Subgroups — #14304739

Order 1920.

568 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11751089	C₂	1	1	yes	maximal, characteristic
2	#11748865	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#90969	C₂	1	1	yes	maximal, characteristic
4	C₂×#90968	C₂	1	1	yes	maximal, characteristic
5	C₂×#90954	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4529	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#64749	C₂	1	1	yes	maximal, characteristic, complemented
8	#10599649	—	3	1	no	maximal, Hall
9	C₂²×D₆₀	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
11	C₂×#6714	—	2	1	no	—
12	C₂×#6714	—	2	1	no	—
13	C₂×C₄×Dic₁₅	C₂²	1	1	yes	characteristic
14	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
15	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
17	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
18	C₂×#6668	—	2	1	no	—
19	#90994	—	2	1	no	—
20	#90969	—	2	2	no	—
21	#90968	C₄	1	4	yes	complemented
22	#90954	—	2	2	no	—
23	#68857	—	5	1	no	maximal, Hall
24	C₂×#3953	—	3	1	no	—
25	C₂×#3947	—	3	1	no	—
26	#65277	—	3	1	no	—
27	#65262	—	3	1	no	—
28	C₂×#3941	—	3	1	no	—
29	C₅×#340	—	3	1	no	—
30	#64749	D₃	1	1	yes	characteristic, complemented
31	C₂³×D₁₅	—	2	1	no	—
32	C₂²×C₃×C₄×C₅	—	2	1	no	—
33	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
34	C₂²×Dic₁₅	D₄	1	1	yes	characteristic
35	C₂²×Dic₁₅	D₄	1	1	yes	characteristic
36	C₂×D₆₀	—	2	1	no	—
37	C₂×D₆₀	—	2	1	no	—
38	C₂×D₆₀	—	2	1	no	—
39	C₂×D₆₀	—	2	1	no	—
40	C₂×D₆₀	—	2	1	no	—
41	C₂×D₆₀	C₂×C₄	1	2	yes	—
42	C₂²×C₅×Dic₃	—	2	1	no	—
43	C₂²×C₃×Dic₅	—	2	1	no	—
44	C₃×C₅×C₄⋊C₄	—	2	1	no	—
45	C₃×C₅×C₄⋊C₄	—	2	1	no	—
46	#6714	—	4	2	no	—
47	#6714	—	4	2	no	—
48	C₄×Dic₁₅	—	2	1	no	—
49	C₄×Dic₁₅	—	2	1	no	—
50	C₅×C₄⋊Dic₃	—	2	1	no	—
51	C₅×C₄⋊Dic₃	—	2	1	no	—
52	C₂×C₅×C₃⋊C₈	—	2	1	no	—
53	C₂×C₅×C₃⋊C₈	—	2	1	no	—
54	C₂×C₅×C₃⋊C₈	C₂×C₄	1	2	yes	—
55	C₃×C₄⋊Dic₅	—	2	1	no	—
56	C₃×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
57	C₂×C₃×#168	—	2	1	no	—
58	C₂×C₃×#168	—	2	1	no	—
59	C₂×C₃×#168	D₄	1	2	yes	—
60	#6668	—	4	2	no	—
61	C₂×#821	—	5	1	no	—
62	C₂×#815	—	5	1	no	—
63	#4988	—	5	1	no	—
64	#4984	—	5	1	no	—
65	C₂×#809	—	5	1	no	—
66	C₃×#340	—	5	1	no	—
67	#4529	D₅	1	1	yes	characteristic, complemented
68	C₂²×D₂₀	—	3	1	no	—
69	C₂²×C₅×C₈	—	3	1	no	—
70	C₂×C₅×C₄⋊C₄	—	3	1	no	—
71	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
72	C₂×#685	—	6	1	no	—
73	C₂×#685	—	6	1	no	—
74	C₂×C₄⋊Dic₅	C₂×D₃	1	1	yes	characteristic
75	C₂×#683	—	6	1	no	—
