Subgroups — C₄×D₅×ΓL(1,𝔽₂₅) #14411246

Order 1920.

1312 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₅×ΓL(1,𝔽₂₅)	C₂	1	2	yes	maximal
2	C₄²×D₃×D₅	C₂	1	1	yes	maximal, characteristic
3	C₄×#6705	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₅×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₄×C₈×D₅	C₂	1	1	yes	maximal, characteristic, complemented
6	#11747592	C₂	1	2	yes	maximal, complemented
7	Dic₅×ΓL(1,𝔽₂₅)	C₂	1	2	yes	maximal, complemented
8	D₅×#815	C₂	1	2	yes	maximal, complemented
9	C₄×#6651	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#6650	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×D₅×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×D₅×M₁₆	—	3	1	no	maximal, Hall
13	C₂×C₄×D₃×D₅	C₄	1	2	yes	—
14	C₂×C₄×D₃×D₅	C₂²	1	1	yes	characteristic
15	C₂×#6705	C₂²	1	2	yes	—
16	C₄²×D₁₅	C₂²	1	1	yes	characteristic
17	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
18	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
20	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
21	C₄×#1200	C₄	1	2	yes	—
22	C₄×#1200	C₂²	1	1	yes	characteristic
23	C₄×D₃×Dic₅	C₄	1	2	yes	—
24	C₄×D₃×Dic₅	C₂²	1	1	yes	characteristic
25	C₄×D₅×Dic₃	C₄	1	2	yes	—
26	C₄×D₅×Dic₃	C₂²	1	1	yes	characteristic
27	C₂×#6651	C₂²	1	2	yes	—
28	C₂×#6650	C₂²	1	2	yes	—
29	C₂×D₅×C₃⋊C₈	C₂²	1	2	yes	—
30	D₅×ΓL(1,𝔽₂₅)	C₄	1	16	yes	direct product factor
31	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
32	#91099	C₂²	1	2	yes	complemented
33	C₄×C₃⋊#168	C₂²	1	1	yes	characteristic, complemented
34	C₅×#815	C₂²	1	2	yes	complemented
35	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
36	C₃×C₈×Dic₅	C₂²	1	2	yes	complemented
37	C₃×C₄×#168	C₂²	1	1	yes	characteristic, complemented
38	#90954	C₂²	1	2	yes	complemented
39	#90953	C₂²	1	2	yes	complemented
40	Dic₅×C₃⋊C₈	C₂²	1	2	yes	complemented
41	C₂×C₄×ΓL(1,𝔽₂₅)	—	5	1	no	maximal, Hall
42	C₂×D₅×M₁₆	—	3	2	no	—
43	C₂×C₄²×D₅	—	3	1	no	—
44	C₄×C₅×M₁₆	—	3	1	no	—
45	M₁₆×Dic₅	—	3	2	no	—
46	C₄×#681	—	3	1	no	—
47	#64996	—	3	2	no	—
48	D₅×#97	—	3	2	no	—
49	C₄×#676	—	3	1	no	—
50	C₄×#676	—	3	1	no	—
51	C₄×C₈×D₅	—	3	1	no	—
52	C₄×C₈×D₅	D₃	1	1	yes	characteristic, complemented
53	C₂²×D₃×D₅	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄×D₁₅	C₂×C₄	1	2	yes	—
