Subgroups — #14415228

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#131	C₂	1	1	yes	maximal, characteristic, complemented
2	#11756591	C₂	1	1	yes	maximal, characteristic
3	C₂×#91790	C₂	1	1	yes	maximal, characteristic, complemented
4	#11751335	C₂	1	1	yes	maximal, characteristic, complemented
5	#11751230	C₂	1	1	yes	maximal, characteristic, complemented
6	#11751229	C₂	1	4	yes	maximal, complemented
7	#11751219	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈×#1220	C₂	1	4	yes	maximal, complemented
9	C₂×C₈×Dic₁₅	C₂	1	1	yes	maximal, characteristic, complemented
10	#10615517	—	3	1	no	maximal, Hall
11	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
12	C₂×#6817	C₂²	1	1	yes	characteristic
13	C₃×C₅×#131	—	2	4	no	—
14	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
16	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
17	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
18	#91836	C₄	1	1	yes	characteristic
19	#91833	C₄	1	1	yes	characteristic
20	#91829	C₄	1	1	yes	characteristic
21	#91828	C₄	1	4	yes	—
22	#91825	C₄	1	1	yes	characteristic
23	C₄×#1220	C₂²	1	4	yes	—
24	C₂×C₄×Dic₁₅	C₂²	1	1	yes	characteristic
25	C₂×#6710	C₂²	1	1	yes	characteristic
26	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
27	#91790	—	2	4	no	—
28	C₂×#6705	C₂²	1	2	yes	—
29	C₂×C₈×D₁₅	C₂²	1	2	yes	—
30	#91114	C₂²	1	4	yes	—
31	#91104	C₂²	1	4	yes	—
32	#91098	C₂²	1	4	yes	—
33	C₈×Dic₁₅	C₂²	1	2	yes	—
34	C₈×Dic₁₅	C₂²	1	2	yes	—
35	#83786	—	5	1	no	maximal, Hall
36	C₂×C₅×#131	D₃	1	1	yes	characteristic, complemented
37	#66166	—	3	1	no	—
38	C₂×#4047	—	3	1	no	—
39	#65523	—	3	1	no	—
40	#65418	—	3	1	no	—
41	#65417	—	3	4	no	—
42	#65407	—	3	1	no	—
43	C₈×C₂²⋊D₅	—	3	4	no	—
44	C₂×C₈×Dic₅	—	3	1	no	—
45	C₃×C₅×#41	—	2	2	no	—
46	C₃×C₅×#41	—	2	2	no	—
47	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
48	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
49	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
50	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
51	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₂×#1220	C₂×C₄	1	4	yes	—
53	C₂×#1220	C₂×C₄	1	2	yes	—
54	C₂²×Dic₁₅	C₂×C₄	1	2	yes	—
55	#6817	—	2	2	no	—
56	#6817	—	2	2	no	—
57	C₂×D₆₀	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×D₁₅	C₂³	1	2	yes	—
59	C₂×Dic₃₀	C₂×C₄	1	1	yes	characteristic
60	C₃×C₅×M₁₆	—	2	2	no	—
61	C₃×C₅×M₁₆	—	2	4	no	—
62	C₂×C₃×C₅×C₈	—	2	4	no	—
63	C₂×C₃×C₅×C₈	D₄	1	4	yes	complemented
64	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
65	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
