Subgroups — #14415364

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5548	C₂	1	1	yes	maximal, characteristic
2	C₂×#91288	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#91286	C₂	1	1	yes	maximal, characteristic, complemented
4	#11751112	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65300	C₂	1	1	yes	maximal, characteristic, complemented
6	#11748508	C₂	1	1	yes	maximal, characteristic, complemented
7	#11748500	C₂	1	1	yes	maximal, characteristic, complemented
8	#11748496	C₂	1	1	yes	maximal, characteristic, complemented
9	#11748490	C₂	1	1	yes	maximal, characteristic, complemented
10	#11748490	C₂	1	1	yes	maximal, characteristic, complemented
11	#11748484	C₂	1	1	yes	maximal, characteristic, complemented
12	#11747011	C₂	1	1	yes	maximal, characteristic, complemented
13	#11746999	C₂	1	1	yes	maximal, characteristic, complemented
14	#11746987	C₂	1	1	yes	maximal, characteristic, complemented
15	D₃×#3935	C₂	1	1	yes	maximal, characteristic, complemented
16	#10615007	—	3	1	no	maximal, Hall
17	C₂×C₅×#235	C₂²	1	1	yes	characteristic
18	C₂×C₅×#235	C₂²	1	1	yes	characteristic
19	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
20	C₂×#6710	C₂²	1	1	yes	characteristic
21	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
22	C₅×#940	C₄	1	1	yes	characteristic
23	C₅×#938	C₄	1	1	yes	characteristic
24	C₄×C₅×#67	C₂²	1	1	yes	characteristic
25	C₄×C₅×#67	C₂²	1	1	yes	characteristic
26	C₅×#895	C₄	1	1	yes	characteristic
27	C₅×#888	C₄	1	1	yes	characteristic
28	C₅×#885	C₄	1	1	yes	characteristic
29	C₅×#885	C₄	1	1	yes	characteristic
30	C₅×#884	C₄	1	1	yes	characteristic
31	C₅×#884	C₄	1	1	yes	characteristic
32	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
33	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
34	C₂×C₃×#681	C₂²	1	1	yes	characteristic
35	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
36	C₂×#6650	C₂²	1	1	yes	characteristic
37	C₂×#6650	C₂²	1	1	yes	characteristic
38	C₂×#6650	C₂²	1	1	yes	characteristic
39	C₂×#6650	C₂²	1	1	yes	characteristic
40	#91288	—	2	4	no	—
41	#91286	—	2	4	no	—
42	C₂×D₃×#168	C₂²	1	1	yes	characteristic
43	C₂×D₃×#168	C₂²	1	1	yes	characteristic
44	C₂×D₃×#168	C₂²	1	1	yes	characteristic
45	C₂×D₃×#168	C₂²	1	1	yes	characteristic
46	#91114	C₂²	1	1	yes	characteristic
47	#91114	C₂²	1	1	yes	characteristic
48	C₄⋊(C₃⋊#168)	C₂²	1	1	yes	characteristic
49	#91087	C₂²	1	1	yes	characteristic
50	C₃×C₂²⋊#168	C₂²	1	1	yes	characteristic
51	C₃×C₂²⋊#168	C₂²	1	1	yes	characteristic
52	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
53	C₃×#3935	C₂²	1	1	yes	characteristic
54	Dic₃⋊#168	C₂²	1	1	yes	characteristic
55	Dic₃⋊#168	C₂²	1	1	yes	characteristic
56	(C₂×D₃)⋊#168	C₂²	1	1	yes	characteristic
57	(C₂×D₃)⋊#168	C₂²	1	1	yes	characteristic
58	(C₂×D₃)⋊#168	C₂²	1	1	yes	characteristic
59	(C₂×D₃)⋊#168	C₂²	1	1	yes	characteristic
60	#90953	C₂²	1	1	yes	characteristic
61	#90953	C₂²	1	1	yes	characteristic
62	#79480	—	5	1	no	maximal, Hall
63	C₅×#532	—	3	1	no	—
64	C₂×#4094	—	3	1	no	—
65	C₂×#4094	—	3	1	no	—
66	#65523	—	3	1	no	—
67	#65523	—	3	1	no	—
68	#65300	—	3	1	no	—
69	#65300	—	3	1	no	—
70	#65300	—	3	1	no	—
71	#65300	—	3	1	no	—
72	#65300	—	3	1	no	—
73	#65300	—	3	1	no	—
74	#65300	—	3	1	no	—
75	#65300	D₃	1	1	yes	characteristic, complemented
