Subgroups — #14297626

Order 1920.

744 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₆₀	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#384	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#91093	C₂	1	2	yes	maximal
4	C₂×C₄⋊(C₃⋊#168)	C₂	1	1	yes	maximal, characteristic, complemented
5	#11746350	C₂	1	2	yes	maximal, complemented
6	#10600377	—	3	1	no	maximal, Hall
7	C₂²×D₆₀	C₂²	1	1	yes	characteristic
8	C₂²×C₄×D₁₅	—	2	1	no	—
9	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
10	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
11	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
12	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
13	C₂×#6714	—	2	1	no	—
14	C₂×C₄⋊Dic₁₅	C₂²	1	1	yes	characteristic
15	C₂²×C₃⋊#168	C₂²	1	2	yes	—
16	C₄×D₆₀	—	2	2	no	—
17	C₄×D₆₀	C₄	1	4	yes	complemented
18	#91093	—	2	4	no	—
19	C₄⋊(C₃⋊#168)	—	2	2	no	—
20	#69584	—	5	1	no	maximal, Hall
21	C₂×C₄×D₂₀	—	3	1	no	—
22	C₅×#384	D₃	1	1	yes	characteristic, complemented
23	C₂×#3941	—	3	2	no	—
24	C₂×C₄⋊#168	—	3	1	no	—
25	#64749	—	3	2	no	—
26	C₂³×D₁₅	—	2	1	no	—
27	C₂²×C₃×C₄×C₅	—	2	2	no	—
28	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
29	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
30	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
31	C₂²×Dic₁₅	—	2	1	no	—
32	C₂×D₆₀	—	2	1	no	—
33	C₂×D₆₀	—	2	1	no	—
34	C₂×D₆₀	—	2	1	no	—
35	C₂×D₆₀	C₂×C₄	1	2	yes	—
36	C₂×D₆₀	D₄	1	2	yes	—
37	C₂×D₆₀	Q₈	1	2	yes	—
38	C₂×C₄×D₁₅	—	2	4	no	—
39	C₂×C₄×D₁₅	—	4	2	no	—
40	C₂×C₄×D₁₅	—	4	2	no	—
41	C₃×C₅×C₄⋊C₄	—	2	2	no	—
42	C₃×C₅×C₄⋊C₄	—	2	2	no	—
43	C₃×C₅×C₄⋊C₄	—	4	2	no	—
44	C₃×C₅×C₄⋊C₄	—	4	2	no	—
45	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
46	C₃×C₄²×C₅	D₄	1	2	yes	—
47	#6714	—	2	4	no	—
48	C₄⋊Dic₁₅	—	2	1	no	—
49	C₄⋊Dic₁₅	C₂×C₄	1	2	yes	—
50	C₂×C₃⋊#168	—	2	2	no	—
51	C₂×C₃⋊#168	—	2	2	no	—
52	C₂×C₃⋊#168	—	2	2	no	—
53	C₂×C₄×D₁₂	—	5	1	no	—
54	C₃×#384	D₅	1	1	yes	characteristic, complemented
55	C₂×#809	—	5	2	no	—
56	C₂×C₄⋊(C₃⋊C₈)	—	5	1	no	—
57	#4529	—	5	2	no	—
58	C₂²×D₂₀	—	3	1	no	—
59	C₂²×C₄×D₅	—	6	1	no	—
60	C₂×C₅×C₄⋊C₄	—	2	1	no	—
61	C₂×C₅×C₄⋊C₄	—	2	1	no	—
62	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	—
63	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
64	C₂×#685	—	6	1	no	—
65	C₂×C₄⋊Dic₅	—	3	1	no	—
66	C₂²×#168	—	3	2	no	—
67	C₄×D₂₀	—	3	4	no	—
68	C₄×D₂₀	—	6	2	no	—
69	#3941	—	6	4	no	—
70	C₄⋊#168	—	6	2	no	—
71	#1802	—	15	1	no	Sylow
