Subgroups — Dic₁₀×ΓL(1,𝔽₂₅) #14418842

Order 1920.

776 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₃×Dic₁₀	C₂	1	1	yes	maximal, characteristic
2	#11750780	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₅×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic
4	C₃×C₈×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
5	#11747819	C₂	1	2	yes	maximal, complemented
6	#11747590	C₂	1	2	yes	maximal
7	Dic₅×ΓL(1,𝔽₂₅)	C₂	1	2	yes	maximal
8	#11747567	C₂	1	2	yes	maximal, complemented
9	#11747011	C₂	1	1	yes	maximal, characteristic
10	#11746865	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃⋊C₈×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
12	M₁₆×Dic₁₀	—	3	1	no	maximal, Hall
13	C₂×D₃×Dic₁₀	C₄	1	1	yes	characteristic
14	C₄×Dic₃₀	C₂²	1	1	yes	characteristic
15	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
16	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
17	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
18	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
19	C₄×#1204	C₂²	1	2	yes	—
20	D₃×C₄⋊Dic₅	C₄	1	1	yes	characteristic
21	D₃×#683	C₄	1	2	yes	—
22	C₄×D₃×Dic₅	C₂²	1	2	yes	—
23	#91340	C₄	1	1	yes	characteristic
24	Dic₃×Dic₁₀	C₄	1	1	yes	characteristic
25	#91324	C₄	1	2	yes	—
26	C₂×#6650	C₂²	1	2	yes	—
27	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
28	#91099	C₂²	1	2	yes	—
29	#91098	C₂²	1	2	yes	—
30	C₄⋊(C₃⋊#168)	C₂²	1	1	yes	characteristic
31	C₅×#815	C₂²	1	1	yes	characteristic
32	C₅×#815	C₂²	1	1	yes	characteristic
33	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
34	C₃×#3946	C₂²	1	2	yes	—
35	C₃×C₈×Dic₅	C₂²	1	2	yes	—
36	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
37	Dic₃⋊#168	C₂²	1	2	yes	—
38	#90983	C₂²	1	2	yes	—
39	#90982	C₂²	1	2	yes	—
40	#90954	C₂²	1	2	yes	—
41	Dic₅×C₃⋊C₈	C₂²	1	2	yes	—
42	Q₈×ΓL(1,𝔽₂₅)	—	5	1	no	maximal, Hall
43	C₂×C₄×Dic₁₀	—	3	1	no	—
44	C₄×C₅×M₁₆	—	3	1	no	—
45	#65407	—	3	2	no	—
46	M₁₆×Dic₅	—	3	2	no	—
47	#65213	—	3	1	no	—
48	#64990	—	3	2	no	—
49	#64990	—	3	2	no	—
50	#64968	—	3	1	no	—
51	#64968	—	3	1	no	—
52	C₈×Dic₁₀	—	3	1	no	—
53	C₈×Dic₁₀	D₃	1	1	yes	characteristic, complemented
54	C₂×Dic₃₀	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
58	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
59	C₂×#1204	C₂×C₄	1	2	yes	—
60	C₂×D₃×Dic₅	C₂×C₄	1	2	yes	—
61	C₂×D₃×Dic₅	C₂×C₄	1	2	yes	—
62	D₃×Dic₁₀	—	2	4	no	—
63	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
64	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
65	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
66	C₄⋊Dic₁₅	C₂×C₄	1	1	yes	characteristic
67	#6712	C₂×C₄	1	2	yes	—
68	C₄×Dic₁₅	C₂³	1	2	yes	—
69	C₂×C₃⋊#168	C₂³	1	2	yes	—
