Subgroups — #14415713

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	C₄×C₅×D₃×D₄	C₂	1	1	yes	maximal, characteristic
2	C₂²×#6650	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₃×#681	C₂	1	1	yes	maximal, characteristic, complemented
4	#11751112	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65300	C₂	1	1	yes	maximal, characteristic, complemented
6	#11748505	C₂	1	1	yes	maximal, characteristic, complemented
7	#11748505	C₂	1	1	yes	maximal, characteristic, complemented
8	#11748501	C₂	1	1	yes	maximal, characteristic, complemented
9	#67⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
10	#67×#168	C₂	1	1	yes	maximal, characteristic, complemented
11	#11748314	C₂	1	1	yes	maximal, characteristic, complemented
12	#11747011	C₂	1	1	yes	maximal, characteristic, complemented
13	#11747005	C₂	1	1	yes	maximal, characteristic, complemented
14	#11746999	C₂	1	1	yes	maximal, characteristic, complemented
15	#11746987	C₂	1	1	yes	maximal, characteristic, complemented
16	D₄×#681	—	3	1	no	maximal, Hall
17	C₂×C₅×D₃×D₄	C₄	1	1	yes	characteristic
18	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
19	C₂²×C₄×C₅×D₃	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	C₅×D₄×Dic₃	C₄	1	1	yes	characteristic
24	C₄×C₅×#67	C₂²	1	1	yes	characteristic
25	C₄×C₅×#67	C₂²	1	1	yes	characteristic
26	C₅×#893	C₄	1	1	yes	characteristic
27	C₅×D₃×C₄⋊C₄	C₄	1	1	yes	characteristic
28	C₅×#67⋊C₄	C₄	1	1	yes	characteristic
29	C₅×#67⋊C₄	C₄	1	1	yes	characteristic
30	C₅×D₃×C₂²⋊C₄	C₄	1	1	yes	characteristic
31	C₅×D₃×C₂²⋊C₄	C₄	1	1	yes	characteristic
32	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
33	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
34	C₂×C₃×#681	C₂²	1	1	yes	characteristic, complemented
35	C₂²×C₃×#168	C₂²	1	1	yes	characteristic, complemented
36	C₂×#6650	—	2	4	no	—
37	C₂×#6650	C₂²	1	1	yes	characteristic
38	C₂×#6650	C₂²	1	1	yes	characteristic
39	C₂×#6650	C₂²	1	1	yes	characteristic
40	C₂×#6650	C₂²	1	1	yes	characteristic
41	C₂×#6650	C₂²	1	1	yes	characteristic, complemented
42	C₂×#6650	C₂²	1	1	yes	characteristic, complemented
43	D₃×#681	—	2	4	no	—
44	C₂×D₃×#168	C₂²	1	1	yes	characteristic, complemented
45	C₂×D₃×#168	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	C₃×C₂²⋊#168	C₂²	1	1	yes	characteristic, complemented
51	C₃×C₂²⋊#168	C₂²	1	1	yes	characteristic, complemented
52	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic, complemented
53	C₃×#3935	C₂²	1	1	yes	characteristic, complemented
54	Dic₃⋊#168	C₂²	1	1	yes	characteristic, complemented
55	Dic₃⋊#168	C₂²	1	1	yes	characteristic, complemented
56	(C₂×D₃)⋊#168	C₂²	1	1	yes	characteristic, complemented
57	(C₂×D₃)⋊#168	C₂²	1	1	yes	characteristic, complemented
58	(C₂×D₃)⋊#168	C₂²	1	1	yes	characteristic, complemented
59	(C₂×D₃)⋊#168	C₂²	1	1	yes	characteristic, complemented
60	Dic₃×#168	C₂²	1	1	yes	characteristic, complemented
61	Dic₃×#168	C₂²	1	1	yes	characteristic, complemented
62	#79483	—	5	1	no	maximal, Hall
63	C₂×C₄×C₅×D₄	—	3	1	no	—
64	C₂²×#681	—	3	1	no	—
65	C₂²×#681	—	3	1	no	—
66	#65496	—	3	1	no	—
67	#65496	—	3	1	no	—
68	#65301	—	3	1	no	—
69	#65301	—	3	1	no	—
70	#65300	—	3	1	no	—
71	#65300	—	3	1	no	—
