Subgroups — #14577565

Order 2432.

1152 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927278	C₂	1	1	yes	maximal, characteristic, complemented
2	#11927248	C₂	1	1	yes	maximal, characteristic, complemented
3	#11927247	C₂	1	1	yes	maximal, characteristic, complemented
4	#11927245	C₂	1	1	yes	maximal, characteristic, complemented
5	#11927237	C₂	1	1	yes	maximal, characteristic, complemented
6	#11927226	C₂	1	1	yes	maximal, characteristic, complemented
7	#11927221	C₂	1	1	yes	maximal, characteristic, complemented
8	#11927219	C₂	1	1	yes	maximal, characteristic, complemented
9	#11927217	C₂	1	1	yes	maximal, characteristic, complemented
10	#11927217	C₂	1	1	yes	maximal, characteristic, complemented
11	#11927196	C₂	1	1	yes	maximal, characteristic, complemented
12	#11927186	C₂	1	1	yes	maximal, characteristic, complemented
13	#11927186	C₂	1	1	yes	maximal, characteristic, complemented
14	#11927186	C₂	1	1	yes	maximal, characteristic, complemented
15	#11927185	C₂	1	1	yes	maximal, characteristic, complemented
16	#11927178	C₂	1	1	yes	maximal, characteristic, complemented
17	#11927164	C₂	1	1	yes	maximal, characteristic, complemented
18	#11927146	C₂	1	1	yes	maximal, characteristic, complemented
19	#11927142	C₂	1	1	yes	maximal, characteristic, complemented
20	#11927133	C₂	1	1	yes	maximal, characteristic, complemented
21	#11927127	C₂	1	1	yes	maximal, characteristic, complemented
22	#11927079	C₂	1	1	yes	maximal, characteristic, complemented
23	#11927077	C₂	1	1	yes	maximal, characteristic, complemented
24	#11927057	C₂	1	1	yes	maximal, characteristic, complemented
25	#11927053	C₂	1	1	yes	maximal, characteristic, complemented
26	C₂×#10597340	C₂	1	1	yes	maximal, characteristic, complemented
27	#123×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
28	#11927025	C₂	1	1	yes	maximal, characteristic, complemented
29	#11927016	C₂	1	1	yes	maximal, characteristic, complemented
30	C₄×D₄×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
31	C₁₉×#539	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#64545	C₂²	1	1	yes	characteristic, complemented
33	C₂×D₄×D₁₉	C₂²	1	1	yes	characteristic
34	C₂×D₄×D₁₉	C₂²	1	1	yes	characteristic
35	C₂×D₄×D₁₉	C₂²	1	1	yes	characteristic
36	C₂×#64541	C₂²	1	1	yes	characteristic
37	C₂×#64541	C₂²	1	1	yes	characteristic, complemented
38	C₂²×D₇₆	C₂²	1	1	yes	characteristic
39	C₂²×C₄×D₁₉	C₂²	1	1	yes	characteristic, complemented
40	C₂²×C₄×D₁₉	C₂²	1	1	yes	characteristic, complemented
41	C₁₉×#126	C₂²	1	1	yes	characteristic, complemented
42	C₁₉×#126	C₂²	1	1	yes	characteristic, complemented
43	C₁₉×#125	C₂²	1	1	yes	characteristic, complemented
44	C₁₉×#125	C₂²	1	1	yes	characteristic, complemented
45	C₁₉×#123	C₂²	1	1	yes	characteristic, complemented
46	C₁₉×#123	C₂²	1	1	yes	characteristic, complemented
47	C₁₉×#123	C₂²	1	1	yes	characteristic, complemented
48	C₁₉×#123	C₂²	1	1	yes	characteristic, complemented
49	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
50	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
51	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
52	C₁₉×#121	C₂²	1	1	yes	characteristic
53	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
54	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
56	#10597393	C₂²	1	1	yes	characteristic, complemented
57	#10597392	C₂²	1	1	yes	characteristic, complemented
58	#10597390	C₂²	1	1	yes	characteristic, complemented
59	#10597386	C₂²	1	1	yes	characteristic
60	#10597385	C₂²	1	1	yes	characteristic, complemented
61	#10597385	C₂²	1	1	yes	characteristic, complemented
62	#10597385	C₂²	1	1	yes	characteristic, complemented
63	#10597383	C₂²	1	1	yes	characteristic
64	#10597383	C₂²	1	1	yes	characteristic
65	#10597381	C₂²	1	1	yes	characteristic, complemented
66	D₄×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
67	D₄×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
68	#10597376	C₂²	1	1	yes	characteristic, complemented
69	#10597375	C₂²	1	1	yes	characteristic, complemented