66	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
67	#6719	C₂×C₄	1	4	yes	—
68	#6714	C₂×C₄	1	4	yes	—
69	#6712	C₂×C₄	1	4	yes	—
70	C₄×Dic₁₅	C₂×C₄	1	1	yes	characteristic
71	C₄×Dic₁₅	C₂×C₄	1	1	yes	characteristic
72	C₄×Dic₁₅	C₂³	1	2	yes	—
73	#6710	—	2	2	no	—
74	C₂×C₃⋊#168	—	2	2	no	—
75	C₂×C₃⋊#168	C₂³	1	2	yes	—
76	C₂×C₃⋊#168	C₂³	1	2	yes	—
77	#6705	—	2	4	no	—
78	C₈×D₁₅	—	2	4	no	—
79	C₂×C₃×#131	D₅	1	1	yes	characteristic, complemented
80	#5832	—	5	1	no	—
81	C₂×#901	—	5	1	no	—
82	#5234	—	5	1	no	—
83	#5129	—	5	1	no	—
84	#5128	—	5	4	no	—
85	#5118	—	5	1	no	—
86	C₈×#67	—	5	4	no	—
87	C₂×C₈×Dic₃	—	5	1	no	—
88	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
89	C₂×#709	—	3	1	no	—
90	C₅×#131	—	2	4	no	—
91	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
92	C₂×C₅×M₁₆	C₂×D₃	1	2	yes	—
93	C₂²×C₅×C₈	C₂×D₃	1	2	yes	—
94	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
95	#4093	—	3	1	no	—
96	#4090	—	3	1	no	—
97	#4086	—	3	1	no	—
98	#4085	—	3	4	no	—
99	#4082	—	3	1	no	—
100	C₄×C₂²⋊D₅	—	3	4	no	—
101	C₂×C₄×Dic₅	—	3	1	no	—
102	C₂×#681	—	3	1	no	—
103	C₂²×#168	—	3	1	no	—
104	#4047	—	6	4	no	—
105	C₂×#676	—	3	2	no	—
106	C₂×C₈×D₅	—	3	2	no	—
107	C₂²⋊#168	—	3	4	no	—
108	#3952	—	3	4	no	—
109	#3946	—	3	4	no	—
110	C₈×Dic₅	—	3	2	no	—
111	C₈×Dic₅	—	3	2	no	—
112	#2931	—	15	1	no	Sylow
113	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
114	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
115	C₂²×D₁₅	C₂²×C₄	1	2	yes	—
116	C₃×C₅×Q₈	—	2	2	no	—
117	C₃×C₅×D₄	—	2	4	no	—
118	C₃×C₅×D₄	—	2	2	no	—
119	C₂×C₃×C₄×C₅	—	2	2	no	—
120	C₂×C₃×C₄×C₅	—	2	2	no	—
121	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
122	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
124	C₂×C₃×C₄×C₅	#41	1	2	yes	—
125	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
126	#1220	—	2	4	no	—
127	#1220	—	2	8	no	—
128	C₂×Dic₁₅	—	2	4	no	—
129	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
130	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
131	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
132	D₆₀	—	2	2	no	—
133	C₄×D₁₅	—	2	2	no	—
134	C₄×D₁₅	—	2	2	no	—
135	Dic₃₀	—	2	2	no	—
136	C₃×C₅×C₈	—	2	2	no	—
137	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
138	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
139	C₃⋊#168	—	2	2	no	—
140	C₃⋊#168	—	2	2	no	—
141	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
142	C₂×#235	—	5	1	no	—
143	C₃×#131	—	2	4	no	—
144	C₂×C₃×M₁₆	C₂×D₅	1	2	yes	—
145	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
