Subgroups — #14415745

Order 1920.

1088 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#6710	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×C₅×#67	C₂	1	1	yes	maximal, characteristic
3	C₂×D₃×#681	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65496	C₂	1	1	yes	maximal, characteristic, complemented
5	#11748508	C₂	1	2	yes	maximal, complemented
6	#11748496	C₂	1	2	yes	maximal, complemented
7	#67⋊#168	C₂	1	2	yes	maximal, complemented
8	#11748440	C₂	1	1	yes	maximal, characteristic, complemented
9	#11748346	C₂	1	1	yes	maximal, characteristic, complemented
10	Dic₃×#681	C₂	1	1	yes	maximal, characteristic, complemented
11	#11748314	C₂	1	2	yes	maximal, complemented
12	D₄×#681	—	3	1	no	maximal, Hall
13	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
14	C₂²×C₅×#67	C₄	1	1	yes	characteristic
15	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
16	C₂×#6710	—	2	4	no	—
17	C₂×#6710	C₂²	1	1	yes	characteristic
18	C₂×#6710	C₂²	1	1	yes	characteristic
19	C₂×#6710	C₂²	1	2	yes	complemented
20	C₂²×C₃⋊#168	C₂²	1	2	yes	complemented
21	C₂×C₅×#217	C₄	1	1	yes	characteristic
22	C₄×C₅×#67	C₄	1	1	yes	characteristic
23	C₄×C₅×#67	C₄	1	1	yes	characteristic
24	C₄×C₅×#67	C₄	1	1	yes	characteristic
25	C₄×C₅×#67	C₄	1	1	yes	characteristic
26	C₄×C₅×#67	C₂²	1	1	yes	characteristic
27	C₄×C₅×#67	C₂²	1	1	yes	characteristic
28	C₄×C₅×#67	C₂²	1	1	yes	characteristic
29	C₄×C₅×#67	C₂²	1	1	yes	characteristic
30	C₂×C₅×(C₂×D₃)⋊C₄	C₄	1	1	yes	characteristic
31	C₂×C₅×Dic₃⋊C₄	C₄	1	1	yes	characteristic
32	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
33	C₂×C₃×#681	C₂²	1	1	yes	characteristic
34	C₂×C₃×#681	C₂²	1	1	yes	characteristic
35	C₂×#6650	C₂²	1	2	yes	complemented
36	D₃×#681	—	2	4	no	—
37	C₂×D₃×#168	C₂²	1	2	yes	complemented
38	C₃×C₂²⋊#168	C₂²	1	2	yes	complemented
39	C₃×C₂²⋊#168	C₂²	1	2	yes	complemented
40	Dic₃⋊#168	C₂²	1	2	yes	complemented
41	Dic₃⋊#168	C₂²	1	2	yes	complemented
42	(C₂×D₃)⋊#168	C₂²	1	2	yes	complemented
43	(C₂×D₃)⋊#168	C₂²	1	2	yes	complemented
44	#90953	C₂²	1	2	yes	complemented
45	Dic₃×#168	C₂²	1	2	yes	complemented
46	#78628	—	5	1	no	maximal, Hall
47	C₂×C₄×C₅×D₄	—	3	1	no	—
48	C₂²×#681	—	3	1	no	—
49	C₂²×#681	—	3	1	no	—
50	#65496	—	3	1	no	—
51	#65496	D₃	1	1	yes	characteristic, complemented
52	#65301	—	3	2	no	—
53	#65300	—	3	2	no	—
54	#65300	—	3	2	no	—
55	D₄×#168	—	3	2	no	—
56	#65213	—	3	1	no	—
57	C₄×#681	—	3	1	no	—
58	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
59	C₂³×C₅×D₃	C₂×C₄	1	1	yes	characteristic
60	C₂²×C₃×C₄×C₅	—	2	2	no	—
61	C₂²×C₃×C₄×C₅	—	2	2	no	—
62	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
63	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
64	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
65	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
66	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
67	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
68	C₂×C₅×#67	—	2	4	no	—
69	C₂×C₅×#67	C₂×C₄	1	1	yes	characteristic
70	C₂×C₅×#67	C₂×C₄	1	1	yes	characteristic
71	C₂×C₅×#67	C₂×C₄	1	1	yes	characteristic
