Subgroups — #14418933

Order 1920.

912 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×#6768	C₂	1	1	yes	maximal, characteristic
2	#11750934	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#4834	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65119	C₂	1	1	yes	maximal, characteristic, complemented
5	#11748044	C₂	1	2	yes	maximal, complemented
6	#11747700	C₂	1	2	yes	maximal, complemented
7	#11747581	C₂	1	2	yes	maximal, complemented
8	D₃×C₈×Dic₅	C₂	1	2	yes	maximal, complemented
9	D₁₂×#168	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#6648	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃⋊C₈×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈×#711	—	3	1	no	maximal, Hall
13	C₂×#6768	C₄	1	1	yes	characteristic
14	C₄²×D₁₅	C₂²	1	1	yes	characteristic
15	C₂×C₅×D₃×C₈	C₂²	1	2	yes	—
16	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
17	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
18	C₄×#1203	C₂²	1	2	yes	—
19	#91435	C₄	1	1	yes	characteristic
20	#91406	C₄	1	2	yes	—
21	#91400	C₄	1	2	yes	—
22	C₄×D₃×Dic₅	C₂²	1	2	yes	—
23	#91347	C₄	1	1	yes	characteristic
24	#91331	C₄	1	1	yes	characteristic
25	C₂×#6648	C₂²	1	1	yes	characteristic
26	C₂×#6648	C₂²	1	1	yes	characteristic
27	C₂×D₃×#168	C₂²	1	2	yes	—
28	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	#91104	C₂²	1	2	yes	—
30	C₈×Dic₁₅	C₂²	1	2	yes	—
31	C₄⋊(C₃⋊#168)	C₂²	1	1	yes	characteristic
32	C₅×(C₂×D₃)⋊C₈	C₂²	1	2	yes	—
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	#90982	C₂²	1	2	yes	—
38	(C₂×D₃)⋊#168	C₂²	1	2	yes	—
39	#90951	C₂²	1	1	yes	characteristic
40	#90951	C₂²	1	1	yes	characteristic
41	Dic₅×C₃⋊C₈	C₂²	1	2	yes	—
42	C₈×#239	—	5	1	no	maximal, Hall
43	C₄×#711	—	3	1	no	—
44	C₅×C₈×D₄	—	3	1	no	—
45	C₈×C₂²⋊D₅	—	3	2	no	—
46	C₂×C₈×Dic₅	—	3	2	no	—
47	D₄×#168	—	3	1	no	—
48	#65122	—	3	1	no	—
49	#65119	D₃	1	1	yes	characteristic, complemented
50	#65014	—	3	2	no	—
51	#65007	—	3	2	no	—
52	C₄×C₈×D₅	—	3	1	no	—
53	C₈×Dic₁₀	—	3	1	no	—
54	C₂×C₄×D₁₅	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄×D₁₅	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄×D₁₅	C₂³	1	1	yes	characteristic
57	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
59	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
60	C₂×#1203	C₂×C₄	1	2	yes	—
61	C₂×D₃×Dic₅	C₂×C₄	1	2	yes	—
62	C₂×D₃×Dic₅	C₂×C₄	1	2	yes	—
63	#6768	C₈	1	8	yes	complemented
64	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
65	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
66	C₄×Dic₁₅	C₂×C₄	1	1	yes	characteristic
