Subgroups — #14303051

Order 1920.

680 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#66079	C₂	1	1	yes	maximal, characteristic, complemented
2	#11754604	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#823	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#90959	C₂	1	1	yes	maximal, characteristic, complemented
5	#11748353	C₂	1	1	yes	maximal, characteristic, complemented
6	#11746380	C₂	1	1	yes	maximal, characteristic, complemented
7	#11745990	C₂	1	1	yes	maximal, characteristic, complemented
8	#10600882	—	3	1	no	maximal, Hall
9	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
10	C₂×C₃×#709	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
12	#91815	C₂²	1	1	yes	characteristic
13	C₂×#6710	C₂²	1	1	yes	characteristic
14	C₂×C₅×#208	C₂²	1	1	yes	characteristic
15	C₂×C₃×#681	C₂²	1	1	yes	characteristic
16	C₃×#4053	—	2	2	no	—
17	C₃×D₅×M₁₆	—	2	2	no	—
18	C₃×#4047	—	2	2	no	—
19	#91568	C₄	1	4	yes	—
20	#91463	—	2	1	no	—
21	#91449	—	2	2	no	—
22	#91370	—	2	1	no	—
23	C₅×#823	—	2	2	no	—
24	#90961	—	2	1	no	—
25	#90959	—	2	2	no	—
26	#90958	—	2	1	no	—
27	#72030	—	5	1	no	maximal, Hall
28	#66139	—	3	1	no	—
29	#66079	D₃	1	1	yes	characteristic, complemented
30	C₂×C₅×#100	—	3	1	no	—
31	C₂×#3965	—	3	1	no	—
32	#65421	—	3	1	no	—
33	#64779	—	3	1	no	—
34	#64776	—	3	1	no	—
35	C₂³×C₅×D₃	C₂×C₄	1	2	yes	—
36	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
37	C₂×C₅×D₁₂	—	2	1	no	—
38	C₂×C₅×D₁₂	—	2	1	no	—
39	C₂×C₅×D₁₂	—	2	1	no	—
40	C₂×C₅×D₁₂	—	2	1	no	—
41	C₂×C₅×D₁₂	—	2	1	no	—
42	C₂×C₅×D₁₂	—	2	1	no	—
43	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	2	yes	—
44	C₃×#709	—	2	1	no	—
45	C₃×#709	—	2	1	no	—
46	C₃×#709	—	2	1	no	—
47	C₃×#709	—	2	1	no	—
48	C₂×C₃×D₂₀	D₄	1	1	yes	characteristic
49	C₂×C₃×C₄×D₅	D₄	1	2	yes	—
50	C₂×C₃×Dic₁₀	D₄	1	1	yes	characteristic
51	C₂×#1201	—	2	4	no	—
52	C₃×C₅×M₁₆	—	2	1	no	—
53	C₃×C₅×M₁₆	D₄	1	2	yes	complemented
54	C₂×C₃×C₅×C₈	—	2	1	no	—
55	#6719	C₂×C₄	1	2	yes	—
56	C₄⋊Dic₁₅	—	2	1	no	—
57	C₄×Dic₁₅	—	2	1	no	—
58	#6710	—	2	1	no	—
59	#6710	—	2	1	no	—
60	C₂×C₃⋊#168	—	2	1	no	—
61	C₅×#208	—	2	1	no	—
62	C₅×#208	—	2	1	no	—
63	C₂×C₅×C₃⋊C₈	—	2	1	no	—
64	C₃×#681	—	2	1	no	—
65	C₃×#681	D₄	1	2	yes	complemented
66	C₂×C₃×#168	—	2	1	no	—
67	C₃×#676	—	2	4	no	—
68	C₃×C₈×D₅	—	2	4	no	—
69	(C₂×D₃)⋊Dic₅	—	2	4	no	—
70	C₃×#568	—	5	1	no	—