72	C₂×C₅×#67	C₂×C₄	1	1	yes	characteristic
73	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
74	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
75	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄×C₅×D₃	—	2	2	no	—
77	C₂×C₄×C₅×D₃	—	2	2	no	—
78	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
81	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
82	#6710	—	2	2	no	—
83	#6710	—	2	4	no	—
84	#6710	D₄	1	4	yes	complemented
85	C₂×C₃⋊#168	—	2	4	no	—
86	C₂×C₃⋊#168	C₂³	1	2	yes	—
87	C₂×C₃⋊#168	C₂³	1	2	yes	—
88	C₅×#217	C₂×C₄	1	1	yes	characteristic
89	C₅×#217	C₂×C₄	1	1	yes	characteristic
90	C₅×#217	C₂×C₄	1	1	yes	characteristic
91	C₅×#217	C₂×C₄	1	1	yes	characteristic
92	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
93	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
94	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
95	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
96	C₅×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
97	C₅×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
98	C₅×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
99	C₅×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
100	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
101	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
102	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
103	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
104	C₃×#681	—	2	2	no	—
105	C₃×#681	—	2	2	no	—
106	C₂×C₃×#168	C₂³	1	2	yes	—
107	C₂×C₃×#168	C₂³	1	2	yes	—
108	#6650	—	2	4	no	—
109	D₃×#168	—	2	4	no	—
110	C₂×C₄×#67	D₅	1	1	yes	characteristic
111	C₂²×#208	—	5	1	no	—
112	C₂×D₃×M₁₆	—	5	1	no	—
113	C₃×#407	—	5	1	no	—
114	#5126	—	5	1	no	—
115	#5118	—	5	1	no	—
116	Dic₃×M₁₆	—	5	1	no	—
117	#4730	—	5	2	no	—
118	#4729	—	5	2	no	—
119	#4728	—	5	2	no	—
120	#67⋊C₈	—	5	2	no	—
121	C₂²×C₅×D₄	—	3	1	no	—
122	C₂³×C₄×C₅	—	3	1	no	—
123	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
124	C₄×C₅×D₄	—	3	1	no	—
125	C₄×C₅×D₄	—	3	1	no	—
126	C₄×C₅×D₄	—	3	1	no	—
127	C₄×C₅×D₄	—	3	1	no	—
128	C₄×C₅×D₄	—	3	1	no	—
129	C₄×C₅×D₄	—	3	1	no	—
130	C₄×C₅×D₄	—	3	1	no	—
131	C₄×C₅×D₄	—	3	1	no	—
132	C₂×C₅×C₄⋊C₄	—	3	1	no	—
133	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
134	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
135	C₂×C₄²×C₅	—	3	1	no	—
136	C₂×#681	—	3	1	no	—
137	C₂×#681	—	3	2	no	—
138	C₂×#681	—	3	1	no	—
139	C₂×#681	—	3	2	no	—
140	C₂×#681	—	6	4	no	—
141	C₂×#681	—	6	4	no	—
142	C₂×#681	C₂×D₃	1	1	yes	characteristic
143	C₂×#681	C₂×D₃	1	1	yes	characteristic
144	C₂²×#168	—	3	2	no	—
145	C₂²×#168	—	3	2	no	—
146	C₂²⋊#168	—	3	2	no	—
147	C₂²⋊#168	—	3	2	no	—
148	C₂²⋊#168	C₂×D₃	1	2	yes	complemented
149	C₂²⋊#168	C₂×D₃	1	2	yes	complemented
150	C₄⋊#168	—	3	2	no	—
151	C₄⋊#168	—	3	2	no	—
152	#3935	—	3	2	no	—
153	C₄×#168	—	3	2	no	—
154	D₄×M₁₆	—	15	1	no	Sylow
155	C₂³×C₃×C₅	—	2	2	no	—
156	C₂³×C₃×C₅	—	2	2	no	—
157	C₂³×C₃×C₅	—	4	1	no	—
158	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
159	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
160	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
