Subgroups — #14297647

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×C₃×C₄×D₂₀	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊(C₃⋊#168)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#4935	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#90964	C₂	1	2	yes	maximal
5	#11745979	C₂	1	2	yes	maximal, complemented
6	#10600377	—	3	1	no	maximal, Hall
7	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
8	C₂²×C₃×C₄×D₅	—	2	1	no	—
9	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
10	C₂²×C₃⋊#168	C₂²	1	2	yes	—
11	C₂×C₅×C₄⋊Dic₃	—	2	1	no	—
12	C₂×C₅×C₄⋊Dic₃	—	2	1	no	—
13	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
14	C₂×C₃×#685	—	2	1	no	—
15	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
16	C₃×C₄×D₂₀	—	2	2	no	—
17	C₃×C₄×D₂₀	C₄	1	4	yes	complemented
18	C₄⋊(C₃⋊#168)	—	2	2	no	—
19	#90964	—	2	4	no	—
20	#71604	—	5	1	no	maximal, Hall
21	C₂×C₄×D₂₀	D₃	1	1	yes	characteristic
22	C₅×#384	—	3	1	no	—
23	C₂×#3941	—	3	2	no	—
24	C₂×C₄⋊#168	—	3	1	no	—
25	#64749	—	3	2	no	—
26	C₂³×C₃×D₅	—	2	1	no	—
27	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
28	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
29	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
30	C₂²×C₅×Dic₃	—	2	2	no	—
31	C₂²×C₃×Dic₅	—	2	1	no	—
32	C₂×C₃×D₂₀	—	2	1	no	—
33	C₂×C₃×D₂₀	—	2	1	no	—
34	C₂×C₃×D₂₀	—	2	1	no	—
35	C₂×C₃×D₂₀	C₂×C₄	1	2	yes	—
36	C₂×C₃×D₂₀	D₄	1	2	yes	—
37	C₂×C₃×D₂₀	Q₈	1	2	yes	—
38	C₂×C₃×C₄×D₅	—	2	4	no	—
39	C₂×C₃×C₄×D₅	—	4	2	no	—
40	C₂×C₃×C₄×D₅	—	4	2	no	—
41	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
42	C₃×C₄²×C₅	D₄	1	2	yes	—
43	C₂×C₃⋊#168	—	2	2	no	—
44	C₂×C₃⋊#168	—	2	2	no	—
45	C₂×C₃⋊#168	—	2	2	no	—
46	C₅×C₄⋊Dic₃	—	2	2	no	—
47	C₅×C₄⋊Dic₃	—	2	2	no	—
48	C₅×C₄⋊Dic₃	—	4	2	no	—
49	C₅×C₄⋊Dic₃	—	4	2	no	—
50	C₃×#685	—	2	4	no	—
51	C₃×C₄⋊Dic₅	—	2	1	no	—
52	C₃×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
53	C₂×C₃×C₄×D₄	—	5	1	no	—
54	C₂×#832	—	5	2	no	—
55	#4935	D₅	1	1	yes	characteristic, complemented
56	C₂×C₄⋊(C₃⋊C₈)	—	5	1	no	—
57	#4529	—	5	2	no	—
58	C₂²×D₂₀	C₂×D₃	1	1	yes	characteristic
59	C₂²×C₄×D₅	—	2	1	no	—
60	C₂×C₅×C₄⋊C₄	—	3	2	no	—
61	C₂×C₅×C₄⋊C₄	—	6	1	no	—
62	C₂×C₅×C₄⋊C₄	—	6	1	no	—
63	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
