Subgroups — #14415711

Order 1920.

1088 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×D₄×D₅	C₂	1	1	yes	maximal, characteristic
2	C₂²×#6649	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₅×#208	C₂	1	1	yes	maximal, characteristic, complemented
4	#11751112	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5011	C₂	1	1	yes	maximal, characteristic, complemented
6	#11748504	C₂	1	1	yes	maximal, characteristic, complemented
7	#11748499	C₂	1	1	yes	maximal, characteristic, complemented
8	#11748499	C₂	1	1	yes	maximal, characteristic, complemented
9	#11748493	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃⋊C₈×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
11	#11748339	C₂	1	1	yes	maximal, characteristic, complemented
12	#11747007	C₂	1	1	yes	maximal, characteristic, complemented
13	#11747003	C₂	1	1	yes	maximal, characteristic, complemented
14	#11746997	C₂	1	1	yes	maximal, characteristic, complemented
15	#11746991	C₂	1	1	yes	maximal, characteristic, complemented
16	#10611214	—	3	1	no	maximal, Hall
17	C₂×C₃×D₄×D₅	C₄	1	1	yes	characteristic
18	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
20	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
21	C₂×#6710	C₂²	1	1	yes	characteristic, complemented
22	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₅×#208	C₂²	1	1	yes	characteristic, complemented
24	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
25	C₃×D₄×Dic₅	C₄	1	1	yes	characteristic
26	C₃×C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
27	C₃×C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
28	C₃×#4039	C₄	1	1	yes	characteristic
29	C₃×D₅×C₄⋊C₄	C₄	1	1	yes	characteristic
30	C₃×#4027	C₄	1	1	yes	characteristic
31	C₃×#4027	C₄	1	1	yes	characteristic
32	C₃×D₅×C₂²⋊C₄	C₄	1	1	yes	characteristic
33	C₃×D₅×C₂²⋊C₄	C₄	1	1	yes	characteristic
34	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
35	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
36	C₂×#6649	—	2	4	no	—
37	C₂×#6649	C₂²	1	1	yes	characteristic
38	C₂×#6649	C₂²	1	1	yes	characteristic
39	C₂×#6649	C₂²	1	1	yes	characteristic
40	C₂×#6649	C₂²	1	1	yes	characteristic
41	C₂×#6649	C₂²	1	1	yes	characteristic, complemented
42	C₂×#6649	C₂²	1	1	yes	characteristic, complemented
43	D₅×#208	—	2	4	no	—
44	C₂×D₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
45	C₂×D₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
46	#91114	C₂²	1	1	yes	characteristic, complemented
47	#91114	C₂²	1	1	yes	characteristic, complemented
48	C₄⋊(C₃⋊#168)	C₂²	1	1	yes	characteristic, complemented
49	#91087	C₂²	1	1	yes	characteristic, complemented
50	C₅×#830	C₂²	1	1	yes	characteristic, complemented
51	C₅×#830	C₂²	1	1	yes	characteristic, complemented
52	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
53	C₅×#803	C₂²	1	1	yes	characteristic, complemented
54	#90982	C₂²	1	1	yes	characteristic, complemented
55	#90982	C₂²	1	1	yes	characteristic, complemented
56	#90955	C₂²	1	1	yes	characteristic, complemented
57	#90955	C₂²	1	1	yes	characteristic, complemented
58	#90955	C₂²	1	1	yes	characteristic, complemented
59	#90955	C₂²	1	1	yes	characteristic, complemented
60	Dic₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
61	Dic₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
62	D₄×#208	—	5	1	no	maximal, Hall
63	C₂×D₅×M₁₆	—	3	1	no	—
64	C₂²×#676	—	3	1	no	—
65	C₄×D₄×D₅	D₃	1	1	yes	characteristic
66	C₅×#435	—	3	1	no	—
67	#65417	—	3	1	no	—
68	C₈×C₂²⋊D₅	—	3	1	no	—
69	#65300	—	3	1	no	—
70	#65126	—	3	1	no	—
71	#65125	—	3	1	no	—
72	#65018	—	3	1	no	—
73	#65015	—	3	1	no	—
74	#65015	—	3	1	no	—
75	#65014	—	3	1	no	—
76	#64996	—	3	1	no	—