161	C₂²×C₅×D₃	—	2	2	no	—
162	C₂²×C₅×D₃	—	2	2	no	—
163	C₂²×C₅×D₃	—	4	1	no	—
164	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
165	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
166	C₂×C₃×C₄×C₅	—	2	2	no	—
167	C₂×C₃×C₄×C₅	—	2	2	no	—
168	C₂×C₃×C₄×C₅	—	2	2	no	—
169	C₂×C₃×C₄×C₅	—	2	1	no	—
170	C₂×C₃×C₄×C₅	—	2	1	no	—
171	C₂×C₃×C₄×C₅	—	2	1	no	—
172	C₂×C₃×C₄×C₅	—	2	1	no	—
173	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
174	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
175	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
176	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
177	C₂×C₃×C₄×C₅	#41	1	2	yes	—
178	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
179	C₅×#67	—	2	2	no	—
180	C₅×#67	—	2	2	no	—
181	C₅×#67	—	2	2	no	—
182	C₅×#67	M₁₆	1	4	yes	complemented
183	C₂×C₅×Dic₃	—	2	2	no	—
184	C₂×C₅×Dic₃	—	2	2	no	—
185	C₂×C₅×Dic₃	—	4	1	no	—
186	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
187	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
188	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
189	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
190	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
191	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
192	C₄×C₅×D₃	—	2	2	no	—
193	C₄×C₅×D₃	—	2	2	no	—
194	C₄×C₅×D₃	—	2	1	no	—
195	C₄×C₅×D₃	—	2	1	no	—
196	C₄×C₅×D₃	—	2	1	no	—
197	C₄×C₅×D₃	—	2	1	no	—
198	C₃⋊#168	—	2	2	no	—
199	C₃⋊#168	C₂×D₄	1	4	yes	complemented
200	C₃×#168	—	2	2	no	—
201	C₃×#168	—	2	2	no	—
202	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
203	C₂²×#67	Dic₅	1	1	yes	characteristic
204	C₂²×C₄×D₃	C₂×D₅	1	1	yes	characteristic
205	C₂×C₃×M₁₆	—	5	1	no	—
206	C₂×C₃×M₁₆	—	5	1	no	—
207	C₂×#217	Dic₅	1	1	yes	characteristic
208	C₄×#67	Dic₅	1	1	yes	characteristic
209	C₄×#67	Dic₅	1	1	yes	characteristic
210	C₄×#67	Dic₅	1	1	yes	characteristic
211	C₄×#67	Dic₅	1	1	yes	characteristic
212	C₄×#67	C₂×D₅	1	1	yes	characteristic
213	C₄×#67	C₂×D₅	1	1	yes	characteristic
214	C₄×#67	C₂×D₅	1	1	yes	characteristic
215	C₄×#67	C₂×D₅	1	1	yes	characteristic
216	C₂×(C₂×D₃)⋊C₄	Dic₅	1	1	yes	characteristic
217	C₂×Dic₃⋊C₄	Dic₅	1	1	yes	characteristic
218	C₂×C₄×Dic₃	C₂×D₅	1	1	yes	characteristic
219	C₂×#208	—	5	1	no	—
220	C₂×#208	—	5	1	no	—
221	C₂×#208	—	5	2	no	—
222	C₂×#208	—	10	4	no	—
223	C₂²×C₃⋊C₈	—	5	2	no	—
224	D₃×M₁₆	—	10	4	no	—
225	C₂×ΓL(1,𝔽₂₅)	—	5	2	no	—
226	C₂×D₃×C₈	—	5	2	no	—
227	C₃×C₂²⋊C₈	—	5	2	no	—
228	C₃×C₂²⋊C₈	—	5	2	no	—
229	(C₂×D₃)⋊C₈	—	5	2	no	—
230	(C₂×D₃)⋊C₈	—	5	2	no	—
231	#815	—	5	2	no	—
232	Dic₃⋊C₈	—	5	2	no	—
233	Dic₃⋊C₈	—	5	2	no	—
234	C₈×Dic₃	—	5	2	no	—
235	C₂⁴×C₅	—	3	1	no	—
236	C₂⁴×C₅	C₄×D₃	1	1	yes	characteristic
237	C₂×C₅×D₄	—	3	1	no	—
238	C₂×C₅×D₄	—	3	1	no	—
239	C₂×C₅×D₄	—	3	1	no	—
240	C₂×C₅×D₄	—	3	1	no	—
241	C₂×C₅×D₄	—	6	4	no	—
242	C₂²×C₄×C₅	—	2	2	no	—
243	C₂²×C₄×C₅	—	2	2	no	—
244	C₂²×C₄×C₅	—	3	1	no	—
245	C₂²×C₄×C₅	—	3	1	no	—
246	C₂²×C₄×C₅	—	3	1	no	—
247	C₂²×C₄×C₅	—	3	1	no	—
248	C₂²×C₄×C₅	—	3	1	no	—
249	C₂²×C₄×C₅	—	3	1	no	—
250	C₂²×C₄×C₅	—	3	1	no	—
251	C₂²×C₄×C₅	—	6	2	no	—
252	C₂²×C₄×C₅	—	6	2	no	—