71	#5830	—	5	1	no	—
72	#5237	—	5	1	no	—
73	C₂×#823	—	5	1	no	—
74	C₂×#823	D₅	1	1	yes	characteristic, complemented
75	#4559	—	5	1	no	—
76	#4559	—	5	1	no	—
77	C₂²×C₅×D₄	—	3	1	no	—
78	C₂×#709	C₂×D₃	1	1	yes	characteristic
79	C₂×C₅×M₁₆	—	3	1	no	—
80	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
81	#4099	—	3	4	no	—
82	#4086	—	6	1	no	—
83	#4084	—	6	2	no	—
84	#4082	—	6	1	no	—
85	#4072	—	3	1	no	—
86	C₂×#681	—	3	1	no	—
87	C₂×#681	C₂×D₃	1	1	yes	characteristic
88	#4053	—	2	2	no	—
89	D₅×M₁₆	—	2	2	no	—
90	#4047	—	2	2	no	—
91	C₅×#100	—	6	2	no	—
92	#3965	—	6	2	no	—
93	#3956	—	6	1	no	—
94	#3955	—	6	1	no	—
95	#1914	—	15	1	no	Sylow
96	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₅×D₃	—	2	2	no	—
98	C₂²×C₅×D₃	—	2	2	no	—
99	C₂²×C₅×D₃	—	2	2	no	—
100	C₂²×C₅×D₃	—	8	2	no	—
101	C₂²×C₃×D₅	C₂²⋊C₄	1	2	yes	—
102	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
103	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
104	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
105	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
108	C₂×Dic₁₅	—	2	2	no	—
109	C₅×D₁₂	—	4	1	no	—
110	C₅×D₁₂	—	4	1	no	—
111	C₅×D₁₂	—	4	1	no	—
112	C₅×D₁₂	—	4	1	no	—
113	C₃×C₂²⋊D₅	—	2	2	no	—
114	C₃×C₂²⋊D₅	—	2	2	no	—
115	C₂×C₃×Dic₅	C₂²⋊C₄	1	2	yes	—
116	C₃×D₂₀	—	2	1	no	—
117	C₃×D₂₀	—	2	1	no	—
118	C₃×C₄×D₅	—	2	2	no	—
119	C₃×C₄×D₅	—	2	2	no	—
120	C₃×Dic₁₀	—	2	1	no	—
121	C₃×Dic₁₀	—	2	1	no	—
122	#1201	—	8	4	no	—
123	C₃×C₅×C₈	—	2	2	no	—
124	C₃⋊#168	—	4	1	no	—
125	C₃×#168	—	2	2	no	—
126	C₅×C₃⋊C₈	—	4	1	no	—
127	C₂×C₃×#41	—	5	1	no	—
128	C₂²×D₁₂	C₂×D₅	1	1	yes	characteristic
129	C₃×#131	—	10	2	no	—
130	C₃×#131	—	10	2	no	—
131	C₂×C₃×M₁₆	—	5	1	no	—
132	C₂×C₃×M₁₆	—	10	2	no	—
133	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
134	#947	—	10	1	no	—
135	#940	—	10	1	no	—
136	#937	—	5	4	no	—
137	#930	—	10	2	no	—
138	#926	—	5	1	no	—
139	C₂×#208	—	5	1	no	—
140	C₂×#208	C₂×D₅	1	1	yes	characteristic
141	#836	—	10	1	no	—
142	#833	—	10	1	no	—
143	#823	—	2	2	no	—
144	#823	—	10	2	no	—
145	C₂⁴×C₅	—	3	2	no	—
146	C₂×C₅×D₄	—	6	1	no	—
147	C₂×C₅×D₄	—	6	1	no	—
148	C₂×C₅×D₄	—	6	1	no	—
149	C₂×C₅×D₄	—	6	1	no	—
150	C₂×C₅×D₄	—	6	1	no	—
151	C₂×C₅×D₄	—	6	1	no	—
152	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
153	C₂×C₂²⋊D₅	—	6	4	no	—
154	C₂×C₂²⋊D₅	C₄×D₃	1	2	yes	—
155	#709	—	2	1	no	—