77	#64995	—	3	1	no	—
78	C₂³×C₃×D₅	C₂×C₄	1	1	yes	characteristic
79	C₂³×C₃×D₅	C₂×C₄	1	1	yes	characteristic
80	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
81	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
82	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
83	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
84	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
85	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
86	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
87	C₃×D₄×D₅	—	2	4	no	—
88	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
89	C₂×C₃×C₄×D₅	—	2	2	no	—
90	C₂×C₃×C₄×D₅	—	2	2	no	—
91	C₂×C₃×C₄×D₅	—	2	2	no	—
92	C₂×C₃×C₄×D₅	—	2	2	no	—
93	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
94	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
95	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
96	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
97	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
98	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
99	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
100	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
101	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
102	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
103	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
104	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
105	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
106	#6710	—	2	2	no	—
107	C₂×C₃⋊#168	—	2	2	no	—
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	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
112	C₅×#208	—	2	2	no	—
113	C₂×C₅×C₃⋊C₈	—	2	2	no	—
114	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
115	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
116	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
117	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
118	C₃×C₂²⋊Dic₅	C₂×C₄	1	1	yes	characteristic
119	C₃×C₂²⋊Dic₅	C₂×C₄	1	1	yes	characteristic
120	C₃×#685	C₂×C₄	1	1	yes	characteristic
121	C₃×#685	C₂×C₄	1	1	yes	characteristic
122	C₃×#685	C₂×C₄	1	1	yes	characteristic
123	C₃×#685	C₂×C₄	1	1	yes	characteristic
124	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
125	C₃×#683	C₂×C₄	1	1	yes	characteristic
126	C₃×#683	C₂×C₄	1	1	yes	characteristic
127	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
128	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
129	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
130	#6649	—	2	2	no	—
131	#6649	—	2	2	no	—
132	#6649	—	2	2	no	—
133	#6649	—	2	2	no	—
134	#6649	—	2	2	no	—
135	#6649	D₄	1	4	yes	complemented
136	D₅×C₃⋊C₈	—	2	2	no	—
137	D₅×C₃⋊C₈	—	2	2	no	—
138	C₂×C₃×C₄×D₄	—	5	1	no	—
139	C₂²×#208	—	5	1	no	—
140	C₂²×#208	—	5	1	no	—
141	#5207	—	5	1	no	—
142	#5207	—	5	1	no	—
143	#5012	—	5	1	no	—
144	#5012	—	5	1	no	—
145	#5011	—	5	1	no	—
146	#5011	—	5	1	no	—
147	#5011	—	5	1	no	—
148	#5011	D₅	1	1	yes	characteristic, complemented
149	D₄×C₃⋊C₈	—	5	1	no	—
150	D₄×C₃⋊C₈	—	5	1	no	—
151	#4924	—	5	1	no	—
152	C₄×#208	—	5	1	no	—
153	C₂×D₄×D₅	Dic₃	1	1	yes	characteristic
154	C₂²×C₄×D₅	C₂×D₃	1	1	yes	characteristic
155	C₂²×C₄×D₅	C₂×D₃	1	1	yes	characteristic
156	C₂×C₅×M₁₆	—	3	1	no	—
157	C₂²×C₅×C₈	—	3	1	no	—
158	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
159	D₄×Dic₅	Dic₃	1	1	yes	characteristic
160	C₄×C₂²⋊D₅	C₂×D₃	1	1	yes	characteristic
161	C₄×C₂²⋊D₅	C₂×D₃	1	1	yes	characteristic
162	C₂×#681	—	3	1	no	—
163	C₂²×#168	—	3	1	no	—
164	D₅×M₁₆	—	6	4	no	—
165	C₂×#676	—	3	1	no	—
166	C₂×#676	—	3	1	no	—
167	C₂×#676	—	3	1	no	—
168	C₂×#676	—	3	1	no	—
169	C₂×#676	—	3	1	no	—
