Subgroups — #14415776

Order 1920.

1088 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×D₃×D₄	C₂	1	1	yes	maximal, characteristic
2	C₂×D₃×#681	C₂	1	2	yes	maximal, complemented
3	#11751113	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65301	C₂	1	1	yes	maximal, characteristic, complemented
5	#11748505	C₂	1	2	yes	maximal, complemented
6	#11748496	C₂	1	2	yes	maximal, complemented
7	#11748484	C₂	1	2	yes	maximal, complemented
8	#11747011	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#6650	C₂	1	1	yes	maximal, characteristic, complemented
10	#11746998	C₂	1	1	yes	maximal, characteristic, complemented
11	D₁₂×#168	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×#681	—	3	1	no	maximal, Hall
13	C₂×C₅×D₃×D₄	C₄	1	1	yes	characteristic
14	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
15	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
16	C₂×#6710	C₂²	1	2	yes	complemented
17	C₅×D₄×Dic₃	C₄	1	1	yes	characteristic
18	C₄×C₅×#67	C₂²	1	2	yes	—
19	C₅×#893	C₄	1	1	yes	characteristic
20	C₅×D₃×C₄⋊C₄	C₄	1	1	yes	characteristic
21	C₅×#67⋊C₄	C₄	1	2	yes	—
22	C₅×D₃×C₂²⋊C₄	C₄	1	2	yes	—
23	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
24	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
25	C₂×C₃×#681	C₂²	1	2	yes	complemented
26	C₂×#6650	C₂²	1	2	yes	—
27	C₂×#6650	C₂²	1	1	yes	characteristic
28	C₂×#6650	C₂²	1	1	yes	characteristic
29	D₃×#681	—	2	8	no	—
30	C₂×D₃×#168	C₂²	1	2	yes	complemented
31	C₂×D₃×#168	C₂²	1	2	yes	complemented
32	#91114	C₂²	1	2	yes	complemented
33	C₄⋊(C₃⋊#168)	C₂²	1	1	yes	characteristic, complemented
34	C₄×C₃⋊#168	C₂²	1	1	yes	characteristic, complemented
35	C₃×C₂²⋊#168	C₂²	1	2	yes	complemented
36	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic, complemented
37	C₃×C₄×#168	C₂²	1	1	yes	characteristic, complemented
38	Dic₃⋊#168	C₂²	1	2	yes	complemented
39	(C₂×D₃)⋊#168	C₂²	1	2	yes	complemented
40	(C₂×D₃)⋊#168	C₂²	1	2	yes	complemented
41	#90953	C₂²	1	1	yes	characteristic, complemented
42	#90953	C₂²	1	1	yes	characteristic, complemented
43	#79540	—	5	1	no	maximal, Hall
44	C₂×C₄×C₅×D₄	—	3	1	no	—
45	C₂²×#681	—	3	2	no	—
46	#65496	—	3	2	no	—
47	#65301	—	3	1	no	—
48	#65301	D₃	1	1	yes	characteristic, complemented
49	#65300	—	3	2	no	—
50	#65300	—	3	2	no	—
51	D₄×#168	—	3	1	no	—
52	D₄×#168	—	3	1	no	—
53	#65213	—	3	1	no	—
54	C₄×#681	—	3	1	no	—
55	C₂³×C₅×D₃	C₂×C₄	1	2	yes	—
