Subgroups — #14419160

Order 1920.

760 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#66014	C₂	1	1	yes	maximal, characteristic
2	#11752447	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×C₃⋊#170	C₂	1	1	yes	maximal, characteristic, complemented
4	#11752433	C₂	1	1	yes	maximal, characteristic, complemented
5	D₄×C₃⋊#170	C₂	1	1	yes	maximal, characteristic, complemented
6	#11752356	C₂	1	2	yes	maximal, complemented
7	#11752353	C₂	1	2	yes	maximal, complemented
8	#11752351	C₂	1	2	yes	maximal, complemented
9	#11752350	C₂	1	2	yes	maximal, complemented
10	#11752342	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×D₅⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
12	#10617312	—	3	1	no	maximal, Hall
13	C₂×#6762	C₂²	1	2	yes	—
14	C₂²×C₃⋊#170	C₂²	1	2	yes	—
15	C₂×D₅⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×D₅⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
17	C₃×C₅×#124	C₄	1	1	yes	characteristic
18	C₃×#4092	C₄	1	1	yes	characteristic
19	C₃×Q₈×Dic₅	C₂²	1	1	yes	characteristic
20	C₃×#4084	C₄	1	1	yes	characteristic
21	C₃×D₄×Dic₅	C₂²	1	1	yes	characteristic
22	C₃×#4029	C₄	1	2	yes	—
23	C₃×#4027	C₂²	1	2	yes	—
24	C₃×#4025	C₄	1	2	yes	—
25	C₃×#4023	C₂²	1	2	yes	—
26	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
27	C₃×#4016	C₄	1	1	yes	characteristic
28	#91241	C₂²	1	2	yes	—
29	#91241	C₂²	1	2	yes	—
30	#91233	C₂²	1	2	yes	—
31	#91232	C₂²	1	2	yes	—
32	#91231	C₂²	1	2	yes	—
33	#91231	C₂²	1	2	yes	—
34	C₄⋊(C₃⋊#170)	C₂²	1	1	yes	characteristic
35	C₄⋊(C₃⋊#170)	C₂²	1	1	yes	characteristic
36	C₄⋊(C₃⋊#170)	C₂²	1	2	yes	—
37	C₄×C₃⋊#170	C₂²	1	1	yes	characteristic
38	C₄×C₃⋊#170	C₂²	1	1	yes	characteristic
39	C₄×C₃⋊#170	C₂²	1	1	yes	characteristic
40	C₄×C₃⋊#170	C₂²	1	1	yes	characteristic
41	C₄×C₃⋊#170	C₂²	1	2	yes	—
42	#83126	—	5	1	no	maximal, Hall
43	#66014	D₃	1	1	yes	characteristic
44	#65788	—	3	1	no	—
45	Q₈×#170	—	3	1	no	—
46	#65774	—	3	1	no	—
47	D₄×#170	—	3	1	no	—
48	#65697	—	3	2	no	—
49	#65694	—	3	2	no	—
50	#65692	—	3	2	no	—
51	#65691	—	3	2	no	—
52	#65683	—	3	1	no	—
53	C₄×D₅⋊C₈	—	3	1	no	—
54	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
55	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
56	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	2	yes	—
57	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