76	C₂×C₄×Dic₅	—	3	1	no	—
77	C₂²×#168	C₂×D₃	1	1	yes	characteristic
78	#3963	—	6	1	no	—
79	#3953	—	3	4	no	—
80	#3947	—	6	2	no	—
81	#3941	—	6	2	no	—
82	#1936	—	15	1	no	Sylow
83	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
84	C₂²×D₁₅	—	2	2	no	—
85	C₂²×D₁₅	—	4	1	no	—
86	C₂²×D₁₅	—	4	1	no	—
87	C₂²×D₁₅	—	4	1	no	—
88	C₂²×D₁₅	—	4	1	no	—
89	C₂²×D₁₅	—	4	1	no	—
90	C₂²×D₁₅	—	4	1	no	—
91	C₂×C₃×C₄×C₅	—	4	1	no	—
92	C₂×C₃×C₄×C₅	—	4	1	no	—
93	C₂×C₃×C₄×C₅	—	4	1	no	—
94	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
95	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
96	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
97	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
99	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
100	C₂×Dic₁₅	—	2	1	no	—
101	C₂×Dic₁₅	—	2	1	no	—
102	C₂×Dic₁₅	—	2	1	no	—
103	C₂×Dic₁₅	—	2	1	no	—
104	C₂×Dic₁₅	—	2	1	no	—
105	C₂×Dic₁₅	—	2	1	no	—
106	D₆₀	—	2	2	no	—
107	D₆₀	—	2	2	no	—
108	D₆₀	—	4	1	no	—
109	D₆₀	—	4	1	no	—
110	C₂×C₅×Dic₃	—	4	1	no	—
111	C₂×C₅×Dic₃	—	4	1	no	—
112	C₂×C₅×Dic₃	—	4	1	no	—
113	C₂×C₃×Dic₅	—	2	2	no	—
114	C₂×C₃×Dic₅	—	4	1	no	—
115	C₂×C₃×Dic₅	—	4	1	no	—
116	C₃×#168	—	2	2	no	—
117	C₅×C₃⋊C₈	—	2	2	no	—
118	C₂²×D₁₂	—	5	1	no	—
119	C₂²×C₃×C₈	—	5	1	no	—
120	C₂×C₃×C₄⋊C₄	—	5	1	no	—
121	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
122	C₂×(C₂×D₃)⋊C₄	—	10	1	no	—
123	C₂×(C₂×D₃)⋊C₄	—	10	1	no	—
124	C₂×C₄⋊Dic₃	—	10	1	no	—
125	C₂×C₄⋊Dic₃	C₂×D₅	1	1	yes	characteristic
126	C₂×C₄×Dic₃	—	5	1	no	—
127	C₂²×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
128	C₃⋊#95	—	10	1	no	—
129	#821	—	10	2	no	—
130	#815	—	10	2	no	—
131	#809	—	5	4	no	—
132	C₂³×D₅	—	6	1	no	—
133	C₂²×C₄×C₅	—	2	1	no	—
134	C₂²×C₄×C₅	—	6	1	no	—
135	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
136	C₂²×Dic₅	—	2	1	no	—
137	C₂²×Dic₅	—	3	1	no	—
138	C₂²×Dic₅	—	3	1	no	—
139	C₂×D₂₀	—	3	2	no	—
140	C₂×D₂₀	—	6	1	no	—
141	C₂×D₂₀	—	6	1	no	—
142	C₂×D₂₀	—	6	1	no	—
143	C₂×D₂₀	—	6	1	no	—
144	C₂×D₂₀	—	6	1	no	—
145	C₂×C₅×C₈	—	3	2	no	—
146	C₂×C₅×C₈	—	6	1	no	—
147	C₂×C₅×C₈	—	6	1	no	—
148	C₅×C₄⋊C₄	—	2	1	no	—
149	C₅×C₄⋊C₄	—	2	1	no	—
150	C₅×C₄⋊C₄	—	6	1	no	—
151	C₅×C₄⋊C₄	—	6	1	no	—
152	#685	—	12	2	no	—
153	#685	—	12	2	no	—
154	C₄⋊Dic₅	—	2	1	no	—
155	C₄⋊Dic₅	C₄×D₃	1	2	yes	—
156	#683	—	12	2	no	—
157	C₄×Dic₅	—	6	1	no	—
158	C₄×Dic₅	—	6	1	no	—
159	C₂×#168	—	2	1	no	—
160	C₂×#168	—	2	1	no	—
161	C₂×#168	D₁₂	1	2	yes	—
162	C₂×#102	—	15	1	no	—
163	C₂×#102	—	15	1	no	—
164	C₂×#97	—	15	1	no	—
165	#390	—	15	1	no	—