170	C₂×#676	—	3	1	no	—
171	C₂×#676	—	6	4	no	—
172	C₂×C₈×D₅	—	3	1	no	—
173	C₂×C₈×D₅	—	3	1	no	—
174	#4039	Dic₃	1	1	yes	characteristic
175	D₅×C₄⋊C₄	Dic₃	1	1	yes	characteristic
176	#4027	Dic₃	1	1	yes	characteristic
177	#4027	Dic₃	1	1	yes	characteristic
178	D₅×C₂²⋊C₄	Dic₃	1	1	yes	characteristic
179	D₅×C₂²⋊C₄	Dic₃	1	1	yes	characteristic
180	C₄×D₂₀	C₂×D₃	1	1	yes	characteristic
181	C₄²×D₅	C₂×D₃	1	1	yes	characteristic
182	C₅×C₄⋊C₈	—	3	1	no	—
183	C₅×C₂²⋊C₈	—	3	1	no	—
184	C₅×C₂²⋊C₈	—	3	1	no	—
185	C₅×#97	—	3	1	no	—
186	C₂²⋊#168	—	3	1	no	—
187	C₂²⋊#168	—	3	1	no	—
188	#3952	—	3	1	no	—
189	#3952	—	3	1	no	—
190	#3952	—	3	1	no	—
191	#3952	—	3	1	no	—
192	#3946	—	3	1	no	—
193	#3946	—	3	1	no	—
194	C₈×Dic₅	—	3	1	no	—
195	C₈×Dic₅	—	3	1	no	—
196	C₄⋊#168	—	3	1	no	—
197	#3935	—	3	1	no	—
198	D₄×M₁₆	—	15	1	no	Sylow
199	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
200	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
201	C₂²×C₃×D₅	—	2	2	no	—
202	C₂²×C₃×D₅	—	2	2	no	—
203	C₂²×C₃×D₅	—	2	2	no	—
204	C₂²×C₃×D₅	—	2	2	no	—
205	C₂²×C₃×D₅	—	4	1	no	—
206	C₂²×C₃×D₅	—	4	1	no	—
207	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
208	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
209	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
210	C₃×C₅×D₄	—	2	2	no	—
211	C₂×C₃×C₄×C₅	—	2	1	no	—
212	C₂×C₃×C₄×C₅	—	2	1	no	—
213	C₂×C₃×C₄×C₅	—	2	1	no	—
214	C₂×C₃×C₄×C₅	—	2	1	no	—
215	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
216	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
217	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
218	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
219	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
220	C₃×C₂²⋊D₅	—	2	2	no	—
221	C₃×C₂²⋊D₅	M₁₆	1	4	yes	complemented
222	C₂×C₃×Dic₅	—	2	2	no	—
223	C₂×C₃×Dic₅	—	2	2	no	—
224	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
225	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
226	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
227	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
228	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
229	C₃×D₂₀	—	2	2	no	—
230	C₃×C₄×D₅	—	2	2	no	—
231	C₃×C₄×D₅	—	2	2	no	—
232	C₃×C₄×D₅	—	2	1	no	—
233	C₃×C₄×D₅	—	2	1	no	—
234	C₃×C₄×D₅	—	2	1	no	—
235	C₃×C₄×D₅	—	2	1	no	—
236	C₃×C₄×D₅	—	2	2	no	—
237	C₃×C₄×D₅	—	2	2	no	—
238	C₃×C₄×D₅	—	2	2	no	—
239	C₃×C₄×D₅	—	4	1	no	—
240	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
241	C₃×C₄×D₅	#41	1	2	yes	—
242	C₃⋊#168	—	2	1	no	—
243	C₃⋊#168	—	2	1	no	—
244	C₃⋊#168	—	2	1	no	—
245	C₃⋊#168	C₂×D₄	1	2	yes	complemented
246	C₅×C₃⋊C₈	—	2	1	no	—
247	C₅×C₃⋊C₈	—	2	1	no	—
248	C₅×C₃⋊C₈	—	2	1	no	—
249	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	complemented
250	C₂²×C₃×D₄	—	5	1	no	—
251	C₂³×C₃×C₄	—	5	1	no	—
252	C₂³×C₃×C₄	—	5	1	no	—
253	C₃×C₄×D₄	—	5	1	no	—
254	C₃×C₄×D₄	—	5	1	no	—
255	C₃×C₄×D₄	—	5	1	no	—
256	C₃×C₄×D₄	—	5	1	no	—
257	C₃×C₄×D₄	—	5	1	no	—
258	C₃×C₄×D₄	—	5	1	no	—
259	C₃×C₄×D₄	—	5	1	no	—
260	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
261	C₂×C₃×C₄⋊C₄	—	5	1	no	—
262	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
263	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
264	C₂×C₃×C₄²	—	5	1	no	—
265	C₂×#208	—	5	1	no	—
266	C₂×#208	—	5	1	no	—
267	C₂×#208	—	5	1	no	—
268	C₂×#208	—	5	1	no	—
269	C₂×#208	—	5	1	no	—
270	C₂×#208	—	5	1	no	—
271	C₂×#208	—	5	1	no	—
272	C₂×#208	—	10	4	no	—
273	C₂×#208	—	10	4	no	—
274	C₂×#208	C₂×D₅	1	1	yes	characteristic, complemented
275	C₂²×C₃⋊C₈	—	5	1	no	—
276	C₂²×C₃⋊C₈	—	5	1	no	—
277	C₂²×C₃⋊C₈	—	5	1	no	—
278	C₂²×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic, complemented