67	C₄×Dic₁₅	C₂×C₄	1	1	yes	characteristic
68	C₄×Dic₁₅	C₂³	1	1	yes	characteristic
69	C₂×C₃⋊#168	C₂³	1	2	yes	—
70	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
71	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
72	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
73	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
74	C₅×D₃×C₈	—	2	4	no	—
75	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
76	C₃×#683	C₂×C₄	1	2	yes	—
77	C₃×C₄×Dic₅	C₂³	1	2	yes	—
78	C₂×C₃×#168	C₂³	1	1	yes	characteristic
79	C₂×C₃×#168	C₂³	1	1	yes	characteristic
80	#6668	C₂×C₄	1	2	yes	—
81	#6667	C₂×C₄	1	2	yes	—
82	(C₂×D₃)⋊Dic₅	C₂×C₄	1	2	yes	—
83	Dic₃×Dic₅	C₂×C₄	1	2	yes	—
84	Dic₃×Dic₅	C₂×C₄	1	2	yes	—
85	#6648	—	2	2	no	—
86	#6648	—	2	2	no	—
87	D₃×#168	—	2	4	no	—
88	C₄×#239	—	5	1	no	—
89	C₃×C₈×Q₈	—	5	1	no	—
90	Q₈×C₃⋊C₈	—	5	1	no	—
91	#4834	—	5	2	no	—
92	#4834	D₅	1	1	yes	characteristic, complemented
93	#4833	—	5	1	no	—
94	#4833	—	5	2	no	—
95	C₈×D₁₂	—	5	1	no	—
96	C₈×D₁₂	—	5	2	no	—
97	C₄×D₃×C₈	—	5	2	no	—
98	C₄×D₃×C₈	—	5	1	no	—
99	C₂×#711	—	3	1	no	—
100	C₂²×C₅×C₈	—	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	C₂²×#168	—	3	2	no	—
106	C₂×C₈×D₅	—	3	1	no	—
107	C₂×C₈×D₅	—	3	1	no	—
108	#4038	—	3	1	no	—
109	#4033	—	3	1	no	—
110	#4027	—	3	2	no	—
111	#4023	—	3	2	no	—
112	C₄²×D₅	—	3	1	no	—
113	C₄×Dic₁₀	C₂×D₃	1	1	yes	characteristic
114	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
115	C₅×C₂²⋊C₈	—	3	2	no	—
116	C₄×C₅×C₈	—	3	1	no	—
117	C₂²⋊#168	—	3	2	no	—
118	#3952	—	3	2	no	—
119	#3946	—	3	2	no	—
120	#3946	C₂×D₃	1	2	yes	—
121	C₈×Dic₅	—	3	2	no	—
122	C₈×Dic₅	—	3	2	no	—
123	C₈×Dic₅	—	3	1	no	—
124	C₈×Dic₅	—	3	1	no	—
125	C₈×Dic₅	C₂×D₃	1	2	yes	—
126	C₄⋊#168	—	3	1	no	—
127	C₄×#168	C₂×D₃	1	1	yes	characteristic
128	C₈×#41	—	15	1	no	Sylow
129	C₂²×D₁₅	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
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	1	yes	characteristic
135	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
136	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
137	C₄×D₁₅	—	2	1	no	—
138	C₄×D₁₅	—	2	1	no	—
139	C₄×D₁₅	—	2	2	no	—
140	C₄×D₁₅	C₂×C₈	1	4	yes	complemented
141	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
142	C₅×D₁₂	C₂×C₈	1	4	yes	complemented
143	C₄×C₅×D₃	—	2	2	no	—
144	C₄×C₅×D₃	—	2	2	no	—
145	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
146	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
147	C₃×Dic₁₀	C₂×C₈	1	4	yes	complemented
148	#1203	C₂×C₈	1	8	yes	complemented
149	D₃×Dic₅	—	2	4	no	—
150	D₃×Dic₅	C₂×C₈	1	8	yes	complemented
151	C₃×C₅×C₈	—	2	2	no	—
