Subgroups — #14415012

Order 1920.

1040 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₈×D₅	C₂	1	1	yes	maximal, characteristic, complemented
2	#11754525	C₂	1	1	yes	maximal, characteristic
3	C₂×#91266	C₂	1	1	yes	maximal, characteristic, complemented
4	#11751212	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5111	C₂	1	1	yes	maximal, characteristic, complemented
6	#11748499	C₂	1	1	yes	maximal, characteristic, complemented
7	#11748485	C₂	1	1	yes	maximal, characteristic, complemented
8	#67×#168	C₂	1	1	yes	maximal, characteristic, complemented
9	#11748134	C₂	1	1	yes	maximal, characteristic, complemented
10	#11747705	C₂	1	1	yes	maximal, characteristic, complemented
11	#11747701	C₂	1	1	yes	maximal, characteristic, complemented
12	#11747698	C₂	1	1	yes	maximal, characteristic, complemented
13	#11747694	C₂	1	1	yes	maximal, characteristic, complemented
14	#11747647	C₂	1	1	yes	maximal, characteristic, complemented
15	#11747646	C₂	1	1	yes	maximal, characteristic, complemented
16	#10611209	—	3	1	no	maximal, Hall
17	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
18	C₂×#6771	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
20	C₄×#1220	C₂²	1	1	yes	characteristic
21	C₂×#6705	C₂²	1	1	yes	characteristic, complemented
22	C₄×C₅×#67	C₂²	1	1	yes	characteristic
23	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic, complemented
24	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₈×D₅	—	2	4	no	—
26	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
30	#91574	C₄	1	1	yes	characteristic
31	#91566	C₄	1	1	yes	characteristic
32	#91564	C₄	1	1	yes	characteristic
33	#91563	C₄	1	1	yes	characteristic
34	#91448	C₄	1	1	yes	characteristic
35	#91447	C₄	1	1	yes	characteristic
36	C₄×#1202	C₂²	1	1	yes	characteristic
37	C₄×#1201	C₂²	1	1	yes	characteristic
38	#91357	C₂²	1	1	yes	characteristic
39	#91349	C₄	1	1	yes	characteristic
40	#91348	C₄	1	1	yes	characteristic
41	C₂×#6649	C₂²	1	1	yes	characteristic
42	C₂×#6649	C₂²	1	1	yes	characteristic
43	C₂×#6648	C₂²	1	1	yes	characteristic, complemented
44	C₂×D₃×#168	C₂²	1	1	yes	characteristic, complemented
45	#91266	—	2	4	no	—
46	#91114	C₂²	1	1	yes	characteristic
47	#91104	C₂²	1	1	yes	characteristic, complemented
48	#91099	C₂²	1	1	yes	characteristic, complemented
49	#91098	C₂²	1	1	yes	characteristic, complemented
50	C₅×#830	C₂²	1	1	yes	characteristic
51	C₅×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
52	C₅×#815	C₂²	1	1	yes	characteristic, complemented
53	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
54	Dic₃⋊#168	C₂²	1	1	yes	characteristic, complemented
55	#90983	C₂²	1	1	yes	characteristic, complemented
56	#90957	C₂²	1	1	yes	characteristic, complemented
57	(C₂×D₃)⋊#168	C₂²	1	1	yes	characteristic, complemented
58	#90955	C₂²	1	1	yes	characteristic
59	#90955	C₂²	1	1	yes	characteristic
60	#90951	C₂²	1	1	yes	characteristic, complemented
61	Dic₃×#168	C₂²	1	1	yes	characteristic, complemented
62	#83734	—	5	1	no	maximal, Hall
63	C₂×#4053	—	3	1	no	—
64	C₂²×C₈×D₅	D₃	1	1	yes	characteristic, complemented
65	#65881	—	3	1	no	—
66	C₅×#435	—	3	1	no	—
67	#65416	—	3	1	no	—
68	#65400	—	3	1	no	—
69	D₄×#168	—	3	1	no	—
70	#65128	—	3	1	no	—
71	#65123	—	3	1	no	—
72	#65016	—	3	1	no	—
73	#65015	—	3	1	no	—
74	#65014	—	3	1	no	—
