Subgroups — #14297567

Order 1920.

672 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#91428	C₂	1	1	yes	maximal, characteristic
2	C₂×#91107	C₂	1	1	yes	maximal, characteristic
3	C₅×#5118	C₂	1	1	yes	maximal, characteristic, complemented
4	#11748440	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#90960	C₂	1	1	yes	maximal, characteristic
6	C₃×#64774	C₂	1	1	yes	maximal, characteristic, complemented
7	#11745985	C₂	1	1	yes	maximal, characteristic, complemented
8	#10601320	—	3	1	no	maximal, Hall
9	C₂²×D₆₀	C₂²	1	1	yes	characteristic
10	C₂²×#1200	C₄	1	2	yes	—
11	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
12	C₂×#6710	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
14	C₂×C₅×#208	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
16	C₂×C₃×#681	C₂²	1	1	yes	characteristic
17	C₂×#6667	C₄	1	2	yes	—
18	#91428	—	2	1	no	—
19	#91428	—	2	1	no	—
20	#91428	—	2	1	no	—
21	#91428	—	2	1	no	—
22	#91107	—	2	2	no	—
23	C₅×Dic₃⋊C₈	—	2	1	no	—
24	C₅×Dic₃⋊C₈	—	2	1	no	—
25	Dic₃⋊#168	—	2	1	no	—
26	Dic₃⋊#168	—	2	1	no	—
27	#90960	—	2	2	no	—
28	#68994	—	5	1	no	maximal, Hall
29	C₂×C₄×D₂₀	—	3	1	no	—
30	C₅×#423	—	3	1	no	—
31	C₂×#3955	—	3	1	no	—
32	C₂×#3955	—	3	1	no	—
33	#65213	—	3	1	no	—
34	#64774	—	3	1	no	—
35	#64774	D₃	1	1	yes	characteristic, complemented
36	C₂³×D₁₅	C₂×C₄	1	2	yes	—
37	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
38	C₂×D₆₀	—	2	1	no	—
39	C₂×D₆₀	—	2	1	no	—
40	C₂×D₆₀	—	2	1	no	—
41	C₂×D₆₀	—	2	1	no	—
42	C₂×D₆₀	D₄	1	2	yes	—
43	C₂×D₆₀	Q₈	1	2	yes	—
44	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
46	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	—
47	C₂×#1200	—	2	2	no	—
48	C₂×#1200	—	2	2	no	—
49	C₂×#1200	—	4	4	no	—
50	C₃×C₅×M₁₆	—	2	1	no	—
51	C₃×C₅×M₁₆	—	2	1	no	—
52	C₂×C₃×C₅×C₈	—	2	1	no	—
53	#6710	—	2	1	no	—
54	#6710	—	2	1	no	—
55	C₂×C₃⋊#168	—	2	1	no	—
56	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
57	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
58	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
59	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
60	C₅×#208	—	2	1	no	—
61	C₅×#208	—	2	1	no	—
62	C₂×C₅×C₃⋊C₈	—	2	1	no	—
63	C₃×C₄⋊Dic₅	—	2	1	no	—
64	C₃×C₄⋊Dic₅	—	2	1	no	—
65	C₃×#681	—	2	1	no	—
66	C₃×#681	—	2	1	no	—
67	C₂×C₃×#168	—	2	1	no	—
68	#6667	—	2	2	no	—
69	#6667	—	2	2	no	—
70	C₂×#893	—	5	1	no	—
71	C₂×#823	—	5	1	no	—
72	C₂×#823	—	5	1	no	—