72	#65300	—	3	1	no	—
73	#65300	D₃	1	1	yes	characteristic, complemented
74	D₄×#168	—	3	1	no	—
75	D₄×#168	—	3	1	no	—
76	#65213	—	3	1	no	—
77	C₄×#681	—	3	1	no	—
78	C₂³×C₅×D₃	C₂×C₄	1	1	yes	characteristic
79	C₂³×C₅×D₃	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×C₅×#67	C₂×C₄	1	1	yes	characteristic
84	C₂×C₅×#67	C₂×C₄	1	1	yes	characteristic
85	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
86	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
87	C₅×D₃×D₄	—	2	4	no	—
88	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
89	C₂×C₄×C₅×D₃	—	2	2	no	—
90	C₂×C₄×C₅×D₃	—	2	2	no	—
91	C₂×C₄×C₅×D₃	—	2	2	no	—
92	C₂×C₄×C₅×D₃	—	2	2	no	—
93	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
97	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
98	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
99	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
100	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
101	C₂×C₄×C₅×D₃	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×#217	C₂×C₄	1	1	yes	characteristic
113	C₅×#217	C₂×C₄	1	1	yes	characteristic
114	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
115	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
116	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
117	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
118	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
119	C₅×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
120	C₅×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
121	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
122	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
123	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
124	C₃×#681	—	2	2	no	—
125	C₂×C₃×#168	—	2	2	no	—
126	C₂×C₃×#168	C₂³	1	1	yes	characteristic
127	C₂×C₃×#168	C₂³	1	1	yes	characteristic
128	C₂×C₃×#168	C₂³	1	1	yes	characteristic
129	C₂×C₃×#168	C₂³	1	1	yes	characteristic
130	#6650	—	2	2	no	—
131	#6650	—	2	2	no	—
132	#6650	—	2	2	no	—
133	#6650	—	2	2	no	—
134	#6650	—	2	2	no	—
135	#6650	D₄	1	4	yes	complemented
136	D₃×#168	—	2	2	no	—
137	D₃×#168	—	2	2	no	—
138	C₂×D₃×M₁₆	—	5	1	no	—
139	C₂²×ΓL(1,𝔽₂₅)	—	5	1	no	—
140	C₄×D₃×D₄	D₅	1	1	yes	characteristic
141	C₃×#435	—	5	1	no	—
142	#5128	—	5	1	no	—
143	C₈×#67	—	5	1	no	—
144	#5011	—	5	1	no	—
145	#4837	—	5	1	no	—
146	#4836	—	5	1	no	—
147	#4729	—	5	1	no	—
148	#4726	—	5	1	no	—
149	#4726	—	5	1	no	—
150	#67⋊C₈	—	5	1	no	—
151	#4707	—	5	1	no	—
152	#4706	—	5	1	no	—
153	C₂²×C₅×D₄	—	3	1	no	—
154	C₂³×C₄×C₅	—	3	1	no	—
155	C₂³×C₄×C₅	—	3	1	no	—
156	C₄×C₅×D₄	—	3	1	no	—
157	C₄×C₅×D₄	—	3	1	no	—
158	C₄×C₅×D₄	—	3	1	no	—
159	C₄×C₅×D₄	—	3	1	no	—
160	C₄×C₅×D₄	—	3	1	no	—
161	C₄×C₅×D₄	—	3	1	no	—
162	C₄×C₅×D₄	—	3	1	no	—
163	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
164	C₂×C₅×C₄⋊C₄	—	3	1	no	—
165	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
166	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
167	C₂×C₄²×C₅	—	3	1	no	—
168	C₂×#681	—	3	1	no	—
169	C₂×#681	—	3	1	no	—
170	C₂×#681	—	3	1	no	—
171	C₂×#681	—	3	1	no	—
172	C₂×#681	—	3	1	no	—
173	C₂×#681	—	3	1	no	—
174	C₂×#681	—	3	1	no	—
175	C₂×#681	—	6	4	no	—
176	C₂×#681	—	6	4	no	—