166	#389	—	15	1	no	—
167	#340	—	3	1	no	—
168	#340	—	5	1	no	—
169	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
170	C₂²×C₃×C₅	#121	1	1	yes	characteristic
171	C₂²×C₃×C₅	#124	1	1	yes	characteristic
172	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
173	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
174	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
175	C₂²×C₃×C₅	#137	1	1	yes	characteristic
176	C₂×D₁₅	—	4	2	no	—
177	C₂×D₁₅	—	4	2	no	—
178	C₂×D₁₅	—	4	2	no	—
179	C₂×D₁₅	—	8	1	no	—
180	C₂×D₁₅	—	8	1	no	—
181	C₂×D₁₅	—	8	1	no	—
182	C₂×D₁₅	—	8	1	no	—
183	C₃×C₄×C₅	—	8	1	no	—
184	C₃×C₄×C₅	#117	1	1	yes	characteristic
185	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
186	C₃×C₄×C₅	#123	1	1	yes	characteristic
187	C₃×C₄×C₅	#126	1	1	yes	characteristic
188	Dic₁₅	—	4	1	no	—
189	Dic₁₅	—	4	1	no	—
190	C₃×Dic₅	—	4	2	no	—
191	C₅×Dic₃	—	8	1	no	—
192	C₂³×D₃	—	10	1	no	—
193	C₂²×C₃×C₄	—	2	1	no	—
194	C₂²×C₃×C₄	—	10	1	no	—
195	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
196	C₂²×Dic₃	—	2	1	no	—
197	C₂²×Dic₃	—	5	1	no	—
198	C₂²×Dic₃	—	5	1	no	—
199	C₂×D₁₂	—	5	2	no	—
200	C₂×D₁₂	—	10	1	no	—
201	C₂×D₁₂	—	10	1	no	—
202	C₂×D₁₂	—	10	1	no	—
203	C₂×D₁₂	—	10	1	no	—
204	C₂×D₁₂	—	10	1	no	—
205	C₂×C₃×C₈	—	5	2	no	—
206	C₂×C₃×C₈	—	10	1	no	—
207	C₂×C₃×C₈	—	10	1	no	—
208	C₃×C₄⋊C₄	—	2	1	no	—
209	C₃×C₄⋊C₄	—	2	1	no	—
210	C₃×C₄⋊C₄	—	5	2	no	—
211	C₃×C₄⋊C₄	—	10	1	no	—
212	(C₂×D₃)⋊C₄	—	20	2	no	—
213	(C₂×D₃)⋊C₄	—	20	2	no	—
214	C₄⋊Dic₃	—	2	1	no	—
215	C₄⋊Dic₃	—	2	1	no	—
216	C₄⋊Dic₃	—	20	2	no	—
217	C₄×Dic₃	—	10	1	no	—
218	C₄×Dic₃	—	10	1	no	—
219	C₂×C₃⋊C₈	—	2	1	no	—
220	C₂×C₃⋊C₈	—	2	1	no	—
221	C₂×C₃⋊C₈	C₄×D₅	1	2	yes	—
222	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
223	C₂²×D₅	—	6	2	no	—
224	C₂²×D₅	—	12	1	no	—
225	C₂²×D₅	—	12	1	no	—
226	C₂²×D₅	—	12	1	no	—
227	C₂²×D₅	—	12	1	no	—
228	C₂²×D₅	—	12	1	no	—
229	C₂²×D₅	—	12	1	no	—
230	C₂×C₄×C₅	—	4	1	no	—
231	C₂×C₄×C₅	—	4	1	no	—
232	C₂×C₄×C₅	—	4	1	no	—
233	C₂×C₄×C₅	—	12	1	no	—
234	C₂×C₄×C₅	—	12	1	no	—
235	C₂×C₄×C₅	—	12	1	no	—
236	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
237	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
238	C₂×C₄×C₅	#235	1	1	yes	characteristic
239	C₂×C₄×C₅	#237	1	1	yes	characteristic
240	C₂×C₄×C₅	#237	1	1	yes	characteristic
241	C₂×C₄×C₅	#239	1	1	yes	characteristic
242	C₂×Dic₅	—	2	2	no	—
243	C₂×Dic₅	—	4	1	no	—
244	C₂×Dic₅	—	4	1	no	—
245	C₂×Dic₅	—	6	1	no	—
246	C₂×Dic₅	—	6	1	no	—
247	C₂×Dic₅	—	6	1	no	—