75	#65014	—	3	1	no	—
76	#64997	—	3	1	no	—
77	#64995	—	3	1	no	—
78	C₂³×C₃×D₅	C₂×C₄	1	1	yes	characteristic
79	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
80	C₂×#1220	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄×D₁₅	C₂³	1	1	yes	characteristic
82	C₂×C₅×#67	C₂×C₄	1	1	yes	characteristic
83	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
84	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
85	C₂×C₃×C₄×D₅	—	2	2	no	—
86	C₂×C₃×C₄×D₅	—	2	2	no	—
87	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
88	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
89	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
90	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
91	C₂×#1204	C₂×C₄	1	1	yes	characteristic
92	C₂×#1203	C₂×C₄	1	1	yes	characteristic
93	C₂×#1202	C₂×C₄	1	1	yes	characteristic
94	C₂×#1202	C₂×C₄	1	1	yes	characteristic
95	C₂×#1201	C₂×C₄	1	1	yes	characteristic
96	C₂×#1201	C₂×C₄	1	1	yes	characteristic
97	#6771	—	2	2	no	—
98	#6771	—	2	2	no	—
99	C₂×C₃×C₅×C₈	—	2	2	no	—
100	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
101	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
102	#6719	C₂×C₄	1	1	yes	characteristic
103	#6714	C₂×C₄	1	1	yes	characteristic
104	#6712	C₂×C₄	1	1	yes	characteristic
105	C₄×Dic₁₅	C₂³	1	1	yes	characteristic
106	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
107	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
108	#6705	—	2	2	no	—
109	C₅×#217	C₂×C₄	1	1	yes	characteristic
110	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
111	C₅×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
112	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
113	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
114	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
115	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
116	C₂×C₃×#168	—	2	2	no	—
117	C₂×C₃×#168	C₂³	1	1	yes	characteristic
118	C₂×C₃×#168	C₂³	1	1	yes	characteristic
119	C₃×C₈×D₅	—	2	2	no	—
120	C₃×C₈×D₅	—	2	2	no	—
121	C₃×C₈×D₅	—	2	2	no	—
122	C₃×C₈×D₅	D₄	1	4	yes	complemented
123	Dic₃⋊Dic₅	C₂×C₄	1	1	yes	characteristic
124	#6669	C₂×C₄	1	1	yes	characteristic
125	#6668	C₂×C₄	1	1	yes	characteristic
126	#6668	C₂×C₄	1	1	yes	characteristic
127	#6667	C₂×C₄	1	1	yes	characteristic
128	(C₂×D₃)⋊Dic₅	C₂×C₄	1	1	yes	characteristic
129	#6665	C₂×C₄	1	1	yes	characteristic
130	#6665	C₂×C₄	1	1	yes	characteristic
131	#6665	C₂×C₄	1	1	yes	characteristic
132	#6665	C₂×C₄	1	1	yes	characteristic
133	#6649	—	2	2	no	—
134	#6649	—	2	2	no	—
135	#6648	—	2	2	no	—
136	D₃×#168	—	2	2	no	—
137	C₂³×C₃×C₈	—	5	1	no	—
138	#5791	—	5	1	no	—
139	C₂×#901	—	5	1	no	—
140	#5207	—	5	1	no	—
141	#5111	—	5	1	no	—
142	#5111	—	5	1	no	—
143	#5111	—	5	1	no	—
144	#5111	D₅	1	1	yes	characteristic, complemented
145	#5110	—	5	1	no	—
146	C₈×#67	—	5	1	no	—
147	C₈×#67	—	5	1	no	—
148	C₈×#67	—	5	1	no	—
149	C₈×#67	—	5	1	no	—
150	#5102	—	5	1	no	—
151	#5101	—	5	1	no	—
152	C₂×#709	—	3	1	no	—
153	C₂²×C₄×D₅	C₂×D₃	1	1	yes	characteristic
154	C₂×C₅×M₁₆	—	3	1	no	—
155	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
156	C₄×C₅×D₄	—	3	1	no	—
157	#4085	—	3	1	no	—
158	#4083	—	3	1	no	—
159	C₄×C₂²⋊D₅	—	3	1	no	—
160	C₄×C₂²⋊D₅	—	3	1	no	—
161	C₂²×#168	—	3	1	no	—
162	C₂²×#168	C₂×D₃	1	1	yes	characteristic
163	#4053	—	6	4	no	—