177	C₂×#681	C₂×D₃	1	1	yes	characteristic, complemented
178	C₂²×#168	—	3	1	no	—
179	C₂²×#168	—	3	1	no	—
180	C₂²×#168	—	3	1	no	—
181	C₂²×#168	C₂×D₃	1	1	yes	characteristic, complemented
182	C₂²⋊#168	—	3	1	no	—
183	C₂²⋊#168	—	3	1	no	—
184	C₂²⋊#168	—	3	1	no	—
185	C₂²⋊#168	—	3	1	no	—
186	C₂²⋊#168	—	3	1	no	—
187	C₂²⋊#168	—	3	1	no	—
188	C₂²⋊#168	C₂×D₃	1	1	yes	characteristic, complemented
189	C₂²⋊#168	C₂×D₃	1	1	yes	characteristic, complemented
190	C₄⋊#168	—	3	1	no	—
191	C₄⋊#168	—	3	1	no	—
192	C₄⋊#168	—	3	1	no	—
193	C₄⋊#168	C₂×D₃	1	1	yes	characteristic, complemented
194	#3935	—	3	1	no	—
195	#3935	C₂×D₃	1	1	yes	characteristic, complemented
196	C₄×#168	—	3	1	no	—
197	C₄×#168	—	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×C₅×D₃	—	2	2	no	—
202	C₂²×C₅×D₃	—	2	2	no	—
203	C₂²×C₅×D₃	—	2	2	no	—
204	C₂²×C₅×D₃	—	2	2	no	—
205	C₂²×C₅×D₃	—	4	1	no	—
206	C₂²×C₅×D₃	—	4	1	no	—
207	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
208	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
209	C₂²×C₅×D₃	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	C₅×#67	—	2	2	no	—
221	C₅×#67	M₁₆	1	4	yes	complemented
222	C₂×C₅×Dic₃	—	2	2	no	—
223	C₂×C₅×Dic₃	—	2	2	no	—
224	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
225	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
226	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
227	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
228	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
229	C₅×D₁₂	—	2	2	no	—
230	C₄×C₅×D₃	—	2	2	no	—
231	C₄×C₅×D₃	—	2	2	no	—
232	C₄×C₅×D₃	—	2	1	no	—
233	C₄×C₅×D₃	—	2	1	no	—
234	C₄×C₅×D₃	—	2	1	no	—
235	C₄×C₅×D₃	—	2	1	no	—
236	C₄×C₅×D₃	—	2	2	no	—
237	C₄×C₅×D₃	—	2	2	no	—
238	C₄×C₅×D₃	—	2	2	no	—
239	C₄×C₅×D₃	—	4	1	no	—
240	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
241	C₄×C₅×D₃	#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	C₃×#168	—	2	1	no	—
247	C₃×#168	—	2	1	no	—
248	C₃×#168	—	2	1	no	—
249	C₃×#168	C₂×D₄	1	2	yes	complemented
250	C₂×D₃×D₄	Dic₅	1	1	yes	characteristic
251	C₂²×C₄×D₃	C₂×D₅	1	1	yes	characteristic
252	C₂²×C₄×D₃	C₂×D₅	1	1	yes	characteristic
253	C₂×C₃×M₁₆	—	5	1	no	—
254	C₂²×C₃×C₈	—	5	1	no	—
255	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
256	D₄×Dic₃	Dic₅	1	1	yes	characteristic
257	C₄×#67	C₂×D₅	1	1	yes	characteristic
258	C₄×#67	C₂×D₅	1	1	yes	characteristic
259	C₂×#208	—	5	1	no	—
260	C₂²×C₃⋊C₈	—	5	1	no	—
261	D₃×M₁₆	—	10	4	no	—
262	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
263	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
264	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
265	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
266	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
267	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
268	C₂×ΓL(1,𝔽₂₅)	—	10	4	no	—
269	C₂×D₃×C₈	—	5	1	no	—
270	C₂×D₃×C₈	—	5	1	no	—
271	#893	Dic₅	1	1	yes	characteristic
272	D₃×C₄⋊C₄	Dic₅	1	1	yes	characteristic
273	#67⋊C₄	Dic₅	1	1	yes	characteristic
274	#67⋊C₄	Dic₅	1	1	yes	characteristic
275	D₃×C₂²⋊C₄	Dic₅	1	1	yes	characteristic
276	D₃×C₂²⋊C₄	Dic₅	1	1	yes	characteristic
277	C₄×D₁₂	C₂×D₅	1	1	yes	characteristic
278	C₄²×D₃	C₂×D₅	1	1	yes	characteristic