72	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
73	C₂²×D₁₅	—	2	2	no	—
74	C₂²×D₁₅	—	2	2	no	—
75	C₂²×D₁₅	—	2	2	no	—
76	C₂²×D₁₅	—	4	1	no	—
77	C₂²×D₁₅	—	4	1	no	—
78	C₂²×D₁₅	—	4	1	no	—
79	C₂²×D₁₅	—	4	1	no	—
80	C₂×C₃×C₄×C₅	—	2	1	no	—
81	C₂×C₃×C₄×C₅	—	2	1	no	—
82	C₂×C₃×C₄×C₅	—	4	2	no	—
83	C₂×C₃×C₄×C₅	—	4	2	no	—
84	C₂×C₃×C₄×C₅	—	4	2	no	—
85	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
86	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
87	C₂×C₃×C₄×C₅	D₈	1	2	yes	—
88	C₂×C₃×C₄×C₅	SD₁₆	1	2	yes	—
89	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
90	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
91	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
92	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
93	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
94	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
95	C₂×Dic₁₅	—	2	2	no	—
96	C₂×Dic₁₅	—	4	1	no	—
97	C₂×Dic₁₅	—	4	1	no	—
98	D₆₀	—	2	2	no	—
99	D₆₀	—	2	2	no	—
100	D₆₀	—	2	2	no	—
101	D₆₀	C₄⋊C₄	1	4	yes	complemented
102	C₄×D₁₅	—	4	8	no	—
103	C₃⋊#168	—	4	2	no	—
104	C₂²×D₁₂	—	5	1	no	—
105	C₂²×C₄×D₃	—	10	1	no	—
106	C₂×C₃×C₄⋊C₄	—	2	1	no	—
107	C₂×C₃×C₄⋊C₄	—	2	1	no	—
108	C₂×C₃×C₄⋊C₄	C₂×D₅	1	2	yes	—
109	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
110	C₂×(C₂×D₃)⋊C₄	—	10	1	no	—
111	C₂×C₄⋊Dic₃	—	5	1	no	—
112	C₂²×C₃⋊C₈	—	5	2	no	—
113	C₄×D₁₂	—	5	4	no	—
114	C₄×D₁₂	—	10	2	no	—
115	#809	—	10	4	no	—
116	C₄⋊(C₃⋊C₈)	—	10	2	no	—
117	C₂³×D₅	—	6	1	no	—
118	C₂²×C₄×C₅	—	2	2	no	—
119	C₂²×C₄×C₅	#67	1	1	yes	characteristic
120	C₂²×C₄×C₅	#67	1	1	yes	characteristic
121	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
122	C₂²×Dic₅	—	6	1	no	—
123	C₂×D₂₀	—	3	2	no	—
124	C₂×D₂₀	—	3	2	no	—
125	C₂×D₂₀	—	3	2	no	—
126	C₂×D₂₀	—	6	1	no	—
127	C₂×D₂₀	—	6	1	no	—
128	C₂×D₂₀	—	6	1	no	—
129	C₂×C₄×D₅	—	6	4	no	—
130	C₂×C₄×D₅	—	12	2	no	—
131	C₂×C₄×D₅	—	12	2	no	—
132	C₅×C₄⋊C₄	—	2	2	no	—
133	C₅×C₄⋊C₄	—	2	2	no	—
134	C₅×C₄⋊C₄	—	4	2	no	—
135	C₅×C₄⋊C₄	—	4	2	no	—
136	C₄²×C₅	C₄×D₃	1	2	yes	—
137	C₄²×C₅	D₁₂	1	2	yes	—
138	#685	—	6	4	no	—
139	C₄⋊Dic₅	—	3	2	no	—
140	C₄⋊Dic₅	—	6	1	no	—
141	C₂×#168	—	6	2	no	—
142	C₂×#168	—	6	2	no	—
143	C₂×#168	—	6	2	no	—
144	C₂×C₄×D₄	—	15	1	no	—
145	C₂×C₄⋊C₈	—	15	1	no	—
146	C₂×#102	—	15	2	no	—
147	#384	D₁₅	1	1	yes	characteristic, complemented
148	#340	—	15	2	no	—
149	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
150	C₂²×C₃×C₅	#121	1	1	yes	characteristic