56	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
58	C₂×C₅×#67	C₂×C₄	1	2	yes	—
59	C₂²×C₅×Dic₃	C₂×C₄	1	2	yes	—
60	C₅×D₃×D₄	—	2	4	no	—
61	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄×C₅×D₃	—	2	4	no	—
63	C₂×C₄×C₅×D₃	—	2	4	no	—
64	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
66	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
67	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
69	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
70	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
71	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
72	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
73	#6710	—	2	4	no	—
74	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
75	C₂×C₃⋊#168	C₂³	1	2	yes	—
76	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
77	C₅×#217	C₂×C₄	1	2	yes	—
78	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
79	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
80	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
81	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
82	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
83	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
84	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
85	C₃×#681	—	2	4	no	—
86	C₂×C₃×#168	C₂³	1	1	yes	characteristic
87	C₂×C₃×#168	C₂³	1	2	yes	—
88	C₂×C₃×#168	C₂³	1	1	yes	characteristic
89	#6650	—	2	4	no	—
90	#6650	—	2	2	no	—
91	#6650	D₄	1	4	yes	complemented
92	D₃×#168	—	2	4	no	—
93	D₃×#168	—	2	4	no	—
94	C₂×D₃×M₁₆	—	5	2	no	—
95	C₄×D₃×D₄	D₅	1	1	yes	characteristic
96	C₃×#436	—	5	1	no	—
97	#5127	—	5	2	no	—
98	#5012	—	5	1	no	—
99	#4837	—	5	1	no	—
100	#4834	—	5	1	no	—
101	#4728	—	5	2	no	—
102	#4726	—	5	2	no	—
103	C₄×ΓL(1,𝔽₂₅)	—	5	1	no	—
104	C₈×D₁₂	—	5	1	no	—
105	C₂²×C₅×D₄	—	3	1	no	—
106	C₂³×C₄×C₅	—	3	2	no	—
107	C₄×C₅×D₄	—	3	1	no	—
108	C₄×C₅×D₄	—	3	2	no	—
109	C₄×C₅×D₄	—	3	1	no	—
110	C₄×C₅×D₄	—	3	2	no	—
111	C₄×C₅×D₄	—	3	1	no	—
112	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
113	C₂×C₅×C₄⋊C₄	—	3	1	no	—
114	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
115	C₂×C₄²×C₅	—	3	1	no	—
116	C₂×#681	—	3	2	no	—
117	C₂×#681	—	3	1	no	—
118	C₂×#681	—	3	2	no	—
119	C₂×#681	—	3	1	no	—
120	C₂×#681	—	6	8	no	—
121	C₂×#681	C₂×D₃	1	2	yes	complemented
122	C₂²×#168	—	3	2	no	—
123	C₂²×#168	—	3	2	no	—
124	C₂²⋊#168	—	3	2	no	—
125	C₂²⋊#168	—	3	2	no	—
126	C₂²⋊#168	—	3	2	no	—