279	C₃×C₄⋊C₈	—	5	1	no	—
280	C₃×C₂²⋊C₈	—	5	1	no	—
281	C₃×C₂²⋊C₈	—	5	1	no	—
282	C₃×#97	—	5	1	no	—
283	#830	—	5	1	no	—
284	#830	—	5	1	no	—
285	(C₂×D₃)⋊C₈	—	5	1	no	—
286	(C₂×D₃)⋊C₈	—	5	1	no	—
287	(C₂×D₃)⋊C₈	—	5	1	no	—
288	(C₂×D₃)⋊C₈	—	5	1	no	—
289	Dic₃⋊C₈	—	5	1	no	—
290	Dic₃⋊C₈	—	5	1	no	—
291	C₈×Dic₃	—	5	1	no	—
292	C₈×Dic₃	—	5	1	no	—
293	C₄⋊(C₃⋊C₈)	—	5	1	no	—
294	#803	—	5	1	no	—
295	C₂⁴×C₅	—	3	1	no	—
296	C₂⁴×C₅	—	3	1	no	—
297	C₂×C₅×D₄	—	3	1	no	—
298	C₂×C₅×D₄	—	3	1	no	—
299	C₂×C₅×D₄	—	3	1	no	—
300	C₂×C₅×D₄	—	6	4	no	—
301	C₂×C₅×D₄	C₄×D₃	1	1	yes	characteristic
302	C₂²×C₄×C₅	—	3	1	no	—
303	C₂²×C₄×C₅	—	3	1	no	—
304	C₂²×C₄×C₅	—	3	1	no	—
305	C₂²×C₄×C₅	—	3	1	no	—
306	C₂²×C₄×C₅	—	3	1	no	—
307	C₂²×C₄×C₅	—	3	1	no	—
308	C₂²×C₄×C₅	—	3	1	no	—
309	C₂²×C₄×C₅	—	3	1	no	—
310	C₂²×C₄×C₅	—	3	1	no	—
311	C₂²×C₄×C₅	—	3	1	no	—
312	C₂²×C₄×C₅	—	3	1	no	—
313	C₂²×C₄×C₅	—	6	2	no	—
314	C₂²×C₄×C₅	—	6	2	no	—
315	C₂²×C₄×C₅	—	6	2	no	—
316	C₂²×C₄×C₅	—	6	2	no	—
317	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
318	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
319	C₅×C₄⋊C₄	—	3	1	no	—
320	C₅×C₄⋊C₄	—	3	1	no	—
321	C₅×C₄⋊C₄	—	3	1	no	—
322	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
323	C₅×C₂²⋊C₄	—	3	1	no	—
324	C₅×C₂²⋊C₄	—	3	1	no	—
325	C₅×C₂²⋊C₄	—	3	1	no	—
326	C₅×C₂²⋊C₄	—	3	1	no	—
327	C₅×C₂²⋊C₄	—	3	1	no	—
328	C₅×C₂²⋊C₄	—	3	1	no	—
329	C₅×C₂²⋊C₄	C₄×D₃	1	1	yes	characteristic
330	C₅×C₂²⋊C₄	C₄×D₃	1	1	yes	characteristic
331	C₄²×C₅	—	3	1	no	—
332	C₄²×C₅	—	3	1	no	—
333	C₄²×C₅	—	3	1	no	—
334	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
335	#681	—	2	2	no	—
336	#681	—	3	4	no	—
337	#681	—	6	2	no	—
338	#681	—	6	2	no	—
339	#681	—	6	2	no	—
340	#681	—	6	2	no	—
341	#681	—	6	2	no	—
342	#681	—	6	2	no	—
343	C₂×#168	—	2	2	no	—
344	C₂×#168	—	3	1	no	—
345	C₂×#168	—	3	1	no	—
346	C₂×#168	—	3	1	no	—
347	C₂×#168	—	3	1	no	—
348	C₂×#168	—	6	2	no	—
349	C₂×#168	—	6	2	no	—
350	C₂×#168	—	6	2	no	—
351	C₂×#168	C₂²×D₃	1	1	yes	characteristic
352	C₂×#168	C₂²×D₃	1	1	yes	characteristic
353	C₂×#168	C₂²×D₃	1	1	yes	characteristic
354	C₂×#168	C₂²×D₃	1	1	yes	characteristic
355	C₂²×M₁₆	—	15	1	no	—
356	C₂²×M₁₆	—	15	1	no	—
357	C₂×C₄×D₄	—	3	1	no	—
358	#436	—	15	1	no	—
359	#436	—	15	1	no	—
360	#435	—	5	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×C₅×D₃	—	2	1	no	—
378	C₂×C₅×D₃	—	2	1	no	—
379	C₂×C₅×D₃	—	2	1	no	—
380	C₂×C₅×D₃	—	2	1	no	—
381	C₂×C₅×D₃	—	2	1	no	—
382	C₂×C₅×D₃	—	2	1	no	—
383	C₂×C₅×D₃	—	2	1	no	—
384	C₂×C₅×D₃	—	4	4	no	—
385	C₂×C₅×D₃	—	4	4	no	—
386	C₂×C₅×D₃	C₄×D₄	1	2	yes	—
387	C₂×C₅×D₃	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	C₅×Dic₃	—	2	1	no	—
395	C₅×Dic₃	—	2	1	no	—
396	C₅×Dic₃	—	2	1	no	—
397	C₅×Dic₃	C₄×D₄	1	2	yes	—
398	C₅×Dic₃	C₂×M₁₆	1	2	yes	complemented
399	C₂³×D₃	C₂×Dic₅	1	1	yes	characteristic
400	C₂³×D₃	C₂×Dic₅	1	1	yes	characteristic
401	C₂×C₃×D₄	C₂×Dic₅	1	1	yes	characteristic
402	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
403	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
404	C₂×#67	C₂×Dic₅	1	1	yes	characteristic
405	C₂×#67	C₂×Dic₅	1	1	yes	characteristic
406	C₂²×Dic₃	C₂×Dic₅	1	1	yes	characteristic
407	C₂²×Dic₃	C₂×Dic₅	1	1	yes	characteristic
408	D₃×D₄	—	2	4	no	—