279	#830	—	5	1	no	—
280	#830	—	5	1	no	—
281	#830	—	5	1	no	—
282	#830	—	5	1	no	—
283	#830	—	5	1	no	—
284	#830	—	5	1	no	—
285	#830	C₂×D₅	1	1	yes	characteristic, complemented
286	#830	C₂×D₅	1	1	yes	characteristic, complemented
287	C₄⋊(C₃⋊C₈)	—	5	1	no	—
288	C₄⋊(C₃⋊C₈)	—	5	1	no	—
289	C₄⋊(C₃⋊C₈)	—	5	1	no	—
290	C₄⋊(C₃⋊C₈)	C₂×D₅	1	1	yes	characteristic, complemented
291	#803	—	5	1	no	—
292	#803	C₂×D₅	1	1	yes	characteristic, complemented
293	C₄×C₃⋊C₈	—	5	1	no	—
294	C₄×C₃⋊C₈	—	5	1	no	—
295	C₂³×D₅	C₂×Dic₃	1	1	yes	characteristic
296	C₂³×D₅	C₂×Dic₃	1	1	yes	characteristic
297	C₂×C₅×D₄	C₂×Dic₃	1	1	yes	characteristic
298	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
299	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
300	C₂×C₂²⋊D₅	C₂×Dic₃	1	1	yes	characteristic
301	C₂×C₂²⋊D₅	C₂×Dic₃	1	1	yes	characteristic
302	C₂²×Dic₅	C₂×Dic₃	1	1	yes	characteristic
303	C₂²×Dic₅	C₂×Dic₃	1	1	yes	characteristic
304	D₄×D₅	—	2	4	no	—
305	C₂×D₂₀	C₂×Dic₃	1	1	yes	characteristic
306	C₂×C₄×D₅	—	2	2	no	—
307	C₂×C₄×D₅	—	2	2	no	—
308	C₂×C₄×D₅	—	2	2	no	—
309	C₂×C₄×D₅	—	2	2	no	—
310	C₂×C₄×D₅	C₂×Dic₃	1	1	yes	characteristic
311	C₂×C₄×D₅	C₂×Dic₃	1	1	yes	characteristic
312	C₂×C₄×D₅	C₂×Dic₃	1	1	yes	characteristic
313	C₂×C₄×D₅	C₂×Dic₃	1	1	yes	characteristic
314	C₂×C₄×D₅	C₂×Dic₃	1	1	yes	characteristic
315	C₂×C₄×D₅	C₂×Dic₃	1	1	yes	characteristic
316	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
317	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
318	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
319	C₅×M₁₆	—	6	2	no	—
320	C₂×C₅×C₈	—	3	1	no	—
321	C₂×C₅×C₈	—	3	1	no	—
322	C₂×C₅×C₈	—	3	1	no	—
323	C₂×C₅×C₈	—	3	1	no	—
324	C₂×C₅×C₈	—	6	2	no	—
325	C₅×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
326	C₅×C₂²⋊C₄	C₂×Dic₃	1	1	yes	characteristic
327	C₅×C₂²⋊C₄	C₂×Dic₃	1	1	yes	characteristic
328	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
329	C₂²⋊Dic₅	C₂×Dic₃	1	1	yes	characteristic
330	C₂²⋊Dic₅	C₂×Dic₃	1	1	yes	characteristic
331	#685	C₂×Dic₃	1	1	yes	characteristic
332	#685	C₂×Dic₃	1	1	yes	characteristic
333	#685	C₂×Dic₃	1	1	yes	characteristic
334	#685	C₂×Dic₃	1	1	yes	characteristic
335	C₄⋊Dic₅	C₂×Dic₃	1	1	yes	characteristic
336	#683	C₂×Dic₃	1	1	yes	characteristic
337	#683	C₂×Dic₃	1	1	yes	characteristic
338	C₄×Dic₅	C₂×Dic₃	1	1	yes	characteristic
339	C₄×Dic₅	C₂×Dic₃	1	1	yes	characteristic
340	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
341	#681	—	6	2	no	—
342	C₂×#168	—	3	1	no	—
343	C₂×#168	—	3	1	no	—
344	C₂×#168	—	3	1	no	—
345	C₂×#168	—	3	1	no	—
346	C₂×#168	—	6	2	no	—
347	#676	—	3	4	no	—
348	#676	—	6	2	no	—
349	#676	—	6	2	no	—
350	#676	—	6	2	no	—
351	#676	—	6	2	no	—
352	#676	—	6	2	no	—
353	C₈×D₅	—	6	2	no	—
354	C₈×D₅	—	6	2	no	—
355	C₂²×M₁₆	—	15	1	no	—
356	C₂²×M₁₆	—	15	1	no	—
357	C₂×C₄×D₄	—	5	1	no	—
358	#436	—	15	1	no	—
359	#436	—	15	1	no	—
360	#435	—	3	1	no	—
361	#435	—	15	1	no	—
362	#435	—	15	1	no	—
363	#435	—	15	1	no	—
364	C₈×D₄	—	15	1	no	—
365	C₈×D₄	—	15	1	no	—
366	#423	—	15	1	no	—
367	#407	—	15	1	no	—
368	#407	—	15	1	no	—
369	C₄×M₁₆	—	15	1	no	—
370	C₂²×C₃×C₅	—	2	1	no	—
371	C₂²×C₃×C₅	—	2	1	no	—
372	C₂²×C₃×C₅	—	2	1	no	—
373	C₂²×C₃×C₅	—	2	1	no	—
374	C₂²×C₃×C₅	—	2	1	no	—
375	C₂²×C₃×C₅	C₂×M₁₆	1	2	yes	complemented
376	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
377	C₂×C₃×D₅	—	2	1	no	—
378	C₂×C₃×D₅	—	2	1	no	—
379	C₂×C₃×D₅	—	2	1	no	—
380	C₂×C₃×D₅	—	2	1	no	—
381	C₂×C₃×D₅	—	2	1	no	—
382	C₂×C₃×D₅	—	2	1	no	—
383	C₂×C₃×D₅	—	2	1	no	—
384	C₂×C₃×D₅	—	4	4	no	—
385	C₂×C₃×D₅	—	4	4	no	—
386	C₂×C₃×D₅	C₄×D₄	1	2	yes	—
387	C₂×C₃×D₅	C₂×M₁₆	1	2	yes	complemented
388	C₃×C₄×C₅	—	2	1	no	—
389	C₃×C₄×C₅	—	2	1	no	—