156	#709	—	2	1	no	—
157	#709	—	2	1	no	—
158	#709	—	2	1	no	—
159	C₂×D₂₀	D₁₂	1	1	yes	characteristic
160	C₂×C₄×D₅	#67	1	2	yes	—
161	C₂×Dic₁₀	D₁₂	1	1	yes	characteristic
162	C₅×M₁₆	—	2	1	no	—
163	C₅×M₁₆	—	6	1	no	—
164	C₅×M₁₆	—	6	1	no	—
165	C₅×M₁₆	#67	1	2	yes	complemented
166	C₂×C₅×C₈	—	2	1	no	—
167	C₂×C₅×C₈	—	6	1	no	—
168	C₂²⋊Dic₅	—	3	2	no	—
169	C₂²⋊Dic₅	—	6	4	no	—
170	C₄⋊Dic₅	—	6	1	no	—
171	C₄×Dic₅	—	6	1	no	—
172	#681	—	2	1	no	—
173	#681	—	6	1	no	—
174	#681	—	6	1	no	—
175	#681	#67	1	2	yes	complemented
176	C₂×#168	—	2	1	no	—
177	C₂×#168	—	6	1	no	—
178	#676	—	2	4	no	—
179	C₈×D₅	—	2	4	no	—
180	#568	—	5	1	no	—
181	#535	—	15	1	no	—
182	#413	—	15	1	no	—
183	C₂×#100	—	3	1	no	—
184	C₂×#100	—	15	1	no	—
185	#344	—	15	1	no	—
186	#344	—	15	1	no	—
187	C₂²×C₃×C₅	—	4	1	no	—
188	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
189	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
190	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
191	C₂×C₅×D₃	—	4	4	no	—
192	C₂×C₅×D₃	—	4	2	no	—
193	C₂×C₅×D₃	—	8	2	no	—
194	C₂×C₅×D₃	—	8	2	no	—
195	C₂×C₃×D₅	—	2	2	no	—
196	C₂×C₃×D₅	—	4	2	no	—
197	C₃×C₄×C₅	#120	1	1	yes	characteristic
198	C₃×C₄×C₅	#121	1	1	yes	characteristic
199	C₃×C₄×C₅	#121	1	1	yes	characteristic
200	C₃×C₄×C₅	#123	1	1	yes	characteristic
201	Dic₁₅	—	4	2	no	—
202	C₃×Dic₅	—	2	2	no	—
203	C₂³×D₃	C₄×D₅	1	2	yes	—
204	C₃×#41	—	10	1	no	—
205	C₃×#41	—	10	1	no	—
206	C₃×#41	—	10	1	no	—
207	C₃×#41	—	10	1	no	—
208	C₂×C₃×Q₈	—	5	1	no	—
209	C₂×C₃×D₄	—	5	2	no	—
210	C₂×C₃×D₄	—	5	1	no	—
211	C₂²×C₃×C₄	—	5	2	no	—
212	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
213	C₂×#67	—	10	4	no	—
214	C₂×D₁₂	—	2	1	no	—
215	C₂×D₁₂	—	2	1	no	—
216	C₂×D₁₂	—	2	1	no	—
217	C₂×D₁₂	—	2	1	no	—
218	C₂×D₁₂	—	2	1	no	—
219	C₂×D₁₂	—	2	1	no	—
220	C₃×M₁₆	—	2	1	no	—
221	C₃×M₁₆	—	5	2	no	—
222	C₃×M₁₆	—	10	4	no	—
223	C₃×M₁₆	—	10	1	no	—
224	C₃×M₁₆	C₂²⋊D₅	1	2	yes	complemented
225	C₂×C₃×C₈	—	2	1	no	—
226	C₂×C₃×C₈	—	10	4	no	—
227	C₂×C₃×C₈	—	10	1	no	—
228	#217	—	5	2	no	—
229	(C₂×D₃)⋊C₄	—	10	4	no	—
230	C₄⋊Dic₃	—	10	1	no	—
231	C₄×Dic₃	—	10	1	no	—
232	#208	—	2	1	no	—
233	#208	—	2	1	no	—
234	#208	—	10	1	no	—
235	#208	—	10	1	no	—
236	C₂×C₃⋊C₈	—	2	1	no	—
237	C₂×C₃⋊C₈	—	10	1	no	—
238	C₂³×C₅	—	6	2	no	—
239	C₂³×C₅	—	6	2	no	—
240	C₂³×C₅	—	6	2	no	—
241	C₂³×C₅	—	24	2	no	—
