Subgroups — #14419020

Order 1920.

824 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	C₄×#6772	C₂	1	1	yes	maximal, characteristic
2	#11750780	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#4688	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₄×C₈×D₅	C₂	1	1	yes	maximal, characteristic, complemented
5	#11747702	C₂	1	2	yes	maximal, complemented
6	#11747701	C₂	1	2	yes	maximal, complemented
7	Dic₅×ΓL(1,𝔽₂₅)	C₂	1	2	yes	maximal, complemented
8	#11747579	C₂	1	2	yes	maximal, complemented
9	#11747008	C₂	1	1	yes	maximal, characteristic, complemented
10	#11746869	C₂	1	1	yes	maximal, characteristic, complemented
11	#11746864	C₂	1	1	yes	maximal, characteristic, complemented
12	#10611248	—	3	1	no	maximal, Hall
13	C₂×#6772	C₄	1	1	yes	characteristic
14	C₄×Dic₃₀	C₂²	1	1	yes	characteristic
15	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
16	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
19	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
20	#91440	C₄	1	2	yes	—
21	C₄×#1201	C₂²	1	2	yes	—
22	Dic₅×D₁₂	C₄	1	1	yes	characteristic
23	#91398	C₄	1	2	yes	—
24	C₄×D₃×Dic₅	C₂²	1	2	yes	—
25	#91358	C₄	1	1	yes	characteristic
26	#91333	C₄	1	1	yes	characteristic
27	C₂×#6650	C₂²	1	2	yes	—
28	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
29	#91099	C₂²	1	2	yes	—
30	#91098	C₂²	1	2	yes	—
31	C₄⋊(C₃⋊#168)	C₂²	1	1	yes	characteristic
32	C₅×(C₂×D₃)⋊C₈	C₂²	1	2	yes	—
33	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
34	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic
35	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic
36	C₃×C₄×#168	C₂²	1	1	yes	characteristic
37	#90983	C₂²	1	2	yes	—
38	(C₂×D₃)⋊#168	C₂²	1	2	yes	—
39	#90955	C₂²	1	2	yes	—
40	#90954	C₂²	1	2	yes	—
41	Dic₅×C₃⋊C₈	C₂²	1	2	yes	—
42	#78447	—	5	1	no	maximal, Hall
43	C₄×#711	—	3	1	no	—
44	C₅×#436	—	3	1	no	—
45	#65416	—	3	2	no	—
46	M₁₆×Dic₅	—	3	2	no	—
47	#65301	—	3	1	no	—
48	#65122	—	3	1	no	—
49	#65120	—	3	1	no	—
50	#65017	—	3	2	no	—
51	#65007	—	3	2	no	—
52	C₄×C₈×D₅	D₃	1	1	yes	characteristic, complemented
53	#64968	—	3	1	no	—
54	C₂×Dic₃₀	C₂×C₄	1	1	yes	characteristic
55	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
57	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
58	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
59	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
60	C₂×#1201	C₂×C₄	1	2	yes	—
61	C₂×D₃×Dic₅	C₂×C₄	1	2	yes	—
62	C₂×D₃×Dic₅	C₂×C₄	1	2	yes	—
63	#6772	—	2	4	no	—
64	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
65	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
66	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
67	C₄⋊Dic₁₅	C₂×C₄	1	1	yes	characteristic
68	#6712	C₂×C₄	1	2	yes	—