55	C₂×C₄×D₁₅	C₂³	1	1	yes	characteristic
56	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
57	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
58	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
59	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
60	C₂×#1200	C₂×C₄	1	2	yes	—
61	C₂×#1200	C₂×C₄	1	1	yes	characteristic
62	C₂×D₃×Dic₅	C₂×C₄	1	2	yes	—
63	C₂×D₃×Dic₅	C₂×C₄	1	1	yes	characteristic
64	C₂×D₅×Dic₃	C₂×C₄	1	2	yes	—
65	C₂×D₅×Dic₃	C₂×C₄	1	1	yes	characteristic
66	C₄×D₃×D₅	—	2	8	no	—
67	C₄×D₃×D₅	C₂×C₄	1	8	yes	—
68	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
69	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
70	C₄×Dic₁₅	C₂×C₄	1	2	yes	—
71	C₄×Dic₁₅	C₂³	1	1	yes	characteristic
72	C₂×C₃⋊#168	C₂³	1	2	yes	—
73	#6705	C₂×C₄	1	8	yes	complemented
74	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
75	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
76	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
77	C₅×ΓL(1,𝔽₂₅)	C₂×C₄	1	8	yes	complemented
78	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
79	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
80	C₂×C₃×#168	C₂³	1	2	yes	—
81	C₃×C₈×D₅	C₂×C₄	1	8	yes	complemented
82	Dic₃×Dic₅	C₂×C₄	1	2	yes	—
83	Dic₃×Dic₅	C₂×C₄	1	2	yes	—
84	Dic₃×Dic₅	C₂×C₄	1	2	yes	—
85	#6651	C₂×C₄	1	8	yes	complemented
86	#6650	C₂×C₄	1	8	yes	complemented
87	D₅×C₃⋊C₈	C₂×C₄	1	8	yes	complemented
88	C₂²×ΓL(1,𝔽₂₅)	—	5	2	no	—
89	C₂×C₄²×D₃	—	5	1	no	—
90	C₂×C₃×C₄×C₈	—	5	1	no	—
91	C₂×#815	—	5	2	no	—
92	C₂×C₄×C₃⋊C₈	—	5	1	no	—
93	C₄×ΓL(1,𝔽₂₅)	—	5	2	no	—
94	C₄×ΓL(1,𝔽₂₅)	—	5	1	no	—
95	C₄×ΓL(1,𝔽₂₅)	—	5	1	no	—
96	C₄×ΓL(1,𝔽₂₅)	—	5	2	no	—
97	C₄×ΓL(1,𝔽₂₅)	—	5	1	no	—
98	C₄×ΓL(1,𝔽₂₅)	D₅	1	1	yes	characteristic, direct product factor
99	C₂²×C₄×D₅	—	3	1	no	—
100	C₂²×C₄×D₅	—	3	2	no	—
101	C₂×C₅×M₁₆	—	3	2	no	—
102	C₂×C₄²×C₅	—	3	1	no	—
103	C₂×C₄×Dic₅	—	3	2	no	—
104	C₂×C₄×Dic₅	—	3	1	no	—
105	C₂×#681	—	3	2	no	—
106	D₅×M₁₆	—	3	16	no	—
107	C₂×#676	—	3	2	no	—
108	C₂×#676	—	3	2	no	—
109	C₂×C₈×D₅	—	3	2	no	—
110	C₂×C₈×D₅	C₂×D₃	1	2	yes	—
111	C₄²×D₅	—	3	2	no	—
112	C₄²×D₅	—	3	1	no	—
113	C₄²×D₅	—	3	1	no	—
114	C₄²×D₅	—	3	2	no	—
115	C₄²×D₅	—	3	1	no	—
116	C₄²×D₅	C₂×D₃	1	1	yes	characteristic
117	C₅×#97	—	3	2	no	—
118	C₄×C₅×C₈	—	3	1	no	—
