Subgroups — #14415680

Order 1920.

1088 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₁₆×D₁₅	C₂	1	2	yes	maximal, complemented
2	C₂×C₄×D₆₀	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#423	C₂	1	1	yes	maximal, characteristic, complemented
4	#11751227	C₂	1	2	yes	maximal, complemented
5	C₄×#6710	C₂	1	1	yes	maximal, characteristic, complemented
6	#11750939	C₂	1	2	yes	maximal, complemented
7	#11750937	C₂	1	4	yes	maximal, complemented
8	#11750935	C₂	1	2	yes	maximal, complemented
9	#10610774	—	3	1	no	maximal, Hall
10	C₂²×D₆₀	C₄	1	1	yes	characteristic
11	C₂²×C₄×D₁₅	C₂²	1	2	yes	—
12	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
13	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
14	C₂×#6714	C₄	1	2	yes	—
15	C₂×C₄⋊Dic₁₅	C₄	1	1	yes	characteristic
16	C₂×#6710	C₂²	1	1	yes	characteristic
17	C₂×#6710	C₂²	1	1	yes	characteristic
18	M₁₆×D₁₅	—	2	8	no	—
19	C₂×#6705	C₂²	1	4	yes	complemented
20	C₂×C₈×D₁₅	C₂²	1	4	yes	complemented
21	C₄×D₆₀	C₄	1	2	yes	—
22	C₄×D₆₀	C₄	1	1	yes	characteristic
23	C₄×D₆₀	C₄	1	1	yes	characteristic
24	C₄×D₆₀	C₂²	1	1	yes	characteristic
25	C₄×D₆₀	C₂²	1	2	yes	—
26	C₄×D₆₀	C₂²	1	1	yes	characteristic
27	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	complemented
28	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	complemented
29	#91104	C₂²	1	4	yes	complemented
30	#91104	C₂²	1	4	yes	complemented
31	#91087	C₂²	1	2	yes	complemented
32	C₄×C₃⋊#168	C₂²	1	2	yes	complemented
33	#79043	—	5	1	no	maximal, Hall
34	C₂×D₅×M₁₆	—	3	2	no	—
35	C₂×C₄×D₂₀	—	3	1	no	—
36	C₅×#423	D₃	1	1	yes	characteristic, complemented
37	#65415	—	3	2	no	—
38	C₄×#681	—	3	1	no	—
39	#65127	—	3	2	no	—
40	#65125	—	3	4	no	—
41	#65123	—	3	2	no	—
42	C₂³×D₁₅	C₂×C₄	1	2	yes	—
43	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₂²×Dic₁₅	C₂×C₄	1	2	yes	—
47	C₂×D₆₀	—	2	4	no	—
48	C₂×D₆₀	C₂×C₄	1	2	yes	—
49	C₂×D₆₀	C₂×C₄	1	1	yes	characteristic
50	C₂×D₆₀	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄×D₁₅	—	2	4	no	—
52	C₂×C₄×D₁₅	—	2	4	no	—
53	C₂×C₄×D₁₅	C₂×C₄	1	2	yes	—
54	C₂×C₄×D₁₅	C₂×C₄	1	2	yes	—
55	C₂×C₄×D₁₅	C₂³	1	2	yes	—
56	C₂×C₄×D₁₅	C₂³	1	2	yes	—
57	C₃×C₅×M₁₆	—	2	4	no	—
58	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
59	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
60	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
61	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