70	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
71	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
72	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic, complemented
73	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic, complemented
74	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic, complemented
75	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic, complemented
76	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic, complemented
77	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	1	yes	characteristic, complemented
78	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	1	yes	characteristic, complemented
79	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	1	yes	characteristic, complemented
80	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	1	yes	characteristic, complemented
81	#10597372	C₂²	1	1	yes	characteristic, complemented
82	C₂×Dic₁₉⋊C₄	C₂²	1	1	yes	characteristic, complemented
83	#10597344	C₂²	1	1	yes	characteristic, complemented
84	#10597344	C₂²	1	1	yes	characteristic, complemented
85	#10597344	C₂²	1	1	yes	characteristic, complemented
86	#10597344	C₂²	1	1	yes	characteristic, complemented
87	#10597344	C₂²	1	1	yes	characteristic, complemented
88	#10597344	C₂²	1	1	yes	characteristic, complemented
89	#10597343	C₂²	1	1	yes	characteristic, complemented
90	#10597343	C₂²	1	1	yes	characteristic, complemented
91	#10597342	C₂²	1	1	yes	characteristic, complemented
92	#10597342	C₂²	1	1	yes	characteristic, complemented
93	#10597342	C₂²	1	1	yes	characteristic, complemented
94	#10597342	C₂²	1	1	yes	characteristic, complemented
95	#10597342	C₂²	1	1	yes	characteristic, complemented
96	#10597341	C₂²	1	1	yes	characteristic
97	#10597341	C₂²	1	1	yes	characteristic
98	#10597341	C₂²	1	1	yes	characteristic, complemented
99	#10597341	C₂²	1	1	yes	characteristic, complemented
100	#10597341	C₂²	1	1	yes	characteristic, complemented
101	#10597341	C₂²	1	1	yes	characteristic, complemented
102	#10597340	C₂²	1	1	yes	characteristic
103	#10597340	C₂²	1	1	yes	characteristic
104	#10597340	C₂²	1	1	yes	characteristic
105	#10597340	C₂²	1	1	yes	characteristic, complemented
106	#10597340	C₂²	1	1	yes	characteristic, complemented
107	#10597340	C₂²	1	1	yes	characteristic, complemented
108	#10597340	C₂²	1	1	yes	characteristic, complemented
109	#10597340	C₂²	1	1	yes	characteristic, complemented
110	#10597340	C₂²	1	1	yes	characteristic, complemented
111	#10597340	C₂²	1	1	yes	characteristic, complemented
112	#10597340	C₂²	1	1	yes	characteristic, complemented
113	#10597340	C₂²	1	1	yes	characteristic, complemented
114	#10597340	C₂²	1	1	yes	characteristic, complemented
115	#10597340	C₂²	1	1	yes	characteristic, complemented
116	#10597339	C₂²	1	1	yes	characteristic
117	#10597339	C₂²	1	1	yes	characteristic, complemented
118	#10597339	C₂²	1	1	yes	characteristic, complemented
119	#10597339	C₂²	1	1	yes	characteristic, complemented
120	#10597339	C₂²	1	1	yes	characteristic, complemented
121	#10597339	C₂²	1	1	yes	characteristic, complemented
122	#10597339	C₂²	1	1	yes	characteristic, complemented
123	#10597339	C₂²	1	1	yes	characteristic, complemented
124	#10597338	C₂²	1	1	yes	characteristic, complemented
125	#10597338	C₂²	1	1	yes	characteristic, complemented
126	#10597338	C₂²	1	1	yes	characteristic, complemented
127	#10597338	C₂²	1	1	yes	characteristic, complemented
128	#10597338	C₂²	1	1	yes	characteristic, complemented
129	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic, complemented
130	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic, complemented
131	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic, complemented
132	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic, complemented
133	#10597335	C₂²	1	1	yes	characteristic, complemented
134	#10597335	C₂²	1	1	yes	characteristic, complemented
135	#10597335	C₂²	1	1	yes	characteristic, complemented
136	#10597333	C₂²	1	1	yes	characteristic, complemented