119	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic, complemented
120	#3947	—	3	2	no	—
121	#3947	—	3	2	no	—
122	C₈×Dic₅	—	3	2	no	—
123	C₈×Dic₅	C₂×D₃	1	2	yes	complemented
124	#3935	—	3	2	no	—
125	C₄×#168	—	3	1	no	—
126	C₄×#168	C₂×D₃	1	1	yes	characteristic, complemented
127	C₂×C₄×M₁₆	—	15	1	no	Sylow
128	C₂²×D₁₅	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
131	C₂×D₃×D₅	—	2	4	no	—
132	C₂×D₃×D₅	C₄²	1	4	yes	—
133	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
134	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
135	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
136	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
137	C₄×D₁₅	—	2	4	no	—
138	C₄×D₁₅	C₂²×C₄	1	4	yes	—
139	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
140	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
141	C₄×C₅×D₃	—	2	4	no	—
142	C₄×C₅×D₃	C₂²×C₄	1	4	yes	—
143	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
144	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
145	C₃×C₄×D₅	M₁₆	1	8	yes	complemented
146	C₃×C₄×D₅	C₂²×C₄	1	4	yes	—
147	#1200	—	2	4	no	—
148	#1200	C₄²	1	4	yes	—
149	D₃×Dic₅	—	2	4	no	—
150	D₃×Dic₅	C₄²	1	4	yes	—
151	D₅×Dic₃	—	2	4	no	—
152	D₅×Dic₃	C₄²	1	4	yes	—
153	C₃×C₅×C₈	C₂²×C₄	1	4	yes	complemented
154	C₃⋊#168	C₂²×C₄	1	4	yes	complemented
155	C₃×#168	C₂²×C₄	1	4	yes	complemented
156	C₅×C₃⋊C₈	C₂²×C₄	1	4	yes	complemented
157	C₂²×C₄×D₃	—	5	1	no	—
158	C₂²×C₄×D₃	—	5	2	no	—
159	C₂²×C₃×C₈	—	5	2	no	—
160	C₂×C₃×C₄²	—	5	1	no	—
161	C₂×C₄×Dic₃	—	5	2	no	—
162	C₂×C₄×Dic₃	—	5	1	no	—
163	C₂²×C₃⋊C₈	—	5	2	no	—
164	C₂×ΓL(1,𝔽₂₅)	—	5	2	no	—
165	C₂×ΓL(1,𝔽₂₅)	—	5	2	no	—
166	C₂×ΓL(1,𝔽₂₅)	—	5	2	no	—
167	C₂×ΓL(1,𝔽₂₅)	—	5	16	no	—
168	C₂×ΓL(1,𝔽₂₅)	C₂×D₅	1	2	yes	—
169	C₄²×D₃	—	5	2	no	—
170	C₄²×D₃	—	5	1	no	—
171	C₄²×D₃	—	5	1	no	—
172	C₄²×D₃	—	5	2	no	—
173	C₄²×D₃	—	5	1	no	—
174	C₄²×D₃	C₂×D₅	1	1	yes	characteristic
175	C₃×C₄×C₈	—	5	2	no	—
176	C₃×C₄×C₈	—	5	1	no	—
177	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic, complemented
178	#815	—	5	2	no	—
179	#815	—	5	2	no	—
180	#815	—	5	2	no	—
181	#815	C₂×D₅	1	2	yes	complemented
182	C₄×C₃⋊C₈	—	5	1	no	—
183	C₄×C₃⋊C₈	—	5	2	no	—
184	C₄×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic, complemented