62	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
63	#6714	C₂×C₄	1	2	yes	—
64	#6714	C₂×C₄	1	2	yes	—
65	#6714	C₂×C₄	1	2	yes	—
66	#6714	C₂×C₄	1	2	yes	—
67	C₄⋊Dic₁₅	C₂×C₄	1	2	yes	—
68	C₄⋊Dic₁₅	C₂×C₄	1	1	yes	characteristic
69	C₄⋊Dic₁₅	C₂×C₄	1	1	yes	characteristic
70	#6710	—	2	2	no	—
71	#6710	D₄	1	4	yes	complemented
72	C₂×C₃⋊#168	C₂³	1	2	yes	—
73	C₂×C₃⋊#168	C₂³	1	2	yes	—
74	#6705	—	2	8	no	—
75	C₈×D₁₅	—	2	8	no	—
76	C₂×D₃×M₁₆	—	5	2	no	—
77	C₂×C₄×D₁₂	—	5	1	no	—
78	C₃×#423	D₅	1	1	yes	characteristic, complemented
79	#5126	—	5	2	no	—
80	C₄×#208	—	5	1	no	—
81	#4838	—	5	2	no	—
82	#4836	—	5	4	no	—
83	#4834	—	5	2	no	—
84	C₂²×D₂₀	—	3	1	no	—
85	C₂²×C₄×D₅	—	3	2	no	—
86	C₂×C₅×M₁₆	C₂×D₃	1	2	yes	—
87	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
88	C₂×#685	—	3	2	no	—
89	C₂×C₄⋊Dic₅	—	3	1	no	—
90	C₂×#681	—	3	1	no	—
91	C₂×#681	—	3	1	no	—
92	D₅×M₁₆	—	6	8	no	—
93	C₂×#676	—	3	4	no	—
94	C₂×C₈×D₅	—	3	4	no	—
95	C₄×D₂₀	—	3	1	no	—
96	C₄×D₂₀	—	3	2	no	—
97	C₄×D₂₀	—	3	1	no	—
98	C₄×D₂₀	—	3	1	no	—
99	C₄×D₂₀	—	3	2	no	—
100	C₄×D₂₀	—	3	1	no	—
101	C₅×C₄⋊C₈	C₂×D₃	1	2	yes	complemented
102	C₅×C₄⋊C₈	C₂×D₃	1	2	yes	complemented
103	#3952	—	3	4	no	—
104	#3952	—	3	4	no	—
105	#3935	—	3	2	no	—
106	C₄×#168	—	3	2	no	—
107	D₄×M₁₆	—	15	1	no	Sylow
108	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
109	C₂²×D₁₅	—	2	4	no	—
110	C₂²×D₁₅	—	2	4	no	—
111	C₂²×D₁₅	—	4	2	no	—
112	C₂²×D₁₅	C₂²×C₄	1	2	yes	—
113	C₂²×D₁₅	C₂²×C₄	1	2	yes	—
114	C₂×C₃×C₄×C₅	—	2	2	no	—
115	C₂×C₃×C₄×C₅	—	4	1	no	—
116	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
122	C₂×C₃×C₄×C₅	#41	1	2	yes	—
123	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
124	C₂×Dic₁₅	—	2	4	no	—
125	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
126	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
127	D₆₀	—	2	4	no	—
128	D₆₀	—	2	2	no	—
129	D₆₀	M₁₆	1	4	yes	complemented
130	C₄×D₁₅	—	2	4	no	—
131	C₄×D₁₅	—	2	4	no	—
132	C₄×D₁₅	—	2	2	no	—
133	C₄×D₁₅	—	2	2	no	—
134	C₄×D₁₅	—	2	2	no	—
135	C₄×D₁₅	—	2	2	no	—
136	C₃×C₅×C₈	—	2	4	no	—
137	C₃⋊#168	—	2	2	no	—
138	C₃⋊#168	C₂×D₄	1	4	yes	complemented
139	C₂²×D₁₂	—	5	1	no	—
140	C₂²×C₄×D₃	—	5	2	no	—
141	C₂×C₃×M₁₆	C₂×D₅	1	2	yes	—
142	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
143	C₂×(C₂×D₃)⋊C₄	—	5	2	no	—
144	C₂×C₄⋊Dic₃	—	5	1	no	—
145	C₂×#208	—	5	1	no	—
146	C₂×#208	—	5	1	no	—
147	D₃×M₁₆	—	10	8	no	—
148	C₂×ΓL(1,𝔽₂₅)	—	5	4	no	—