409	C₂×D₁₂	C₂×Dic₅	1	1	yes	characteristic
410	C₂×C₄×D₃	—	2	2	no	—
411	C₂×C₄×D₃	—	2	2	no	—
412	C₂×C₄×D₃	—	2	2	no	—
413	C₂×C₄×D₃	—	2	2	no	—
414	C₂×C₄×D₃	C₂×Dic₅	1	1	yes	characteristic
415	C₂×C₄×D₃	C₂×Dic₅	1	1	yes	characteristic
416	C₂×C₄×D₃	C₂×Dic₅	1	1	yes	characteristic
417	C₂×C₄×D₃	C₂×Dic₅	1	1	yes	characteristic
418	C₂×C₄×D₃	C₂×Dic₅	1	1	yes	characteristic
419	C₂×C₄×D₃	C₂×Dic₅	1	1	yes	characteristic
420	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
421	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
422	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
423	C₃×M₁₆	—	10	2	no	—
424	C₂×C₃×C₈	—	5	1	no	—
425	C₂×C₃×C₈	—	5	1	no	—
426	C₂×C₃×C₈	—	5	1	no	—
427	C₂×C₃×C₈	—	5	1	no	—
428	C₂×C₃×C₈	—	10	2	no	—
429	C₃×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
430	C₃×C₂²⋊C₄	C₂×Dic₅	1	1	yes	characteristic
431	C₃×C₂²⋊C₄	C₂×Dic₅	1	1	yes	characteristic
432	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
433	#217	C₂×Dic₅	1	1	yes	characteristic
434	#217	C₂×Dic₅	1	1	yes	characteristic
435	(C₂×D₃)⋊C₄	C₂×Dic₅	1	1	yes	characteristic
436	(C₂×D₃)⋊C₄	C₂×Dic₅	1	1	yes	characteristic
437	(C₂×D₃)⋊C₄	C₂×Dic₅	1	1	yes	characteristic
438	(C₂×D₃)⋊C₄	C₂×Dic₅	1	1	yes	characteristic
439	C₄⋊Dic₃	C₂×Dic₅	1	1	yes	characteristic
440	Dic₃⋊C₄	C₂×Dic₅	1	1	yes	characteristic
441	Dic₃⋊C₄	C₂×Dic₅	1	1	yes	characteristic
442	C₄×Dic₃	C₂×Dic₅	1	1	yes	characteristic
443	C₄×Dic₃	C₂×Dic₅	1	1	yes	characteristic
444	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
445	#208	—	10	2	no	—
446	C₂×C₃⋊C₈	—	5	1	no	—
447	C₂×C₃⋊C₈	—	5	1	no	—
448	C₂×C₃⋊C₈	—	5	1	no	—
449	C₂×C₃⋊C₈	—	5	1	no	—
450	C₂×C₃⋊C₈	—	10	2	no	—
451	ΓL(1,𝔽₂₅)	—	5	4	no	—
452	ΓL(1,𝔽₂₅)	—	10	2	no	—
453	ΓL(1,𝔽₂₅)	—	10	2	no	—
454	ΓL(1,𝔽₂₅)	—	10	2	no	—
455	ΓL(1,𝔽₂₅)	—	10	2	no	—
456	ΓL(1,𝔽₂₅)	—	10	2	no	—
457	D₃×C₈	—	10	2	no	—
458	D₃×C₈	—	10	2	no	—
459	C₂³×C₅	—	3	1	no	—
460	C₂³×C₅	—	3	1	no	—
461	C₂³×C₅	—	3	1	no	—
462	C₂³×C₅	—	6	2	no	—
463	C₂³×C₅	—	6	2	no	—
464	C₂³×C₅	—	6	2	no	—
465	C₂³×C₅	—	6	2	no	—
466	C₂³×C₅	—	12	1	no	—
467	C₂³×C₅	—	12	1	no	—
468	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
469	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
470	C₅×D₄	—	2	2	no	—
471	C₅×D₄	—	3	4	no	—
472	C₅×D₄	—	6	2	no	—
473	C₅×D₄	—	6	2	no	—
474	C₂×C₄×C₅	—	2	1	no	—
475	C₂×C₄×C₅	—	2	1	no	—
476	C₂×C₄×C₅	—	2	1	no	—
477	C₂×C₄×C₅	—	2	1	no	—
478	C₂×C₄×C₅	—	3	1	no	—
479	C₂×C₄×C₅	—	3	1	no	—
480	C₂×C₄×C₅	—	3	2	no	—
481	C₂×C₄×C₅	—	3	2	no	—
482	C₂×C₄×C₅	—	3	1	no	—
483	C₂×C₄×C₅	—	3	1	no	—
484	C₂×C₄×C₅	—	3	1	no	—
485	C₂×C₄×C₅	—	6	2	no	—
486	C₂×C₄×C₅	—	6	2	no	—
487	C₂×C₄×C₅	—	6	2	no	—
488	C₂×C₄×C₅	—	6	2	no	—
489	C₂×C₄×C₅	—	6	2	no	—
490	C₂×C₄×C₅	—	6	2	no	—
491	C₂×C₄×C₅	—	6	2	no	—
492	C₂×C₄×C₅	—	6	1	no	—
493	C₂×C₄×C₅	—	6	1	no	—
494	C₂×C₄×C₅	—	6	1	no	—
495	C₂×C₄×C₅	—	6	1	no	—
496	C₂×C₄×C₅	—	12	1	no	—
497	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
498	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
499	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
500	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
501	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
502	#168	—	2	1	no	—
503	#168	—	2	1	no	—