69	C₄×Dic₁₅	C₂³	1	2	yes	—
70	C₂×C₃⋊#168	C₂³	1	2	yes	—
71	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
72	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
73	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
74	C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
75	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
76	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
77	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
78	C₂×C₃×#168	C₂³	1	1	yes	characteristic
79	C₂×C₃×#168	C₂³	1	1	yes	characteristic
80	C₃×C₈×D₅	—	2	2	no	—
81	C₃×C₈×D₅	—	2	2	no	—
82	#6669	C₂×C₄	1	2	yes	—
83	(C₂×D₃)⋊Dic₅	C₂×C₄	1	2	yes	—
84	#6665	C₂×C₄	1	2	yes	—
85	Dic₃×Dic₅	C₂×C₄	1	2	yes	—
86	Dic₃×Dic₅	C₂×C₄	1	2	yes	—
87	#6650	—	2	4	no	—
88	C₄×#235	—	5	1	no	—
89	C₂×C₃×C₄×C₈	—	5	1	no	—
90	#5111	—	5	2	no	—
91	#5111	—	5	2	no	—
92	#4925	—	5	1	no	—
93	#4688	—	5	1	no	—
94	#4688	D₅	1	1	yes	characteristic, complemented
95	C₄×ΓL(1,𝔽₂₅)	—	5	2	no	—
96	#4685	—	5	2	no	—
97	#4679	—	5	1	no	—
98	#4679	—	5	1	no	—
99	C₂×#711	—	3	1	no	—
100	C₂×C₅×M₁₆	—	3	2	no	—
101	C₄×C₅×D₄	—	3	1	no	—
102	D₄×Dic₅	—	3	1	no	—
103	C₄×C₂²⋊D₅	—	3	2	no	—
104	C₂×C₄×Dic₅	—	3	2	no	—
105	C₂×#681	—	3	2	no	—
106	C₂×C₈×D₅	C₂×D₃	1	1	yes	characteristic
107	C₂×C₈×D₅	C₂×D₃	1	1	yes	characteristic
108	#4038	—	3	1	no	—
109	#4033	—	3	1	no	—
110	#4027	—	3	2	no	—
111	#4023	—	3	2	no	—
112	C₄²×D₅	C₂×D₃	1	1	yes	characteristic
113	C₄×Dic₁₀	—	3	1	no	—
114	C₅×C₄⋊C₈	—	3	1	no	—
115	C₅×C₂²⋊C₈	—	3	2	no	—
116	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
117	C₂²⋊#168	—	3	2	no	—
118	#3952	—	3	2	no	—
119	#3947	—	3	2	no	—
120	#3947	—	3	2	no	—
121	#3946	—	3	2	no	—
122	#3946	—	3	2	no	—
123	C₈×Dic₅	—	3	2	no	—
124	C₈×Dic₅	C₂×D₃	1	1	yes	characteristic
125	C₈×Dic₅	C₂×D₃	1	1	yes	characteristic
126	C₄⋊#168	—	3	1	no	—
127	C₄×#168	C₂×D₃	1	1	yes	characteristic
128	#2965	—	15	1	no	Sylow
129	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
130	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
134	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
135	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
136	Dic₃₀	—	2	2	no	—
137	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
138	C₅×D₁₂	—	2	2	no	—
139	C₄×C₅×D₃	—	2	2	no	—
140	C₄×C₅×D₃	—	2	2	no	—
141	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
143	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
144	C₃×C₄×D₅	—	2	1	no	—
145	C₃×C₄×D₅	—	2	1	no	—
146	C₃×C₄×D₅	—	2	2	no	—
147	C₃×C₄×D₅	M₁₆	1	4	yes	complemented
148	#1201	—	2	4	no	—
149	D₃×Dic₅	—	2	4	no	—
150	D₃×Dic₅	—	2	4	no	—
151	C₃×C₅×C₈	—	2	1	no	—
152	C₃×C₅×C₈	#41	1	2	yes	complemented
153	C₃⋊#168	—	2	2	no	—
154	C₃×#168	—	2	1	no	—
155	C₃×#168	#41	1	2	yes	complemented
