
231	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
232	D₂₄	—	2	8	no	—
233	ΓL(1,𝔽₂₅)	C₅×D₄	1	8	yes	complemented
234	C₂³×C₅	—	2	2	no	—
235	C₂³×C₅	—	3	1	no	—
236	C₂³×C₅	—	6	2	no	—
237	C₂³×C₅	—	6	2	no	—
238	C₂³×C₅	—	12	4	no	—
239	C₂³×C₅	—	12	8	no	—
240	C₅×Q₈	—	2	4	no	—
241	C₅×D₄	—	2	4	no	—
242	C₅×D₄	—	4	4	no	—
243	C₅×D₄	—	6	4	no	—
244	C₅×D₄	—	6	4	no	—
245	C₅×D₄	—	12	4	no	—
246	C₅×D₄	—	12	4	no	—
247	C₅×D₄	—	12	8	no	—
248	C₅×D₄	—	12	4	no	—
249	C₅×D₄	—	12	4	no	—
250	C₂×C₄×C₅	—	2	2	no	—
251	C₂×C₄×C₅	—	3	1	no	—
252	C₂×C₄×C₅	—	3	4	no	—
253	C₂×C₄×C₅	—	3	2	no	—
254	C₂×C₄×C₅	—	6	4	no	—
255	C₂×C₄×C₅	—	12	4	no	—
256	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
257	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
258	C₅×C₈	—	3	4	no	—
259	C₅×C₈	D₃×D₄	1	4	yes	complemented
260	C₂×#41	—	3	2	no	—
261	C₂²×D₄	—	3	2	no	—
262	C₂²×D₄	—	6	2	no	—
263	AGL(1,ℤ/8)	—	6	16	no	—
264	C₂×SD₁₆	—	3	4	no	—
265	C₂×SD₁₆	C₂×C₅×D₃	1	4	yes	complemented
266	C₂×D₈	—	3	4	no	—
267	C₂×D₈	—	3	4	no	—
268	C₂×M₁₆	—	3	2	no	—
269	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
270	#127	—	3	2	no	—
271	#127	—	3	1	no	—
272	#127	—	3	1	no	—
273	#127	—	6	2	no	—
274	#127	C₂×C₅×D₃	1	1	yes	characteristic
275	#124	—	3	2	no	—
276	#121	—	6	2	no	—
277	C₄×D₄	—	6	2	no	—
278	C₂×C₄²	—	3	1	no	—
279	#97	—	3	2	no	—
280	C₄×C₈	—	3	1	no	—
281	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
282	C₂×C₃×C₅	—	8	2	no	—
283	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
284	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	2	yes	—
285	C₅×D₃	—	2	2	no	—
286	C₅×D₃	—	8	2	no	—
287	C₅×D₃	—	8	2	no	—
288	C₂³×C₃	—	2	2	no	—
289	C₂²×D₃	—	2	2	no	—
290	C₂²×D₃	—	2	2	no	—
291	C₂²×D₃	—	4	8	no	—
292	C₂²×D₃	—	4	4	no	—
293	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
294	C₃×Q₈	—	2	4	no	—
295	C₃×D₄	—	2	4	no	—
296	C₃×D₄	—	4	4	no	—
297	C₂×C₃×C₄	—	2	2	no	—
298	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
299	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
300	#67	—	4	8	no	—
301	#67	—	4	4	no	—
302	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
303	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
304	D₁₂	—	2	4	no	—
305	D₁₂	—	2	4	no	—
306	D₁₂	—	4	4	no	—
307	D₁₂	—	4	4	no	—
308	D₁₂	—	4	4	no	—
309	C₄×D₃	—	2	4	no	—
310	C₄×D₃	—	4	4	no	—
311	C₄×D₃	C₂×C₅×D₄	1	4	yes	—
312	C₃×C₈	C₂×C₅×D₄	1	4	yes	complemented
313	C₃⋊C₈	C₂×C₅×D₄	1	4	yes	complemented
314	C₂²×C₅	—	3	2	no	—
315	C₂²×C₅	—	4	2	no	—
316	C₂²×C₅	—	4	4	no	—
317	C₂²×C₅	—	6	2	no	—
318	C₂²×C₅	—	12	2	no	—
319	C₂²×C₅	—	12	2	no	—
320	C₂²×C₅	—	12	4	no	—
321	C₂²×C₅	—	12	4	no	—
322	C₂²×C₅	—	24	8	no	—
323	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
324	C₄×C₅	—	3	2	no	—
325	C₄×C₅	—	4	2	no	—