248	C₂×Dic₅	—	6	1	no	—
249	C₂×Dic₅	—	6	1	no	—
250	C₂×Dic₅	—	6	1	no	—
251	D₂₀	—	6	2	no	—
252	D₂₀	—	6	2	no	—
253	D₂₀	—	12	1	no	—
254	D₂₀	—	12	1	no	—
255	C₅×C₈	—	6	2	no	—
256	#168	—	2	2	no	—
257	C₂²×D₄	—	15	1	no	—
258	C₂²×C₈	—	3	1	no	—
259	C₂²×C₈	—	5	1	no	—
260	C₂×C₄⋊C₄	—	3	1	no	—
261	C₂×C₄⋊C₄	—	5	1	no	—
262	C₂×C₄⋊C₄	—	30	1	no	—
263	C₂×C₄⋊C₄	D₃×D₅	1	1	yes	characteristic
264	C₂×C₂²⋊C₄	—	30	1	no	—
265	C₂×C₂²⋊C₄	—	30	1	no	—
266	C₂×C₄²	—	15	1	no	—
267	#102	—	15	4	no	—
268	#102	—	30	2	no	—
269	#97	—	30	2	no	—
270	#95	—	30	1	no	—
271	C₂×C₃×C₅	#388	1	1	yes	characteristic
272	C₂×C₃×C₅	#440	1	1	yes	characteristic
273	C₂×C₃×C₅	#442	1	1	yes	characteristic
274	C₂×C₃×C₅	#468	1	1	yes	characteristic
275	C₂×C₃×C₅	#469	1	1	yes	characteristic
276	C₂×C₃×C₅	#489	1	1	yes	characteristic
277	C₂×C₃×C₅	#490	1	1	yes	characteristic
278	D₁₅	—	8	2	no	—
279	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
280	C₂²×D₃	—	10	2	no	—
281	C₂²×D₃	—	20	1	no	—
282	C₂²×D₃	—	20	1	no	—
283	C₂²×D₃	—	20	1	no	—
284	C₂²×D₃	—	20	1	no	—
285	C₂²×D₃	—	20	1	no	—
286	C₂²×D₃	—	20	1	no	—
287	C₂×C₃×C₄	—	4	1	no	—
288	C₂×C₃×C₄	—	4	1	no	—
289	C₂×C₃×C₄	—	4	1	no	—
290	C₂×C₃×C₄	—	10	2	no	—
291	C₂×C₃×C₄	—	20	1	no	—
292	C₂×C₃×C₄	—	20	1	no	—
293	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
294	C₂×C₃×C₄	#709	1	1	yes	characteristic
295	C₂×C₃×C₄	#709	1	1	yes	characteristic
296	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
297	C₂×C₃×C₄	#711	1	1	yes	characteristic
298	C₂×C₃×C₄	#713	1	1	yes	characteristic
299	C₂×Dic₃	—	4	1	no	—
300	C₂×Dic₃	—	4	1	no	—
301	C₂×Dic₃	—	4	1	no	—
302	C₂×Dic₃	—	10	1	no	—
303	C₂×Dic₃	—	10	1	no	—
304	C₂×Dic₃	—	10	1	no	—
305	C₂×Dic₃	—	10	1	no	—
306	C₂×Dic₃	—	10	1	no	—
307	C₂×Dic₃	—	10	1	no	—
308	D₁₂	—	10	2	no	—
309	D₁₂	—	10	2	no	—
310	D₁₂	—	20	1	no	—
311	D₁₂	—	20	1	no	—
312	C₃×C₈	—	10	2	no	—
313	C₃⋊C₈	—	2	2	no	—
314	C₂²×C₅	#67⋊C₄	1	1	yes	characteristic
315	C₂²×C₅	#885	1	1	yes	characteristic
316	C₂²×C₅	#895	1	1	yes	characteristic
317	C₂²×C₅	#911	1	1	yes	characteristic
318	C₂²×C₅	#914	1	1	yes	characteristic
319	C₂²×C₅	#914	1	1	yes	characteristic
320	C₂²×C₅	#918	1	1	yes	characteristic
321	C₂×D₅	—	12	2	no	—
322	C₂×D₅	—	12	2	no	—
323	C₂×D₅	—	12	2	no	—
324	C₂×D₅	—	24	1	no	—
325	C₂×D₅	—	24	1	no	—
326	C₂×D₅	—	24	1	no	—
327	C₂×D₅	—	24	1	no	—
328	C₄×C₅	—	8	1	no	—
329	C₄×C₅	—	24	1	no	—
330	C₄×C₅	C₄×D₁₂	1	1	yes	characteristic
331	C₄×C₅	#886	1	1	yes	characteristic
332	C₄×C₅	#892	1	1	yes	characteristic