185	C₂³×D₅	—	3	1	no	—
186	C₂²×C₄×C₅	—	3	1	no	—
187	C₂²×C₄×C₅	—	3	2	no	—
188	C₂²×Dic₅	—	3	1	no	—
189	C₂²×Dic₅	—	3	2	no	—
190	C₂×C₄×D₅	—	3	1	no	—
191	C₂×C₄×D₅	—	3	1	no	—
192	C₂×C₄×D₅	—	3	1	no	—
193	C₂×C₄×D₅	—	3	8	no	—
194	C₂×C₄×D₅	—	3	2	no	—
195	C₂×C₄×D₅	—	3	2	no	—
196	C₂×C₄×D₅	—	3	2	no	—
197	C₂×C₄×D₅	—	6	8	no	—
198	C₂×C₄×D₅	C₄×D₃	1	2	yes	—
199	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
200	C₅×M₁₆	—	3	8	no	—
201	C₂×C₅×C₈	—	3	2	no	—
202	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
203	C₄²×C₅	—	3	2	no	—
204	C₄²×C₅	—	3	1	no	—
205	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
206	C₄×Dic₅	—	3	2	no	—
207	C₄×Dic₅	—	3	1	no	—
208	C₄×Dic₅	—	3	2	no	—
209	C₄×Dic₅	—	3	2	no	—
210	C₄×Dic₅	—	3	2	no	—
211	C₄×Dic₅	C₄×D₃	1	2	yes	—
212	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
213	#681	—	3	8	no	—
214	C₂×#168	—	3	2	no	—
215	C₂×#168	C₂²×D₃	1	2	yes	—
216	#676	—	3	8	no	—
217	#676	—	3	8	no	—
218	C₈×D₅	—	3	8	no	—
219	C₈×D₅	C₄×D₃	1	8	yes	complemented
220	C₂²×M₁₆	—	15	2	no	—
221	C₂²×C₄²	—	15	1	no	—
222	C₄×M₁₆	—	3	1	no	—
223	C₄×M₁₆	—	15	1	no	—
224	C₄×M₁₆	—	15	2	no	—
225	C₄×M₁₆	—	15	1	no	—
226	C₄×M₁₆	—	15	2	no	—
227	C₄×M₁₆	—	15	1	no	—
228	C₂×#97	—	15	2	no	—
229	C₂×C₄×C₈	—	5	1	no	—
230	C₂×C₄×C₈	—	15	1	no	—
231	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
232	C₂×D₁₅	—	2	2	no	—
233	C₂×D₁₅	C₂×C₄²	1	2	yes	—
234	C₂×C₅×D₃	—	2	2	no	—
235	C₂×C₅×D₃	C₂×C₄²	1	2	yes	—
236	C₂×C₃×D₅	C₂×C₄²	1	2	yes	—
237	C₂×C₃×D₅	C₂×M₁₆	1	4	yes	—
238	D₃×D₅	—	2	8	no	—
239	C₃×C₄×C₅	C₂×M₁₆	1	4	yes	complemented
240	C₃×C₄×C₅	C₂³×C₄	1	2	yes	—
241	Dic₁₅	—	2	2	no	—
242	Dic₁₅	C₂×C₄²	1	2	yes	—
243	C₃×Dic₅	C₂×C₄²	1	2	yes	—
244	C₃×Dic₅	C₂×M₁₆	1	4	yes	complemented
245	C₅×Dic₃	—	2	2	no	—
246	C₅×Dic₃	C₂×C₄²	1	2	yes	—
247	C₂³×D₃	—	5	1	no	—
248	C₂²×C₃×C₄	—	5	2	no	—
249	C₂²×C₃×C₄	—	5	1	no	—
250	C₂²×Dic₃	—	5	1	no	—
251	C₂²×Dic₃	—	5	2	no	—
252	C₂×C₄×D₃	—	5	1	no	—
253	C₂×C₄×D₃	—	5	1	no	—
254	C₂×C₄×D₃	—	5	1	no	—
255	C₂×C₄×D₃	—	5	8	no	—
256	C₂×C₄×D₃	—	5	2	no	—
257	C₂×C₄×D₃	—	5	2	no	—
258	C₂×C₄×D₃	—	5	2	no	—
259	C₂×C₄×D₃	—	10	8	no	—
260	C₂×C₄×D₃	C₄×D₅	1	2	yes	—
261	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
262	C₂×C₃×C₈	—	5	2	no	—
263	C₂×C₃×C₈	—	5	8	no	—
264	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