127	C₂²⋊#168	C₂×D₃	1	2	yes	complemented
128	C₄⋊#168	—	3	1	no	—
129	C₄⋊#168	—	3	2	no	—
130	C₄⋊#168	C₂×D₃	1	1	yes	characteristic, complemented
131	#3935	—	3	1	no	—
132	#3935	—	3	1	no	—
133	C₄×#168	—	3	1	no	—
134	C₄×#168	C₂×D₃	1	1	yes	characteristic, complemented
135	D₄×M₁₆	—	15	1	no	Sylow
136	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
137	C₂²×C₅×D₃	—	2	4	no	—
138	C₂²×C₅×D₃	—	2	4	no	—
139	C₂²×C₅×D₃	—	4	2	no	—
140	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
142	C₃×C₅×D₄	—	2	2	no	—
143	C₂×C₃×C₄×C₅	—	2	2	no	—
144	C₂×C₃×C₄×C₅	—	2	2	no	—
145	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
147	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
149	C₅×#67	—	2	4	no	—
150	C₂×C₅×Dic₃	—	2	4	no	—
151	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
154	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
155	C₅×D₁₂	M₁₆	1	4	yes	complemented
156	C₄×C₅×D₃	—	2	4	no	—
157	C₄×C₅×D₃	—	2	2	no	—
158	C₄×C₅×D₃	—	2	2	no	—
159	C₄×C₅×D₃	—	2	2	no	—
160	C₄×C₅×D₃	—	2	4	no	—
161	C₄×C₅×D₃	—	4	1	no	—
162	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
163	C₄×C₅×D₃	#41	1	2	yes	—
164	C₃⋊#168	—	2	2	no	—
165	C₃⋊#168	—	2	1	no	—
166	C₃⋊#168	C₂×D₄	1	2	yes	complemented
167	C₃×#168	—	2	2	no	—
168	C₃×#168	—	2	1	no	—
169	C₃×#168	C₂×D₄	1	2	yes	complemented
170	C₂×D₃×D₄	Dic₅	1	1	yes	characteristic
171	C₂²×C₄×D₃	C₂×D₅	1	2	yes	—
172	C₂×C₃×M₁₆	—	5	2	no	—
173	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
174	D₄×Dic₃	Dic₅	1	1	yes	characteristic
175	C₄×#67	C₂×D₅	1	2	yes	—
176	C₂×#208	—	5	2	no	—
177	D₃×M₁₆	—	10	8	no	—
178	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
179	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
180	C₂×ΓL(1,𝔽₂₅)	—	5	2	no	—
181	C₂×D₃×C₈	—	5	2	no	—
182	C₂×D₃×C₈	—	5	2	no	—
183	#893	Dic₅	1	1	yes	characteristic
184	D₃×C₄⋊C₄	Dic₅	1	1	yes	characteristic
185	#67⋊C₄	Dic₅	1	2	yes	—
186	D₃×C₂²⋊C₄	Dic₅	1	2	yes	—
187	C₄×D₁₂	C₂×D₅	1	1	yes	characteristic
188	C₄²×D₃	C₂×D₅	1	1	yes	characteristic
189	C₃×C₄⋊C₈	—	5	1	no	—
190	C₃×C₂²⋊C₈	—	5	2	no	—
191	C₃×C₄×C₈	—	5	1	no	—
192	#830	—	5	2	no	—
193	(C₂×D₃)⋊C₈	—	5	2	no	—
194	(C₂×D₃)⋊C₈	—	5	2	no	—
195	#815	—	5	1	no	—
196	#815	—	5	1	no	—
197	Dic₃⋊C₈	—	5	2	no	—
198	C₄⋊(C₃⋊C₈)	—	5	1	no	—
199	C₄×C₃⋊C₈	—	5	1	no	—
200	C₂⁴×C₅	—	3	2	no	—
201	C₂×C₅×D₄	—	3	2	no	—
202	C₂×C₅×D₄	—	3	1	no	—
203	C₂×C₅×D₄	—	6	4	no	—
204	C₂×C₅×D₄	C₄×D₃	1	1	yes	characteristic
