Subgroups — #14418971

Order 1920.

824 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#6817	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#11751229	C₂	1	2	yes	maximal, complemented
4	#11751228	C₂	1	2	yes	maximal, complemented
5	#11751026	C₂	1	1	yes	maximal, characteristic, complemented
6	#11750807	C₂	1	2	yes	maximal, complemented
7	#11750802	C₂	1	2	yes	maximal, complemented
8	C₄×#6705	C₂	1	1	yes	maximal, characteristic, complemented
9	#11750786	C₂	1	1	yes	maximal, characteristic, complemented
10	#11750786	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₈×D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
12	#10610254	—	3	1	no	maximal, Hall
13	C₂×#6817	C₄	1	1	yes	characteristic
14	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
15	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
16	C₄×#1220	C₄	1	1	yes	characteristic
17	C₄×#1220	C₄	1	1	yes	characteristic
18	C₄×#1220	C₂²	1	1	yes	characteristic
19	C₄×#1220	C₂²	1	1	yes	characteristic
20	#91815	C₄	1	1	yes	characteristic
21	C₂×#6705	C₂²	1	2	yes	—
22	C₂×C₈×D₁₅	C₂²	1	2	yes	—
23	C₄×D₆₀	C₄	1	1	yes	characteristic
24	C₄×D₆₀	C₂²	1	1	yes	characteristic
25	#91761	C₄	1	1	yes	characteristic
26	#91761	C₄	1	1	yes	characteristic
27	C₄²×D₁₅	C₂²	1	1	yes	characteristic
28	C₄²×D₁₅	C₂²	1	1	yes	characteristic
29	C₄×Dic₃₀	C₄	1	1	yes	characteristic
30	C₄×Dic₃₀	C₂²	1	1	yes	characteristic
31	C₃×C₅×#97	C₂²	1	2	yes	—
32	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
33	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
34	#91114	C₂²	1	2	yes	—
35	#91104	C₂²	1	2	yes	—
36	#91104	C₂²	1	2	yes	—
37	#91099	C₂²	1	2	yes	—
38	#91098	C₂²	1	2	yes	—
39	#91098	C₂²	1	2	yes	—
40	C₈×Dic₁₅	C₂²	1	2	yes	—
41	C₄⋊(C₃⋊#168)	C₂²	1	2	yes	—
42	C₄×C₃⋊#168	C₂²	1	1	yes	characteristic
43	C₄×C₃⋊#168	C₂²	1	1	yes	characteristic
44	#78523	—	5	1	no	maximal, Hall
45	C₄×#709	—	3	1	no	—
46	C₄×C₅×M₁₆	D₃	1	1	yes	characteristic, complemented
47	#65417	—	3	2	no	—
48	#65416	—	3	2	no	—
49	#65214	—	3	1	no	—
50	#64995	—	3	2	no	—
51	#64990	—	3	2	no	—
52	C₄×#676	—	3	1	no	—
53	#64974	—	3	1	no	—
54	#64974	—	3	1	no	—
55	C₄×C₈×D₅	—	3	1	no	—
56	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
58	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
59	C₂×#1220	C₂×C₄	1	1	yes	characteristic
60	C₂×#1220	C₂×C₄	1	1	yes	characteristic
61	#6817	—	2	4	no	—
62	C₂×D₆₀	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄×D₁₅	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄×D₁₅	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄×D₁₅	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄×D₁₅	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄×D₁₅	C₂³	1	1	yes	characteristic