242	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
243	C₂²×D₅	(C₂×D₃)⋊C₄	1	2	yes	—
244	C₅×D₄	—	12	1	no	—
245	C₅×D₄	—	12	1	no	—
246	C₅×D₄	—	12	1	no	—
247	C₅×D₄	—	12	1	no	—
248	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
249	C₂×C₄×C₅	#235	1	1	yes	characteristic
250	C₂×C₄×C₅	#235	1	1	yes	characteristic
251	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
252	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
253	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
254	C₂²⋊D₅	—	2	2	no	—
255	C₂²⋊D₅	—	2	2	no	—
256	C₂²⋊D₅	—	24	4	no	—
257	C₂×Dic₅	—	6	2	no	—
258	C₂×Dic₅	(C₂×D₃)⋊C₄	1	2	yes	—
259	D₂₀	—	2	1	no	—
260	D₂₀	—	2	1	no	—
261	C₄×D₅	—	2	2	no	—
262	C₄×D₅	—	2	2	no	—
263	Dic₁₀	—	2	1	no	—
264	Dic₁₀	—	2	1	no	—
265	C₅×C₈	—	2	2	no	—
266	C₅×C₈	—	12	1	no	—
267	#168	—	2	2	no	—
268	#168	—	12	1	no	—
269	C₂×#41	—	5	1	no	—
270	C₂²×D₄	—	3	1	no	—
271	#131	—	10	2	no	—
272	#131	—	10	2	no	—
273	C₂×M₁₆	—	3	1	no	—
274	C₂×M₁₆	—	5	1	no	—
275	C₂×M₁₆	—	10	2	no	—
276	C₂×M₁₆	—	15	1	no	—
277	C₂×M₁₆	D₃×D₅	1	1	yes	characteristic
278	#127	—	30	1	no	—
279	#124	—	30	1	no	—
280	#121	—	30	2	no	—
281	#120	—	15	4	no	—
282	#117	—	15	1	no	—
283	#101	—	30	1	no	—
284	#100	—	6	2	no	—
285	#100	—	30	2	no	—
286	#100	—	30	1	no	—
287	C₂×C₃×C₅	—	2	1	no	—
288	C₂×C₃×C₅	—	2	1	no	—
289	C₂×C₃×C₅	—	2	1	no	—
290	C₂×C₃×C₅	#386	1	1	yes	characteristic
291	C₃×D₅	—	4	2	no	—
292	C₅×D₃	—	8	2	no	—
293	C₂³×C₃	—	5	2	no	—
294	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
295	C₂²×D₃	—	2	2	no	—
296	C₂²×D₃	—	2	2	no	—
297	C₂²×D₃	—	2	2	no	—
298	C₂²×D₃	—	8	2	no	—
299	C₃×Q₈	—	10	1	no	—
300	C₃×Q₈	—	10	1	no	—
301	C₃×D₄	—	10	2	no	—
302	C₃×D₄	—	10	2	no	—
303	C₃×D₄	—	10	1	no	—
304	C₃×D₄	—	10	1	no	—
305	C₂×C₃×C₄	—	5	2	no	—
306	C₂×C₃×C₄	—	10	2	no	—
307	C₂×C₃×C₄	—	10	2	no	—
308	C₂×C₃×C₄	#709	1	1	yes	characteristic
309	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
310	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
311	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
312	C₂×C₃×C₄	#711	1	1	yes	characteristic
313	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
314	#67	—	40	4	no	—
315	C₂×Dic₃	—	10	2	no	—
316	D₁₂	—	4	1	no	—
317	D₁₂	—	4	1	no	—
318	D₁₂	—	4	1	no	—
319	D₁₂	—	4	1	no	—
320	C₃×C₈	—	2	2	no	—
321	C₃×C₈	—	10	2	no	—
322	C₃⋊C₈	—	4	1	no	—
323	C₃⋊C₈	—	20	1	no	—
324	C₂²×C₅	—	4	1	no	—