164	C₂×#676	—	3	1	no	—
165	C₂×#676	—	3	1	no	—
166	C₂×#676	—	3	1	no	—
167	C₂×C₈×D₅	—	2	4	no	—
168	C₂×C₈×D₅	—	3	1	no	—
169	C₂×C₈×D₅	C₂×D₃	1	1	yes	characteristic
170	C₂×C₈×D₅	C₂×D₃	1	1	yes	characteristic
171	C₂×C₈×D₅	C₂×D₃	1	1	yes	characteristic
172	C₂×C₈×D₅	C₂×D₃	1	1	yes	characteristic
173	#4042	—	3	1	no	—
174	#4040	—	3	1	no	—
175	#4030	—	3	1	no	—
176	#4029	—	3	1	no	—
177	#4028	—	3	1	no	—
178	#4024	—	3	1	no	—
179	C₄×D₂₀	—	3	1	no	—
180	#4018	—	3	1	no	—
181	C₅×C₄⋊C₈	—	3	1	no	—
182	C₅×C₂²⋊C₈	—	3	1	no	—
183	C₅×C₂²⋊C₈	—	3	1	no	—
184	C₅×#97	—	3	1	no	—
185	C₂²⋊#168	—	3	1	no	—
186	C₂²⋊#168	—	3	1	no	—
187	#3952	—	3	1	no	—
188	#3952	—	3	1	no	—
189	#3952	—	3	1	no	—
190	#3952	—	3	1	no	—
191	#3947	—	3	1	no	—
192	#3946	—	3	1	no	—
193	#3946	—	3	1	no	—
194	C₈×Dic₅	—	3	1	no	—
195	C₄⋊#168	—	3	1	no	—
196	C₄×#168	—	3	1	no	—
197	#2929	—	15	1	no	Sylow
198	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
199	C₂²×D₁₅	C₂²×C₄	1	1	yes	characteristic
200	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
201	C₂²×C₃×D₅	—	2	2	no	—
202	C₂²×C₃×D₅	—	2	2	no	—
203	C₂²×C₃×D₅	—	2	2	no	—
204	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
205	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
206	C₂×C₃×C₄×C₅	—	2	1	no	—
207	C₂×C₃×C₄×C₅	—	2	1	no	—
208	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
209	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
210	#1220	—	2	2	no	—
211	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
212	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
213	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
214	C₄×D₁₅	—	2	1	no	—
215	C₄×D₁₅	—	2	1	no	—
216	C₅×#67	—	2	2	no	—
217	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
218	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
219	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
220	C₄×C₅×D₃	—	2	1	no	—
221	C₄×C₅×D₃	—	2	1	no	—
222	C₂×C₃×Dic₅	—	2	2	no	—
223	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
224	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
225	C₃×C₄×D₅	—	2	2	no	—
226	C₃×C₄×D₅	—	2	1	no	—
227	C₃×C₄×D₅	—	2	1	no	—
228	C₃×C₄×D₅	—	2	2	no	—
229	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
230	C₃×C₄×D₅	#41	1	2	yes	—
231	#1204	—	2	2	no	—
232	#1203	—	2	2	no	—
233	#1202	—	2	2	no	—
234	#1202	—	2	2	no	—
235	#1201	—	2	2	no	—
236	#1201	—	2	2	no	—
237	C₃×C₅×C₈	—	2	1	no	—
238	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
239	C₃⋊#168	—	2	1	no	—
240	C₃⋊#168	—	2	1	no	—
241	C₃×#168	—	2	1	no	—
242	C₃×#168	C₂×D₄	1	2	yes	—
243	C₅×C₃⋊C₈	—	2	1	no	—
244	C₅×C₃⋊C₈	—	2	1	no	—
245	C₂³×C₃×C₄	—	5	1	no	—
246	C₂×#235	—	5	1	no	—
247	C₂²×C₃×C₈	—	5	1	no	—
248	C₂²×C₃×C₈	—	5	1	no	—
249	C₂²×C₃×C₈	—	5	1	no	—
250	C₂²×C₃×C₈	—	5	1	no	—
251	C₂²×C₃×C₈	—	5	1	no	—
252	C₂²×C₃×C₈	—	10	4	no	—
253	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
254	#953	—	5	1	no	—
255	#953	—	5	1	no	—
256	#930	—	5	1	no	—
257	#930	—	5	1	no	—
258	#929	—	5	1	no	—
259	#929	—	5	1	no	—
260	C₄×#67	—	5	1	no	—
261	C₄×#67	—	5	1	no	—
262	C₄×#67	—	5	1	no	—
263	C₄×#67	C₂×D₅	1	1	yes	characteristic
264	#926	—	5	1	no	—
265	#924	—	5	1	no	—
266	#924	—	5	1	no	—
267	C₂×#208	—	5	1	no	—
268	C₂×#208	—	5	1	no	—
269	#901	—	10	4	no	—
270	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