205	C₂²×C₄×C₅	—	3	1	no	—
206	C₂²×C₄×C₅	—	3	2	no	—
207	C₂²×C₄×C₅	—	3	1	no	—
208	C₂²×C₄×C₅	—	3	2	no	—
209	C₂²×C₄×C₅	—	3	2	no	—
210	C₂²×C₄×C₅	—	3	2	no	—
211	C₂²×C₄×C₅	—	3	1	no	—
212	C₂²×C₄×C₅	—	6	4	no	—
213	C₂²×C₄×C₅	—	6	4	no	—
214	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
215	C₅×C₄⋊C₄	—	3	2	no	—
216	C₅×C₄⋊C₄	—	3	1	no	—
217	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
218	C₅×C₂²⋊C₄	—	3	2	no	—
219	C₅×C₂²⋊C₄	—	3	2	no	—
220	C₅×C₂²⋊C₄	—	3	2	no	—
221	C₅×C₂²⋊C₄	C₄×D₃	1	2	yes	—
222	C₄²×C₅	—	3	1	no	—
223	C₄²×C₅	—	3	1	no	—
224	C₄²×C₅	—	3	1	no	—
225	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
226	#681	—	2	4	no	—
227	#681	—	3	4	no	—
228	#681	—	6	4	no	—
229	#681	—	6	2	no	—
230	#681	—	6	4	no	—
231	C₂×#168	—	3	1	no	—
232	C₂×#168	—	3	1	no	—
233	C₂×#168	—	3	2	no	—
234	C₂×#168	—	6	4	no	—
235	C₂×#168	—	6	4	no	—
236	C₂×#168	C₂²×D₃	1	1	yes	characteristic
237	C₂×#168	C₂²×D₃	1	2	yes	—
238	C₂×#168	C₂²×D₃	1	1	yes	characteristic
239	C₂²×M₁₆	—	15	2	no	—
240	C₂×C₄×D₄	—	3	1	no	—
241	#436	—	5	1	no	—
242	#436	—	15	1	no	—
243	#435	—	15	2	no	—
244	#435	—	15	2	no	—
245	C₈×D₄	—	15	1	no	—
246	C₈×D₄	—	15	1	no	—
247	#423	—	15	1	no	—
248	#407	—	15	2	no	—
249	C₄×M₁₆	—	15	1	no	—
250	C₂²×C₃×C₅	—	2	2	no	—
251	C₂²×C₃×C₅	—	2	2	no	—
252	C₂²×C₃×C₅	—	2	2	no	—
253	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
254	C₂×C₅×D₃	—	2	2	no	—
255	C₂×C₅×D₃	—	2	1	no	—
256	C₂×C₅×D₃	—	2	1	no	—
257	C₂×C₅×D₃	—	2	2	no	—
258	C₂×C₅×D₃	—	4	8	no	—
259	C₂×C₅×D₃	C₄×D₄	1	2	yes	—
260	C₂×C₅×D₃	C₂×M₁₆	1	4	yes	complemented
261	C₃×C₄×C₅	—	2	2	no	—
262	C₃×C₄×C₅	—	2	1	no	—
263	C₃×C₄×C₅	C₂×M₁₆	1	2	yes	complemented
264	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
265	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
266	C₅×Dic₃	—	2	2	no	—
267	C₅×Dic₃	—	2	1	no	—
268	C₅×Dic₃	—	2	1	no	—
269	C₅×Dic₃	C₄×D₄	1	2	yes	—
270	C₂³×D₃	C₂×Dic₅	1	2	yes	—
271	C₂×C₃×D₄	C₂×Dic₅	1	1	yes	characteristic
272	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
273	C₂×#67	C₂×Dic₅	1	2	yes	—
274	C₂²×Dic₃	C₂×Dic₅	1	2	yes	—
275	D₃×D₄	—	2	4	no	—
276	C₂×D₁₂	C₂×Dic₅	1	1	yes	characteristic
277	C₂×C₄×D₃	—	2	4	no	—
278	C₂×C₄×D₃	—	2	4	no	—
279	C₂×C₄×D₃	C₂×Dic₅	1	1	yes	characteristic
280	C₂×C₄×D₃	C₂×Dic₅	1	2	yes	—
281	C₂×C₄×D₃	C₂×Dic₅	1	2	yes	—
282	C₂×C₄×D₃	C₂×Dic₅	1	1	yes	characteristic
283	C₂×C₄×D₃	C₂²×D₅	1	2	yes	—
