Subgroups — #14413129

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×#676	C₂	1	1	yes	maximal, characteristic
2	C₂×D₅×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic
3	#11752723	C₂	1	1	yes	maximal, characteristic
4	#11750938	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4839	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65128	C₂	1	1	yes	maximal, characteristic, complemented
7	#11747661	C₂	1	1	yes	maximal, characteristic, complemented
8	#11747655	C₂	1	1	yes	maximal, characteristic, complemented
9	#11747648	C₂	1	1	yes	maximal, characteristic, complemented
10	#11747647	C₂	1	1	yes	maximal, characteristic, complemented
11	#11747594	C₂	1	1	yes	maximal, characteristic, complemented
12	#11747594	C₂	1	1	yes	maximal, characteristic, complemented
13	#11747015	C₂	1	1	yes	maximal, characteristic, complemented
14	#11746993	C₂	1	1	yes	maximal, characteristic, complemented
15	#11746985	C₂	1	1	yes	maximal, characteristic, complemented
16	#10610811	—	3	1	no	maximal, Hall
17	C₂×C₄×D₃×D₅	C₂²	1	1	yes	characteristic
18	C₂×#6705	C₂²	1	1	yes	characteristic
19	C₂×#6705	C₂²	1	1	yes	characteristic
20	C₄²×D₁₅	C₂²	1	1	yes	characteristic
21	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
22	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
23	C₅×#872	C₂²	1	1	yes	characteristic
24	C₂×C₃×#676	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
26	C₃×#4018	C₂²	1	1	yes	characteristic
27	#91473	C₄	1	1	yes	characteristic
28	#91473	C₄	1	1	yes	characteristic
29	#91404	C₄	1	1	yes	characteristic
30	#91404	C₄	1	1	yes	characteristic
31	C₄×#1200	C₂²	1	1	yes	characteristic
32	#91400	C₄	1	1	yes	characteristic
33	#91400	C₄	1	1	yes	characteristic
34	#91394	C₄	1	1	yes	characteristic
35	#91394	C₄	1	1	yes	characteristic
36	#91371	C₂²	1	1	yes	characteristic
37	#91357	C₂²	1	1	yes	characteristic
38	C₂×#6651	C₂²	1	1	yes	characteristic
39	C₂×#6651	C₂²	1	1	yes	characteristic
40	C₂×#6650	C₂²	1	1	yes	characteristic
41	C₂×#6649	C₂²	1	1	yes	characteristic
42	C₂×D₃×#168	C₂²	1	1	yes	characteristic
43	C₂×D₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
44	D₃×#676	—	2	4	no	—
45	D₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
46	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
47	#91098	C₂²	1	1	yes	characteristic, complemented
48	#91098	C₂²	1	1	yes	characteristic, complemented
49	C₄⋊(C₃⋊#168)	C₂²	1	1	yes	characteristic, complemented
50	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
51	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
52	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
53	C₃×#3946	C₂²	1	1	yes	characteristic, complemented
54	C₃×#3946	C₂²	1	1	yes	characteristic, complemented
55	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic, complemented
56	Dic₃⋊#168	C₂²	1	1	yes	characteristic, complemented
57	Dic₃⋊#168	C₂²	1	1	yes	characteristic, complemented
58	#90983	C₂²	1	1	yes	characteristic, complemented
59	#90983	C₂²	1	1	yes	characteristic, complemented
60	#90982	C₂²	1	1	yes	characteristic, complemented
61	#90982	C₂²	1	1	yes	characteristic, complemented
62	#79080	—	5	1	no	maximal, Hall