64	C₂×#685	—	2	1	no	—
65	C₂×C₄⋊Dic₅	C₂×D₃	1	1	yes	characteristic
66	C₂²×#168	—	3	2	no	—
67	C₄×D₂₀	—	2	2	no	—
68	C₄×D₂₀	Dic₃	1	4	yes	complemented
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×C₃×D₅	—	2	2	no	—
74	C₂²×C₃×D₅	—	2	2	no	—
75	C₂²×C₃×D₅	—	2	2	no	—
76	C₂²×C₃×D₅	—	4	1	no	—
77	C₂²×C₃×D₅	—	4	1	no	—
78	C₂²×C₃×D₅	—	4	1	no	—
79	C₂²×C₃×D₅	—	4	1	no	—
80	C₂×C₃×C₄×C₅	—	2	1	no	—
81	C₂×C₃×C₄×C₅	—	2	1	no	—
82	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
83	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
84	C₂×C₃×C₄×C₅	D₈	1	2	yes	—
85	C₂×C₃×C₄×C₅	SD₁₆	1	2	yes	—
86	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
87	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
88	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
89	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
90	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
91	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
92	C₂×C₅×Dic₃	—	4	2	no	—
93	C₂×C₅×Dic₃	—	4	2	no	—
94	C₂×C₅×Dic₃	—	4	2	no	—
95	C₂×C₃×Dic₅	—	2	2	no	—
96	C₂×C₃×Dic₅	—	4	1	no	—
97	C₂×C₃×Dic₅	—	4	1	no	—
98	C₃×D₂₀	—	2	2	no	—
99	C₃×D₂₀	—	2	2	no	—
100	C₃×D₂₀	—	2	2	no	—
101	C₃×D₂₀	C₄⋊C₄	1	4	yes	complemented
102	C₃×C₄×D₅	—	4	8	no	—
103	C₃⋊#168	—	4	2	no	—
104	C₂²×C₃×D₄	—	5	1	no	—
105	C₂³×C₃×C₄	—	10	1	no	—
106	C₃×C₄×D₄	—	5	4	no	—
107	C₃×C₄×D₄	—	10	2	no	—
108	C₂×C₃×C₄⋊C₄	—	5	1	no	—
109	C₂×C₃×C₂²⋊C₄	—	10	1	no	—
110	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
111	C₂×C₄⋊Dic₃	—	2	1	no	—
112	C₂×C₄⋊Dic₃	—	2	1	no	—
113	C₂×C₄⋊Dic₃	C₂×D₅	1	2	yes	—
114	C₂²×C₃⋊C₈	—	5	2	no	—
115	#832	—	10	4	no	—
116	C₄⋊(C₃⋊C₈)	—	10	2	no	—
117	C₂³×D₅	—	2	1	no	—
118	C₂²×C₄×C₅	—	6	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	—	2	1	no	—
123	C₂×D₂₀	—	2	1	no	—
124	C₂×D₂₀	—	2	1	no	—
125	C₂×D₂₀	—	2	1	no	—
126	C₂×D₂₀	Dic₆	1	2	yes	—
127	C₂×D₂₀	D₁₂	1	2	yes	—
128	C₂×D₂₀	C₂×Dic₃	1	2	yes	—
129	C₂×C₄×D₅	—	2	4	no	—
130	C₂×C₄×D₅	—	4	2	no	—
131	C₂×C₄×D₅	—	4	2	no	—
132	C₅×C₄⋊C₄	—	6	2	no	—
133	C₅×C₄⋊C₄	—	6	2	no	—
134	C₅×C₄⋊C₄	—	12	2	no	—
135	C₅×C₄⋊C₄	—	12	2	no	—
136	C₄²×C₅	C₂×Dic₃	1	2	yes	—
137	C₄²×C₅	#67	1	2	yes	—
138	#685	—	2	4	no	—
139	C₄⋊Dic₅	—	2	1	no	—
140	C₄⋊Dic₅	C₂×Dic₃	1	2	yes	—
141	C₂×#168	—	6	2	no	—
142	C₂×#168	—	6	2	no	—