149	C₂×D₃×C₈	—	5	4	no	—
150	C₄×D₁₂	—	5	1	no	—
151	C₄×D₁₂	—	5	2	no	—
152	C₄×D₁₂	—	5	1	no	—
153	C₄×D₁₂	—	5	1	no	—
154	C₄×D₁₂	—	5	2	no	—
155	C₄×D₁₂	—	5	1	no	—
156	C₃×C₄⋊C₈	C₂×D₅	1	2	yes	complemented
157	C₃×C₄⋊C₈	C₂×D₅	1	2	yes	complemented
158	(C₂×D₃)⋊C₈	—	5	4	no	—
159	(C₂×D₃)⋊C₈	—	5	4	no	—
160	#803	—	5	2	no	—
161	C₄×C₃⋊C₈	—	5	2	no	—
162	C₂³×D₅	—	3	2	no	—
163	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
164	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
165	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
166	C₂²×Dic₅	—	3	2	no	—
167	C₂×D₂₀	—	3	1	no	—
168	C₂×D₂₀	—	3	2	no	—
169	C₂×D₂₀	—	3	1	no	—
170	C₂×D₂₀	—	6	4	no	—
171	C₂×C₄×D₅	—	3	2	no	—
172	C₂×C₄×D₅	—	3	2	no	—
173	C₂×C₄×D₅	—	3	2	no	—
174	C₂×C₄×D₅	—	3	2	no	—
175	C₂×C₄×D₅	—	6	4	no	—
176	C₂×C₄×D₅	—	6	4	no	—
177	C₅×M₁₆	—	2	4	no	—
178	C₂×C₅×C₈	C₂²×D₃	1	4	yes	—
179	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
180	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
181	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
182	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
183	#685	—	3	2	no	—
184	#685	—	3	2	no	—
185	#685	—	3	2	no	—
186	#685	—	3	2	no	—
187	C₄⋊Dic₅	—	3	2	no	—
188	C₄⋊Dic₅	—	3	1	no	—
189	C₄⋊Dic₅	—	3	1	no	—
190	#681	—	3	4	no	—
191	#681	—	6	2	no	—
192	C₂×#168	—	3	2	no	—
193	C₂×#168	—	3	2	no	—
194	#676	—	6	8	no	—
195	C₈×D₅	—	6	8	no	—
196	C₂²×M₁₆	—	15	2	no	—
197	C₂×C₄×D₄	—	15	1	no	—
198	#436	—	15	2	no	—
199	#435	—	15	4	no	—
200	C₈×D₄	—	15	2	no	—
201	#423	D₁₅	1	1	yes	characteristic, complemented
202	#407	—	15	2	no	—
203	C₄×M₁₆	—	15	1	no	—
204	C₂²×C₃×C₅	—	2	1	no	—
205	C₂²×C₃×C₅	—	2	1	no	—
206	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
207	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
208	C₂×D₁₅	—	2	2	no	—
209	C₂×D₁₅	—	2	2	no	—
210	C₂×D₁₅	—	2	2	no	—
211	C₂×D₁₅	—	2	2	no	—
212	C₂×D₁₅	—	2	2	no	—
213	C₂×D₁₅	—	4	8	no	—
214	C₂×D₁₅	C₂×M₁₆	1	4	yes	complemented
215	C₃×C₄×C₅	—	2	1	no	—
216	C₃×C₄×C₅	—	2	1	no	—
217	C₃×C₄×C₅	—	2	1	no	—
218	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
219	C₃×C₄×C₅	C₂×M₁₆	1	2	yes	complemented
220	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
221	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
222	Dic₁₅	—	2	2	no	—
223	Dic₁₅	—	2	2	no	—
224	C₂³×D₃	—	5	2	no	—
225	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