137	#10597333	C₂²	1	1	yes	characteristic, complemented
138	#10597333	C₂²	1	1	yes	characteristic, complemented
139	#10597332	C₂²	1	1	yes	characteristic, complemented
140	#10597332	C₂²	1	1	yes	characteristic, complemented
141	#10597331	C₂²	1	1	yes	characteristic, complemented
142	#10597331	C₂²	1	1	yes	characteristic, complemented
143	#10597331	C₂²	1	1	yes	characteristic, complemented
144	#10597331	C₂²	1	1	yes	characteristic, complemented
145	#10597331	C₂²	1	1	yes	characteristic, complemented
146	#10597330	C₂²	1	1	yes	characteristic
147	#10597330	C₂²	1	1	yes	characteristic
148	#10597330	C₂²	1	1	yes	characteristic, complemented
149	#10597330	C₂²	1	1	yes	characteristic, complemented
150	#10597330	C₂²	1	1	yes	characteristic, complemented
151	#10597330	C₂²	1	1	yes	characteristic, complemented
152	#10597329	C₂²	1	1	yes	characteristic, complemented
153	#10597329	C₂²	1	1	yes	characteristic, complemented
154	#10597329	C₂²	1	1	yes	characteristic, complemented
155	#10597329	C₂²	1	1	yes	characteristic, complemented
156	#10597328	C₂²	1	1	yes	characteristic
157	#10597328	C₂²	1	1	yes	characteristic
158	#10597328	C₂²	1	1	yes	characteristic, complemented
159	#10597328	C₂²	1	1	yes	characteristic, complemented
160	#10597328	C₂²	1	1	yes	characteristic, complemented
161	#10597328	C₂²	1	1	yes	characteristic, complemented
162	(C₂²⋊D₁₉)⋊C₄	C₂²	1	1	yes	characteristic
163	(C₂²⋊D₁₉)⋊C₄	C₂²	1	1	yes	characteristic
164	(C₂²⋊D₁₉)⋊C₄	C₂²	1	1	yes	characteristic, complemented
165	(C₂²⋊D₁₉)⋊C₄	C₂²	1	1	yes	characteristic, complemented
166	(C₂²⋊D₁₉)⋊C₄	C₂²	1	1	yes	characteristic, complemented
167	(C₂²⋊D₁₉)⋊C₄	C₂²	1	1	yes	characteristic, complemented
168	(C₂²⋊D₁₉)⋊C₄	C₂²	1	1	yes	characteristic, complemented
169	C₂²⋊C₄×D₁₉	C₂²	1	1	yes	characteristic, complemented
170	C₂²⋊C₄×D₁₉	C₂²	1	1	yes	characteristic, complemented
171	C₂²⋊C₄×D₁₉	C₂²	1	1	yes	characteristic, complemented
172	C₂²⋊C₄×D₁₉	C₂²	1	1	yes	characteristic, complemented
173	C₂²⋊C₄×D₁₉	C₂²	1	1	yes	characteristic, complemented
174	C₂²⋊C₄×D₁₉	C₂²	1	1	yes	characteristic, complemented
175	#10597325	C₂²	1	1	yes	characteristic, complemented
176	#10597324	C₂²	1	1	yes	characteristic, complemented
177	#10597324	C₂²	1	1	yes	characteristic, complemented
178	#10597323	C₂²	1	1	yes	characteristic, complemented
179	#10597322	C₂²	1	1	yes	characteristic, complemented
180	#10597321	C₂²	1	1	yes	characteristic, complemented
181	C₄×D₇₆	C₂²	1	1	yes	characteristic, complemented
182	C₄×D₇₆	C₂²	1	1	yes	characteristic, complemented
183	C₄×D₇₆	C₂²	1	1	yes	characteristic, complemented
184	#10597318	C₂²	1	1	yes	characteristic, complemented
185	#10597318	C₂²	1	1	yes	characteristic, complemented
186	C₄²×D₁₉	C₂²	1	1	yes	characteristic, complemented
187	C₂³×D₁₉	C₂³	1	1	yes	characteristic
188	C₂³×D₁₉	C₂³	1	1	yes	characteristic
189	C₂³×D₁₉	C₂³	1	1	yes	characteristic
190	C₂³×D₁₉	C₂³	1	1	yes	characteristic
191	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
192	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
193	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
194	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
195	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
196	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
197	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
198	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
199	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
200	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
201	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
202	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
209	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
210	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
211	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
212	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
213	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
214	#64545	—	4	2	no	—
215	D₄×D₁₉	—	2	4	no	—
216	D₄×D₁₉	—	2	4	no	—
217	D₄×D₁₉	—	4	2	no	—