73	#5118	—	5	1	no	—
74	#5118	D₅	1	1	yes	characteristic, complemented
75	C₃×#343	—	5	1	no	—
76	#4530	—	5	1	no	—
77	C₂²×D₂₀	—	3	1	no	—
78	C₂²×C₄×D₅	—	3	2	no	—
79	C₂×C₅×M₁₆	—	3	1	no	—
80	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
81	C₂×C₄²×C₅	—	3	1	no	—
82	C₂×#685	—	3	2	no	—
83	C₂×C₄⋊Dic₅	C₂×D₃	1	1	yes	characteristic
84	C₂×#681	—	3	1	no	—
85	C₂×#681	C₂×D₃	1	1	yes	characteristic
86	C₄×D₂₀	—	6	1	no	—
87	C₄×D₂₀	—	6	1	no	—
88	C₄×D₂₀	—	6	1	no	—
89	C₄×D₂₀	—	6	1	no	—
90	C₅×C₄⋊C₈	—	6	1	no	—
91	C₅×C₄⋊C₈	—	6	1	no	—
92	#3955	—	6	2	no	—
93	#3955	—	6	2	no	—
94	C₄⋊#168	—	6	1	no	—
95	C₄⋊#168	—	6	1	no	—
96	#1800	—	15	1	no	Sylow
97	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
98	C₂²×D₁₅	—	2	2	no	—
99	C₂²×D₁₅	—	2	2	no	—
100	C₂²×D₁₅	—	4	2	no	—
101	C₂²×D₁₅	—	4	2	no	—
102	C₂²×D₁₅	C₄⋊C₄	1	4	yes	—
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	C₂×Q₈	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
109	D₆₀	—	2	2	no	—
110	D₆₀	—	2	2	no	—
111	D₆₀	—	2	2	no	—
112	D₆₀	—	2	2	no	—
113	C₂×C₅×Dic₃	—	2	2	no	—
114	C₂×C₅×Dic₃	—	4	1	no	—
115	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
116	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
117	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
118	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
119	C₂×C₃×Dic₅	—	2	2	no	—
120	C₂×C₃×Dic₅	—	4	2	no	—
121	#1200	—	4	4	no	—
122	#1200	—	4	4	no	—
123	C₃×C₅×C₈	—	4	1	no	—
124	C₃⋊#168	—	4	1	no	—
125	C₃×#168	—	4	1	no	—
126	C₅×C₃⋊C₈	—	4	1	no	—
127	C₂²×D₁₂	—	5	1	no	—
128	C₂²×C₄×D₃	—	5	2	no	—
129	C₂×C₃×M₁₆	—	5	1	no	—
130	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
131	C₂×C₃×C₄⋊C₄	—	5	1	no	—
132	C₂×(C₂×D₃)⋊C₄	—	5	2	no	—
133	C₂×C₄×Dic₃	C₂×D₅	1	1	yes	characteristic
134	C₂×#208	—	5	1	no	—
135	C₂×#208	C₂×D₅	1	1	yes	characteristic
136	#893	—	10	1	no	—
137	#893	—	10	1	no	—
138	#893	—	10	1	no	—
139	#893	—	10	1	no	—
140	#823	—	10	2	no	—
141	#823	—	10	2	no	—
142	Dic₃⋊C₈	—	2	1	no	—
143	Dic₃⋊C₈	—	2	1	no	—
144	Dic₃⋊C₈	—	10	1	no	—
145	Dic₃⋊C₈	—	10	1	no	—
146	C₂³×D₅	—	3	2	no	—
147	C₂²×C₄×C₅	—	3	1	no	—
148	C₂²×C₄×C₅	—	3	1	no	—
149	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
150	C₂²×Dic₅	C₄×D₃	1	2	yes	—
151	C₂×D₂₀	—	3	2	no	—
152	C₂×D₂₀	—	3	2	no	—
153	C₂×D₂₀	—	6	1	no	—
154	C₂×D₂₀	—	6	1	no	—
155	C₂×D₂₀	—	6	1	no	—
156	C₂×D₂₀	—	6	1	no	—
157	C₂×C₄×D₅	—	6	2	no	—
158	C₂×C₄×D₅	—	6	2	no	—
