Subgroups — #14300889

Order 1920.

804 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₃×D₂₀	C₂	1	1	yes	maximal, characteristic
2	C₂²×#6657	C₂	1	1	yes	maximal, characteristic
3	C₂×#91100	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#3953	C₂	1	1	yes	maximal, characteristic
5	#11748599	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4550	C₂	1	1	yes	maximal, characteristic, complemented
7	#11745980	C₂	1	1	yes	maximal, characteristic, complemented
8	#10599465	—	3	1	no	maximal, Hall
9	C₂²×Dic₃₀	C₂²	1	1	yes	characteristic
10	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
11	C₂²×D₅×Dic₃	—	2	1	no	—
12	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Dic₁₅	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₅×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	C₂×#6665	—	2	1	no	—
18	Dic₃×D₂₀	—	2	2	no	—
19	Dic₃×D₂₀	—	2	2	no	—
20	C₂×#6657	—	2	2	no	—
21	C₂×#6657	—	2	2	no	—
22	C₂×#6657	C₄	1	4	yes	complemented
23	#91100	—	2	2	no	—
24	C₃×#3953	—	2	2	no	—
25	#90994	—	2	1	no	—
26	#90994	—	2	1	no	—
27	#70171	—	5	1	no	maximal, Hall
28	C₂²×#677	—	3	1	no	—
29	C₂×C₄×D₂₀	—	3	1	no	—
30	C₂×#3953	D₃	1	1	yes	characteristic
31	C₂×#3948	—	3	1	no	—
32	#65218	—	3	1	no	—
33	C₅×#336	—	3	1	no	—
34	#64771	—	3	1	no	—
35	C₂³×C₃×D₅	—	2	1	no	—
36	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
37	C₂²×Dic₁₅	—	2	1	no	—
38	C₂²×Dic₁₅	—	2	1	no	—
39	C₂×Dic₃₀	—	2	1	no	—
40	C₂×Dic₃₀	—	2	1	no	—
41	C₂×Dic₃₀	—	2	1	no	—
42	C₂×Dic₃₀	—	2	1	no	—
43	C₂×Dic₃₀	—	2	1	no	—
44	C₂×Dic₃₀	C₂×C₄	1	2	yes	complemented
45	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
46	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
47	C₂²×C₃×Dic₅	—	2	1	no	—
48	C₂×C₃×D₂₀	—	2	1	no	—
49	C₂×C₃×D₂₀	—	2	1	no	—
50	C₂×C₃×D₂₀	—	2	1	no	—
51	C₂×C₃×D₂₀	C₂×C₄	1	2	yes	—
52	C₂×C₃×D₂₀	D₄	1	2	yes	—
53	C₂×C₃×D₂₀	D₄	1	2	yes	—
54	C₂×D₅×Dic₃	—	2	4	no	—
55	C₂×D₅×Dic₃	—	4	2	no	—
56	C₂×D₅×Dic₃	—	4	2	no	—
57	C₂×C₃×C₅×C₈	—	2	1	no	—
58	C₂×C₃×C₅×C₈	—	2	1	no	—
59	C₂×C₃×C₅×C₈	—	2	1	no	—
60	C₄⋊Dic₁₅	—	2	1	no	—
61	C₄⋊Dic₁₅	D₄	1	2	yes	—
62	C₄×C₅×Dic₃	—	2	1	no	—
63	C₄×C₅×Dic₃	—	2	1	no	—
64	C₂×C₅×C₃⋊C₈	—	2	1	no	—
65	C₂×C₅×C₃⋊C₈	—	2	1	no	—
66	C₂×C₅×C₃⋊C₈	C₂×C₄	1	2	yes	complemented
67	C₃×C₄⋊Dic₅	—	2	1	no	—
68	C₃×C₄⋊Dic₅	—	2	1	no	—
69	#6665	—	2	4	no	—
70	#6657	—	2	8	no	—
71	C₂×D₄×Dic₃	—	5	1	no	—
72	C₂²×#214	—	5	1	no	—