156	C₅×C₃⋊C₈	—	2	2	no	—
157	C₂×#235	—	5	1	no	—
158	C₂²×C₃×C₈	—	5	1	no	—
159	C₂²×C₃×C₈	—	5	1	no	—
160	C₂×C₃×C₄²	—	5	1	no	—
161	C₄×#67	—	5	2	no	—
162	C₄×#67	—	5	2	no	—
163	#926	—	5	1	no	—
164	C₂×ΓL(1,𝔽₂₅)	—	5	2	no	—
165	C₂×ΓL(1,𝔽₂₅)	C₂×D₅	1	2	yes	—
166	C₄×D₁₂	—	5	1	no	—
167	C₄×D₁₂	C₂×D₅	1	1	yes	characteristic
168	#872	—	5	2	no	—
169	C₄²×D₃	—	5	2	no	—
170	C₄×Dic₆	—	5	1	no	—
171	C₄×Dic₆	—	5	1	no	—
172	C₃×C₄×C₈	—	5	1	no	—
173	C₃×C₄×C₈	—	5	1	no	—
174	C₃×C₄×C₈	—	5	1	no	—
175	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
176	#830	—	5	2	no	—
177	(C₂×D₃)⋊C₈	—	5	2	no	—
178	(C₂×D₃)⋊C₈	C₂×D₅	1	2	yes	—
179	#815	—	5	2	no	—
180	#815	—	5	2	no	—
181	Dic₃⋊C₈	—	5	2	no	—
182	Dic₃⋊C₈	—	5	2	no	—
183	C₄⋊(C₃⋊C₈)	—	5	1	no	—
184	C₄⋊(C₃⋊C₈)	C₂×D₅	1	1	yes	characteristic
185	C₄×C₃⋊C₈	—	5	2	no	—
186	C₂×C₅×D₄	—	3	1	no	—
187	C₂²×C₄×C₅	—	3	2	no	—
188	C₂×C₂²⋊D₅	—	3	2	no	—
189	C₂²×Dic₅	—	3	2	no	—
190	C₂²×Dic₅	—	3	2	no	—
191	#711	—	6	4	no	—
192	C₂×C₄×D₅	C₄×D₃	1	1	yes	characteristic
193	C₂×C₄×D₅	C₄×D₃	1	1	yes	characteristic
194	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
195	C₂×Dic₁₀	—	3	1	no	—
196	C₅×M₁₆	—	6	4	no	—
197	C₂×C₅×C₈	—	3	2	no	—
198	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
199	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
200	C₅×C₄⋊C₄	—	3	1	no	—
201	C₅×C₂²⋊C₄	—	3	2	no	—
202	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
203	C₂²⋊Dic₅	—	3	2	no	—
204	#685	—	3	2	no	—
205	C₄⋊Dic₅	—	3	1	no	—
206	#683	—	3	2	no	—
207	#683	—	3	2	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	1	yes	characteristic
212	C₄×Dic₅	C₄×D₃	1	1	yes	characteristic
213	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
214	#681	—	6	4	no	—
215	C₂×#168	—	3	2	no	—
216	C₂×#168	C₂²×D₃	1	1	yes	characteristic
217	C₂×#168	C₂²×D₃	1	1	yes	characteristic
218	C₈×D₅	—	2	2	no	—
219	C₈×D₅	—	2	2	no	—
220	C₄×#41	—	15	1	no	—
221	#446	—	15	1	no	—
222	#446	—	15	1	no	—
223	#436	—	3	1	no	—
224	#436	—	15	1	no	—
225	#435	—	15	2	no	—
226	#435	—	15	2	no	—
227	#431	—	15	2	no	—
228	#431	—	15	1	no	—
229	C₄×M₁₆	—	15	2	no	—
230	C₂×C₄×C₈	—	5	1	no	—
231	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
232	C₂×C₅×D₃	—	2	2	no	—
233	C₂×C₅×D₃	—	2	2	no	—
234	C₂×C₅×D₃	—	2	2	no	—
235	C₂×C₃×D₅	—	2	1	no	—
236	C₂×C₃×D₅	—	2	1	no	—
237	C₂×C₃×D₅	C₂×M₁₆	1	2	yes	—
238	C₃×C₄×C₅	—	2	1	no	—
239	C₃×C₄×C₅	C₂×M₁₆	1	2	yes	—
240	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
241	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
242	Dic₁₅	—	2	2	no	—
243	Dic₁₅	—	2	2	no	—
244	C₃×Dic₅	—	2	1	no	—
245	C₃×Dic₅	C₂×M₁₆	1	2	yes	—
246	C₃×Dic₅	#131	1	2	yes	—
247	C₅×Dic₃	—	2	2	no	—
248	C₂²×C₃×C₄	—	5	1	no	—
249	C₂²×C₃×C₄	—	5	1	no	—
250	C₂²×C₃×C₄	—	5	1	no	—
251	C₂×#67	—	5	2	no	—