253	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
254	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
255	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
256	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
257	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
258	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
259	C₅×C₄⋊C₄	—	3	1	no	—
260	C₅×C₄⋊C₄	—	3	1	no	—
261	C₅×C₄⋊C₄	—	3	1	no	—
262	C₅×C₄⋊C₄	—	3	1	no	—
263	C₅×C₂²⋊C₄	—	3	1	no	—
264	C₅×C₂²⋊C₄	—	3	1	no	—
265	C₅×C₂²⋊C₄	—	3	1	no	—
266	C₅×C₂²⋊C₄	—	3	1	no	—
267	C₅×C₂²⋊C₄	—	3	1	no	—
268	C₅×C₂²⋊C₄	—	3	1	no	—
269	C₅×C₂²⋊C₄	—	3	1	no	—
270	C₅×C₂²⋊C₄	—	3	1	no	—
271	C₄²×C₅	—	3	1	no	—
272	C₄²×C₅	—	3	1	no	—
273	C₄²×C₅	—	3	1	no	—
274	C₄²×C₅	—	3	1	no	—
275	#681	—	2	2	no	—
276	#681	—	2	2	no	—
277	#681	—	3	4	no	—
278	#681	—	6	4	no	—
279	#681	—	6	4	no	—
280	#681	—	6	2	no	—
281	C₂×#168	—	3	2	no	—
282	C₂×#168	—	3	2	no	—
283	C₂×#168	—	6	4	no	—
284	C₂×#168	—	6	4	no	—
285	C₂×#168	C₂²×D₃	1	2	yes	—
286	C₂×#168	C₂²×D₃	1	2	yes	—
287	C₂²×M₁₆	—	15	1	no	—
288	C₂²×M₁₆	—	15	1	no	—
289	C₂×C₄×D₄	—	3	1	no	—
290	#436	—	15	2	no	—
291	#435	—	15	2	no	—
292	#435	—	15	2	no	—
293	C₈×D₄	—	15	2	no	—
294	#423	—	15	1	no	—
295	#407	—	5	1	no	—
296	#407	—	15	1	no	—
297	C₄×M₁₆	—	15	1	no	—
298	C₂²×C₃×C₅	—	2	1	no	—
299	C₂²×C₃×C₅	—	2	1	no	—
300	C₂²×C₃×C₅	—	2	1	no	—
301	C₂²×C₃×C₅	—	2	1	no	—
302	C₂²×C₃×C₅	—	2	1	no	—
303	C₂²×C₃×C₅	—	2	1	no	—
304	C₂²×C₃×C₅	—	2	1	no	—
305	C₂²×C₃×C₅	—	4	4	no	—
306	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
307	C₂²×C₃×C₅	C₂×M₁₆	1	2	yes	complemented
308	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
309	C₂×C₅×D₃	—	2	1	no	—
310	C₂×C₅×D₃	—	2	1	no	—
311	C₂×C₅×D₃	—	2	1	no	—
312	C₂×C₅×D₃	—	2	1	no	—
313	C₂×C₅×D₃	—	2	1	no	—
314	C₂×C₅×D₃	—	4	4	no	—
315	C₂×C₅×D₃	C₂×M₁₆	1	2	yes	complemented
316	C₃×C₄×C₅	—	2	1	no	—
317	C₃×C₄×C₅	—	2	1	no	—
318	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
319	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
320	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
321	C₅×Dic₃	—	2	1	no	—
322	C₅×Dic₃	—	2	1	no	—
323	C₅×Dic₃	—	2	1	no	—
324	C₅×Dic₃	—	2	1	no	—
325	C₅×Dic₃	—	2	1	no	—
326	C₅×Dic₃	C₂×M₁₆	1	2	yes	complemented
327	C₂⁴×C₃	C₂×Dic₅	1	1	yes	characteristic
328	C₂³×D₃	C₂×Dic₅	1	1	yes	characteristic
329	C₂²×C₃×C₄	—	2	2	no	—
330	C₂²×C₃×C₄	—	2	2	no	—
331	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
332	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
333	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
334	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
335	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
336	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
337	C₂×#67	—	2	4	no	—
338	C₂×#67	C₂×Dic₅	1	1	yes	characteristic
339	C₂×#67	C₂×Dic₅	1	1	yes	characteristic
340	C₂×#67	C₂×Dic₅	1	1	yes	characteristic
341	C₂×#67	C₂×Dic₅	1	1	yes	characteristic
342	C₂²×Dic₃	C₂×Dic₅	1	1	yes	characteristic
343	C₂²×Dic₃	C₂×Dic₅	1	1	yes	characteristic
344	C₂²×Dic₃	C₂×Dic₅	1	1	yes	characteristic
345	C₂×C₄×D₃	—	2	2	no	—
346	C₂×C₄×D₃	—	2	2	no	—