151	C₂²×C₃×C₅	C₂²⋊Q₈	1	1	yes	characteristic
152	C₂²×C₃×C₅	C₂×D₈	1	1	yes	characteristic
153	C₂²×C₃×C₅	C₂×SD₁₆	1	1	yes	characteristic
154	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
155	C₂²×C₃×C₅	#137	1	1	yes	characteristic
156	C₂×D₁₅	—	2	4	no	—
157	C₂×D₁₅	—	4	2	no	—
158	C₂×D₁₅	—	4	2	no	—
159	C₂×D₁₅	—	4	2	no	—
160	C₂×D₁₅	—	4	2	no	—
161	C₂×D₁₅	—	4	2	no	—
162	C₂×D₁₅	—	4	2	no	—
163	C₃×C₄×C₅	—	2	2	no	—
164	C₃×C₄×C₅	—	8	2	no	—
165	C₃×C₄×C₅	#102	1	4	yes	complemented
166	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₃×C₄×C₅	#117	1	1	yes	characteristic
168	C₃×C₄×C₅	#121	1	1	yes	characteristic
169	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
170	Dic₁₅	—	4	2	no	—
171	C₂³×D₃	—	10	1	no	—
172	C₂²×C₃×C₄	—	2	2	no	—
173	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
174	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
175	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
176	C₂²×Dic₃	—	10	1	no	—
177	C₂×D₁₂	—	5	2	no	—
178	C₂×D₁₂	—	5	2	no	—
179	C₂×D₁₂	—	5	2	no	—
180	C₂×D₁₂	—	10	1	no	—
181	C₂×D₁₂	—	10	1	no	—
182	C₂×D₁₂	—	10	1	no	—
183	C₂×C₄×D₃	—	10	4	no	—
184	C₂×C₄×D₃	—	20	2	no	—
185	C₂×C₄×D₃	—	20	2	no	—
186	C₃×C₄⋊C₄	—	2	2	no	—
187	C₃×C₄⋊C₄	—	2	2	no	—
188	C₃×C₄⋊C₄	—	4	2	no	—
189	C₃×C₄⋊C₄	—	4	2	no	—
190	C₃×C₄²	C₄×D₅	1	2	yes	—
191	C₃×C₄²	D₂₀	1	2	yes	—
192	(C₂×D₃)⋊C₄	—	10	4	no	—
193	C₄⋊Dic₃	—	5	2	no	—
194	C₄⋊Dic₃	—	10	1	no	—
195	C₂×C₃⋊C₈	—	10	2	no	—
196	C₂×C₃⋊C₈	—	10	2	no	—
197	C₂×C₃⋊C₈	—	10	2	no	—
198	C₂³×C₅	C₂×#67	1	1	yes	characteristic
199	C₂²×D₅	—	6	2	no	—
200	C₂²×D₅	—	6	2	no	—
201	C₂²×D₅	—	6	2	no	—
202	C₂²×D₅	—	12	1	no	—
203	C₂²×D₅	—	12	1	no	—
204	C₂²×D₅	—	12	1	no	—
205	C₂²×D₅	—	12	1	no	—
206	C₂×C₄×C₅	—	2	1	no	—
207	C₂×C₄×C₅	—	2	1	no	—
208	C₂×C₄×C₅	—	4	2	no	—
209	C₂×C₄×C₅	—	4	2	no	—
210	C₂×C₄×C₅	—	4	2	no	—
211	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	2	yes	—
212	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	2	yes	—
213	C₂×C₄×C₅	#213	1	2	yes	—
214	C₂×C₄×C₅	#215	1	2	yes	—
215	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
216	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
217	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
218	C₂×C₄×C₅	#237	1	1	yes	characteristic
219	C₂×C₄×C₅	D₃×Q₈	1	1	yes	characteristic
220	C₂×C₄×C₅	#239	1	1	yes	characteristic
221	C₂×Dic₅	—	6	2	no	—
222	C₂×Dic₅	—	12	1	no	—
223	C₂×Dic₅	—	12	1	no	—
224	D₂₀	—	3	4	no	—
225	D₂₀	—	6	2	no	—
226	D₂₀	—	6	2	no	—
227	D₂₀	—	6	2	no	—
