Subgroups — #14327725

Order 1920.

1264 conjugacy classes of subgroups.

The subgroup lattice has 456 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×#91358	C₂	1	2	yes	maximal, complemented
3	#11751036	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₅×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
5	#11748785	C₂	1	2	yes	maximal
6	#11748772	C₂	1	4	yes	maximal, complemented
7	#11748759	C₂	1	2	yes	maximal, complemented
8	Dic₃×C₄⋊Dic₅	C₂	1	2	yes	maximal, complemented
9	#10605369	—	3	1	no	maximal, Hall
10	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
12	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Dic₁₅	C₂²	1	2	yes	—
14	C₂×C₄⋊Dic₁₅	C₂²	1	2	yes	—
15	C₂×C₄⋊Dic₁₅	C₂²	1	2	yes	—
16	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
17	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
19	C₂×C₃×#685	C₂²	1	2	yes	—
20	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
21	C₃×C₄×D₂₀	C₄	1	8	yes	complemented
22	C₂×#6665	C₂²	1	4	yes	—
23	C₂×#6665	C₂²	1	4	yes	—
24	C₂×Dic₃×Dic₅	C₂²	1	4	yes	—
25	#91358	—	2	8	no	—
26	C₅×C₃⋊#95	C₂²	1	2	yes	—
27	#90994	C₂²	1	4	yes	—
28	#82337	—	5	1	no	maximal, Hall
29	C₂×#4038	—	3	2	no	—
30	C₂×C₄×D₂₀	D₃	1	1	yes	characteristic
31	C₄×C₅×C₄⋊C₄	—	3	1	no	—
32	#65276	—	3	2	no	—
33	#65228	—	3	2	no	—
34	#65224	—	3	1	no	—
35	C₄×C₄⋊Dic₅	—	3	2	no	—
36	#64959	—	3	4	no	—
37	C₂³×C₃×D₅	C₂³	1	2	yes	—
38	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
39	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
40	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₂²×Dic₁₅	C₂³	1	4	yes	—
42	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
43	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
44	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
45	C₂×C₃×D₂₀	—	2	2	no	—
46	C₂×C₃×D₂₀	—	2	2	no	—
47	C₂×C₃×D₂₀	C₂×C₄	1	4	yes	—
48	C₂×C₃×C₄×D₅	—	2	4	no	—
49	C₂×C₃×C₄×D₅	—	2	4	no	—
50	C₂×C₃×C₄×D₅	C₂×C₄	1	8	yes	—
51	C₃×C₄²×C₅	C₂×C₄	1	4	yes	—
52	C₄⋊Dic₁₅	—	2	4	no	—
53	C₄⋊Dic₁₅	—	2	4	no	—
54	C₄⋊Dic₁₅	—	4	2	no	—
55	C₅×C₄⋊Dic₃	—	2	2	no	—
56	C₅×C₄⋊Dic₃	D₄	1	4	yes	complemented
57	C₄×C₅×Dic₃	—	2	4	no	—
58	C₃×#685	C₂×C₄	1	8	yes	—
59	C₃×C₄⋊Dic₅	C₂×C₄	1	4	yes	—
60	#6665	—	2	8	no	—
61	#6665	—	4	4	no	—
62	Dic₃×Dic₅	—	2	8	no	—
63	C₂×C₃×C₄×D₄	—	5	1	no	—
64	C₂×#926	—	5	2	no	—
65	#5221	—	5	2	no	—
66	#5212	—	5	2	no	—
67	Dic₃×C₄⋊C₄	—	5	2	no	—
68	#4951	—	5	4	no	—
69	#4935	—	5	1	no	—
70	C₄×C₄⋊Dic₃	D₅	1	1	yes	characteristic, complemented
71	C₂²×D₂₀	C₂×D₃	1	1	yes	characteristic
72	C₂²×C₄×D₅	C₂×D₃	1	2	yes	—