218	#64541	—	2	4	no	—
219	#64541	—	4	2	no	—
220	C₂×D₇₆	—	4	2	no	—
221	C₂×D₇₆	C₂³	1	1	yes	characteristic
222	C₂×D₇₆	C₂³	1	1	yes	characteristic
223	C₂×D₇₆	C₂³	1	1	yes	characteristic
224	C₂×D₇₆	C₂³	1	1	yes	characteristic
225	C₂×D₇₆	C₂³	1	1	yes	characteristic
226	C₂×D₇₆	C₂³	1	1	yes	characteristic
227	C₂×D₇₆	C₂³	1	1	yes	characteristic
228	C₂×D₇₆	C₂³	1	1	yes	characteristic
229	C₂×D₇₆	C₂³	1	1	yes	characteristic
230	C₂×D₇₆	C₂³	1	1	yes	characteristic
231	C₂×D₇₆	C₂³	1	1	yes	characteristic
232	C₂×C₄×D₁₉	—	4	2	no	—
233	C₂×C₄×D₁₉	—	4	2	no	—
234	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
235	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
236	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
237	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
238	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
239	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
240	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
241	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
242	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
243	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
244	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
245	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
246	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
247	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
248	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
249	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
250	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
251	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
252	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
253	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
254	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
255	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
256	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
257	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
258	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
259	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
260	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
261	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
262	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
263	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
264	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
265	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
266	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
267	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
268	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
269	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
270	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
271	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
272	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
273	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
274	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
275	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
276	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
277	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
278	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
279	C₄²×C₁₉	C₂³	1	1	yes	characteristic
280	C₄²×C₁₉	C₂³	1	1	yes	characteristic
281	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
282	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
283	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
284	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
285	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
286	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
287	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
288	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
289	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
290	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
291	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
292	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