228	C₄×D₅	—	12	8	no	—
229	#168	—	12	2	no	—
230	C₂²×D₄	—	15	1	no	—
231	C₂³×C₄	—	30	1	no	—
232	C₂²×C₈	—	15	2	no	—
233	C₄×D₄	—	15	4	no	—
234	C₄×D₄	—	30	2	no	—
235	C₂×C₄⋊C₄	—	2	1	no	—
236	C₂×C₄⋊C₄	—	2	1	no	—
237	C₂×C₄⋊C₄	—	15	1	no	—
238	C₂×C₄⋊C₄	C₂×D₁₅	1	2	yes	—
239	C₂×C₂²⋊C₄	—	30	1	no	—
240	C₂×C₄²	C₂×D₁₅	1	1	yes	characteristic
241	C₄⋊C₈	—	30	2	no	—
242	#102	—	30	4	no	—
243	C₂×C₃×C₅	#380	1	1	yes	characteristic
244	C₂×C₃×C₅	C₂×#102	1	1	yes	characteristic
245	C₂×C₃×C₅	#417	1	1	yes	characteristic
246	C₂×C₃×C₅	#459	1	1	yes	characteristic
247	C₂×C₃×C₅	#461	1	1	yes	characteristic
248	C₂×C₃×C₅	#474	1	1	yes	characteristic
249	C₂×C₃×C₅	#476	1	1	yes	characteristic
250	D₁₅	—	4	4	no	—
251	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
252	C₂²×D₃	—	10	2	no	—
253	C₂²×D₃	—	10	2	no	—
254	C₂²×D₃	—	10	2	no	—
255	C₂²×D₃	—	20	1	no	—
256	C₂²×D₃	—	20	1	no	—
257	C₂²×D₃	—	20	1	no	—
258	C₂²×D₃	—	20	1	no	—
259	C₂×C₃×C₄	—	2	1	no	—
260	C₂×C₃×C₄	—	2	1	no	—
261	C₂×C₃×C₄	—	4	2	no	—
262	C₂×C₃×C₄	—	4	2	no	—
263	C₂×C₃×C₄	—	4	2	no	—
264	C₂×C₃×C₄	#685	1	2	yes	—
265	C₂×C₃×C₄	#685	1	2	yes	—
266	C₂×C₃×C₄	#686	1	2	yes	—
267	C₂×C₃×C₄	#688	1	2	yes	—
268	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
269	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
270	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
271	C₂×C₃×C₄	#711	1	1	yes	characteristic
272	C₂×C₃×C₄	Q₈×D₅	1	1	yes	characteristic
273	C₂×C₃×C₄	#713	1	1	yes	characteristic
274	C₂×Dic₃	—	10	2	no	—
275	C₂×Dic₃	—	20	1	no	—
276	C₂×Dic₃	—	20	1	no	—
277	D₁₂	—	5	4	no	—
278	D₁₂	—	10	2	no	—
279	D₁₂	—	10	2	no	—
280	D₁₂	—	10	2	no	—
281	C₄×D₃	—	20	8	no	—
282	C₃⋊C₈	—	20	2	no	—
283	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
284	C₂²×C₅	C₂×#213	1	1	yes	characteristic
285	C₂²×C₅	#932	1	1	yes	characteristic
286	C₂²×C₅	#938	1	1	yes	characteristic
287	C₂²×C₅	C₂×#215	1	1	yes	characteristic
288	C₂²×C₅	#942	1	1	yes	characteristic
289	C₂²×C₅	#946	1	1	yes	characteristic
290	C₂×D₅	—	6	4	no	—
291	C₂×D₅	—	12	2	no	—
292	C₂×D₅	—	12	2	no	—
293	C₂×D₅	—	12	2	no	—
294	C₂×D₅	—	12	2	no	—
295	C₂×D₅	—	12	2	no	—
296	C₂×D₅	—	12	2	no	—
297	C₄×C₅	—	2	2	no	—
298	C₄×C₅	—	8	2	no	—
299	C₄×C₅	#809	1	4	yes	complemented
300	C₄×C₅	D₃×C₄⋊C₄	1	1	yes	characteristic
301	C₄×C₅	#892	1	1	yes	characteristic
302	C₄×C₅	#895	1	1	yes	characteristic
303	C₄×C₅	#897	1	1	yes	characteristic
304	Dic₅	—	12	2	no	—
305	C₂⁴	—	30	1	no	—
306	C₂×D₄	—	15	2	no	—