73	C₂×C₅×C₄⋊C₄	—	3	1	no	—
74	C₂×C₅×C₄⋊C₄	—	3	1	no	—
75	C₂×C₄²×C₅	—	3	2	no	—
76	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
77	C₂×#685	—	3	4	no	—
78	C₂×#685	—	3	4	no	—
79	C₂×#685	C₂×D₃	1	2	yes	—
80	C₂×C₄⋊Dic₅	—	3	2	no	—
81	C₂×C₄⋊Dic₅	—	3	2	no	—
82	C₂×C₄⋊Dic₅	—	3	2	no	—
83	C₂×C₄⋊Dic₅	C₂×D₃	1	1	yes	characteristic
84	C₂×C₄×Dic₅	—	3	4	no	—
85	#4038	—	6	8	no	—
86	C₄×D₂₀	Dic₃	1	8	yes	complemented
87	C₅×#95	—	3	2	no	—
88	#3963	—	3	4	no	—
89	#2354	—	15	1	no	Sylow
90	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
91	C₂²×C₃×D₅	—	2	2	no	—
92	C₂²×C₃×D₅	—	2	2	no	—
93	C₂²×C₃×D₅	—	2	2	no	—
94	C₂²×C₃×D₅	—	2	2	no	—
95	C₂²×C₃×D₅	—	2	2	no	—
96	C₂²×C₃×D₅	—	2	2	no	—
97	C₂²×C₃×D₅	C₂²×C₄	1	4	yes	—
98	C₂×C₃×C₄×C₅	—	2	1	no	—
99	C₂×C₃×C₄×C₅	—	2	1	no	—
100	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
101	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
102	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
103	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
104	C₂×C₃×C₄×C₅	#41	1	2	yes	—
105	C₂×C₃×C₄×C₅	#41	1	2	yes	—
106	C₂×C₃×C₄×C₅	#41	1	2	yes	—
107	C₂×Dic₁₅	—	2	4	no	—
108	C₂×Dic₁₅	—	2	4	no	—
109	C₂×Dic₁₅	—	2	4	no	—
110	C₂×C₅×Dic₃	—	2	2	no	—
111	C₂×C₅×Dic₃	—	2	2	no	—
112	C₂×C₅×Dic₃	—	2	2	no	—
113	C₂×C₅×Dic₃	—	2	2	no	—
114	C₂×C₅×Dic₃	—	2	2	no	—
115	C₂×C₅×Dic₃	C₂×D₄	1	4	yes	—
116	C₂×C₃×Dic₅	—	2	2	no	—
117	C₂×C₃×Dic₅	—	2	2	no	—
118	C₂×C₃×Dic₅	C₂²×C₄	1	4	yes	—
119	C₃×D₂₀	—	2	8	no	—
120	C₃×C₄×D₅	—	2	16	no	—
121	C₂²×C₃×D₄	—	5	1	no	—
122	C₂³×C₃×C₄	—	5	2	no	—
123	C₃×C₄×D₄	—	5	8	no	—
124	C₂×C₃×C₄⋊C₄	—	5	1	no	—
125	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
126	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
127	C₂×#217	—	5	4	no	—
128	C₂×#217	—	5	4	no	—
129	#926	—	10	8	no	—
130	C₂×C₄⋊Dic₃	—	5	2	no	—
131	C₂×C₄⋊Dic₃	—	5	2	no	—
132	C₂×C₄⋊Dic₃	—	5	2	no	—
133	C₂×C₄⋊Dic₃	C₂×D₅	1	1	yes	characteristic
134	C₂×C₄⋊Dic₃	C₂×D₅	1	1	yes	characteristic
135	C₂×C₄×Dic₃	—	5	4	no	—
136	C₂×C₄×Dic₃	C₂×D₅	1	2	yes	—
137	C₃⋊#95	—	5	4	no	—
138	C₃⋊#95	C₂×D₅	1	2	yes	—
139	C₂³×D₅	C₂²×D₃	1	2	yes	—
140	C₂²×C₄×C₅	—	3	2	no	—
141	C₂²×C₄×C₅	—	3	2	no	—
142	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
143	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
144	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
145	C₂²×Dic₅	—	3	4	no	—
146	C₂²×Dic₅	C₂²×D₃	1	2	yes	—
147	C₂×D₂₀	—	2	2	no	—
148	C₂×D₂₀	—	2	2	no	—
149	C₂×D₂₀	C₂×Dic₃	1	4	yes	—
150	C₂×C₄×D₅	—	2	4	no	—
151	C₂×C₄×D₅	—	2	4	no	—
152	C₂×C₄×D₅	C₂×Dic₃	1	8	yes	—