70	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
71	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
72	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
73	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
74	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
75	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
76	C₅×ΓL(1,𝔽₂₅)	Q₈	1	4	yes	complemented
77	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
78	C₃×#683	C₂×C₄	1	2	yes	—
79	C₃×C₄×Dic₅	C₂³	1	2	yes	—
80	C₂×C₃×#168	C₂³	1	2	yes	—
81	Dic₃⋊Dic₅	C₂×C₄	1	2	yes	—
82	#6669	C₂×C₄	1	2	yes	—
83	#6668	C₂×C₄	1	2	yes	—
84	Dic₃×Dic₅	C₂×C₄	1	2	yes	—
85	Dic₃×Dic₅	C₂×C₄	1	2	yes	—
86	#6650	—	2	4	no	—
87	C₄×D₃×Q₈	—	5	1	no	—
88	C₃×C₈×Q₈	—	5	1	no	—
89	Q₈×C₃⋊C₈	—	5	1	no	—
90	#4837	—	5	2	no	—
91	#4837	—	5	1	no	—
92	#4831	—	5	2	no	—
93	#4831	—	5	1	no	—
94	C₄×ΓL(1,𝔽₂₅)	—	5	2	no	—
95	C₄×ΓL(1,𝔽₂₅)	D₅	1	1	yes	characteristic
96	#4679	—	5	1	no	—
97	#4679	—	5	2	no	—
98	C₂²×Dic₁₀	—	3	1	no	—
99	C₂×C₅×M₁₆	—	3	1	no	—
100	C₂×C₅×M₁₆	—	3	1	no	—
101	C₂×C₄²×C₅	—	3	1	no	—
102	C₂×C₄⋊Dic₅	—	3	1	no	—
103	C₂×#683	—	3	2	no	—
104	C₂×C₄×Dic₅	—	3	2	no	—
105	C₂×#681	—	3	2	no	—
106	C₄×Dic₁₀	—	3	1	no	—
107	C₄×Dic₁₀	—	3	1	no	—
108	C₄×Dic₁₀	—	3	1	no	—
109	C₄×Dic₁₀	—	3	2	no	—
110	C₄×Dic₁₀	—	3	2	no	—
111	C₄×Dic₁₀	C₂×D₃	1	1	yes	characteristic
112	C₅×#97	—	3	1	no	—
113	C₅×#97	—	3	1	no	—
114	C₄×C₅×C₈	—	3	1	no	—
115	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
116	#3947	—	3	2	no	—
117	#3947	—	3	2	no	—
118	#3946	—	3	2	no	—
119	#3946	—	3	2	no	—
120	#3946	—	3	2	no	—
121	#3946	C₂×D₃	1	2	yes	—
122	C₈×Dic₅	—	3	2	no	—
123	C₈×Dic₅	C₂×D₃	1	2	yes	—
124	C₄⋊#168	—	3	1	no	—
125	C₄⋊#168	—	3	2	no	—
126	C₄⋊#168	C₂×D₃	1	1	yes	characteristic
127	Q₈×M₁₆	—	15	1	no	Sylow
128	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
132	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
133	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
134	Dic₃₀	—	2	2	no	—
135	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
138	C₄×C₅×D₃	—	2	2	no	—
139	C₄×C₅×D₃	—	4	1	no	—
140	C₄×C₅×D₃	C₂×Q₈	1	2	yes	—
141	C₄×C₅×D₃	#41	1	2	yes	—
142	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
143	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
144	C₃×Dic₁₀	M₁₆	1	4	yes	complemented
145	#1204	—	2	4	no	—
146	D₃×Dic₅	—	2	4	no	—
147	D₃×Dic₅	—	4	2	no	—
148	C₃×C₅×C₈	—	2	1	no	—
149	C₃×C₅×C₈	C₂×Q₈	1	2	yes	complemented
150	C₃⋊#168	—	2	2	no	—
151	C₃×#168	—	2	2	no	—
152	C₅×C₃⋊C₈	—	2	1	no	—
153	C₅×C₃⋊C₈	C₂×Q₈	1	2	yes	complemented
154	C₂×D₃×Q₈	—	5	1	no	—
155	C₃×C₄×Q₈	—	5	1	no	—
156	Q₈×Dic₃	—	5	1	no	—
157	C₂×ΓL(1,𝔽₂₅)	—	5	2	no	—
158	C₂×ΓL(1,𝔽₂₅)	C₂×D₅	1	1	yes	characteristic