73	C₂×C₃×#102	—	5	1	no	—
74	C₂×#816	—	5	1	no	—
75	#4973	—	5	1	no	—
76	#4550	D₅	1	1	yes	characteristic, complemented
77	#4529	—	5	1	no	—
78	C₂²×D₂₀	C₂×D₃	1	1	yes	characteristic
79	C₂²×C₄×D₅	—	6	1	no	—
80	C₂²×Dic₁₀	—	3	1	no	—
81	C₂²×C₅×C₈	—	3	1	no	—
82	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
83	C₂×C₄²×C₅	—	3	1	no	—
84	C₂×#685	—	6	1	no	—
85	C₂×C₄⋊Dic₅	—	3	1	no	—
86	C₂×C₄⋊Dic₅	C₂×D₃	1	1	yes	characteristic
87	C₂×#677	—	3	4	no	—
88	C₂×#677	—	6	2	no	—
89	C₂×#677	—	6	2	no	—
90	C₄×D₂₀	—	6	2	no	—
91	C₄×D₂₀	—	6	2	no	—
92	#3963	—	6	1	no	—
93	#3963	—	6	1	no	—
94	#3953	—	2	2	no	—
95	#3948	—	6	2	no	—
96	#1877	—	15	1	no	Sylow
97	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₃×D₅	—	2	2	no	—
99	C₂²×C₃×D₅	—	2	2	no	—
100	C₂²×C₃×D₅	—	2	2	no	—
101	C₂²×C₃×D₅	—	4	1	no	—
102	C₂²×C₃×D₅	—	4	1	no	—
103	C₂²×C₃×D₅	—	4	1	no	—
104	C₂²×C₃×D₅	—	4	1	no	—
105	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
109	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
110	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
111	C₂×Dic₁₅	—	2	2	no	—
112	C₂×Dic₁₅	—	2	2	no	—
113	C₂×Dic₁₅	—	4	1	no	—
114	C₂×Dic₁₅	—	4	1	no	—
115	C₂×Dic₁₅	—	4	1	no	—
116	C₂×Dic₁₅	—	4	1	no	—
117	Dic₃₀	—	2	2	no	—
118	Dic₃₀	—	2	2	no	—
119	Dic₃₀	—	4	1	no	—
120	Dic₃₀	—	4	1	no	—
121	C₂×C₅×Dic₃	—	2	1	no	—
122	C₂×C₅×Dic₃	—	2	1	no	—
123	C₂×C₅×Dic₃	—	2	1	no	—
124	C₂×C₅×Dic₃	—	2	1	no	—
125	C₂×C₅×Dic₃	—	2	1	no	—
126	C₂×C₅×Dic₃	SD₁₆	1	2	yes	complemented
127	C₂×C₃×Dic₅	—	4	1	no	—
128	C₂×C₃×Dic₅	—	4	1	no	—
129	C₂×C₃×Dic₅	—	4	1	no	—
130	C₃×D₂₀	—	2	2	no	—
131	C₃×D₂₀	—	2	2	no	—
132	C₃×D₂₀	—	2	2	no	—
133	C₃×D₂₀	C₂²⋊C₄	1	4	yes	—
134	D₅×Dic₃	—	4	8	no	—
135	C₃×C₅×C₈	—	4	1	no	—
136	C₅×C₃⋊C₈	—	2	2	no	—
137	C₂²×C₃×D₄	—	5	1	no	—
138	C₂³×Dic₃	—	10	1	no	—
139	C₂²×Dic₆	—	5	1	no	—
140	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
141	C₂×C₃×C₄⋊C₄	—	5	1	no	—
142	C₂×#217	—	10	1	no	—
143	D₄×Dic₃	—	10	2	no	—
144	D₄×Dic₃	—	10	2	no	—
145	C₂×#214	—	5	4	no	—
146	C₂×#214	—	10	2	no	—
147	C₂×#214	—	10	2	no	—
148	C₂×C₄⋊Dic₃	—	5	1	no	—
149	C₂×C₄×Dic₃	C₂×D₅	1	1	yes	characteristic
150	C₂²×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
151	C₃×#102	—	10	2	no	—
152	C₃⋊#95	—	10	1	no	—
153	C₃⋊#95	—	10	1	no	—
154	#816	—	10	2	no	—
155	C₂³×D₅	—	2	1	no	—
156	C₂²×C₄×C₅	—	3	1	no	—
157	C₂²×C₄×C₅	—	3	1	no	—