153	C₅×C₄⋊C₄	—	3	4	no	—
154	C₅×C₄⋊C₄	—	6	2	no	—
155	C₄²×C₅	—	6	4	no	—
156	C₄²×C₅	C₂×Dic₃	1	4	yes	—
157	#685	—	6	8	no	—
158	#685	—	12	4	no	—
159	#685	C₂×Dic₃	1	8	yes	—
160	C₄⋊Dic₅	—	6	4	no	—
161	C₄⋊Dic₅	—	6	4	no	—
162	C₄⋊Dic₅	—	12	2	no	—
163	C₄⋊Dic₅	C₂×Dic₃	1	4	yes	—
164	C₄×Dic₅	—	6	8	no	—
165	C₂×C₄×D₄	—	5	1	no	—
166	C₂×#117	—	15	2	no	—
167	#390	—	15	2	no	—
168	#388	—	15	4	no	—
169	#384	—	15	1	no	—
170	#380	—	15	2	no	—
171	C₄×C₄⋊C₄	—	3	1	no	—
172	C₄×C₄⋊C₄	—	15	2	no	—
173	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
174	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
175	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
176	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
177	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
178	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
179	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
180	C₂×C₃×D₅	—	2	4	no	—
181	C₂×C₃×D₅	—	2	4	no	—
182	C₂×C₃×D₅	—	2	4	no	—
183	C₂×C₃×D₅	—	4	2	no	—
184	C₂×C₃×D₅	—	4	2	no	—
185	C₂×C₃×D₅	—	4	2	no	—
186	C₂×C₃×D₅	—	4	2	no	—
187	C₃×C₄×C₅	—	2	2	no	—
188	C₃×C₄×C₅	#117	1	4	yes	complemented
189	C₃×C₄×C₅	C₄×D₄	1	4	yes	—
190	Dic₁₅	—	4	4	no	—
191	C₃×Dic₅	—	2	4	no	—
192	C₅×Dic₃	—	2	4	no	—
193	C₅×Dic₃	—	4	2	no	—
194	C₂⁴×C₃	—	5	2	no	—
195	C₂×C₃×D₄	—	5	4	no	—
196	C₂×C₃×D₄	—	10	2	no	—
197	C₂×C₃×D₄	—	10	2	no	—
198	C₂²×C₃×C₄	—	5	2	no	—
199	C₂²×C₃×C₄	—	5	8	no	—
200	C₂²×C₃×C₄	—	10	4	no	—
201	C₂²×C₃×C₄	—	10	4	no	—
202	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
203	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
204	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
205	C₂²×Dic₃	—	5	4	no	—
206	C₂²×Dic₃	C₂²×D₅	1	2	yes	—
207	C₂²×Dic₃	C₂²×D₅	1	2	yes	—
208	C₃×C₄⋊C₄	—	5	4	no	—
209	C₃×C₂²⋊C₄	—	5	8	no	—
210	C₃×C₄²	C₄×D₅	1	4	yes	—
211	#217	—	10	8	no	—
212	#217	—	20	4	no	—
213	C₄⋊Dic₃	—	2	2	no	—
214	C₄⋊Dic₃	—	10	4	no	—
215	C₄⋊Dic₃	—	10	4	no	—
216	C₄⋊Dic₃	—	20	2	no	—
217	C₄⋊Dic₃	D₂₀	1	4	yes	complemented
218	C₄×Dic₃	—	2	4	no	—
219	C₄×Dic₃	—	10	8	no	—
220	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
221	C₂²×D₅	—	2	2	no	—
222	C₂²×D₅	—	2	2	no	—
223	C₂²×D₅	—	2	2	no	—
224	C₂²×D₅	—	2	2	no	—
225	C₂²×D₅	—	2	2	no	—
226	C₂²×D₅	—	2	2	no	—
227	C₂²×D₅	C₂²×Dic₃	1	4	yes	—
228	C₂×C₄×C₅	—	2	1	no	—
229	C₂×C₄×C₅	—	2	1	no	—
230	C₂×C₄×C₅	—	3	4	no	—
231	C₂×C₄×C₅	—	6	2	no	—
232	C₂×C₄×C₅	—	6	2	no	—
233	C₂×C₄×C₅	—	6	2	no	—
234	C₂×C₄×C₅	—	6	2	no	—
235	C₂×C₄×C₅	—	6	2	no	—
236	C₂×C₄×C₅	#235	1	2	yes	—
237	C₂×C₄×C₅	#235	1	2	yes	—