143	C₂×#168	—	6	2	no	—
144	C₂×C₄×D₄	—	5	1	no	—
145	C₂×C₄⋊C₈	—	15	1	no	—
146	C₂×#102	—	15	2	no	—
147	#384	—	3	1	no	—
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×C₃×D₅	—	2	4	no	—
157	C₂×C₃×D₅	—	4	2	no	—
158	C₂×C₃×D₅	—	4	2	no	—
159	C₂×C₃×D₅	—	4	2	no	—
160	C₂×C₃×D₅	—	4	2	no	—
161	C₂×C₃×D₅	—	4	2	no	—
162	C₂×C₃×D₅	—	4	2	no	—
163	C₃×C₄×C₅	—	2	2	no	—
164	C₃×C₄×C₅	#102	1	4	yes	complemented
165	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
166	C₃×C₄×C₅	#117	1	1	yes	characteristic
167	C₃×C₄×C₅	#121	1	1	yes	characteristic
168	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
169	C₃×Dic₅	—	4	2	no	—
170	C₅×Dic₃	—	8	2	no	—
171	C₂⁴×C₃	—	10	1	no	—
172	C₂×C₃×D₄	—	5	2	no	—
173	C₂×C₃×D₄	—	5	2	no	—
174	C₂×C₃×D₄	—	5	2	no	—
175	C₂×C₃×D₄	—	10	1	no	—
176	C₂×C₃×D₄	—	10	1	no	—
177	C₂×C₃×D₄	—	10	1	no	—
178	C₂²×C₃×C₄	—	10	1	no	—
179	C₂²×C₃×C₄	—	10	4	no	—
180	C₂²×C₃×C₄	—	20	2	no	—
181	C₂²×C₃×C₄	—	20	2	no	—
182	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
183	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
184	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
185	C₂²×Dic₃	—	2	2	no	—
186	C₃×C₄⋊C₄	—	5	2	no	—
187	C₃×C₄⋊C₄	—	10	1	no	—
188	C₃×C₂²⋊C₄	—	10	4	no	—
189	C₃×C₄²	C₄×D₅	1	2	yes	—
190	C₃×C₄²	D₂₀	1	2	yes	—
191	C₄⋊Dic₃	—	2	2	no	—
192	C₄⋊Dic₃	—	2	2	no	—
193	C₄⋊Dic₃	—	4	2	no	—
194	C₄⋊Dic₃	—	4	2	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	—	2	2	no	—
200	C₂²×D₅	—	2	2	no	—
201	C₂²×D₅	—	2	2	no	—
202	C₂²×D₅	—	4	1	no	—
203	C₂²×D₅	—	4	1	no	—
204	C₂²×D₅	—	4	1	no	—
205	C₂²×D₅	—	4	1	no	—
206	C₂×C₄×C₅	—	2	1	no	—
207	C₂×C₄×C₅	—	2	1	no	—
208	C₂×C₄×C₅	—	12	2	no	—
209	C₂×C₄×C₅	—	12	2	no	—
210	C₂×C₄×C₅	—	12	2	no	—
211	C₂×C₄×C₅	#213	1	2	yes	—
212	C₂×C₄×C₅	#214	1	2	yes	—
213	C₂×C₄×C₅	#217	1	2	yes	—
214	C₂×C₄×C₅	#217	1	2	yes	—
215	C₂×C₄×C₅	C₂×Dic₆	1	1	yes	characteristic
216	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
217	C₂×C₄×C₅	#235	1	1	yes	characteristic
218	C₂×C₄×C₅	#235	1	1	yes	characteristic
219	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
220	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
221	C₂×Dic₅	—	2	2	no	—
222	C₂×Dic₅	—	4	1	no	—
223	C₂×Dic₅	—	4	1	no	—
224	D₂₀	—	2	2	no	—
225	D₂₀	—	2	2	no	—
226	D₂₀	—	2	2	no	—