76	#65213	—	3	1	no	—
77	C₂×#3935	—	3	1	no	—
78	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
79	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
80	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
81	C₂×C₅×#67	C₂×C₄	1	1	yes	characteristic
82	C₂×C₅×#67	C₂×C₄	1	1	yes	characteristic
83	C₂×C₅×#67	C₂×C₄	1	1	yes	characteristic
84	C₂×C₅×#67	C₂×C₄	1	1	yes	characteristic
85	C₂×C₅×#67	C₂×C₄	1	1	yes	characteristic
86	C₂×C₅×#67	C₂×C₄	1	1	yes	characteristic
87	C₅×#235	—	2	2	no	—
88	C₅×#235	—	2	2	no	—
89	C₅×#235	—	2	2	no	—
90	C₅×#235	—	2	2	no	—
91	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
92	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
93	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
97	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
98	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
99	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
100	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
101	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
102	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
103	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
104	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
105	#6710	—	2	2	no	—
106	C₂×C₃⋊#168	—	2	2	no	—
107	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
108	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
109	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
110	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
111	C₅×#217	C₂×C₄	1	1	yes	characteristic
112	C₅×#217	C₂×C₄	1	1	yes	characteristic
113	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
114	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
115	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
116	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
117	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
118	C₅×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
119	C₅×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
120	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
121	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
122	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
123	C₃×#681	—	2	2	no	—
124	C₂×C₃×#168	—	2	2	no	—
125	C₂×C₃×#168	C₂³	1	1	yes	characteristic
126	C₂×C₃×#168	C₂³	1	1	yes	characteristic
127	C₂×C₃×#168	C₂³	1	1	yes	characteristic
128	C₂×C₃×#168	C₂³	1	1	yes	characteristic
129	#6650	—	2	2	no	—
130	#6650	—	2	2	no	—
131	#6650	—	2	2	no	—
132	#6650	—	2	2	no	—
133	D₃×#168	—	2	2	no	—
134	D₃×#168	—	2	2	no	—
135	D₃×#168	—	2	2	no	—
136	D₃×#168	D₄	1	4	yes	complemented
137	C₂×#907	—	5	1	no	—
138	C₂×#901	—	5	1	no	—
139	#5548	D₅	1	1	yes	characteristic
140	C₃×#435	—	5	1	no	—
141	#5127	—	5	1	no	—
142	#5111	—	5	1	no	—
143	#5011	—	5	1	no	—
144	#4837	—	5	1	no	—
145	#4836	—	5	1	no	—
146	#4730	—	5	1	no	—
147	#4728	—	5	1	no	—
148	#4727	—	5	1	no	—
149	#4727	—	5	1	no	—
150	#4706	—	5	1	no	—
151	D₃×#97	—	5	1	no	—
152	C₂×C₅×#41	—	3	1	no	—
153	C₂×C₅×#41	—	3	1	no	—
154	C₅×C₄⋊Q₈	—	3	1	no	—
155	C₅×#127	—	3	1	no	—
156	C₅×#124	—	3	1	no	—
157	C₅×#124	—	3	1	no	—
158	C₅×#121	—	3	1	no	—
159	C₅×#121	—	3	1	no	—
160	C₅×#121	—	3	1	no	—
161	C₅×#121	—	3	1	no	—
162	C₄×C₅×D₄	—	3	1	no	—
163	C₄×C₅×D₄	—	3	1	no	—
164	C₄×C₅×D₄	—	3	1	no	—