293	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
294	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
295	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
296	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
297	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
298	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
299	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
300	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
301	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
302	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
303	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
304	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
305	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
306	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
307	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
308	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
309	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
310	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
311	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
312	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
313	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
314	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
315	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
316	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
317	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
318	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
319	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
320	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
321	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
322	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
323	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
324	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
325	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
326	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
327	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
328	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
329	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
330	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
331	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
332	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
333	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
334	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
335	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
336	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
337	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
338	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
339	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
340	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
341	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
342	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
343	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
344	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
345	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
346	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
347	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
348	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
349	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
350	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
351	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
352	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
353	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
354	C₂²×D₁₉	—	2	2	no	—
355	C₂²×D₁₉	—	2	2	no	—
356	C₂²×D₁₉	—	2	2	no	—
357	C₂²×D₁₉	—	2	2	no	—
358	C₂²×D₁₉	—	2	2	no	—
359	C₂²×D₁₉	—	2	2	no	—
360	C₂²×D₁₉	—	4	1	no	—
361	C₂²×D₁₉	—	4	1	no	—
362	C₂²×D₁₉	—	4	1	no	—
363	C₂²×D₁₉	—	4	1	no	—
364	C₂²×D₁₉	—	4	1	no	—
365	C₂²×D₁₉	—	4	1	no	—
366	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