326	C₄×C₅	—	6	2	no	—
327	C₄×C₅	#914	1	4	yes	complemented
328	C₄×C₅	C₂×D₃×D₄	1	2	yes	—
329	C₂⁴	—	6	2	no	—
330	#41	—	6	8	no	—
331	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	3	2	no	—
334	C₂×D₄	—	3	2	no	—
335	C₂×D₄	—	6	2	no	—
336	C₂×D₄	—	6	8	no	—
337	C₂×D₄	—	6	4	no	—
338	C₂×D₄	—	6	2	no	—
339	C₂×D₄	—	6	2	no	—
340	C₂×D₄	—	6	2	no	—
341	C₂×D₄	—	12	8	no	—
342	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
343	C₂²×C₄	—	3	1	no	—
344	C₂²×C₄	—	3	2	no	—
345	C₂²×C₄	—	6	2	no	—
346	SD₁₆	—	2	8	no	—
347	SD₁₆	—	6	8	no	—
348	D₈	—	6	8	no	—
349	D₈	—	6	8	no	—
350	M₁₆	—	3	8	no	—
351	C₂×C₈	—	3	2	no	—
352	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
353	C₄⋊C₄	—	2	2	no	—
354	C₂²⋊C₄	—	6	4	no	—
355	C₄²	—	3	2	no	—
356	C₄²	—	3	1	no	—
357	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
358	C₃×C₅	#3151	1	1	yes	characteristic, complemented, Hall
359	C₂²×C₃	—	4	2	no	—
360	C₂²×C₃	—	4	4	no	—
361	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
362	C₂×D₃	—	2	2	no	—
363	C₂×D₃	—	4	2	no	—
364	C₂×D₃	—	4	2	no	—
365	C₂×D₃	—	4	4	no	—
366	C₂×D₃	—	4	4	no	—
367	C₂×D₃	—	8	8	no	—
368	C₂×D₃	C₅×#127	1	2	yes	—
369	C₃×C₄	—	4	2	no	—
370	C₃×C₄	C₅×AGL(1,ℤ/8)	1	4	yes	complemented
371	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
372	Dic₃	—	2	2	no	—
373	Dic₃	C₅×#127	1	2	yes	—
374	C₂×C₅	—	6	2	no	—
375	C₂×C₅	—	8	2	no	—
376	C₂×C₅	—	24	2	no	—
377	C₂×C₅	—	24	2	no	—
378	C₂×C₅	D₃×#127	1	1	yes	characteristic
379	C₂×C₅	C₂×#914	1	2	yes	—
380	C₂³	—	2	2	no	—
381	C₂³	—	3	1	no	—
382	C₂³	—	6	2	no	—
383	C₂³	—	6	2	no	—
384	C₂³	—	12	4	no	—
385	C₂³	—	12	8	no	—
386	Q₈	—	2	4	no	—
387	D₄	—	2	4	no	—
388	D₄	—	4	4	no	—
389	D₄	—	6	4	no	—
390	D₄	—	6	4	no	—
391	D₄	—	12	4	no	—
392	D₄	—	12	4	no	—
393	D₄	—	12	8	no	—
394	D₄	—	12	4	no	—
395	D₄	—	12	4	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	3	1	no	—
398	C₂×C₄	—	3	4	no	—
399	C₂×C₄	—	3	2	no	—
400	C₂×C₄	—	6	4	no	—
401	C₂×C₄	—	12	4	no	—
402	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
403	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
404	C₈	—	3	4	no	—
405	C₈	C₅×D₃×D₄	1	4	yes	complemented
406	C₂×C₃	—	8	2	no	—
407	C₂×C₃	C₂×C₅×#127	1	1	yes	characteristic
408	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	2	yes	—
409	D₃	—	2	2	no	—
410	D₃	—	8	2	no	—
411	D₃	—	8	2	no	—
412	C₅	#81761	1	1	yes	characteristic, direct product factor, Sylow
413	C₂²	—	3	2	no	—
414	C₂²	—	4	2	no	—
415	C₂²	—	4	4	no	—
416	C₂²	—	6	2	no	—
417	C₂²	—	12	2	no	—
418	C₂²	—	12	2	no	—
419	C₂²	—	12	4	no	—
420	C₂²	—	12	4	no	—
421	C₂²	—	24	8	no	—
422	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
423	C₄	—	3	2	no	—
424	C₄	—	4	2	no	—
425	C₄	—	6	2	no	—
426	C₄	C₅×#914	1	4	yes	complemented
427	C₄	C₂×C₅×D₃×D₄	1	2	yes	—