165	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
166	C₂×C₄²×C₅	—	3	1	no	—
167	#4094	—	6	4	no	—
168	#4094	—	6	4	no	—
169	C₂×#681	—	3	1	no	—
170	C₂×#681	—	3	1	no	—
171	C₂×#681	—	3	1	no	—
172	C₂×#681	—	3	1	no	—
173	C₂×#681	—	3	1	no	—
174	C₂×#681	C₂×D₃	1	1	yes	characteristic
175	C₂²×#168	—	3	1	no	—
176	C₂²×#168	—	3	1	no	—
177	C₂²×#168	—	3	1	no	—
178	C₂²×#168	—	3	1	no	—
179	C₂²×#168	—	3	1	no	—
180	C₂²×#168	C₂×D₃	1	1	yes	characteristic
181	C₂²⋊#168	—	3	1	no	—
182	C₂²⋊#168	—	3	1	no	—
183	C₂²⋊#168	—	3	1	no	—
184	C₂²⋊#168	—	3	1	no	—
185	C₂²⋊#168	—	3	1	no	—
186	C₂²⋊#168	—	3	1	no	—
187	C₂²⋊#168	C₂×D₃	1	1	yes	characteristic
188	C₂²⋊#168	C₂×D₃	1	1	yes	characteristic
189	C₄⋊#168	—	3	1	no	—
190	C₄⋊#168	—	3	1	no	—
191	C₄⋊#168	—	3	1	no	—
192	C₄⋊#168	C₂×D₃	1	1	yes	characteristic
193	#3935	—	3	1	no	—
194	#3935	—	3	1	no	—
195	#3935	—	3	1	no	—
196	#3935	C₂×D₃	1	1	yes	characteristic
197	#2932	—	15	1	no	Sylow
198	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
199	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
200	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
201	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
202	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
203	C₃×C₅×D₄	—	4	1	no	—
204	C₂×C₃×C₄×C₅	—	2	1	no	—
205	C₂×C₃×C₄×C₅	—	2	1	no	—
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	C₂²×C₄	1	1	yes	characteristic
210	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
211	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
212	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
213	C₅×#67	—	2	2	no	—
214	C₅×#67	—	2	2	no	—
215	C₅×#67	—	2	2	no	—
216	C₅×#67	—	2	2	no	—
217	C₅×#67	—	4	1	no	—
218	C₅×#67	—	4	1	no	—
219	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
220	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
221	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
222	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
223	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
224	C₅×D₁₂	—	2	2	no	—
225	C₅×D₁₂	—	2	2	no	—
226	C₅×D₁₂	—	4	1	no	—
227	C₄×C₅×D₃	—	2	1	no	—
228	C₄×C₅×D₃	—	2	1	no	—
229	C₄×C₅×D₃	—	2	1	no	—
230	C₄×C₅×D₃	—	2	1	no	—
231	C₄×C₅×D₃	—	4	1	no	—
232	C₄×C₅×D₃	—	4	1	no	—
233	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
234	C₄×C₅×D₃	#41	1	2	yes	—
235	C₅×Dic₆	—	2	2	no	—
236	C₅×Dic₆	—	2	2	no	—
237	C₃⋊#168	—	2	1	no	—
238	C₃⋊#168	—	2	1	no	—
239	C₃⋊#168	—	2	1	no	—
240	C₃⋊#168	C₂×D₄	1	2	yes	—
241	C₃×#168	—	2	1	no	—
242	C₃×#168	—	2	1	no	—
243	C₃×#168	—	2	1	no	—
244	C₃×#168	C₂×D₄	1	2	yes	—
245	C₂×#235	C₂×D₅	1	1	yes	characteristic
246	C₂×#235	C₂×D₅	1	1	yes	characteristic
247	C₂×C₃×M₁₆	—	5	1	no	—
248	C₂²×C₃×C₈	—	5	1	no	—
249	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
250	#940	Dic₅	1	1	yes	characteristic
251	#938	Dic₅	1	1	yes	characteristic
252	C₄×#67	C₂×D₅	1	1	yes	characteristic
253	C₄×#67	C₂×D₅	1	1	yes	characteristic
254	C₂×#208	—	5	1	no	—
255	C₂²×C₃⋊C₈	—	5	1	no	—
256	#907	—	10	4	no	—
257	#901	—	10	4	no	—
258	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
259	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
260	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
261	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
262	C₂×D₃×C₈	—	5	1	no	—