152	C₃⋊#168	—	2	2	no	—
153	C₃×#168	—	2	1	no	—
154	C₃×#168	#41	1	2	yes	complemented
155	C₅×C₃⋊C₈	—	2	1	no	—
156	C₅×C₃⋊C₈	#41	1	2	yes	complemented
157	C₂×#239	—	5	1	no	—
158	C₃×C₄×Q₈	—	5	1	no	—
159	Q₈×Dic₃	—	5	1	no	—
160	C₂×D₃×C₈	—	5	2	no	—
161	C₂×D₃×C₈	—	5	1	no	—
162	C₂×D₃×C₈	—	5	1	no	—
163	C₂×D₃×C₈	C₂×D₅	1	2	yes	—
164	#893	—	5	1	no	—
165	#893	—	5	2	no	—
166	#892	—	5	2	no	—
167	#892	—	5	1	no	—
168	C₄×D₁₂	—	5	2	no	—
169	C₄×D₁₂	C₂×D₅	1	1	yes	characteristic
170	C₄²×D₃	—	5	2	no	—
171	C₄²×D₃	—	5	1	no	—
172	C₃×C₄⋊C₈	—	5	2	no	—
173	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
174	C₃×C₄×C₈	—	5	2	no	—
175	C₃×C₄×C₈	—	5	1	no	—
176	(C₂×D₃)⋊C₈	—	5	2	no	—
177	(C₂×D₃)⋊C₈	—	5	2	no	—
178	(C₂×D₃)⋊C₈	C₂×D₅	1	2	yes	—
179	C₈×Dic₃	—	5	2	no	—
180	C₈×Dic₃	—	5	1	no	—
181	C₈×Dic₃	—	5	1	no	—
182	C₄⋊(C₃⋊C₈)	—	5	1	no	—
183	C₄⋊(C₃⋊C₈)	—	5	2	no	—
184	C₄×C₃⋊C₈	—	5	2	no	—
185	C₄×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
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	—	3	8	no	—
192	C₂×C₄×D₅	—	3	1	no	—
193	C₂×C₄×D₅	—	3	1	no	—
194	C₂×C₄×D₅	—	3	1	no	—
195	C₂×Dic₁₀	C₄×D₃	1	1	yes	characteristic
196	C₂×C₅×C₈	—	3	1	no	—
197	C₂×C₅×C₈	—	3	1	no	—
198	C₂×C₅×C₈	—	6	4	no	—
199	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
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	C₄×D₃	1	1	yes	characteristic
206	#683	—	3	2	no	—
207	#683	C₄×D₃	1	2	yes	—
208	C₄×Dic₅	—	3	1	no	—
209	C₄×Dic₅	—	3	1	no	—
210	C₄×Dic₅	—	3	1	no	—
211	C₄×Dic₅	—	3	2	no	—
212	C₄×Dic₅	—	3	2	no	—
213	C₄×Dic₅	C₂²×D₃	1	2	yes	—
214	C₂×#168	—	3	2	no	—
215	C₂×#168	—	6	4	no	—
216	C₂×#168	C₂²×D₃	1	1	yes	characteristic
217	C₂×#168	C₂²×D₃	1	1	yes	characteristic
218	C₈×D₅	—	6	2	no	—
219	C₈×D₅	—	6	2	no	—
220	C₄×#41	—	15	1	no	—
221	C₈×Q₈	—	5	1	no	—
222	C₈×Q₈	—	15	1	no	—
223	C₈×D₄	—	3	1	no	—
224	C₈×D₄	—	15	2	no	—
225	C₈×D₄	—	15	1	no	—
226	C₈×D₄	—	15	2	no	—
227	#431	—	15	2	no	—
228	#431	—	15	1	no	—
229	C₂×C₄×C₈	—	15	1	no	—
230	C₂×C₄×C₈	—	15	2	no	—
231	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
232	C₂×D₁₅	—	2	1	no	—
233	C₂×D₁₅	—	2	1	no	—
234	C₂×D₁₅	C₂²×C₈	1	2	yes	—
235	C₂×C₅×D₃	—	2	2	no	—
236	C₂×C₅×D₃	—	2	2	no	—
237	C₂×C₅×D₃	C₂²×C₈	1	4	yes	—
238	C₃×C₄×C₅	—	2	1	no	—
239	C₃×C₄×C₅	C₂²×C₈	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	1	no	—
243	Dic₁₅	C₂²×C₈	1	2	yes	—
244	Dic₁₅	#131	1	2	yes	—
245	C₃×Dic₅	—	2	2	no	—
246	C₃×Dic₅	C₂²×C₈	1	4	yes	—
247	C₅×Dic₃	—	2	2	no	—
248	C₂×C₃×Q₈	—	5	1	no	—
249	#239	—	5	8	no	—
250	C₂×D₁₂	—	5	2	no	—
251	C₂×D₁₂	C₄×D₅	1	1	yes	characteristic
252	C₂×C₄×D₃	—	5	2	no	—