333	C₄×C₅	#898	1	1	yes	characteristic
334	Dic₅	—	4	2	no	—
335	Dic₅	—	12	1	no	—
336	Dic₅	—	12	1	no	—
337	C₂⁴	—	30	1	no	—
338	C₂×D₄	—	15	2	no	—
339	C₂×D₄	—	30	1	no	—
340	C₂×D₄	—	30	1	no	—
341	C₂×D₄	—	30	1	no	—
342	C₂×D₄	—	30	1	no	—
343	C₂×D₄	—	30	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	6	1	no	—
346	C₂²×C₄	—	10	1	no	—
347	C₂²×C₄	—	15	1	no	—
348	C₂²×C₄	—	15	1	no	—
349	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
350	C₂×C₈	—	3	2	no	—
351	C₂×C₈	—	5	2	no	—
352	C₂×C₈	—	6	1	no	—
353	C₂×C₈	—	6	1	no	—
354	C₂×C₈	—	10	1	no	—
355	C₂×C₈	—	10	1	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	5	2	no	—
359	C₄⋊C₄	—	6	1	no	—
360	C₄⋊C₄	—	6	1	no	—
361	C₄⋊C₄	—	10	1	no	—
362	C₄⋊C₄	—	60	2	no	—
363	C₂²⋊C₄	—	60	2	no	—
364	C₂²⋊C₄	—	60	2	no	—
365	C₄²	—	30	1	no	—
366	C₄²	—	30	1	no	—
367	C₃×C₅	#1936	1	1	yes	characteristic, complemented, Hall
368	C₂²×C₃	#4030	1	1	yes	characteristic
369	C₂²×C₃	#4031	1	1	yes	characteristic
370	C₂²×C₃	#4039	1	1	yes	characteristic
371	C₂²×C₃	#4057	1	1	yes	characteristic
372	C₂²×C₃	#4060	1	1	yes	characteristic
373	C₂²×C₃	#4060	1	1	yes	characteristic
374	C₂²×C₃	#4064	1	1	yes	characteristic
375	C₂×D₃	—	20	2	no	—
376	C₂×D₃	—	20	2	no	—
377	C₂×D₃	—	20	2	no	—
378	C₂×D₃	—	40	1	no	—
379	C₂×D₃	—	40	1	no	—
380	C₂×D₃	—	40	1	no	—
381	C₂×D₃	—	40	1	no	—
382	C₃×C₄	—	8	1	no	—
383	C₃×C₄	—	20	2	no	—
384	C₃×C₄	#4018	1	1	yes	characteristic
385	C₃×C₄	#4027	1	1	yes	characteristic
386	C₃×C₄	#4040	1	1	yes	characteristic
387	C₃×C₄	#4044	1	1	yes	characteristic
388	Dic₃	—	8	1	no	—
389	Dic₃	—	20	1	no	—
390	Dic₃	—	20	1	no	—
391	C₂×C₅	#4670	1	1	yes	characteristic
392	C₂×C₅	#4764	1	1	yes	characteristic
393	C₂×C₅	#4785	1	1	yes	characteristic
394	C₂×C₅	#4794	1	1	yes	characteristic
395	C₂×C₅	#4817	1	1	yes	characteristic
396	C₂×C₅	#4865	1	1	yes	characteristic
397	C₂×C₅	#4886	1	1	yes	characteristic
398	D₅	—	24	2	no	—
399	C₂³	—	30	2	no	—
400	C₂³	—	60	1	no	—
401	C₂³	—	60	1	no	—
402	C₂³	—	60	1	no	—
403	C₂³	—	60	1	no	—
404	C₂³	—	60	1	no	—
405	C₂³	—	60	1	no	—
406	C₂³	#6790	1	1	yes	characteristic
407	D₄	—	30	2	no	—
408	D₄	—	30	2	no	—
409	D₄	—	60	1	no	—
410	D₄	—	60	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	10	2	no	—
415	C₂×C₄	—	12	1	no	—
416	C₂×C₄	—	12	1	no	—
417	C₂×C₄	—	12	1	no	—
418	C₂×C₄	—	20	1	no	—
419	C₂×C₄	—	20	1	no	—
420	C₂×C₄	—	30	1	no	—
421	C₂×C₄	—	30	1	no	—
422	C₂×C₄	—	30	1	no	—
423	C₂×C₄	—	30	1	no	—
424	C₂×C₄	—	30	1	no	—
425	C₂×C₄	—	30	1	no	—