58	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
59	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
60	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
61	#6762	—	2	4	no	—
62	C₂×C₃⋊#170	—	2	4	no	—
63	C₂×C₃⋊#170	C₂³	1	1	yes	characteristic
64	C₂×C₃⋊#170	C₂³	1	1	yes	characteristic
65	C₂×C₃⋊#170	C₂³	1	2	yes	—
66	C₂×C₃⋊#170	C₂³	1	2	yes	—
67	C₂×C₃⋊#170	C₂³	1	1	yes	characteristic
68	C₂×C₃⋊#170	C₂³	1	1	yes	characteristic
69	D₅⋊(C₃⋊C₈)	—	2	2	no	—
70	D₅⋊(C₃⋊C₈)	—	2	2	no	—
71	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
72	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
73	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
74	C₃×C₂²⋊Dic₅	C₂×C₄	1	2	yes	—
75	C₃×C₂²⋊Dic₅	C₂×C₄	1	2	yes	—
76	C₃×#685	C₂×C₄	1	2	yes	—
77	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
78	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
79	C₃×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
80	C₃×#683	C₂×C₄	1	2	yes	—
81	C₃×#683	C₂×C₄	1	2	yes	—
82	C₃×#683	C₂×C₄	1	2	yes	—
83	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
84	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
85	C₃×C₄×Dic₅	C₂³	1	2	yes	—
86	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
87	C₃×#529	—	5	1	no	—
88	#5024	—	5	1	no	—
89	Q₈×C₃⋊C₈	—	5	1	no	—
90	#5012	—	5	1	no	—
91	#5011	—	5	2	no	—
92	D₄×C₃⋊C₈	—	5	2	no	—
93	D₄×C₃⋊C₈	—	5	1	no	—
94	#5000	—	5	2	no	—
95	#4997	—	5	2	no	—
96	#4926	—	5	1	no	—
97	C₂×C₄×C₃⋊C₈	—	5	1	no	—
98	C₂×#704	—	3	2	no	—
99	C₂²×#170	—	3	2	no	—
100	C₂×D₅⋊C₈	—	3	1	no	—
101	C₂×D₅⋊C₈	—	3	1	no	—
102	C₅×#124	Dic₃	1	1	yes	characteristic
103	#4092	Dic₃	1	1	yes	characteristic
104	Q₈×Dic₅	C₂×D₃	1	1	yes	characteristic
105	#4084	Dic₃	1	1	yes	characteristic
106	D₄×Dic₅	C₂×D₃	1	1	yes	characteristic
107	#4029	Dic₃	1	2	yes	—
108	#4027	C₂×D₃	1	2	yes	—
109	#4025	Dic₃	1	2	yes	—
110	#4023	C₂×D₃	1	2	yes	—
111	C₄²×D₅	C₂×D₃	1	1	yes	characteristic
112	#4016	Dic₃	1	1	yes	characteristic
113	C₂²⋊#170	—	3	2	no	—
114	C₂²⋊#170	—	3	2	no	—
115	#4004	—	3	2	no	—
116	#4003	—	3	2	no	—
117	#4002	—	3	2	no	—
118	#4002	—	3	2	no	—
119	C₄⋊#170	—	3	1	no	—
120	C₄⋊#170	—	3	1	no	—
121	C₄⋊#170	—	3	2	no	—
122	C₄×#170	—	3	1	no	—
123	C₄×#170	—	3	1	no	—
124	C₄×#170	—	3	1	no	—
125	C₄×#170	—	3	1	no	—
126	C₄×#170	—	3	2	no	—