271	C₂×ΓL(1,𝔽₂₅)	C₂×D₅	1	1	yes	characteristic, complemented
272	C₂×D₃×C₈	—	5	1	no	—
273	C₂×D₃×C₈	—	5	1	no	—
274	#830	—	5	1	no	—
275	#830	—	5	1	no	—
276	#830	—	5	1	no	—
277	#830	C₂×D₅	1	1	yes	characteristic
278	(C₂×D₃)⋊C₈	—	5	1	no	—
279	(C₂×D₃)⋊C₈	—	5	1	no	—
280	(C₂×D₃)⋊C₈	—	5	1	no	—
281	(C₂×D₃)⋊C₈	C₂×D₅	1	1	yes	characteristic, complemented
282	#815	—	5	1	no	—
283	#815	C₂×D₅	1	1	yes	characteristic, complemented
284	Dic₃⋊C₈	—	5	1	no	—
285	Dic₃⋊C₈	—	5	1	no	—
286	Dic₃⋊C₈	—	5	1	no	—
287	Dic₃⋊C₈	C₂×D₅	1	1	yes	characteristic, complemented
288	C₈×Dic₃	—	5	1	no	—
289	C₈×Dic₃	—	5	1	no	—
290	C₂³×D₅	C₄×D₃	1	1	yes	characteristic
291	C₂×C₅×D₄	—	3	1	no	—
292	C₂²×C₄×C₅	—	3	1	no	—
293	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
294	C₂×C₂²⋊D₅	—	3	1	no	—
295	C₂×C₂²⋊D₅	—	3	1	no	—
296	C₂×C₂²⋊D₅	—	3	1	no	—
297	C₂×C₂²⋊D₅	—	3	1	no	—
298	C₂²×Dic₅	C₄×D₃	1	1	yes	characteristic
299	#709	—	6	2	no	—
300	#709	—	6	2	no	—
301	C₂×D₂₀	—	3	1	no	—
302	C₂×D₂₀	—	3	1	no	—
303	C₂×C₄×D₅	—	2	2	no	—
304	C₂×C₄×D₅	—	2	2	no	—
305	C₂×C₄×D₅	—	3	1	no	—
306	C₂×C₄×D₅	C₄×D₃	1	1	yes	characteristic
307	C₂×C₄×D₅	C₄×D₃	1	1	yes	characteristic
308	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
309	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
310	C₂×Dic₁₀	—	3	1	no	—
311	C₅×M₁₆	—	6	2	no	—
312	C₂×C₅×C₈	—	2	2	no	—
313	C₂×C₅×C₈	—	3	1	no	—
314	C₂×C₅×C₈	—	3	1	no	—
315	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
316	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
317	C₅×C₄⋊C₄	—	3	1	no	—
318	C₅×C₂²⋊C₄	—	3	1	no	—
319	C₅×C₂²⋊C₄	—	3	1	no	—
320	C₄²×C₅	—	3	1	no	—
321	C₂²⋊Dic₅	—	3	1	no	—
322	C₂²⋊Dic₅	—	3	1	no	—
323	#685	—	3	1	no	—
324	#685	—	3	1	no	—
325	#685	—	3	1	no	—
326	#685	—	3	1	no	—
327	#685	—	3	1	no	—
328	#685	—	3	1	no	—
329	C₄⋊Dic₅	—	3	1	no	—
330	#683	—	3	1	no	—
331	#683	—	3	1	no	—
332	#683	—	3	1	no	—
333	#683	—	3	1	no	—
334	C₄×Dic₅	—	3	1	no	—
335	C₂×#168	—	2	2	no	—
336	C₂×#168	—	3	1	no	—
337	C₂×#168	—	3	1	no	—
338	C₂×#168	—	6	2	no	—
339	C₂×#168	C₂²×D₃	1	1	yes	characteristic
340	C₂×#168	C₂²×D₃	1	1	yes	characteristic
341	#676	—	6	2	no	—
342	#676	—	6	2	no	—
343	#676	—	6	2	no	—
344	C₈×D₅	—	2	2	no	—
345	C₈×D₅	—	2	2	no	—
346	C₈×D₅	—	2	2	no	—
347	C₈×D₅	—	6	2	no	—
348	C₈×D₅	#67	1	4	yes	complemented
349	C₂×#131	—	15	1	no	—
350	C₂³×C₈	—	5	1	no	—
351	#525	—	15	1	no	—
352	#435	—	3	1	no	—
353	#435	—	15	1	no	—
354	#435	—	15	1	no	—
355	#435	—	15	1	no	—
356	C₈×D₄	—	15	1	no	—
357	C₈×D₄	—	15	1	no	—
358	C₈×D₄	—	15	1	no	—
359	C₈×D₄	—	15	1	no	—
360	#424	—	15	1	no	—
361	#408	—	15	1	no	—
362	#407	—	15	1	no	—
363	#405	—	15	1	no	—
364	C₂²×C₃×C₅	—	2	1	no	—
365	C₂²×C₃×C₅	—	2	1	no	—
366	C₂²×C₃×C₅	#131	1	2	yes	complemented
367	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
368	C₂×D₁₅	—	2	1	no	—
369	C₂×D₁₅	—	2	1	no	—
370	C₂×D₁₅	—	2	1	no	—
371	C₂×C₅×D₃	—	2	1	no	—
372	C₂×C₅×D₃	—	2	1	no	—
373	C₂×C₅×D₃	—	2	1	no	—
374	C₂×C₃×D₅	—	2	8	no	—
375	C₂×C₃×D₅	—	2	1	no	—
376	C₂×C₃×D₅	—	2	1	no	—
377	C₂×C₃×D₅	—	2	1	no	—
378	C₂×C₃×D₅	—	2	1	no	—
379	C₂×C₃×D₅	C₄×D₄	1	2	yes	—
380	C₂×C₃×D₅	#131	1	2	yes	complemented
381	C₃×C₄×C₅	—	2	1	no	—
382	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
383	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
384	Dic₁₅	—	2	1	no	—
385	Dic₁₅	—	2	1	no	—
386	Dic₁₅	—	2	1	no	—
387	C₃×Dic₅	—	2	1	no	—