159	C₂×C₄×D₅	—	12	4	no	—
160	C₅×M₁₆	—	2	1	no	—
161	C₅×M₁₆	—	2	1	no	—
162	C₅×M₁₆	—	6	1	no	—
163	C₅×M₁₆	—	6	1	no	—
164	C₂×C₅×C₈	—	2	1	no	—
165	C₂×C₅×C₈	—	6	1	no	—
166	C₄²×C₅	—	3	1	no	—
167	C₄²×C₅	—	3	1	no	—
168	C₄²×C₅	—	3	1	no	—
169	C₄²×C₅	—	3	1	no	—
170	#685	—	6	2	no	—
171	#685	—	6	2	no	—
172	C₄⋊Dic₅	—	2	1	no	—
173	C₄⋊Dic₅	—	2	1	no	—
174	#681	—	2	1	no	—
175	#681	—	2	1	no	—
176	#681	—	6	1	no	—
177	#681	—	6	1	no	—
178	C₂×#168	—	2	1	no	—
179	C₂×#168	—	6	1	no	—
180	C₂×C₄×D₄	—	15	1	no	—
181	#423	—	3	1	no	—
182	#423	—	15	1	no	—
183	C₂×#100	—	15	1	no	—
184	C₂×#100	—	15	1	no	—
185	#343	—	5	1	no	—
186	#343	—	15	1	no	—
187	C₂²×C₃×C₅	—	2	1	no	—
188	C₂²×C₃×C₅	—	2	1	no	—
189	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
190	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
191	C₂²×C₃×C₅	#117	1	1	yes	characteristic
192	C₂×D₁₅	—	2	4	no	—
193	C₂×D₁₅	—	4	4	no	—
194	C₂×D₁₅	—	4	2	no	—
195	C₂×D₁₅	—	4	2	no	—
196	C₂×D₁₅	—	4	4	no	—
197	C₃×C₄×C₅	#121	1	1	yes	characteristic
198	C₃×C₄×C₅	#121	1	1	yes	characteristic
199	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
200	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
201	C₃×Dic₅	—	4	2	no	—
202	C₅×Dic₃	—	2	1	no	—
203	C₅×Dic₃	—	2	1	no	—
204	C₅×Dic₃	—	2	1	no	—
205	C₅×Dic₃	#100	1	2	yes	complemented
206	C₂³×D₃	—	5	2	no	—
207	C₂²×C₃×C₄	—	5	2	no	—
208	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
209	C₂²×Dic₃	C₄×D₅	1	1	yes	characteristic
210	C₂²×Dic₃	C₄×D₅	1	1	yes	characteristic
211	C₂×D₁₂	—	5	2	no	—
212	C₂×D₁₂	—	5	2	no	—
213	C₂×D₁₂	—	10	1	no	—
214	C₂×D₁₂	—	10	1	no	—
215	C₂×D₁₂	—	10	1	no	—
216	C₂×D₁₂	—	10	1	no	—
217	C₂×C₄×D₃	—	10	2	no	—
218	C₂×C₄×D₃	—	10	2	no	—
219	C₂×C₄×D₃	—	20	4	no	—
220	C₃×M₁₆	—	2	1	no	—
221	C₃×M₁₆	—	2	1	no	—
222	C₃×M₁₆	—	10	1	no	—
223	C₃×M₁₆	—	10	1	no	—
224	C₂×C₃×C₈	—	2	1	no	—
225	C₂×C₃×C₈	—	10	1	no	—
226	C₃×C₄⋊C₄	—	10	1	no	—
227	C₃×C₄⋊C₄	—	10	1	no	—
228	(C₂×D₃)⋊C₄	—	10	2	no	—
229	(C₂×D₃)⋊C₄	—	10	2	no	—
230	C₄×Dic₃	D₂₀	1	1	yes	characteristic
231	C₄×Dic₃	D₂₀	1	1	yes	characteristic
232	C₄×Dic₃	C₂²⋊D₅	1	1	yes	characteristic
233	C₄×Dic₃	C₂²⋊D₅	1	1	yes	characteristic
234	#208	—	2	1	no	—
235	#208	—	2	1	no	—
236	#208	—	10	1	no	—
237	#208	—	10	1	no	—
238	C₂×C₃⋊C₈	—	2	1	no	—
239	C₂×C₃⋊C₈	—	10	1	no	—
240	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
241	C₂²×D₅	—	3	4	no	—
242	C₂²×D₅	—	6	2	no	—
243	C₂²×D₅	—	6	2	no	—
