Subgroups — #14479229

Order 1920.

3320 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#92100	C₂	1	1	yes	maximal, characteristic
2	C₅×#5827	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#41×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
4	#11755200	C₂	1	2	yes	maximal, complemented
5	#11755149	C₂	1	2	yes	maximal, complemented
6	#11754922	C₂	1	6	yes	maximal, complemented
7	D₄×#1200	C₂	1	6	yes	maximal, complemented
8	#11754515	C₂	1	3	yes	maximal, complemented
9	#11754506	C₂	1	3	yes	maximal, complemented
10	#11754414	C₂	1	3	yes	maximal, complemented
11	C₂×#91418	C₂	1	3	yes	maximal, complemented
12	#10617787	—	3	1	no	maximal, Hall
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	#92100	C₄	1	16	yes	complemented
15	C₂×#6821	C₂²	1	2	yes	—
16	C₂×D₄×D₁₅	C₂²	1	6	yes	—
17	C₂×#6817	C₂²	1	3	yes	—
18	C₂²×D₆₀	C₂²	1	3	yes	—
19	C₂²×#1200	C₂²	1	6	yes	complemented
20	C₅×Q₈×Dic₃	C₂²	1	2	yes	complemented
21	C₅×D₄×Dic₃	C₂²	1	6	yes	complemented
22	C₅×#926	C₂²	1	3	yes	complemented
23	C₂×C₅×C₄⋊Dic₃	C₂²	1	3	yes	complemented
24	C₃×Q₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
25	C₃×Q₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
26	C₃×D₄×Dic₅	C₂²	1	3	yes	complemented
27	C₃×D₄×Dic₅	C₂²	1	3	yes	complemented
28	C₃×#4072	C₂²	1	3	yes	complemented
29	C₂×C₃×C₄×Dic₅	C₂²	1	3	yes	complemented
30	#91561	C₂²	1	12	yes	complemented
31	#91556	C₂²	1	12	yes	complemented
32	#91552	C₂²	1	6	yes	complemented
33	#91552	C₂²	1	6	yes	complemented
34	C₂×#6667	C₂²	1	6	yes	complemented
35	#91437	C₂²	1	6	yes	complemented
36	#91428	C₂²	1	6	yes	complemented
37	#91428	C₂²	1	6	yes	complemented
38	#91418	C₂²	1	6	yes	complemented
39	#91418	C₂²	1	3	yes	complemented
40	#91418	C₂²	1	6	yes	complemented
41	#91418	C₂²	1	3	yes	complemented
42	#91418	C₂²	1	6	yes	complemented
43	C₄×#1200	C₂²	1	6	yes	complemented
44	#91386	C₂²	1	6	yes	complemented
45	#91347	C₂²	1	6	yes	complemented
46	#91333	C₂²	1	3	yes	complemented
47	#91333	C₂²	1	1	yes	characteristic, complemented
48	C₄×#1009	—	5	1	no	maximal, Hall
49	C₂×#4149	—	3	1	no	—
50	C₅×#520	—	3	1	no	—
51	#41×Dic₅	D₃	1	1	yes	characteristic, complemented
52	#65908	—	3	2	no	—
53	C₄×#713	—	3	2	no	—
54	#65879	—	3	6	no	—
55	C₄×D₄×D₅	—	3	6	no	—
56	#65856	—	3	3	no	—
57	#65855	—	3	3	no	—
58	#65838	—	3	3	no	—
59	C₂×#4039	—	3	3	no	—
60	C₂³×D₁₅	C₂³	1	6	yes	—