68	C₂×C₄×D₁₅	C₂³	1	1	yes	characteristic
69	C₂×Dic₃₀	C₂×C₄	1	1	yes	characteristic
70	C₃×C₅×M₁₆	—	2	4	no	—
71	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
72	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
73	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
74	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
75	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
76	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
77	#6719	C₂×C₄	1	1	yes	characteristic
78	#6719	C₂×C₄	1	1	yes	characteristic
79	#6714	C₂×C₄	1	1	yes	characteristic
80	#6714	C₂×C₄	1	1	yes	characteristic
81	#6714	C₂×C₄	1	1	yes	characteristic
82	#6714	C₂×C₄	1	1	yes	characteristic
83	C₄⋊Dic₁₅	C₂×C₄	1	1	yes	characteristic
84	C₄⋊Dic₁₅	C₂×C₄	1	1	yes	characteristic
85	#6712	C₂×C₄	1	1	yes	characteristic
86	#6712	C₂×C₄	1	1	yes	characteristic
87	#6712	C₂×C₄	1	1	yes	characteristic
88	#6712	C₂×C₄	1	1	yes	characteristic
89	C₄×Dic₁₅	C₂×C₄	1	1	yes	characteristic
90	C₄×Dic₁₅	C₂×C₄	1	1	yes	characteristic
91	C₄×Dic₁₅	C₂×C₄	1	1	yes	characteristic
92	C₄×Dic₁₅	C₂×C₄	1	1	yes	characteristic
93	C₄×Dic₁₅	C₂³	1	1	yes	characteristic
94	C₄×Dic₁₅	C₂³	1	1	yes	characteristic
95	C₂×C₃⋊#168	C₂³	1	2	yes	—
96	C₂×C₃⋊#168	C₂³	1	2	yes	—
97	#6705	—	2	4	no	—
98	C₈×D₁₅	—	2	4	no	—
99	C₄×#235	—	5	1	no	—
100	C₃×C₄×M₁₆	D₅	1	1	yes	characteristic, complemented
101	#5128	—	5	2	no	—
102	#5127	—	5	2	no	—
103	#4925	—	5	1	no	—
104	#4706	—	5	2	no	—
105	#4701	—	5	2	no	—
106	C₄×ΓL(1,𝔽₂₅)	—	5	1	no	—
107	#4685	—	5	1	no	—
108	#4685	—	5	1	no	—
109	C₄×D₃×C₈	—	5	1	no	—
110	C₂×#709	—	3	1	no	—
111	C₂×C₅×M₁₆	C₂×D₃	1	2	yes	—
112	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
113	C₄×C₂²⋊D₅	—	3	1	no	—
114	C₄×C₂²⋊D₅	—	3	1	no	—
115	C₄×C₂²⋊D₅	—	3	1	no	—
116	C₄×C₂²⋊D₅	—	3	1	no	—
117	#4072	—	3	1	no	—
118	C₂×#676	—	3	2	no	—
119	C₂×C₈×D₅	—	3	2	no	—
120	C₄×D₂₀	—	3	1	no	—
121	C₄×D₂₀	—	3	1	no	—
122	#4018	—	3	1	no	—
123	#4018	—	3	1	no	—
124	C₄²×D₅	—	3	1	no	—
125	C₄²×D₅	—	3	1	no	—
126	C₄×Dic₁₀	—	3	1	no	—
127	C₄×Dic₁₀	—	3	1	no	—
128	C₅×#97	C₂×D₃	1	2	yes	—
129	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
130	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
131	C₂²⋊#168	—	3	2	no	—
132	#3952	—	3	2	no	—
133	#3952	—	3	2	no	—
134	#3947	—	3	2	no	—
135	#3946	—	3	2	no	—
136	#3946	—	3	2	no	—
137	C₈×Dic₅	—	3	2	no	—
138	C₄⋊#168	—	3	2	no	—
139	C₄×#168	—	3	1	no	—
140	C₄×#168	—	3	1	no	—
141	#2965	—	15	1	no	Sylow
142	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
143	C₂²×D₁₅	C₂²×C₄	1	1	yes	characteristic
144	C₂²×D₁₅	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₃×C₄×C₅	—	2	2	no	—
146	C₂×C₃×C₄×C₅	—	2	2	no	—
147	C₂×C₃×C₄×C₅	—	2	2	no	—
148	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