390	C₃×C₄×C₅	—	2	1	no	—
391	C₃×C₄×C₅	—	2	1	no	—
392	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
393	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
394	C₃×Dic₅	—	2	1	no	—
395	C₃×Dic₅	—	2	1	no	—
396	C₃×Dic₅	—	2	1	no	—
397	C₃×Dic₅	C₄×D₄	1	2	yes	—
398	C₃×Dic₅	C₂×M₁₆	1	2	yes	complemented
399	C₂⁴×C₃	—	5	1	no	—
400	C₂⁴×C₃	—	5	1	no	—
401	C₂×C₃×D₄	—	5	1	no	—
402	C₂×C₃×D₄	—	5	1	no	—
403	C₂×C₃×D₄	—	5	1	no	—
404	C₂×C₃×D₄	—	10	4	no	—
405	C₂×C₃×D₄	C₄×D₅	1	1	yes	characteristic
406	C₂²×C₃×C₄	—	5	1	no	—
407	C₂²×C₃×C₄	—	5	1	no	—
408	C₂²×C₃×C₄	—	5	1	no	—
409	C₂²×C₃×C₄	—	5	1	no	—
410	C₂²×C₃×C₄	—	5	1	no	—
411	C₂²×C₃×C₄	—	5	1	no	—
412	C₂²×C₃×C₄	—	5	1	no	—
413	C₂²×C₃×C₄	—	5	1	no	—
414	C₂²×C₃×C₄	—	5	1	no	—
415	C₂²×C₃×C₄	—	5	1	no	—
416	C₂²×C₃×C₄	—	5	1	no	—
417	C₂²×C₃×C₄	—	10	2	no	—
418	C₂²×C₃×C₄	—	10	2	no	—
419	C₂²×C₃×C₄	—	10	2	no	—
420	C₂²×C₃×C₄	—	10	2	no	—
421	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
422	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
423	C₃×C₄⋊C₄	—	5	1	no	—
424	C₃×C₄⋊C₄	—	5	1	no	—
425	C₃×C₄⋊C₄	—	5	1	no	—
426	C₃×C₄⋊C₄	C₄×D₅	1	1	yes	characteristic
427	C₃×C₂²⋊C₄	—	5	1	no	—
428	C₃×C₂²⋊C₄	—	5	1	no	—
429	C₃×C₂²⋊C₄	—	5	1	no	—
430	C₃×C₂²⋊C₄	—	5	1	no	—
431	C₃×C₂²⋊C₄	—	5	1	no	—
432	C₃×C₂²⋊C₄	—	5	1	no	—
433	C₃×C₂²⋊C₄	C₄×D₅	1	1	yes	characteristic
434	C₃×C₂²⋊C₄	C₄×D₅	1	1	yes	characteristic
435	C₃×C₄²	—	5	1	no	—
436	C₃×C₄²	—	5	1	no	—
437	C₃×C₄²	—	5	1	no	—
438	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
439	#208	—	2	2	no	—
440	#208	—	5	4	no	—
441	#208	—	10	2	no	—
442	#208	—	10	2	no	—
443	#208	—	10	2	no	—
444	#208	—	10	2	no	—
445	#208	—	10	2	no	—
446	#208	—	10	2	no	—
447	C₂×C₃⋊C₈	—	2	2	no	—
448	C₂×C₃⋊C₈	—	5	1	no	—
449	C₂×C₃⋊C₈	—	5	1	no	—
450	C₂×C₃⋊C₈	—	5	1	no	—
451	C₂×C₃⋊C₈	—	5	1	no	—
452	C₂×C₃⋊C₈	—	10	2	no	—
453	C₂×C₃⋊C₈	—	10	2	no	—
454	C₂×C₃⋊C₈	—	10	2	no	—
455	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
456	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
457	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
458	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
459	C₂³×C₅	C₂²×Dic₃	1	1	yes	characteristic
460	C₂³×C₅	C₂²×Dic₃	1	1	yes	characteristic
461	C₂²×D₅	—	2	2	no	—
462	C₂²×D₅	—	2	2	no	—
463	C₂²×D₅	—	2	2	no	—
464	C₂²×D₅	—	2	2	no	—
465	C₂²×D₅	—	4	1	no	—
466	C₂²×D₅	—	4	1	no	—
467	C₂²×D₅	C₂²×Dic₃	1	1	yes	characteristic
468	C₂²×D₅	C₂²×Dic₃	1	1	yes	characteristic
469	C₂²×D₅	C₂²×Dic₃	1	1	yes	characteristic
470	C₅×D₄	—	2	2	no	—
471	C₂×C₄×C₅	—	2	1	no	—
472	C₂×C₄×C₅	—	2	1	no	—
473	C₂×C₄×C₅	—	2	1	no	—
474	C₂×C₄×C₅	—	2	1	no	—
475	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
476	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
477	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
478	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
479	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
480	C₂²⋊D₅	—	2	2	no	—
481	C₂²⋊D₅	#208	1	4	yes	complemented
482	C₂×Dic₅	—	2	2	no	—
483	C₂×Dic₅	—	2	2	no	—
484	C₂×Dic₅	C₂²×Dic₃	1	1	yes	characteristic
485	C₂×Dic₅	C₂²×Dic₃	1	1	yes	characteristic
486	C₂×Dic₅	C₂²×Dic₃	1	1	yes	characteristic
487	C₂×Dic₅	C₂²×Dic₃	1	1	yes	characteristic
488	C₂×Dic₅	C₂²×Dic₃	1	1	yes	characteristic
489	D₂₀	—	2	2	no	—
490	C₄×D₅	—	2	2	no	—
491	C₄×D₅	—	2	2	no	—
492	C₄×D₅	—	2	1	no	—
493	C₄×D₅	—	2	1	no	—
494	C₄×D₅	—	2	1	no	—
495	C₄×D₅	—	2	1	no	—
496	C₄×D₅	—	2	2	no	—
497	C₄×D₅	—	2	2	no	—
498	C₄×D₅	—	2	2	no	—
499	C₄×D₅	—	4	1	no	—
500	C₄×D₅	D₃×D₄	1	2	yes	—
501	C₄×D₅	#237	1	2	yes	—
502	C₅×C₈	—	3	2	no	—
503	C₅×C₈	—	6	1	no	—
504	C₅×C₈	—	6	1	no	—
505	C₅×C₈	—	6	1	no	—
506	#168	—	3	2	no	—
507	#168	—	6	1	no	—
508	#168	—	6	1	no	—