347	C₂×C₄×D₃	C₂×Dic₅	1	1	yes	characteristic
348	C₂×C₄×D₃	C₂×Dic₅	1	1	yes	characteristic
349	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
350	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
351	C₃×M₁₆	—	10	2	no	—
352	C₃×M₁₆	—	10	2	no	—
353	C₂×C₃×C₈	—	5	2	no	—
354	C₂×C₃×C₈	—	5	2	no	—
355	#217	C₂×Dic₅	1	1	yes	characteristic
356	#217	C₂×Dic₅	1	1	yes	characteristic
357	#217	C₂×Dic₅	1	1	yes	characteristic
358	#217	C₂×Dic₅	1	1	yes	characteristic
359	(C₂×D₃)⋊C₄	C₂×Dic₅	1	1	yes	characteristic
360	(C₂×D₃)⋊C₄	C₂×Dic₅	1	1	yes	characteristic
361	(C₂×D₃)⋊C₄	C₂×Dic₅	1	1	yes	characteristic
362	(C₂×D₃)⋊C₄	C₂×Dic₅	1	1	yes	characteristic
363	Dic₃⋊C₄	C₂×Dic₅	1	1	yes	characteristic
364	Dic₃⋊C₄	C₂×Dic₅	1	1	yes	characteristic
365	Dic₃⋊C₄	C₂×Dic₅	1	1	yes	characteristic
366	Dic₃⋊C₄	C₂×Dic₅	1	1	yes	characteristic
367	C₄×Dic₃	C₂×Dic₅	1	1	yes	characteristic
368	C₄×Dic₃	C₂×Dic₅	1	1	yes	characteristic
369	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
370	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
371	#208	—	5	4	no	—
372	#208	—	10	4	no	—
373	#208	—	10	2	no	—
374	C₂×C₃⋊C₈	—	5	2	no	—
375	C₂×C₃⋊C₈	—	5	2	no	—
376	C₂×C₃⋊C₈	—	10	4	no	—
377	ΓL(1,𝔽₂₅)	—	10	4	no	—
378	D₃×C₈	—	10	4	no	—
379	C₂³×C₅	—	2	2	no	—
380	C₂³×C₅	—	2	2	no	—
381	C₂³×C₅	—	3	1	no	—
382	C₂³×C₅	—	3	1	no	—
383	C₂³×C₅	—	4	1	no	—
384	C₂³×C₅	—	6	2	no	—
385	C₂³×C₅	—	6	2	no	—
386	C₂³×C₅	—	12	1	no	—
387	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
388	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
389	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
390	C₅×D₄	—	3	4	no	—
391	C₅×D₄	—	6	2	no	—
392	C₅×D₄	—	6	2	no	—
393	C₅×D₄	—	6	2	no	—
394	C₂×C₄×C₅	—	2	2	no	—
395	C₂×C₄×C₅	—	2	2	no	—
396	C₂×C₄×C₅	—	2	2	no	—
397	C₂×C₄×C₅	—	2	1	no	—
398	C₂×C₄×C₅	—	2	1	no	—
399	C₂×C₄×C₅	—	2	1	no	—
400	C₂×C₄×C₅	—	2	1	no	—
401	C₂×C₄×C₅	—	3	1	no	—
402	C₂×C₄×C₅	—	3	1	no	—
403	C₂×C₄×C₅	—	3	1	no	—
404	C₂×C₄×C₅	—	3	1	no	—
405	C₂×C₄×C₅	—	3	1	no	—
406	C₂×C₄×C₅	—	3	1	no	—
407	C₂×C₄×C₅	—	6	2	no	—
408	C₂×C₄×C₅	—	6	2	no	—
409	C₂×C₄×C₅	—	6	2	no	—
410	C₂×C₄×C₅	—	6	2	no	—
411	C₂×C₄×C₅	—	6	1	no	—
412	C₂×C₄×C₅	—	6	1	no	—
413	C₂×C₄×C₅	—	6	1	no	—
414	C₂×C₄×C₅	—	6	1	no	—
415	C₂×C₄×C₅	—	12	1	no	—
416	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
417	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
418	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
419	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
420	C₂×C₄×C₅	#237	1	2	yes	—
421	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
422	#168	—	2	2	no	—
423	#168	—	2	2	no	—
424	#168	—	3	4	no	—
425	#168	—	6	2	no	—
426	C₂²×D₄	—	3	1	no	—
427	C₂³×C₄	—	3	1	no	—
428	C₂³×C₄	D₃×D₅	1	1	yes	characteristic
429	C₂×M₁₆	—	5	1	no	—
430	C₂×M₁₆	—	5	1	no	—
431	C₂×M₁₆	—	15	2	no	—
432	C₂×M₁₆	—	15	1	no	—
433	C₂×M₁₆	—	15	1	no	—
434	C₂×M₁₆	—	15	2	no	—
435	C₂×M₁₆	—	30	4	no	—
436	C₂×M₁₆	—	30	4	no	—
437	C₂²×C₈	—	15	2	no	—
438	C₂²×C₈	—	15	2	no	—
439	C₄×D₄	—	3	1	no	—
440	C₄×D₄	—	3	1	no	—
441	C₄×D₄	—	3	1	no	—
442	C₄×D₄	—	3	1	no	—
443	C₄×D₄	—	3	1	no	—
444	C₄×D₄	—	3	1	no	—