61	C₃×C₅×#41	C₂×C₄	1	8	yes	complemented
62	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₅×D₄	C₂³	1	3	yes	—
64	C₂²×C₃×C₄×C₅	C₂³	1	3	yes	—
65	C₂×#1220	C₂³	1	6	yes	—
66	#6821	C₂×C₄	1	16	yes	complemented
67	D₄×D₁₅	C₂×C₄	1	48	yes	complemented
68	#6817	C₂×C₄	1	24	yes	complemented
69	C₂×D₆₀	C₂×C₄	1	24	yes	complemented
70	C₂×D₆₀	C₂³	1	3	yes	—
71	C₂×D₆₀	C₂³	1	6	yes	—
72	C₂×C₄×D₁₅	C₂³	1	6	yes	—
73	C₂×Dic₃₀	C₂³	1	1	yes	characteristic
74	C₂²×C₅×Dic₃	C₂³	1	6	yes	—
75	C₂²×C₃×Dic₅	C₂³	1	3	yes	—
76	C₂²×C₃×Dic₅	C₂³	1	3	yes	—
77	C₂×#1200	—	4	12	no	—
78	C₂×#1200	C₂³	1	6	yes	—
79	C₂×#1200	C₂³	1	6	yes	—
80	C₂×#1200	C₂³	1	12	yes	—
81	C₅×#217	C₂³	1	6	yes	—
82	C₅×C₄⋊Dic₃	C₂³	1	3	yes	—
83	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
84	C₅×C₄⋊Dic₃	C₂³	1	6	yes	—
85	C₄×C₅×Dic₃	C₂³	1	6	yes	—
86	C₃×C₂²⋊Dic₅	C₂³	1	6	yes	—
87	C₃×C₄⋊Dic₅	C₂³	1	3	yes	—
88	C₃×C₄⋊Dic₅	C₂³	1	3	yes	—
89	C₃×C₄×Dic₅	C₂³	1	3	yes	—
90	C₃×C₄×Dic₅	C₂³	1	3	yes	—
91	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
92	C₃×C₄×Dic₅	C₂³	1	3	yes	—
93	#6669	C₂³	1	6	yes	—
94	#6669	C₂³	1	2	yes	—
95	#6667	C₂³	1	6	yes	—
96	#6667	C₂³	1	12	yes	—
97	#6667	C₂³	1	6	yes	—
98	Dic₃×Dic₅	C₂³	1	2	yes	—
99	Dic₃×Dic₅	C₂³	1	6	yes	—
100	C₂×#1009	—	5	1	no	—
101	C₃×C₄×#41	—	5	1	no	—
102	#5827	D₅	1	1	yes	characteristic, complemented
103	#5574	—	5	2	no	—
104	C₄×#239	—	5	2	no	—
105	#5545	—	5	6	no	—
106	C₄×D₃×D₄	—	5	6	no	—
107	#5523	—	5	3	no	—
108	#5521	—	5	3	no	—
109	C₄×#235	—	5	3	no	—
110	C₂×C₄×D₁₂	—	5	3	no	—
111	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
112	#4149	—	3	16	no	—
113	C₂×#713	—	3	2	no	—
114	C₂×D₄×D₅	—	3	6	no	—
115	C₂×#709	—	3	3	no	—
116	C₂²×D₂₀	—	3	3	no	—
117	C₂²×C₄×D₅	—	3	6	no	—
118	C₄×C₅×Q₈	—	3	2	no	—
119	C₄×C₅×D₄	—	3	6	no	—
120	C₅×#117	—	3	3	no	—
121	C₂×C₅×C₄⋊C₄	—	3	3	no	—
122	Q₈×Dic₅	C₂×D₃	1	1	yes	characteristic, complemented
123	Q₈×Dic₅	C₂×D₃	1	1	yes	characteristic, complemented
124	D₄×Dic₅	C₂×D₃	1	3	yes	complemented
125	D₄×Dic₅	C₂×D₃	1	3	yes	complemented
126	C₄×C₂²⋊D₅	—	3	12	no	—
127	C₂×#685	—	3	6	no	—
128	#4072	C₂×D₃	1	3	yes	complemented
129	C₂×C₄×Dic₅	C₂×D₃	1	3	yes	complemented
130	#4039	—	3	3	no	—
131	#4039	—	3	6	no	—
132	#4039	—	3	6	no	—
133	#4039	—	3	6	no	—
134	#4039	—	3	3	no	—
135	#4038	—	3	6	no	—
136	D₅×C₄⋊C₄	—	3	6	no	—
137	#4033	—	3	3	no	—
138	#4033	—	3	1	no	—
139	#4027	—	3	6	no	—
140	#4027	—	3	6	no	—