509	#168	—	6	1	no	—
510	C₂²×D₄	—	5	1	no	—
511	C₂³×C₄	—	5	1	no	—
512	C₂³×C₄	—	5	1	no	—
513	C₂×M₁₆	—	3	1	no	—
514	C₂×M₁₆	—	15	1	no	—
515	C₂×M₁₆	—	15	1	no	—
516	C₂×M₁₆	—	15	1	no	—
517	C₂×M₁₆	—	15	1	no	—
518	C₂×M₁₆	—	15	1	no	—
519	C₂×M₁₆	—	15	1	no	—
520	C₂×M₁₆	—	15	1	no	—
521	C₂×M₁₆	—	30	4	no	—
522	C₂×M₁₆	—	30	4	no	—
523	C₂²×C₈	—	3	1	no	—
524	C₂²×C₈	—	15	1	no	—
525	C₂²×C₈	—	15	1	no	—
526	C₂²×C₈	—	15	1	no	—
527	C₄×D₄	—	5	1	no	—
528	C₄×D₄	—	5	1	no	—
529	C₄×D₄	—	5	1	no	—
530	C₄×D₄	—	5	1	no	—
531	C₄×D₄	—	5	1	no	—
532	C₄×D₄	—	5	1	no	—
533	C₄×D₄	—	5	1	no	—
534	C₄×D₄	D₃×D₅	1	1	yes	characteristic
535	C₂×C₄⋊C₄	—	5	1	no	—
536	C₂×C₂²⋊C₄	—	5	1	no	—
537	C₂×C₂²⋊C₄	—	5	1	no	—
538	C₂×C₄²	—	5	1	no	—
539	C₄⋊C₈	—	3	1	no	—
540	C₄⋊C₈	—	15	1	no	—
541	C₄⋊C₈	—	15	1	no	—
542	C₄⋊C₈	—	15	1	no	—
543	C₂²⋊C₈	—	3	1	no	—
544	C₂²⋊C₈	—	3	1	no	—
545	C₂²⋊C₈	—	15	1	no	—
546	C₂²⋊C₈	—	15	1	no	—
547	C₂²⋊C₈	—	15	1	no	—
548	C₂²⋊C₈	—	15	1	no	—
549	C₂²⋊C₈	—	15	1	no	—
550	C₂²⋊C₈	—	15	1	no	—
551	#97	—	3	1	no	—
552	#97	—	15	1	no	—
553	C₄×C₈	—	15	1	no	—
554	C₄×C₈	—	15	1	no	—
555	C₂×C₃×C₅	—	2	2	no	—
556	C₂×C₃×C₅	—	4	1	no	—
557	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
558	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
559	C₂×C₃×C₅	#568	1	1	yes	characteristic
560	C₃×D₅	—	2	2	no	—
561	C₃×D₅	—	2	2	no	—
562	C₃×D₅	—	4	1	no	—
563	C₂³×C₃	—	5	1	no	—
564	C₂³×C₃	—	5	1	no	—
565	C₂³×C₃	—	5	1	no	—
566	C₂³×C₃	—	10	2	no	—
567	C₂³×C₃	—	10	2	no	—
568	C₂³×C₃	—	10	2	no	—
569	C₂³×C₃	—	10	2	no	—
570	C₂³×C₃	—	20	1	no	—
571	C₂³×C₃	—	20	1	no	—
572	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
573	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
574	C₃×D₄	—	2	2	no	—
575	C₃×D₄	—	5	4	no	—
576	C₃×D₄	—	10	2	no	—
577	C₃×D₄	—	10	2	no	—
578	C₂×C₃×C₄	—	2	1	no	—
579	C₂×C₃×C₄	—	2	1	no	—
580	C₂×C₃×C₄	—	2	1	no	—
581	C₂×C₃×C₄	—	2	1	no	—
582	C₂×C₃×C₄	—	5	1	no	—
583	C₂×C₃×C₄	—	5	1	no	—
584	C₂×C₃×C₄	—	5	2	no	—
585	C₂×C₃×C₄	—	5	2	no	—
586	C₂×C₃×C₄	—	5	1	no	—
587	C₂×C₃×C₄	—	5	1	no	—
588	C₂×C₃×C₄	—	5	1	no	—
589	C₂×C₃×C₄	—	10	2	no	—
590	C₂×C₃×C₄	—	10	2	no	—
591	C₂×C₃×C₄	—	10	2	no	—
592	C₂×C₃×C₄	—	10	2	no	—
593	C₂×C₃×C₄	—	10	2	no	—
594	C₂×C₃×C₄	—	10	2	no	—
595	C₂×C₃×C₄	—	10	2	no	—
596	C₂×C₃×C₄	—	10	1	no	—
597	C₂×C₃×C₄	—	10	1	no	—
598	C₂×C₃×C₄	—	10	1	no	—
599	C₂×C₃×C₄	—	10	1	no	—
600	C₂×C₃×C₄	—	20	1	no	—
601	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
602	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
603	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
604	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
605	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
606	C₃⋊C₈	—	2	1	no	—
607	C₃⋊C₈	—	2	1	no	—
608	C₃⋊C₈	—	2	1	no	—
609	C₃⋊C₈	—	5	2	no	—
610	C₃⋊C₈	—	10	1	no	—
611	C₃⋊C₈	—	10	1	no	—
612	C₃⋊C₈	—	10	1	no	—
613	C₃⋊C₈	D₄×D₅	1	2	yes	complemented
614	C₂²×C₅	—	2	1	no	—
615	C₂²×C₅	—	2	1	no	—
616	C₂²×C₅	—	2	1	no	—
617	C₂²×C₅	—	2	1	no	—
618	C₂²×C₅	—	2	1	no	—
619	C₂²×C₅	C₂×#208	1	2	yes	complemented
620	C₂²×C₅	C₂³×Dic₃	1	1	yes	characteristic
621	C₂×D₅	—	2	1	no	—
622	C₂×D₅	—	2	1	no	—
623	C₂×D₅	—	2	1	no	—
624	C₂×D₅	—	2	1	no	—
625	C₂×D₅	—	2	1	no	—
626	C₂×D₅	—	2	1	no	—
627	C₂×D₅	—	2	1	no	—
628	C₂×D₅	—	4	4	no	—
629	C₂×D₅	—	4	4	no	—
630	C₂×D₅	C₂×#208	1	2	yes	complemented
631	C₂×D₅	D₄×Dic₃	1	2	yes	—
632	C₄×C₅	—	2	1	no	—
633	C₄×C₅	—	2	1	no	—
634	C₄×C₅	—	2	1	no	—
635	C₄×C₅	—	2	1	no	—
636	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
637	C₄×C₅	C₂×#237	1	1	yes	characteristic
638	Dic₅	—	2	1	no	—
639	Dic₅	—	2	1	no	—
640	Dic₅	—	2	1	no	—
641	Dic₅	C₂×#208	1	2	yes	complemented
642	Dic₅	D₄×Dic₃	1	2	yes	—
643	C₂⁴	—	5	1	no	—