263	C₂×D₃×C₈	—	5	1	no	—
264	C₂×D₃×C₈	—	5	1	no	—
265	C₂×D₃×C₈	—	5	1	no	—
266	#895	Dic₅	1	1	yes	characteristic
267	#888	Dic₅	1	1	yes	characteristic
268	#885	Dic₅	1	1	yes	characteristic
269	#885	Dic₅	1	1	yes	characteristic
270	#884	Dic₅	1	1	yes	characteristic
271	#884	Dic₅	1	1	yes	characteristic
272	C₄×D₁₂	C₂×D₅	1	1	yes	characteristic
273	C₄²×D₃	C₂×D₅	1	1	yes	characteristic
274	C₃×C₄⋊C₈	—	5	1	no	—
275	C₃×C₂²⋊C₈	—	5	1	no	—
276	C₃×C₂²⋊C₈	—	5	1	no	—
277	C₃×#97	—	5	1	no	—
278	#830	—	5	1	no	—
279	#830	—	5	1	no	—
280	(C₂×D₃)⋊C₈	—	5	1	no	—
281	(C₂×D₃)⋊C₈	—	5	1	no	—
282	(C₂×D₃)⋊C₈	—	5	1	no	—
283	(C₂×D₃)⋊C₈	—	5	1	no	—
284	#815	—	5	1	no	—
285	#815	—	5	1	no	—
286	Dic₃⋊C₈	—	5	1	no	—
287	Dic₃⋊C₈	—	5	1	no	—
288	C₄⋊(C₃⋊C₈)	—	5	1	no	—
289	#803	—	5	1	no	—
290	C₅×#41	—	6	2	no	—
291	C₅×#41	—	6	2	no	—
292	C₅×#41	—	6	2	no	—
293	C₅×#41	—	6	2	no	—
294	C₂×C₅×Q₈	—	3	1	no	—
295	C₂×C₅×Q₈	—	3	1	no	—
296	C₂×C₅×D₄	—	3	1	no	—
297	C₂×C₅×D₄	—	3	1	no	—
298	C₂×C₅×D₄	—	3	1	no	—
299	C₂×C₅×D₄	—	3	1	no	—
300	C₂×C₅×D₄	—	3	1	no	—
301	C₂×C₅×D₄	—	3	1	no	—
302	C₂×C₅×D₄	—	3	1	no	—
303	C₂×C₅×D₄	—	3	1	no	—
304	C₂×C₅×D₄	—	3	1	no	—
305	C₂×C₅×D₄	C₄×D₃	1	1	yes	characteristic
306	C₂²×C₄×C₅	—	3	1	no	—
307	C₂²×C₄×C₅	—	3	1	no	—
308	C₂²×C₄×C₅	—	3	1	no	—
309	C₂²×C₄×C₅	—	3	1	no	—
310	C₂²×C₄×C₅	—	3	1	no	—
311	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
312	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
313	C₅×C₄⋊C₄	—	3	1	no	—
314	C₅×C₄⋊C₄	—	3	1	no	—
315	C₅×C₄⋊C₄	—	3	1	no	—
316	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
317	C₅×C₂²⋊C₄	—	3	1	no	—
318	C₅×C₂²⋊C₄	—	3	1	no	—
319	C₅×C₂²⋊C₄	—	3	1	no	—
320	C₅×C₂²⋊C₄	—	3	1	no	—
321	C₅×C₂²⋊C₄	—	3	1	no	—
322	C₅×C₂²⋊C₄	—	3	1	no	—
323	C₅×C₂²⋊C₄	C₄×D₃	1	1	yes	characteristic
324	C₅×C₂²⋊C₄	C₄×D₃	1	1	yes	characteristic
325	C₄²×C₅	—	3	1	no	—
326	C₄²×C₅	—	3	1	no	—
327	C₄²×C₅	—	3	1	no	—
328	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
329	#681	—	2	2	no	—
330	#681	—	6	2	no	—
331	#681	—	6	2	no	—
332	#681	—	6	2	no	—
333	#681	—	6	2	no	—
334	#681	—	6	2	no	—
335	C₂×#168	—	2	2	no	—
336	C₂×#168	—	3	1	no	—
337	C₂×#168	—	3	4	no	—
338	C₂×#168	—	3	1	no	—
339	C₂×#168	—	3	1	no	—
340	C₂×#168	—	3	1	no	—
341	C₂×#168	—	6	2	no	—
342	C₂×#168	—	6	2	no	—
343	C₂×#168	—	6	2	no	—
344	C₂×#168	—	6	2	no	—
345	C₂×#168	C₂²×D₃	1	1	yes	characteristic
346	C₂×#168	C₂²×D₃	1	1	yes	characteristic
347	C₂×#168	C₂²×D₃	1	1	yes	characteristic
348	C₂×#168	C₂²×D₃	1	1	yes	characteristic
349	C₂×#131	—	15	1	no	—
350	C₂×#131	—	15	1	no	—
351	#532	—	3	1	no	—
352	#435	—	5	1	no	—
353	#435	—	15	1	no	—
354	#435	—	15	1	no	—
355	#435	—	15	1	no	—
356	#435	—	15	1	no	—
357	#435	—	15	1	no	—
358	#435	—	15	1	no	—
359	#435	—	15	1	no	—
360	#423	—	15	1	no	—
361	#408	—	15	1	no	—
362	#408	—	15	1	no	—
363	C₂×#97	—	15	1	no	—
364	C₂²×C₃×C₅	—	2	1	no	—
365	C₂²×C₃×C₅	—	2	1	no	—
366	C₂²×C₃×C₅	—	2	1	no	—
367	C₂²×C₃×C₅	—	2	1	no	—
368	C₂²×C₃×C₅	—	2	1	no	—
369	C₂²×C₃×C₅	—	2	1	no	—
370	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
371	C₂×C₅×D₃	—	2	1	no	—
372	C₂×C₅×D₃	—	2	1	no	—
373	C₂×C₅×D₃	—	2	1	no	—
374	C₂×C₅×D₃	—	2	1	no	—
375	C₂×C₅×D₃	—	2	1	no	—
376	C₂×C₅×D₃	—	2	1	no	—
377	C₂×C₅×D₃	—	2	1	no	—
378	C₂×C₅×D₃	—	2	1	no	—
379	C₂×C₅×D₃	C₄×D₄	1	2	yes	—
380	C₃×C₄×C₅	—	2	1	no	—
381	C₃×C₄×C₅	—	2	1	no	—