159	C₂×ΓL(1,𝔽₂₅)	C₂×D₅	1	1	yes	characteristic
160	D₃×C₄⋊C₄	—	5	2	no	—
161	D₃×C₄⋊C₄	—	5	1	no	—
162	#887	—	5	2	no	—
163	#887	—	5	1	no	—
164	C₄²×D₃	—	5	2	no	—
165	C₄²×D₃	C₂×D₅	1	1	yes	characteristic
166	C₄×Dic₆	—	5	1	no	—
167	C₄×Dic₆	—	5	2	no	—
168	C₃×C₄⋊C₈	—	5	2	no	—
169	C₃×C₄⋊C₈	—	5	1	no	—
170	C₃×C₄×C₈	—	5	2	no	—
171	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
172	#815	—	5	2	no	—
173	#815	—	5	2	no	—
174	#815	C₂×D₅	1	1	yes	characteristic
175	#815	C₂×D₅	1	1	yes	characteristic
176	Dic₃⋊C₈	—	5	2	no	—
177	Dic₃⋊C₈	—	5	2	no	—
178	Dic₃⋊C₈	—	5	2	no	—
179	C₄⋊(C₃⋊C₈)	—	5	1	no	—
180	C₄⋊(C₃⋊C₈)	—	5	2	no	—
181	C₄×C₃⋊C₈	—	5	2	no	—
182	C₄×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
183	C₂²×C₄×C₅	—	3	1	no	—
184	C₂²×C₄×C₅	—	3	1	no	—
185	C₂²×C₄×C₅	—	3	1	no	—
186	C₂²×Dic₅	—	3	2	no	—
187	C₂²×Dic₅	—	3	2	no	—
188	C₂×Dic₁₀	—	3	1	no	—
189	C₂×Dic₁₀	—	3	2	no	—
190	C₂×Dic₁₀	—	6	4	no	—
191	C₂×Dic₁₀	C₄×D₃	1	1	yes	characteristic
192	C₅×M₁₆	—	3	4	no	—
193	C₅×M₁₆	—	6	2	no	—
194	C₂×C₅×C₈	—	3	1	no	—
195	C₂×C₅×C₈	—	3	1	no	—
196	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
197	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
198	C₄²×C₅	—	3	1	no	—
199	C₄²×C₅	—	3	1	no	—
200	C₄²×C₅	—	3	1	no	—
201	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
202	C₄⋊Dic₅	—	3	1	no	—
203	C₄⋊Dic₅	—	3	2	no	—
204	C₄⋊Dic₅	C₄×D₃	1	1	yes	characteristic
205	#683	—	3	2	no	—
206	#683	—	3	2	no	—
207	#683	—	3	2	no	—
208	#683	C₄×D₃	1	2	yes	—
209	C₄×Dic₅	—	3	2	no	—
210	C₄×Dic₅	—	3	2	no	—
211	C₄×Dic₅	—	3	2	no	—
212	C₄×Dic₅	C₂²×D₃	1	2	yes	—
213	#681	—	6	4	no	—
214	C₂×#168	—	3	2	no	—
215	C₂×#168	C₂²×D₃	1	2	yes	—
216	C₂×C₄×Q₈	—	15	1	no	—
217	#446	—	15	1	no	—
218	#446	—	15	2	no	—
219	#446	—	15	2	no	—
220	#446	—	15	1	no	—
221	C₈×Q₈	—	5	1	no	—
222	C₈×Q₈	—	15	1	no	—
223	#423	—	15	1	no	—
224	#423	—	15	2	no	—
225	C₄×M₁₆	—	3	1	no	—
226	C₄×M₁₆	—	15	2	no	—
227	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
228	C₂×C₅×D₃	—	2	1	no	—
229	C₂×C₅×D₃	—	2	1	no	—
230	C₂×C₅×D₃	C₄×Q₈	1	2	yes	—
231	C₃×C₄×C₅	—	2	1	no	—
232	C₃×C₄×C₅	C₂×M₁₆	1	2	yes	—
233	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
234	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
235	Dic₁₅	—	2	2	no	—
236	Dic₁₅	—	2	2	no	—
237	C₃×Dic₅	—	2	2	no	—
238	C₃×Dic₅	C₂×M₁₆	1	4	yes	—
239	C₅×Dic₃	—	2	1	no	—
240	C₅×Dic₃	—	2	1	no	—
241	C₅×Dic₃	C₄×Q₈	1	2	yes	—
242	C₂×C₃×Q₈	—	5	1	no	—
243	D₃×Q₈	—	10	4	no	—
244	C₂×C₄×D₃	—	5	2	no	—
245	C₂×C₄×D₃	—	5	2	no	—
246	C₂×C₄×D₃	C₄×D₅	1	1	yes	characteristic
247	C₂×C₄×D₃	C₄×D₅	1	1	yes	characteristic
248	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
249	C₂×Dic₆	—	5	1	no	—
250	C₂×Dic₆	—	5	2	no	—
251	C₂×C₃×C₈	—	5	2	no	—