644	C₂⁴	—	5	1	no	—
645	C₂×D₄	—	5	1	no	—
646	C₂×D₄	—	5	1	no	—
647	C₂×D₄	—	5	1	no	—
648	C₂×D₄	—	10	4	no	—
649	C₂×D₄	D₅×Dic₃	1	1	yes	characteristic
650	C₂²×C₄	—	5	1	no	—
651	C₂²×C₄	—	5	1	no	—
652	C₂²×C₄	—	5	1	no	—
653	C₂²×C₄	—	5	1	no	—
654	C₂²×C₄	—	5	1	no	—
655	C₂²×C₄	—	5	1	no	—
656	C₂²×C₄	—	5	1	no	—
657	C₂²×C₄	—	5	1	no	—
658	C₂²×C₄	—	5	1	no	—
659	C₂²×C₄	—	5	1	no	—
660	C₂²×C₄	—	5	1	no	—
661	C₂²×C₄	—	10	2	no	—
662	C₂²×C₄	—	10	2	no	—
663	C₂²×C₄	—	10	2	no	—
664	C₂²×C₄	—	10	2	no	—
665	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
666	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
667	M₁₆	—	6	2	no	—
668	M₁₆	—	15	4	no	—
669	M₁₆	—	30	2	no	—
670	M₁₆	—	30	2	no	—
671	M₁₆	—	30	2	no	—
672	M₁₆	—	30	2	no	—
673	M₁₆	—	30	2	no	—
674	M₁₆	—	30	2	no	—
675	C₂×C₈	—	3	1	no	—
676	C₂×C₈	—	3	1	no	—
677	C₂×C₈	—	3	1	no	—
678	C₂×C₈	—	3	1	no	—
679	C₂×C₈	—	6	2	no	—
680	C₂×C₈	—	15	1	no	—
681	C₂×C₈	—	15	1	no	—
682	C₂×C₈	—	15	1	no	—
683	C₂×C₈	—	15	1	no	—
684	C₂×C₈	—	30	2	no	—
685	C₂×C₈	—	30	2	no	—
686	C₂×C₈	—	30	2	no	—
687	C₄⋊C₄	—	5	1	no	—
688	C₄⋊C₄	—	5	1	no	—
689	C₄⋊C₄	—	5	1	no	—
690	C₄⋊C₄	D₅×Dic₃	1	1	yes	characteristic
691	C₂²⋊C₄	—	5	1	no	—
692	C₂²⋊C₄	—	5	1	no	—
693	C₂²⋊C₄	—	5	1	no	—
694	C₂²⋊C₄	—	5	1	no	—
695	C₂²⋊C₄	—	5	1	no	—
696	C₂²⋊C₄	—	5	1	no	—
697	C₂²⋊C₄	D₅×Dic₃	1	1	yes	characteristic
698	C₂²⋊C₄	D₅×Dic₃	1	1	yes	characteristic
699	C₄²	—	5	1	no	—
700	C₄²	—	5	1	no	—
701	C₄²	—	5	1	no	—
702	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
703	C₃×C₅	D₄×M₁₆	1	1	yes	characteristic, complemented, Hall
704	C₂²×C₃	—	2	1	no	—
705	C₂²×C₃	—	2	1	no	—
706	C₂²×C₃	—	2	1	no	—
707	C₂²×C₃	—	2	1	no	—
708	C₂²×C₃	—	2	1	no	—
709	C₂²×C₃	—	5	2	no	—
710	C₂²×C₃	—	5	2	no	—
711	C₂²×C₃	—	10	1	no	—
712	C₂²×C₃	—	10	1	no	—
713	C₂²×C₃	—	10	1	no	—
714	C₂²×C₃	—	10	1	no	—
715	C₂²×C₃	—	10	1	no	—
716	C₂²×C₃	—	10	1	no	—
717	C₂²×C₃	—	10	1	no	—
718	C₂²×C₃	—	20	4	no	—
719	C₂²×C₃	—	20	4	no	—
720	C₂²×C₃	D₅×M₁₆	1	2	yes	complemented
721	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
722	C₃×C₄	—	2	1	no	—
723	C₃×C₄	—	2	1	no	—
724	C₃×C₄	—	2	1	no	—
725	C₃×C₄	—	2	1	no	—
726	C₃×C₄	—	5	2	no	—
727	C₃×C₄	—	5	2	no	—
728	C₃×C₄	—	10	1	no	—
729	C₃×C₄	—	10	1	no	—
730	C₃×C₄	—	10	1	no	—
731	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
732	C₃×C₄	D₅×#41	1	1	yes	characteristic
733	C₂×C₅	—	2	2	no	—
734	C₂×C₅	—	4	1	no	—
735	C₂×C₅	C₂²×#208	1	1	yes	characteristic
736	C₂×C₅	C₂×D₄×Dic₃	1	1	yes	characteristic
737	C₂×C₅	#5819	1	1	yes	characteristic
738	D₅	—	2	2	no	—
739	D₅	—	2	2	no	—
740	D₅	—	4	1	no	—
741	C₂³	—	5	1	no	—
742	C₂³	—	5	1	no	—
743	C₂³	—	5	1	no	—
744	C₂³	—	10	2	no	—
745	C₂³	—	10	2	no	—
746	C₂³	—	10	2	no	—
747	C₂³	—	10	2	no	—
748	C₂³	—	20	1	no	—
749	C₂³	—	20	1	no	—
750	C₂³	C₂×D₅×Dic₃	1	1	yes	characteristic
751	C₂³	C₂×D₅×Dic₃	1	1	yes	characteristic
752	D₄	—	2	2	no	—
753	D₄	—	5	4	no	—
754	D₄	—	10	2	no	—
755	D₄	—	10	2	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	1	no	—
758	C₂×C₄	—	2	1	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	5	1	no	—
761	C₂×C₄	—	5	1	no	—
762	C₂×C₄	—	5	2	no	—
763	C₂×C₄	—	5	2	no	—
764	C₂×C₄	—	5	1	no	—
765	C₂×C₄	—	5	1	no	—
766	C₂×C₄	—	5	1	no	—
767	C₂×C₄	—	10	2	no	—
768	C₂×C₄	—	10	2	no	—
769	C₂×C₄	—	10	2	no	—
770	C₂×C₄	—	10	2	no	—
771	C₂×C₄	—	10	2	no	—
772	C₂×C₄	—	10	2	no	—
773	C₂×C₄	—	10	2	no	—
774	C₂×C₄	—	10	1	no	—
775	C₂×C₄	—	10	1	no	—
776	C₂×C₄	—	10	1	no	—
777	C₂×C₄	—	10	1	no	—
778	C₂×C₄	—	20	1	no	—
779	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
780	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
781	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
782	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