158	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
159	C₂²×Dic₅	—	2	1	no	—
160	C₂²×Dic₅	—	6	1	no	—
161	C₂²×Dic₅	—	6	1	no	—
162	C₂×D₂₀	—	2	1	no	—
163	C₂×D₂₀	—	2	1	no	—
164	C₂×D₂₀	—	2	1	no	—
165	C₂×D₂₀	C₄×D₃	1	2	yes	—
166	C₂×D₂₀	D₁₂	1	2	yes	—
167	C₂×D₂₀	#67	1	2	yes	—
168	C₂×C₄×D₅	—	6	4	no	—
169	C₂×C₄×D₅	—	12	2	no	—
170	C₂×C₄×D₅	—	12	2	no	—
171	C₂×Dic₁₀	—	3	2	no	—
172	C₂×Dic₁₀	—	6	1	no	—
173	C₂×Dic₁₀	—	6	1	no	—
174	C₂×Dic₁₀	—	6	1	no	—
175	C₂×Dic₁₀	—	6	1	no	—
176	C₂×Dic₁₀	—	6	1	no	—
177	C₂×C₅×C₈	—	2	1	no	—
178	C₂×C₅×C₈	—	2	1	no	—
179	C₂×C₅×C₈	—	2	1	no	—
180	C₂×C₅×C₈	—	3	2	no	—
181	C₂×C₅×C₈	—	6	1	no	—
182	C₂×C₅×C₈	—	6	1	no	—
183	C₄²×C₅	—	6	1	no	—
184	C₄²×C₅	—	6	1	no	—
185	#685	—	6	4	no	—
186	C₄⋊Dic₅	—	2	1	no	—
187	C₄⋊Dic₅	—	2	1	no	—
188	C₄⋊Dic₅	—	3	2	no	—
189	C₄⋊Dic₅	—	6	1	no	—
190	#677	—	6	8	no	—
191	C₂²×SD₁₆	—	15	1	no	—
192	C₂×C₄×D₄	—	15	1	no	—
193	C₂×#103	—	15	1	no	—
194	C₂×#102	—	5	1	no	—
195	#391	—	15	1	no	—
196	#340	—	15	1	no	—
197	#336	—	3	1	no	—
198	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
199	C₂²×C₃×C₅	#120	1	1	yes	characteristic
200	C₂²×C₃×C₅	#121	1	1	yes	characteristic
201	C₂²×C₃×C₅	C₂×SD₁₆	1	1	yes	characteristic
202	C₂²×C₃×C₅	#135	1	1	yes	characteristic
203	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
204	C₂²×C₃×C₅	#137	1	1	yes	characteristic
205	C₂×C₃×D₅	—	2	4	no	—
206	C₂×C₃×D₅	—	4	2	no	—
207	C₂×C₃×D₅	—	4	2	no	—
208	C₂×C₃×D₅	—	4	2	no	—
209	C₂×C₃×D₅	—	4	2	no	—
210	C₂×C₃×D₅	—	4	2	no	—
211	C₂×C₃×D₅	—	4	2	no	—
212	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
213	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
214	C₃×C₄×C₅	#121	1	1	yes	characteristic
215	C₃×C₄×C₅	#123	1	1	yes	characteristic
216	Dic₁₅	—	4	2	no	—
217	Dic₁₅	—	4	2	no	—
218	C₃×Dic₅	—	8	1	no	—
219	C₅×Dic₃	—	2	2	no	—
220	C₅×Dic₃	—	4	1	no	—
221	C₂⁴×C₃	—	10	1	no	—
222	C₂×C₃×D₄	—	5	2	no	—
223	C₂×C₃×D₄	—	5	2	no	—
224	C₂×C₃×D₄	—	5	2	no	—
225	C₂×C₃×D₄	—	10	1	no	—
226	C₂×C₃×D₄	—	10	1	no	—
227	C₂×C₃×D₄	—	10	1	no	—
228	C₂²×C₃×C₄	—	10	1	no	—
229	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
230	C₂²×Dic₃	—	10	4	no	—
231	C₂²×Dic₃	—	10	1	no	—
232	C₂²×Dic₃	—	10	1	no	—
233	C₂²×Dic₃	—	20	2	no	—
234	C₂²×Dic₃	—	20	2	no	—
235	C₂²×Dic₃	D₂₀	1	1	yes	characteristic
236	C₂²×Dic₃	D₂₀	1	1	yes	characteristic
237	C₂×Dic₆	—	5	2	no	—
238	C₂×Dic₆	—	10	1	no	—
239	C₂×Dic₆	—	10	1	no	—
240	C₂×Dic₆	—	10	1	no	—