154	#1220	—	2	2	no	—
155	#1220	—	2	2	no	—
156	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
157	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
158	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
159	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
160	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
161	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
162	D₆₀	—	2	2	no	—
163	C₄×D₁₅	—	2	2	no	—
164	C₄×D₁₅	—	2	2	no	—
165	C₄×D₁₅	—	2	2	no	—
166	C₄×D₁₅	—	2	2	no	—
167	C₄×D₁₅	—	2	2	no	—
168	C₄×D₁₅	M₁₆	1	4	yes	complemented
169	Dic₃₀	—	2	2	no	—
170	C₃×C₅×C₈	—	2	2	no	—
171	C₃×C₅×C₈	#41	1	4	yes	complemented
172	C₃⋊#168	—	2	2	no	—
173	C₃⋊#168	—	2	2	no	—
174	C₂×#235	—	5	1	no	—
175	C₂×C₃×M₁₆	C₂×D₅	1	2	yes	—
176	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
177	C₄×#67	—	5	1	no	—
178	C₄×#67	—	5	1	no	—
179	C₄×#67	—	5	1	no	—
180	C₄×#67	—	5	1	no	—
181	#926	—	5	1	no	—
182	C₂×ΓL(1,𝔽₂₅)	—	5	2	no	—
183	C₂×D₃×C₈	—	5	2	no	—
184	C₄×D₁₂	—	5	1	no	—
185	C₄×D₁₂	—	5	1	no	—
186	#872	—	5	1	no	—
187	#872	—	5	1	no	—
188	C₄²×D₃	—	5	1	no	—
189	C₄²×D₃	—	5	1	no	—
190	C₄×Dic₆	—	5	1	no	—
191	C₄×Dic₆	—	5	1	no	—
192	C₃×#97	C₂×D₅	1	2	yes	—
193	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
194	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
195	#830	—	5	2	no	—
196	(C₂×D₃)⋊C₈	—	5	2	no	—
197	(C₂×D₃)⋊C₈	—	5	2	no	—
198	#815	—	5	2	no	—
199	Dic₃⋊C₈	—	5	2	no	—
200	Dic₃⋊C₈	—	5	2	no	—
201	C₈×Dic₃	—	5	2	no	—
202	C₄⋊(C₃⋊C₈)	—	5	2	no	—
203	C₄×C₃⋊C₈	—	5	1	no	—
204	C₄×C₃⋊C₈	—	5	1	no	—
205	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
206	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
207	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
208	C₂×C₂²⋊D₅	—	3	1	no	—
209	C₂×C₂²⋊D₅	—	3	1	no	—
210	#709	—	6	4	no	—
211	C₂×D₂₀	—	3	1	no	—
212	C₂×C₄×D₅	—	3	1	no	—
213	C₂×C₄×D₅	—	3	1	no	—
214	C₂×C₄×D₅	—	3	1	no	—
215	C₂×C₄×D₅	—	3	1	no	—
216	C₂×C₄×D₅	—	3	1	no	—
217	C₂×C₄×D₅	—	3	1	no	—
218	C₂×Dic₁₀	—	3	1	no	—
219	C₅×M₁₆	—	2	4	no	—
220	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
221	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
222	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
223	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
224	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
225	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
226	C₂²⋊Dic₅	—	3	1	no	—
227	C₂²⋊Dic₅	—	3	1	no	—
228	#685	—	3	1	no	—
229	#685	—	3	1	no	—
230	#685	—	3	1	no	—
231	#685	—	3	1	no	—
232	C₄⋊Dic₅	—	3	1	no	—
233	C₄⋊Dic₅	—	3	1	no	—
234	#683	—	3	1	no	—
235	#683	—	3	1	no	—
236	#683	—	3	1	no	—
237	#683	—	3	1	no	—
238	C₄×Dic₅	—	3	1	no	—
239	C₄×Dic₅	—	3	1	no	—
240	C₄×Dic₅	—	3	1	no	—