445	C₄×D₄	—	3	1	no	—
446	C₄×D₄	—	3	1	no	—
447	C₂×C₄⋊C₄	—	3	1	no	—
448	C₂×C₂²⋊C₄	—	3	1	no	—
449	C₂×C₂²⋊C₄	—	3	1	no	—
450	C₂×C₄²	—	3	1	no	—
451	C₄⋊C₈	—	15	2	no	—
452	C₄⋊C₈	—	15	2	no	—
453	C₂²⋊C₈	—	5	2	no	—
454	C₂²⋊C₈	—	5	2	no	—
455	C₂²⋊C₈	—	15	2	no	—
456	C₂²⋊C₈	—	15	2	no	—
457	#97	—	15	2	no	—
458	C₄×C₈	—	15	2	no	—
459	C₂×C₃×C₅	—	2	2	no	—
460	C₂×C₃×C₅	—	2	2	no	—
461	C₂×C₃×C₅	—	4	1	no	—
462	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
463	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
464	C₂×C₃×C₅	#568	1	1	yes	characteristic
465	C₅×D₃	—	2	2	no	—
466	C₅×D₃	—	4	1	no	—
467	C₂³×C₃	—	2	2	no	—
468	C₂³×C₃	—	2	2	no	—
469	C₂³×C₃	—	4	1	no	—
470	C₂³×C₃	C₂²×Dic₅	1	1	yes	characteristic
471	C₂³×C₃	C₂²×Dic₅	1	1	yes	characteristic
472	C₂³×C₃	C₂²×Dic₅	1	1	yes	characteristic
473	C₂²×D₃	—	2	2	no	—
474	C₂²×D₃	—	2	2	no	—
475	C₂²×D₃	—	4	1	no	—
476	C₂²×D₃	C₂²×Dic₅	1	1	yes	characteristic
477	C₂²×D₃	C₂²×Dic₅	1	1	yes	characteristic
478	C₂×C₃×C₄	—	2	2	no	—
479	C₂×C₃×C₄	—	2	1	no	—
480	C₂×C₃×C₄	—	2	1	no	—
481	C₂×C₃×C₄	—	2	1	no	—
482	C₂×C₃×C₄	—	2	1	no	—
483	C₂×C₃×C₄	—	2	2	no	—
484	C₂×C₃×C₄	—	2	2	no	—
485	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
486	C₂×C₃×C₄	#711	1	2	yes	—
487	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
488	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
489	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
490	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
491	#67	—	2	2	no	—
492	#67	—	2	2	no	—
493	#67	—	2	2	no	—
494	#67	#681	1	4	yes	complemented
495	C₂×Dic₃	—	2	2	no	—
496	C₂×Dic₃	—	2	2	no	—
497	C₂×Dic₃	—	4	1	no	—
498	C₂×Dic₃	C₂²×Dic₅	1	1	yes	characteristic
499	C₂×Dic₃	C₂²×Dic₅	1	1	yes	characteristic
500	C₂×Dic₃	C₂²×Dic₅	1	1	yes	characteristic
501	C₂×Dic₃	C₂²×Dic₅	1	1	yes	characteristic
502	C₂×Dic₃	C₂²×Dic₅	1	1	yes	characteristic
503	C₂×Dic₃	C₂²×Dic₅	1	1	yes	characteristic
504	C₄×D₃	—	2	1	no	—
505	C₄×D₃	—	2	1	no	—
506	C₄×D₃	—	2	1	no	—
507	C₄×D₃	—	2	1	no	—
508	C₄×D₃	—	2	2	no	—
509	C₄×D₃	—	2	2	no	—
510	C₃×C₈	—	10	2	no	—
511	C₃×C₈	—	10	2	no	—
512	C₃⋊C₈	—	5	4	no	—
513	C₃⋊C₈	—	10	2	no	—
514	C₂²×C₅	—	2	1	no	—
515	C₂²×C₅	—	2	1	no	—
516	C₂²×C₅	—	2	1	no	—
517	C₂²×C₅	—	2	1	no	—
518	C₂²×C₅	—	2	1	no	—
519	C₂²×C₅	—	2	1	no	—
520	C₂²×C₅	—	2	1	no	—
521	C₂²×C₅	—	3	2	no	—
522	C₂²×C₅	—	4	4	no	—
523	C₂²×C₅	—	6	1	no	—
524	C₂²×C₅	—	6	1	no	—
525	C₂²×C₅	—	6	1	no	—
526	C₂²×C₅	—	6	1	no	—
527	C₂²×C₅	—	6	1	no	—
528	C₂²×C₅	—	12	4	no	—
529	C₂²×C₅	#67⋊C₄	1	2	yes	—
530	C₂²×C₅	D₃×M₁₆	1	2	yes	complemented
531	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
532	C₄×C₅	—	2	1	no	—
533	C₄×C₅	—	2	1	no	—
534	C₄×C₅	—	3	2	no	—
535	C₄×C₅	—	6	1	no	—
536	C₄×C₅	—	6	1	no	—
537	C₄×C₅	—	6	1	no	—
538	C₄×C₅	—	6	1	no	—
539	C₄×C₅	—	6	1	no	—
540	C₄×C₅	#67⋊C₄	1	2	yes	—
541	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
542	C₄×C₅	C₂×#237	1	1	yes	characteristic
543	C₂⁴	—	3	1	no	—
544	C₂⁴	D₃×Dic₅	1	1	yes	characteristic
545	C₂×D₄	—	3	1	no	—
546	C₂×D₄	—	3	1	no	—
547	C₂×D₄	—	3	1	no	—
548	C₂×D₄	—	3	1	no	—
549	C₂×D₄	—	6	4	no	—
550	C₂²×C₄	—	2	2	no	—
551	C₂²×C₄	—	2	2	no	—