127	#2966	—	15	1	no	Sylow
128	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
129	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
130	C₃×C₅×Q₈	—	2	2	no	—
131	C₃×C₅×D₄	—	2	2	no	—
132	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
135	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
136	C₃×C₂²⋊D₅	—	2	4	no	—
137	C₂×C₃×Dic₅	—	2	2	no	—
138	C₂×C₃×Dic₅	—	2	2	no	—
139	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
142	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
143	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
144	C₃×C₄×D₅	—	2	2	no	—
145	C₃×C₄×D₅	—	2	2	no	—
146	C₃×C₄×D₅	—	2	1	no	—
147	C₃×C₄×D₅	—	2	1	no	—
148	C₃⋊#170	—	2	1	no	—
149	C₃⋊#170	—	2	1	no	—
150	C₃⋊#170	—	2	2	no	—
151	C₃⋊#170	—	2	2	no	—
152	C₃⋊#170	#41	1	2	yes	—
153	C₃⋊#170	#41	1	2	yes	—
154	C₃×#126	—	5	2	no	—
155	C₃×#125	—	5	1	no	—
156	C₃×#124	AGL(1,𝔽₅)	1	1	yes	characteristic
157	C₃×#123	—	5	2	no	—
158	C₃×C₂²⋊Q₈	—	5	1	no	—
159	C₃×#121	—	5	1	no	—
160	C₃×C₄×Q₈	—	5	1	no	—
161	C₃×C₄×D₄	—	5	1	no	—
162	C₃×C₄×D₄	—	5	2	no	—
163	C₃×#117	—	5	2	no	—
164	C₂×C₃×C₄²	—	5	1	no	—
165	C₂×#208	—	5	2	no	—
166	C₂²×C₃⋊C₈	—	5	1	no	—
167	C₂²×C₃⋊C₈	—	5	1	no	—
168	C₂²×C₃⋊C₈	—	5	2	no	—
169	#830	—	5	2	no	—
170	#830	—	5	2	no	—
171	#830	—	5	2	no	—
172	C₄⋊(C₃⋊C₈)	—	5	1	no	—
173	C₄⋊(C₃⋊C₈)	—	5	1	no	—
174	C₄⋊(C₃⋊C₈)	—	5	2	no	—
175	C₄⋊(C₃⋊C₈)	—	5	2	no	—
176	#803	—	5	2	no	—
177	#803	—	5	2	no	—
178	C₄×C₃⋊C₈	—	5	1	no	—
179	C₄×C₃⋊C₈	—	5	1	no	—
180	C₄×C₃⋊C₈	—	5	1	no	—
181	C₄×C₃⋊C₈	—	5	1	no	—
182	C₄×C₃⋊C₈	—	5	2	no	—
183	C₂×C₅×Q₈	C₂×Dic₃	1	1	yes	characteristic
184	C₂×C₅×D₄	C₂×Dic₃	1	1	yes	characteristic
185	C₂×C₂²⋊D₅	C₂×Dic₃	1	2	yes	—
186	C₂²×Dic₅	C₂²×D₃	1	2	yes	—
187	C₂×C₄×D₅	C₂×Dic₃	1	1	yes	characteristic
188	C₂×C₄×D₅	C₂×Dic₃	1	1	yes	characteristic
189	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
190	#704	—	6	4	no	—
191	C₂×#170	—	3	1	no	—
192	C₂×#170	—	3	1	no	—
193	C₂×#170	—	3	1	no	—
194	C₂×#170	—	3	1	no	—
195	C₂×#170	—	3	2	no	—
196	C₂×#170	—	3	2	no	—
197	C₂×#170	—	6	4	no	—
198	D₅⋊C₈	—	6	2	no	—
199	D₅⋊C₈	—	6	2	no	—
200	C₅×C₂²⋊C₄	C₂×Dic₃	1	2	yes	—
201	C₅×C₂²⋊C₄	C₂×Dic₃	1	2	yes	—
202	C₄²×C₅	C₂×Dic₃	1	1	yes	characteristic
203	C₂²⋊Dic₅	C₂×Dic₃	1	2	yes	—
204	C₂²⋊Dic₅	C₂×Dic₃	1	2	yes	—
205	#685	C₂×Dic₃	1	2	yes	—
206	C₄⋊Dic₅	C₂×Dic₃	1	1	yes	characteristic