141	D₅×C₂²⋊C₄	—	3	12	no	—
142	C₄×D₂₀	—	3	6	no	—
143	C₄×D₂₀	—	3	6	no	—
144	#4018	—	3	6	no	—
145	C₄²×D₅	—	3	6	no	—
146	C₄×H(5,𝔽₂)	—	15	1	no	Sylow
147	C₂³×C₃×C₅	C₂⁴	1	3	yes	—
148	C₂²×D₁₅	—	4	6	no	—
149	C₂²×D₁₅	—	4	6	no	—
150	C₂²×D₁₅	C₂²×C₄	1	24	yes	complemented
151	C₂²×D₁₅	C₂⁴	1	6	yes	—
152	C₃×C₅×Q₈	C₂²×C₄	1	4	yes	complemented
153	C₃×C₅×D₄	C₂²×C₄	1	12	yes	complemented
154	C₂×C₃×C₄×C₅	C₂²×C₄	1	12	yes	complemented
155	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
156	C₂×C₃×C₄×C₅	C₂⁴	1	3	yes	—
157	#1220	C₂²×C₄	1	24	yes	complemented
158	C₂×Dic₁₅	C₂⁴	1	2	yes	—
159	D₆₀	C₂²×C₄	1	12	yes	complemented
160	D₆₀	C₂²×C₄	1	24	yes	complemented
161	C₄×D₁₅	C₂²×C₄	1	24	yes	complemented
162	Dic₃₀	C₂²×C₄	1	4	yes	complemented
163	C₂×C₅×Dic₃	—	4	6	no	—
164	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
165	C₂×C₅×Dic₃	C₂⁴	1	6	yes	—
166	C₂×C₃×Dic₅	—	2	6	no	—
167	C₂×C₃×Dic₅	—	4	3	no	—
168	C₂×C₃×Dic₅	C₂⁴	1	3	yes	—
169	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
170	C₂×C₃×Dic₅	C₂⁴	1	3	yes	—
171	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
172	#1200	—	2	12	no	—
173	#1200	—	4	12	no	—
174	#1200	—	4	6	no	—
175	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
176	#1009	—	5	16	no	—
177	C₂×#239	—	5	2	no	—
178	C₂×D₃×D₄	—	5	6	no	—
179	C₂×#235	—	5	3	no	—
180	C₂²×D₁₂	—	5	3	no	—
181	C₂²×C₄×D₃	—	5	6	no	—
182	C₃×C₄×Q₈	—	5	1	no	—
183	C₃×C₄×Q₈	—	5	1	no	—
184	C₃×C₄×D₄	—	5	3	no	—
185	C₃×C₄×D₄	—	5	3	no	—
186	C₃×#117	—	5	3	no	—
187	C₂×C₃×C₄²	—	5	3	no	—
188	Q₈×Dic₃	C₂×D₅	1	2	yes	complemented
189	D₄×Dic₃	C₂×D₅	1	6	yes	complemented
190	C₄×#67	—	5	6	no	—
191	C₄×#67	—	5	6	no	—
192	C₂×(C₂×D₃)⋊C₄	—	5	6	no	—
193	#926	C₂×D₅	1	3	yes	complemented
194	C₂×C₄⋊Dic₃	C₂×D₅	1	3	yes	complemented
195	#893	—	5	6	no	—
196	#893	—	5	6	no	—
197	#892	—	5	6	no	—
198	D₃×C₄⋊C₄	—	5	6	no	—
199	#67⋊C₄	—	5	12	no	—
200	D₃×C₂²⋊C₄	—	5	12	no	—
201	C₄×D₁₂	—	5	3	no	—
202	C₄×D₁₂	—	5	6	no	—
203	C₄×D₁₂	—	5	6	no	—
204	C₄×D₁₂	—	5	6	no	—
205	C₄×D₁₂	—	5	3	no	—
206	#872	—	5	6	no	—
207	C₄²×D₃	—	5	6	no	—
208	C₄×Dic₆	—	5	1	no	—
209	C₄×Dic₆	—	5	3	no	—
210	C₂³×D₅	—	3	6	no	—
211	C₅×#41	C₄×D₃	1	8	yes	complemented
212	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
213	C₂×C₅×D₄	C₂²×D₃	1	3	yes	—
214	C₂²×C₄×C₅	—	3	6	no	—
215	C₂²×C₄×C₅	C₂²×D₃	1	3	yes	—
216	C₂×C₂²⋊D₅	—	3	6	no	—
217	C₂²×Dic₅	C₂²×D₃	1	3	yes	—
218	C₂²×Dic₅	C₂²×D₃	1	3	yes	—