388	C₃×Dic₅	C₄×D₄	1	2	yes	—
389	C₅×Dic₃	—	2	1	no	—
390	C₅×Dic₃	—	2	1	no	—
391	C₅×Dic₃	—	2	1	no	—
392	C₂⁴×C₃	—	5	1	no	—
393	C₂²×C₃×C₄	—	5	1	no	—
394	C₂²×C₃×C₄	—	5	1	no	—
395	C₂²×C₃×C₄	—	5	1	no	—
396	C₂²×C₃×C₄	—	5	1	no	—
397	C₂²×C₃×C₄	—	5	1	no	—
398	C₂²×C₃×C₄	—	10	2	no	—
399	C₂²×C₃×C₄	—	10	2	no	—
400	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
401	C₂×#67	—	5	1	no	—
402	C₂×#67	—	5	1	no	—
403	C₂×#67	—	5	1	no	—
404	C₂×#67	—	5	1	no	—
405	C₂×#67	—	5	1	no	—
406	C₂×#67	C₄×D₅	1	1	yes	characteristic
407	#235	—	10	2	no	—
408	#235	—	10	2	no	—
409	C₂×D₁₂	—	5	1	no	—
410	C₂×C₄×D₃	—	5	1	no	—
411	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
412	C₂×Dic₆	—	5	1	no	—
413	C₂×C₃×C₈	—	2	2	no	—
414	C₂×C₃×C₈	—	5	1	no	—
415	C₂×C₃×C₈	—	5	4	no	—
416	C₂×C₃×C₈	—	5	1	no	—
417	C₂×C₃×C₈	—	10	2	no	—
418	C₂×C₃×C₈	—	10	2	no	—
419	C₂×C₃×C₈	—	10	2	no	—
420	C₂×C₃×C₈	—	10	2	no	—
421	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
422	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
423	#217	—	5	1	no	—
424	#217	—	5	1	no	—
425	#217	—	5	1	no	—
426	#217	—	5	1	no	—
427	#217	—	5	1	no	—
428	#217	C₄×D₅	1	1	yes	characteristic
429	(C₂×D₃)⋊C₄	—	5	1	no	—
430	(C₂×D₃)⋊C₄	—	5	1	no	—
431	(C₂×D₃)⋊C₄	—	5	1	no	—
432	(C₂×D₃)⋊C₄	C₄×D₅	1	1	yes	characteristic
433	C₄⋊Dic₃	—	5	1	no	—
434	C₄⋊Dic₃	—	5	1	no	—
435	Dic₃⋊C₄	—	5	1	no	—
436	Dic₃⋊C₄	—	5	1	no	—
437	Dic₃⋊C₄	—	5	1	no	—
438	Dic₃⋊C₄	C₄×D₅	1	1	yes	characteristic
439	C₄×Dic₃	—	5	1	no	—
440	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
441	#208	—	10	2	no	—
442	#208	—	10	2	no	—
443	C₂×C₃⋊C₈	—	5	1	no	—
444	C₂×C₃⋊C₈	—	5	1	no	—
445	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
446	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
447	ΓL(1,𝔽₂₅)	—	2	2	no	—
448	ΓL(1,𝔽₂₅)	—	10	2	no	—
449	D₃×C₈	—	10	2	no	—
450	D₃×C₈	—	10	2	no	—
451	C₂³×C₅	—	3	1	no	—
452	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
453	C₂²×D₅	—	2	2	no	—
454	C₂²×D₅	—	2	2	no	—
455	C₂²×D₅	—	2	2	no	—
456	C₂²×D₅	—	3	1	no	—
457	C₂²×D₅	C₂×C₄×D₃	1	1	yes	characteristic
458	C₂²×D₅	C₂×C₄×D₃	1	1	yes	characteristic
459	C₅×D₄	—	6	2	no	—
460	C₂×C₄×C₅	—	2	1	no	—
461	C₂×C₄×C₅	—	2	1	no	—
462	C₂×C₄×C₅	—	3	1	no	—
463	C₂×C₄×C₅	—	3	1	no	—
464	C₂×C₄×C₅	—	3	1	no	—
465	C₂×C₄×C₅	—	6	1	no	—
466	C₂×C₄×C₅	—	6	1	no	—
467	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
468	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
469	C₂²⋊D₅	—	6	2	no	—
470	C₂²⋊D₅	—	6	2	no	—
471	C₂²⋊D₅	—	6	2	no	—
472	C₂²⋊D₅	—	6	2	no	—
473	C₂×Dic₅	—	2	2	no	—
474	C₂×Dic₅	—	3	1	no	—
475	C₂×Dic₅	—	3	1	no	—
476	C₂×Dic₅	—	3	1	no	—
477	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
478	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
479	D₂₀	—	6	2	no	—
480	D₂₀	—	6	2	no	—
481	C₄×D₅	—	2	2	no	—
482	C₄×D₅	—	2	1	no	—
483	C₄×D₅	—	2	1	no	—
484	C₄×D₅	—	2	2	no	—
485	C₄×D₅	—	6	1	no	—
486	C₄×D₅	—	6	1	no	—
487	C₄×D₅	#235	1	2	yes	—
488	C₄×D₅	C₂×#67	1	2	yes	—
489	Dic₁₀	—	6	2	no	—
490	C₅×C₈	—	2	1	no	—
491	C₅×C₈	—	6	1	no	—
492	C₅×C₈	—	6	1	no	—
493	C₅×C₈	C₂×#67	1	2	yes	—
494	#168	—	2	1	no	—
495	#168	—	6	1	no	—
496	#168	—	6	1	no	—
497	#168	C₂×#67	1	2	yes	—
498	C₂×#41	—	15	1	no	—
499	C₂³×C₄	—	5	1	no	—
500	#131	—	30	4	no	—
501	C₂×M₁₆	—	3	1	no	—
502	C₂×M₁₆	—	15	1	no	—
503	C₂×M₁₆	—	15	1	no	—
504	C₂×M₁₆	—	15	1	no	—