265	C₃×C₄²	—	5	2	no	—
266	C₃×C₄²	—	5	1	no	—
267	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
268	C₄×Dic₃	—	5	2	no	—
269	C₄×Dic₃	—	5	1	no	—
270	C₄×Dic₃	—	5	2	no	—
271	C₄×Dic₃	—	5	2	no	—
272	C₄×Dic₃	—	5	2	no	—
273	C₄×Dic₃	C₄×D₅	1	2	yes	—
274	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
275	C₂×C₃⋊C₈	—	5	2	no	—
276	C₂×C₃⋊C₈	—	5	8	no	—
277	C₂×C₃⋊C₈	C₂²×D₅	1	2	yes	—
278	ΓL(1,𝔽₂₅)	—	5	8	no	—
279	ΓL(1,𝔽₂₅)	—	5	8	no	—
280	ΓL(1,𝔽₂₅)	—	5	8	no	—
281	ΓL(1,𝔽₂₅)	C₄×D₅	1	8	yes	direct product factor
282	C₂³×C₅	—	3	1	no	—
283	C₂²×D₅	—	3	1	no	—
284	C₂²×D₅	—	3	4	no	—
285	C₂²×D₅	—	6	4	no	—
286	C₂²×D₅	C₂×C₄×D₃	1	1	yes	characteristic
287	C₂×C₄×C₅	—	3	1	no	—
288	C₂×C₄×C₅	—	3	4	no	—
289	C₂×C₄×C₅	—	3	2	no	—
290	C₂×C₄×C₅	—	6	4	no	—
291	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
292	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
293	C₂×Dic₅	—	3	1	no	—
294	C₂×Dic₅	—	3	4	no	—
295	C₂×Dic₅	—	3	2	no	—
296	C₂×Dic₅	—	6	4	no	—
297	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
298	C₂×Dic₅	C₂×C₄×D₃	1	2	yes	—
299	C₄×D₅	—	3	4	no	—
300	C₄×D₅	—	3	4	no	—
301	C₄×D₅	—	3	4	no	—
302	C₄×D₅	—	6	4	no	—
303	C₄×D₅	—	6	4	no	—
304	C₄×D₅	—	6	4	no	—
305	C₄×D₅	ΓL(1,𝔽₂₅)	1	8	yes	direct product factor
306	C₄×D₅	C₂×C₄×D₃	1	4	yes	—
307	C₅×C₈	—	3	4	no	—
308	C₅×C₈	C₂×C₄×D₃	1	4	yes	complemented
309	#168	—	3	4	no	—
310	#168	C₂×C₄×D₃	1	4	yes	complemented
311	C₂³×C₄	—	15	1	no	—
312	C₂³×C₄	—	15	2	no	—
313	C₂×M₁₆	—	3	2	no	—
314	C₂×M₁₆	—	15	2	no	—
315	C₂×M₁₆	—	15	16	no	—
316	C₂×M₁₆	—	15	2	no	—
317	C₂×M₁₆	—	15	2	no	—
318	C₂²×C₈	—	5	2	no	—
319	C₂²×C₈	—	15	2	no	—
320	C₂×C₄²	—	3	1	no	—
321	C₂×C₄²	—	5	1	no	—
322	C₂×C₄²	—	15	1	no	—
323	C₂×C₄²	—	15	2	no	—
324	C₂×C₄²	—	15	1	no	—
325	C₂×C₄²	—	15	2	no	—
326	C₂×C₄²	—	15	1	no	—
327	C₂×C₄²	—	15	2	no	—
328	C₂×C₄²	—	15	1	no	—
329	#97	—	3	2	no	—
330	#97	—	15	2	no	—
331	#97	—	15	2	no	—
332	#97	—	15	2	no	—
333	C₄×C₈	—	3	1	no	—
334	C₄×C₈	—	5	2	no	—
335	C₄×C₈	—	5	1	no	—
336	C₄×C₈	—	15	2	no	—
337	C₄×C₈	—	15	1	no	—
338	C₄×C₈	D₃×D₅	1	1	yes	characteristic, complemented
339	C₂×C₃×C₅	C₂²×C₄²	1	1	yes	characteristic
340	C₂×C₃×C₅	C₂²×M₁₆	1	2	yes	—
341	D₁₅	—	2	2	no	—
342	C₃×D₅	C₄×M₁₆	1	4	yes	complemented
343	C₅×D₃	—	2	2	no	—