244	C₂²×D₅	—	12	2	no	—
245	C₂²×D₅	—	12	2	no	—
246	C₂×C₄×C₅	—	3	1	no	—
247	C₂×C₄×C₅	—	3	1	no	—
248	C₂×C₄×C₅	—	3	1	no	—
249	C₂×C₄×C₅	—	3	1	no	—
250	C₂×C₄×C₅	—	6	2	no	—
251	C₂×C₄×C₅	—	12	1	no	—
252	C₂×C₄×C₅	#235	1	1	yes	characteristic
253	C₂×C₄×C₅	#235	1	1	yes	characteristic
254	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
255	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
256	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
257	C₂×C₄×C₅	D₃×Q₈	1	1	yes	characteristic
258	C₂×Dic₅	—	2	2	no	—
259	C₂×Dic₅	—	4	2	no	—
260	D₂₀	—	6	2	no	—
261	D₂₀	—	6	2	no	—
262	D₂₀	—	6	2	no	—
263	D₂₀	—	6	2	no	—
264	C₄×D₅	—	12	4	no	—
265	C₄×D₅	—	12	4	no	—
266	C₅×C₈	—	4	1	no	—
267	C₅×C₈	—	12	1	no	—
268	#168	—	4	1	no	—
269	#168	—	12	1	no	—
270	C₂²×D₄	—	15	1	no	—
271	C₂³×C₄	—	15	2	no	—
272	C₂×M₁₆	—	3	1	no	—
273	C₂×M₁₆	—	5	1	no	—
274	C₂×M₁₆	—	15	1	no	—
275	C₂×M₁₆	D₃×D₅	1	1	yes	characteristic
276	C₄×D₄	—	30	1	no	—
277	C₄×D₄	—	30	1	no	—
278	C₄×D₄	—	30	1	no	—
279	C₄×D₄	—	30	1	no	—
280	C₂×C₄⋊C₄	—	5	1	no	—
281	C₂×C₂²⋊C₄	—	15	2	no	—
282	C₂×C₄²	—	3	1	no	—
283	C₄⋊C₈	—	6	1	no	—
284	C₄⋊C₈	—	6	1	no	—
285	C₄⋊C₈	—	30	1	no	—
286	C₄⋊C₈	—	30	1	no	—
287	#100	—	30	2	no	—
288	#100	—	30	2	no	—
289	C₂×C₃×C₅	—	2	1	no	—
290	C₂×C₃×C₅	—	2	1	no	—
291	C₂×C₃×C₅	#380	1	1	yes	characteristic
292	C₂×C₃×C₅	C₂×#100	1	1	yes	characteristic
293	C₂×C₃×C₅	#413	1	1	yes	characteristic
294	D₁₅	—	4	4	no	—
295	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
296	C₂²×D₃	—	5	4	no	—
297	C₂²×D₃	—	10	2	no	—
298	C₂²×D₃	—	10	2	no	—
299	C₂²×D₃	—	20	2	no	—
300	C₂²×D₃	—	20	2	no	—
301	C₂×C₃×C₄	—	10	2	no	—
302	C₂×C₃×C₄	—	20	2	no	—
303	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
304	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
305	C₂×C₃×C₄	#711	1	1	yes	characteristic
306	C₂×C₃×C₄	Q₈×D₅	1	1	yes	characteristic
307	C₂×C₃×C₄	#713	1	1	yes	characteristic
308	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
309	C₂×Dic₃	—	2	2	no	—
310	C₂×Dic₃	—	4	1	no	—
311	C₂×Dic₃	#685	1	1	yes	characteristic
312	C₂×Dic₃	#685	1	1	yes	characteristic
313	C₂×Dic₃	#685	1	1	yes	characteristic
314	C₂×Dic₃	#685	1	1	yes	characteristic
315	D₁₂	—	10	2	no	—
316	D₁₂	—	10	2	no	—
317	D₁₂	—	10	2	no	—
318	D₁₂	—	10	2	no	—
319	C₄×D₃	—	20	4	no	—
320	C₄×D₃	—	20	4	no	—
321	C₃×C₈	—	4	1	no	—
322	C₃×C₈	—	20	1	no	—
323	C₃⋊C₈	—	4	1	no	—
324	C₃⋊C₈	—	20	1	no	—