63	C₂×D₅×M₁₆	—	3	1	no	—
64	C₂²×#676	—	3	1	no	—
65	D₅×#117	—	3	1	no	—
66	C₅×#424	—	3	1	no	—
67	#65408	—	3	1	no	—
68	#65391	—	3	1	no	—
69	#65288	—	3	1	no	—
70	#65128	—	3	1	no	—
71	#65128	—	3	1	no	—
72	#65128	—	3	1	no	—
73	#65128	D₃	1	1	yes	characteristic, complemented
74	#65126	—	3	1	no	—
75	#65126	—	3	1	no	—
76	#65126	—	3	1	no	—
77	#65126	—	3	1	no	—
78	C₂²×D₃×D₅	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄×D₁₅	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄×D₁₅	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄×D₁₅	C₂³	1	1	yes	characteristic
82	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
83	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
84	C₂×#1200	C₂×C₄	1	1	yes	characteristic
85	C₂×#1200	C₂×C₄	1	1	yes	characteristic
86	C₂×#1200	C₂×C₄	1	1	yes	characteristic
87	C₂×D₃×Dic₅	C₂×C₄	1	1	yes	characteristic
88	C₂×D₅×Dic₃	C₂×C₄	1	1	yes	characteristic
89	C₄×D₃×D₅	D₄	1	4	yes	—
90	C₄×D₃×D₅	Q₈	1	4	yes	—
91	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
92	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
93	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
94	C₄×Dic₁₅	C₂×C₄	1	1	yes	characteristic
95	C₄×Dic₁₅	C₂×C₄	1	1	yes	characteristic
96	C₄×Dic₁₅	C₂³	1	1	yes	characteristic
97	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
98	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
99	#6705	—	2	2	no	—
100	#6705	—	2	2	no	—
101	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
102	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
103	C₅×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
104	C₅×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
105	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
106	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
107	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
108	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
109	C₅×D₃×C₈	—	2	2	no	—
110	C₃×#685	C₂×C₄	1	1	yes	characteristic
111	C₃×#685	C₂×C₄	1	1	yes	characteristic
112	C₃×#683	C₂×C₄	1	1	yes	characteristic
113	C₃×#683	C₂×C₄	1	1	yes	characteristic
114	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
115	C₂×C₃×#168	C₂³	1	1	yes	characteristic
116	C₂×C₃×#168	C₂³	1	1	yes	characteristic
117	C₃×#676	—	2	2	no	—
118	C₃×C₈×D₅	—	2	2	no	—
119	Dic₃⋊Dic₅	C₂×C₄	1	1	yes	characteristic
120	Dic₃⋊Dic₅	C₂×C₄	1	1	yes	characteristic
121	#6668	C₂×C₄	1	1	yes	characteristic
122	#6668	C₂×C₄	1	1	yes	characteristic
123	(C₂×D₃)⋊Dic₅	C₂×C₄	1	1	yes	characteristic
124	(C₂×D₃)⋊Dic₅	C₂×C₄	1	1	yes	characteristic
125	#6665	C₂×C₄	1	1	yes	characteristic
126	#6665	C₂×C₄	1	1	yes	characteristic
127	Dic₃×Dic₅	C₂×C₄	1	1	yes	characteristic
128	Dic₃×Dic₅	C₂×C₄	1	1	yes	characteristic
129	#6651	—	2	2	no	—
130	#6651	—	2	2	no	—
131	#6650	—	2	2	no	—
132	#6649	—	2	2	no	—
133	D₃×#168	—	2	2	no	—
134	D₅×C₃⋊C₈	—	2	2	no	—
135	C₂×D₃×M₁₆	—	5	1	no	—
136	C₂²×ΓL(1,𝔽₂₅)	—	5	1	no	—
137	D₃×#117	—	5	1	no	—
138	C₃×#424	—	5	1	no	—
139	#5119	—	5	1	no	—
140	#5102	—	5	1	no	—
141	#4999	—	5	1	no	—
142	#4839	—	5	1	no	—
143	#4839	—	5	1	no	—
144	#4839	—	5	1	no	—
145	#4839	D₅	1	1	yes	characteristic, complemented
146	#4837	—	5	1	no	—