552	C₂²×C₄	—	3	1	no	—
553	C₂²×C₄	—	3	1	no	—
554	C₂²×C₄	—	3	1	no	—
555	C₂²×C₄	—	3	1	no	—
556	C₂²×C₄	—	3	1	no	—
557	C₂²×C₄	—	3	1	no	—
558	C₂²×C₄	—	3	1	no	—
559	C₂²×C₄	—	6	2	no	—
560	C₂²×C₄	—	6	2	no	—
561	C₂²×C₄	D₃×Dic₅	1	1	yes	characteristic
562	C₂²×C₄	D₃×Dic₅	1	1	yes	characteristic
563	C₂²×C₄	D₃×Dic₅	1	1	yes	characteristic
564	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
565	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
566	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
567	M₁₆	—	10	2	no	—
568	M₁₆	—	10	2	no	—
569	M₁₆	—	15	4	no	—
570	M₁₆	—	30	4	no	—
571	M₁₆	—	30	4	no	—
572	M₁₆	—	30	2	no	—
573	C₂×C₈	—	5	2	no	—
574	C₂×C₈	—	5	2	no	—
575	C₂×C₈	—	15	2	no	—
576	C₂×C₈	—	15	2	no	—
577	C₂×C₈	—	30	4	no	—
578	C₂×C₈	—	30	4	no	—
579	C₄⋊C₄	—	3	1	no	—
580	C₄⋊C₄	—	3	1	no	—
581	C₄⋊C₄	—	3	1	no	—
582	C₄⋊C₄	—	3	1	no	—
583	C₂²⋊C₄	—	3	1	no	—
584	C₂²⋊C₄	—	3	1	no	—
585	C₂²⋊C₄	—	3	1	no	—
586	C₂²⋊C₄	—	3	1	no	—
587	C₂²⋊C₄	—	3	1	no	—
588	C₂²⋊C₄	—	3	1	no	—
589	C₂²⋊C₄	—	3	1	no	—
590	C₂²⋊C₄	—	3	1	no	—
591	C₄²	—	3	1	no	—
592	C₄²	—	3	1	no	—
593	C₄²	—	3	1	no	—
594	C₄²	—	3	1	no	—
595	C₃×C₅	D₄×M₁₆	1	1	yes	characteristic, complemented, Hall
596	C₂²×C₃	—	2	1	no	—
597	C₂²×C₃	—	2	1	no	—
598	C₂²×C₃	—	2	1	no	—
599	C₂²×C₃	—	2	1	no	—
600	C₂²×C₃	—	2	1	no	—
601	C₂²×C₃	—	2	1	no	—
602	C₂²×C₃	—	2	1	no	—
603	C₂²×C₃	—	4	4	no	—
604	C₂²×C₃	C₂×#681	1	2	yes	complemented
605	C₂²×C₃	D₄×Dic₅	1	2	yes	—
606	C₂²×C₃	C₂³×Dic₅	1	1	yes	characteristic
607	C₂×D₃	—	2	1	no	—
608	C₂×D₃	—	2	1	no	—
609	C₂×D₃	—	2	1	no	—
610	C₂×D₃	—	2	1	no	—
611	C₂×D₃	—	2	1	no	—
612	C₂×D₃	—	4	4	no	—
613	C₂×D₃	C₂×#681	1	2	yes	complemented
614	C₃×C₄	—	2	1	no	—
615	C₃×C₄	—	2	1	no	—
616	C₃×C₄	D₄×Dic₅	1	2	yes	—
617	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
618	C₃×C₄	C₂×#711	1	1	yes	characteristic
619	Dic₃	—	2	1	no	—
620	Dic₃	—	2	1	no	—
621	Dic₃	—	2	1	no	—
622	Dic₃	—	2	1	no	—
623	Dic₃	—	2	1	no	—
624	Dic₃	C₂×#681	1	2	yes	complemented
625	C₂×C₅	—	2	2	no	—
626	C₂×C₅	—	2	2	no	—
627	C₂×C₅	—	4	1	no	—
628	C₂×C₅	—	6	2	no	—
629	C₂×C₅	—	12	1	no	—
630	C₂×C₅	C₂×#67⋊C₄	1	1	yes	characteristic
631	C₂×C₅	C₂×D₃×M₁₆	1	1	yes	characteristic
632	C₂×C₅	#5745	1	1	yes	characteristic
633	C₂³	—	2	2	no	—
634	C₂³	—	2	2	no	—
635	C₂³	—	3	1	no	—
636	C₂³	—	3	1	no	—
637	C₂³	—	4	1	no	—
638	C₂³	—	6	2	no	—
639	C₂³	—	6	2	no	—
640	C₂³	—	12	1	no	—
641	C₂³	C₂×D₃×Dic₅	1	1	yes	characteristic
642	C₂³	C₂×D₃×Dic₅	1	1	yes	characteristic
643	C₂³	C₂×D₃×Dic₅	1	1	yes	characteristic
644	D₄	—	3	4	no	—
645	D₄	—	6	2	no	—
646	D₄	—	6	2	no	—
647	D₄	—	6	2	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	3	1	no	—
656	C₂×C₄	—	3	1	no	—
657	C₂×C₄	—	3	1	no	—
658	C₂×C₄	—	3	1	no	—
659	C₂×C₄	—	3	1	no	—
660	C₂×C₄	—	3	1	no	—
661	C₂×C₄	—	6	2	no	—
662	C₂×C₄	—	6	2	no	—
663	C₂×C₄	—	6	1	no	—
664	C₂×C₄	—	6	1	no	—
665	C₂×C₄	—	6	1	no	—
666	C₂×C₄	—	6	1	no	—
667	C₂×C₄	—	6	2	no	—
668	C₂×C₄	—	6	2	no	—
669	C₂×C₄	—	12	1	no	—
670	C₂×C₄	#6780	1	2	yes	—
671	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
672	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