367	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
368	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
369	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
370	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
371	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
372	Q₈×C₁₉	—	4	1	no	—
373	D₄×C₁₉	—	2	2	no	—
374	D₄×C₁₉	—	2	2	no	—
375	D₄×C₁₉	—	4	1	no	—
376	C₂×C₄×C₁₉	—	2	2	no	—
377	C₂×C₄×C₁₉	—	4	1	no	—
378	C₂×C₄×C₁₉	—	4	1	no	—
379	C₂×C₄×C₁₉	—	4	1	no	—
380	C₂×C₄×C₁₉	—	4	1	no	—
381	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
382	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
383	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
384	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
385	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
386	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
387	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
388	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
389	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
390	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
391	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
392	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
393	C₂²⋊D₁₉	—	2	2	no	—
394	C₂²⋊D₁₉	—	2	2	no	—
395	C₂²⋊D₁₉	—	2	2	no	—
396	C₂²⋊D₁₉	—	2	2	no	—
397	C₂²⋊D₁₉	—	4	1	no	—
398	C₂²⋊D₁₉	—	4	1	no	—
399	C₂²⋊D₁₉	—	4	1	no	—
400	C₂²⋊D₁₉	—	4	1	no	—
401	C₂²⋊D₁₉	—	4	1	no	—
402	C₂²⋊D₁₉	#41	1	4	yes	complemented
403	C₂×Dic₁₉	—	4	1	no	—
404	C₂×Dic₁₉	—	4	1	no	—
405	C₂×Dic₁₉	—	4	1	no	—
406	C₂×Dic₁₉	—	4	1	no	—
407	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
408	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
409	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
410	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
411	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
412	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
413	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
414	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
415	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
416	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
417	D₇₆	—	2	2	no	—
418	D₇₆	—	2	2	no	—
419	D₇₆	—	2	2	no	—
420	D₇₆	—	2	2	no	—
421	D₇₆	—	2	2	no	—
422	D₇₆	—	2	2	no	—
423	D₇₆	—	4	1	no	—
424	D₇₆	—	4	1	no	—
425	D₇₆	—	4	1	no	—
426	D₇₆	—	4	1	no	—
427	D₇₆	—	4	1	no	—
428	C₄×D₁₉	—	2	2	no	—
429	C₄×D₁₉	—	2	2	no	—
430	C₄×D₁₉	—	2	2	no	—
431	C₄×D₁₉	—	2	2	no	—
432	C₄×D₁₉	—	2	2	no	—
433	C₄×D₁₉	—	2	2	no	—
434	C₄×D₁₉	—	2	2	no	—
435	C₄×D₁₉	—	4	1	no	—
436	C₄×D₁₉	—	4	1	no	—
437	C₄×D₁₉	—	4	1	no	—
438	C₄×D₁₉	—	4	1	no	—
439	C₄×D₁₉	—	4	1	no	—
440	C₄×D₁₉	—	4	1	no	—
441	C₄×D₁₉	—	4	1	no	—
442	C₄×D₁₉	—	4	1	no	—
443	C₄×D₁₉	—	4	1	no	—
444	C₄×D₁₉	—	4	1	no	—
445	C₄×D₁₉	—	4	1	no	—
446	Dic₃₈	—	2	2	no	—
447	Dic₃₈	—	4	1	no	—
448	Dic₃₈	—	4	1	no	—
449	#3513	—	19	1	no	maximal, Sylow
450	C₂²×C₁₉	—	2	1	no	—
451	C₂²×C₁₉	—	2	1	no	—
452	C₂²×C₁₉	—	2	1	no	—
453	C₂²×C₁₉	—	2	1	no	—
454	C₂²×C₁₉	—	2	1	no	—
455	C₂²×C₁₉	—	2	1	no	—
456	C₂²×C₁₉	—	2	1	no	—
457	C₂²×C₁₉	—	2	1	no	—
458	C₂²×C₁₉	C₂×#41	1	2	yes	—
459	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
460	C₂×D₁₉	—	2	1	no	—
461	C₂×D₁₉	—	2	1	no	—
462	C₂×D₁₉	—	2	1	no	—
463	C₂×D₁₉	—	2	1	no	—
464	C₂×D₁₉	—	2	1	no	—
465	C₂×D₁₉	—	2	1	no	—
466	C₂×D₁₉	—	2	1	no	—
467	C₂×D₁₉	—	2	1	no	—
468	C₂×D₁₉	—	2	1	no	—
469	C₂×D₁₉	—	2	1	no	—
470	C₂×D₁₉	—	2	1	no	—
471	C₂×D₁₉	—	2	1	no	—
472	C₂×D₁₉	—	2	1	no	—
473	C₂×D₁₉	—	2	1	no	—
474	C₂×D₁₉	—	2	1	no	—
475	C₂×D₁₉	—	2	1	no	—
476	C₂×D₁₉	—	4	4	no	—
477	C₂×D₁₉	—	4	4	no	—
478	C₂×D₁₉	—	8	2	no	—
479	C₂×D₁₉	—	8	2	no	—
480	C₂×D₁₉	C₂×#41	1	2	yes	—
481	C₂×D₁₉	H(5,𝔽₂)	1	2	yes	—
482	C₄×C₁₉	—	2	1	no	—
483	C₄×C₁₉	—	2	1	no	—
484	C₄×C₁₉	—	2	1	no	—
485	C₄×C₁₉	—	2	1	no	—
486	C₄×C₁₉	—	2	1	no	—
487	C₄×C₁₉	—	2	1	no	—
488	C₄×C₁₉	—	2	1	no	—
489	C₄×C₁₉	—	2	1	no	—
490	C₄×C₁₉	—	2	1	no	—
491	C₄×C₁₉	—	2	1	no	—
492	C₄×C₁₉	—	2	1	no	—
493	C₄×C₁₉	—	2	1	no	—
494	Dic₁₉	—	2	1	no	—
495	Dic₁₉	—	2	1	no	—
496	Dic₁₉	—	2	1	no	—