505	C₂²×C₈	—	5	1	no	—
506	C₂²×C₈	—	5	1	no	—
507	C₂²×C₈	—	5	1	no	—
508	C₂²×C₈	—	5	1	no	—
509	C₂²×C₈	—	5	1	no	—
510	C₂²×C₈	—	10	4	no	—
511	C₂²×C₈	—	15	1	no	—
512	C₂²×C₈	—	15	1	no	—
513	C₂²×C₈	D₃×D₅	1	1	yes	characteristic
514	#123	—	15	1	no	—
515	#123	—	15	1	no	—
516	C₂²⋊Q₈	—	15	1	no	—
517	C₂²⋊Q₈	—	15	1	no	—
518	#121	—	15	1	no	—
519	#121	—	15	1	no	—
520	#120	—	15	1	no	—
521	#120	—	15	1	no	—
522	C₄×D₄	—	3	1	no	—
523	C₄×D₄	—	15	1	no	—
524	C₄×D₄	—	15	1	no	—
525	C₄×D₄	—	15	1	no	—
526	#117	—	15	1	no	—
527	C₄⋊C₈	—	3	1	no	—
528	C₄⋊C₈	—	15	1	no	—
529	C₄⋊C₈	—	15	1	no	—
530	C₄⋊C₈	—	15	1	no	—
531	C₂²⋊C₈	—	3	1	no	—
532	C₂²⋊C₈	—	3	1	no	—
533	C₂²⋊C₈	—	15	1	no	—
534	C₂²⋊C₈	—	15	1	no	—
535	C₂²⋊C₈	—	15	1	no	—
536	C₂²⋊C₈	—	15	1	no	—
537	C₂²⋊C₈	—	15	1	no	—
538	C₂²⋊C₈	—	15	1	no	—
539	#97	—	3	1	no	—
540	#97	—	15	1	no	—
541	C₄×C₈	—	15	1	no	—
542	C₄×C₈	—	15	1	no	—
543	C₂×C₃×C₅	—	2	2	no	—
544	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
545	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
546	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
547	D₁₅	—	4	1	no	—
548	C₃×D₅	—	2	2	no	—
549	C₃×D₅	—	2	2	no	—
550	C₅×D₃	—	4	1	no	—
551	C₂³×C₃	—	5	1	no	—
552	C₂³×C₃	—	5	1	no	—
553	C₂³×C₃	—	10	2	no	—
554	C₂³×C₃	—	10	2	no	—
555	C₂³×C₃	—	10	2	no	—
556	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
557	C₂²×D₃	—	5	1	no	—
558	C₂²×D₃	C₂×C₄×D₅	1	1	yes	characteristic
559	C₂×C₃×C₄	—	2	1	no	—
560	C₂×C₃×C₄	—	2	1	no	—
561	C₂×C₃×C₄	—	5	1	no	—
562	C₂×C₃×C₄	—	5	2	no	—
563	C₂×C₃×C₄	—	5	2	no	—
564	C₂×C₃×C₄	—	5	1	no	—
565	C₂×C₃×C₄	—	10	2	no	—
566	C₂×C₃×C₄	—	10	2	no	—
567	C₂×C₃×C₄	—	10	2	no	—
568	C₂×C₃×C₄	—	10	1	no	—
569	C₂×C₃×C₄	—	10	1	no	—
570	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
571	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
572	#67	—	2	2	no	—
573	#67	—	10	2	no	—
574	#67	—	10	2	no	—
575	#67	—	10	2	no	—
576	#67	—	10	2	no	—
577	#67	—	10	2	no	—
578	C₂×Dic₃	—	5	1	no	—
579	C₂×Dic₃	—	5	1	no	—
580	C₂×Dic₃	—	5	1	no	—
581	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
582	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
583	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
584	D₁₂	—	10	2	no	—
585	C₄×D₃	—	2	1	no	—
586	C₄×D₃	—	2	1	no	—
587	C₄×D₃	—	10	1	no	—
588	C₄×D₃	—	10	1	no	—
589	Dic₆	—	10	2	no	—
590	C₃×C₈	—	2	1	no	—
591	C₃×C₈	—	5	2	no	—
592	C₃×C₈	—	10	1	no	—
593	C₃×C₈	D₄×D₅	1	2	yes	—
594	C₃⋊C₈	—	2	1	no	—
595	C₃⋊C₈	—	2	1	no	—
596	C₃⋊C₈	—	10	1	no	—
597	C₃⋊C₈	—	10	1	no	—
598	C₂²×C₅	—	2	1	no	—
599	C₂²×C₅	—	2	1	no	—
600	C₂²×C₅	—	6	1	no	—
601	C₂²×C₅	—	6	1	no	—
602	C₂²×C₅	—	6	1	no	—
603	C₂²×C₅	#901	1	2	yes	complemented
604	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
605	C₂×D₅	—	2	8	no	—
606	C₂×D₅	—	2	1	no	—
607	C₂×D₅	—	2	1	no	—
608	C₂×D₅	—	2	1	no	—
609	C₂×D₅	—	2	1	no	—
610	C₂×D₅	—	6	1	no	—
611	C₂×D₅	—	6	1	no	—
612	C₂×D₅	—	6	1	no	—
613	C₂×D₅	#901	1	2	yes	complemented
614	C₂×D₅	C₄×#67	1	2	yes	—
615	C₄×C₅	—	2	1	no	—
616	C₄×C₅	—	6	1	no	—
617	C₄×C₅	—	6	1	no	—
618	C₄×C₅	—	6	1	no	—
619	C₄×C₅	C₂×#235	1	1	yes	characteristic
620	C₄×C₅	C₂²×#67	1	1	yes	characteristic
621	Dic₅	—	2	1	no	—
622	Dic₅	—	6	1	no	—
623	Dic₅	—	6	1	no	—
624	Dic₅	—	6	1	no	—
625	Dic₅	C₄×#67	1	2	yes	—
626	C₂⁴	—	5	1	no	—
627	#41	—	30	2	no	—
628	#41	—	30	2	no	—
629	C₂×Q₈	—	15	1	no	—