227	D₂₀	C₄⋊Dic₃	1	4	yes	complemented
228	C₄×D₅	—	4	8	no	—
229	#168	—	12	2	no	—
230	C₂²×D₄	—	5	1	no	—
231	C₂³×C₄	—	10	1	no	—
232	C₂²×C₈	—	15	2	no	—
233	C₄×D₄	—	5	4	no	—
234	C₄×D₄	—	10	2	no	—
235	C₂×C₄⋊C₄	—	3	2	no	—
236	C₂×C₄⋊C₄	—	5	1	no	—
237	C₂×C₄⋊C₄	—	6	1	no	—
238	C₂×C₄⋊C₄	—	6	1	no	—
239	C₂×C₂²⋊C₄	—	10	1	no	—
240	C₂×C₄²	D₃×D₅	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	C₃×D₅	—	4	4	no	—
251	C₂³×C₃	—	10	2	no	—
252	C₂³×C₃	—	10	2	no	—
253	C₂³×C₃	—	10	2	no	—
254	C₂³×C₃	—	20	1	no	—
255	C₂³×C₃	—	20	1	no	—
256	C₂³×C₃	—	20	1	no	—
257	C₂³×C₃	—	20	1	no	—
258	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
259	C₃×D₄	—	5	4	no	—
260	C₃×D₄	—	10	2	no	—
261	C₃×D₄	—	10	2	no	—
262	C₃×D₄	—	10	2	no	—
263	C₂×C₃×C₄	—	2	1	no	—
264	C₂×C₃×C₄	—	2	1	no	—
265	C₂×C₃×C₄	—	10	2	no	—
266	C₂×C₃×C₄	—	20	1	no	—
267	C₂×C₃×C₄	—	20	1	no	—
268	C₂×C₃×C₄	—	20	8	no	—
269	C₂×C₃×C₄	#685	1	2	yes	—
270	C₂×C₃×C₄	#685	1	2	yes	—
271	C₂×C₃×C₄	#686	1	2	yes	—
272	C₂×C₃×C₄	#688	1	2	yes	—
273	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
274	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
275	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
276	C₂×C₃×C₄	#711	1	1	yes	characteristic
277	C₂×C₃×C₄	Q₈×D₅	1	1	yes	characteristic
278	C₂×C₃×C₄	#713	1	1	yes	characteristic
279	C₂×Dic₃	—	4	2	no	—
280	C₂×Dic₃	—	4	2	no	—
281	C₂×Dic₃	—	4	2	no	—
282	C₃⋊C₈	—	20	2	no	—
283	C₂²×C₅	#924	1	1	yes	characteristic
284	C₂²×C₅	#930	1	1	yes	characteristic
285	C₂²×C₅	C₂×#213	1	1	yes	characteristic
286	C₂²×C₅	C₂×#214	1	1	yes	characteristic
287	C₂²×C₅	#949	1	1	yes	characteristic
288	C₂²×C₅	#951	1	1	yes	characteristic
289	C₂²×C₅	C₂×#217	1	1	yes	characteristic
290	C₂×D₅	—	2	4	no	—
291	C₂×D₅	—	4	2	no	—
292	C₂×D₅	—	4	2	no	—
293	C₂×D₅	—	4	2	no	—
294	C₂×D₅	—	4	2	no	—
295	C₂×D₅	—	4	2	no	—
296	C₂×D₅	—	4	2	no	—
297	C₄×C₅	—	2	2	no	—
298	C₄×C₅	—	24	2	no	—
299	C₄×C₅	#832	1	4	yes	complemented
300	C₄×C₅	#924	1	1	yes	characteristic
301	C₄×C₅	C₂×C₄⋊Dic₃	1	1	yes	characteristic
302	C₄×C₅	#926	1	1	yes	characteristic
303	C₄×C₅	#930	1	1	yes	characteristic
304	Dic₅	—	4	2	no	—
305	C₂⁴	—	10	1	no	—
306	C₂×D₄	—	5	2	no	—
307	C₂×D₄	—	5	2	no	—
308	C₂×D₄	—	5	2	no	—
309	C₂×D₄	—	10	1	no	—
310	C₂×D₄	—	10	1	no	—
311	C₂×D₄	—	10	1	no	—