147	#4837	—	5	1	no	—
148	#4837	—	5	1	no	—
149	#4837	—	5	1	no	—
150	C₂²×C₄×D₅	—	3	1	no	—
151	C₂×C₅×M₁₆	—	3	1	no	—
152	C₂²×C₅×C₈	—	3	1	no	—
153	C₅×#117	—	3	1	no	—
154	#4072	—	3	1	no	—
155	C₂×#681	—	3	1	no	—
156	C₂²×#168	—	3	1	no	—
157	D₅×M₁₆	—	6	4	no	—
158	C₂×#676	—	3	1	no	—
159	C₂×#676	—	3	1	no	—
160	C₂×#676	—	3	1	no	—
161	C₂×#676	—	3	1	no	—
162	C₂×#676	—	3	1	no	—
163	C₂×#676	—	6	4	no	—
164	C₂×#676	C₂×D₃	1	1	yes	characteristic
165	C₂×C₈×D₅	—	3	1	no	—
166	C₂×C₈×D₅	C₂×D₃	1	1	yes	characteristic
167	#4038	—	3	1	no	—
168	#4038	—	3	1	no	—
169	D₅×C₄⋊C₄	—	3	1	no	—
170	D₅×C₄⋊C₄	—	3	1	no	—
171	D₅×C₂²⋊C₄	—	3	1	no	—
172	D₅×C₂²⋊C₄	—	3	1	no	—
173	#4023	—	3	1	no	—
174	#4023	—	3	1	no	—
175	#4018	—	3	1	no	—
176	#4018	C₂×D₃	1	1	yes	characteristic
177	C₄²×D₅	—	3	1	no	—
178	C₄²×D₅	—	3	1	no	—
179	C₅×C₄⋊C₈	—	3	1	no	—
180	C₅×C₄⋊C₈	—	3	1	no	—
181	C₅×C₄⋊C₈	—	3	1	no	—
182	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
183	#3946	—	3	1	no	—
184	#3946	—	3	1	no	—
185	#3946	—	3	1	no	—
186	#3946	—	3	1	no	—
187	#3946	—	3	1	no	—
188	#3946	—	3	1	no	—
189	#3946	C₂×D₃	1	1	yes	characteristic, complemented
190	#3946	C₂×D₃	1	1	yes	characteristic, complemented
191	C₄⋊#168	—	3	1	no	—
192	C₄⋊#168	—	3	1	no	—
193	C₄⋊#168	—	3	1	no	—
194	C₄⋊#168	C₂×D₃	1	1	yes	characteristic, complemented
195	#2905	—	15	1	no	Sylow
196	C₂²×D₁₅	C₂²×C₄	1	1	yes	characteristic
197	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
198	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
199	C₂×D₃×D₅	—	4	1	no	—
200	C₂×D₃×D₅	—	4	1	no	—
201	C₂×D₃×D₅	C₄⋊C₄	1	4	yes	—
202	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
203	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
204	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
205	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
206	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
207	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
208	C₄×D₁₅	—	4	1	no	—
209	C₄×D₁₅	—	4	1	no	—
210	C₄×D₁₅	C₂×D₄	1	2	yes	—
211	C₄×D₁₅	C₂×Q₈	1	2	yes	—
212	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
213	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
214	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
215	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
216	C₄×C₅×D₃	C₂×Q₈	1	2	yes	—
217	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
218	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
219	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
220	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
221	C₃×C₄×D₅	C₂×Q₈	1	2	yes	—
222	#1200	—	4	1	no	—
223	#1200	—	4	1	no	—
224	#1200	C₄⋊C₄	1	4	yes	—
225	D₃×Dic₅	C₄⋊C₄	1	4	yes	—
226	D₅×Dic₃	C₄⋊C₄	1	4	yes	—
227	C₃×C₅×C₈	—	2	1	no	—
228	C₃×C₅×C₈	—	2	1	no	—
229	C₃⋊#168	—	2	1	no	—
230	C₃⋊#168	—	2	1	no	—
231	C₃×#168	—	2	1	no	—
232	C₃×#168	—	2	1	no	—
233	C₅×C₃⋊C₈	—	2	1	no	—
234	C₅×C₃⋊C₈	—	2	1	no	—
235	C₂²×C₄×D₃	—	5	1	no	—
236	C₂×C₃×M₁₆	—	5	1	no	—
237	C₂²×C₃×C₈	—	5	1	no	—
238	C₃×#117	—	5	1	no	—
239	#926	—	5	1	no	—
240	C₂×#208	—	5	1	no	—
241	C₂²×C₃⋊C₈	—	5	1	no	—
242	D₃×M₁₆	—	10	4	no	—
243	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