783	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
784	C₈	—	3	2	no	—
785	C₈	—	6	1	no	—
786	C₈	—	6	1	no	—
787	C₈	—	6	1	no	—
788	C₈	—	15	2	no	—
789	C₈	—	30	1	no	—
790	C₈	—	30	1	no	—
791	C₈	—	30	1	no	—
792	C₂×C₃	—	2	2	no	—
793	C₂×C₃	—	4	1	no	—
794	C₂×C₃	—	10	2	no	—
795	C₂×C₃	—	10	2	no	—
796	C₂×C₃	—	20	1	no	—
797	C₂×C₃	C₄×D₄×D₅	1	1	yes	characteristic
798	C₂×C₃	C₂×D₅×M₁₆	1	1	yes	characteristic
799	C₂×C₃	#66084	1	1	yes	characteristic
800	C₅	D₄×#208	1	1	yes	characteristic, complemented, Sylow
801	C₂²	—	2	1	no	—
802	C₂²	—	2	1	no	—
803	C₂²	—	2	1	no	—
804	C₂²	—	2	1	no	—
805	C₂²	—	2	1	no	—
806	C₂²	—	5	2	no	—
807	C₂²	—	5	2	no	—
808	C₂²	—	10	1	no	—
809	C₂²	—	10	1	no	—
810	C₂²	—	10	1	no	—
811	C₂²	—	10	1	no	—
812	C₂²	—	10	1	no	—
813	C₂²	—	10	1	no	—
814	C₂²	—	10	1	no	—
815	C₂²	—	20	4	no	—
816	C₂²	—	20	4	no	—
817	C₂²	D₅×#208	1	2	yes	complemented
818	C₂²	C₂²×D₅×Dic₃	1	1	yes	characteristic
819	C₄	—	2	1	no	—
820	C₄	—	2	1	no	—
821	C₄	—	2	1	no	—
822	C₄	—	2	1	no	—
823	C₄	—	5	2	no	—
824	C₄	—	5	2	no	—
825	C₄	—	10	1	no	—
826	C₄	—	10	1	no	—
827	C₄	—	10	1	no	—
828	C₄	D₃×D₄×D₅	1	1	yes	characteristic
829	C₄	D₅×#237	1	1	yes	characteristic
830	C₃	#10611214	1	1	yes	characteristic, complemented, Sylow
831	C₂	—	2	2	no	—
832	C₂	—	4	1	no	—
833	C₂	—	10	2	no	—
834	C₂	—	10	2	no	—
835	C₂	—	20	1	no	—
836	C₂	C₂×D₅×#208	1	1	yes	characteristic
837	C₂	D₄×D₅×Dic₃	1	1	yes	characteristic
838	C₂	#11755296	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×C₃×D₄×D₅	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. C₂²×#6649	C₂	semidirect
3. C₂×D₅×#208	C₂	semidirect
4. #11751112	C₂	semidirect
5. C₅×#5011	C₂	semidirect
6. #11748504	C₂	semidirect
7. #11748499	C₂	semidirect
8. #11748499	C₂	semidirect
9. #11748493	C₂	semidirect
10. C₃⋊C₈×C₂²⋊D₅	C₂	semidirect
11. #11748339	C₂	semidirect
12. #11747007	C₂	semidirect
13. #11747003	C₂	semidirect
14. #11746997	C₂	semidirect
15. #11746991	C₂	semidirect
21. C₂×#6710	C₂²	semidirect
22. C₂²×C₃⋊#168	C₂²	semidirect
23. C₂×C₅×#208	C₂²	semidirect
24. C₂²×C₅×C₃⋊C₈	C₂²	semidirect
41. C₂×#6649	C₂²	semidirect
42. C₂×#6649	C₂²	semidirect
44. C₂×D₅×C₃⋊C₈	C₂²	semidirect
45. C₂×D₅×C₃⋊C₈	C₂²	semidirect
46. #91114	C₂²	semidirect
47. #91114	C₂²	semidirect
48. C₄⋊(C₃⋊#168)	C₂²	semidirect
49. #91087	C₂²	semidirect
50. C₅×#830	C₂²	semidirect
51. C₅×#830	C₂²	semidirect
52. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
53. C₅×#803	C₂²	semidirect
54. #90982	C₂²	semidirect
55. #90982	C₂²	semidirect
56. #90955	C₂²	semidirect
57. #90955	C₂²	semidirect
58. #90955	C₂²	semidirect
59. #90955	C₂²	semidirect
60. Dic₅×C₃⋊C₈	C₂²	semidirect
61. Dic₅×C₃⋊C₈	C₂²	semidirect
135. #6649	D₄	semidirect
148. #5011	D₅	semidirect
221. C₃×C₂²⋊D₅	M₁₆	semidirect
245. C₃⋊#168	C₂×D₄	semidirect
249. C₅×C₃⋊C₈	C₂×D₄	semidirect
274. C₂×#208	C₂×D₅	semidirect
278. C₂²×C₃⋊C₈	C₂×D₅	semidirect
285. #830	C₂×D₅	semidirect
286. #830	C₂×D₅	semidirect
290. C₄⋊(C₃⋊C₈)	C₂×D₅	semidirect
292. #803	C₂×D₅	semidirect
375. C₂²×C₃×C₅	C₂×M₁₆	semidirect
387. C₂×C₃×D₅	C₂×M₁₆	semidirect
398. C₃×Dic₅	C₂×M₁₆	semidirect
481. C₂²⋊D₅	#208	semidirect
613. C₃⋊C₈	D₄×D₅	semidirect
619. C₂²×C₅	C₂×#208	semidirect
630. C₂×D₅	C₂×#208	semidirect
641. Dic₅	C₂×#208	semidirect
703. C₃×C₅	D₄×M₁₆	semidirect
720. C₂²×C₃	D₅×M₁₆	semidirect
800. C₅	D₄×#208	semidirect
817. C₂²	D₅×#208	semidirect
830. C₃	#10611214	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄×D₄×D₅	2
C₂²×#6649	2
C₂×D₅×#208	2
#11751112	2
C₅×#5011	2
#11748504	2
#11748499	2
#11748493	2
C₃⋊C₈×C₂²⋊D₅	2
#11748339	2
#11747007	2
#11747003	2
#11746997	2
#11746991	2
#10611214	3
D₄×#208	5