219	#713	—	3	16	no	—
220	D₄×D₅	—	3	48	no	—
221	#709	—	3	24	no	—
222	C₂×D₂₀	—	3	24	no	—
223	C₂×D₂₀	—	3	3	no	—
224	C₂×D₂₀	—	3	6	no	—
225	C₂×C₄×D₅	—	3	6	no	—
226	C₂×C₄×D₅	—	3	6	no	—
227	C₂×C₄×D₅	—	3	12	no	—
228	C₂×C₄×D₅	—	3	6	no	—
229	C₂×C₄×D₅	—	12	12	no	—
230	C₂×Dic₁₀	—	3	1	no	—
231	C₅×C₄⋊C₄	—	3	3	no	—
232	C₅×C₄⋊C₄	—	3	6	no	—
233	C₅×C₄⋊C₄	—	3	1	no	—
234	C₅×C₂²⋊C₄	—	3	6	no	—
235	C₄²×C₅	—	3	6	no	—
236	C₂²⋊Dic₅	C₂²×D₃	1	6	yes	—
237	#685	—	3	6	no	—
238	#685	—	3	6	no	—
239	#685	—	3	12	no	—
240	C₄⋊Dic₅	C₂²×D₃	1	3	yes	—
241	C₄⋊Dic₅	C₂²×D₃	1	3	yes	—
242	#683	—	3	2	no	—
243	#683	—	3	6	no	—
244	C₄×Dic₅	—	3	2	no	—
245	C₄×Dic₅	—	3	6	no	—
246	C₄×Dic₅	C₂²×D₃	1	3	yes	—
247	C₄×Dic₅	C₂²×D₃	1	3	yes	—
248	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
249	C₄×Dic₅	C₂²×D₃	1	3	yes	—
250	C₂×H(5,𝔽₂)	—	15	1	no	—
251	#520	—	3	1	no	—
252	#520	—	15	3	no	—
253	#520	—	15	2	no	—
254	#518	—	15	3	no	—
255	#518	—	15	6	no	—
256	C₄×#41	—	5	1	no	—
257	C₄×#41	—	15	3	no	—
258	C₄×#41	—	15	2	no	—
259	C₂×C₄×D₄	—	15	3	no	—
260	C₂×C₄×D₄	—	15	6	no	—
261	C₂²×C₃×C₅	—	2	3	no	—
262	C₂²×C₃×C₅	—	2	3	no	—
263	C₂²×C₃×C₅	C₂³×C₄	1	6	yes	—
264	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
265	C₂×D₁₅	—	2	6	no	—
266	C₂×D₁₅	—	2	6	no	—
267	C₂×D₁₅	—	4	24	no	—
268	C₂×D₁₅	C₂³×C₄	1	12	yes	—
269	C₃×C₄×C₅	C₂³×C₄	1	2	yes	—
270	C₃×C₄×C₅	C₂³×C₄	1	6	yes	—
271	Dic₁₅	C₂³×C₄	1	4	yes	—
272	C₃×Dic₅	—	2	3	no	—
273	C₃×Dic₅	—	2	3	no	—
274	C₃×Dic₅	—	2	1	no	—
275	C₃×Dic₅	H(5,𝔽₂)	1	2	yes	complemented
276	C₅×Dic₃	—	2	6	no	—
277	C₅×Dic₃	—	2	2	no	—
278	C₂³×D₃	—	5	6	no	—
279	C₃×#41	C₄×D₅	1	8	yes	complemented
280	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
281	C₂×C₃×D₄	C₂²×D₅	1	3	yes	—
282	C₂²×C₃×C₄	—	5	3	no	—
283	C₂²×C₃×C₄	—	5	3	no	—
284	C₂²×C₃×C₄	C₂²×D₅	1	3	yes	—
285	C₂×#67	—	5	6	no	—
286	C₂²×Dic₃	C₂²×D₅	1	6	yes	—
287	#239	—	5	16	no	—
288	D₃×D₄	—	5	48	no	—
289	#235	—	5	24	no	—
290	C₂×D₁₂	—	5	24	no	—
291	C₂×D₁₂	—	5	3	no	—
292	C₂×D₁₂	—	5	6	no	—
293	C₂×C₄×D₃	—	5	6	no	—
294	C₂×C₄×D₃	—	5	6	no	—
295	C₂×C₄×D₃	—	5	6	no	—
296	C₂×C₄×D₃	—	5	12	no	—
297	C₂×C₄×D₃	—	20	12	no	—
298	C₂×Dic₆	—	5	1	no	—
299	C₃×C₄⋊C₄	—	5	3	no	—
300	C₃×C₄⋊C₄	—	5	3	no	—
301	C₃×C₂²⋊C₄	—	5	6	no	—
302	C₃×C₄²	—	5	1	no	—
303	C₃×C₄²	—	5	3	no	—
304	C₃×C₄²	—	5	3	no	—
305	C₃×C₄²	—	5	3	no	—
306	#217	C₂²×D₅	1	6	yes	—
307	(C₂×D₃)⋊C₄	—	5	6	no	—
308	(C₂×D₃)⋊C₄	—	5	6	no	—
309	(C₂×D₃)⋊C₄	—	5	12	no	—