244	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
245	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
246	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
247	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
248	C₂×ΓL(1,𝔽₂₅)	—	10	4	no	—
249	C₂×ΓL(1,𝔽₂₅)	C₂×D₅	1	1	yes	characteristic
250	C₂×D₃×C₈	—	5	1	no	—
251	C₂×D₃×C₈	C₂×D₅	1	1	yes	characteristic
252	#892	—	5	1	no	—
253	#892	—	5	1	no	—
254	D₃×C₄⋊C₄	—	5	1	no	—
255	D₃×C₄⋊C₄	—	5	1	no	—
256	D₃×C₂²⋊C₄	—	5	1	no	—
257	D₃×C₂²⋊C₄	—	5	1	no	—
258	#877	—	5	1	no	—
259	#877	—	5	1	no	—
260	#872	—	5	1	no	—
261	#872	C₂×D₅	1	1	yes	characteristic
262	C₄²×D₃	—	5	1	no	—
263	C₄²×D₃	—	5	1	no	—
264	C₃×C₄⋊C₈	—	5	1	no	—
265	C₃×C₄⋊C₈	—	5	1	no	—
266	C₃×C₄⋊C₈	—	5	1	no	—
267	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic, complemented
268	Dic₃⋊C₈	—	5	1	no	—
269	Dic₃⋊C₈	—	5	1	no	—
270	Dic₃⋊C₈	—	5	1	no	—
271	Dic₃⋊C₈	—	5	1	no	—
272	Dic₃⋊C₈	—	5	1	no	—
273	Dic₃⋊C₈	—	5	1	no	—
274	Dic₃⋊C₈	C₂×D₅	1	1	yes	characteristic, complemented
275	Dic₃⋊C₈	C₂×D₅	1	1	yes	characteristic, complemented
276	C₄⋊(C₃⋊C₈)	—	5	1	no	—
277	C₄⋊(C₃⋊C₈)	—	5	1	no	—
278	C₄⋊(C₃⋊C₈)	—	5	1	no	—
279	C₄⋊(C₃⋊C₈)	C₂×D₅	1	1	yes	characteristic, complemented
280	C₂³×D₅	—	3	1	no	—
281	C₂²×C₄×C₅	—	3	1	no	—
282	C₂²×Dic₅	—	3	1	no	—
283	C₂×C₄×D₅	—	3	1	no	—
284	C₂×C₄×D₅	—	3	1	no	—
285	C₂×C₄×D₅	—	3	1	no	—
286	C₂×C₄×D₅	—	3	4	no	—
287	C₂×C₄×D₅	—	3	4	no	—
288	C₂×C₄×D₅	—	3	1	no	—
289	C₂×C₄×D₅	—	3	1	no	—
290	C₂×C₄×D₅	—	3	1	no	—
291	C₂×C₄×D₅	—	3	1	no	—
292	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
293	C₅×M₁₆	—	6	2	no	—
294	C₂×C₅×C₈	—	3	1	no	—
295	C₂×C₅×C₈	—	3	1	no	—
296	C₂×C₅×C₈	—	6	2	no	—
297	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
298	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
299	C₅×C₄⋊C₄	—	3	1	no	—
300	C₅×C₄⋊C₄	—	3	1	no	—
301	C₅×C₂²⋊C₄	—	3	1	no	—
302	C₅×C₂²⋊C₄	—	3	1	no	—
303	C₄²×C₅	—	3	1	no	—
304	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
305	C₂²⋊Dic₅	—	3	1	no	—
306	C₂²⋊Dic₅	—	3	1	no	—
307	#685	—	3	1	no	—
308	#685	—	3	1	no	—
309	#685	C₄×D₃	1	1	yes	characteristic
310	#685	C₄×D₃	1	1	yes	characteristic
311	C₄⋊Dic₅	—	3	1	no	—
312	C₄⋊Dic₅	—	3	1	no	—
313	#683	—	3	1	no	—
314	#683	—	3	1	no	—
315	#683	C₄×D₃	1	1	yes	characteristic
316	#683	C₄×D₃	1	1	yes	characteristic
317	C₄×Dic₅	—	3	1	no	—
318	C₄×Dic₅	—	3	1	no	—
319	C₄×Dic₅	—	3	1	no	—
320	C₄×Dic₅	—	3	1	no	—
321	C₄×Dic₅	—	3	1	no	—
322	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
323	#681	—	6	2	no	—
324	C₂×#168	—	3	1	no	—
325	C₂×#168	—	3	1	no	—
326	C₂×#168	—	6	2	no	—
327	C₂×#168	C₂²×D₃	1	1	yes	characteristic
328	C₂×#168	C₂²×D₃	1	1	yes	characteristic
329	#676	—	2	2	no	—
330	#676	—	6	2	no	—
331	#676	—	6	2	no	—
332	#676	—	6	2	no	—
333	#676	—	6	2	no	—
334	#676	—	6	2	no	—
335	C₈×D₅	—	2	2	no	—
336	C₈×D₅	—	6	2	no	—
337	C₂²×M₁₆	—	15	1	no	—
338	C₂²×M₁₆	—	15	1	no	—
339	C₂×#117	—	15	1	no	—
340	#424	—	3	1	no	—
341	#424	—	5	1	no	—
342	#424	—	15	1	no	—
343	#424	—	15	1	no	—
344	#424	—	15	1	no	—
345	#424	—	15	1	no	—
346	#424	—	15	1	no	—
347	#424	—	15	1	no	—
348	#423	—	15	1	no	—
349	#423	—	15	1	no	—
350	#423	—	15	1	no	—
351	#423	—	15	1	no	—