307	C₂×D₄	—	15	2	no	—
308	C₂×D₄	—	15	2	no	—
309	C₂×D₄	—	30	1	no	—
310	C₂×D₄	—	30	1	no	—
311	C₂×D₄	—	30	1	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	30	1	no	—
314	C₂²×C₄	—	30	4	no	—
315	C₂²×C₄	—	60	2	no	—
316	C₂²×C₄	—	60	2	no	—
317	C₂²×C₄	#1220	1	1	yes	characteristic
318	C₂²×C₄	#1220	1	1	yes	characteristic
319	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
320	C₂×C₈	—	30	2	no	—
321	C₂×C₈	—	30	2	no	—
322	C₂×C₈	—	30	2	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	4	2	no	—
326	C₄⋊C₄	—	4	2	no	—
327	C₄⋊C₄	—	15	2	no	—
328	C₄⋊C₄	—	30	1	no	—
329	C₂²⋊C₄	—	30	4	no	—
330	C₄²	C₄×D₁₅	1	2	yes	—
331	C₄²	D₆₀	1	2	yes	—
332	C₃×C₅	#1802	1	1	yes	characteristic, complemented, Hall
333	C₂²×C₃	C₂×#685	1	1	yes	characteristic
334	C₂²×C₃	C₂×#686	1	1	yes	characteristic
335	C₂²×C₃	#4078	1	1	yes	characteristic
336	C₂²×C₃	#4084	1	1	yes	characteristic
337	C₂²×C₃	C₂×#688	1	1	yes	characteristic
338	C₂²×C₃	#4088	1	1	yes	characteristic
339	C₂²×C₃	#4092	1	1	yes	characteristic
340	C₂×D₃	—	10	4	no	—
341	C₂×D₃	—	20	2	no	—
342	C₂×D₃	—	20	2	no	—
343	C₂×D₃	—	20	2	no	—
344	C₂×D₃	—	20	2	no	—
345	C₂×D₃	—	20	2	no	—
346	C₂×D₃	—	20	2	no	—
347	C₃×C₄	—	2	2	no	—
348	C₃×C₄	—	8	2	no	—
349	C₃×C₄	#3941	1	4	yes	complemented
350	C₃×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
351	C₃×C₄	#4038	1	1	yes	characteristic
352	C₃×C₄	#4041	1	1	yes	characteristic
353	C₃×C₄	#4043	1	1	yes	characteristic
354	Dic₃	—	20	2	no	—
355	C₂×C₅	C₂×#809	1	1	yes	characteristic
356	C₂×C₅	#4966	1	1	yes	characteristic
357	C₂×C₅	#4987	1	1	yes	characteristic
358	C₂×C₅	#5072	1	1	yes	characteristic
359	C₂×C₅	#5083	1	1	yes	characteristic
360	C₂×C₅	#5084	1	1	yes	characteristic
361	C₂×C₅	#5087	1	1	yes	characteristic
362	D₅	—	12	4	no	—
363	C₂³	—	30	2	no	—
364	C₂³	—	30	2	no	—
365	C₂³	—	30	2	no	—
366	C₂³	—	60	1	no	—
367	C₂³	—	60	1	no	—
368	C₂³	—	60	1	no	—
369	C₂³	—	60	1	no	—
370	C₂³	C₂×#1220	1	1	yes	characteristic
371	D₄	—	15	4	no	—
372	D₄	—	30	2	no	—
373	D₄	—	30	2	no	—
374	D₄	—	30	2	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	30	2	no	—
381	C₂×C₄	—	60	1	no	—
382	C₂×C₄	—	60	1	no	—
383	C₂×C₄	—	60	8	no	—
384	C₂×C₄	#6714	1	2	yes	—
385	C₂×C₄	#6714	1	2	yes	—
386	C₂×C₄	#6715	1	2	yes	—
387	C₂×C₄	#6717	1	2	yes	—
388	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
389	C₂×C₄	C₂×D₆₀	1	1	yes	characteristic
390	C₂×C₄	D₄×D₁₅	1	1	yes	characteristic
391	C₂×C₄	#6819	1	1	yes	characteristic