504	#168	—	2	1	no	—
505	#168	—	3	2	no	—
506	#168	—	6	1	no	—
507	#168	—	6	1	no	—
508	#168	—	6	1	no	—
509	#168	D₃×D₄	1	2	yes	complemented
510	C₂²×D₄	—	3	1	no	—
511	C₂³×C₄	—	3	1	no	—
512	C₂³×C₄	—	3	1	no	—
513	C₂×M₁₆	—	5	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	—	5	1	no	—
524	C₂²×C₈	—	15	1	no	—
525	C₂²×C₈	—	15	1	no	—
526	C₂²×C₈	—	15	1	no	—
527	C₄×D₄	—	3	1	no	—
528	C₄×D₄	—	3	1	no	—
529	C₄×D₄	—	3	1	no	—
530	C₄×D₄	—	3	1	no	—
531	C₄×D₄	—	3	1	no	—
532	C₄×D₄	—	3	1	no	—
533	C₄×D₄	—	3	1	no	—
534	C₄×D₄	D₃×D₅	1	1	yes	characteristic
535	C₂×C₄⋊C₄	—	3	1	no	—
536	C₂×C₂²⋊C₄	—	3	1	no	—
537	C₂×C₂²⋊C₄	—	3	1	no	—
538	C₂×C₄²	—	3	1	no	—
539	C₄⋊C₈	—	5	1	no	—
540	C₄⋊C₈	—	15	1	no	—
541	C₄⋊C₈	—	15	1	no	—
542	C₄⋊C₈	—	15	1	no	—
543	C₂²⋊C₈	—	5	1	no	—
544	C₂²⋊C₈	—	5	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	—	5	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	C₅×D₃	—	2	2	no	—
561	C₅×D₃	—	2	2	no	—
562	C₅×D₃	—	4	1	no	—
563	C₂³×C₃	C₂²×Dic₅	1	1	yes	characteristic
564	C₂³×C₃	C₂²×Dic₅	1	1	yes	characteristic
565	C₂²×D₃	—	2	2	no	—
566	C₂²×D₃	—	2	2	no	—
567	C₂²×D₃	—	2	2	no	—
568	C₂²×D₃	—	2	2	no	—
569	C₂²×D₃	—	4	1	no	—
570	C₂²×D₃	—	4	1	no	—
571	C₂²×D₃	C₂²×Dic₅	1	1	yes	characteristic
572	C₂²×D₃	C₂²×Dic₅	1	1	yes	characteristic
573	C₂²×D₃	C₂²×Dic₅	1	1	yes	characteristic
574	C₃×D₄	—	2	2	no	—
575	C₂×C₃×C₄	—	2	1	no	—
576	C₂×C₃×C₄	—	2	1	no	—
577	C₂×C₃×C₄	—	2	1	no	—
578	C₂×C₃×C₄	—	2	1	no	—
579	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
580	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
581	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
582	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
583	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
584	#67	—	2	2	no	—
585	#67	#681	1	4	yes	complemented
586	C₂×Dic₃	—	2	2	no	—
587	C₂×Dic₃	—	2	2	no	—
588	C₂×Dic₃	C₂²×Dic₅	1	1	yes	characteristic
589	C₂×Dic₃	C₂²×Dic₅	1	1	yes	characteristic
590	C₂×Dic₃	C₂²×Dic₅	1	1	yes	characteristic
591	C₂×Dic₃	C₂²×Dic₅	1	1	yes	characteristic
592	C₂×Dic₃	C₂²×Dic₅	1	1	yes	characteristic
593	D₁₂	—	2	2	no	—
594	C₄×D₃	—	2	2	no	—
595	C₄×D₃	—	2	2	no	—
596	C₄×D₃	—	2	1	no	—
597	C₄×D₃	—	2	1	no	—
598	C₄×D₃	—	2	1	no	—
599	C₄×D₃	—	2	1	no	—
600	C₄×D₃	—	2	2	no	—
601	C₄×D₃	—	2	2	no	—
602	C₄×D₃	—	2	2	no	—
603	C₄×D₃	—	4	1	no	—
604	C₄×D₃	D₄×D₅	1	2	yes	—
605	C₄×D₃	#711	1	2	yes	—
606	C₃×C₈	—	5	2	no	—
607	C₃×C₈	—	10	1	no	—
608	C₃×C₈	—	10	1	no	—
609	C₃×C₈	—	10	1	no	—
610	C₃⋊C₈	—	5	2	no	—
611	C₃⋊C₈	—	10	1	no	—
612	C₃⋊C₈	—	10	1	no	—
613	C₃⋊C₈	—	10	1	no	—
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	—	3	2	no	—
620	C₂²×C₅	—	3	2	no	—
621	C₂²×C₅	—	6	1	no	—
622	C₂²×C₅	—	6	1	no	—
623	C₂²×C₅	—	6	1	no	—
624	C₂²×C₅	—	6	1	no	—
625	C₂²×C₅	—	6	1	no	—
626	C₂²×C₅	—	6	1	no	—
627	C₂²×C₅	—	6	1	no	—
628	C₂²×C₅	—	12	4	no	—
629	C₂²×C₅	—	12	4	no	—
630	C₂²×C₅	D₃×M₁₆	1	2	yes	complemented
631	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
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	—	3	2	no	—
637	C₄×C₅	—	3	2	no	—
638	C₄×C₅	—	6	1	no	—
639	C₄×C₅	—	6	1	no	—
640	C₄×C₅	—	6	1	no	—
641	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
642	C₄×C₅	D₃×#41	1	1	yes	characteristic
643	C₂⁴	—	3	1	no	—