352	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
353	C₂×D₁₅	—	2	1	no	—
354	C₂×D₁₅	—	2	1	no	—
355	C₂×D₁₅	C₂×C₄⋊C₄	1	2	yes	—
356	C₂×C₅×D₃	—	2	1	no	—
357	C₂×C₅×D₃	—	2	1	no	—
358	C₂×C₅×D₃	C₂×C₄⋊C₄	1	2	yes	—
359	C₂×C₃×D₅	—	2	1	no	—
360	C₂×C₃×D₅	—	2	1	no	—
361	C₂×C₃×D₅	C₂×C₄⋊C₄	1	2	yes	—
362	D₃×D₅	—	4	4	no	—
363	C₃×C₄×C₅	—	2	1	no	—
364	C₃×C₄×C₅	—	2	1	no	—
365	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
366	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
367	Dic₁₅	—	2	1	no	—
368	Dic₁₅	—	2	1	no	—
369	Dic₁₅	C₂×C₄⋊C₄	1	2	yes	—
370	C₃×Dic₅	—	2	1	no	—
371	C₃×Dic₅	—	2	1	no	—
372	C₃×Dic₅	C₂×C₄⋊C₄	1	2	yes	—
373	C₅×Dic₃	—	2	1	no	—
374	C₅×Dic₃	—	2	1	no	—
375	C₅×Dic₃	C₂×C₄⋊C₄	1	2	yes	—
376	C₂³×D₃	—	5	1	no	—
377	C₂²×C₃×C₄	—	5	1	no	—
378	C₂²×Dic₃	—	5	1	no	—
379	C₂×C₄×D₃	—	5	1	no	—
380	C₂×C₄×D₃	—	5	1	no	—
381	C₂×C₄×D₃	—	5	1	no	—
382	C₂×C₄×D₃	—	5	4	no	—
383	C₂×C₄×D₃	—	5	4	no	—
384	C₂×C₄×D₃	—	5	1	no	—
385	C₂×C₄×D₃	—	5	1	no	—
386	C₂×C₄×D₃	—	5	1	no	—
387	C₂×C₄×D₃	—	5	1	no	—
388	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
389	C₃×M₁₆	—	10	2	no	—
390	C₂×C₃×C₈	—	5	1	no	—
391	C₂×C₃×C₈	—	5	1	no	—
392	C₂×C₃×C₈	—	10	2	no	—
393	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
394	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
395	C₃×C₄⋊C₄	—	5	1	no	—
396	C₃×C₄⋊C₄	—	5	1	no	—
397	C₃×C₂²⋊C₄	—	5	1	no	—
398	C₃×C₂²⋊C₄	—	5	1	no	—
399	C₃×C₄²	—	5	1	no	—
400	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
401	#217	—	5	1	no	—
402	#217	—	5	1	no	—
403	(C₂×D₃)⋊C₄	—	5	1	no	—
404	(C₂×D₃)⋊C₄	—	5	1	no	—
405	(C₂×D₃)⋊C₄	C₄×D₅	1	1	yes	characteristic
406	(C₂×D₃)⋊C₄	C₄×D₅	1	1	yes	characteristic
407	C₄⋊Dic₃	—	5	1	no	—
408	C₄⋊Dic₃	—	5	1	no	—
409	Dic₃⋊C₄	—	5	1	no	—
410	Dic₃⋊C₄	—	5	1	no	—
411	Dic₃⋊C₄	C₄×D₅	1	1	yes	characteristic
412	Dic₃⋊C₄	C₄×D₅	1	1	yes	characteristic
413	C₄×Dic₃	—	5	1	no	—
414	C₄×Dic₃	—	5	1	no	—
415	C₄×Dic₃	—	5	1	no	—
416	C₄×Dic₃	—	5	1	no	—
417	C₄×Dic₃	—	5	1	no	—
418	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
419	#208	—	10	2	no	—
420	C₂×C₃⋊C₈	—	5	1	no	—
421	C₂×C₃⋊C₈	—	5	1	no	—
422	C₂×C₃⋊C₈	—	10	2	no	—
423	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
424	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
425	ΓL(1,𝔽₂₅)	—	2	2	no	—
426	ΓL(1,𝔽₂₅)	—	10	2	no	—
427	ΓL(1,𝔽₂₅)	—	10	2	no	—
428	ΓL(1,𝔽₂₅)	—	10	2	no	—
429	ΓL(1,𝔽₂₅)	—	10	2	no	—
430	ΓL(1,𝔽₂₅)	—	10	2	no	—
431	D₃×C₈	—	2	2	no	—
432	D₃×C₈	—	10	2	no	—
433	C₂³×C₅	—	3	1	no	—
434	C₂²×D₅	—	3	1	no	—
435	C₂²×D₅	—	3	4	no	—
436	C₂²×D₅	—	12	1	no	—
437	C₂²×D₅	—	12	1	no	—
438	C₂²×D₅	C₂×C₄×D₃	1	1	yes	characteristic
439	C₂×C₄×C₅	—	3	1	no	—
440	C₂×C₄×C₅	—	3	2	no	—
441	C₂×C₄×C₅	—	3	2	no	—
442	C₂×C₄×C₅	—	3	1	no	—
443	C₂×C₄×C₅	—	3	1	no	—
444	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
445	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
446	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
447	C₂×Dic₅	—	3	1	no	—
448	C₂×Dic₅	—	3	4	no	—
449	C₂×Dic₅	—	3	1	no	—
450	C₂×Dic₅	—	3	1	no	—
451	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
452	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
453	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