226	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
227	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
228	C₂²×Dic₃	—	5	2	no	—
229	C₂×D₁₂	—	5	1	no	—
230	C₂×D₁₂	—	5	2	no	—
231	C₂×D₁₂	—	5	1	no	—
232	C₂×D₁₂	—	10	4	no	—
233	C₂×C₄×D₃	—	5	2	no	—
234	C₂×C₄×D₃	—	5	2	no	—
235	C₂×C₄×D₃	—	5	2	no	—
236	C₂×C₄×D₃	—	5	2	no	—
237	C₂×C₄×D₃	—	10	4	no	—
238	C₂×C₄×D₃	—	10	4	no	—
239	C₃×M₁₆	—	2	4	no	—
240	C₂×C₃×C₈	C₂²×D₅	1	4	yes	—
241	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
242	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
243	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
244	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
245	(C₂×D₃)⋊C₄	—	5	2	no	—
246	(C₂×D₃)⋊C₄	—	5	2	no	—
247	(C₂×D₃)⋊C₄	—	5	2	no	—
248	(C₂×D₃)⋊C₄	—	5	2	no	—
249	C₄⋊Dic₃	—	5	2	no	—
250	C₄⋊Dic₃	—	5	1	no	—
251	C₄⋊Dic₃	—	5	1	no	—
252	#208	—	5	4	no	—
253	#208	—	10	2	no	—
254	C₂×C₃⋊C₈	—	5	2	no	—
255	C₂×C₃⋊C₈	—	5	2	no	—
256	ΓL(1,𝔽₂₅)	—	10	8	no	—
257	D₃×C₈	—	10	8	no	—
258	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
259	C₂²×D₅	—	3	2	no	—
260	C₂²×D₅	—	3	2	no	—
261	C₂²×D₅	—	6	4	no	—
262	C₂²×D₅	—	6	4	no	—
263	C₂²×D₅	—	12	2	no	—
264	C₂×C₄×C₅	—	2	2	no	—
265	C₂×C₄×C₅	—	4	1	no	—
266	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
267	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
268	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
269	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
270	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
271	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
272	C₂×C₄×C₅	#239	1	2	yes	—
273	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
274	C₂×Dic₅	—	3	2	no	—
275	C₂×Dic₅	—	3	2	no	—
276	C₂×Dic₅	—	6	4	no	—
277	D₂₀	—	3	4	no	—
278	D₂₀	—	6	4	no	—
279	D₂₀	—	6	2	no	—
280	C₄×D₅	—	6	4	no	—
281	C₄×D₅	—	6	4	no	—
282	C₄×D₅	—	6	2	no	—
283	C₄×D₅	—	6	2	no	—
284	C₄×D₅	—	6	2	no	—
285	C₄×D₅	—	6	2	no	—
286	C₅×C₈	—	2	4	no	—
287	#168	—	3	4	no	—
288	#168	—	6	2	no	—
289	C₂²×D₄	—	15	1	no	—
290	C₂³×C₄	—	15	2	no	—
291	C₂×M₁₆	—	15	1	no	—
292	C₂×M₁₆	—	15	1	no	—
293	C₂×M₁₆	—	15	4	no	—
294	C₂×M₁₆	—	30	8	no	—
295	C₂×M₁₆	C₂×D₁₅	1	2	yes	—
296	C₂²×C₈	—	15	4	no	—
297	C₄×D₄	—	15	1	no	—
298	C₄×D₄	—	15	2	no	—
299	C₄×D₄	—	15	1	no	—
300	C₄×D₄	—	15	1	no	—
301	C₄×D₄	—	15	2	no	—
302	C₄×D₄	—	15	1	no	—
303	C₂×C₄⋊C₄	—	15	1	no	—
304	C₂×C₂²⋊C₄	—	15	2	no	—
305	C₂×C₄²	C₂×D₁₅	1	1	yes	characteristic