284	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
285	C₃×M₁₆	—	10	4	no	—
286	C₂×C₃×C₈	—	5	1	no	—
287	C₂×C₃×C₈	—	5	2	no	—
288	C₂×C₃×C₈	—	5	1	no	—
289	C₃×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
290	C₃×C₂²⋊C₄	C₂×Dic₅	1	2	yes	—
291	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
292	#217	C₂×Dic₅	1	2	yes	—
293	(C₂×D₃)⋊C₄	C₂×Dic₅	1	2	yes	—
294	(C₂×D₃)⋊C₄	C₂×Dic₅	1	2	yes	—
295	C₄⋊Dic₃	C₂×Dic₅	1	1	yes	characteristic
296	Dic₃⋊C₄	C₂×Dic₅	1	2	yes	—
297	C₄×Dic₃	C₂×Dic₅	1	1	yes	characteristic
298	C₄×Dic₃	C₂×Dic₅	1	1	yes	characteristic
299	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
300	#208	—	10	4	no	—
301	C₂×C₃⋊C₈	—	5	1	no	—
302	C₂×C₃⋊C₈	—	5	1	no	—
303	C₂×C₃⋊C₈	—	5	2	no	—
304	ΓL(1,𝔽₂₅)	—	5	4	no	—
305	ΓL(1,𝔽₂₅)	—	10	4	no	—
306	ΓL(1,𝔽₂₅)	—	10	2	no	—
307	D₃×C₈	—	10	4	no	—
308	D₃×C₈	—	10	4	no	—
309	C₂³×C₅	—	3	2	no	—
310	C₂³×C₅	—	3	1	no	—
311	C₂³×C₅	—	6	4	no	—
312	C₂³×C₅	—	6	4	no	—
313	C₂³×C₅	—	12	2	no	—
314	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
315	C₅×D₄	—	2	2	no	—
316	C₅×D₄	—	3	4	no	—
317	C₅×D₄	—	6	4	no	—
318	C₂×C₄×C₅	—	2	2	no	—
319	C₂×C₄×C₅	—	2	2	no	—
320	C₂×C₄×C₅	—	3	1	no	—
321	C₂×C₄×C₅	—	3	2	no	—
322	C₂×C₄×C₅	—	3	2	no	—
323	C₂×C₄×C₅	—	3	1	no	—
324	C₂×C₄×C₅	—	3	1	no	—
325	C₂×C₄×C₅	—	3	2	no	—
326	C₂×C₄×C₅	—	6	4	no	—
327	C₂×C₄×C₅	—	6	4	no	—
328	C₂×C₄×C₅	—	6	4	no	—
329	C₂×C₄×C₅	—	6	2	no	—
330	C₂×C₄×C₅	—	6	2	no	—
331	C₂×C₄×C₅	—	6	2	no	—
332	C₂×C₄×C₅	—	12	1	no	—
333	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
334	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
335	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
336	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
337	#168	—	2	2	no	—
338	#168	—	2	1	no	—
339	#168	—	3	2	no	—
340	#168	—	6	2	no	—
341	#168	—	6	1	no	—
342	#168	D₃×D₄	1	2	yes	complemented
343	C₂²×D₄	—	3	1	no	—
344	C₂³×C₄	—	3	2	no	—
345	C₂×M₁₆	—	5	2	no	—
346	C₂×M₁₆	—	15	1	no	—
347	C₂×M₁₆	—	15	2	no	—
348	C₂×M₁₆	—	15	1	no	—
349	C₂×M₁₆	—	15	2	no	—
350	C₂×M₁₆	—	30	8	no	—
351	C₂²×C₈	—	15	2	no	—
352	C₂²×C₈	—	15	2	no	—
353	C₄×D₄	—	3	1	no	—
354	C₄×D₄	—	3	2	no	—
355	C₄×D₄	—	3	1	no	—
356	C₄×D₄	—	3	2	no	—
357	C₄×D₄	—	3	1	no	—
358	C₄×D₄	D₃×D₅	1	1	yes	characteristic
359	C₂×C₄⋊C₄	—	3	1	no	—
360	C₂×C₂²⋊C₄	—	3	2	no	—
361	C₂×C₄²	—	3	1	no	—
362	C₄⋊C₈	—	5	1	no	—
363	C₄⋊C₈	—	15	2	no	—
364	C₄⋊C₈	—	15	1	no	—
365	C₂²⋊C₈	—	5	2	no	—
366	C₂²⋊C₈	—	15	2	no	—
367	C₂²⋊C₈	—	15	2	no	—