252	#235	—	10	4	no	—
253	C₂×D₁₂	C₄×D₅	1	1	yes	characteristic
254	C₂×C₄×D₃	—	5	2	no	—
255	C₂×C₄×D₃	—	5	2	no	—
256	C₂×C₄×D₃	C₂²×D₅	1	2	yes	—
257	C₂×Dic₆	—	5	1	no	—
258	C₂×C₃×C₈	—	5	1	no	—
259	C₂×C₃×C₈	—	5	1	no	—
260	C₂×C₃×C₈	—	10	2	no	—
261	C₂×C₃×C₈	—	10	2	no	—
262	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
263	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
264	C₃×C₄²	—	5	1	no	—
265	C₃×C₄²	—	5	1	no	—
266	C₃×C₄²	—	5	1	no	—
267	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
268	#217	—	5	2	no	—
269	(C₂×D₃)⋊C₄	—	5	2	no	—
270	(C₂×D₃)⋊C₄	C₄×D₅	1	2	yes	—
271	C₄⋊Dic₃	—	5	1	no	—
272	C₄⋊Dic₃	C₄×D₅	1	1	yes	characteristic
273	Dic₃⋊C₄	—	5	2	no	—
274	Dic₃⋊C₄	—	5	2	no	—
275	C₄×Dic₃	—	5	2	no	—
276	C₄×Dic₃	—	5	2	no	—
277	C₄×Dic₃	—	5	2	no	—
278	C₂×C₃⋊C₈	—	5	2	no	—
279	C₂×C₃⋊C₈	C₂²×D₅	1	2	yes	—
280	ΓL(1,𝔽₂₅)	—	2	4	no	—
281	ΓL(1,𝔽₂₅)	—	10	4	no	—
282	C₂³×C₅	—	3	2	no	—
283	C₂²×D₅	C₂×C₄×D₃	1	1	yes	characteristic
284	C₅×D₄	—	6	2	no	—
285	C₂×C₄×C₅	—	3	2	no	—
286	C₂×C₄×C₅	—	6	2	no	—
287	C₂×C₄×C₅	—	6	2	no	—
288	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
289	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
290	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
291	C₂²⋊D₅	—	6	4	no	—
292	C₂×Dic₅	—	3	2	no	—
293	C₂×Dic₅	—	3	2	no	—
294	C₂×Dic₅	—	6	4	no	—
295	C₂×Dic₅	—	6	4	no	—
296	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
297	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
298	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
299	C₄×D₅	—	2	1	no	—
300	C₄×D₅	—	2	1	no	—
301	C₄×D₅	—	2	2	no	—
302	C₄×D₅	ΓL(1,𝔽₂₅)	1	4	yes	complemented
303	Dic₁₀	—	6	2	no	—
304	C₅×C₈	—	2	1	no	—
305	C₅×C₈	—	6	2	no	—
306	C₅×C₈	#235	1	2	yes	complemented
307	#168	—	2	1	no	—
308	#168	—	6	2	no	—
309	#168	#235	1	2	yes	complemented
310	C₂×#41	—	15	1	no	—
311	C₂×M₁₆	—	3	2	no	—
312	C₂×M₁₆	—	15	2	no	—
313	C₂²×C₈	—	5	1	no	—
314	C₂²×C₈	—	5	1	no	—
315	C₄×Q₈	—	15	1	no	—
316	C₄×Q₈	—	15	1	no	—
317	C₄×D₄	—	3	1	no	—
318	C₄×D₄	—	15	1	no	—
319	C₄×D₄	—	15	2	no	—
320	C₄×D₄	—	15	2	no	—
321	#117	—	15	2	no	—
322	#117	—	15	1	no	—
323	C₂×C₄²	—	5	1	no	—
324	C₂×C₄²	—	15	2	no	—
325	C₄⋊C₈	—	3	1	no	—
326	C₄⋊C₈	—	15	2	no	—
327	C₄⋊C₈	—	15	2	no	—
328	C₄⋊C₈	—	15	1	no	—
329	C₂²⋊C₈	—	3	2	no	—
330	C₂²⋊C₈	—	15	2	no	—
331	C₂²⋊C₈	—	15	2	no	—
332	#97	—	15	2	no	—
333	#97	—	15	2	no	—
334	C₄×C₈	—	5	1	no	—
335	C₄×C₈	—	5	1	no	—
336	C₄×C₈	—	5	1	no	—
337	C₄×C₈	—	15	2	no	—
338	C₄×C₈	D₃×D₅	1	1	yes	characteristic
339	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
340	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
341	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
342	C₃×D₅	—	2	2	no	—
343	C₅×D₃	—	4	2	no	—
344	C₂³×C₃	—	5	1	no	—
345	C₂²×D₃	C₂×C₄×D₅	1	2	yes	—