253	C₂×C₄×D₃	—	5	1	no	—
254	C₂×C₄×D₃	—	5	2	no	—
255	C₂×C₄×D₃	—	5	1	no	—
256	C₂×C₄×D₃	—	5	1	no	—
257	C₂×C₄×D₃	C₂²×D₅	1	2	yes	—
258	C₂×C₃×C₈	—	5	1	no	—
259	C₂×C₃×C₈	—	5	1	no	—
260	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
261	C₃×C₄⋊C₄	—	5	2	no	—
262	C₃×C₄⋊C₄	—	5	1	no	—
263	C₃×C₄²	—	5	2	no	—
264	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
265	(C₂×D₃)⋊C₄	—	5	2	no	—
266	(C₂×D₃)⋊C₄	—	5	2	no	—
267	(C₂×D₃)⋊C₄	C₄×D₅	1	2	yes	—
268	C₄⋊Dic₃	—	5	2	no	—
269	C₄⋊Dic₃	C₄×D₅	1	1	yes	characteristic
270	C₄×Dic₃	—	5	1	no	—
271	C₄×Dic₃	—	5	1	no	—
272	C₄×Dic₃	—	5	1	no	—
273	C₄×Dic₃	—	5	2	no	—
274	C₄×Dic₃	—	5	2	no	—
275	C₂×C₃⋊C₈	—	5	2	no	—
276	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
277	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
278	D₃×C₈	—	2	4	no	—
279	D₃×C₈	—	10	2	no	—
280	D₃×C₈	—	10	4	no	—
281	D₃×C₈	—	10	2	no	—
282	C₂³×C₅	—	3	2	no	—
283	C₂²×D₅	—	3	1	no	—
284	C₅×D₄	—	3	4	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	—	3	8	no	—
292	C₂×Dic₅	—	3	1	no	—
293	C₂×Dic₅	—	3	1	no	—
294	C₂×Dic₅	—	3	8	no	—
295	C₂×Dic₅	—	3	1	no	—
296	C₂×Dic₅	—	6	4	no	—
297	C₂×Dic₅	C₂×C₄×D₃	1	2	yes	—
298	C₂×Dic₅	C₂×C₄×D₃	1	2	yes	—
299	C₄×D₅	—	3	4	no	—
300	C₄×D₅	—	6	2	no	—
301	C₄×D₅	—	6	1	no	—
302	C₄×D₅	—	6	1	no	—
303	Dic₁₀	D₃×C₈	1	4	yes	complemented
304	C₅×C₈	—	2	2	no	—
305	C₅×C₈	—	3	2	no	—
306	C₅×C₈	—	6	1	no	—
307	#168	—	2	1	no	—
308	#168	—	6	2	no	—
309	#168	#239	1	2	yes	complemented
310	C₂×#41	—	15	1	no	—
311	C₂²×C₈	—	3	2	no	—
312	C₂²×C₈	—	15	1	no	—
313	C₂²×C₈	—	15	1	no	—
314	C₂²×C₈	—	15	2	no	—
315	C₄×Q₈	—	5	1	no	—
316	C₄×Q₈	—	15	1	no	—
317	C₄×D₄	—	3	1	no	—
318	C₄×D₄	—	15	2	no	—
319	C₄×D₄	—	15	2	no	—
320	C₄×D₄	—	15	1	no	—
321	#117	—	15	2	no	—
322	#117	—	15	1	no	—
323	C₂×C₄²	—	15	2	no	—
324	C₂×C₄²	—	15	1	no	—
325	C₄⋊C₈	—	5	2	no	—
326	C₄⋊C₈	—	15	2	no	—
327	C₄⋊C₈	—	15	1	no	—
328	C₄⋊C₈	D₃×D₅	1	1	yes	characteristic
329	C₂²⋊C₈	—	3	2	no	—
330	C₂²⋊C₈	—	15	2	no	—
331	C₂²⋊C₈	—	15	2	no	—
332	C₄×C₈	—	3	1	no	—
333	C₄×C₈	—	5	2	no	—
334	C₄×C₈	—	5	1	no	—
335	C₄×C₈	—	15	2	no	—
336	C₄×C₈	—	15	1	no	—
337	C₄×C₈	—	15	1	no	—
338	C₄×C₈	—	15	2	no	—
339	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
340	C₂×C₃×C₅	C₂³×C₈	1	1	yes	characteristic
341	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
342	D₁₅	—	2	2	no	—
343	C₅×D₃	—	2	4	no	—
344	C₂²×D₃	—	5	1	no	—
345	C₂²×D₃	C₂×C₄×D₅	1	2	yes	—
346	C₃×Q₈	—	5	4	no	—
347	C₂×C₃×C₄	—	5	2	no	—
348	C₂×C₃×C₄	—	5	2	no	—
349	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
350	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