146	C₂²×C₃×C₈	C₂×D₅	1	2	yes	—
147	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
148	#947	—	5	1	no	—
149	#944	—	5	1	no	—
150	#940	—	5	1	no	—
151	#939	—	5	4	no	—
152	#936	—	5	1	no	—
153	C₄×#67	—	5	4	no	—
154	C₂×C₄×Dic₃	—	5	1	no	—
155	C₂×#208	—	5	1	no	—
156	C₂²×C₃⋊C₈	—	5	1	no	—
157	#901	—	10	4	no	—
158	C₂×ΓL(1,𝔽₂₅)	—	5	2	no	—
159	C₂×D₃×C₈	—	5	2	no	—
160	#830	—	5	4	no	—
161	(C₂×D₃)⋊C₈	—	5	4	no	—
162	Dic₃⋊C₈	—	5	4	no	—
163	C₈×Dic₃	—	5	2	no	—
164	C₈×Dic₃	—	5	2	no	—
165	C₅×#41	—	2	2	no	—
166	C₅×#41	—	2	2	no	—
167	C₂×C₅×Q₈	C₄×D₃	1	1	yes	characteristic
168	C₂×C₅×D₄	C₄×D₃	1	1	yes	characteristic
169	C₂×C₅×D₄	C₄×D₃	1	2	yes	—
170	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
171	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
172	C₂×C₂²⋊D₅	—	3	2	no	—
173	C₂×C₂²⋊D₅	—	3	4	no	—
174	C₂²×Dic₅	—	3	2	no	—
175	#709	—	6	2	no	—
176	#709	—	6	2	no	—
177	C₂×D₂₀	—	3	1	no	—
178	C₂×C₄×D₅	—	3	2	no	—
179	C₂×Dic₁₀	—	3	1	no	—
180	C₅×M₁₆	—	2	2	no	—
181	C₅×M₁₆	—	2	4	no	—
182	C₂×C₅×C₈	—	2	4	no	—
183	C₂×C₅×C₈	#67	1	4	yes	complemented
184	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
185	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
186	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
187	C₂²⋊Dic₅	—	3	4	no	—
188	#685	—	3	4	no	—
189	#683	—	3	4	no	—
190	C₄×Dic₅	—	3	1	no	—
191	C₄×Dic₅	—	3	1	no	—
192	C₄×Dic₅	—	3	2	no	—
193	#681	—	6	2	no	—
194	C₂×#168	—	3	2	no	—
195	C₂×#168	—	3	2	no	—
196	C₂×#168	—	6	2	no	—
197	#676	—	6	4	no	—
198	C₈×D₅	—	6	4	no	—
199	C₂×#131	—	15	1	no	—
200	C₂×#131	D₁₅	1	1	yes	characteristic, complemented
201	#532	—	15	1	no	—
202	#436	—	15	4	no	—
203	C₈×D₄	—	15	4	no	—
204	#423	—	15	1	no	—
205	#408	—	15	1	no	—
206	#408	—	15	1	no	—
207	C₂×C₄×C₈	—	15	1	no	—
208	C₂²×C₃×C₅	—	2	2	no	—
209	C₂²×C₃×C₅	—	2	2	no	—
210	C₂²×C₃×C₅	—	2	4	no	—
211	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
212	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
213	C₂×D₁₅	—	2	2	no	—
214	C₂×D₁₅	—	2	4	no	—
215	C₃×C₄×C₅	—	2	2	no	—
216	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
217	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
218	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
219	Dic₁₅	—	2	2	no	—
220	Dic₁₅	—	2	2	no	—
221	Dic₁₅	#131	1	4	yes	complemented
222	C₃×#41	—	2	2	no	—
223	C₃×#41	—	2	2	no	—
224	C₂×C₃×Q₈	C₄×D₅	1	1	yes	characteristic
225	C₂×C₃×D₄	C₄×D₅	1	1	yes	characteristic
226	C₂×C₃×D₄	C₄×D₅	1	2	yes	—
227	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
228	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