238	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
239	C₂×C₄×C₅	#237	1	2	yes	—
240	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
241	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
242	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
243	C₂×Dic₅	—	2	2	no	—
244	C₂×Dic₅	—	2	2	no	—
245	C₂×Dic₅	—	6	4	no	—
246	C₂×Dic₅	—	6	4	no	—
247	C₂×Dic₅	—	6	4	no	—
248	C₂×Dic₅	C₂²×Dic₃	1	4	yes	—
249	D₂₀	—	2	8	no	—
250	C₄×D₅	—	2	16	no	—
251	C₂²×D₄	—	5	1	no	—
252	C₂³×C₄	—	5	2	no	—
253	C₄×D₄	—	5	8	no	—
254	#117	—	30	8	no	—
255	C₂×C₄⋊C₄	—	3	1	no	—
256	C₂×C₄⋊C₄	—	3	1	no	—
257	C₂×C₄⋊C₄	—	5	1	no	—
258	C₂×C₄⋊C₄	—	15	2	no	—
259	C₂×C₄⋊C₄	—	15	2	no	—
260	C₂×C₄⋊C₄	—	15	2	no	—
261	C₂×C₂²⋊C₄	—	5	2	no	—
262	C₂×C₂²⋊C₄	—	15	4	no	—
263	C₂×C₂²⋊C₄	—	15	4	no	—
264	C₂×C₄²	—	3	2	no	—
265	C₂×C₄²	—	15	4	no	—
266	C₂×C₄²	D₃×D₅	1	1	yes	characteristic
267	#95	—	3	2	no	—
268	#95	—	15	4	no	—
269	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
270	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
271	C₂×C₃×C₅	#520	1	1	yes	characteristic
272	C₂×C₃×C₅	#547	1	1	yes	characteristic
273	C₂×C₃×C₅	#550	1	1	yes	characteristic
274	C₂×C₃×C₅	#555	1	1	yes	characteristic
275	C₂×C₃×C₅	#556	1	1	yes	characteristic
276	C₃×D₅	—	4	4	no	—
277	C₂³×C₃	—	5	4	no	—
278	C₂³×C₃	—	10	2	no	—
279	C₂³×C₃	—	10	2	no	—
280	C₂³×C₃	—	10	2	no	—
281	C₂³×C₃	—	10	2	no	—
282	C₂³×C₃	—	10	2	no	—
283	C₂³×C₃	—	10	2	no	—
284	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
285	C₃×D₄	—	10	8	no	—
286	C₂×C₃×C₄	—	2	1	no	—
287	C₂×C₃×C₄	—	2	1	no	—
288	C₂×C₃×C₄	—	5	4	no	—
289	C₂×C₃×C₄	—	10	2	no	—
290	C₂×C₃×C₄	—	10	2	no	—
291	C₂×C₃×C₄	—	10	16	no	—
292	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
293	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
294	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
295	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
296	C₂×C₃×C₄	#709	1	2	yes	—
297	C₂×C₃×C₄	#711	1	2	yes	—
298	C₂×C₃×C₄	#713	1	2	yes	—
299	C₂×Dic₃	—	2	2	no	—
300	C₂×Dic₃	—	2	2	no	—
301	C₂×Dic₃	—	2	2	no	—
302	C₂×Dic₃	—	2	2	no	—
303	C₂×Dic₃	—	2	2	no	—
304	C₂×Dic₃	—	10	4	no	—
305	C₂×Dic₃	—	10	4	no	—
306	C₂×Dic₃	—	10	4	no	—
307	C₂×Dic₃	C₂×D₂₀	1	4	yes	—
308	C₂²×C₅	C₂×#235	1	1	yes	characteristic
309	C₂²×C₅	C₂×#235	1	1	yes	characteristic
310	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
311	C₂²×C₅	C₂×#237	1	1	yes	characteristic
312	C₂²×C₅	#1009	1	1	yes	characteristic
313	C₂²×C₅	#1010	1	1	yes	characteristic
314	C₂²×C₅	C₂³×Dic₃	1	1	yes	characteristic
315	C₂×D₅	—	2	4	no	—