241	C₂×Dic₆	—	10	1	no	—
242	C₂×Dic₆	—	10	1	no	—
243	C₂×C₃×C₈	—	2	1	no	—
244	C₂×C₃×C₈	—	2	1	no	—
245	C₂×C₃×C₈	—	2	1	no	—
246	C₃×C₄⋊C₄	—	10	1	no	—
247	C₃×C₄⋊C₄	—	10	1	no	—
248	#217	—	10	4	no	—
249	#214	—	10	8	no	—
250	C₄⋊Dic₃	—	5	2	no	—
251	C₄⋊Dic₃	—	10	1	no	—
252	C₄×Dic₃	—	2	1	no	—
253	C₄×Dic₃	—	2	1	no	—
254	C₂×C₃⋊C₈	—	2	1	no	—
255	C₂×C₃⋊C₈	—	2	1	no	—
256	C₂×C₃⋊C₈	C₄×D₅	1	2	yes	complemented
257	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
258	C₂²×D₅	—	2	2	no	—
259	C₂²×D₅	—	2	2	no	—
260	C₂²×D₅	—	2	2	no	—
261	C₂²×D₅	—	4	1	no	—
262	C₂²×D₅	—	4	1	no	—
263	C₂²×D₅	—	4	1	no	—
264	C₂²×D₅	—	4	1	no	—
265	C₂×C₄×C₅	—	3	2	no	—
266	C₂×C₄×C₅	—	6	1	no	—
267	C₂×C₄×C₅	—	6	1	no	—
268	C₂×C₄×C₅	—	6	1	no	—
269	C₂×C₄×C₅	—	6	1	no	—
270	C₂×C₄×C₅	—	6	1	no	—
271	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
272	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
273	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
274	C₂×C₄×C₅	#237	1	1	yes	characteristic
275	C₂×C₄×C₅	#237	1	1	yes	characteristic
276	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
277	C₂×Dic₅	—	4	1	no	—
278	C₂×Dic₅	—	4	1	no	—
279	C₂×Dic₅	—	4	1	no	—
280	C₂×Dic₅	—	6	2	no	—
281	C₂×Dic₅	—	6	2	no	—
282	C₂×Dic₅	—	12	1	no	—
283	C₂×Dic₅	—	12	1	no	—
284	C₂×Dic₅	—	12	1	no	—
285	C₂×Dic₅	—	12	1	no	—
286	D₂₀	—	2	2	no	—
287	D₂₀	—	2	2	no	—
288	D₂₀	—	2	2	no	—
289	D₂₀	(C₂×D₃)⋊C₄	1	4	yes	—
290	C₄×D₅	—	12	8	no	—
291	Dic₁₀	—	6	2	no	—
292	Dic₁₀	—	6	2	no	—
293	Dic₁₀	—	12	1	no	—
294	Dic₁₀	—	12	1	no	—
295	C₅×C₈	—	4	1	no	—
296	C₅×C₈	—	6	2	no	—
297	C₂²×Q₈	—	15	1	no	—
298	C₂²×D₄	—	5	1	no	—
299	C₂³×C₄	—	30	1	no	—
300	C₂×SD₁₆	—	15	4	no	—
301	C₂×SD₁₆	—	30	2	no	—
302	C₂×SD₁₆	—	30	2	no	—
303	C₂²×C₈	—	3	1	no	—
304	C₂²×C₈	D₃×D₅	1	1	yes	characteristic
305	C₄×D₄	—	30	2	no	—
306	C₄×D₄	—	30	2	no	—
307	C₂×C₄⋊C₄	—	5	1	no	—
308	C₂×C₄⋊C₄	—	15	1	no	—
309	C₂×C₂²⋊C₄	—	30	1	no	—
310	C₂×C₄²	—	3	1	no	—
311	#103	—	30	2	no	—
312	#102	—	10	2	no	—
313	#95	—	30	1	no	—
314	#95	—	30	1	no	—
315	C₂×C₃×C₅	#386	1	1	yes	characteristic
316	C₂×C₃×C₅	C₄×SD₁₆	1	1	yes	characteristic
317	C₂×C₃×C₅	#440	1	1	yes	characteristic
318	C₂×C₃×C₅	#450	1	1	yes	characteristic
319	C₂×C₃×C₅	#452	1	1	yes	characteristic
320	C₂×C₃×C₅	#461	1	1	yes	characteristic
321	C₂×C₃×C₅	#463	1	1	yes	characteristic
322	C₃×D₅	—	4	4	no	—
323	C₂³×C₃	—	10	2	no	—
324	C₂³×C₃	—	10	2	no	—