207	C₄⋊Dic₅	C₂×Dic₃	1	1	yes	characteristic
208	C₄⋊Dic₅	C₂×Dic₃	1	2	yes	—
209	#683	C₂×Dic₃	1	2	yes	—
210	#683	C₂×Dic₃	1	2	yes	—
211	#683	C₂×Dic₃	1	2	yes	—
212	C₄×Dic₅	C₂×Dic₃	1	1	yes	characteristic
213	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
214	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
215	C₄×Dic₅	C₂²×D₃	1	2	yes	—
216	#529	—	5	1	no	—
217	#446	—	15	1	no	—
218	C₈×Q₈	—	15	1	no	—
219	#436	—	15	1	no	—
220	#435	—	15	2	no	—
221	C₈×D₄	—	15	2	no	—
222	C₈×D₄	—	15	1	no	—
223	#433	—	15	2	no	—
224	#432	—	15	1	no	—
225	#405	—	15	2	no	—
226	C₂×C₄×C₈	—	15	1	no	—
227	C₂²×C₃×C₅	—	2	2	no	—
228	C₂²×C₃×C₅	—	2	2	no	—
229	C₂²×C₃×C₅	—	2	2	no	—
230	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
231	C₂×C₃×D₅	—	2	1	no	—
232	C₂×C₃×D₅	—	2	1	no	—
233	C₂×C₃×D₅	#131	1	2	yes	—
234	C₃×C₄×C₅	—	2	1	no	—
235	C₃×C₄×C₅	—	2	1	no	—
236	C₃×C₄×C₅	—	2	2	no	—
237	C₃×C₄×C₅	#131	1	2	yes	—
238	C₃×Dic₅	—	2	2	no	—
239	C₃×Dic₅	—	2	1	no	—
240	C₃×Dic₅	—	2	1	no	—
241	C₃×Dic₅	—	2	2	no	—
242	C₃×Dic₅	C₂×#41	1	1	yes	characteristic
243	C₃×Dic₅	C₂×#41	1	1	yes	characteristic
244	C₂×C₃×Q₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
245	C₂×C₃×D₄	—	5	2	no	—
246	C₂×C₃×D₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
247	C₂²×C₃×C₄	—	5	2	no	—
248	C₂²×C₃×C₄	—	5	1	no	—
249	C₂²×C₃×C₄	—	5	1	no	—
250	C₂²×C₃×C₄	—	5	1	no	—
251	C₃×C₄⋊C₄	—	5	2	no	—
252	C₃×C₄⋊C₄	—	5	2	no	—
253	C₃×C₄⋊C₄	—	5	2	no	—
254	C₃×C₄⋊C₄	—	5	1	no	—
255	C₃×C₄⋊C₄	—	5	1	no	—
256	C₃×C₄⋊C₄	—	5	2	no	—
257	C₃×C₂²⋊C₄	—	5	2	no	—
258	C₃×C₂²⋊C₄	—	5	2	no	—
259	C₃×C₂²⋊C₄	—	5	2	no	—
260	C₃×C₂²⋊C₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
261	C₃×C₂²⋊C₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
262	C₃×C₄²	—	5	1	no	—
263	C₃×C₄²	—	5	1	no	—
264	C₃×C₄²	—	5	1	no	—
265	C₃×C₄²	—	5	2	no	—
266	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
267	#208	—	10	4	no	—
268	C₂×C₃⋊C₈	—	5	1	no	—
269	C₂×C₃⋊C₈	—	5	1	no	—
270	C₂×C₃⋊C₈	—	5	1	no	—
271	C₂×C₃⋊C₈	—	5	1	no	—
272	C₂×C₃⋊C₈	—	5	2	no	—
273	C₂×C₃⋊C₈	—	5	2	no	—
274	C₂×C₃⋊C₈	—	10	2	no	—
275	C₂×C₃⋊C₈	—	10	2	no	—
276	C₂×C₃⋊C₈	—	10	4	no	—
277	C₂³×C₅	C₂²×Dic₃	1	2	yes	—
278	C₂²×D₅	C₂²×Dic₃	1	1	yes	characteristic
279	C₅×Q₈	—	2	2	no	—
280	C₅×D₄	—	2	2	no	—
281	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