229	C₂×#67	—	5	4	no	—
230	C₂×#67	—	5	2	no	—
231	C₂²×Dic₃	—	5	2	no	—
232	#235	—	10	2	no	—
233	#235	—	10	2	no	—
234	C₂×D₁₂	—	5	1	no	—
235	C₂×C₄×D₃	—	5	2	no	—
236	C₂×Dic₆	—	5	1	no	—
237	C₃×M₁₆	—	2	2	no	—
238	C₃×M₁₆	—	2	4	no	—
239	C₂×C₃×C₈	—	2	4	no	—
240	C₂×C₃×C₈	C₂²⋊D₅	1	4	yes	complemented
241	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
242	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
243	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
244	#217	—	5	4	no	—
245	(C₂×D₃)⋊C₄	—	5	4	no	—
246	Dic₃⋊C₄	—	5	4	no	—
247	C₄×Dic₃	—	5	1	no	—
248	C₄×Dic₃	—	5	1	no	—
249	C₄×Dic₃	—	5	2	no	—
250	#208	—	10	2	no	—
251	C₂×C₃⋊C₈	—	5	2	no	—
252	C₂×C₃⋊C₈	—	5	2	no	—
253	C₂×C₃⋊C₈	—	10	2	no	—
254	ΓL(1,𝔽₂₅)	—	10	4	no	—
255	D₃×C₈	—	10	4	no	—
256	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
257	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
258	C₂²×D₅	—	3	2	no	—
259	C₅×Q₈	—	2	2	no	—
260	C₅×D₄	—	2	4	no	—
261	C₅×D₄	—	2	2	no	—
262	C₂×C₄×C₅	—	2	2	no	—
263	C₂×C₄×C₅	—	2	2	no	—
264	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
265	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
266	C₂×C₄×C₅	#235	1	2	yes	—
267	C₂×C₄×C₅	C₂×#67	1	2	yes	—
268	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
269	C₂²⋊D₅	—	6	8	no	—
270	C₂²⋊D₅	—	6	4	no	—
271	C₂×Dic₅	—	3	2	no	—
272	C₂×Dic₅	—	3	2	no	—
273	C₂×Dic₅	—	3	2	no	—
274	C₂×Dic₅	—	6	4	no	—
275	D₂₀	—	6	2	no	—
276	C₄×D₅	—	6	2	no	—
277	C₄×D₅	—	6	2	no	—
278	Dic₁₀	—	6	2	no	—
279	C₅×C₈	—	2	2	no	—
280	C₅×C₈	C₂×#67	1	2	yes	—
281	C₅×C₈	C₂×#67	1	2	yes	—
282	#168	—	6	2	no	—
283	#168	—	6	2	no	—
284	C₂×#41	—	15	1	no	—
285	C₂×#41	C₂×D₁₅	1	1	yes	characteristic
286	#131	—	2	4	no	—
287	#131	—	30	4	no	—
288	C₂×M₁₆	—	15	1	no	—
289	C₂×M₁₆	—	15	2	no	—
290	C₂×M₁₆	C₂×D₁₅	1	1	yes	characteristic
291	C₂×M₁₆	C₂×D₁₅	1	2	yes	—
292	C₂²×C₈	—	15	1	no	—
293	C₂²×C₈	—	15	2	no	—
294	C₂²×C₈	C₂×D₁₅	1	2	yes	—
295	C₂²×C₈	C₂×D₁₅	1	1	yes	characteristic
296	C₄⋊Q₈	—	15	1	no	—
297	#127	—	15	1	no	—
298	#124	—	15	1	no	—
299	#124	—	15	1	no	—
300	#121	—	15	4	no	—
301	C₄×D₄	—	15	4	no	—
302	C₂×C₄²	—	15	1	no	—
303	C₄⋊C₈	—	15	4	no	—
304	C₂²⋊C₈	—	15	4	no	—
305	C₂²⋊C₈	—	15	4	no	—
306	C₄×C₈	—	15	2	no	—
307	C₄×C₈	—	15	2	no	—
308	C₂×C₃×C₅	—	2	2	no	—
309	C₂×C₃×C₅	—	4	2	no	—
310	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
311	C₂×C₃×C₅	C₂×#131	1	2	yes	—
312	D₁₅	—	4	2	no	—
313	C₂³×C₃	C₂×C₄×D₅	1	2	yes	—
314	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
315	C₂²×D₃	—	5	2	no	—
316	C₃×Q₈	—	2	2	no	—
317	C₃×D₄	—	2	4	no	—
318	C₃×D₄	—	2	2	no	—