325	C₂³×C₃	—	10	2	no	—
326	C₂³×C₃	—	20	1	no	—
327	C₂³×C₃	—	20	1	no	—
328	C₂³×C₃	—	20	1	no	—
329	C₂³×C₃	—	20	1	no	—
330	C₂³×C₃	C₂×D₂₀	1	1	yes	characteristic
331	C₃×D₄	—	5	4	no	—
332	C₃×D₄	—	10	2	no	—
333	C₃×D₄	—	10	2	no	—
334	C₃×D₄	—	10	2	no	—
335	C₂×C₃×C₄	—	20	1	no	—
336	C₂×C₃×C₄	—	20	1	no	—
337	C₂×C₃×C₄	—	20	1	no	—
338	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
339	C₂×C₃×C₄	#709	1	1	yes	characteristic
340	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
341	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
342	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
343	C₂×C₃×C₄	#713	1	1	yes	characteristic
344	C₂×Dic₃	—	2	1	no	—
345	C₂×Dic₃	—	2	1	no	—
346	C₂×Dic₃	—	2	1	no	—
347	C₂×Dic₃	—	2	1	no	—
348	C₂×Dic₃	—	2	1	no	—
349	C₂×Dic₃	—	10	2	no	—
350	C₂×Dic₃	—	10	2	no	—
351	C₂×Dic₃	—	20	8	no	—
352	C₂×Dic₃	—	20	1	no	—
353	C₂×Dic₃	—	20	1	no	—
354	C₂×Dic₃	—	20	1	no	—
355	C₂×Dic₃	—	20	1	no	—
356	C₂×Dic₃	#677	1	2	yes	complemented
357	Dic₆	—	10	2	no	—
358	Dic₆	—	10	2	no	—
359	Dic₆	—	20	1	no	—
360	Dic₆	—	20	1	no	—
361	C₃×C₈	—	4	1	no	—
362	C₃⋊C₈	—	2	2	no	—
363	C₂²×C₅	#67⋊C₄	1	1	yes	characteristic
364	C₂²×C₅	#882	1	1	yes	characteristic
365	C₂²×C₅	#911	1	1	yes	characteristic
366	C₂²×C₅	#912	1	1	yes	characteristic
367	C₂²×C₅	D₃×SD₁₆	1	1	yes	characteristic
368	C₂²×C₅	#915	1	1	yes	characteristic
369	C₂²×C₅	#939	1	1	yes	characteristic
370	C₂×D₅	—	2	4	no	—
371	C₂×D₅	—	4	2	no	—
372	C₂×D₅	—	4	2	no	—
373	C₂×D₅	—	4	2	no	—
374	C₂×D₅	—	4	2	no	—
375	C₂×D₅	—	4	2	no	—
376	C₂×D₅	—	4	2	no	—
377	C₄×C₅	—	6	2	no	—
378	C₄×C₅	—	12	1	no	—
379	C₄×C₅	#67⋊C₄	1	1	yes	characteristic
380	C₄×C₅	#886	1	1	yes	characteristic
381	C₄×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
382	C₄×C₅	#939	1	1	yes	characteristic
383	Dic₅	—	8	1	no	—
384	Dic₅	—	12	2	no	—
385	Dic₅	—	12	2	no	—
386	C₂⁴	—	10	1	no	—
387	C₂×Q₈	—	15	2	no	—
388	C₂×Q₈	—	30	1	no	—
389	C₂×Q₈	—	30	1	no	—
390	C₂×Q₈	—	30	1	no	—
391	C₂×Q₈	—	30	1	no	—
392	C₂×Q₈	—	30	1	no	—
393	C₂×D₄	—	5	2	no	—
394	C₂×D₄	—	5	2	no	—
395	C₂×D₄	—	5	2	no	—
396	C₂×D₄	—	10	1	no	—
397	C₂×D₄	—	10	1	no	—
398	C₂×D₄	—	10	1	no	—
399	C₂²×C₄	—	3	1	no	—
400	C₂²×C₄	—	3	1	no	—
401	C₂²×C₄	—	10	1	no	—
402	C₂²×C₄	—	30	4	no	—
403	C₂²×C₄	—	30	1	no	—
404	C₂²×C₄	—	30	1	no	—
405	C₂²×C₄	—	60	2	no	—
406	C₂²×C₄	—	60	2	no	—
407	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