426	C₂×C₄	#6766	1	1	yes	characteristic
427	C₂×C₄	#6769	1	1	yes	characteristic
428	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
429	C₂×C₄	D₅×D₁₂	1	1	yes	characteristic
430	C₂×C₄	#6779	1	1	yes	characteristic
431	C₂×C₄	#6782	1	1	yes	characteristic
432	C₈	—	6	2	no	—
433	C₈	—	10	2	no	—
434	C₂×C₃	#64958	1	1	yes	characteristic
435	C₂×C₃	#65053	1	1	yes	characteristic
436	C₂×C₃	#65071	1	1	yes	characteristic
437	C₂×C₃	#65084	1	1	yes	characteristic
438	C₂×C₃	#65101	1	1	yes	characteristic
439	C₂×C₃	#65158	1	1	yes	characteristic
440	C₂×C₃	#65178	1	1	yes	characteristic
441	D₃	—	40	2	no	—
442	C₅	#68857	1	1	yes	characteristic, complemented, Sylow
443	C₂²	—	60	2	no	—
444	C₂²	—	60	2	no	—
445	C₂²	—	60	2	no	—
446	C₂²	—	120	1	no	—
447	C₂²	—	120	1	no	—
448	C₂²	—	120	1	no	—
449	C₂²	—	120	1	no	—
450	C₂²	#91396	1	1	yes	characteristic
451	C₂²	#91420	1	1	yes	characteristic
452	C₂²	#91498	1	1	yes	characteristic
453	C₂²	#91500	1	1	yes	characteristic
454	C₂²	#91506	1	1	yes	characteristic
455	C₂²	#91512	1	1	yes	characteristic
456	C₂²	#91526	1	1	yes	characteristic
457	C₄	—	8	1	no	—
458	C₄	—	20	2	no	—
459	C₄	—	24	1	no	—
460	C₄	—	60	1	no	—
461	C₄	—	60	1	no	—
462	C₄	#91345	1	1	yes	characteristic
463	C₄	#91403	1	1	yes	characteristic
464	C₄	#91405	1	1	yes	characteristic
465	C₄	#91413	1	1	yes	characteristic
466	C₃	#10599649	1	1	yes	characteristic, complemented, Sylow
467	C₂	—	120	2	no	—
468	C₂	#11747229	1	1	yes	characteristic
469	C₂	#11747273	1	1	yes	characteristic
470	C₂	#11747317	1	1	yes	characteristic
471	C₂	#11747346	1	1	yes	characteristic
472	C₂	#11748671	1	1	yes	characteristic
473	C₂	#11749090	1	1	yes	characteristic
474	C₂	#11749363	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#6790
commutator	C₂×C₃×C₄×C₅	C₂²×C₄
Frattini	C₂²×C₄	C₂×D₃×D₅
Fitting	C₂×C₃×C₅×C₄⋊C₄	C₂²
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×D₆₀	C₂²
cosocle	C₂²×C₃×C₄×C₅	C₂³
hypercenter	C₂×C₄⋊C₄	D₃×D₅
hypocenter	C₃×C₅	#1936
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
2. #11748865	C₂	semidirect
5. C₂×#90954	C₂	semidirect
6. C₅×#4529	C₂	semidirect
7. C₃×#64749	C₂	semidirect
21. #90968	C₄	semidirect
30. #64749	D₃	semidirect
67. #4529	D₅	semidirect
367. C₃×C₅	#1936	semidirect
442. C₅	#68857	semidirect
466. C₃	#10599649	semidirect

Maximal subgroups

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

subgroup	index
#11751089	2
#11748865	2
C₂×#90969	2
C₂×#90968	2
C₂×#90954	2
C₅×#4529	2
C₃×#64749	2
#10599649	3
#68857	5