368	C₂²⋊C₈	—	15	2	no	—
369	#97	—	15	1	no	—
370	#97	—	15	1	no	—
371	C₄×C₈	—	5	1	no	—
372	C₄×C₈	—	15	1	no	—
373	C₂×C₃×C₅	—	4	2	no	—
374	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
375	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
376	C₂×C₃×C₅	#568	1	1	yes	characteristic
377	C₅×D₃	—	2	2	no	—
378	C₅×D₃	—	2	4	no	—
379	C₂³×C₃	C₂²×Dic₅	1	2	yes	—
380	C₂²×D₃	—	2	4	no	—
381	C₂²×D₃	—	2	4	no	—
382	C₂²×D₃	—	4	2	no	—
383	C₂²×D₃	C₂²×Dic₅	1	2	yes	—
384	C₂²×D₃	C₂²×Dic₅	1	1	yes	characteristic
385	C₃×D₄	—	2	2	no	—
386	C₂×C₃×C₄	—	2	2	no	—
387	C₂×C₃×C₄	—	2	2	no	—
388	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
389	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
390	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
391	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
392	#67	—	2	4	no	—
393	C₂×Dic₃	—	2	4	no	—
394	C₂×Dic₃	C₂²×Dic₅	1	1	yes	characteristic
395	C₂×Dic₃	C₂²×Dic₅	1	1	yes	characteristic
396	C₂×Dic₃	C₂²×Dic₅	1	2	yes	—
397	C₂×Dic₃	C₂²×Dic₅	1	1	yes	characteristic
398	D₁₂	#681	1	4	yes	complemented
399	C₄×D₃	—	2	4	no	—
400	C₄×D₃	—	2	2	no	—
401	C₄×D₃	—	2	2	no	—
402	C₄×D₃	—	2	2	no	—
403	C₄×D₃	—	2	4	no	—
404	C₄×D₃	—	4	1	no	—
405	C₄×D₃	D₄×D₅	1	2	yes	—
406	C₄×D₃	#711	1	2	yes	—
407	C₃×C₈	—	5	2	no	—
408	C₃×C₈	—	10	2	no	—
409	C₃×C₈	—	10	1	no	—
410	C₃⋊C₈	—	5	2	no	—
411	C₃⋊C₈	—	10	2	no	—
412	C₃⋊C₈	—	10	1	no	—
413	C₂²×C₅	—	2	2	no	—
414	C₂²×C₅	—	2	2	no	—
415	C₂²×C₅	—	2	2	no	—
416	C₂²×C₅	—	3	4	no	—
417	C₂²×C₅	—	3	2	no	—
418	C₂²×C₅	—	6	1	no	—
419	C₂²×C₅	—	6	1	no	—
420	C₂²×C₅	—	6	2	no	—
421	C₂²×C₅	—	6	2	no	—
422	C₂²×C₅	—	12	8	no	—
423	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
424	C₄×C₅	—	2	1	no	—
425	C₄×C₅	—	2	2	no	—
426	C₄×C₅	—	3	2	no	—
427	C₄×C₅	—	6	1	no	—
428	C₄×C₅	—	6	1	no	—
429	C₄×C₅	—	6	2	no	—
430	C₄×C₅	D₃×M₁₆	1	2	yes	complemented
431	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
432	C₄×C₅	D₃×#41	1	1	yes	characteristic
433	C₂⁴	—	3	2	no	—
434	C₂×D₄	—	3	2	no	—
435	C₂×D₄	—	3	1	no	—
436	C₂×D₄	—	6	4	no	—
437	C₂×D₄	D₃×Dic₅	1	1	yes	characteristic
438	C₂²×C₄	—	3	1	no	—
439	C₂²×C₄	—	3	2	no	—
440	C₂²×C₄	—	3	1	no	—
441	C₂²×C₄	—	3	2	no	—
442	C₂²×C₄	—	3	2	no	—
443	C₂²×C₄	—	3	2	no	—
444	C₂²×C₄	—	3	1	no	—
445	C₂²×C₄	—	6	4	no	—
446	C₂²×C₄	—	6	4	no	—
447	C₂²×C₄	C₂×D₃×D₅	1	2	yes	—
448	M₁₆	—	10	4	no	—
449	M₁₆	—	15	4	no	—
450	M₁₆	—	30	4	no	—
451	M₁₆	—	30	2	no	—