241	C₄×Dic₅	—	3	1	no	—
242	C₄×Dic₅	—	3	1	no	—
243	C₄×Dic₅	—	3	1	no	—
244	C₂×#168	—	3	2	no	—
245	C₂×#168	—	3	2	no	—
246	#676	—	6	4	no	—
247	C₈×D₅	—	6	4	no	—
248	C₄×#41	—	15	1	no	—
249	#446	—	15	2	no	—
250	#436	—	15	2	no	—
251	#435	—	15	2	no	—
252	#435	—	15	2	no	—
253	#431	—	15	1	no	—
254	#431	—	15	1	no	—
255	#431	—	15	1	no	—
256	C₄×M₁₆	—	15	1	no	—
257	C₄×M₁₆	D₁₅	1	1	yes	characteristic, complemented
258	C₂×C₄×C₈	—	15	1	no	—
259	C₂²×C₃×C₅	—	2	1	no	—
260	C₂²×C₃×C₅	—	2	1	no	—
261	C₂²×C₃×C₅	—	2	1	no	—
262	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
263	C₂×D₁₅	—	2	1	no	—
264	C₂×D₁₅	—	2	1	no	—
265	C₂×D₁₅	—	2	1	no	—
266	C₂×D₁₅	—	2	1	no	—
267	C₂×D₁₅	—	2	1	no	—
268	C₂×D₁₅	C₂×M₁₆	1	2	yes	—
269	C₃×C₄×C₅	—	2	1	no	—
270	C₃×C₄×C₅	—	2	1	no	—
271	C₃×C₄×C₅	—	2	1	no	—
272	C₃×C₄×C₅	C₂×M₁₆	1	2	yes	—
273	C₃×C₄×C₅	#131	1	2	yes	—
274	C₃×C₄×C₅	C₂×#41	1	2	yes	—
275	Dic₁₅	—	2	1	no	—
276	Dic₁₅	—	2	1	no	—
277	Dic₁₅	—	2	1	no	—
278	Dic₁₅	—	2	1	no	—
279	Dic₁₅	—	2	1	no	—
280	Dic₁₅	C₂×M₁₆	1	2	yes	—
281	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
282	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
283	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
284	C₂×#67	—	5	1	no	—
285	C₂×#67	—	5	1	no	—
286	#235	—	10	4	no	—
287	C₂×D₁₂	—	5	1	no	—
288	C₂×C₄×D₃	—	5	1	no	—
289	C₂×C₄×D₃	—	5	1	no	—
290	C₂×C₄×D₃	—	5	1	no	—
291	C₂×C₄×D₃	—	5	1	no	—
292	C₂×C₄×D₃	—	5	1	no	—
293	C₂×C₄×D₃	—	5	1	no	—
294	C₂×Dic₆	—	5	1	no	—
295	C₃×M₁₆	—	2	4	no	—
296	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
297	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
298	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
299	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
300	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
301	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
302	#217	—	5	1	no	—
303	#217	—	5	1	no	—
304	(C₂×D₃)⋊C₄	—	5	1	no	—
305	(C₂×D₃)⋊C₄	—	5	1	no	—
306	(C₂×D₃)⋊C₄	—	5	1	no	—
307	(C₂×D₃)⋊C₄	—	5	1	no	—
308	C₄⋊Dic₃	—	5	1	no	—
309	C₄⋊Dic₃	—	5	1	no	—
310	Dic₃⋊C₄	—	5	1	no	—
311	Dic₃⋊C₄	—	5	1	no	—
312	Dic₃⋊C₄	—	5	1	no	—
313	Dic₃⋊C₄	—	5	1	no	—
314	C₄×Dic₃	—	5	1	no	—
315	C₄×Dic₃	—	5	1	no	—
316	C₄×Dic₃	—	5	1	no	—
317	C₄×Dic₃	—	5	1	no	—
318	C₄×Dic₃	—	5	1	no	—
319	C₄×Dic₃	—	5	1	no	—
320	C₂×C₃⋊C₈	—	5	2	no	—
321	C₂×C₃⋊C₈	—	5	2	no	—
322	ΓL(1,𝔽₂₅)	—	10	4	no	—
323	D₃×C₈	—	10	4	no	—
324	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
325	C₂²×D₅	—	3	1	no	—
326	C₂²×D₅	—	3	1	no	—
327	C₂×C₄×C₅	—	2	2	no	—
328	C₂×C₄×C₅	—	2	2	no	—
329	C₂×C₄×C₅	—	2	2	no	—
330	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
331	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
332	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