351	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
352	C₂×Dic₃	—	5	1	no	—
353	C₂×Dic₃	—	5	1	no	—
354	C₂×Dic₃	—	5	1	no	—
355	C₂×Dic₃	C₂×C₄×D₅	1	2	yes	—
356	D₁₂	—	5	8	no	—
357	D₁₂	C₈×D₅	1	4	yes	complemented
358	C₄×D₃	—	2	2	no	—
359	C₄×D₃	—	2	2	no	—
360	C₄×D₃	—	5	8	no	—
361	C₄×D₃	—	5	4	no	—
362	C₄×D₃	—	10	2	no	—
363	C₄×D₃	—	10	4	no	—
364	C₄×D₃	—	10	1	no	—
365	C₄×D₃	—	10	1	no	—
366	C₃×C₈	—	2	2	no	—
367	C₃×C₈	—	5	2	no	—
368	C₃×C₈	—	10	1	no	—
369	C₃⋊C₈	—	2	1	no	—
370	C₃⋊C₈	—	10	2	no	—
371	C₃⋊C₈	#711	1	2	yes	complemented
372	C₂²×C₅	—	3	4	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	—	3	2	no	—
377	C₂×D₅	—	6	1	no	—
378	C₂×D₅	—	6	1	no	—
379	C₄×C₅	—	2	1	no	—
380	C₄×C₅	—	6	2	no	—
381	C₄×C₅	C₂×D₃×C₈	1	2	yes	—
382	C₄×C₅	C₂×#239	1	1	yes	characteristic
383	C₄×C₅	D₃×#41	1	1	yes	characteristic
384	Dic₅	—	2	2	no	—
385	Dic₅	—	3	2	no	—
386	Dic₅	—	3	2	no	—
387	Dic₅	—	6	1	no	—
388	Dic₅	C₂×D₃×C₈	1	4	yes	—
389	#41	—	15	8	no	—
390	C₂×Q₈	—	5	1	no	—
391	C₂×D₄	—	3	1	no	—
392	C₂×D₄	—	15	2	no	—
393	C₂²×C₄	—	3	2	no	—
394	C₂²×C₄	—	15	2	no	—
395	C₂²×C₄	—	15	2	no	—
396	C₂²×C₄	—	15	1	no	—
397	C₂²×C₄	—	15	1	no	—
398	C₂²×C₄	—	15	1	no	—
399	C₂×C₈	—	3	1	no	—
400	C₂×C₈	—	3	1	no	—
401	C₂×C₈	—	5	1	no	—
402	C₂×C₈	—	5	1	no	—
403	C₂×C₈	—	6	4	no	—
404	C₂×C₈	—	15	2	no	—
405	C₂×C₈	—	30	2	no	—
406	C₂×C₈	—	30	2	no	—
407	C₂×C₈	—	30	4	no	—
408	C₂×C₈	C₂×D₃×D₅	1	2	yes	—
409	C₄⋊C₄	—	3	1	no	—
410	C₄⋊C₄	—	5	2	no	—
411	C₄⋊C₄	—	5	1	no	—
412	C₄⋊C₄	—	15	2	no	—
413	C₂²⋊C₄	—	3	2	no	—
414	C₂²⋊C₄	—	15	2	no	—
415	C₂²⋊C₄	—	15	2	no	—
416	C₄²	—	5	2	no	—
417	C₄²	—	15	2	no	—
418	C₄²	—	15	2	no	—
419	C₄²	—	15	1	no	—
420	C₄²	—	15	1	no	—
421	C₄²	—	15	1	no	—
422	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
423	C₃×C₅	C₈×#41	1	1	yes	characteristic, complemented, Hall
424	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
425	C₂×D₃	—	2	2	no	—
426	C₂×D₃	—	2	2	no	—
427	C₂×D₃	—	5	2	no	—
428	C₂×D₃	—	10	1	no	—
429	C₂×D₃	—	10	1	no	—
430	C₂×D₃	C₂×C₈×D₅	1	4	yes	—
431	C₃×C₄	—	2	1	no	—
432	C₃×C₄	—	5	4	no	—
433	C₃×C₄	—	10	2	no	—
434	C₃×C₄	C₂×C₈×D₅	1	2	yes	—
435	C₃×C₄	C₂×#711	1	1	yes	characteristic
436	C₃×C₄	D₅×#41	1	1	yes	characteristic
437	Dic₃	—	2	2	no	—
438	Dic₃	—	5	2	no	—
439	Dic₃	—	5	2	no	—
440	Dic₃	—	10	1	no	—
441	C₂×C₅	—	6	4	no	—
442	C₂×C₅	C₄×#239	1	1	yes	characteristic
443	C₂×C₅	C₂²×D₃×C₈	1	1	yes	characteristic
444	C₂×C₅	D₃×#131	1	1	yes	characteristic
445	D₅	—	6	2	no	—
446	C₂³	—	3	2	no	—
447	C₂³	—	15	1	no	—
448	Q₈	—	5	4	no	—
449	D₄	—	3	4	no	—
450	D₄	—	15	8	no	—
451	C₂×C₄	—	3	2	no	—
452	C₂×C₄	—	5	2	no	—
453	C₂×C₄	—	5	2	no	—