306	C₄⋊C₈	C₂×D₁₅	1	2	yes	complemented
307	C₄⋊C₈	C₂×D₁₅	1	2	yes	complemented
308	C₂²⋊C₈	—	15	4	no	—
309	C₂²⋊C₈	—	15	4	no	—
310	#97	—	15	2	no	—
311	C₄×C₈	—	15	2	no	—
312	C₂×C₃×C₅	—	2	2	no	—
313	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
314	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
315	C₂×C₃×C₅	#568	1	1	yes	characteristic
316	D₁₅	—	2	4	no	—
317	D₁₅	—	4	2	no	—
318	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
319	C₂²×D₃	—	5	2	no	—
320	C₂²×D₃	—	5	2	no	—
321	C₂²×D₃	—	10	4	no	—
322	C₂²×D₃	—	10	4	no	—
323	C₂²×D₃	—	20	2	no	—
324	C₂×C₃×C₄	—	2	2	no	—
325	C₂×C₃×C₄	—	4	1	no	—
326	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
327	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
328	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
329	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
330	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
331	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
332	C₂×C₃×C₄	#713	1	2	yes	—
333	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
334	C₂×Dic₃	—	5	2	no	—
335	C₂×Dic₃	—	5	2	no	—
336	C₂×Dic₃	—	10	4	no	—
337	D₁₂	—	5	4	no	—
338	D₁₂	—	10	4	no	—
339	D₁₂	—	10	2	no	—
340	C₄×D₃	—	10	2	no	—
341	C₄×D₃	—	10	2	no	—
342	C₄×D₃	—	10	2	no	—
343	C₄×D₃	—	10	2	no	—
344	C₄×D₃	—	10	4	no	—
345	C₄×D₃	—	10	4	no	—
346	C₃×C₈	—	2	4	no	—
347	C₃⋊C₈	—	5	4	no	—
348	C₃⋊C₈	—	10	2	no	—
349	C₂²×C₅	—	2	1	no	—
350	C₂²×C₅	—	2	1	no	—
351	C₂²×C₅	#893	1	2	yes	—
352	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
353	C₂×D₅	—	3	4	no	—
354	C₂×D₅	—	6	2	no	—
355	C₂×D₅	—	6	2	no	—
356	C₂×D₅	—	6	2	no	—
357	C₂×D₅	—	6	2	no	—
358	C₂×D₅	—	6	2	no	—
359	C₂×D₅	—	12	8	no	—
360	C₄×C₅	—	2	1	no	—
361	C₄×C₅	—	2	1	no	—
362	C₄×C₅	—	2	1	no	—
363	C₄×C₅	#893	1	2	yes	—
364	C₄×C₅	D₃×M₁₆	1	2	yes	complemented
365	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
366	C₄×C₅	C₂×#239	1	1	yes	characteristic
367	Dic₅	—	6	2	no	—
368	Dic₅	—	6	2	no	—
369	C₂⁴	—	15	2	no	—
370	C₂×D₄	—	15	1	no	—
371	C₂×D₄	—	15	2	no	—
372	C₂×D₄	—	15	1	no	—
373	C₂×D₄	—	30	4	no	—
374	C₂²×C₄	—	15	2	no	—
375	C₂²×C₄	—	15	2	no	—
376	C₂²×C₄	—	15	2	no	—
377	C₂²×C₄	—	15	2	no	—
378	C₂²×C₄	—	15	2	no	—
379	C₂²×C₄	—	30	4	no	—
380	C₂²×C₄	—	30	4	no	—
381	C₂²×C₄	C₄×D₁₅	1	1	yes	characteristic
382	C₂²×C₄	C₄×D₁₅	1	1	yes	characteristic
383	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
384	M₁₆	—	2	4	no	—