310	C₄⋊Dic₃	C₂²×D₅	1	3	yes	—
311	C₄⋊Dic₃	C₂²×D₅	1	1	yes	characteristic
312	C₄⋊Dic₃	C₂²×D₅	1	6	yes	—
313	Dic₃⋊C₄	—	5	2	no	—
314	Dic₃⋊C₄	—	5	6	no	—
315	C₄×Dic₃	—	5	2	no	—
316	C₄×Dic₃	—	5	6	no	—
317	C₄×Dic₃	C₂²×D₅	1	6	yes	—
318	C₂³×C₅	C₂³×D₃	1	3	yes	—
319	C₂²×D₅	—	3	6	no	—
320	C₂²×D₅	—	3	24	no	—
321	C₂²×D₅	—	12	6	no	—
322	C₂²×D₅	—	12	6	no	—
323	C₅×Q₈	C₂×C₄×D₃	1	4	yes	complemented
324	C₅×D₄	C₂×C₄×D₃	1	12	yes	complemented
325	C₂×C₄×C₅	—	3	2	no	—
326	C₂×C₄×C₅	—	3	6	no	—
327	C₂×C₄×C₅	—	12	6	no	—
328	C₂×C₄×C₅	C₂×C₄×D₃	1	12	yes	complemented
329	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
330	C₂×C₄×C₅	C₂³×D₃	1	3	yes	—
331	C₂²⋊D₅	—	3	24	no	—
332	C₂×Dic₅	—	2	6	no	—
333	C₂×Dic₅	—	3	2	no	—
334	C₂×Dic₅	—	4	3	no	—
335	C₂×Dic₅	C₂³×D₃	1	3	yes	—
336	C₂×Dic₅	C₂³×D₃	1	1	yes	characteristic
337	C₂×Dic₅	C₂³×D₃	1	3	yes	—
338	C₂×Dic₅	C₂³×D₃	1	1	yes	characteristic
339	D₂₀	—	3	12	no	—
340	D₂₀	—	3	24	no	—
341	C₄×D₅	—	3	24	no	—
342	C₄×D₅	—	6	12	no	—
343	C₄×D₅	—	12	6	no	—
344	C₄×D₅	—	12	12	no	—
345	Dic₁₀	—	3	4	no	—
346	H(5,𝔽₂)	—	15	16	no	—
347	C₂×#41	—	15	2	no	—
348	C₂×#41	—	15	3	no	—
349	C₂×#41	D₃×D₅	1	1	yes	characteristic
350	C₂²×D₄	—	15	6	no	—
351	C₂²×D₄	—	15	3	no	—
352	C₂³×C₄	—	15	6	no	—
353	C₄×Q₈	—	3	2	no	—
354	C₄×Q₈	—	5	1	no	—
355	C₄×Q₈	—	5	1	no	—
356	C₄×Q₈	—	15	1	no	—
357	C₄×Q₈	—	15	3	no	—
358	C₄×D₄	—	3	6	no	—
359	C₄×D₄	—	5	3	no	—
360	C₄×D₄	—	5	3	no	—
361	C₄×D₄	—	15	6	no	—
362	C₄×D₄	—	15	6	no	—
363	C₄×D₄	—	15	3	no	—
364	C₄×D₄	—	15	6	no	—
365	C₄×D₄	—	15	6	no	—
366	C₄×D₄	—	15	6	no	—
367	C₄×D₄	—	15	3	no	—
368	C₄×D₄	—	15	6	no	—
369	C₄×D₄	—	15	6	no	—
370	C₄×D₄	—	15	12	no	—
371	#117	—	3	3	no	—
372	#117	—	5	3	no	—
373	#117	—	15	6	no	—
374	#117	—	15	6	no	—
375	C₂×C₄⋊C₄	—	3	3	no	—
376	C₂×C₄⋊C₄	—	15	6	no	—
377	C₂×C₂²⋊C₄	—	15	12	no	—
378	C₂×C₂²⋊C₄	—	15	6	no	—
379	C₂×C₄²	—	5	3	no	—
380	C₂×C₄²	—	15	6	no	—
381	C₂×C₃×C₅	—	2	6	no	—
382	C₂×C₃×C₅	C₂⁴×C₄	1	1	yes	characteristic
383	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
384	C₂×C₃×C₅	#585	1	1	yes	characteristic
385	D₁₅	—	2	12	no	—
386	C₂³×C₃	C₂³×D₅	1	3	yes	—
387	C₂²×D₃	—	5	6	no	—
388	C₂²×D₃	—	5	24	no	—
389	C₂²×D₃	—	20	6	no	—
390	C₂²×D₃	—	20	6	no	—
391	C₃×Q₈	C₂×C₄×D₅	1	4	yes	complemented
392	C₃×D₄	C₂×C₄×D₅	1	12	yes	complemented
393	C₂×C₃×C₄	—	5	1	no	—
394	C₂×C₃×C₄	—	5	3	no	—
395	C₂×C₃×C₄	—	5	1	no	—
396	C₂×C₃×C₄	—	5	3	no	—