252	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
253	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
254	C₃×C₄⋊C₄	—	5	2	no	—
255	C₃×C₄⋊C₄	—	5	1	no	—
256	C₃×C₄²	—	5	2	no	—
257	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
258	C₄⋊Dic₃	—	5	1	no	—
259	C₄⋊Dic₃	—	5	2	no	—
260	Dic₃⋊C₄	—	5	2	no	—
261	Dic₃⋊C₄	—	5	2	no	—
262	Dic₃⋊C₄	—	5	2	no	—
263	C₄×Dic₃	—	5	2	no	—
264	C₄×Dic₃	—	5	2	no	—
265	C₄×Dic₃	—	5	2	no	—
266	C₄×Dic₃	C₄×D₅	1	1	yes	characteristic
267	C₄×Dic₃	C₄×D₅	1	1	yes	characteristic
268	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
269	C₂×C₃⋊C₈	—	5	2	no	—
270	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
271	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
272	ΓL(1,𝔽₂₅)	—	2	2	no	—
273	ΓL(1,𝔽₂₅)	—	10	4	no	—
274	ΓL(1,𝔽₂₅)	Dic₁₀	1	4	yes	direct product factor
275	C₂³×C₅	—	3	1	no	—
276	C₂×C₄×C₅	—	3	1	no	—
277	C₂×C₄×C₅	—	3	2	no	—
278	C₂×C₄×C₅	—	3	2	no	—
279	C₂×C₄×C₅	—	3	1	no	—
280	C₂×C₄×C₅	—	3	1	no	—
281	C₂×C₄×C₅	—	6	2	no	—
282	C₂×C₄×C₅	—	12	1	no	—
283	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
284	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
285	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
286	C₂×Dic₅	—	3	2	no	—
287	C₂×Dic₅	—	3	2	no	—
288	C₂×Dic₅	—	6	4	no	—
289	C₂×Dic₅	—	12	2	no	—
290	C₂×Dic₅	C₂×C₄×D₃	1	2	yes	—
291	C₂×Dic₅	C₂×C₄×D₃	1	2	yes	—
292	Dic₁₀	—	6	2	no	—
293	Dic₁₀	—	6	4	no	—
294	Dic₁₀	ΓL(1,𝔽₂₅)	1	4	yes	direct product factor
295	C₅×C₈	—	2	1	no	—
296	C₅×C₈	—	3	2	no	—
297	C₅×C₈	—	6	1	no	—
298	C₅×C₈	D₃×Q₈	1	2	yes	complemented
299	#168	—	2	2	no	—
300	#168	—	6	2	no	—
301	C₂²×Q₈	—	15	1	no	—
302	C₂×M₁₆	—	3	1	no	—
303	C₂×M₁₆	—	3	1	no	—
304	C₂×M₁₆	—	15	2	no	—
305	C₄×Q₈	—	5	1	no	—
306	C₄×Q₈	—	15	2	no	—
307	C₄×Q₈	—	15	2	no	—
308	C₄×Q₈	—	15	1	no	—
309	C₄×Q₈	—	15	1	no	—
310	C₄×Q₈	—	15	1	no	—
311	C₂×C₄⋊C₄	—	15	2	no	—
312	C₂×C₄⋊C₄	—	15	1	no	—
313	C₂×C₄²	—	3	1	no	—
314	C₂×C₄²	—	15	2	no	—
315	C₄⋊C₈	—	5	2	no	—
316	C₄⋊C₈	—	5	1	no	—
317	C₄⋊C₈	—	15	2	no	—
318	C₄⋊C₈	—	15	2	no	—
319	C₄⋊C₈	—	15	2	no	—
320	C₄⋊C₈	—	15	2	no	—
321	C₄⋊C₈	—	15	1	no	—
322	#97	—	3	1	no	—
323	#97	—	3	1	no	—
324	#97	—	15	2	no	—
325	#97	—	15	2	no	—
326	C₄×C₈	—	3	1	no	—
327	C₄×C₈	—	5	2	no	—
328	C₄×C₈	—	15	2	no	—
329	C₄×C₈	D₃×D₅	1	1	yes	characteristic
330	C₂×C₃×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
331	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
332	C₂×C₃×C₅	#568	1	1	yes	characteristic
333	C₅×D₃	—	2	2	no	—
334	C₂²×D₃	C₂×C₄×D₅	1	1	yes	characteristic
335	C₃×Q₈	—	5	4	no	—
336	C₂×C₃×C₄	—	5	2	no	—
337	C₂×C₃×C₄	—	5	2	no	—
338	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
339	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