454	C₄×D₅	—	3	4	no	—
455	C₄×D₅	—	3	2	no	—
456	C₄×D₅	—	3	2	no	—
457	C₄×D₅	—	3	4	no	—
458	C₄×D₅	—	12	1	no	—
459	C₄×D₅	—	12	1	no	—
460	C₄×D₅	—	12	1	no	—
461	C₄×D₅	—	12	1	no	—
462	C₄×D₅	D₃×D₄	1	2	yes	—
463	C₄×D₅	D₃×Q₈	1	2	yes	—
464	C₅×C₈	—	2	1	no	—
465	C₅×C₈	—	2	1	no	—
466	C₅×C₈	—	6	1	no	—
467	C₅×C₈	—	6	1	no	—
468	#168	—	2	1	no	—
469	#168	—	2	1	no	—
470	#168	—	6	1	no	—
471	#168	—	6	1	no	—
472	C₂³×C₄	—	15	1	no	—
473	C₂×M₁₆	—	3	1	no	—
474	C₂×M₁₆	—	5	1	no	—
475	C₂×M₁₆	—	15	1	no	—
476	C₂×M₁₆	—	15	1	no	—
477	C₂×M₁₆	—	15	1	no	—
478	C₂×M₁₆	—	15	1	no	—
479	C₂×M₁₆	—	15	1	no	—
480	C₂×M₁₆	—	15	1	no	—
481	C₂×M₁₆	—	30	4	no	—
482	C₂×M₁₆	—	30	4	no	—
483	C₂²×C₈	—	3	1	no	—
484	C₂²×C₈	—	5	1	no	—
485	C₂²×C₈	—	15	1	no	—
486	C₂²×C₈	—	15	1	no	—
487	#117	—	3	1	no	—
488	#117	—	5	1	no	—
489	#117	—	15	1	no	—
490	#117	—	15	1	no	—
491	#117	—	15	1	no	—
492	#117	—	15	1	no	—
493	#117	—	15	1	no	—
494	#117	—	15	1	no	—
495	C₂×C₄⋊C₄	—	15	1	no	—
496	C₂×C₄⋊C₄	—	15	1	no	—
497	C₂×C₂²⋊C₄	—	15	1	no	—
498	C₂×C₂²⋊C₄	—	15	1	no	—
499	C₂×C₄²	—	15	1	no	—
500	C₂×C₄²	—	15	1	no	—
501	C₄⋊C₈	—	3	1	no	—
502	C₄⋊C₈	—	3	1	no	—
503	C₄⋊C₈	—	3	1	no	—
504	C₄⋊C₈	—	5	1	no	—
505	C₄⋊C₈	—	5	1	no	—
506	C₄⋊C₈	—	5	1	no	—
507	C₄⋊C₈	—	15	1	no	—
508	C₄⋊C₈	—	15	1	no	—
509	C₄⋊C₈	—	15	1	no	—
510	C₄⋊C₈	—	15	1	no	—
511	C₄⋊C₈	—	15	1	no	—
512	C₄⋊C₈	—	15	1	no	—
513	C₄⋊C₈	—	15	1	no	—
514	C₄⋊C₈	—	15	1	no	—
515	C₄⋊C₈	—	15	1	no	—
516	C₄⋊C₈	D₃×D₅	1	1	yes	characteristic, complemented
517	C₂×C₃×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
518	C₂×C₃×C₅	#568	1	1	yes	characteristic
519	C₂×C₃×C₅	#568	1	1	yes	characteristic
520	D₁₅	—	2	2	no	—
521	C₃×D₅	—	2	2	no	—
522	C₅×D₃	—	2	2	no	—
523	C₂³×C₃	—	5	1	no	—
524	C₂²×D₃	—	5	1	no	—
525	C₂²×D₃	—	5	4	no	—
526	C₂²×D₃	—	20	1	no	—
527	C₂²×D₃	—	20	1	no	—
528	C₂²×D₃	C₂×C₄×D₅	1	1	yes	characteristic
529	C₂×C₃×C₄	—	5	1	no	—
530	C₂×C₃×C₄	—	5	2	no	—
531	C₂×C₃×C₄	—	5	2	no	—
532	C₂×C₃×C₄	—	5	1	no	—
533	C₂×C₃×C₄	—	5	1	no	—
534	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
535	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
536	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
537	C₂×Dic₃	—	5	1	no	—
538	C₂×Dic₃	—	5	4	no	—
539	C₂×Dic₃	—	5	1	no	—
540	C₂×Dic₃	—	5	1	no	—
541	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
542	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
543	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
544	C₄×D₃	—	5	4	no	—
545	C₄×D₃	—	5	2	no	—
546	C₄×D₃	—	5	2	no	—
547	C₄×D₃	—	5	4	no	—
548	C₄×D₃	—	20	1	no	—
549	C₄×D₃	—	20	1	no	—
550	C₄×D₃	—	20	1	no	—
551	C₄×D₃	—	20	1	no	—
552	C₄×D₃	D₄×D₅	1	2	yes	—
553	C₄×D₃	Q₈×D₅	1	2	yes	—
554	C₃×C₈	—	2	1	no	—
555	C₃×C₈	—	2	1	no	—
556	C₃×C₈	—	10	1	no	—
557	C₃×C₈	—	10	1	no	—
558	C₃⋊C₈	—	2	1	no	—
559	C₃⋊C₈	—	2	1	no	—
560	C₃⋊C₈	—	10	1	no	—
561	C₃⋊C₈	—	10	1	no	—
562	C₂²×C₅	—	3	2	no	—
563	C₂²×C₅	—	6	1	no	—
564	C₂²×C₅	—	6	1	no	—
565	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
566	C₂×D₅	—	2	1	no	—
567	C₂×D₅	—	2	1	no	—
568	C₂×D₅	—	3	2	no	—
569	C₂×D₅	—	6	1	no	—
570	C₂×D₅	—	6	1	no	—
571	C₂×D₅	—	12	4	no	—
572	C₂×D₅	D₃×C₄⋊C₄	1	2	yes	—
573	C₄×C₅	—	2	1	no	—
574	C₄×C₅	—	2	1	no	—
575	C₄×C₅	—	3	2	no	—