385	M₁₆	—	15	4	no	—
386	M₁₆	—	30	8	no	—
387	M₁₆	—	30	2	no	—
388	C₂×C₈	—	15	2	no	—
389	C₂×C₈	—	15	2	no	—
390	C₂×C₈	—	30	8	no	—
391	C₂×C₈	C₂²×D₁₅	1	4	yes	—
392	C₄⋊C₄	—	15	2	no	—
393	C₄⋊C₄	—	15	1	no	—
394	C₄⋊C₄	—	15	1	no	—
395	C₂²⋊C₄	—	15	2	no	—
396	C₂²⋊C₄	—	15	2	no	—
397	C₂²⋊C₄	—	15	2	no	—
398	C₂²⋊C₄	—	15	2	no	—
399	C₄²	C₄×D₁₅	1	1	yes	characteristic
400	C₄²	C₄×D₁₅	1	1	yes	characteristic
401	C₄²	C₂²×D₁₅	1	1	yes	characteristic
402	C₄²	C₂²×D₁₅	1	1	yes	characteristic
403	C₃×C₅	D₄×M₁₆	1	1	yes	characteristic, complemented, Hall
404	C₂²×C₃	—	2	1	no	—
405	C₂²×C₃	—	2	1	no	—
406	C₂²×C₃	#4039	1	2	yes	—
407	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
408	C₂×D₃	—	5	4	no	—
409	C₂×D₃	—	10	2	no	—
410	C₂×D₃	—	10	2	no	—
411	C₂×D₃	—	10	2	no	—
412	C₂×D₃	—	10	2	no	—
413	C₂×D₃	—	10	2	no	—
414	C₂×D₃	—	20	8	no	—
415	C₃×C₄	—	2	1	no	—
416	C₃×C₄	—	2	1	no	—
417	C₃×C₄	—	2	1	no	—
418	C₃×C₄	#4039	1	2	yes	—
419	C₃×C₄	D₅×M₁₆	1	2	yes	complemented
420	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
421	C₃×C₄	C₂×#713	1	1	yes	characteristic
422	Dic₃	—	10	2	no	—
423	Dic₃	—	10	2	no	—
424	C₂×C₅	—	2	2	no	—
425	C₂×C₅	C₂×#893	1	1	yes	characteristic
426	C₂×C₅	C₂×D₃×M₁₆	1	1	yes	characteristic
427	C₂×C₅	#5745	1	1	yes	characteristic
428	D₅	—	6	4	no	—
429	D₅	—	12	2	no	—
430	C₂³	—	15	2	no	—
431	C₂³	—	15	2	no	—
432	C₂³	—	30	4	no	—
433	C₂³	—	30	4	no	—
434	C₂³	—	60	2	no	—
435	C₂³	C₂×C₄×D₁₅	1	1	yes	characteristic
436	D₄	—	15	4	no	—
437	D₄	—	30	4	no	—
438	D₄	—	30	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	15	2	no	—
442	C₂×C₄	—	15	2	no	—
443	C₂×C₄	—	30	4	no	—
444	C₂×C₄	—	30	4	no	—
445	C₂×C₄	—	30	4	no	—
446	C₂×C₄	—	30	2	no	—
447	C₂×C₄	—	30	2	no	—
448	C₂×C₄	—	30	2	no	—
449	C₂×C₄	—	30	2	no	—
450	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
451	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
452	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
453	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
454	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
455	C₂×C₄	D₄×D₁₅	1	2	yes	—
456	C₂×C₄	#6821	1	2	yes	—
457	C₂×C₄	C₂³×D₁₅	1	1	yes	characteristic
458	C₈	—	2	4	no	—
459	C₈	—	15	4	no	—
460	C₈	—	30	2	no	—
461	C₂×C₃	—	2	2	no	—
462	C₂×C₃	C₂×#4039	1	1	yes	characteristic
463	C₂×C₃	C₂×D₅×M₁₆	1	1	yes	characteristic
464	C₂×C₃	#66079	1	1	yes	characteristic
465	D₃	—	10	4	no	—
466	D₃	—	20	2	no	—