346	C₂×C₃×C₄	—	5	1	no	—
347	C₂×C₃×C₄	—	5	1	no	—
348	C₂×C₃×C₄	—	5	4	no	—
349	C₂×C₃×C₄	—	5	1	no	—
350	C₂×C₃×C₄	—	10	2	no	—
351	C₂×C₃×C₄	—	10	1	no	—
352	C₂×C₃×C₄	—	10	1	no	—
353	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
354	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
355	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
356	#67	—	10	4	no	—
357	C₂×Dic₃	—	5	2	no	—
358	C₂×Dic₃	—	5	2	no	—
359	C₂×Dic₃	C₂×C₄×D₅	1	2	yes	—
360	D₁₂	—	2	2	no	—
361	C₄×D₃	—	2	2	no	—
362	C₄×D₃	—	2	2	no	—
363	C₄×D₃	—	10	4	no	—
364	C₄×D₃	—	10	4	no	—
365	Dic₆	—	10	2	no	—
366	C₃×C₈	—	2	1	no	—
367	C₃×C₈	—	5	2	no	—
368	C₃×C₈	—	10	1	no	—
369	C₃×C₈	#711	1	2	yes	complemented
370	C₃⋊C₈	—	2	2	no	—
371	C₃⋊C₈	—	10	2	no	—
372	C₂²×C₅	—	6	2	no	—
373	C₂²×C₅	—	6	2	no	—
374	C₂²×C₅	—	6	2	no	—
375	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
376	C₂×D₅	—	2	1	no	—
377	C₂×D₅	—	2	1	no	—
378	C₂×D₅	C₂×ΓL(1,𝔽₂₅)	1	2	yes	—
379	C₄×C₅	—	2	1	no	—
380	C₄×C₅	—	6	2	no	—
381	C₄×C₅	C₂×ΓL(1,𝔽₂₅)	1	2	yes	—
382	C₄×C₅	C₂×#235	1	1	yes	characteristic
383	C₄×C₅	C₂×#235	1	1	yes	characteristic
384	Dic₅	—	2	1	no	—
385	Dic₅	—	6	2	no	—
386	Dic₅	—	6	2	no	—
387	Dic₅	C₂×ΓL(1,𝔽₂₅)	1	2	yes	—
388	Dic₅	#901	1	2	yes	—
389	#41	—	30	4	no	—
390	C₂×Q₈	—	15	1	no	—
391	C₂×D₄	—	3	1	no	—
392	C₂×D₄	—	15	2	no	—
393	C₂²×C₄	—	3	2	no	—
394	C₂²×C₄	—	5	1	no	—
395	C₂²×C₄	—	5	1	no	—
396	C₂²×C₄	—	5	1	no	—
397	C₂²×C₄	—	15	2	no	—
398	C₂²×C₄	—	15	2	no	—
399	M₁₆	—	6	4	no	—
400	M₁₆	—	30	4	no	—
401	C₂×C₈	—	3	2	no	—
402	C₂×C₈	—	5	1	no	—
403	C₂×C₈	—	5	1	no	—
404	C₂×C₈	—	10	2	no	—
405	C₂×C₈	—	10	2	no	—
406	C₂×C₈	—	15	2	no	—
407	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
408	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
409	C₄⋊C₄	—	3	1	no	—
410	C₄⋊C₄	—	15	2	no	—
411	C₄⋊C₄	—	15	2	no	—
412	C₄⋊C₄	—	15	1	no	—
413	C₂²⋊C₄	—	3	2	no	—
414	C₂²⋊C₄	—	15	2	no	—
415	C₂²⋊C₄	—	15	2	no	—
416	C₄²	—	5	1	no	—
417	C₄²	—	5	1	no	—
418	C₄²	—	5	1	no	—
419	C₄²	—	15	2	no	—
420	C₄²	—	15	2	no	—
421	C₄²	—	15	2	no	—
422	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
423	C₃×C₅	#2965	1	1	yes	characteristic, complemented, Hall
424	C₂²×C₃	—	5	2	no	—
425	C₂²×C₃	—	10	1	no	—
426	C₂²×C₃	—	10	1	no	—
427	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
428	C₂×D₃	—	2	2	no	—
429	C₂×D₃	—	2	2	no	—
430	C₂×D₃	—	2	2	no	—
431	C₃×C₄	—	2	1	no	—
432	C₃×C₄	—	5	2	no	—
433	C₃×C₄	—	5	2	no	—
434	C₃×C₄	—	10	1	no	—
435	C₃×C₄	D₅×M₁₆	1	2	yes	—
436	C₃×C₄	C₂×#711	1	1	yes	characteristic
437	C₃×C₄	D₅×#41	1	1	yes	characteristic
438	Dic₃	—	2	2	no	—
439	Dic₃	—	10	2	no	—
440	Dic₃	—	10	2	no	—
441	C₂×C₅	—	12	2	no	—
442	C₂×C₅	C₄×#235	1	1	yes	characteristic
443	C₂×C₅	C₂²×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