319	C₂×C₃×C₄	—	2	2	no	—
320	C₂×C₃×C₄	—	2	2	no	—
321	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
322	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
323	C₂×C₃×C₄	#709	1	2	yes	—
324	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
325	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
326	#67	—	10	8	no	—
327	#67	—	10	4	no	—
328	C₂×Dic₃	—	5	2	no	—
329	C₂×Dic₃	—	5	2	no	—
330	C₂×Dic₃	—	5	2	no	—
331	C₂×Dic₃	—	10	4	no	—
332	D₁₂	—	10	2	no	—
333	C₄×D₃	—	10	2	no	—
334	C₄×D₃	—	10	2	no	—
335	Dic₆	—	10	2	no	—
336	C₃×C₈	—	2	2	no	—
337	C₃×C₈	C₂×C₂²⋊D₅	1	2	yes	—
338	C₃×C₈	C₂×C₂²⋊D₅	1	2	yes	—
339	C₃⋊C₈	—	10	2	no	—
340	C₃⋊C₈	—	10	2	no	—
341	C₂²×C₅	—	2	2	no	—
342	C₂²×C₅	—	2	4	no	—
343	C₂²×C₅	—	2	2	no	—
344	C₂²×C₅	C₄×#67	1	2	yes	—
345	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
346	C₂×D₅	—	6	4	no	—
347	C₂×D₅	—	6	2	no	—
348	C₄×C₅	—	2	2	no	—
349	C₄×C₅	C₄×#67	1	2	yes	—
350	C₄×C₅	C₂×#235	1	1	yes	characteristic
351	C₄×C₅	C₂²×#67	1	1	yes	characteristic
352	Dic₅	—	3	4	no	—
353	Dic₅	—	6	2	no	—
354	Dic₅	—	6	2	no	—
355	#41	—	2	2	no	—
356	#41	—	2	2	no	—
357	#41	—	30	2	no	—
358	#41	—	30	2	no	—
359	C₂×Q₈	—	15	1	no	—
360	C₂×Q₈	C₄×D₁₅	1	1	yes	characteristic
361	C₂×D₄	—	15	4	no	—
362	C₂×D₄	—	15	2	no	—
363	C₂×D₄	—	15	1	no	—
364	C₂×D₄	C₄×D₁₅	1	2	yes	—
365	C₂×D₄	C₄×D₁₅	1	1	yes	characteristic
366	C₂²×C₄	—	15	2	no	—
367	C₂²×C₄	—	15	2	no	—
368	C₂²×C₄	C₂²×D₁₅	1	2	yes	—
369	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
370	M₁₆	—	2	2	no	—
371	M₁₆	—	2	4	no	—
372	M₁₆	—	30	2	no	—
373	M₁₆	—	30	4	no	—
374	C₂×C₈	—	2	4	no	—
375	C₂×C₈	—	15	2	no	—
376	C₂×C₈	—	15	2	no	—
377	C₂×C₈	—	30	2	no	—
378	C₂×C₈	—	30	4	no	—
379	C₂×C₈	#1220	1	4	yes	complemented
380	C₂×C₈	C₂²×D₁₅	1	2	yes	—
381	C₂×C₈	C₂²×D₁₅	1	1	yes	characteristic
382	C₂×C₈	C₂²×D₁₅	1	1	yes	characteristic
383	C₄⋊C₄	—	15	4	no	—
384	C₂²⋊C₄	—	15	4	no	—
385	C₂²⋊C₄	—	15	4	no	—
386	C₄²	—	15	1	no	—
387	C₄²	—	15	1	no	—
388	C₄²	—	15	2	no	—
389	C₃×C₅	#2931	1	1	yes	characteristic, complemented, Hall
390	C₂²×C₃	—	2	2	no	—
391	C₂²×C₃	—	2	4	no	—
392	C₂²×C₃	—	2	2	no	—
393	C₂²×C₃	C₄×C₂²⋊D₅	1	2	yes	—
394	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
395	C₂×D₃	—	10	4	no	—
396	C₂×D₃	—	10	2	no	—
397	C₃×C₄	—	2	2	no	—
398	C₃×C₄	C₄×C₂²⋊D₅	1	2	yes	—
399	C₃×C₄	C₂×#709	1	1	yes	characteristic
400	C₃×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
401	Dic₃	—	5	4	no	—
402	Dic₃	—	10	2	no	—
403	Dic₃	—	10	2	no	—
404	C₂×C₅	—	2	2	no	—
405	C₂×C₅	—	4	2	no	—
406	C₂×C₅	D₃×#131	1	2	yes	—
407	C₂×C₅	C₂×C₄×#67	1	1	yes	characteristic