282	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
283	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
284	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
285	C₂²⋊D₅	—	2	4	no	—
286	C₂×Dic₅	—	2	2	no	—
287	C₂×Dic₅	—	2	2	no	—
288	C₂×Dic₅	C₂²×Dic₃	1	1	yes	characteristic
289	C₂×Dic₅	C₂²×Dic₃	1	1	yes	characteristic
290	C₂×Dic₅	C₂²×Dic₃	1	2	yes	—
291	C₂×Dic₅	C₂²×Dic₃	1	2	yes	—
292	C₂×Dic₅	C₂³×D₃	1	1	yes	characteristic
293	C₄×D₅	—	2	2	no	—
294	C₄×D₅	—	2	2	no	—
295	C₄×D₅	—	2	1	no	—
296	C₄×D₅	—	2	1	no	—
297	#170	—	3	2	no	—
298	#170	—	3	2	no	—
299	#170	—	6	1	no	—
300	#170	—	6	1	no	—
301	#170	—	6	2	no	—
302	#170	—	6	2	no	—
303	C₂×M₁₆	—	15	2	no	—
304	C₂²×C₈	—	15	1	no	—
305	C₂²×C₈	—	15	1	no	—
306	C₂²×C₈	—	15	2	no	—
307	#126	—	5	2	no	—
308	#125	—	5	1	no	—
309	#124	ΓL(1,𝔽₁₆)	1	1	yes	characteristic
310	#123	—	5	2	no	—
311	C₂²⋊Q₈	—	5	1	no	—
312	#121	—	5	1	no	—
313	C₄×Q₈	—	5	1	no	—
314	C₄×D₄	—	5	1	no	—
315	C₄×D₄	—	5	2	no	—
316	#117	—	5	2	no	—
317	C₂×C₄²	—	5	1	no	—
318	C₄⋊C₈	—	15	1	no	—
319	C₄⋊C₈	—	15	1	no	—
320	C₄⋊C₈	—	15	2	no	—
321	C₄⋊C₈	—	15	2	no	—
322	C₂²⋊C₈	—	15	2	no	—
323	C₂²⋊C₈	—	15	2	no	—
324	C₂²⋊C₈	—	15	2	no	—
325	#97	—	15	2	no	—
326	#97	—	15	2	no	—
327	C₄×C₈	—	15	1	no	—
328	C₄×C₈	—	15	1	no	—
329	C₄×C₈	—	15	1	no	—
330	C₄×C₈	—	15	1	no	—
331	C₄×C₈	—	15	2	no	—
332	C₂×C₃×C₅	—	4	2	no	—
333	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
334	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
335	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
336	C₃×D₅	—	2	2	no	—
337	C₂³×C₃	—	5	1	no	—
338	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	2	yes	—
339	C₃×Q₈	—	2	2	no	—
340	C₃×D₄	—	2	2	no	—
341	C₃×D₄	—	10	4	no	—
342	C₂×C₃×C₄	—	5	1	no	—
343	C₂×C₃×C₄	—	5	1	no	—
344	C₂×C₃×C₄	—	5	1	no	—
345	C₂×C₃×C₄	—	5	2	no	—
346	C₂×C₃×C₄	—	5	2	no	—
347	C₂×C₃×C₄	—	10	1	no	—
348	C₂×C₃×C₄	—	10	1	no	—
349	C₂×C₃×C₄	—	10	2	no	—
350	C₂×C₃×C₄	—	10	2	no	—
351	C₂×C₃×C₄	—	10	2	no	—
352	C₂×C₃×C₄	—	10	2	no	—
353	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
354	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
355	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
356	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
357	C₃⋊C₈	—	5	2	no	—
358	C₃⋊C₈	—	5	2	no	—
359	C₃⋊C₈	—	10	1	no	—
360	C₃⋊C₈	—	10	1	no	—