325	C₂²×C₅	—	12	4	no	—
326	C₂²×C₅	—	12	2	no	—
327	C₂²×C₅	—	24	2	no	—
328	C₂²×C₅	—	24	2	no	—
329	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
330	C₂²×C₅	C₄×#67	1	1	yes	characteristic
331	C₂²×C₅	C₄×#67	1	1	yes	characteristic
332	C₂×D₅	—	2	2	no	—
333	C₂×D₅	—	4	2	no	—
334	C₄×C₅	#929	1	1	yes	characteristic
335	C₄×C₅	#930	1	1	yes	characteristic
336	C₄×C₅	#930	1	1	yes	characteristic
337	C₄×C₅	#953	1	1	yes	characteristic
338	Dic₅	—	2	2	no	—
339	Dic₅	—	12	2	no	—
340	C₂⁴	—	3	2	no	—
341	#41	—	10	1	no	—
342	#41	—	10	1	no	—
343	#41	—	10	1	no	—
344	#41	—	10	1	no	—
345	C₂×Q₈	—	5	1	no	—
346	C₂×D₄	—	5	2	no	—
347	C₂×D₄	—	5	1	no	—
348	C₂×D₄	—	6	1	no	—
349	C₂×D₄	—	6	1	no	—
350	C₂×D₄	—	6	1	no	—
351	C₂×D₄	—	6	1	no	—
352	C₂×D₄	—	6	1	no	—
353	C₂×D₄	—	6	1	no	—
354	C₂×D₄	—	30	4	no	—
355	C₂²×C₄	—	5	2	no	—
356	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
357	M₁₆	—	2	1	no	—
358	M₁₆	—	5	2	no	—
359	M₁₆	—	6	1	no	—
360	M₁₆	—	6	1	no	—
361	M₁₆	—	10	4	no	—
362	M₁₆	—	10	1	no	—
363	M₁₆	—	30	1	no	—
364	M₁₆	—	30	1	no	—
365	M₁₆	#1201	1	2	yes	complemented
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	6	1	no	—
368	C₂×C₈	—	10	4	no	—
369	C₂×C₈	—	10	1	no	—
370	C₂×C₈	—	30	1	no	—
371	C₄⋊C₄	—	30	1	no	—
372	C₂²⋊C₄	—	15	2	no	—
373	C₂²⋊C₄	—	30	4	no	—
374	C₄²	—	30	1	no	—
375	C₃×C₅	#1914	1	1	yes	characteristic, complemented, Hall
376	C₂²×C₃	—	4	1	no	—
377	C₂²×C₃	—	10	2	no	—
378	C₂²×C₃	—	20	2	no	—
379	C₂²×C₃	D₅×C₂²⋊C₄	1	1	yes	characteristic
380	C₂²×C₃	#4027	1	1	yes	characteristic
381	C₂²×C₃	C₄×C₂²⋊D₅	1	1	yes	characteristic
382	C₂×D₃	—	4	4	no	—
383	C₂×D₃	—	4	2	no	—
384	C₂×D₃	—	8	2	no	—
385	C₂×D₃	—	8	2	no	—
386	C₃×C₄	—	10	2	no	—
387	C₃×C₄	#4029	1	1	yes	characteristic
388	C₃×C₄	#4030	1	1	yes	characteristic
389	C₃×C₄	#4083	1	1	yes	characteristic
390	C₃×C₄	#4084	1	1	yes	characteristic
391	Dic₃	—	20	2	no	—
392	C₂×C₅	—	2	1	no	—
393	C₂×C₅	—	2	1	no	—
394	C₂×C₅	—	2	1	no	—
395	C₂×C₅	—	24	2	no	—
396	C₂×C₅	#5213	1	1	yes	characteristic
397	D₅	—	4	2	no	—
398	C₂³	—	5	2	no	—
399	C₂³	—	6	2	no	—
400	C₂³	—	6	2	no	—
401	C₂³	—	6	2	no	—
402	C₂³	—	24	2	no	—
403	C₂³	C₄×D₃×D₅	1	1	yes	characteristic
404	Q₈	—	10	1	no	—
405	Q₈	—	10	1	no	—
406	D₄	—	10	2	no	—
407	D₄	—	10	2	no	—
408	D₄	—	10	1	no	—
409	D₄	—	10	1	no	—
410	D₄	—	12	1	no	—
411	D₄	—	12	1	no	—
412	D₄	—	12	1	no	—