576	C₄×C₅	—	6	1	no	—
577	C₄×C₅	—	6	1	no	—
578	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
579	C₄×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
580	Dic₅	—	2	1	no	—
581	Dic₅	—	2	1	no	—
582	Dic₅	—	3	2	no	—
583	Dic₅	—	6	1	no	—
584	Dic₅	—	6	1	no	—
585	Dic₅	D₃×C₄⋊C₄	1	2	yes	—
586	C₂⁴	—	15	1	no	—
587	C₂²×C₄	—	3	1	no	—
588	C₂²×C₄	—	5	1	no	—
589	C₂²×C₄	—	15	1	no	—
590	C₂²×C₄	—	15	4	no	—
591	C₂²×C₄	—	15	4	no	—
592	C₂²×C₄	—	15	1	no	—
593	C₂²×C₄	—	15	1	no	—
594	C₂²×C₄	—	15	1	no	—
595	C₂²×C₄	—	15	1	no	—
596	C₂²×C₄	—	15	1	no	—
597	C₂²×C₄	—	15	1	no	—
598	C₂²×C₄	—	15	1	no	—
599	M₁₆	—	6	2	no	—
600	M₁₆	—	10	2	no	—
601	M₁₆	—	30	2	no	—
602	M₁₆	—	30	2	no	—
603	M₁₆	—	30	2	no	—
604	M₁₆	—	30	2	no	—
605	M₁₆	—	30	2	no	—
606	M₁₆	—	30	2	no	—
607	C₂×C₈	—	3	1	no	—
608	C₂×C₈	—	3	1	no	—
609	C₂×C₈	—	5	1	no	—
610	C₂×C₈	—	5	1	no	—
611	C₂×C₈	—	6	2	no	—
612	C₂×C₈	—	10	2	no	—
613	C₂×C₈	—	15	1	no	—
614	C₂×C₈	—	15	1	no	—
615	C₂×C₈	—	30	2	no	—
616	C₂×C₈	—	30	2	no	—
617	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
618	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
619	C₄⋊C₄	—	3	1	no	—
620	C₄⋊C₄	—	3	1	no	—
621	C₄⋊C₄	—	5	1	no	—
622	C₄⋊C₄	—	5	1	no	—
623	C₄⋊C₄	—	15	1	no	—
624	C₄⋊C₄	—	15	1	no	—
625	C₄⋊C₄	—	15	1	no	—
626	C₄⋊C₄	—	15	1	no	—
627	C₂²⋊C₄	—	3	1	no	—
628	C₂²⋊C₄	—	3	1	no	—
629	C₂²⋊C₄	—	5	1	no	—
630	C₂²⋊C₄	—	5	1	no	—
631	C₂²⋊C₄	—	15	1	no	—
632	C₂²⋊C₄	—	15	1	no	—
633	C₂²⋊C₄	—	15	1	no	—
634	C₂²⋊C₄	—	15	1	no	—
635	C₄²	—	3	1	no	—
636	C₄²	—	5	1	no	—
637	C₄²	—	15	1	no	—
638	C₄²	—	15	1	no	—
639	C₄²	—	15	1	no	—
640	C₄²	—	15	1	no	—
641	C₄²	—	15	1	no	—
642	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
643	C₃×C₅	#2905	1	1	yes	characteristic, complemented, Hall
644	C₂²×C₃	—	5	2	no	—
645	C₂²×C₃	—	10	1	no	—
646	C₂²×C₃	—	10	1	no	—
647	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
648	C₂×D₃	—	2	1	no	—
649	C₂×D₃	—	2	1	no	—
650	C₂×D₃	—	5	2	no	—
651	C₂×D₃	—	10	1	no	—
652	C₂×D₃	—	10	1	no	—
653	C₂×D₃	—	20	4	no	—
654	C₂×D₃	D₅×C₄⋊C₄	1	2	yes	—
655	C₃×C₄	—	2	1	no	—
656	C₃×C₄	—	2	1	no	—
657	C₃×C₄	—	5	2	no	—
658	C₃×C₄	—	10	1	no	—
659	C₃×C₄	—	10	1	no	—
660	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
661	C₃×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
662	Dic₃	—	2	1	no	—
663	Dic₃	—	2	1	no	—
664	Dic₃	—	5	2	no	—
665	Dic₃	—	10	1	no	—
666	Dic₃	—	10	1	no	—
667	Dic₃	D₅×C₄⋊C₄	1	2	yes	—
668	C₂×C₅	—	6	2	no	—
669	C₂×C₅	C₂×D₃×C₄⋊C₄	1	1	yes	characteristic
670	C₂×C₅	#5750	1	1	yes	characteristic
671	C₂×C₅	#5750	1	1	yes	characteristic
672	D₅	—	2	2	no	—
673	D₅	—	6	2	no	—
674	C₂³	—	3	1	no	—
675	C₂³	—	5	1	no	—
676	C₂³	—	15	4	no	—
677	C₂³	—	15	1	no	—
678	C₂³	—	60	1	no	—
679	C₂³	—	60	1	no	—
680	C₂×C₄	—	3	1	no	—
681	C₂×C₄	—	3	2	no	—
682	C₂×C₄	—	3	2	no	—
683	C₂×C₄	—	3	1	no	—
684	C₂×C₄	—	3	1	no	—
685	C₂×C₄	—	5	1	no	—
686	C₂×C₄	—	5	2	no	—
687	C₂×C₄	—	5	2	no	—
688	C₂×C₄	—	5	1	no	—
689	C₂×C₄	—	5	1	no	—
690	C₂×C₄	—	15	4	no	—
691	C₂×C₄	—	15	4	no	—
692	C₂×C₄	—	15	4	no	—
693	C₂×C₄	—	15	1	no	—
694	C₂×C₄	—	15	2	no	—
695	C₂×C₄	—	15	2	no	—
696	C₂×C₄	—	15	1	no	—
697	C₂×C₄	—	15	1	no	—
698	C₂×C₄	—	60	1	no	—
699	C₂×C₄	—	60	1	no	—
700	C₂×C₄	—	60	1	no	—