361	C₃⋊C₈	—	10	2	no	—
362	C₃⋊C₈	—	10	2	no	—
363	C₂²×C₅	—	2	2	no	—
364	C₂²×C₅	—	2	2	no	—
365	C₂²×C₅	—	2	2	no	—
366	C₂²×C₅	C₂³×Dic₃	1	1	yes	characteristic
367	C₂×D₅	—	2	1	no	—
368	C₂×D₅	—	2	1	no	—
369	C₂×D₅	#948	1	2	yes	—
370	C₄×C₅	—	2	1	no	—
371	C₄×C₅	—	2	2	no	—
372	C₄×C₅	—	2	1	no	—
373	C₄×C₅	#948	1	2	yes	—
374	Dic₅	—	2	1	no	—
375	Dic₅	—	2	1	no	—
376	Dic₅	—	2	2	no	—
377	Dic₅	—	2	2	no	—
378	Dic₅	D₃×#41	1	1	yes	characteristic
379	Dic₅	D₃×#41	1	1	yes	characteristic
380	C₂×Q₈	C₂×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
381	C₂×D₄	—	5	2	no	—
382	C₂×D₄	C₂×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
383	C₂²×C₄	—	5	2	no	—
384	C₂²×C₄	—	5	1	no	—
385	C₂²×C₄	—	5	1	no	—
386	C₂²×C₄	—	5	1	no	—
387	M₁₆	—	30	4	no	—
388	C₂×C₈	—	15	1	no	—
389	C₂×C₈	—	15	1	no	—
390	C₂×C₈	—	15	1	no	—
391	C₂×C₈	—	15	1	no	—
392	C₂×C₈	—	15	2	no	—
393	C₂×C₈	—	15	2	no	—
394	C₂×C₈	—	30	2	no	—
395	C₂×C₈	—	30	2	no	—
396	C₂×C₈	—	30	4	no	—
397	C₄⋊C₄	—	5	2	no	—
398	C₄⋊C₄	—	5	2	no	—
399	C₄⋊C₄	—	5	1	no	—
400	C₄⋊C₄	—	5	2	no	—
401	C₄⋊C₄	—	5	1	no	—
402	C₄⋊C₄	—	5	2	no	—
403	C₂²⋊C₄	—	5	2	no	—
404	C₂²⋊C₄	—	5	2	no	—
405	C₂²⋊C₄	—	5	2	no	—
406	C₂²⋊C₄	C₂×ΓL(1,𝔽₁₆)	1	2	yes	—
407	C₂²⋊C₄	C₂×ΓL(1,𝔽₁₆)	1	2	yes	—
408	C₄²	—	5	1	no	—
409	C₄²	—	5	1	no	—
410	C₄²	—	5	2	no	—
411	C₄²	—	5	1	no	—
412	C₄²	C₂×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
413	C₃×C₅	#2966	1	1	yes	characteristic, complemented, Hall
414	C₂²×C₃	—	2	2	no	—
415	C₂²×C₃	—	2	2	no	—
416	C₂²×C₃	—	2	2	no	—
417	C₂²×C₃	—	5	2	no	—
418	C₂²×C₃	—	10	1	no	—
419	C₂²×C₃	—	10	1	no	—
420	C₂²×C₃	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
421	C₃×C₄	—	2	2	no	—
422	C₃×C₄	—	2	1	no	—
423	C₃×C₄	—	2	1	no	—
424	C₃×C₄	—	5	1	no	—
425	C₃×C₄	—	5	1	no	—
426	C₃×C₄	—	10	1	no	—
427	C₃×C₄	—	10	1	no	—
428	C₃×C₄	—	10	2	no	—
429	C₃×C₄	—	10	2	no	—
430	C₃×C₄	#4131	1	2	yes	—
431	C₂×C₅	—	4	2	no	—
432	C₂×C₅	C₂×#948	1	1	yes	characteristic
433	C₂×C₅	C₂×#948	1	1	yes	characteristic
434	C₂×C₅	Dic₃×#41	1	1	yes	characteristic
435	D₅	—	2	2	no	—
436	C₂³	—	5	1	no	—
437	C₂³	C₂²×ΓL(1,𝔽₁₆)	1	2	yes	—
438	Q₈	—	2	2	no	—
439	D₄	—	2	2	no	—
440	D₄	—	10	4	no	—
441	C₂×C₄	—	5	1	no	—
442	C₂×C₄	—	5	1	no	—
443	C₂×C₄	—	5	1	no	—
444	C₂×C₄	—	5	2	no	—
445	C₂×C₄	—	5	2	no	—
446	C₂×C₄	—	10	1	no	—
447	C₂×C₄	—	10	1	no	—