312	C₂²×C₄	—	6	2	no	—
313	C₂²×C₄	—	10	1	no	—
314	C₂²×C₄	—	10	4	no	—
315	C₂²×C₄	—	20	2	no	—
316	C₂²×C₄	—	20	2	no	—
317	C₂²×C₄	#1201	1	1	yes	characteristic
318	C₂²×C₄	#1201	1	1	yes	characteristic
319	C₂²×C₄	C₂×D₃×D₅	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	—	5	2	no	—
324	C₄⋊C₄	—	6	2	no	—
325	C₄⋊C₄	—	6	2	no	—
326	C₄⋊C₄	—	10	1	no	—
327	C₄⋊C₄	—	12	2	no	—
328	C₄⋊C₄	—	12	2	no	—
329	C₂²⋊C₄	—	10	4	no	—
330	C₄²	D₅×Dic₃	1	2	yes	—
331	C₄²	#1202	1	2	yes	—
332	C₃×C₅	#1802	1	1	yes	characteristic, complemented, Hall
333	C₂²×C₃	—	10	4	no	—
334	C₂²×C₃	—	20	2	no	—
335	C₂²×C₃	—	20	2	no	—
336	C₂²×C₃	—	20	2	no	—
337	C₂²×C₃	—	20	2	no	—
338	C₂²×C₃	—	20	2	no	—
339	C₂²×C₃	—	20	2	no	—
340	C₂²×C₃	C₂×#685	1	1	yes	characteristic
341	C₂²×C₃	C₂×#686	1	1	yes	characteristic
342	C₂²×C₃	#4078	1	1	yes	characteristic
343	C₂²×C₃	#4084	1	1	yes	characteristic
344	C₂²×C₃	C₂×#688	1	1	yes	characteristic
345	C₂²×C₃	#4088	1	1	yes	characteristic
346	C₂²×C₃	#4092	1	1	yes	characteristic
347	C₃×C₄	—	2	2	no	—
348	C₃×C₄	—	20	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	—	8	2	no	—
355	C₂×C₅	#5007	1	1	yes	characteristic
356	C₂×C₅	#5008	1	1	yes	characteristic
357	C₂×C₅	#5015	1	1	yes	characteristic
358	C₂×C₅	#5019	1	1	yes	characteristic
359	C₂×C₅	#5212	1	1	yes	characteristic
360	C₂×C₅	C₂×#832	1	1	yes	characteristic
361	C₂×C₅	#5232	1	1	yes	characteristic
362	D₅	—	4	4	no	—
363	C₂³	—	10	2	no	—
364	C₂³	—	10	2	no	—
365	C₂³	—	10	2	no	—
366	C₂³	—	20	1	no	—
367	C₂³	—	20	1	no	—
368	C₂³	—	20	1	no	—
369	C₂³	—	20	1	no	—
370	C₂³	C₂×#1201	1	1	yes	characteristic
371	D₄	—	5	4	no	—
372	D₄	—	10	2	no	—
373	D₄	—	10	2	no	—
374	D₄	—	10	2	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	10	2	no	—
378	C₂×C₄	—	12	2	no	—
379	C₂×C₄	—	12	2	no	—
380	C₂×C₄	—	12	2	no	—
381	C₂×C₄	—	20	1	no	—
382	C₂×C₄	—	20	1	no	—
383	C₂×C₄	—	20	8	no	—
384	C₂×C₄	#6652	1	2	yes	—
385	C₂×C₄	#6655	1	2	yes	—
386	C₂×C₄	#6665	1	2	yes	—
387	C₂×C₄	#6665	1	2	yes	—
388	C₂×C₄	D₅×Dic₆	1	1	yes	characteristic
389	C₂×C₄	#6772	1	1	yes	characteristic
390	C₂×C₄	#6773	1	1	yes	characteristic
391	C₂×C₄	D₅×D₁₂	1	1	yes	characteristic
392	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
393	C₂×C₄	C₂×#1202	1	1	yes	characteristic
394	C₈	—	60	2	no	—
395	C₂×C₃	—	20	4	no	—