382	C₃×C₄×C₅	—	2	1	no	—
383	C₃×C₄×C₅	—	2	1	no	—
384	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
385	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
386	C₅×Dic₃	—	2	1	no	—
387	C₅×Dic₃	—	2	1	no	—
388	C₅×Dic₃	—	2	1	no	—
389	C₅×Dic₃	—	2	1	no	—
390	C₅×Dic₃	C₄×D₄	1	2	yes	—
391	C₂×C₃×D₄	C₂×Dic₅	1	1	yes	characteristic
392	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
393	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
394	C₂×#67	C₂×Dic₅	1	1	yes	characteristic
395	C₂×#67	C₂×Dic₅	1	1	yes	characteristic
396	C₂×#67	C₂×Dic₅	1	1	yes	characteristic
397	C₂×#67	C₂×Dic₅	1	1	yes	characteristic
398	C₂×#67	C₂×Dic₅	1	1	yes	characteristic
399	C₂×#67	C₂×Dic₅	1	1	yes	characteristic
400	#235	—	2	2	no	—
401	#235	—	2	2	no	—
402	#235	—	2	2	no	—
403	#235	—	2	2	no	—
404	C₂×D₁₂	C₂×Dic₅	1	1	yes	characteristic
405	C₂×D₁₂	C₂×Dic₅	1	1	yes	characteristic
406	C₂×D₁₂	C₂×Dic₅	1	1	yes	characteristic
407	C₂×C₄×D₃	C₂×Dic₅	1	1	yes	characteristic
408	C₂×C₄×D₃	C₂×Dic₅	1	1	yes	characteristic
409	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
410	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
411	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
412	C₂×Dic₆	C₂×Dic₅	1	1	yes	characteristic
413	C₂×Dic₆	C₂×Dic₅	1	1	yes	characteristic
414	C₃×M₁₆	—	10	2	no	—
415	C₂×C₃×C₈	—	5	1	no	—
416	C₂×C₃×C₈	—	5	1	no	—
417	C₂×C₃×C₈	—	5	1	no	—
418	C₂×C₃×C₈	—	5	1	no	—
419	C₂×C₃×C₈	—	10	2	no	—
420	C₃×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
421	C₃×C₂²⋊C₄	C₂×Dic₅	1	1	yes	characteristic
422	C₃×C₂²⋊C₄	C₂×Dic₅	1	1	yes	characteristic
423	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
424	#217	C₂×Dic₅	1	1	yes	characteristic
425	#217	C₂×Dic₅	1	1	yes	characteristic
426	(C₂×D₃)⋊C₄	C₂×Dic₅	1	1	yes	characteristic
427	(C₂×D₃)⋊C₄	C₂×Dic₅	1	1	yes	characteristic
428	(C₂×D₃)⋊C₄	C₂×Dic₅	1	1	yes	characteristic
429	(C₂×D₃)⋊C₄	C₂×Dic₅	1	1	yes	characteristic
430	C₄⋊Dic₃	C₂×Dic₅	1	1	yes	characteristic
431	Dic₃⋊C₄	C₂×Dic₅	1	1	yes	characteristic
432	Dic₃⋊C₄	C₂×Dic₅	1	1	yes	characteristic
433	C₄×Dic₃	C₂×Dic₅	1	1	yes	characteristic
434	C₄×Dic₃	C₂×Dic₅	1	1	yes	characteristic
435	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
436	#208	—	10	2	no	—
437	C₂×C₃⋊C₈	—	5	1	no	—
438	C₂×C₃⋊C₈	—	5	1	no	—
439	C₂×C₃⋊C₈	—	5	1	no	—
440	C₂×C₃⋊C₈	—	5	1	no	—
441	C₂×C₃⋊C₈	—	10	2	no	—
442	ΓL(1,𝔽₂₅)	—	10	2	no	—
443	ΓL(1,𝔽₂₅)	—	10	2	no	—
444	ΓL(1,𝔽₂₅)	—	10	2	no	—
445	ΓL(1,𝔽₂₅)	—	10	2	no	—
446	D₃×C₈	—	5	4	no	—
447	D₃×C₈	—	10	2	no	—
448	D₃×C₈	—	10	2	no	—
449	D₃×C₈	—	10	2	no	—
450	C₂³×C₅	—	3	1	no	—
451	C₂³×C₅	—	3	1	no	—
452	C₂³×C₅	—	3	1	no	—
453	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
454	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
455	C₅×Q₈	—	6	2	no	—
456	C₅×Q₈	—	6	2	no	—
457	C₅×D₄	—	4	1	no	—
458	C₅×D₄	—	6	2	no	—
459	C₅×D₄	—	6	2	no	—
460	C₅×D₄	—	6	2	no	—
461	C₅×D₄	—	6	2	no	—
462	C₅×D₄	—	6	2	no	—
463	C₅×D₄	—	6	2	no	—
464	C₅×D₄	—	12	1	no	—
465	C₅×D₄	—	12	1	no	—
466	C₅×D₄	—	12	1	no	—
467	C₂×C₄×C₅	—	2	1	no	—
468	C₂×C₄×C₅	—	2	1	no	—
469	C₂×C₄×C₅	—	2	1	no	—
470	C₂×C₄×C₅	—	2	1	no	—
471	C₂×C₄×C₅	—	3	1	no	—
472	C₂×C₄×C₅	—	3	2	no	—
473	C₂×C₄×C₅	—	3	2	no	—
474	C₂×C₄×C₅	—	3	1	no	—
475	C₂×C₄×C₅	—	3	1	no	—
476	C₂×C₄×C₅	—	3	1	no	—
477	C₂×C₄×C₅	—	3	1	no	—
478	C₂×C₄×C₅	—	6	1	no	—