452	M₁₆	—	30	4	no	—
453	C₂×C₈	—	5	1	no	—
454	C₂×C₈	—	5	1	no	—
455	C₂×C₈	—	5	2	no	—
456	C₂×C₈	—	15	1	no	—
457	C₂×C₈	—	15	1	no	—
458	C₂×C₈	—	15	2	no	—
459	C₂×C₈	—	30	4	no	—
460	C₂×C₈	—	30	4	no	—
461	C₄⋊C₄	—	3	2	no	—
462	C₄⋊C₄	—	3	1	no	—
463	C₄⋊C₄	D₃×Dic₅	1	1	yes	characteristic
464	C₂²⋊C₄	—	3	2	no	—
465	C₂²⋊C₄	—	3	2	no	—
466	C₂²⋊C₄	—	3	2	no	—
467	C₂²⋊C₄	D₃×Dic₅	1	2	yes	—
468	C₄²	—	3	1	no	—
469	C₄²	—	3	1	no	—
470	C₄²	—	3	1	no	—
471	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
472	C₃×C₅	D₄×M₁₆	1	1	yes	characteristic, complemented, Hall
473	C₂²×C₃	—	2	2	no	—
474	C₂²×C₃	—	2	2	no	—
475	C₂²×C₃	—	2	2	no	—
476	C₂²×C₃	C₂³×Dic₅	1	1	yes	characteristic
477	C₂×D₃	—	2	1	no	—
478	C₂×D₃	—	2	2	no	—
479	C₂×D₃	—	2	1	no	—
480	C₂×D₃	—	2	2	no	—
481	C₂×D₃	—	4	8	no	—
482	C₂×D₃	C₂×#681	1	4	yes	complemented
483	C₂×D₃	D₄×Dic₅	1	2	yes	—
484	C₃×C₄	—	2	2	no	—
485	C₃×C₄	—	2	1	no	—
486	C₃×C₄	C₂×#681	1	2	yes	complemented
487	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
488	C₃×C₄	C₂×#711	1	1	yes	characteristic
489	Dic₃	—	2	1	no	—
490	Dic₃	—	2	2	no	—
491	Dic₃	—	2	1	no	—
492	Dic₃	D₄×Dic₅	1	2	yes	—
493	C₂×C₅	—	4	2	no	—
494	C₂×C₅	—	6	2	no	—
495	C₂×C₅	—	6	4	no	—
496	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
497	C₂×C₅	C₂×D₃×M₁₆	1	1	yes	characteristic
498	C₂×C₅	#5750	1	1	yes	characteristic
499	C₂³	—	3	2	no	—
500	C₂³	—	3	1	no	—
501	C₂³	—	6	4	no	—
502	C₂³	—	6	4	no	—
503	C₂³	—	12	2	no	—
504	C₂³	C₂×D₃×Dic₅	1	2	yes	—
505	D₄	—	2	2	no	—
506	D₄	—	3	4	no	—
507	D₄	—	6	4	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	3	1	no	—
511	C₂×C₄	—	3	2	no	—
512	C₂×C₄	—	3	2	no	—
513	C₂×C₄	—	3	1	no	—
514	C₂×C₄	—	3	1	no	—
515	C₂×C₄	—	3	2	no	—
516	C₂×C₄	—	6	4	no	—
517	C₂×C₄	—	6	4	no	—
518	C₂×C₄	—	6	4	no	—
519	C₂×C₄	—	6	2	no	—
520	C₂×C₄	—	6	2	no	—
521	C₂×C₄	—	6	2	no	—
522	C₂×C₄	—	12	1	no	—
523	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
524	C₂×C₄	C₂×D₃×Dic₅	1	2	yes	—
525	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
526	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
527	C₈	—	5	2	no	—
528	C₈	—	10	2	no	—
529	C₈	—	10	1	no	—
530	C₈	—	15	2	no	—
531	C₈	—	30	2	no	—
532	C₈	—	30	1	no	—
533	C₂×C₃	—	4	2	no	—
534	C₂×C₃	C₂²×#681	1	1	yes	characteristic
535	C₂×C₃	C₂×D₄×Dic₅	1	1	yes	characteristic
536	C₂×C₃	#66153	1	1	yes	characteristic
537	D₃	—	2	2	no	—
538	D₃	—	2	4	no	—
539	C₅	#79540	1	1	yes	characteristic, complemented, Sylow