396	C₂×C₃	C₂×#3941	1	1	yes	characteristic
397	C₂×C₃	#65255	1	1	yes	characteristic
398	C₂×C₃	#65276	1	1	yes	characteristic
399	C₂×C₃	#65361	1	1	yes	characteristic
400	C₂×C₃	#65372	1	1	yes	characteristic
401	C₂×C₃	#65373	1	1	yes	characteristic
402	C₂×C₃	#65376	1	1	yes	characteristic
403	C₅	#71604	1	1	yes	characteristic, complemented, Sylow
404	C₂²	—	10	4	no	—
405	C₂²	—	20	2	no	—
406	C₂²	—	20	2	no	—
407	C₂²	—	20	2	no	—
408	C₂²	—	20	2	no	—
409	C₂²	—	20	2	no	—
410	C₂²	—	20	2	no	—
411	C₂²	C₂×#6652	1	1	yes	characteristic
412	C₂²	#91299	1	1	yes	characteristic
413	C₂²	C₂×#6655	1	1	yes	characteristic
414	C₂²	#91307	1	1	yes	characteristic
415	C₂²	#91359	1	1	yes	characteristic
416	C₂²	#91449	1	1	yes	characteristic
417	C₂²	C₂×#6665	1	1	yes	characteristic
418	C₄	—	2	2	no	—
419	C₄	—	20	2	no	—
420	C₄	—	24	2	no	—
421	C₄	#90964	1	4	yes	complemented
422	C₄	#91358	1	1	yes	characteristic
423	C₄	#91360	1	1	yes	characteristic
424	C₄	D₅×C₄⋊Dic₃	1	1	yes	characteristic
425	C₄	#91450	1	1	yes	characteristic
426	C₃	#10600377	1	1	yes	characteristic, complemented, Sylow
427	C₂	—	20	4	no	—
428	C₂	#11746880	1	1	yes	characteristic
429	C₂	#11746886	1	1	yes	characteristic
430	C₂	#11747026	1	1	yes	characteristic
431	C₂	#11747059	1	1	yes	characteristic
432	C₂	C₂×#90964	1	1	yes	characteristic
433	C₂	#11748368	1	1	yes	characteristic
434	C₂	#11748759	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×#1201
commutator	C₂×C₃×C₄×C₅	C₂²×C₄
Frattini	C₂²×C₄	C₂×D₃×D₅
Fitting	C₂×C₃×C₄²×C₅	C₂²
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×C₃×D₂₀	C₂²
cosocle	C₂²×C₃×C₄×C₅	C₂³
hypercenter	C₂×C₄²	D₃×D₅
hypocenter	C₃×C₅	#1802
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
2. C₂×C₄⋊(C₃⋊#168)	C₂	semidirect
3. C₅×#4935	C₂	semidirect
5. #11745979	C₂	semidirect
17. C₃×C₄×D₂₀	C₄	semidirect
55. #4935	D₅	semidirect
68. C₄×D₂₀	Dic₃	semidirect
101. C₃×D₂₀	C₄⋊C₄	semidirect
164. C₃×C₄×C₅	#102	semidirect
227. D₂₀	C₄⋊Dic₃	semidirect
299. C₄×C₅	#832	semidirect
332. C₃×C₅	#1802	semidirect
349. C₃×C₄	#3941	semidirect
403. C₅	#71604	semidirect
421. C₄	#90964	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×C₃×C₄×D₂₀	2
C₂×C₄⋊(C₃⋊#168)	2
C₅×#4935	2
C₂×#90964	2
#11745979	2
#10600377	3
#71604	5