316	C₂×D₅	—	2	4	no	—
317	C₂×D₅	—	2	4	no	—
318	C₂×D₅	—	4	2	no	—
319	C₂×D₅	—	4	2	no	—
320	C₂×D₅	—	4	2	no	—
321	C₂×D₅	—	4	2	no	—
322	C₄×C₅	—	2	2	no	—
323	C₄×C₅	—	6	4	no	—
324	C₄×C₅	—	12	2	no	—
325	C₄×C₅	#926	1	4	yes	complemented
326	C₄×C₅	D₄×Dic₃	1	4	yes	—
327	Dic₅	—	2	4	no	—
328	Dic₅	—	12	4	no	—
329	C₂⁴	—	5	2	no	—
330	C₂×D₄	—	5	4	no	—
331	C₂×D₄	—	10	2	no	—
332	C₂×D₄	—	10	2	no	—
333	C₂²×C₄	—	3	2	no	—
334	C₂²×C₄	—	3	2	no	—
335	C₂²×C₄	—	5	2	no	—
336	C₂²×C₄	—	5	8	no	—
337	C₂²×C₄	—	10	4	no	—
338	C₂²×C₄	—	10	4	no	—
339	C₂²×C₄	—	15	4	no	—
340	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
341	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
342	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
343	C₄⋊C₄	—	3	4	no	—
344	C₄⋊C₄	—	5	4	no	—
345	C₄⋊C₄	—	6	2	no	—
346	C₄⋊C₄	—	30	4	no	—
347	C₄⋊C₄	—	30	4	no	—
348	C₄⋊C₄	—	60	2	no	—
349	C₂²⋊C₄	—	5	8	no	—
350	C₂²⋊C₄	—	30	8	no	—
351	C₂²⋊C₄	—	60	4	no	—
352	C₄²	—	6	4	no	—
353	C₄²	—	30	8	no	—
354	C₄²	D₅×Dic₃	1	4	yes	—
355	C₃×C₅	#2354	1	1	yes	characteristic, complemented, Hall
356	C₂²×C₃	—	10	4	no	—
357	C₂²×C₃	—	10	4	no	—
358	C₂²×C₃	—	10	4	no	—
359	C₂²×C₃	—	20	2	no	—
360	C₂²×C₃	—	20	2	no	—
361	C₂²×C₃	—	20	2	no	—
362	C₂²×C₃	—	20	2	no	—
363	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
364	C₂²×C₃	C₂²×D₂₀	1	1	yes	characteristic
365	C₂²×C₃	C₂×#709	1	1	yes	characteristic
366	C₂²×C₃	C₂×#711	1	1	yes	characteristic
367	C₂²×C₃	C₂×#713	1	1	yes	characteristic
368	C₂²×C₃	#4149	1	1	yes	characteristic
369	C₂²×C₃	#4150	1	1	yes	characteristic
370	C₃×C₄	—	2	2	no	—
371	C₃×C₄	—	10	4	no	—
372	C₃×C₄	C₄×D₂₀	1	4	yes	—
373	C₃×C₄	#4038	1	4	yes	complemented
374	Dic₃	—	2	4	no	—
375	Dic₃	—	4	2	no	—
376	Dic₃	—	20	4	no	—
377	C₂×C₅	#5542	1	1	yes	characteristic
378	C₂×C₅	#5551	1	1	yes	characteristic
379	C₂×C₅	#5553	1	1	yes	characteristic
380	C₂×C₅	#5563	1	1	yes	characteristic
381	C₂×C₅	C₂×#926	1	1	yes	characteristic
382	C₂×C₅	C₂×D₄×Dic₃	1	1	yes	characteristic
383	C₂×C₅	#5827	1	1	yes	characteristic
384	D₅	—	4	4	no	—
385	C₂³	—	5	4	no	—
386	C₂³	—	10	2	no	—
387	C₂³	—	10	2	no	—
388	C₂³	—	10	2	no	—
389	C₂³	—	10	2	no	—
390	C₂³	—	10	2	no	—
391	C₂³	—	10	2	no	—
392	C₂³	C₂²×D₃×D₅	1	1	yes	characteristic
393	D₄	—	10	8	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	3	4	no	—
397	C₂×C₄	—	5	4	no	—
398	C₂×C₄	—	6	2	no	—
399	C₂×C₄	—	6	2	no	—
400	C₂×C₄	—	6	2	no	—
401	C₂×C₄	—	6	2	no	—
402	C₂×C₄	—	6	2	no	—
403	C₂×C₄	—	10	2	no	—
404	C₂×C₄	—	10	2	no	—
405	C₂×C₄	—	10	16	no	—
406	C₂×C₄	—	30	4	no	—
407	C₂×C₄	—	30	4	no	—