479	C₂×C₄×C₅	—	6	1	no	—
480	C₂×C₄×C₅	—	6	1	no	—
481	C₂×C₄×C₅	—	6	1	no	—
482	C₂×C₄×C₅	—	12	1	no	—
483	C₂×C₄×C₅	—	12	1	no	—
484	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
485	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
486	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
487	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
488	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
489	#168	—	2	1	no	—
490	#168	—	2	1	no	—
491	#168	—	2	1	no	—
492	#168	—	3	2	no	—
493	#168	—	6	1	no	—
494	#168	—	6	1	no	—
495	#168	—	6	1	no	—
496	#168	D₃×D₄	1	2	yes	—
497	C₂×#41	—	3	1	no	—
498	C₂×#41	—	3	1	no	—
499	#131	—	30	4	no	—
500	#131	—	30	4	no	—
501	C₂×M₁₆	—	5	1	no	—
502	C₂×M₁₆	—	15	1	no	—
503	C₂×M₁₆	—	15	1	no	—
504	C₂×M₁₆	—	15	1	no	—
505	C₂×M₁₆	—	15	1	no	—
506	C₂×M₁₆	—	15	1	no	—
507	C₂²×C₈	—	5	1	no	—
508	C₂²×C₈	—	15	1	no	—
509	C₂²×C₈	—	15	1	no	—
510	C₂²×C₈	—	15	1	no	—
511	C₂²×C₈	—	15	1	no	—
512	C₂²×C₈	—	15	1	no	—
513	C₄⋊Q₈	—	3	1	no	—
514	#127	—	3	1	no	—
515	#124	—	3	1	no	—
516	#124	—	3	1	no	—
517	#121	—	3	1	no	—
518	#121	—	3	1	no	—
519	#121	—	3	1	no	—
520	#121	—	3	1	no	—
521	C₄×D₄	—	3	1	no	—
522	C₄×D₄	—	3	1	no	—
523	C₄×D₄	—	3	1	no	—
524	C₄×D₄	D₃×D₅	1	1	yes	characteristic
525	C₂×C₄²	—	3	1	no	—
526	C₄⋊C₈	—	5	1	no	—
527	C₄⋊C₈	—	15	1	no	—
528	C₄⋊C₈	—	15	1	no	—
529	C₄⋊C₈	—	15	1	no	—
530	C₂²⋊C₈	—	5	1	no	—
531	C₂²⋊C₈	—	5	1	no	—
532	C₂²⋊C₈	—	15	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	#97	—	5	1	no	—
539	#97	—	15	1	no	—
540	#97	—	15	1	no	—
541	#97	—	15	1	no	—
542	C₂×C₃×C₅	—	4	1	no	—
543	C₂×C₃×C₅	—	4	1	no	—
544	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
545	C₂×C₃×C₅	#568	1	1	yes	characteristic
546	C₂×C₃×C₅	#568	1	1	yes	characteristic
547	C₅×D₃	—	2	2	no	—
548	C₅×D₃	—	4	1	no	—
549	C₅×D₃	—	4	1	no	—
550	C₂³×C₃	C₂²×Dic₅	1	1	yes	characteristic
551	C₂³×C₃	C₂²×Dic₅	1	1	yes	characteristic
552	C₂²×D₃	C₂²×Dic₅	1	1	yes	characteristic
553	C₂²×D₃	C₂²×Dic₅	1	1	yes	characteristic
554	C₂²×D₃	C₂²×Dic₅	1	1	yes	characteristic
555	C₃×D₄	—	4	1	no	—
556	C₂×C₃×C₄	—	2	1	no	—
557	C₂×C₃×C₄	—	2	1	no	—
558	C₂×C₃×C₄	—	2	1	no	—
559	C₂×C₃×C₄	—	2	1	no	—
560	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
561	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
562	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
563	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
564	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
565	#67	—	2	2	no	—
566	#67	—	2	2	no	—
567	#67	—	2	2	no	—
568	#67	—	2	2	no	—
569	#67	—	4	1	no	—
570	#67	—	4	1	no	—
571	C₂×Dic₃	C₂²×Dic₅	1	1	yes	characteristic
572	C₂×Dic₃	C₂²×Dic₅	1	1	yes	characteristic
573	C₂×Dic₃	C₂²×Dic₅	1	1	yes	characteristic
574	C₂×Dic₃	C₂²×Dic₅	1	1	yes	characteristic
575	C₂×Dic₃	C₂²×Dic₅	1	1	yes	characteristic
576	D₁₂	—	2	2	no	—
577	D₁₂	—	2	2	no	—
578	D₁₂	—	4	1	no	—
579	C₄×D₃	—	2	1	no	—
580	C₄×D₃	—	2	1	no	—
581	C₄×D₃	—	2	1	no	—
582	C₄×D₃	—	2	1	no	—
583	C₄×D₃	—	4	1	no	—
584	C₄×D₃	—	4	1	no	—
585	C₄×D₃	D₄×D₅	1	2	yes	—
586	C₄×D₃	#711	1	2	yes	—
587	Dic₆	—	2	2	no	—
588	Dic₆	—	2	2	no	—
589	C₃×C₈	—	5	2	no	—
590	C₃×C₈	—	10	1	no	—
591	C₃×C₈	—	10	1	no	—
592	C₃×C₈	—	10	1	no	—
593	C₃⋊C₈	—	5	2	no	—
594	C₃⋊C₈	—	10	1	no	—
595	C₃⋊C₈	—	10	1	no	—
596	C₃⋊C₈	—	10	1	no	—
597	C₂²×C₅	—	2	1	no	—