454	C₂×C₄	—	6	2	no	—
455	C₂×C₄	—	6	2	no	—
456	C₂×C₄	—	15	8	no	—
457	C₂×C₄	—	15	1	no	—
458	C₂×C₄	—	15	1	no	—
459	C₂×C₄	—	15	4	no	—
460	C₂×C₄	—	15	1	no	—
461	C₂×C₄	—	30	2	no	—
462	C₂×C₄	—	30	4	no	—
463	C₂×C₄	—	30	1	no	—
464	C₂×C₄	—	30	1	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	2	no	—
469	C₈	—	3	2	no	—
470	C₈	—	5	2	no	—
471	C₈	—	6	1	no	—
472	C₈	—	10	1	no	—
473	C₈	—	30	2	no	—
474	C₂×C₃	C₄×#711	1	1	yes	characteristic
475	C₂×C₃	C₂²×C₈×D₅	1	1	yes	characteristic
476	C₂×C₃	D₅×#131	1	1	yes	characteristic
477	D₃	—	2	4	no	—
478	D₃	—	10	2	no	—
479	C₅	C₈×#239	1	1	yes	characteristic, complemented, Sylow
480	C₂²	—	3	4	no	—
481	C₂²	—	6	2	no	—
482	C₂²	—	6	2	no	—
483	C₂²	—	15	2	no	—
484	C₂²	—	30	1	no	—
485	C₂²	—	30	1	no	—
486	C₂²	C₂×C₄×D₃×D₅	1	1	yes	characteristic
487	C₄	—	2	1	no	—
488	C₄	—	5	4	no	—
489	C₄	—	6	2	no	—
490	C₄	—	10	2	no	—
491	C₄	—	15	2	no	—
492	C₄	—	15	2	no	—
493	C₄	—	30	1	no	—
494	C₄	D₃×C₈×D₅	1	2	yes	—
495	C₄	D₃×#711	1	1	yes	characteristic
496	C₄	D₅×#239	1	1	yes	characteristic
497	C₃	C₈×#711	1	1	yes	characteristic, complemented, Sylow
498	C₂	—	6	4	no	—
499	C₂	—	30	2	no	—
500	C₂	#11753406	1	1	yes	characteristic
501	C₂	C₂×D₃×C₈×D₅	1	1	yes	characteristic
502	C₂	#11754017	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃×D₅
commutator	C₂×C₃×C₅	C₂³×C₈
Fitting	C₃×C₅×C₄⋊C₈	C₂²
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂×#6768	C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₄⋊C₈	D₃×D₅
hypocenter	C₃×C₅	C₈×#41
LCS	G ▷ C₂×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. #11750934	C₂	semidirect
3. C₅×#4834	C₂	semidirect
4. C₃×#65119	C₂	semidirect
5. #11748044	C₂	semidirect
6. #11747700	C₂	semidirect
7. #11747581	C₂	semidirect
8. D₃×C₈×Dic₅	C₂	semidirect
9. D₁₂×#168	C₂	semidirect
10. C₄×#6648	C₂	semidirect
11. C₃⋊C₈×Dic₁₀	C₂	semidirect
49. #65119	D₃	semidirect
63. #6768	C₈	semidirect
92. #4834	D₅	semidirect
140. C₄×D₁₅	C₂×C₈	semidirect
142. C₅×D₁₂	C₂×C₈	semidirect
147. C₃×Dic₁₀	C₂×C₈	semidirect
148. #1203	C₂×C₈	semidirect
150. D₃×Dic₅	C₂×C₈	semidirect
154. C₃×#168	#41	semidirect
156. C₅×C₃⋊C₈	#41	semidirect
303. Dic₁₀	D₃×C₈	semidirect
309. #168	#239	semidirect
357. D₁₂	C₈×D₅	semidirect
371. C₃⋊C₈	#711	semidirect
423. C₃×C₅	C₈×#41	semidirect
479. C₅	C₈×#239	semidirect
497. C₃	C₈×#711	semidirect

Maximal subgroups

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

subgroup	index
C₄×#6768	2
#11750934	2
C₅×#4834	2
C₃×#65119	2
#11748044	2
#11747700	2
#11747581	2
D₃×C₈×Dic₅	2
D₁₂×#168	2
C₄×#6648	2
C₃⋊C₈×Dic₁₀	2
C₈×#711	3
C₈×#239	5