344	C₂³×C₃	—	5	1	no	—
345	C₂²×D₃	—	5	1	no	—
346	C₂²×D₃	—	5	4	no	—
347	C₂²×D₃	—	10	4	no	—
348	C₂²×D₃	C₂×C₄×D₅	1	1	yes	characteristic
349	C₂×C₃×C₄	—	5	1	no	—
350	C₂×C₃×C₄	—	5	2	no	—
351	C₂×C₃×C₄	—	5	4	no	—
352	C₂×C₃×C₄	—	5	8	no	—
353	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
354	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
355	C₂×Dic₃	—	5	1	no	—
356	C₂×Dic₃	—	5	4	no	—
357	C₂×Dic₃	—	5	2	no	—
358	C₂×Dic₃	—	10	4	no	—
359	C₂×Dic₃	C₂×C₄×D₅	1	2	yes	—
360	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
361	C₄×D₃	—	2	4	no	—
362	C₄×D₃	—	5	4	no	—
363	C₄×D₃	—	5	4	no	—
364	C₄×D₃	—	5	4	no	—
365	C₄×D₃	—	10	4	no	—
366	C₄×D₃	—	10	4	no	—
367	C₄×D₃	—	10	4	no	—
368	C₄×D₃	C₂×C₄×D₅	1	4	yes	—
369	C₃×C₈	—	5	4	no	—
370	C₃×C₈	C₂×C₄×D₅	1	4	yes	complemented
371	C₃⋊C₈	—	5	4	no	—
372	C₃⋊C₈	C₂×C₄×D₅	1	4	yes	complemented
373	C₂²×C₅	—	3	2	no	—
374	C₂²×C₅	—	6	2	no	—
375	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
376	C₂×D₅	—	3	2	no	—
377	C₂×D₅	—	6	2	no	—
378	C₂×D₅	—	6	8	no	—
379	C₂×D₅	C₄²×D₃	1	2	yes	—
380	C₂×D₅	C₂×ΓL(1,𝔽₂₅)	1	4	yes	—
381	C₄×C₅	—	3	2	no	—
382	C₄×C₅	—	6	2	no	—
383	C₄×C₅	C₂×ΓL(1,𝔽₂₅)	1	4	yes	complemented
384	C₄×C₅	C₂²×C₄×D₃	1	2	yes	—
385	Dic₅	—	3	2	no	—
386	Dic₅	—	6	2	no	—
387	Dic₅	C₄²×D₃	1	2	yes	—
388	Dic₅	C₂×ΓL(1,𝔽₂₅)	1	4	yes	complemented
389	C₂⁴	—	15	1	no	—
390	C₂²×C₄	—	3	1	no	—
391	C₂²×C₄	—	3	2	no	—
392	C₂²×C₄	—	5	2	no	—
393	C₂²×C₄	—	5	1	no	—
394	C₂²×C₄	—	15	1	no	—
395	C₂²×C₄	—	15	8	no	—
396	C₂²×C₄	—	15	2	no	—
397	C₂²×C₄	—	15	1	no	—
398	C₂²×C₄	—	15	2	no	—
399	C₂²×C₄	—	15	1	no	—
400	C₂²×C₄	—	15	2	no	—
401	C₂²×C₄	—	15	1	no	—
402	C₂²×C₄	—	15	2	no	—
403	C₂²×C₄	—	30	8	no	—
404	M₁₆	—	3	8	no	—
405	M₁₆	—	15	8	no	—
406	M₁₆	—	15	8	no	—
407	M₁₆	—	15	8	no	—
408	C₂×C₈	—	3	2	no	—
409	C₂×C₈	—	5	2	no	—
410	C₂×C₈	—	5	8	no	—
411	C₂×C₈	—	15	8	no	—
412	C₂×C₈	—	15	2	no	—
413	C₂×C₈	C₂×D₃×D₅	1	2	yes	—
414	C₄²	—	3	2	no	—
415	C₄²	—	3	1	no	—
416	C₄²	—	5	2	no	—
417	C₄²	—	5	1	no	—
418	C₄²	—	15	2	no	—
419	C₄²	—	15	2	no	—
420	C₄²	—	15	2	no	—
421	C₄²	—	15	2	no	—
422	C₄²	—	15	1	no	—
423	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
424	C₃×C₅	C₂×C₄×M₁₆	1	1	yes	characteristic, complemented, Hall
425	C₂²×C₃	—	5	2	no	—
426	C₂²×C₃	—	5	4	no	—