598	C₂²×C₅	—	2	1	no	—
599	C₂²×C₅	—	2	1	no	—
600	C₂²×C₅	—	2	1	no	—
601	C₂²×C₅	—	2	1	no	—
602	C₂²×C₅	—	2	1	no	—
603	C₂²×C₅	—	3	2	no	—
604	C₂²×C₅	—	6	1	no	—
605	C₂²×C₅	—	6	1	no	—
606	C₂²×C₅	—	6	1	no	—
607	C₂²×C₅	—	6	1	no	—
608	C₂²×C₅	—	6	1	no	—
609	C₂²×C₅	—	6	1	no	—
610	C₂²×C₅	—	6	1	no	—
611	C₂²×C₅	—	6	1	no	—
612	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
613	C₄×C₅	—	2	1	no	—
614	C₄×C₅	—	2	1	no	—
615	C₄×C₅	—	2	1	no	—
616	C₄×C₅	—	2	1	no	—
617	C₄×C₅	—	3	2	no	—
618	C₄×C₅	—	6	1	no	—
619	C₄×C₅	—	6	1	no	—
620	C₄×C₅	—	6	1	no	—
621	C₄×C₅	—	6	1	no	—
622	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
623	C₄×C₅	D₃×#41	1	1	yes	characteristic
624	#41	—	6	2	no	—
625	#41	—	6	2	no	—
626	#41	—	6	2	no	—
627	#41	—	6	2	no	—
628	C₂×Q₈	—	3	1	no	—
629	C₂×Q₈	—	3	1	no	—
630	C₂×D₄	—	3	1	no	—
631	C₂×D₄	—	3	1	no	—
632	C₂×D₄	—	3	1	no	—
633	C₂×D₄	—	3	1	no	—
634	C₂×D₄	—	3	1	no	—
635	C₂×D₄	—	3	1	no	—
636	C₂×D₄	—	3	1	no	—
637	C₂×D₄	—	3	1	no	—
638	C₂×D₄	—	3	1	no	—
639	C₂×D₄	D₃×Dic₅	1	1	yes	characteristic
640	C₂²×C₄	—	3	1	no	—
641	C₂²×C₄	—	3	1	no	—
642	C₂²×C₄	—	3	1	no	—
643	C₂²×C₄	—	3	1	no	—
644	C₂²×C₄	—	3	1	no	—
645	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
646	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
647	M₁₆	—	10	2	no	—
648	M₁₆	—	30	2	no	—
649	M₁₆	—	30	2	no	—
650	M₁₆	—	30	2	no	—
651	M₁₆	—	30	2	no	—
652	M₁₆	—	30	2	no	—
653	C₂×C₈	—	5	1	no	—
654	C₂×C₈	—	5	1	no	—
655	C₂×C₈	—	5	1	no	—
656	C₂×C₈	—	5	1	no	—
657	C₂×C₈	—	10	2	no	—
658	C₂×C₈	—	15	4	no	—
659	C₂×C₈	—	15	1	no	—
660	C₂×C₈	—	15	1	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	—	30	2	no	—
666	C₂×C₈	—	30	2	no	—
667	C₄⋊C₄	—	3	1	no	—
668	C₄⋊C₄	—	3	1	no	—
669	C₄⋊C₄	—	3	1	no	—
670	C₄⋊C₄	D₃×Dic₅	1	1	yes	characteristic
671	C₂²⋊C₄	—	3	1	no	—
672	C₂²⋊C₄	—	3	1	no	—
673	C₂²⋊C₄	—	3	1	no	—
674	C₂²⋊C₄	—	3	1	no	—
675	C₂²⋊C₄	—	3	1	no	—
676	C₂²⋊C₄	—	3	1	no	—
677	C₂²⋊C₄	D₃×Dic₅	1	1	yes	characteristic
678	C₂²⋊C₄	D₃×Dic₅	1	1	yes	characteristic
679	C₄²	—	3	1	no	—
680	C₄²	—	3	1	no	—
681	C₄²	—	3	1	no	—
682	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
683	C₃×C₅	#2932	1	1	yes	characteristic, complemented, Hall
684	C₂²×C₃	—	2	1	no	—
685	C₂²×C₃	—	2	1	no	—
686	C₂²×C₃	—	2	1	no	—
687	C₂²×C₃	—	2	1	no	—
688	C₂²×C₃	—	2	1	no	—
689	C₂²×C₃	—	2	1	no	—
690	C₂²×C₃	C₂³×Dic₅	1	1	yes	characteristic
691	C₂×D₃	—	2	1	no	—
692	C₂×D₃	—	2	1	no	—
693	C₂×D₃	—	2	1	no	—
694	C₂×D₃	—	2	1	no	—
695	C₂×D₃	—	2	1	no	—
696	C₂×D₃	—	2	1	no	—
697	C₂×D₃	—	2	1	no	—
698	C₂×D₃	—	2	1	no	—
699	C₂×D₃	D₄×Dic₅	1	2	yes	—
700	C₃×C₄	—	2	1	no	—
701	C₃×C₄	—	2	1	no	—
702	C₃×C₄	—	2	1	no	—
703	C₃×C₄	—	2	1	no	—
704	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
705	C₃×C₄	C₂×#711	1	1	yes	characteristic
706	Dic₃	—	2	1	no	—
707	Dic₃	—	2	1	no	—
708	Dic₃	—	2	1	no	—
709	Dic₃	—	2	1	no	—
710	Dic₃	D₄×Dic₅	1	2	yes	—
711	C₂×C₅	—	4	1	no	—
712	C₂×C₅	—	4	1	no	—
713	C₂×C₅	—	6	2	no	—
714	C₂×C₅	—	12	1	no	—
715	C₂×C₅	—	12	1	no	—
716	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
717	C₂×C₅	#5745	1	1	yes	characteristic
718	C₂×C₅	#5750	1	1	yes	characteristic
719	C₂³	—	3	1	no	—
720	C₂³	—	3	1	no	—
721	C₂³	—	3	1	no	—
722	C₂³	C₂×D₃×Dic₅	1	1	yes	characteristic
723	C₂³	C₂×D₃×Dic₅	1	1	yes	characteristic
724	Q₈	—	6	2	no	—
725	Q₈	—	6	2	no	—
726	D₄	—	4	1	no	—