340	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
341	C₂×Dic₃	—	5	2	no	—
342	C₂×Dic₃	—	5	2	no	—
343	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
344	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
345	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
346	C₄×D₃	—	2	2	no	—
347	C₄×D₃	—	4	1	no	—
348	C₄×D₃	—	10	4	no	—
349	C₄×D₃	—	20	2	no	—
350	C₄×D₃	C₂×Dic₁₀	1	2	yes	—
351	C₄×D₃	#709	1	2	yes	—
352	Dic₆	—	10	4	no	—
353	Dic₆	—	10	2	no	—
354	C₃×C₈	—	2	1	no	—
355	C₃×C₈	—	10	2	no	—
356	C₃×C₈	C₂×Dic₁₀	1	2	yes	complemented
357	C₃⋊C₈	—	2	1	no	—
358	C₃⋊C₈	—	10	2	no	—
359	C₃⋊C₈	C₂×Dic₁₀	1	2	yes	complemented
360	C₂²×C₅	—	3	2	no	—
361	C₂²×C₅	—	6	1	no	—
362	C₂²×C₅	—	6	1	no	—
363	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
364	C₄×C₅	—	2	1	no	—
365	C₄×C₅	—	3	2	no	—
366	C₄×C₅	—	6	1	no	—
367	C₄×C₅	—	6	1	no	—
368	C₄×C₅	C₂×ΓL(1,𝔽₂₅)	1	2	yes	—
369	C₄×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
370	C₄×C₅	D₃×#41	1	1	yes	characteristic
371	Dic₅	—	2	2	no	—
372	Dic₅	—	6	2	no	—
373	Dic₅	—	6	2	no	—
374	Dic₅	C₂×ΓL(1,𝔽₂₅)	1	4	yes	—
375	C₂×Q₈	—	5	1	no	—
376	C₂×Q₈	—	15	2	no	—
377	C₂×Q₈	—	15	1	no	—
378	C₂×Q₈	—	30	4	no	—
379	C₂²×C₄	—	3	1	no	—
380	C₂²×C₄	—	3	1	no	—
381	C₂²×C₄	—	3	1	no	—
382	C₂²×C₄	—	15	2	no	—
383	C₂²×C₄	—	15	2	no	—
384	M₁₆	—	3	4	no	—
385	M₁₆	—	6	2	no	—
386	M₁₆	—	30	4	no	—
387	C₂×C₈	—	3	1	no	—
388	C₂×C₈	—	3	1	no	—
389	C₂×C₈	—	5	2	no	—
390	C₂×C₈	—	15	2	no	—
391	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
392	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
393	C₄⋊C₄	—	5	2	no	—
394	C₄⋊C₄	—	5	1	no	—
395	C₄⋊C₄	—	15	2	no	—
396	C₄⋊C₄	—	15	2	no	—
397	C₄⋊C₄	—	15	2	no	—
398	C₄⋊C₄	—	15	2	no	—
399	C₄⋊C₄	—	15	1	no	—
400	C₄²	—	3	1	no	—
401	C₄²	—	3	1	no	—
402	C₄²	—	3	1	no	—
403	C₄²	—	5	2	no	—
404	C₄²	—	15	2	no	—
405	C₄²	—	15	2	no	—
406	C₄²	—	15	2	no	—
407	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
408	C₃×C₅	Q₈×M₁₆	1	1	yes	characteristic, complemented, Hall
409	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
410	C₂×D₃	—	2	1	no	—
411	C₂×D₃	—	2	1	no	—
412	C₂×D₃	C₄×Dic₁₀	1	2	yes	—
413	C₃×C₄	—	2	1	no	—
414	C₃×C₄	—	5	4	no	—
415	C₃×C₄	—	10	2	no	—
416	C₃×C₄	D₅×M₁₆	1	2	yes	—
417	C₃×C₄	C₂²×Dic₁₀	1	1	yes	characteristic
418	C₃×C₄	C₂×#709	1	1	yes	characteristic
419	Dic₃	—	2	1	no	—
420	Dic₃	—	2	1	no	—
421	Dic₃	—	10	2	no	—
422	Dic₃	—	10	2	no	—
423	Dic₃	C₄×Dic₁₀	1	2	yes	—
424	C₂×C₅	—	6	2	no	—
425	C₂×C₅	C₄×D₃×Q₈	1	1	yes	characteristic
426	C₂×C₅	C₂²×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
427	C₂×C₅	#5750	1	1	yes	characteristic
428	C₂³	—	3	1	no	—
429	Q₈	—	5	4	no	—
430	Q₈	—	30	4	no	—
431	Q₈	—	30	2	no	—
432	C₂×C₄	—	3	1	no	—