333	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
334	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
335	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
336	C₂²⋊D₅	—	6	2	no	—
337	C₂²⋊D₅	—	6	2	no	—
338	C₂×Dic₅	—	3	1	no	—
339	C₂×Dic₅	—	3	1	no	—
340	C₂×Dic₅	—	3	1	no	—
341	C₂×Dic₅	—	3	1	no	—
342	C₂×Dic₅	—	3	1	no	—
343	C₂×Dic₅	—	3	1	no	—
344	D₂₀	—	6	2	no	—
345	C₄×D₅	—	3	4	no	—
346	C₄×D₅	—	6	2	no	—
347	C₄×D₅	—	6	2	no	—
348	C₄×D₅	—	6	2	no	—
349	C₄×D₅	—	6	2	no	—
350	C₄×D₅	—	6	2	no	—
351	Dic₁₀	—	6	2	no	—
352	C₅×C₈	—	2	2	no	—
353	C₅×C₈	#235	1	4	yes	complemented
354	#168	—	6	2	no	—
355	#168	—	6	2	no	—
356	C₂×#41	—	15	1	no	—
357	C₂×M₁₆	—	15	2	no	—
358	C₂×M₁₆	C₂×D₁₅	1	2	yes	—
359	C₂²×C₈	—	15	2	no	—
360	C₄×Q₈	—	15	1	no	—
361	C₄×Q₈	—	15	1	no	—
362	C₄×D₄	—	15	1	no	—
363	C₄×D₄	—	15	1	no	—
364	C₄×D₄	—	15	1	no	—
365	C₄×D₄	—	15	1	no	—
366	C₄×D₄	—	15	1	no	—
367	C₄×D₄	—	15	1	no	—
368	#117	—	15	1	no	—
369	#117	—	15	1	no	—
370	#117	—	15	1	no	—
371	C₂×C₄²	—	15	1	no	—
372	C₂×C₄²	—	15	1	no	—
373	C₂×C₄²	C₂×D₁₅	1	1	yes	characteristic
374	C₄⋊C₈	—	15	2	no	—
375	C₄⋊C₈	—	15	2	no	—
376	C₄⋊C₈	—	15	2	no	—
377	C₂²⋊C₈	—	15	2	no	—
378	C₂²⋊C₈	—	15	2	no	—
379	C₂²⋊C₈	—	15	2	no	—
380	#97	—	15	2	no	—
381	#97	C₂×D₁₅	1	2	yes	—
382	C₄×C₈	—	15	2	no	—
383	C₄×C₈	—	15	1	no	—
384	C₄×C₈	—	15	1	no	—
385	C₄×C₈	C₂×D₁₅	1	1	yes	characteristic
386	C₄×C₈	C₂×D₁₅	1	1	yes	characteristic
387	C₂×C₃×C₅	—	4	1	no	—
388	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
389	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
390	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
391	D₁₅	—	2	2	no	—
392	D₁₅	—	4	1	no	—
393	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
394	C₂²×D₃	—	5	1	no	—
395	C₂²×D₃	—	5	1	no	—
396	C₂×C₃×C₄	—	2	2	no	—
397	C₂×C₃×C₄	—	2	2	no	—
398	C₂×C₃×C₄	—	2	2	no	—
399	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
400	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
401	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
402	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
403	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
404	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
405	#67	—	10	2	no	—
406	#67	—	10	2	no	—
407	C₂×Dic₃	—	5	1	no	—
408	C₂×Dic₃	—	5	1	no	—
409	C₂×Dic₃	—	5	1	no	—
410	C₂×Dic₃	—	5	1	no	—
411	C₂×Dic₃	—	5	1	no	—
412	C₂×Dic₃	—	5	1	no	—
413	D₁₂	—	10	2	no	—
414	C₄×D₃	—	5	4	no	—
415	C₄×D₃	—	10	2	no	—
416	C₄×D₃	—	10	2	no	—
417	C₄×D₃	—	10	2	no	—
418	C₄×D₃	—	10	2	no	—
419	C₄×D₃	—	10	2	no	—
420	Dic₆	—	10	2	no	—
421	C₃×C₈	—	2	2	no	—
422	C₃×C₈	#709	1	4	yes	complemented
423	C₃⋊C₈	—	10	2	no	—
424	C₃⋊C₈	—	10	2	no	—
425	C₂²×C₅	—	2	1	no	—
426	C₂²×C₅	—	2	1	no	—