727	D₄	—	6	2	no	—
728	D₄	—	6	2	no	—
729	D₄	—	6	2	no	—
730	D₄	—	6	2	no	—
731	D₄	—	6	2	no	—
732	D₄	—	6	2	no	—
733	D₄	—	12	1	no	—
734	D₄	—	12	1	no	—
735	D₄	—	12	1	no	—
736	C₂×C₄	—	2	1	no	—
737	C₂×C₄	—	2	1	no	—
738	C₂×C₄	—	2	1	no	—
739	C₂×C₄	—	2	1	no	—
740	C₂×C₄	—	3	1	no	—
741	C₂×C₄	—	3	2	no	—
742	C₂×C₄	—	3	2	no	—
743	C₂×C₄	—	3	1	no	—
744	C₂×C₄	—	3	1	no	—
745	C₂×C₄	—	3	1	no	—
746	C₂×C₄	—	3	1	no	—
747	C₂×C₄	—	6	1	no	—
748	C₂×C₄	—	6	1	no	—
749	C₂×C₄	—	6	1	no	—
750	C₂×C₄	—	6	1	no	—
751	C₂×C₄	—	12	1	no	—
752	C₂×C₄	—	12	1	no	—
753	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
754	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
755	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
756	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
757	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
758	C₈	—	5	2	no	—
759	C₈	—	10	1	no	—
760	C₈	—	10	1	no	—
761	C₈	—	10	1	no	—
762	C₈	—	15	2	no	—
763	C₈	—	30	1	no	—
764	C₈	—	30	1	no	—
765	C₈	—	30	1	no	—
766	C₂×C₃	—	4	1	no	—
767	C₂×C₃	—	4	1	no	—
768	C₂×C₃	C₂×D₄×Dic₅	1	1	yes	characteristic
769	C₂×C₃	#66153	1	1	yes	characteristic
770	C₂×C₃	#66153	1	1	yes	characteristic
771	D₃	—	2	2	no	—
772	D₃	—	4	1	no	—
773	D₃	—	4	1	no	—
774	C₅	#79480	1	1	yes	characteristic, complemented, Sylow
775	C₂²	—	2	1	no	—
776	C₂²	—	2	1	no	—
777	C₂²	—	2	1	no	—
778	C₂²	—	2	1	no	—
779	C₂²	—	2	1	no	—
780	C₂²	—	2	1	no	—
781	C₂²	—	3	2	no	—
782	C₂²	—	6	1	no	—
783	C₂²	—	6	1	no	—
784	C₂²	—	6	1	no	—
785	C₂²	—	6	1	no	—
786	C₂²	—	6	1	no	—
787	C₂²	—	6	1	no	—
788	C₂²	—	6	1	no	—
789	C₂²	—	6	1	no	—
790	C₂²	C₂²×D₃×Dic₅	1	1	yes	characteristic
791	C₄	—	2	1	no	—
792	C₄	—	2	1	no	—
793	C₄	—	2	1	no	—
794	C₄	—	2	1	no	—
795	C₄	—	3	2	no	—
796	C₄	—	6	1	no	—
797	C₄	—	6	1	no	—
798	C₄	—	6	1	no	—
799	C₄	—	6	1	no	—
800	C₄	D₃×D₄×D₅	1	1	yes	characteristic
801	C₄	D₃×#711	1	1	yes	characteristic
802	C₃	#10615007	1	1	yes	characteristic, complemented, Sylow
803	C₂	—	4	1	no	—
804	C₂	—	4	1	no	—
805	C₂	—	6	2	no	—
806	C₂	—	12	1	no	—
807	C₂	—	12	1	no	—
808	C₂	#11754125	1	1	yes	characteristic
809	C₂	D₃×D₄×Dic₅	1	1	yes	characteristic
810	C₂	#11755298	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃×D₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Fitting	C₃×C₄×C₅×D₄	C₂²
prime radical	C₅×#5548	C₂
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₄×D₄	D₃×D₅
hypocenter	C₃×C₅	#2932
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄×D₄

Complements

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

N	H ≅ G/N	type
2. C₂×#91288	C₂	semidirect
3. C₂×#91286	C₂	semidirect
4. #11751112	C₂	semidirect
5. C₃×#65300	C₂	semidirect
6. #11748508	C₂	semidirect
7. #11748500	C₂	semidirect
8. #11748496	C₂	semidirect
9. #11748490	C₂	semidirect
10. #11748490	C₂	semidirect
11. #11748484	C₂	semidirect
12. #11747011	C₂	semidirect
13. #11746999	C₂	semidirect
14. #11746987	C₂	semidirect
15. D₃×#3935	C₂	semidirect
75. #65300	D₃	semidirect
136. D₃×#168	D₄	semidirect
683. C₃×C₅	#2932	semidirect
774. C₅	#79480	semidirect
802. C₃	#10615007	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5548	2
C₂×#91288	2
C₂×#91286	2
#11751112	2
C₃×#65300	2
#11748508	2
#11748500	2
#11748496	2
#11748490	2
#11748484	2
#11747011	2
#11746999	2
#11746987	2
D₃×#3935	2
#10615007	3
#79480	5