325	C₂²×C₅	—	2	1	no	—
326	C₂²×C₅	—	2	1	no	—
327	C₂²×C₅	#872	1	1	yes	characteristic
328	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
329	C₂²×C₅	D₃×C₄⋊C₄	1	1	yes	characteristic
330	C₂×D₅	—	6	4	no	—
331	C₂×D₅	—	12	4	no	—
332	C₂×D₅	—	12	2	no	—
333	C₂×D₅	—	12	2	no	—
334	C₂×D₅	—	12	4	no	—
335	C₄×C₅	—	3	2	no	—
336	C₄×C₅	—	6	1	no	—
337	C₄×C₅	—	6	1	no	—
338	C₄×C₅	—	6	1	no	—
339	C₄×C₅	#884	1	1	yes	characteristic
340	C₄×C₅	#884	1	1	yes	characteristic
341	C₄×C₅	#896	1	1	yes	characteristic
342	C₄×C₅	#896	1	1	yes	characteristic
343	Dic₅	—	4	2	no	—
344	C₂⁴	—	15	2	no	—
345	C₂×D₄	—	15	2	no	—
346	C₂×D₄	—	15	2	no	—
347	C₂×D₄	—	30	1	no	—
348	C₂×D₄	—	30	1	no	—
349	C₂×D₄	—	30	1	no	—
350	C₂×D₄	—	30	1	no	—
351	C₂²×C₄	—	3	1	no	—
352	C₂²×C₄	—	3	1	no	—
353	C₂²×C₄	—	5	2	no	—
354	C₂²×C₄	—	30	2	no	—
355	C₂²×C₄	—	30	2	no	—
356	C₂²×C₄	—	60	4	no	—
357	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
358	M₁₆	—	2	1	no	—
359	M₁₆	—	2	1	no	—
360	M₁₆	—	6	1	no	—
361	M₁₆	—	6	1	no	—
362	M₁₆	—	10	1	no	—
363	M₁₆	—	10	1	no	—
364	M₁₆	—	30	1	no	—
365	M₁₆	—	30	1	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	6	1	no	—
368	C₂×C₈	—	10	1	no	—
369	C₂×C₈	—	30	1	no	—
370	C₄⋊C₄	—	10	1	no	—
371	C₄⋊C₄	—	10	1	no	—
372	C₂²⋊C₄	—	30	2	no	—
373	C₂²⋊C₄	—	30	2	no	—
374	C₄²	—	3	1	no	—
375	C₄²	—	3	1	no	—
376	C₄²	—	3	1	no	—
377	C₄²	—	3	1	no	—
378	C₃×C₅	#1800	1	1	yes	characteristic, complemented, Hall
379	C₂²×C₃	—	2	1	no	—
380	C₂²×C₃	—	2	1	no	—
381	C₂²×C₃	D₅×C₄⋊C₄	1	1	yes	characteristic
382	C₂²×C₃	#4038	1	1	yes	characteristic
383	C₂²×C₃	C₂×#685	1	1	yes	characteristic
384	C₂×D₃	—	10	4	no	—
385	C₂×D₃	—	20	4	no	—
386	C₂×D₃	—	20	2	no	—
387	C₂×D₃	—	20	2	no	—
388	C₂×D₃	—	20	4	no	—
389	C₃×C₄	—	20	2	no	—
390	C₃×C₄	#4041	1	1	yes	characteristic
391	C₃×C₄	#4043	1	1	yes	characteristic
392	C₃×C₄	#4084	1	1	yes	characteristic
393	C₃×C₄	#4092	1	1	yes	characteristic
394	Dic₃	—	2	1	no	—
395	Dic₃	—	2	1	no	—
396	Dic₃	—	2	1	no	—
397	Dic₃	#3955	1	2	yes	complemented
398	C₂×C₅	—	2	1	no	—
399	C₂×C₅	—	2	1	no	—
400	C₂×C₅	#4667	1	1	yes	characteristic
401	C₂×C₅	D₃×#100	1	1	yes	characteristic
402	C₂×C₅	#4751	1	1	yes	characteristic
403	D₅	—	12	4	no	—
404	C₂³	—	15	4	no	—
405	C₂³	—	30	2	no	—
406	C₂³	—	30	2	no	—
407	C₂³	—	60	2	no	—
408	C₂³	—	60	2	no	—
409	C₂³	C₄×D₃×D₅	1	1	yes	characteristic
410	D₄	—	30	2	no	—
411	D₄	—	30	2	no	—
412	D₄	—	30	2	no	—
413	D₄	—	30	2	no	—