644	C₂⁴	—	3	1	no	—
645	C₂×D₄	—	3	1	no	—
646	C₂×D₄	—	3	1	no	—
647	C₂×D₄	—	3	1	no	—
648	C₂×D₄	—	6	4	no	—
649	C₂×D₄	D₃×Dic₅	1	1	yes	characteristic
650	C₂²×C₄	—	3	1	no	—
651	C₂²×C₄	—	3	1	no	—
652	C₂²×C₄	—	3	1	no	—
653	C₂²×C₄	—	3	1	no	—
654	C₂²×C₄	—	3	1	no	—
655	C₂²×C₄	—	3	1	no	—
656	C₂²×C₄	—	3	1	no	—
657	C₂²×C₄	—	3	1	no	—
658	C₂²×C₄	—	3	1	no	—
659	C₂²×C₄	—	3	1	no	—
660	C₂²×C₄	—	3	1	no	—
661	C₂²×C₄	—	6	2	no	—
662	C₂²×C₄	—	6	2	no	—
663	C₂²×C₄	—	6	2	no	—
664	C₂²×C₄	—	6	2	no	—
665	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
666	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
667	M₁₆	—	10	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	—	5	1	no	—
676	C₂×C₈	—	5	1	no	—
677	C₂×C₈	—	5	1	no	—
678	C₂×C₈	—	5	1	no	—
679	C₂×C₈	—	10	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	—	3	1	no	—
688	C₄⋊C₄	—	3	1	no	—
689	C₄⋊C₄	—	3	1	no	—
690	C₄⋊C₄	D₃×Dic₅	1	1	yes	characteristic
691	C₂²⋊C₄	—	3	1	no	—
692	C₂²⋊C₄	—	3	1	no	—
693	C₂²⋊C₄	—	3	1	no	—
694	C₂²⋊C₄	—	3	1	no	—
695	C₂²⋊C₄	—	3	1	no	—
696	C₂²⋊C₄	—	3	1	no	—
697	C₂²⋊C₄	D₃×Dic₅	1	1	yes	characteristic
698	C₂²⋊C₄	D₃×Dic₅	1	1	yes	characteristic
699	C₄²	—	3	1	no	—
700	C₄²	—	3	1	no	—
701	C₄²	—	3	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	C₂×#681	1	2	yes	complemented
710	C₂²×C₃	C₂³×Dic₅	1	1	yes	characteristic
711	C₂×D₃	—	2	1	no	—
712	C₂×D₃	—	2	1	no	—
713	C₂×D₃	—	2	1	no	—
714	C₂×D₃	—	2	1	no	—
715	C₂×D₃	—	2	1	no	—
716	C₂×D₃	—	2	1	no	—
717	C₂×D₃	—	2	1	no	—
718	C₂×D₃	—	4	4	no	—
719	C₂×D₃	—	4	4	no	—
720	C₂×D₃	C₂×#681	1	2	yes	complemented
721	C₂×D₃	D₄×Dic₅	1	2	yes	—
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	C₂×D₄×D₅	1	1	yes	characteristic
727	C₃×C₄	C₂×#711	1	1	yes	characteristic
728	Dic₃	—	2	1	no	—
729	Dic₃	—	2	1	no	—
730	Dic₃	—	2	1	no	—
731	Dic₃	C₂×#681	1	2	yes	complemented
732	Dic₃	D₄×Dic₅	1	2	yes	—
733	C₂×C₅	—	2	2	no	—
734	C₂×C₅	—	4	1	no	—
735	C₂×C₅	—	6	2	no	—
736	C₂×C₅	—	6	2	no	—
737	C₂×C₅	—	12	1	no	—
738	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
739	C₂×C₅	C₂×D₃×M₁₆	1	1	yes	characteristic
740	C₂×C₅	#5750	1	1	yes	characteristic
741	C₂³	—	3	1	no	—
742	C₂³	—	3	1	no	—
743	C₂³	—	3	1	no	—
744	C₂³	—	6	2	no	—
745	C₂³	—	6	2	no	—
746	C₂³	—	6	2	no	—
747	C₂³	—	6	2	no	—
748	C₂³	—	12	1	no	—
749	C₂³	—	12	1	no	—
750	C₂³	C₂×D₃×Dic₅	1	1	yes	characteristic
751	C₂³	C₂×D₃×Dic₅	1	1	yes	characteristic
752	D₄	—	2	2	no	—
753	D₄	—	3	4	no	—
754	D₄	—	6	2	no	—
755	D₄	—	6	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	—	3	1	no	—
761	C₂×C₄	—	3	1	no	—
762	C₂×C₄	—	3	2	no	—
763	C₂×C₄	—	3	2	no	—
764	C₂×C₄	—	3	1	no	—
765	C₂×C₄	—	3	1	no	—
766	C₂×C₄	—	3	1	no	—
767	C₂×C₄	—	6	2	no	—
768	C₂×C₄	—	6	2	no	—
769	C₂×C₄	—	6	2	no	—
770	C₂×C₄	—	6	2	no	—
771	C₂×C₄	—	6	2	no	—
772	C₂×C₄	—	6	2	no	—
773	C₂×C₄	—	6	2	no	—
774	C₂×C₄	—	6	1	no	—
775	C₂×C₄	—	6	1	no	—
776	C₂×C₄	—	6	1	no	—
777	C₂×C₄	—	6	1	no	—
778	C₂×C₄	—	12	1	no	—
779	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
780	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
781	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
782	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
783	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
784	C₈	—	5	2	no	—