397	C₂×C₃×C₄	—	10	6	no	—
398	C₂×C₃×C₄	—	20	3	no	—
399	C₂×C₃×C₄	C₂×C₄×D₅	1	12	yes	complemented
400	C₂×C₃×C₄	C₂³×D₅	1	3	yes	—
401	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
402	#67	—	5	24	no	—
403	C₂×Dic₃	—	4	6	no	—
404	C₂×Dic₃	—	5	2	no	—
405	C₂×Dic₃	C₂³×D₅	1	2	yes	—
406	C₂×Dic₃	C₂³×D₅	1	6	yes	—
407	D₁₂	—	5	12	no	—
408	D₁₂	—	5	24	no	—
409	C₄×D₃	—	5	24	no	—
410	C₄×D₃	—	10	12	no	—
411	C₄×D₃	—	20	6	no	—
412	C₄×D₃	—	20	12	no	—
413	Dic₆	—	5	4	no	—
414	C₂²×C₅	—	2	3	no	—
415	C₂²×C₅	—	2	3	no	—
416	C₂²×C₅	C₂²×C₄×D₃	1	6	yes	—
417	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
418	C₂×D₅	—	3	12	no	—
419	C₂×D₅	—	6	6	no	—
420	C₂×D₅	—	6	6	no	—
421	C₂×D₅	—	12	24	no	—
422	C₄×C₅	—	6	6	no	—
423	C₄×C₅	—	6	2	no	—
424	C₄×C₅	C₂²×C₄×D₃	1	2	yes	—
425	C₄×C₅	C₂²×C₄×D₃	1	6	yes	—
426	Dic₅	—	2	3	no	—
427	Dic₅	—	2	3	no	—
428	Dic₅	—	2	1	no	—
429	Dic₅	—	3	4	no	—
430	Dic₅	#1009	1	2	yes	complemented
431	C₂⁴	—	15	6	no	—
432	#41	—	15	16	no	—
433	#41	—	15	24	no	—
434	#41	#1200	1	8	yes	complemented
435	C₂×Q₈	—	15	1	no	—
436	C₂×Q₈	C₂×D₃×D₅	1	1	yes	characteristic
437	C₂×D₄	—	15	6	no	—
438	C₂×D₄	—	15	48	no	—
439	C₂×D₄	—	15	24	no	—
440	C₂×D₄	—	15	6	no	—
441	C₂×D₄	—	15	3	no	—
442	C₂×D₄	C₂×D₃×D₅	1	3	yes	—
443	C₂²×C₄	—	3	6	no	—
444	C₂²×C₄	—	5	3	no	—
445	C₂²×C₄	—	5	3	no	—
446	C₂²×C₄	—	15	6	no	—
447	C₂²×C₄	—	15	6	no	—
448	C₂²×C₄	—	15	12	no	—
449	C₂²×C₄	—	15	6	no	—
450	C₂²×C₄	—	60	12	no	—
451	C₂²×C₄	C₂×D₃×D₅	1	3	yes	—
452	C₄⋊C₄	—	3	3	no	—
453	C₄⋊C₄	—	3	6	no	—
454	C₄⋊C₄	—	3	1	no	—
455	C₄⋊C₄	—	5	3	no	—
456	C₄⋊C₄	—	5	3	no	—
457	C₄⋊C₄	—	15	6	no	—
458	C₄⋊C₄	—	15	2	no	—
459	C₂²⋊C₄	—	3	6	no	—
460	C₂²⋊C₄	—	5	6	no	—
461	C₂²⋊C₄	—	15	6	no	—
462	C₂²⋊C₄	—	15	6	no	—
463	C₂²⋊C₄	—	15	12	no	—
464	C₄²	—	3	6	no	—
465	C₄²	—	5	1	no	—
466	C₄²	—	5	3	no	—
467	C₄²	—	5	3	no	—
468	C₄²	—	5	3	no	—
469	C₄²	—	15	2	no	—
470	C₄²	—	15	6	no	—
471	C₃×C₅	C₄×H(5,𝔽₂)	1	1	yes	characteristic, complemented, Hall
472	C₂²×C₃	—	2	3	no	—
473	C₂²×C₃	—	2	3	no	—
474	C₂²×C₃	C₂²×C₄×D₅	1	6	yes	—
475	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
476	C₂×D₃	—	5	12	no	—
477	C₂×D₃	—	10	6	no	—
478	C₂×D₃	—	10	6	no	—
479	C₂×D₃	—	20	24	no	—
480	C₃×C₄	—	5	2	no	—
481	C₃×C₄	—	10	3	no	—
482	C₃×C₄	—	10	3	no	—
483	C₃×C₄	—	10	1	no	—
484	C₃×C₄	C₂²×C₄×D₅	1	2	yes	—
485	C₃×C₄	C₂²×C₄×D₅	1	6	yes	—
486	Dic₃	—	2	6	no	—
487	Dic₃	—	2	2	no	—
488	Dic₃	—	5	4	no	—
489	C₂×C₅	—	2	6	no	—