427	C₂²×C₅	—	2	1	no	—
428	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
429	C₂×D₅	—	3	2	no	—
430	C₂×D₅	—	6	1	no	—
431	C₂×D₅	—	6	1	no	—
432	C₂×D₅	—	6	1	no	—
433	C₂×D₅	—	6	1	no	—
434	C₂×D₅	—	6	1	no	—
435	C₄×C₅	—	2	1	no	—
436	C₄×C₅	—	2	1	no	—
437	C₄×C₅	—	2	1	no	—
438	C₄×C₅	D₃×M₁₆	1	2	yes	—
439	C₄×C₅	#907	1	2	yes	—
440	C₄×C₅	C₂×#235	1	2	yes	—
441	Dic₅	—	3	2	no	—
442	Dic₅	—	6	1	no	—
443	Dic₅	—	6	1	no	—
444	Dic₅	—	6	1	no	—
445	Dic₅	—	6	1	no	—
446	Dic₅	—	6	1	no	—
447	#41	—	30	4	no	—
448	C₂×Q₈	—	15	1	no	—
449	C₂×D₄	—	15	1	no	—
450	C₂×D₄	—	15	1	no	—
451	C₂×D₄	—	15	1	no	—
452	C₂²×C₄	—	15	1	no	—
453	C₂²×C₄	—	15	1	no	—
454	C₂²×C₄	—	15	1	no	—
455	C₂²×C₄	—	15	1	no	—
456	C₂²×C₄	—	15	1	no	—
457	C₂²×C₄	—	15	1	no	—
458	C₂²×C₄	C₄×D₁₅	1	1	yes	characteristic
459	C₂²×C₄	C₄×D₁₅	1	1	yes	characteristic
460	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
461	M₁₆	—	2	4	no	—
462	M₁₆	—	30	4	no	—
463	C₂×C₈	—	15	2	no	—
464	C₂×C₈	—	15	2	no	—
465	C₂×C₈	—	30	4	no	—
466	C₂×C₈	C₂²×D₁₅	1	2	yes	—
467	C₂×C₈	C₂²×D₁₅	1	2	yes	—
468	C₄⋊C₄	—	15	1	no	—
469	C₄⋊C₄	—	15	1	no	—
470	C₄⋊C₄	—	15	1	no	—
471	C₄⋊C₄	—	15	1	no	—
472	C₄⋊C₄	—	15	1	no	—
473	C₄⋊C₄	—	15	1	no	—
474	C₂²⋊C₄	—	15	1	no	—
475	C₂²⋊C₄	—	15	1	no	—
476	C₂²⋊C₄	—	15	1	no	—
477	C₂²⋊C₄	—	15	1	no	—
478	C₂²⋊C₄	—	15	1	no	—
479	C₂²⋊C₄	—	15	1	no	—
480	C₄²	—	15	1	no	—
481	C₄²	—	15	1	no	—
482	C₄²	—	15	1	no	—
483	C₄²	—	15	1	no	—
484	C₄²	—	15	1	no	—
485	C₄²	—	15	1	no	—
486	C₄²	C₄×D₁₅	1	1	yes	characteristic
487	C₄²	C₄×D₁₅	1	1	yes	characteristic
488	C₄²	C₂²×D₁₅	1	1	yes	characteristic
489	C₄²	C₂²×D₁₅	1	1	yes	characteristic
490	C₃×C₅	#2965	1	1	yes	characteristic, complemented, Hall
491	C₂²×C₃	—	2	1	no	—
492	C₂²×C₃	—	2	1	no	—
493	C₂²×C₃	—	2	1	no	—
494	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
495	C₂×D₃	—	5	2	no	—
496	C₂×D₃	—	10	1	no	—
497	C₂×D₃	—	10	1	no	—
498	C₂×D₃	—	10	1	no	—
499	C₂×D₃	—	10	1	no	—
500	C₂×D₃	—	10	1	no	—
501	C₃×C₄	—	2	1	no	—
502	C₃×C₄	—	2	1	no	—
503	C₃×C₄	—	2	1	no	—
504	C₃×C₄	D₅×M₁₆	1	2	yes	—
505	C₃×C₄	#4053	1	2	yes	—
506	C₃×C₄	C₂×#709	1	2	yes	—
507	Dic₃	—	5	2	no	—
508	Dic₃	—	10	1	no	—
509	Dic₃	—	10	1	no	—
510	Dic₃	—	10	1	no	—
511	Dic₃	—	10	1	no	—
512	Dic₃	—	10	1	no	—
513	C₂×C₅	—	4	1	no	—
514	C₂×C₅	C₄×#235	1	1	yes	characteristic
515	C₂×C₅	C₂×D₃×M₁₆	1	1	yes	characteristic
516	C₂×C₅	C₂×#907	1	1	yes	characteristic
517	D₅	—	6	2	no	—
518	D₅	—	12	1	no	—
519	C₂³	—	15	1	no	—
520	C₂³	—	15	1	no	—
521	C₂³	C₂×C₄×D₁₅	1	1	yes	characteristic
522	Q₈	—	30	2	no	—
523	D₄	—	30	2	no	—
524	D₄	—	30	2	no	—
525	D₄	—	30	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	15	1	no	—
530	C₂×C₄	—	15	4	no	—
531	C₂×C₄	—	15	1	no	—
532	C₂×C₄	—	15	1	no	—
533	C₂×C₄	—	15	1	no	—
534	C₂×C₄	—	15	1	no	—