467	C₅	#79043	1	1	yes	characteristic, complemented, Sylow
468	C₂²	—	2	1	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	15	4	no	—
471	C₂²	—	30	2	no	—
472	C₂²	—	30	2	no	—
473	C₂²	—	30	2	no	—
474	C₂²	—	30	2	no	—
475	C₂²	—	30	2	no	—
476	C₂²	—	60	8	no	—
477	C₂²	#91782	1	2	yes	—
478	C₂²	C₂²×C₄×D₁₅	1	1	yes	characteristic
479	C₄	—	2	1	no	—
480	C₄	—	2	1	no	—
481	C₄	—	2	1	no	—
482	C₄	—	30	2	no	—
483	C₄	—	30	2	no	—
484	C₄	#91782	1	2	yes	—
485	C₄	M₁₆×D₁₅	1	2	yes	complemented
486	C₄	C₂×D₄×D₁₅	1	1	yes	characteristic
487	C₄	C₂×#6821	1	1	yes	characteristic
488	C₃	#10610774	1	1	yes	characteristic, complemented, Sylow
489	C₂	—	2	2	no	—
490	C₂	—	30	4	no	—
491	C₂	—	60	2	no	—
492	C₂	C₂×#91782	1	1	yes	characteristic
493	C₂	C₂×M₁₆×D₁₅	1	1	yes	characteristic
494	C₂	#11756504	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₁₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Fitting	C₃×C₅×#423	C₂
prime radical	C₂²×D₆₀	C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	#423	D₁₅
hypocenter	C₃×C₅	D₄×M₁₆
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ #423

Complements

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

N	H ≅ G/N	type
1. C₂×M₁₆×D₁₅	C₂	semidirect
3. C₃×C₅×#423	C₂	semidirect
4. #11751227	C₂	semidirect
5. C₄×#6710	C₂	semidirect
6. #11750939	C₂	semidirect
7. #11750937	C₂	semidirect
8. #11750935	C₂	semidirect
19. C₂×#6705	C₂²	semidirect
20. C₂×C₈×D₁₅	C₂²	semidirect
27. C₃×C₅×C₄⋊C₈	C₂²	semidirect
28. C₃×C₅×C₄⋊C₈	C₂²	semidirect
29. #91104	C₂²	semidirect
30. #91104	C₂²	semidirect
31. #91087	C₂²	semidirect
32. C₄×C₃⋊#168	C₂²	semidirect
36. C₅×#423	D₃	semidirect
71. #6710	D₄	semidirect
78. C₃×#423	D₅	semidirect
101. C₅×C₄⋊C₈	C₂×D₃	semidirect
102. C₅×C₄⋊C₈	C₂×D₃	semidirect
129. D₆₀	M₁₆	semidirect
138. C₃⋊#168	C₂×D₄	semidirect
156. C₃×C₄⋊C₈	C₂×D₅	semidirect
157. C₃×C₄⋊C₈	C₂×D₅	semidirect
201. #423	D₁₅	semidirect
214. C₂×D₁₅	C₂×M₁₆	semidirect
219. C₃×C₄×C₅	C₂×M₁₆	semidirect
306. C₄⋊C₈	C₂×D₁₅	semidirect
307. C₄⋊C₈	C₂×D₁₅	semidirect
364. C₄×C₅	D₃×M₁₆	semidirect
403. C₃×C₅	D₄×M₁₆	semidirect
419. C₃×C₄	D₅×M₁₆	semidirect
467. C₅	#79043	semidirect
485. C₄	M₁₆×D₁₅	semidirect
488. C₃	#10610774	semidirect

Maximal subgroups

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

subgroup	index
C₂×M₁₆×D₁₅	2
C₂×C₄×D₆₀	2
C₃×C₅×#423	2
#11751227	2
C₄×#6710	2
#11750939	2
#11750937	2
#11750935	2
#10610774	3
#79043	5