408	SD₁₆	—	30	8	no	—
409	C₂×C₈	—	2	1	no	—
410	C₂×C₈	—	2	1	no	—
411	C₂×C₈	—	2	1	no	—
412	C₂×C₈	—	3	2	no	—
413	C₂×C₈	—	6	1	no	—
414	C₂×C₈	—	6	1	no	—
415	C₄⋊C₄	—	10	1	no	—
416	C₄⋊C₄	—	10	1	no	—
417	C₄⋊C₄	—	15	2	no	—
418	C₄⋊C₄	—	30	1	no	—
419	C₂²⋊C₄	—	30	4	no	—
420	C₄²	—	6	1	no	—
421	C₄²	—	6	1	no	—
422	C₃×C₅	#1877	1	1	yes	characteristic, complemented, Hall
423	C₂²×C₃	—	10	4	no	—
424	C₂²×C₃	—	20	2	no	—
425	C₂²×C₃	—	20	2	no	—
426	C₂²×C₃	—	20	2	no	—
427	C₂²×C₃	—	20	2	no	—
428	C₂²×C₃	—	20	2	no	—
429	C₂²×C₃	—	20	2	no	—
430	C₂²×C₃	C₄×D₂₀	1	1	yes	characteristic
431	C₂²×C₃	#4028	1	1	yes	characteristic
432	C₂²×C₃	#4041	1	1	yes	characteristic
433	C₂²×C₃	C₂×#677	1	1	yes	characteristic
434	C₂²×C₃	#4050	1	1	yes	characteristic
435	C₂²×C₃	#4054	1	1	yes	characteristic
436	C₂²×C₃	#4055	1	1	yes	characteristic
437	C₃×C₄	—	40	1	no	—
438	C₃×C₄	D₅×C₂²⋊C₄	1	1	yes	characteristic
439	C₃×C₄	#4030	1	1	yes	characteristic
440	C₃×C₄	#4039	1	1	yes	characteristic
441	C₃×C₄	#4040	1	1	yes	characteristic
442	Dic₃	—	2	2	no	—
443	Dic₃	—	4	1	no	—
444	Dic₃	—	20	2	no	—
445	Dic₃	—	20	2	no	—
446	C₂×C₅	#4757	1	1	yes	characteristic
447	C₂×C₅	#4758	1	1	yes	characteristic
448	C₂×C₅	#4776	1	1	yes	characteristic
449	C₂×C₅	#4783	1	1	yes	characteristic
450	C₂×C₅	#4958	1	1	yes	characteristic
451	C₂×C₅	#5153	1	1	yes	characteristic
452	C₂×C₅	#5162	1	1	yes	characteristic
453	D₅	—	4	4	no	—
454	C₂³	—	10	2	no	—
455	C₂³	—	10	2	no	—
456	C₂³	—	10	2	no	—
457	C₂³	—	20	1	no	—
458	C₂³	—	20	1	no	—
459	C₂³	—	20	1	no	—
460	C₂³	—	20	1	no	—
461	C₂³	D₃×D₂₀	1	1	yes	characteristic
462	Q₈	—	30	2	no	—
463	Q₈	—	30	2	no	—
464	Q₈	—	60	1	no	—
465	Q₈	—	60	1	no	—
466	D₄	—	5	4	no	—
467	D₄	—	10	2	no	—
468	D₄	—	10	2	no	—
469	D₄	—	10	2	no	—
470	C₂×C₄	—	3	2	no	—
471	C₂×C₄	—	6	1	no	—
472	C₂×C₄	—	6	1	no	—
473	C₂×C₄	—	6	1	no	—
474	C₂×C₄	—	6	1	no	—
475	C₂×C₄	—	6	1	no	—
476	C₂×C₄	—	20	1	no	—
477	C₂×C₄	—	20	1	no	—
478	C₂×C₄	—	20	1	no	—
479	C₂×C₄	—	30	2	no	—
480	C₂×C₄	—	30	2	no	—
481	C₂×C₄	—	60	8	no	—
482	C₂×C₄	—	60	1	no	—
483	C₂×C₄	—	60	1	no	—
484	C₂×C₄	—	60	1	no	—
485	C₂×C₄	—	60	1	no	—
486	C₂×C₄	#6766	1	1	yes	characteristic
487	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
488	C₂×C₄	D₅×D₁₂	1	1	yes	characteristic
489	C₂×C₄	#6779	1	1	yes	characteristic
490	C₂×C₄	D₅×#67	1	1	yes	characteristic
491	C₂×C₄	#6790	1	1	yes	characteristic