408	D₅	—	12	2	no	—
409	C₂³	—	15	2	no	—
410	C₂³	C₂×C₄×D₁₅	1	2	yes	—
411	C₂³	C₂×C₄×D₁₅	1	1	yes	characteristic
412	Q₈	—	2	2	no	—
413	Q₈	—	30	2	no	—
414	D₄	—	2	4	no	—
415	D₄	—	2	2	no	—
416	D₄	—	30	8	no	—
417	D₄	—	30	4	no	—
418	D₄	—	30	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	15	2	no	—
422	C₂×C₄	—	15	2	no	—
423	C₂×C₄	—	15	2	no	—
424	C₂×C₄	—	30	4	no	—
425	C₂×C₄	—	30	2	no	—
426	C₂×C₄	—	30	2	no	—
427	C₂×C₄	C₂×C₄×D₁₅	1	2	yes	—
428	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
429	C₂×C₄	#6817	1	2	yes	—
430	C₂×C₄	C₂×#1220	1	2	yes	—
431	C₂×C₄	C₂³×D₁₅	1	1	yes	characteristic
432	C₈	—	2	2	no	—
433	C₈	—	30	2	no	—
434	C₈	—	30	2	no	—
435	C₈	C₂×#1220	1	2	yes	—
436	C₈	C₂×#1220	1	2	yes	—
437	C₂×C₃	—	2	2	no	—
438	C₂×C₃	—	4	2	no	—
439	C₂×C₃	D₅×#131	1	2	yes	—
440	C₂×C₃	C₂×C₄×C₂²⋊D₅	1	1	yes	characteristic
441	D₃	—	20	2	no	—
442	C₅	#83786	1	1	yes	characteristic, complemented, Sylow
443	C₂²	—	2	2	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	2	4	no	—
446	C₂²	—	30	2	no	—
447	C₂²	—	30	4	no	—
448	C₂²	C₄×#1220	1	2	yes	—
449	C₂²	C₂²×C₄×D₁₅	1	1	yes	characteristic
450	C₄	—	2	2	no	—
451	C₄	—	15	4	no	—
452	C₄	—	30	2	no	—
453	C₄	—	30	2	no	—
454	C₄	C₄×#1220	1	2	yes	—
455	C₄	C₂×#6817	1	1	yes	characteristic
456	C₄	C₂²×#1220	1	1	yes	characteristic
457	C₃	#10615517	1	1	yes	characteristic, complemented, Sylow
458	C₂	—	2	2	no	—
459	C₂	—	4	2	no	—
460	C₂	—	60	2	no	—
461	C₂	D₁₅×#131	1	2	yes	—
462	C₂	C₂×C₄×#1220	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²×D₁₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₁₅
Fitting	C₂×C₃×C₅×#131	C₂
prime radical	#11756591	C₂
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂×#131	D₁₅
hypocenter	C₃×C₅	#2931
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₈ ◁ C₂×#131

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#131	C₂	semidirect
3. C₂×#91790	C₂	semidirect
4. #11751335	C₂	semidirect
5. #11751230	C₂	semidirect
6. #11751229	C₂	semidirect
7. #11751219	C₂	semidirect
8. C₈×#1220	C₂	semidirect
9. C₂×C₈×Dic₁₅	C₂	semidirect
36. C₂×C₅×#131	D₃	semidirect
63. C₂×C₃×C₅×C₈	D₄	semidirect
79. C₂×C₃×#131	D₅	semidirect
183. C₂×C₅×C₈	#67	semidirect
200. C₂×#131	D₁₅	semidirect
221. Dic₁₅	#131	semidirect
240. C₂×C₃×C₈	C₂²⋊D₅	semidirect
379. C₂×C₈	#1220	semidirect
389. C₃×C₅	#2931	semidirect
442. C₅	#83786	semidirect
457. C₃	#10615517	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×#131	2
#11756591	2
C₂×#91790	2
#11751335	2
#11751230	2
#11751229	2
#11751219	2
C₈×#1220	2
C₂×C₈×Dic₁₅	2
#10615517	3
#83786	5