535	C₂×C₄	—	15	1	no	—
536	C₂×C₄	—	30	2	no	—
537	C₂×C₄	—	30	2	no	—
538	C₂×C₄	—	30	2	no	—
539	C₂×C₄	—	30	2	no	—
540	C₂×C₄	—	30	2	no	—
541	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
542	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
543	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
544	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
545	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
546	C₂×C₄	C₂³×D₁₅	1	1	yes	characteristic
547	C₈	—	2	2	no	—
548	C₈	—	30	2	no	—
549	C₈	—	30	2	no	—
550	C₈	#6817	1	4	yes	complemented
551	C₂×C₃	—	4	1	no	—
552	C₂×C₃	C₄×#709	1	1	yes	characteristic
553	C₂×C₃	C₂×D₅×M₁₆	1	1	yes	characteristic
554	C₂×C₃	C₂×#4053	1	1	yes	characteristic
555	D₃	—	10	2	no	—
556	D₃	—	20	1	no	—
557	C₅	#78523	1	1	yes	characteristic, complemented, Sylow
558	C₂²	—	2	1	no	—
559	C₂²	—	2	1	no	—
560	C₂²	—	2	1	no	—
561	C₂²	—	15	2	no	—
562	C₂²	—	30	1	no	—
563	C₂²	—	30	1	no	—
564	C₂²	—	30	1	no	—
565	C₂²	—	30	1	no	—
566	C₂²	—	30	1	no	—
567	C₂²	C₂²×C₄×D₁₅	1	1	yes	characteristic
568	C₄	—	2	1	no	—
569	C₄	—	2	1	no	—
570	C₄	—	2	1	no	—
571	C₄	—	15	2	no	—
572	C₄	—	30	1	no	—
573	C₄	—	30	1	no	—
574	C₄	—	30	1	no	—
575	C₄	—	30	1	no	—
576	C₄	—	30	1	no	—
577	C₄	M₁₆×D₁₅	1	2	yes	—
578	C₄	#91796	1	2	yes	—
579	C₄	C₂×#6817	1	2	yes	—
580	C₃	#10610254	1	1	yes	characteristic, complemented, Sylow
581	C₂	—	4	1	no	—
582	C₂	—	30	2	no	—
583	C₂	—	60	1	no	—
584	C₂	C₄×#6817	1	1	yes	characteristic
585	C₂	C₂×M₁₆×D₁₅	1	1	yes	characteristic
586	C₂	C₂×#91796	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂²×D₁₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₁₅
Fitting	C₃×C₄×C₅×M₁₆	C₂
prime radical	C₂×#6817	C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₄×M₁₆	D₁₅
hypocenter	C₃×C₅	#2965
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₄² ◁ C₄×M₁₆

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×C₅×M₁₆	C₂	semidirect
3. #11751229	C₂	semidirect
4. #11751228	C₂	semidirect
5. #11751026	C₂	semidirect
6. #11750807	C₂	semidirect
7. #11750802	C₂	semidirect
8. C₄×#6705	C₂	semidirect
9. #11750786	C₂	semidirect
10. #11750786	C₂	semidirect
11. C₄×C₈×D₁₅	C₂	semidirect
46. C₄×C₅×M₁₆	D₃	semidirect
100. C₃×C₄×M₁₆	D₅	semidirect
168. C₄×D₁₅	M₁₆	semidirect
171. C₃×C₅×C₈	#41	semidirect
257. C₄×M₁₆	D₁₅	semidirect
353. C₅×C₈	#235	semidirect
422. C₃×C₈	#709	semidirect
490. C₃×C₅	#2965	semidirect
550. C₈	#6817	semidirect
557. C₅	#78523	semidirect
580. C₃	#10610254	semidirect

Maximal subgroups

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

subgroup	index
C₄×#6817	2
C₃×C₄×C₅×M₁₆	2
#11751229	2
#11751228	2
#11751026	2
#11750807	2
#11750802	2
C₄×#6705	2
#11750786	2
C₄×C₈×D₁₅	2
#10610254	3
#78523	5