413	D₄	—	12	1	no	—
414	D₄	—	120	4	no	—
415	C₂×C₄	—	5	2	no	—
416	C₂×C₄	—	10	2	no	—
417	C₂×C₄	—	10	2	no	—
418	C₂×C₄	—	30	2	no	—
419	C₂×C₄	#6771	1	1	yes	characteristic
420	C₂×C₄	#6772	1	1	yes	characteristic
421	C₂×C₄	D₅×D₁₂	1	1	yes	characteristic
422	C₂×C₄	C₂×#1201	1	1	yes	characteristic
423	C₂×C₄	D₅×#67	1	1	yes	characteristic
424	C₂×C₄	D₅×#67	1	1	yes	characteristic
425	C₈	—	2	2	no	—
426	C₈	—	10	2	no	—
427	C₈	—	12	1	no	—
428	C₈	—	60	1	no	—
429	C₂×C₃	—	2	1	no	—
430	C₂×C₃	—	2	1	no	—
431	C₂×C₃	—	2	1	no	—
432	C₂×C₃	—	20	2	no	—
433	C₂×C₃	#65245	1	1	yes	characteristic
434	D₃	—	8	2	no	—
435	C₅	#72030	1	1	yes	characteristic, complemented, Sylow
436	C₂²	—	4	1	no	—
437	C₂²	—	10	2	no	—
438	C₂²	—	12	4	no	—
439	C₂²	—	12	2	no	—
440	C₂²	—	20	2	no	—
441	C₂²	—	24	2	no	—
442	C₂²	—	24	2	no	—
443	C₂²	C₄×#1201	1	1	yes	characteristic
444	C₂²	#91440	1	1	yes	characteristic
445	C₂²	D₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
446	C₄	—	10	2	no	—
447	C₄	—	60	2	no	—
448	C₄	#91447	1	1	yes	characteristic
449	C₄	#91448	1	1	yes	characteristic
450	C₄	#91449	1	1	yes	characteristic
451	C₄	#91563	1	1	yes	characteristic
452	C₃	#10600882	1	1	yes	characteristic, complemented, Sylow
453	C₂	—	2	1	no	—
454	C₂	—	2	1	no	—
455	C₂	—	2	1	no	—
456	C₂	—	20	2	no	—
457	C₂	—	24	2	no	—
458	C₂	#11748905	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11748905
commutator	C₂³×C₃×C₅	C₂²×C₄
Frattini	C₂²×C₄	C₂×D₃×D₅
Fitting	C₂×C₃×C₅×M₁₆	C₂²
socle	C₂×C₃×C₅	#386
prime radical	#11754604	C₂
cosocle	C₂²×C₃×C₄×C₅	C₂³
hypercenter	C₂×M₁₆	D₃×D₅
hypocenter	C₃×C₅	#1914
LCS	G ▷ C₂³×C₃×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
1. C₃×#66079	C₂	semidirect
3. C₂×C₅×#823	C₂	semidirect
4. C₂×#90959	C₂	semidirect
5. #11748353	C₂	semidirect
6. #11746380	C₂	semidirect
7. #11745990	C₂	semidirect
29. #66079	D₃	semidirect
53. C₃×C₅×M₁₆	D₄	semidirect
65. C₃×#681	D₄	semidirect
74. C₂×#823	D₅	semidirect
165. C₅×M₁₆	#67	semidirect
175. #681	#67	semidirect
224. C₃×M₁₆	C₂²⋊D₅	semidirect
365. M₁₆	#1201	semidirect
375. C₃×C₅	#1914	semidirect
435. C₅	#72030	semidirect
452. C₃	#10600882	semidirect

Maximal subgroups

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

subgroup	index
C₃×#66079	2
#11754604	2
C₂×C₅×#823	2
C₂×#90959	2
#11748353	2
#11746380	2
#11745990	2
#10600882	3
#72030	5