630	C₂×D₄	—	3	1	no	—
631	C₂×D₄	—	15	1	no	—
632	C₂×D₄	—	15	1	no	—
633	C₂×D₄	—	15	1	no	—
634	C₂×D₄	—	15	1	no	—
635	C₂×D₄	—	15	1	no	—
636	C₂×D₄	—	15	1	no	—
637	C₂²×C₄	—	3	1	no	—
638	C₂²×C₄	—	5	1	no	—
639	C₂²×C₄	—	5	1	no	—
640	C₂²×C₄	—	5	1	no	—
641	C₂²×C₄	—	5	1	no	—
642	C₂²×C₄	—	5	1	no	—
643	C₂²×C₄	—	10	2	no	—
644	C₂²×C₄	—	10	2	no	—
645	C₂²×C₄	—	15	1	no	—
646	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
647	M₁₆	—	6	2	no	—
648	M₁₆	—	30	2	no	—
649	M₁₆	—	30	2	no	—
650	M₁₆	—	30	2	no	—
651	C₂×C₈	—	2	2	no	—
652	C₂×C₈	—	3	1	no	—
653	C₂×C₈	—	3	1	no	—
654	C₂×C₈	—	5	1	no	—
655	C₂×C₈	—	5	4	no	—
656	C₂×C₈	—	5	1	no	—
657	C₂×C₈	—	10	2	no	—
658	C₂×C₈	—	10	2	no	—
659	C₂×C₈	—	10	2	no	—
660	C₂×C₈	—	10	2	no	—
661	C₂×C₈	—	15	1	no	—
662	C₂×C₈	—	15	1	no	—
663	C₂×C₈	—	30	2	no	—
664	C₂×C₈	—	30	2	no	—
665	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
666	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
667	C₄⋊C₄	—	3	1	no	—
668	C₄⋊C₄	—	15	1	no	—
669	C₄⋊C₄	—	15	1	no	—
670	C₄⋊C₄	—	15	1	no	—
671	C₄⋊C₄	—	15	1	no	—
672	C₄⋊C₄	—	15	1	no	—
673	C₂²⋊C₄	—	3	1	no	—
674	C₂²⋊C₄	—	3	1	no	—
675	C₂²⋊C₄	—	15	1	no	—
676	C₂²⋊C₄	—	15	1	no	—
677	C₂²⋊C₄	—	15	1	no	—
678	C₂²⋊C₄	—	15	1	no	—
679	C₂²⋊C₄	—	15	1	no	—
680	C₂²⋊C₄	—	15	1	no	—
681	C₂²⋊C₄	—	15	1	no	—
682	C₂²⋊C₄	—	15	1	no	—
683	C₄²	—	3	1	no	—
684	C₄²	—	15	1	no	—
685	C₃×C₅	#2929	1	1	yes	characteristic, complemented, Hall
686	C₂²×C₃	—	2	1	no	—
687	C₂²×C₃	—	2	1	no	—
688	C₂²×C₃	—	5	2	no	—
689	C₂²×C₃	—	5	2	no	—
690	C₂²×C₃	—	10	8	no	—
691	C₂²×C₃	—	10	1	no	—
692	C₂²×C₃	—	10	1	no	—
693	C₂²×C₃	—	10	1	no	—
694	C₂²×C₃	—	10	1	no	—
695	C₂²×C₃	#4053	1	2	yes	complemented
696	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
697	C₂×D₃	—	2	1	no	—
698	C₂×D₃	—	2	1	no	—
699	C₂×D₃	—	2	1	no	—
700	C₂×D₃	—	10	1	no	—
701	C₂×D₃	—	10	1	no	—
702	C₂×D₃	—	10	1	no	—
703	C₃×C₄	—	2	1	no	—
704	C₃×C₄	—	5	2	no	—
705	C₃×C₄	—	10	1	no	—
706	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
707	C₃×C₄	D₅×#41	1	1	yes	characteristic
708	Dic₃	—	2	1	no	—
709	Dic₃	—	2	1	no	—
710	Dic₃	—	2	1	no	—
711	Dic₃	—	10	1	no	—
712	Dic₃	—	10	1	no	—
713	Dic₃	—	10	1	no	—
714	C₂×C₅	—	2	2	no	—
715	C₂×C₅	—	12	1	no	—
716	C₂×C₅	C₂×#901	1	1	yes	characteristic
717	C₂×C₅	C₂×#901	1	1	yes	characteristic
718	C₂×C₅	C₂×C₄×#67	1	1	yes	characteristic
719	D₅	—	2	2	no	—
720	D₅	—	2	2	no	—
721	D₅	—	12	1	no	—
722	C₂³	—	3	1	no	—
723	C₂³	—	5	1	no	—
724	C₂³	—	5	1	no	—
725	C₂³	—	10	2	no	—
726	C₂³	—	10	2	no	—
727	C₂³	—	10	2	no	—
728	C₂³	—	15	1	no	—
729	C₂³	C₄×D₃×D₅	1	1	yes	characteristic
730	Q₈	—	30	2	no	—
731	D₄	—	6	2	no	—
732	D₄	—	30	2	no	—
733	D₄	—	30	2	no	—
734	D₄	—	30	2	no	—
735	D₄	—	30	2	no	—
736	D₄	—	30	2	no	—
737	D₄	—	30	2	no	—
738	C₂×C₄	—	2	1	no	—
739	C₂×C₄	—	2	1	no	—
740	C₂×C₄	—	3	1	no	—
741	C₂×C₄	—	3	1	no	—
742	C₂×C₄	—	3	1	no	—
743	C₂×C₄	—	5	1	no	—
744	C₂×C₄	—	5	2	no	—
745	C₂×C₄	—	5	2	no	—
746	C₂×C₄	—	5	1	no	—
747	C₂×C₄	—	6	1	no	—
748	C₂×C₄	—	6	1	no	—
749	C₂×C₄	—	10	2	no	—
750	C₂×C₄	—	10	2	no	—
751	C₂×C₄	—	10	2	no	—
752	C₂×C₄	—	10	1	no	—
753	C₂×C₄	—	10	1	no	—
754	C₂×C₄	—	15	1	no	—
755	C₂×C₄	—	15	1	no	—
756	C₂×C₄	—	15	1	no	—
757	C₂×C₄	—	30	1	no	—
758	C₂×C₄	—	30	1	no	—
759	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
760	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
761	C₈	—	2	1	no	—