490	C₂×C₅	C₂³×C₄×D₃	1	1	yes	characteristic
491	C₂×C₅	C₂×#1009	1	1	yes	characteristic
492	C₂×C₅	#5964	1	1	yes	characteristic
493	D₅	—	6	12	no	—
494	C₂³	—	15	6	no	—
495	C₂³	—	15	24	no	—
496	C₂³	—	60	6	no	—
497	C₂³	—	60	6	no	—
498	C₂³	C₂²×D₃×D₅	1	3	yes	—
499	Q₈	—	15	4	no	—
500	Q₈	C₂×#1200	1	4	yes	complemented
501	D₄	—	15	24	no	—
502	D₄	—	15	24	no	—
503	D₄	—	15	12	no	—
504	D₄	C₂×#1200	1	12	yes	complemented
505	C₂×C₄	—	3	2	no	—
506	C₂×C₄	—	3	6	no	—
507	C₂×C₄	—	5	1	no	—
508	C₂×C₄	—	5	1	no	—
509	C₂×C₄	—	5	3	no	—
510	C₂×C₄	—	5	3	no	—
511	C₂×C₄	—	10	6	no	—
512	C₂×C₄	—	12	6	no	—
513	C₂×C₄	—	15	2	no	—
514	C₂×C₄	—	15	24	no	—
515	C₂×C₄	—	20	3	no	—
516	C₂×C₄	—	30	12	no	—
517	C₂×C₄	—	60	12	no	—
518	C₂×C₄	—	60	6	no	—
519	C₂×C₄	C₂×#1200	1	12	yes	complemented
520	C₂×C₄	C₂²×D₃×D₅	1	3	yes	—
521	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
522	C₂×C₃	—	2	6	no	—
523	C₂×C₃	C₂³×C₄×D₅	1	1	yes	characteristic
524	C₂×C₃	D₅×H(5,𝔽₂)	1	1	yes	characteristic
525	C₂×C₃	#66287	1	1	yes	characteristic
526	D₃	—	10	12	no	—
527	C₅	C₄×#1009	1	1	yes	characteristic, complemented, Sylow
528	C₂²	—	2	3	no	—
529	C₂²	—	2	3	no	—
530	C₂²	—	15	12	no	—
531	C₂²	—	30	6	no	—
532	C₂²	—	30	6	no	—
533	C₂²	—	60	24	no	—
534	C₂²	C₂²×#1200	1	6	yes	—
535	C₂²	C₂³×D₃×D₅	1	1	yes	characteristic
536	C₄	—	5	2	no	—
537	C₄	—	6	2	no	—
538	C₄	—	6	6	no	—
539	C₄	—	10	1	no	—
540	C₄	—	10	3	no	—
541	C₄	—	10	3	no	—
542	C₄	—	15	4	no	—
543	C₄	C₂²×#1200	1	6	yes	—
544	C₄	C₂²×#1200	1	2	yes	—
545	C₃	#10617787	1	1	yes	characteristic, complemented, Sylow
546	C₂	—	2	6	no	—
547	C₂	—	30	12	no	—
548	C₂	D₅×#1009	1	1	yes	characteristic
549	C₂	#11757060	1	1	yes	characteristic
550	C₂	C₂³×#1200	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₃×D₅
commutator	C₂×C₃×C₅	C₂⁴×C₄
Fitting	C₂×C₃×C₅×#41	C₂²
socle, cosocle	C₂²×C₃×C₅	C₂⁵
prime radical	C₂×#92100	C₂
hypercenter	C₂×#41	D₃×D₅
hypocenter	C₃×C₅	C₄×H(5,𝔽₂)
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₂×#41

Complements

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

N	H ≅ G/N	type
2. C₅×#5827	C₂	semidirect
3. C₃×#41×Dic₅	C₂	semidirect
4. #11755200	C₂	semidirect
5. #11755149	C₂	semidirect
6. #11754922	C₂	semidirect
7. D₄×#1200	C₂	semidirect
8. #11754515	C₂	semidirect
9. #11754506	C₂	semidirect
10. #11754414	C₂	semidirect
11. C₂×#91418	C₂	semidirect
14. #92100	C₄	semidirect