408	C₂×C₄	—	30	4	no	—
409	C₂×C₄	#6765	1	2	yes	—
410	C₂×C₄	#6772	1	2	yes	—
411	C₂×C₄	#6773	1	2	yes	—
412	C₂×C₄	D₃×D₂₀	1	2	yes	—
413	C₂×C₄	C₂×D₅×Dic₃	1	2	yes	—
414	C₂×C₄	C₂×D₅×Dic₃	1	2	yes	—
415	C₂×C₄	C₂×D₅×Dic₃	1	2	yes	—
416	C₂×C₃	—	20	4	no	—
417	C₂×C₃	C₂×C₄×D₂₀	1	1	yes	characteristic
418	C₂×C₃	C₂×#4038	1	1	yes	characteristic
419	C₂×C₃	#65857	1	1	yes	characteristic
420	C₂×C₃	#65889	1	1	yes	characteristic
421	C₂×C₃	#65897	1	1	yes	characteristic
422	C₂×C₃	#65911	1	1	yes	characteristic
423	C₂×C₃	#65918	1	1	yes	characteristic
424	C₅	#82337	1	1	yes	characteristic, complemented, Sylow
425	C₂²	—	10	4	no	—
426	C₂²	—	10	4	no	—
427	C₂²	—	10	4	no	—
428	C₂²	—	20	2	no	—
429	C₂²	—	20	2	no	—
430	C₂²	—	20	2	no	—
431	C₂²	—	20	2	no	—
432	C₂²	C₂×#6765	1	1	yes	characteristic
433	C₂²	#92001	1	1	yes	characteristic
434	C₂²	C₂×#6772	1	1	yes	characteristic
435	C₂²	C₂×#6773	1	1	yes	characteristic
436	C₂²	C₂×D₃×D₂₀	1	1	yes	characteristic
437	C₂²	#92019	1	1	yes	characteristic
438	C₂²	C₂²×D₅×Dic₃	1	1	yes	characteristic
439	C₄	—	2	2	no	—
440	C₄	—	6	4	no	—
441	C₄	—	10	4	no	—
442	C₄	—	12	2	no	—
443	C₄	—	60	4	no	—
444	C₄	#91358	1	4	yes	complemented
445	C₄	Dic₃×D₂₀	1	4	yes	—
446	C₃	#10605369	1	1	yes	characteristic, complemented, Sylow
447	C₂	—	20	4	no	—
448	C₂	#11752507	1	1	yes	characteristic
449	C₂	#11752676	1	1	yes	characteristic
450	C₂	#11752677	1	1	yes	characteristic
451	C₂	#11752718	1	1	yes	characteristic
452	C₂	C₂×#91358	1	1	yes	characteristic
453	C₂	C₂×Dic₃×D₂₀	1	1	yes	characteristic
454	C₂	#11754509	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₃×D₅
commutator	C₂²×C₃×C₅	C₂³×C₄
Fitting	C₂×C₃×C₄²×C₅	C₂²
socle, cosocle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×C₃×D₂₀	C₂²
hypercenter	C₂×C₄²	D₃×D₅
hypocenter	C₃×C₅	#2354
LCS	G ▷ C₂²×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×#91358	C₂	semidirect
3. #11751036	C₂	semidirect
4. C₄×C₅×C₄⋊Dic₃	C₂	semidirect
6. #11748772	C₂	semidirect
7. #11748759	C₂	semidirect
8. Dic₃×C₄⋊Dic₅	C₂	semidirect
21. C₃×C₄×D₂₀	C₄	semidirect
56. C₅×C₄⋊Dic₃	D₄	semidirect
70. C₄×C₄⋊Dic₃	D₅	semidirect
86. C₄×D₂₀	Dic₃	semidirect
188. C₃×C₄×C₅	#117	semidirect
217. C₄⋊Dic₃	D₂₀	semidirect
325. C₄×C₅	#926	semidirect
355. C₃×C₅	#2354	semidirect
373. C₃×C₄	#4038	semidirect
424. C₅	#82337	semidirect
444. C₄	#91358	semidirect
446. C₃	#10605369	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×#91358	2
#11751036	2
C₄×C₅×C₄⋊Dic₃	2
#11748785	2
#11748772	2
#11748759	2
Dic₃×C₄⋊Dic₅	2
#10605369	3
#82337	5