392	C₂×C₄	Q₈×D₁₅	1	1	yes	characteristic
393	C₂×C₄	#6821	1	1	yes	characteristic
394	C₈	—	60	2	no	—
395	C₂×C₃	C₂×#3941	1	1	yes	characteristic
396	C₂×C₃	#65255	1	1	yes	characteristic
397	C₂×C₃	#65276	1	1	yes	characteristic
398	C₂×C₃	#65361	1	1	yes	characteristic
399	C₂×C₃	#65372	1	1	yes	characteristic
400	C₂×C₃	#65373	1	1	yes	characteristic
401	C₂×C₃	#65376	1	1	yes	characteristic
402	D₃	—	20	4	no	—
403	C₅	#69584	1	1	yes	characteristic, complemented, Sylow
404	C₂²	—	30	4	no	—
405	C₂²	—	60	2	no	—
406	C₂²	—	60	2	no	—
407	C₂²	—	60	2	no	—
408	C₂²	—	60	2	no	—
409	C₂²	—	60	2	no	—
410	C₂²	—	60	2	no	—
411	C₂²	C₂×#6714	1	1	yes	characteristic
412	C₂²	C₂×#6715	1	1	yes	characteristic
413	C₂²	#91821	1	1	yes	characteristic
414	C₂²	#91827	1	1	yes	characteristic
415	C₂²	C₂×#6717	1	1	yes	characteristic
416	C₂²	#91831	1	1	yes	characteristic
417	C₂²	#91835	1	1	yes	characteristic
418	C₄	—	2	2	no	—
419	C₄	—	8	2	no	—
420	C₄	—	60	2	no	—
421	C₄	#91093	1	4	yes	complemented
422	C₄	C₄⋊C₄×D₁₅	1	1	yes	characteristic
423	C₄	#91781	1	1	yes	characteristic
424	C₄	#91784	1	1	yes	characteristic
425	C₄	#91786	1	1	yes	characteristic
426	C₃	#10600377	1	1	yes	characteristic, complemented, Sylow
427	C₂	—	60	4	no	—
428	C₂	C₂×#91093	1	1	yes	characteristic
429	C₂	#11751067	1	1	yes	characteristic
430	C₂	#11751088	1	1	yes	characteristic
431	C₂	#11751173	1	1	yes	characteristic
432	C₂	#11751184	1	1	yes	characteristic
433	C₂	#11751185	1	1	yes	characteristic
434	C₂	#11751188	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×#1220
commutator	C₂×C₃×C₄×C₅	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₅
Fitting	C₃×C₅×#384	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×D₆₀	C₂²
cosocle	C₂²×C₃×C₄×C₅	C₂³
hypercenter	#384	D₁₅
hypocenter	C₃×C₅	#1802
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #384

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#384	C₂	semidirect
4. C₂×C₄⋊(C₃⋊#168)	C₂	semidirect
5. #11746350	C₂	semidirect
17. C₄×D₆₀	C₄	semidirect
22. C₅×#384	D₃	semidirect
54. C₃×#384	D₅	semidirect
101. D₆₀	C₄⋊C₄	semidirect
147. #384	D₁₅	semidirect
165. C₃×C₄×C₅	#102	semidirect
299. C₄×C₅	#809	semidirect
332. C₃×C₅	#1802	semidirect
349. C₃×C₄	#3941	semidirect
403. C₅	#69584	semidirect
421. C₄	#91093	semidirect
426. C₃	#10600377	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×D₆₀	2
C₃×C₅×#384	2
C₂×#91093	2
C₂×C₄⋊(C₃⋊#168)	2
#11746350	2
#10600377	3
#69584	5