492	C₈	—	4	1	no	—
493	C₈	—	6	2	no	—
494	C₂×C₃	—	20	4	no	—
495	C₂×C₃	#64954	1	1	yes	characteristic
496	C₂×C₃	C₄×#677	1	1	yes	characteristic
497	C₂×C₃	#64999	1	1	yes	characteristic
498	C₂×C₃	#65020	1	1	yes	characteristic
499	C₂×C₃	#65022	1	1	yes	characteristic
500	C₂×C₃	#65130	1	1	yes	characteristic
501	C₂×C₃	#65133	1	1	yes	characteristic
502	C₅	#70171	1	1	yes	characteristic, complemented, Sylow
503	C₂²	—	10	4	no	—
504	C₂²	—	20	2	no	—
505	C₂²	—	20	2	no	—
506	C₂²	—	20	2	no	—
507	C₂²	—	20	2	no	—
508	C₂²	—	20	2	no	—
509	C₂²	—	20	2	no	—
510	C₂²	D₃×#677	1	1	yes	characteristic
511	C₂²	#91254	1	1	yes	characteristic
512	C₂²	#91273	1	1	yes	characteristic
513	C₂²	#91274	1	1	yes	characteristic
514	C₂²	#91395	1	1	yes	characteristic
515	C₂²	#91409	1	1	yes	characteristic
516	C₂²	#91476	1	1	yes	characteristic
517	C₄	—	6	2	no	—
518	C₄	—	12	1	no	—
519	C₄	—	40	1	no	—
520	C₄	—	60	2	no	—
521	C₄	—	60	2	no	—
522	C₄	#91396	1	1	yes	characteristic
523	C₄	#91413	1	1	yes	characteristic
524	C₄	D₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
525	C₄	#91550	1	1	yes	characteristic
526	C₃	#10599465	1	1	yes	characteristic, complemented, Sylow
527	C₂	—	20	4	no	—
528	C₂	#11747739	1	1	yes	characteristic
529	C₂	#11747742	1	1	yes	characteristic
530	C₂	#11747753	1	1	yes	characteristic
531	C₂	#11747756	1	1	yes	characteristic
532	C₂	#11748120	1	1	yes	characteristic
533	C₂	#11748162	1	1	yes	characteristic
534	C₂	#11748872	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₃×D₂₀
commutator	C₂×C₃×C₄×C₅	C₂²×C₄
Frattini	C₂²×C₄	C₂×D₃×D₅
Fitting	C₂²×C₃×C₅×C₈	C₂²
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×C₃×D₂₀	C₂²
cosocle	C₂²×C₃×C₄×C₅	C₂³
hypercenter	C₂²×C₈	D₃×D₅
hypocenter	C₃×C₅	#1877
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
3. C₂×#91100	C₂	semidirect
5. #11748599	C₂	semidirect
6. C₅×#4550	C₂	semidirect
7. #11745980	C₂	semidirect
22. C₂×#6657	C₄	semidirect
44. C₂×Dic₃₀	C₂×C₄	semidirect
66. C₂×C₅×C₃⋊C₈	C₂×C₄	semidirect
76. #4550	D₅	semidirect
126. C₂×C₅×Dic₃	SD₁₆	semidirect
256. C₂×C₃⋊C₈	C₄×D₅	semidirect
356. C₂×Dic₃	#677	semidirect
422. C₃×C₅	#1877	semidirect
502. C₅	#70171	semidirect
526. C₃	#10599465	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₃×D₂₀	2
C₂²×#6657	2
C₂×#91100	2
C₂×C₃×#3953	2
#11748599	2
C₅×#4550	2
#11745980	2
#10599465	3
#70171	5