762	C₈	—	5	2	no	—
763	C₈	—	6	1	no	—
764	C₈	—	6	1	no	—
765	C₈	—	10	1	no	—
766	C₈	—	30	1	no	—
767	C₈	—	30	1	no	—
768	C₈	D₅×#67	1	2	yes	—
769	C₂×C₃	—	2	2	no	—
770	C₂×C₃	—	10	2	no	—
771	C₂×C₃	—	10	2	no	—
772	C₂×C₃	C₄×D₄×D₅	1	1	yes	characteristic
773	C₂×C₃	C₂×#4053	1	1	yes	characteristic
774	C₂×C₃	D₅×#131	1	1	yes	characteristic
775	D₃	—	4	1	no	—
776	D₃	—	20	1	no	—
777	C₅	#83734	1	1	yes	characteristic, complemented, Sylow
778	C₂²	—	2	1	no	—
779	C₂²	—	2	1	no	—
780	C₂²	—	5	2	no	—
781	C₂²	—	5	2	no	—
782	C₂²	—	6	1	no	—
783	C₂²	—	6	1	no	—
784	C₂²	—	6	1	no	—
785	C₂²	—	10	8	no	—
786	C₂²	—	10	1	no	—
787	C₂²	—	10	1	no	—
788	C₂²	—	10	1	no	—
789	C₂²	—	10	1	no	—
790	C₂²	—	30	1	no	—
791	C₂²	—	30	1	no	—
792	C₂²	—	30	1	no	—
793	C₂²	#91266	1	2	yes	complemented
794	C₂²	C₂×C₄×D₃×D₅	1	1	yes	characteristic
795	C₄	—	2	1	no	—
796	C₄	—	5	2	no	—
797	C₄	—	6	1	no	—
798	C₄	—	6	1	no	—
799	C₄	—	6	1	no	—
800	C₄	—	10	1	no	—
801	C₄	—	30	1	no	—
802	C₄	—	30	1	no	—
803	C₄	—	30	1	no	—
804	C₄	D₅×#235	1	1	yes	characteristic
805	C₄	C₂×D₅×#67	1	1	yes	characteristic
806	C₃	#10611209	1	1	yes	characteristic, complemented, Sylow
807	C₂	—	2	2	no	—
808	C₂	—	10	2	no	—
809	C₂	—	10	2	no	—
810	C₂	—	12	1	no	—
811	C₂	—	60	1	no	—
812	C₂	D₅×#901	1	1	yes	characteristic
813	C₂	C₂×#91266	1	1	yes	characteristic
814	C₂	C₄×D₅×#67	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃×D₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Fitting	C₂²×C₃×C₅×C₈	C₂²
prime radical	#11754525	C₂
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂²×C₈	D₃×D₅
hypocenter	C₃×C₅	#2929
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₈×D₅	C₂	semidirect
3. C₂×#91266	C₂	semidirect
4. #11751212	C₂	semidirect
5. C₅×#5111	C₂	semidirect
6. #11748499	C₂	semidirect
7. #11748485	C₂	semidirect
8. #67×#168	C₂	semidirect
9. #11748134	C₂	semidirect
10. #11747705	C₂	semidirect
11. #11747701	C₂	semidirect
12. #11747698	C₂	semidirect
13. #11747694	C₂	semidirect
14. #11747647	C₂	semidirect
15. #11747646	C₂	semidirect
21. C₂×#6705	C₂²	semidirect
23. C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	semidirect
43. C₂×#6648	C₂²	semidirect
44. C₂×D₃×#168	C₂²	semidirect
47. #91104	C₂²	semidirect
48. #91099	C₂²	semidirect
49. #91098	C₂²	semidirect
51. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
52. C₅×#815	C₂²	semidirect
53. C₅×Dic₃⋊C₈	C₂²	semidirect
54. Dic₃⋊#168	C₂²	semidirect
55. #90983	C₂²	semidirect
56. #90957	C₂²	semidirect
57. (C₂×D₃)⋊#168	C₂²	semidirect
60. #90951	C₂²	semidirect
61. Dic₃×#168	C₂²	semidirect
64. C₂²×C₈×D₅	D₃	semidirect
122. C₃×C₈×D₅	D₄	semidirect
144. #5111	D₅	semidirect
271. C₂×ΓL(1,𝔽₂₅)	C₂×D₅	semidirect
281. (C₂×D₃)⋊C₈	C₂×D₅	semidirect
283. #815	C₂×D₅	semidirect
287. Dic₃⋊C₈	C₂×D₅	semidirect
348. C₈×D₅	#67	semidirect
366. C₂²×C₃×C₅	#131	semidirect
380. C₂×C₃×D₅	#131	semidirect
603. C₂²×C₅	#901	semidirect
613. C₂×D₅	#901	semidirect
685. C₃×C₅	#2929	semidirect
695. C₂²×C₃	#4053	semidirect
777. C₅	#83734	semidirect
793. C₂²	#91266	semidirect
806. C₃	#10611209	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₈×D₅	2
#11754525	2
C₂×#91266	2
#11751212	2
C₅×#5111	2
#11748499	2
#11748485	2
#67×#168	2
#11748134	2
#11747705	2
#11747701	2
#11747698	2
#11747694	2
#11747647	2
#11747646	2
#10611209	3
#83734	5