19. C₂²×#1200	C₂²	semidirect
20. C₅×Q₈×Dic₃	C₂²	semidirect
21. C₅×D₄×Dic₃	C₂²	semidirect
22. C₅×#926	C₂²	semidirect
23. C₂×C₅×C₄⋊Dic₃	C₂²	semidirect
24. C₃×Q₈×Dic₅	C₂²	semidirect
25. C₃×Q₈×Dic₅	C₂²	semidirect
26. C₃×D₄×Dic₅	C₂²	semidirect
27. C₃×D₄×Dic₅	C₂²	semidirect
28. C₃×#4072	C₂²	semidirect
29. C₂×C₃×C₄×Dic₅	C₂²	semidirect
30. #91561	C₂²	semidirect
31. #91556	C₂²	semidirect
32. #91552	C₂²	semidirect
33. #91552	C₂²	semidirect
34. C₂×#6667	C₂²	semidirect
35. #91437	C₂²	semidirect
36. #91428	C₂²	semidirect
37. #91428	C₂²	semidirect
38. #91418	C₂²	semidirect
39. #91418	C₂²	semidirect
40. #91418	C₂²	semidirect
41. #91418	C₂²	semidirect
42. #91418	C₂²	semidirect
43. C₄×#1200	C₂²	semidirect
44. #91386	C₂²	semidirect
45. #91347	C₂²	semidirect
46. #91333	C₂²	semidirect
47. #91333	C₂²	semidirect
51. #41×Dic₅	D₃	semidirect
61. C₃×C₅×#41	C₂×C₄	semidirect
66. #6821	C₂×C₄	semidirect
67. D₄×D₁₅	C₂×C₄	semidirect
68. #6817	C₂×C₄	semidirect
69. C₂×D₆₀	C₂×C₄	semidirect
102. #5827	D₅	semidirect
122. Q₈×Dic₅	C₂×D₃	semidirect
123. Q₈×Dic₅	C₂×D₃	semidirect
124. D₄×Dic₅	C₂×D₃	semidirect
125. D₄×Dic₅	C₂×D₃	semidirect
128. #4072	C₂×D₃	semidirect
129. C₂×C₄×Dic₅	C₂×D₃	semidirect
150. C₂²×D₁₅	C₂²×C₄	semidirect
152. C₃×C₅×Q₈	C₂²×C₄	semidirect
153. C₃×C₅×D₄	C₂²×C₄	semidirect
154. C₂×C₃×C₄×C₅	C₂²×C₄	semidirect
157. #1220	C₂²×C₄	semidirect
159. D₆₀	C₂²×C₄	semidirect
160. D₆₀	C₂²×C₄	semidirect
161. C₄×D₁₅	C₂²×C₄	semidirect
162. Dic₃₀	C₂²×C₄	semidirect
188. Q₈×Dic₃	C₂×D₅	semidirect
189. D₄×Dic₃	C₂×D₅	semidirect
193. #926	C₂×D₅	semidirect
194. C₂×C₄⋊Dic₃	C₂×D₅	semidirect
211. C₅×#41	C₄×D₃	semidirect
275. C₃×Dic₅	H(5,𝔽₂)	semidirect
279. C₃×#41	C₄×D₅	semidirect
323. C₅×Q₈	C₂×C₄×D₃	semidirect
324. C₅×D₄	C₂×C₄×D₃	semidirect
328. C₂×C₄×C₅	C₂×C₄×D₃	semidirect
391. C₃×Q₈	C₂×C₄×D₅	semidirect
392. C₃×D₄	C₂×C₄×D₅	semidirect
399. C₂×C₃×C₄	C₂×C₄×D₅	semidirect
430. Dic₅	#1009	semidirect
434. #41	#1200	semidirect
471. C₃×C₅	C₄×H(5,𝔽₂)	semidirect
500. Q₈	C₂×#1200	semidirect
504. D₄	C₂×#1200	semidirect
519. C₂×C₄	C₂×#1200	semidirect
527. C₅	C₄×#1009	semidirect
545. C₃	#10617787	semidirect

Maximal subgroups

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

subgroup	index
C₂×#92100	2
C₅×#5827	2
C₃×#41×Dic₅	2
#11755200	2
#11755149	2
#11754922	2
D₄×#1200	2
#11754515	2
#11754506	2
#11754414	2
C₂×#91418	2
#10617787	3
C₄×#1009	5