673	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
674	C₂×C₄	#6790	1	2	yes	—
675	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
676	C₈	—	10	2	no	—
677	C₈	—	10	2	no	—
678	C₈	—	15	4	no	—
679	C₈	—	30	2	no	—
680	C₂×C₃	—	2	2	no	—
681	C₂×C₃	—	2	2	no	—
682	C₂×C₃	—	4	1	no	—
683	C₂×C₃	C₂²×#681	1	1	yes	characteristic
684	C₂×C₃	C₂×D₄×Dic₅	1	1	yes	characteristic
685	C₂×C₃	#66153	1	1	yes	characteristic
686	D₃	—	2	2	no	—
687	D₃	—	4	1	no	—
688	C₅	#78628	1	1	yes	characteristic, complemented, Sylow
689	C₂²	—	2	1	no	—
690	C₂²	—	2	1	no	—
691	C₂²	—	2	1	no	—
692	C₂²	—	2	1	no	—
693	C₂²	—	2	1	no	—
694	C₂²	—	2	1	no	—
695	C₂²	—	2	1	no	—
696	C₂²	—	3	2	no	—
697	C₂²	—	4	4	no	—
698	C₂²	—	6	1	no	—
699	C₂²	—	6	1	no	—
700	C₂²	—	6	1	no	—
701	C₂²	—	6	1	no	—
702	C₂²	—	6	1	no	—
703	C₂²	—	12	4	no	—
704	C₂²	D₃×#681	1	2	yes	complemented
705	C₂²	#67⋊Dic₅	1	2	yes	—
706	C₂²	C₂²×D₃×Dic₅	1	1	yes	characteristic
707	C₄	—	2	1	no	—
708	C₄	—	2	1	no	—
709	C₄	—	3	2	no	—
710	C₄	—	6	1	no	—
711	C₄	—	6	1	no	—
712	C₄	—	6	1	no	—
713	C₄	—	6	1	no	—
714	C₄	—	6	1	no	—
715	C₄	#67⋊Dic₅	1	2	yes	—
716	C₄	C₂×#6780	1	1	yes	characteristic
717	C₄	C₂×#6790	1	1	yes	characteristic
718	C₃	D₄×#681	1	1	yes	characteristic, complemented, Sylow
719	C₂	—	2	2	no	—
720	C₂	—	2	2	no	—
721	C₂	—	4	1	no	—
722	C₂	—	6	2	no	—
723	C₂	—	12	1	no	—
724	C₂	C₂×D₃×#681	1	1	yes	characteristic
725	C₂	#11754125	1	1	yes	characteristic
726	C₂	C₂×#67⋊Dic₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃×D₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Fitting	C₂³×C₃×C₄×C₅	C₂²
prime radical	C₂²×C₅×#67	C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂³×C₄	D₃×D₅
hypocenter	C₃×C₅	D₄×M₁₆
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
1. C₂²×#6710	C₂	semidirect
3. C₂×D₃×#681	C₂	semidirect
4. C₃×#65496	C₂	semidirect
5. #11748508	C₂	semidirect
6. #11748496	C₂	semidirect
7. #67⋊#168	C₂	semidirect
8. #11748440	C₂	semidirect
9. #11748346	C₂	semidirect
10. Dic₃×#681	C₂	semidirect
11. #11748314	C₂	semidirect
19. C₂×#6710	C₂²	semidirect
20. C₂²×C₃⋊#168	C₂²	semidirect
35. C₂×#6650	C₂²	semidirect
37. C₂×D₃×#168	C₂²	semidirect
38. C₃×C₂²⋊#168	C₂²	semidirect
39. C₃×C₂²⋊#168	C₂²	semidirect
40. Dic₃⋊#168	C₂²	semidirect
41. Dic₃⋊#168	C₂²	semidirect
42. (C₂×D₃)⋊#168	C₂²	semidirect
43. (C₂×D₃)⋊#168	C₂²	semidirect
44. #90953	C₂²	semidirect
45. Dic₃×#168	C₂²	semidirect
51. #65496	D₃	semidirect
84. #6710	D₄	semidirect
148. C₂²⋊#168	C₂×D₃	semidirect
149. C₂²⋊#168	C₂×D₃	semidirect
182. C₅×#67	M₁₆	semidirect
199. C₃⋊#168	C₂×D₄	semidirect
307. C₂²×C₃×C₅	C₂×M₁₆	semidirect
315. C₂×C₅×D₃	C₂×M₁₆	semidirect
326. C₅×Dic₃	C₂×M₁₆	semidirect
494. #67	#681	semidirect
530. C₂²×C₅	D₃×M₁₆	semidirect
595. C₃×C₅	D₄×M₁₆	semidirect
604. C₂²×C₃	C₂×#681	semidirect
613. C₂×D₃	C₂×#681	semidirect
624. Dic₃	C₂×#681	semidirect
688. C₅	#78628	semidirect
704. C₂²	D₃×#681	semidirect
718. 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
C₂²×#6710	2
C₂×C₄×C₅×#67	2
C₂×D₃×#681	2
C₃×#65496	2
#11748508	2
#11748496	2
#67⋊#168	2
#11748440	2
#11748346	2
Dic₃×#681	2
#11748314	2
D₄×#681	3
#78628	5