433	C₂×C₄	—	3	2	no	—
434	C₂×C₄	—	3	2	no	—
435	C₂×C₄	—	3	1	no	—
436	C₂×C₄	—	3	1	no	—
437	C₂×C₄	—	5	2	no	—
438	C₂×C₄	—	5	2	no	—
439	C₂×C₄	—	6	2	no	—
440	C₂×C₄	—	12	1	no	—
441	C₂×C₄	—	15	2	no	—
442	C₂×C₄	—	15	2	no	—
443	C₂×C₄	—	30	4	no	—
444	C₂×C₄	—	60	2	no	—
445	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
446	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
447	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
448	C₈	—	2	1	no	—
449	C₈	—	3	2	no	—
450	C₈	—	6	1	no	—
451	C₈	—	10	2	no	—
452	C₈	—	30	2	no	—
453	C₈	D₃×Dic₁₀	1	2	yes	complemented
454	C₂×C₃	C₂×C₄×Dic₁₀	1	1	yes	characteristic
455	C₂×C₃	C₂×D₅×M₁₆	1	1	yes	characteristic
456	C₂×C₃	#66079	1	1	yes	characteristic
457	D₃	—	2	2	no	—
458	C₅	Q₈×ΓL(1,𝔽₂₅)	1	1	yes	characteristic, complemented, Sylow
459	C₂²	—	3	2	no	—
460	C₂²	—	6	1	no	—
461	C₂²	—	6	1	no	—
462	C₂²	C₂×C₄×D₃×D₅	1	1	yes	characteristic
463	C₄	—	2	1	no	—
464	C₄	—	3	2	no	—
465	C₄	—	5	4	no	—
466	C₄	—	6	1	no	—
467	C₄	—	6	1	no	—
468	C₄	—	10	2	no	—
469	C₄	—	30	2	no	—
470	C₄	—	30	2	no	—
471	C₄	D₅×ΓL(1,𝔽₂₅)	1	2	yes	—
472	C₄	C₂×D₃×Dic₁₀	1	1	yes	characteristic
473	C₄	D₃×#709	1	1	yes	characteristic
474	C₃	M₁₆×Dic₁₀	1	1	yes	characteristic, complemented, Sylow
475	C₂	—	6	2	no	—
476	C₂	C₄×D₃×Dic₁₀	1	1	yes	characteristic
477	C₂	C₂×D₅×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
478	C₂	#11753951	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃×D₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Fitting	C₃×C₄×C₅×C₈	C₂²
prime radical	C₂²×C₅×D₃	C₂²×C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₄×C₈	D₃×D₅
hypocenter	C₃×C₅	Q₈×M₁₆
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #11750780	C₂	semidirect
4. C₃×C₈×Dic₁₀	C₂	semidirect
5. #11747819	C₂	semidirect
8. #11747567	C₂	semidirect
10. #11746865	C₂	semidirect
11. C₃⋊C₈×Dic₁₀	C₂	semidirect
53. C₈×Dic₁₀	D₃	semidirect
76. C₅×ΓL(1,𝔽₂₅)	Q₈	semidirect
144. C₃×Dic₁₀	M₁₆	semidirect
149. C₃×C₅×C₈	C₂×Q₈	semidirect
153. C₅×C₃⋊C₈	C₂×Q₈	semidirect
274. ΓL(1,𝔽₂₅)	Dic₁₀	direct (N × H)
294. Dic₁₀	ΓL(1,𝔽₂₅)	direct (N × H)
298. C₅×C₈	D₃×Q₈	semidirect
356. C₃×C₈	C₂×Dic₁₀	semidirect
359. C₃⋊C₈	C₂×Dic₁₀	semidirect
408. C₃×C₅	Q₈×M₁₆	semidirect
453. C₈	D₃×Dic₁₀	semidirect
458. C₅	Q₈×ΓL(1,𝔽₂₅)	semidirect
474. C₃	M₁₆×Dic₁₀	semidirect

Maximal subgroups

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

subgroup	index
C₄×D₃×Dic₁₀	2
#11750780	2
C₄×C₅×ΓL(1,𝔽₂₅)	2
C₃×C₈×Dic₁₀	2
#11747819	2
#11747590	2
Dic₅×ΓL(1,𝔽₂₅)	2
#11747567	2
#11747011	2
#11746865	2
C₃⋊C₈×Dic₁₀	2
M₁₆×Dic₁₀	3
Q₈×ΓL(1,𝔽₂₅)	5

Subgroups — Dic10×ΓL(1,𝔽25) #14418842

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₁₀×ΓL(1,𝔽₂₅) #14418842