785	C₈	—	10	1	no	—
786	C₈	—	10	1	no	—
787	C₈	—	10	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	C₂²×#681	1	1	yes	characteristic
795	C₂×C₃	C₂×D₄×Dic₅	1	1	yes	characteristic
796	C₂×C₃	#66153	1	1	yes	characteristic
797	D₃	—	2	2	no	—
798	D₃	—	2	2	no	—
799	D₃	—	4	1	no	—
800	C₅	#79483	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	—	3	2	no	—
807	C₂²	—	3	2	no	—
808	C₂²	—	6	1	no	—
809	C₂²	—	6	1	no	—
810	C₂²	—	6	1	no	—
811	C₂²	—	6	1	no	—
812	C₂²	—	6	1	no	—
813	C₂²	—	6	1	no	—
814	C₂²	—	6	1	no	—
815	C₂²	—	12	4	no	—
816	C₂²	—	12	4	no	—
817	C₂²	D₃×#681	1	2	yes	complemented
818	C₂²	C₂²×D₃×Dic₅	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	—	3	2	no	—
824	C₄	—	3	2	no	—
825	C₄	—	6	1	no	—
826	C₄	—	6	1	no	—
827	C₄	—	6	1	no	—
828	C₄	D₃×D₄×D₅	1	1	yes	characteristic
829	C₄	D₃×#711	1	1	yes	characteristic
830	C₃	D₄×#681	1	1	yes	characteristic, complemented, Sylow
831	C₂	—	2	2	no	—
832	C₂	—	4	1	no	—
833	C₂	—	6	2	no	—
834	C₂	—	6	2	no	—
835	C₂	—	12	1	no	—
836	C₂	C₂×D₃×#681	1	1	yes	characteristic
837	C₂	D₃×D₄×Dic₅	1	1	yes	characteristic
838	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. C₂²×#6650	C₂	semidirect
3. C₂×D₃×#681	C₂	semidirect
4. #11751112	C₂	semidirect
5. C₃×#65300	C₂	semidirect
6. #11748505	C₂	semidirect
7. #11748505	C₂	semidirect
8. #11748501	C₂	semidirect
9. #67⋊#168	C₂	semidirect
10. #67×#168	C₂	semidirect
11. #11748314	C₂	semidirect
12. #11747011	C₂	semidirect
13. #11747005	C₂	semidirect
14. #11746999	C₂	semidirect
15. #11746987	C₂	semidirect
21. C₂×#6710	C₂²	semidirect
22. C₂²×C₃⋊#168	C₂²	semidirect
34. C₂×C₃×#681	C₂²	semidirect
35. C₂²×C₃×#168	C₂²	semidirect
41. C₂×#6650	C₂²	semidirect
42. C₂×#6650	C₂²	semidirect
44. C₂×D₃×#168	C₂²	semidirect
45. C₂×D₃×#168	C₂²	semidirect
46. #91114	C₂²	semidirect
47. #91114	C₂²	semidirect
48. C₄⋊(C₃⋊#168)	C₂²	semidirect
49. #91087	C₂²	semidirect
50. C₃×C₂²⋊#168	C₂²	semidirect
51. C₃×C₂²⋊#168	C₂²	semidirect
52. C₃×C₄⋊#168	C₂²	semidirect
53. C₃×#3935	C₂²	semidirect
54. Dic₃⋊#168	C₂²	semidirect
55. Dic₃⋊#168	C₂²	semidirect
56. (C₂×D₃)⋊#168	C₂²	semidirect
57. (C₂×D₃)⋊#168	C₂²	semidirect
58. (C₂×D₃)⋊#168	C₂²	semidirect
59. (C₂×D₃)⋊#168	C₂²	semidirect
60. Dic₃×#168	C₂²	semidirect
61. Dic₃×#168	C₂²	semidirect
73. #65300	D₃	semidirect
135. #6650	D₄	semidirect
177. C₂×#681	C₂×D₃	semidirect
181. C₂²×#168	C₂×D₃	semidirect
188. C₂²⋊#168	C₂×D₃	semidirect
189. C₂²⋊#168	C₂×D₃	semidirect
193. C₄⋊#168	C₂×D₃	semidirect
195. #3935	C₂×D₃	semidirect
221. C₅×#67	M₁₆	semidirect
245. C₃⋊#168	C₂×D₄	semidirect
249. C₃×#168	C₂×D₄	semidirect
375. C₂²×C₃×C₅	C₂×M₁₆	semidirect
387. C₂×C₅×D₃	C₂×M₁₆	semidirect
398. C₅×Dic₃	C₂×M₁₆	semidirect
509. #168	D₃×D₄	semidirect
585. #67	#681	semidirect
630. C₂²×C₅	D₃×M₁₆	semidirect
703. C₃×C₅	D₄×M₁₆	semidirect
709. C₂²×C₃	C₂×#681	semidirect
720. C₂×D₃	C₂×#681	semidirect
731. Dic₃	C₂×#681	semidirect
800. C₅	#79483	semidirect
817. C₂²	D₃×#681	semidirect
830. 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
C₂²×#6650	2
C₂×D₃×#681	2
#11751112	2
C₃×#65300	2
#11748505	2
#11748501	2
#67⋊#168	2
#67×#168	2
#11748314	2
#11747011	2
#11747005	2
#11746999	2
#11746987	2
D₄×#681	3
#79483	5