540	C₂²	—	2	2	no	—
541	C₂²	—	2	2	no	—
542	C₂²	—	2	2	no	—
543	C₂²	—	3	2	no	—
544	C₂²	—	3	4	no	—
545	C₂²	—	6	2	no	—
546	C₂²	—	6	1	no	—
547	C₂²	—	6	2	no	—
548	C₂²	—	6	1	no	—
549	C₂²	—	12	8	no	—
550	C₂²	C₂²×D₃×Dic₅	1	1	yes	characteristic
551	C₄	—	2	2	no	—
552	C₄	—	2	1	no	—
553	C₄	—	3	2	no	—
554	C₄	—	6	2	no	—
555	C₄	—	6	1	no	—
556	C₄	—	6	1	no	—
557	C₄	D₃×#681	1	2	yes	complemented
558	C₄	D₃×D₄×D₅	1	1	yes	characteristic
559	C₄	D₃×#711	1	1	yes	characteristic
560	C₃	D₄×#681	1	1	yes	characteristic, complemented, Sylow
561	C₂	—	4	2	no	—
562	C₂	—	6	2	no	—
563	C₂	—	6	4	no	—
564	C₂	C₂×D₃×#681	1	1	yes	characteristic
565	C₂	D₃×D₄×Dic₅	1	1	yes	characteristic
566	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	C₂×C₅×D₃×D₄	C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₄×D₄	D₃×D₅
hypocenter	C₃×C₅	D₄×M₁₆
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×D₃×#681	C₂	semidirect
3. #11751113	C₂	semidirect
4. C₃×#65301	C₂	semidirect
5. #11748505	C₂	semidirect
6. #11748496	C₂	semidirect
7. #11748484	C₂	semidirect
8. #11747011	C₂	semidirect
9. C₄×#6650	C₂	semidirect
10. #11746998	C₂	semidirect
11. D₁₂×#168	C₂	semidirect
16. C₂×#6710	C₂²	semidirect
25. C₂×C₃×#681	C₂²	semidirect
30. C₂×D₃×#168	C₂²	semidirect
31. C₂×D₃×#168	C₂²	semidirect
32. #91114	C₂²	semidirect
33. C₄⋊(C₃⋊#168)	C₂²	semidirect
34. C₄×C₃⋊#168	C₂²	semidirect
35. C₃×C₂²⋊#168	C₂²	semidirect
36. C₃×C₄⋊#168	C₂²	semidirect
37. C₃×C₄×#168	C₂²	semidirect
38. Dic₃⋊#168	C₂²	semidirect
39. (C₂×D₃)⋊#168	C₂²	semidirect
40. (C₂×D₃)⋊#168	C₂²	semidirect
41. #90953	C₂²	semidirect
42. #90953	C₂²	semidirect
48. #65301	D₃	semidirect
91. #6650	D₄	semidirect
121. C₂×#681	C₂×D₃	semidirect
127. C₂²⋊#168	C₂×D₃	semidirect
130. C₄⋊#168	C₂×D₃	semidirect
134. C₄×#168	C₂×D₃	semidirect
155. C₅×D₁₂	M₁₆	semidirect
166. C₃⋊#168	C₂×D₄	semidirect
169. C₃×#168	C₂×D₄	semidirect
260. C₂×C₅×D₃	C₂×M₁₆	semidirect
263. C₃×C₄×C₅	C₂×M₁₆	semidirect
342. #168	D₃×D₄	semidirect
398. D₁₂	#681	semidirect
430. C₄×C₅	D₃×M₁₆	semidirect
472. C₃×C₅	D₄×M₁₆	semidirect
482. C₂×D₃	C₂×#681	semidirect
486. C₃×C₄	C₂×#681	semidirect
539. C₅	#79540	semidirect
557. C₄	D₃×#681	semidirect
560. C₃	D₄×#681	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₅×D₃×D₄	2
C₂×D₃×#681	2
#11751113	2
C₃×#65301	2
#11748505	2
#11748496	2
#11748484	2
#11747011	2
C₄×#6650	2
#11746998	2
D₁₂×#168	2
D₄×#681	3
#79540	5