427	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
428	C₂×D₃	—	2	2	no	—
429	C₂×D₃	—	5	2	no	—
430	C₂×D₃	—	10	8	no	—
431	C₂×D₃	—	10	2	no	—
432	C₂×D₃	C₄²×D₅	1	2	yes	—
433	C₃×C₄	—	5	2	no	—
434	C₃×C₄	—	5	4	no	—
435	C₃×C₄	D₅×M₁₆	1	4	yes	complemented
436	C₃×C₄	C₂²×C₄×D₅	1	2	yes	—
437	Dic₃	—	2	2	no	—
438	Dic₃	—	5	2	no	—
439	Dic₃	—	10	2	no	—
440	Dic₃	C₄²×D₅	1	2	yes	—
441	C₂×C₅	—	6	2	no	—
442	C₂×C₅	C₂×C₄²×D₃	1	1	yes	characteristic
443	C₂×C₅	C₂²×ΓL(1,𝔽₂₅)	1	2	yes	—
444	D₅	—	6	2	no	—
445	D₅	C₄×ΓL(1,𝔽₂₅)	1	4	yes	direct product factor
446	C₂³	—	3	1	no	—
447	C₂³	—	5	1	no	—
448	C₂³	—	15	4	no	—
449	C₂³	—	15	1	no	—
450	C₂³	—	30	4	no	—
451	C₂×C₄	—	3	1	no	—
452	C₂×C₄	—	3	4	no	—
453	C₂×C₄	—	3	2	no	—
454	C₂×C₄	—	5	1	no	—
455	C₂×C₄	—	5	2	no	—
456	C₂×C₄	—	5	4	no	—
457	C₂×C₄	—	5	8	no	—
458	C₂×C₄	—	6	4	no	—
459	C₂×C₄	—	15	4	no	—
460	C₂×C₄	—	15	4	no	—
461	C₂×C₄	—	15	4	no	—
462	C₂×C₄	—	15	1	no	—
463	C₂×C₄	—	15	4	no	—
464	C₂×C₄	—	15	2	no	—
465	C₂×C₄	—	30	4	no	—
466	C₂×C₄	—	30	4	no	—
467	C₂×C₄	—	30	4	no	—
468	C₂×C₄	—	30	4	no	—
469	C₂×C₄	C₄×D₃×D₅	1	2	yes	—
470	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
471	C₈	—	3	4	no	—
472	C₈	—	5	4	no	—
473	C₈	—	15	4	no	—
474	C₈	C₄×D₃×D₅	1	4	yes	complemented
475	C₂×C₃	—	5	4	no	—
476	C₂×C₃	C₂×C₄²×D₅	1	1	yes	characteristic
477	C₂×C₃	C₂×D₅×M₁₆	1	2	yes	—
478	D₃	—	2	2	no	—
479	D₃	—	10	2	no	—
480	C₅	C₂×C₄×ΓL(1,𝔽₂₅)	1	1	yes	characteristic, complemented, Sylow
481	C₂²	—	3	2	no	—
482	C₂²	—	5	2	no	—
483	C₂²	—	5	4	no	—
484	C₂²	—	6	2	no	—
485	C₂²	—	15	2	no	—
486	C₂²	—	30	8	no	—
487	C₂²	—	30	2	no	—
488	C₂²	C₂×C₄×D₃×D₅	1	1	yes	characteristic
489	C₄	—	3	2	no	—
490	C₄	—	5	2	no	—
491	C₄	—	5	4	no	—
492	C₄	—	6	2	no	—
493	C₄	—	15	2	no	—
494	C₄	—	30	2	no	—
495	C₄	D₅×ΓL(1,𝔽₂₅)	1	4	yes	direct product factor
496	C₄	C₂×C₄×D₃×D₅	1	2	yes	—
497	C₃	C₄×D₅×M₁₆	1	1	yes	characteristic, complemented, Sylow
498	C₂	—	5	4	no	—
499	C₂	—	6	2	no	—
500	C₂	—	30	2	no	—
501	C₂	C₄²×D₃×D₅	1	1	yes	characteristic
502	C₂	C₂×D₅×ΓL(1,𝔽₂₅)	1	2	yes	—

	subgroup	G/H
center	C₄²	C₂×D₃×D₅
commutator	C₂×C₃×C₅	C₂²×C₄²
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₃×C₄×C₅×C₈	C₂²
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂²×D₃×D₅	C₂×C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₄×C₈	D₃×D₅