701	C₂×C₄	—	60	1	no	—
702	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
703	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
704	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
705	C₈	—	2	1	no	—
706	C₈	—	2	1	no	—
707	C₈	—	6	1	no	—
708	C₈	—	6	1	no	—
709	C₈	—	10	1	no	—
710	C₈	—	10	1	no	—
711	C₈	—	30	1	no	—
712	C₈	—	30	1	no	—
713	C₂×C₃	—	10	2	no	—
714	C₂×C₃	C₂×D₅×C₄⋊C₄	1	1	yes	characteristic
715	C₂×C₃	#66084	1	1	yes	characteristic
716	C₂×C₃	#66084	1	1	yes	characteristic
717	D₃	—	2	2	no	—
718	D₃	—	10	2	no	—
719	C₅	#79080	1	1	yes	characteristic, complemented, Sylow
720	C₂²	—	3	2	no	—
721	C₂²	—	5	2	no	—
722	C₂²	—	6	1	no	—
723	C₂²	—	6	1	no	—
724	C₂²	—	10	1	no	—
725	C₂²	—	10	1	no	—
726	C₂²	—	15	2	no	—
727	C₂²	—	30	1	no	—
728	C₂²	—	30	1	no	—
729	C₂²	—	60	4	no	—
730	C₂²	C₂×C₄×D₃×D₅	1	1	yes	characteristic
731	C₄	—	2	1	no	—
732	C₄	—	2	1	no	—
733	C₄	—	3	2	no	—
734	C₄	—	5	2	no	—
735	C₄	—	6	1	no	—
736	C₄	—	6	1	no	—
737	C₄	—	10	1	no	—
738	C₄	—	10	1	no	—
739	C₄	—	15	2	no	—
740	C₄	—	30	1	no	—
741	C₄	—	30	1	no	—
742	C₄	D₃×D₄×D₅	1	1	yes	characteristic
743	C₄	D₃×Q₈×D₅	1	1	yes	characteristic
744	C₃	#10610811	1	1	yes	characteristic, complemented, Sylow
745	C₂	—	6	2	no	—
746	C₂	—	10	2	no	—
747	C₂	—	30	2	no	—
748	C₂	D₃×D₅×C₄⋊C₄	1	1	yes	characteristic
749	C₂	#11753953	1	1	yes	characteristic
750	C₂	#11754018	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃×D₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Fitting	C₃×C₅×C₄⋊C₈	C₂²
prime radical	C₂²×D₃×D₅	C₂×C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₄⋊C₈	D₃×D₅
hypocenter	C₃×C₅	#2905
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
4. #11750938	C₂	semidirect
5. C₅×#4839	C₂	semidirect
6. C₃×#65128	C₂	semidirect
7. #11747661	C₂	semidirect
8. #11747655	C₂	semidirect
9. #11747648	C₂	semidirect
10. #11747647	C₂	semidirect
11. #11747594	C₂	semidirect
12. #11747594	C₂	semidirect
13. #11747015	C₂	semidirect
14. #11746993	C₂	semidirect
15. #11746985	C₂	semidirect
46. C₃×C₅×C₄⋊C₈	C₂²	semidirect
47. #91098	C₂²	semidirect
48. #91098	C₂²	semidirect
49. C₄⋊(C₃⋊#168)	C₂²	semidirect
50. C₅×Dic₃⋊C₈	C₂²	semidirect
51. C₅×Dic₃⋊C₈	C₂²	semidirect
52. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
53. C₃×#3946	C₂²	semidirect
54. C₃×#3946	C₂²	semidirect
55. C₃×C₄⋊#168	C₂²	semidirect
56. Dic₃⋊#168	C₂²	semidirect
57. Dic₃⋊#168	C₂²	semidirect
58. #90983	C₂²	semidirect
59. #90983	C₂²	semidirect
60. #90982	C₂²	semidirect
61. #90982	C₂²	semidirect
73. #65128	D₃	semidirect
145. #4839	D₅	semidirect
182. C₅×C₄⋊C₈	C₂×D₃	semidirect
189. #3946	C₂×D₃	semidirect
190. #3946	C₂×D₃	semidirect
194. C₄⋊#168	C₂×D₃	semidirect
267. C₃×C₄⋊C₈	C₂×D₅	semidirect
274. Dic₃⋊C₈	C₂×D₅	semidirect
275. Dic₃⋊C₈	C₂×D₅	semidirect
279. C₄⋊(C₃⋊C₈)	C₂×D₅	semidirect
516. C₄⋊C₈	D₃×D₅	semidirect
643. C₃×C₅	#2905	semidirect
719. C₅	#79080	semidirect
744. C₃	#10610811	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃×#676	2
C₂×D₅×ΓL(1,𝔽₂₅)	2
#11752723	2
#11750938	2
C₅×#4839	2
C₃×#65128	2
#11747661	2
#11747655	2
#11747648	2
#11747647	2
#11747594	2
#11747015	2
#11746993	2
#11746985	2
#10610811	3
#79080	5