428	C₃	C₅×#3151	1	1	yes	characteristic, complemented, Sylow
429	C₂	—	6	2	no	—
430	C₂	—	8	2	no	—
431	C₂	—	24	2	no	—
432	C₂	—	24	2	no	—
433	C₂	C₅×D₃×#127	1	1	yes	characteristic
434	C₂	C₂×C₅×#914	1	2	yes	—

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#492	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₅×#492	D₃
hypocenter	C₃	C₅×#3151
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#492

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#914	C₂	semidirect
2. C₅×#5725	C₂	semidirect
3. C₅×D₃×#127	C₂	semidirect
4. C₃×C₅×#492	C₂	semidirect
5. C₅×#5176	C₂	semidirect
6. C₅×#5085	C₂	semidirect
7. C₅×#5073	C₂	semidirect
8. C₅×#4695	C₂	semidirect
9. C₄×C₅×ΓL(1,𝔽₂₅)	C₂	semidirect
14. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
15. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
17. C₅×#947	C₂²	semidirect
18. C₂×C₅×#215	C₂²	semidirect
21. C₂×C₅×#213	C₂²	semidirect
23. C₂×C₅×D₂₄	C₂²	semidirect
28. C₅×#874	C₂²	semidirect
30. C₃×C₄×C₅×C₈	C₂²	semidirect
31. C₅×#815	C₂²	semidirect
32. C₄×C₅×C₃⋊C₈	C₂²	semidirect
33. #81761	C₅	direct (N × H)
41. C₅×#492	D₃	semidirect
71. C₅×ΓL(1,𝔽₂₅)	D₄	semidirect
72. C₂×#914	C₂×C₅	semidirect
73. #5725	C₂×C₅	semidirect
74. D₃×#127	C₂×C₅	semidirect
75. C₃×#492	C₂×C₅	semidirect
76. #5176	C₂×C₅	semidirect
77. #5085	C₂×C₅	semidirect
78. #5073	C₂×C₅	semidirect
79. #4695	C₂×C₅	semidirect
80. C₄×ΓL(1,𝔽₂₅)	C₂×C₅	semidirect
86. C₂×C₅×SD₁₆	C₂×D₃	semidirect
90. C₅×C₄⋊Q₈	C₂×D₃	semidirect
102. C₄×C₅×C₈	C₂×D₃	semidirect
128. C₃×C₅×C₈	C₂×D₄	semidirect
129. C₅×C₃⋊C₈	C₂×D₄	semidirect
133. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
134. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
136. #947	C₂²×C₅	semidirect
137. C₂×#215	C₂²×C₅	semidirect
140. C₂×#213	C₂²×C₅	semidirect
142. C₂×D₂₄	C₂²×C₅	semidirect
147. #874	C₂²×C₅	semidirect
149. C₃×C₄×C₈	C₂²×C₅	semidirect
150. #815	C₂²×C₅	semidirect
151. C₄×C₃⋊C₈	C₂²×C₅	semidirect
188. #492	C₅×D₃	semidirect
201. C₃×C₄×C₅	AGL(1,ℤ/8)	semidirect
233. ΓL(1,𝔽₂₅)	C₅×D₄	semidirect
259. C₅×C₈	D₃×D₄	semidirect
265. C₂×SD₁₆	C₂×C₅×D₃	semidirect
269. C₄⋊Q₈	C₂×C₅×D₃	semidirect
281. C₄×C₈	C₂×C₅×D₃	semidirect
312. C₃×C₈	C₂×C₅×D₄	semidirect
313. C₃⋊C₈	C₂×C₅×D₄	semidirect
327. C₄×C₅	#914	semidirect
358. C₃×C₅	#3151	semidirect
370. C₃×C₄	C₅×AGL(1,ℤ/8)	semidirect
405. C₈	C₅×D₃×D₄	semidirect
412. C₅	#81761	direct (N × H)
426. C₄	C₅×#914	semidirect
428. C₃	C₅×#3151	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#914	2
C₅×#5725	2
C₅×D₃×#127	2
C₃×C₅×#492	2
C₅×#5176	2
C₅×#5085	2
C₅×#5073	2
C₅×#4695	2
C₄×C₅×ΓL(1,𝔽₂₅)	2
C₅×#3151	3
#81761	5

Subgroups — C5×#81761 #14439123

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#81761 #14439123