hypocenter	C₃×C₅	C₂×C₄×M₁₆
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
3. C₄×#6705	C₂	semidirect
4. C₄×C₅×ΓL(1,𝔽₂₅)	C₂	semidirect
5. C₃×C₄×C₈×D₅	C₂	semidirect
6. #11747592	C₂	semidirect
7. Dic₅×ΓL(1,𝔽₂₅)	C₂	semidirect
8. D₅×#815	C₂	semidirect
9. C₄×#6651	C₂	semidirect
10. C₄×#6650	C₂	semidirect
11. C₄×D₅×C₃⋊C₈	C₂	semidirect
30. D₅×ΓL(1,𝔽₂₅)	C₄	direct (N × H)
31. C₃×C₄×C₅×C₈	C₂²	semidirect
32. #91099	C₂²	semidirect
33. C₄×C₃⋊#168	C₂²	semidirect
34. C₅×#815	C₂²	semidirect
35. C₄×C₅×C₃⋊C₈	C₂²	semidirect
36. C₃×C₈×Dic₅	C₂²	semidirect
37. C₃×C₄×#168	C₂²	semidirect
38. #90954	C₂²	semidirect
39. #90953	C₂²	semidirect
40. Dic₅×C₃⋊C₈	C₂²	semidirect
52. C₄×C₈×D₅	D₃	semidirect
73. #6705	C₂×C₄	semidirect
77. C₅×ΓL(1,𝔽₂₅)	C₂×C₄	semidirect
81. C₃×C₈×D₅	C₂×C₄	semidirect
85. #6651	C₂×C₄	semidirect
86. #6650	C₂×C₄	semidirect
87. D₅×C₃⋊C₈	C₂×C₄	semidirect
98. C₄×ΓL(1,𝔽₂₅)	D₅	direct (N × H)
119. C₄×C₅×C₈	C₂×D₃	semidirect
123. C₈×Dic₅	C₂×D₃	semidirect
126. C₄×#168	C₂×D₃	semidirect
145. C₃×C₄×D₅	M₁₆	semidirect
153. C₃×C₅×C₈	C₂²×C₄	semidirect
154. C₃⋊#168	C₂²×C₄	semidirect
155. C₃×#168	C₂²×C₄	semidirect
156. C₅×C₃⋊C₈	C₂²×C₄	semidirect
177. C₃×C₄×C₈	C₂×D₅	semidirect
181. #815	C₂×D₅	semidirect
184. C₄×C₃⋊C₈	C₂×D₅	semidirect
219. C₈×D₅	C₄×D₃	semidirect
239. C₃×C₄×C₅	C₂×M₁₆	semidirect
244. C₃×Dic₅	C₂×M₁₆	semidirect
281. ΓL(1,𝔽₂₅)	C₄×D₅	direct (N × H)
305. C₄×D₅	ΓL(1,𝔽₂₅)	direct (N × H)
308. C₅×C₈	C₂×C₄×D₃	semidirect
310. #168	C₂×C₄×D₃	semidirect
338. C₄×C₈	D₃×D₅	semidirect
342. C₃×D₅	C₄×M₁₆	semidirect
370. C₃×C₈	C₂×C₄×D₅	semidirect
372. C₃⋊C₈	C₂×C₄×D₅	semidirect
383. C₄×C₅	C₂×ΓL(1,𝔽₂₅)	semidirect
388. Dic₅	C₂×ΓL(1,𝔽₂₅)	semidirect
424. C₃×C₅	C₂×C₄×M₁₆	semidirect
435. C₃×C₄	D₅×M₁₆	semidirect
445. D₅	C₄×ΓL(1,𝔽₂₅)	direct (N × H)
474. C₈	C₄×D₃×D₅	semidirect
480. C₅	C₂×C₄×ΓL(1,𝔽₂₅)	semidirect
495. C₄	D₅×ΓL(1,𝔽₂₅)	direct (N × H)
497. C₃	C₄×D₅×M₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₅×ΓL(1,𝔽₂₅)	2
C₄²×D₃×D₅	2
C₄×#6705	2
C₄×C₅×ΓL(1,𝔽₂₅)	2
C₃×C₄×C₈×D₅	2
#11747592	2
Dic₅×ΓL(1,𝔽₂₅)	2
D₅×#815	2
C₄×#6651	2
C₄×#6650	2
C₄×D₅×C₃⋊C₈	2
C₄×D₅×M₁₆	3
C₂×C₄×ΓL(1,𝔽₂₅)	5

Subgroups — C4×D5×ΓL(1,𝔽25) #14411246

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×D₅×ΓL(1,𝔽₂₅) #14411246