444	C₂×C₅	C₂×#901	1	1	yes	characteristic
445	D₅	—	2	2	no	—
446	C₂³	—	3	2	no	—
447	C₂³	—	5	1	no	—
448	Q₈	—	30	2	no	—
449	D₄	—	6	2	no	—
450	D₄	—	30	4	no	—
451	C₂×C₄	—	3	2	no	—
452	C₂×C₄	—	5	1	no	—
453	C₂×C₄	—	5	1	no	—
454	C₂×C₄	—	5	4	no	—
455	C₂×C₄	—	5	1	no	—
456	C₂×C₄	—	6	2	no	—
457	C₂×C₄	—	6	2	no	—
458	C₂×C₄	—	10	2	no	—
459	C₂×C₄	—	10	1	no	—
460	C₂×C₄	—	10	1	no	—
461	C₂×C₄	—	15	2	no	—
462	C₂×C₄	—	15	2	no	—
463	C₂×C₄	—	30	4	no	—
464	C₂×C₄	—	30	4	no	—
465	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
466	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
467	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
468	C₈	—	2	1	no	—
469	C₈	—	5	2	no	—
470	C₈	—	6	2	no	—
471	C₈	—	10	1	no	—
472	C₈	—	30	2	no	—
473	C₈	#6772	1	2	yes	complemented
474	C₂×C₃	—	10	2	no	—
475	C₂×C₃	C₄×#711	1	1	yes	characteristic
476	C₂×C₃	C₂×D₅×M₁₆	1	1	yes	characteristic
477	C₂×C₃	D₅×#131	1	1	yes	characteristic
478	D₃	—	4	2	no	—
479	C₅	#78447	1	1	yes	characteristic, complemented, Sylow
480	C₂²	—	5	2	no	—
481	C₂²	—	6	2	no	—
482	C₂²	—	6	2	no	—
483	C₂²	—	6	2	no	—
484	C₂²	—	10	1	no	—
485	C₂²	—	10	1	no	—
486	C₂²	C₂×C₄×D₃×D₅	1	1	yes	characteristic
487	C₄	—	2	1	no	—
488	C₄	—	5	2	no	—
489	C₄	—	5	2	no	—
490	C₄	—	6	2	no	—
491	C₄	—	10	1	no	—
492	C₄	—	30	2	no	—
493	C₄	—	30	2	no	—
494	C₄	D₅×ΓL(1,𝔽₂₅)	1	2	yes	—
495	C₄	C₂×#6772	1	1	yes	characteristic
496	C₄	D₅×#235	1	1	yes	characteristic
497	C₃	#10611248	1	1	yes	characteristic, complemented, Sylow
498	C₂	—	10	2	no	—
499	C₂	—	12	2	no	—
500	C₂	C₄×#6772	1	1	yes	characteristic
501	C₂	C₂×D₅×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
502	C₂	D₅×#901	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	C₂×#6772	C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₄×C₈	D₃×D₅
hypocenter	C₃×C₅	#2965
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
3. C₅×#4688	C₂	semidirect
4. C₃×C₄×C₈×D₅	C₂	semidirect
5. #11747702	C₂	semidirect
6. #11747701	C₂	semidirect
7. Dic₅×ΓL(1,𝔽₂₅)	C₂	semidirect
8. #11747579	C₂	semidirect
9. #11747008	C₂	semidirect
10. #11746869	C₂	semidirect
11. #11746864	C₂	semidirect
52. C₄×C₈×D₅	D₃	semidirect
94. #4688	D₅	semidirect
147. C₃×C₄×D₅	M₁₆	semidirect
152. C₃×C₅×C₈	#41	semidirect
155. C₃×#168	#41	semidirect
302. C₄×D₅	ΓL(1,𝔽₂₅)	semidirect
306. C₅×C₈	#235	semidirect
309. #168	#235	semidirect
369. C₃×C₈	#711	semidirect
423. C₃×C₅	#2965	semidirect
473. C₈	#6772	semidirect
479. C₅	#78447	semidirect
497. C₃	#10611248	semidirect

Maximal subgroups

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

subgroup	index
C₄×#6772	2
#11750780	2
C₅×#4688	2
C₃×C₄×C₈×D₅	2
#11747702	2
#11747701	2
Dic₅×ΓL(1,𝔽₂₅)	2
#11747579	2
#11747008	2
#11746869	2
#11746864	2
#10611248	3
#78447	5