448	C₂×C₄	—	10	2	no	—
449	C₂×C₄	—	10	2	no	—
450	C₂×C₄	—	10	2	no	—
451	C₂×C₄	—	10	2	no	—
452	C₂×C₄	C₂²×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
453	C₂×C₄	C₂²×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
454	C₂×C₄	C₂²×ΓL(1,𝔽₁₆)	1	2	yes	—
455	C₂×C₄	C₂²×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
456	C₈	—	15	2	no	—
457	C₈	—	15	2	no	—
458	C₈	—	30	1	no	—
459	C₈	—	30	1	no	—
460	C₈	—	30	2	no	—
461	C₈	—	30	2	no	—
462	C₂×C₃	—	4	2	no	—
463	C₂×C₃	—	10	2	no	—
464	C₂×C₃	C₂×#4131	1	1	yes	characteristic
465	C₂×C₃	D₅⋊#131	1	1	yes	characteristic
466	C₂×C₃	#41×AGL(1,𝔽₅)	1	1	yes	characteristic
467	C₅	#83126	1	1	yes	characteristic, complemented, Sylow
468	C₂²	—	2	2	no	—
469	C₂²	—	2	2	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	5	2	no	—
472	C₂²	—	10	1	no	—
473	C₂²	—	10	1	no	—
474	C₂²	C₂³×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
475	C₄	—	2	2	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	5	1	no	—
479	C₄	—	5	1	no	—
480	C₄	—	10	1	no	—
481	C₄	—	10	1	no	—
482	C₄	—	10	2	no	—
483	C₄	—	10	2	no	—
484	C₄	#91990	1	2	yes	—
485	C₃	#10617312	1	1	yes	characteristic, complemented, Sylow
486	C₂	—	4	2	no	—
487	C₂	—	10	2	no	—
488	C₂	C₂×#91990	1	1	yes	characteristic
489	C₂	D₅⋊#948	1	1	yes	characteristic
490	C₂	#41×ΓL(1,𝔽₁₆)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×ΓL(1,𝔽₁₆)
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Fitting	C₃×C₅×#124	C₄
prime radical	C₃×#4084	C₄
cosocle	C₂×C₃×Dic₅	C₂⁴
hypercenter	#124	ΓL(1,𝔽₁₆)
hypocenter	C₃×C₅	#2966
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ #124

Complements

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

N	H ≅ G/N	type
2. #11752447	C₂	semidirect
3. Q₈×C₃⋊#170	C₂	semidirect
4. #11752433	C₂	semidirect
5. D₄×C₃⋊#170	C₂	semidirect
6. #11752356	C₂	semidirect
7. #11752353	C₂	semidirect
8. #11752351	C₂	semidirect
9. #11752350	C₂	semidirect
10. #11752342	C₂	semidirect
11. C₄×D₅⋊(C₃⋊C₈)	C₂	semidirect
413. C₃×C₅	#2966	semidirect
467. C₅	#83126	semidirect
485. C₃	#10617312	semidirect

Maximal subgroups

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

subgroup	index
C₃×#66014	2
#11752447	2
Q₈×C₃⋊#170	2
#11752433	2
D₄×C₃⋊#170	2
#11752356	2
#11752353	2
#11752351	2
#11752350	2
#11752342	2
C₄×D₅⋊(C₃⋊C₈)	2
#10617312	3
#83126	5