414	C₂×C₄	—	3	1	no	—
415	C₂×C₄	—	3	1	no	—
416	C₂×C₄	—	3	1	no	—
417	C₂×C₄	—	3	1	no	—
418	C₂×C₄	—	6	2	no	—
419	C₂×C₄	—	10	2	no	—
420	C₂×C₄	—	12	1	no	—
421	C₂×C₄	—	20	2	no	—
422	C₂×C₄	—	60	4	no	—
423	C₂×C₄	—	60	4	no	—
424	C₂×C₄	D₁₅⋊Q₈	1	1	yes	characteristic
425	C₂×C₄	#6773	1	1	yes	characteristic
426	C₂×C₄	D₃×D₂₀	1	1	yes	characteristic
427	C₂×C₄	#6782	1	1	yes	characteristic
428	C₂×C₄	D₃×C₂²⋊D₅	1	1	yes	characteristic
429	C₂×C₄	#6790	1	1	yes	characteristic
430	C₈	—	4	1	no	—
431	C₈	—	12	1	no	—
432	C₈	—	20	1	no	—
433	C₈	—	60	1	no	—
434	C₂×C₃	—	2	1	no	—
435	C₂×C₃	—	2	1	no	—
436	C₂×C₃	#65276	1	1	yes	characteristic
437	C₂×C₃	C₂×#3955	1	1	yes	characteristic
438	C₂×C₃	#65421	1	1	yes	characteristic
439	D₃	—	20	4	no	—
440	C₅	#68994	1	1	yes	characteristic, complemented, Sylow
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	30	4	no	—
444	C₂²	—	60	4	no	—
445	C₂²	—	60	4	no	—
446	C₂²	—	60	2	no	—
447	C₂²	—	60	2	no	—
448	C₂²	#91402	1	1	yes	characteristic
449	C₂²	#91404	1	1	yes	characteristic
450	C₂²	D₃×#685	1	1	yes	characteristic
451	C₄	—	3	2	no	—
452	C₄	—	6	1	no	—
453	C₄	—	6	1	no	—
454	C₄	—	6	1	no	—
455	C₄	—	20	2	no	—
456	C₄	#91424	1	1	yes	characteristic
457	C₄	#91429	1	1	yes	characteristic
458	C₄	#91459	1	1	yes	characteristic
459	C₄	#91557	1	1	yes	characteristic
460	C₃	#10601320	1	1	yes	characteristic, complemented, Sylow
461	C₂	—	2	1	no	—
462	C₂	—	2	1	no	—
463	C₂	—	60	4	no	—
464	C₂	D₃×#3955	1	1	yes	characteristic
465	C₂	#11748235	1	1	yes	characteristic
466	C₂	#11748882	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₃×#685
commutator	C₂³×C₃×C₅	C₂²×C₄
Frattini	C₂²×C₄	C₂×D₃×D₅
Fitting	C₂×C₃×C₅×M₁₆	C₂²
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂²×D₆₀	C₂²
cosocle	C₂²×C₃×C₄×C₅	C₂³
hypercenter	C₂×M₁₆	D₃×D₅
hypocenter	C₃×C₅	#1800
LCS	G ▷ C₂³×C₃×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
3. C₅×#5118	C₂	semidirect
4. #11748440	C₂	semidirect
6. C₃×#64774	C₂	semidirect
7. #11745985	C₂	semidirect
35. #64774	D₃	semidirect
74. #5118	D₅	semidirect
205. C₅×Dic₃	#100	semidirect
378. C₃×C₅	#1800	semidirect
397. Dic₃	#3955	semidirect
440. C₅	#68994	semidirect
460. C₃	#10601320	semidirect

Maximal subgroups

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

subgroup	index
C₂×#91428	2
C₂×#91107	2
C₅×#5118	2
#11748440	2
C₂×#90960	2
C₃×#64774	2
#11745985	2
#10601320	3
#68994	5