497	Dic₁₉	—	2	1	no	—
498	Dic₁₉	—	2	1	no	—
499	Dic₁₉	—	2	1	no	—
500	Dic₁₉	—	2	1	no	—
501	Dic₁₉	—	2	1	no	—
502	Dic₁₉	—	2	1	no	—
503	Dic₁₉	C₂×#41	1	2	yes	—
504	#559	—	19	1	no	—
505	#554	—	19	1	no	—
506	#553	—	19	1	no	—
507	#553	—	19	1	no	—
508	#553	—	19	1	no	—
509	#552	—	19	1	no	—
510	#551	—	19	1	no	—
511	#551	—	19	1	no	—
512	#551	—	19	1	no	—
513	#551	—	19	1	no	—
514	#547	—	19	1	no	—
515	#546	—	19	1	no	—
516	#546	—	19	1	no	—
517	#546	—	19	1	no	—
518	#546	—	19	1	no	—
519	D₄²	—	19	1	no	—
520	#542	—	19	1	no	—
521	#540	—	19	1	no	—
522	#539	—	19	1	no	—
523	#539	D₁₉	1	1	yes	characteristic, complemented
524	#538	—	19	1	no	—
525	#538	—	19	1	no	—
526	#529	—	19	1	no	—
527	#529	—	19	1	no	—
528	#525	—	19	1	no	—
529	#525	—	19	1	no	—
530	C₂×#123	—	19	1	no	—
531	C₂×#123	—	19	1	no	—
532	#520	—	19	1	no	—
533	#518	—	19	1	no	—
534	C₂×C₄×D₄	—	19	1	no	—
535	C₂×C₁₉	—	2	2	no	—
536	C₂×C₁₉	—	4	1	no	—
537	C₂×C₁₉	—	4	1	no	—
538	C₂×C₁₉	C₂²×#41	1	1	yes	characteristic
539	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
540	C₂×C₁₉	#585	1	1	yes	characteristic
541	D₁₉	—	2	2	no	—
542	D₁₉	—	2	2	no	—
543	D₁₉	—	4	1	no	—
544	D₁₉	—	4	1	no	—
545	D₁₉	—	4	1	no	—
546	D₁₉	—	4	1	no	—
547	C₂×#41	—	19	1	no	—
548	C₂×#41	—	19	1	no	—
549	C₂×#41	—	19	1	no	—
550	C₂²×D₄	—	19	1	no	—
551	C₂²×D₄	—	19	1	no	—
552	C₂²×D₄	—	19	1	no	—
553	C₂²×D₄	—	19	1	no	—
554	C₂³×C₄	—	19	1	no	—
555	C₂³×C₄	—	19	1	no	—
556	C₄⋊Q₈	—	19	1	no	—
557	#127	—	19	1	no	—
558	#126	—	19	1	no	—
559	#126	—	19	1	no	—
560	#126	—	19	1	no	—
561	#126	—	19	1	no	—
562	#126	—	19	1	no	—
563	#126	—	19	1	no	—
564	#126	—	19	1	no	—
565	#126	—	19	1	no	—
566	#126	C₂×D₁₉	1	1	yes	characteristic, complemented
567	#126	C₂×D₁₉	1	1	yes	characteristic, complemented
568	#125	—	19	1	no	—
569	#125	—	19	1	no	—
570	#125	—	19	1	no	—
571	#125	C₂×D₁₉	1	1	yes	characteristic, complemented
572	#125	C₂×D₁₉	1	1	yes	characteristic, complemented
573	#124	—	19	1	no	—
574	#124	—	19	1	no	—
575	#124	—	19	1	no	—
576	#124	—	19	1	no	—
577	#124	—	19	1	no	—
578	#124	—	19	1	no	—
579	#124	—	19	1	no	—
580	#123	—	19	1	no	—
581	#123	—	19	1	no	—
582	#123	—	19	1	no	—
583	#123	—	19	1	no	—
584	#123	—	19	1	no	—
585	#123	—	19	1	no	—
586	#123	—	19	1	no	—
587	#123	—	19	1	no	—
588	#123	—	19	1	no	—
589	#123	—	19	1	no	—
590	#123	—	19	1	no	—
591	#123	—	19	1	no	—
592	#123	—	19	1	no	—
593	#123	—	19	1	no	—
594	#123	—	19	1	no	—
595	#123	—	19	1	no	—
596	#123	—	19	1	no	—
597	#123	—	19	1	no	—
598	#123	—	19	1	no	—
599	#123	—	19	1	no	—
600	#123	—	19	1	no	—
601	#123	—	19	1	no	—
602	#123	C₂×D₁₉	1	1	yes	characteristic, complemented
603	#123	C₂×D₁₉	1	1	yes	characteristic, complemented
604	#123	C₂×D₁₉	1	1	yes	characteristic, complemented
605	#123	C₂×D₁₉	1	1	yes	characteristic, complemented
606	C₂²⋊Q₈	—	19	1	no	—
607	C₂²⋊Q₈	—	19	1	no	—
608	C₂²⋊Q₈	—	19	1	no	—
609	C₂²⋊Q₈	—	19	1	no	—
610	C₂²⋊Q₈	—	19	1	no	—
611	C₂²⋊Q₈	—	19	1	no	—
612	C₂²⋊Q₈	—	19	1	no	—
613	C₂²⋊Q₈	—	19	1	no	—
614	C₂²⋊Q₈	—	19	1	no	—
615	C₂²⋊Q₈	—	19	1	no	—
616	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
617	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
618	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
619	#121	—	19	1	no	—
620	#121	—	19	1	no	—
621	#121	—	19	1	no	—
622	#121	—	19	1	no	—
623	#121	—	19	1	no	—
624	#121	—	19	1	no	—
625	#121	—	19	1	no	—
626	#121	—	19	1	no	—
627	#121	—	19	1	no	—
628	#121	—	19	1	no	—
629	#121	—	19	1	no	—
630	#121	—	19	1	no	—
631	#121	—	19	1	no	—
632	#121	—	19	1	no	—
633	#121	—	19	1	no	—
634	#121	—	19	1	no	—
635	#121	C₂×D₁₉	1	1	yes	characteristic
636	#120	—	19	1	no	—
637	#120	—	19	1	no	—
638	#120	—	19	1	no	—
639	#120	—	19	1	no	—
640	#120	—	19	1	no	—
641	#120	—	19	1	no	—
642	#120	—	19	1	no	—
643	#120	—	19	1	no	—
644	C₄×Q₈	—	19	1	no	—
645	C₄×Q₈	—	19	1	no	—
646	C₄×Q₈	—	19	1	no	—
647	C₄×D₄	—	19	1	no	—
648	C₄×D₄	—	19	1	no	—
649	C₄×D₄	—	19	1	no	—
650	C₄×D₄	—	19	1	no	—
651	C₄×D₄	—	19	1	no	—
652	C₄×D₄	—	19	1	no	—
653	C₄×D₄	—	19	1	no	—
654	C₄×D₄	—	19	1	no	—
655	C₄×D₄	—	19	1	no	—
656	C₄×D₄	—	19	1	no	—
657	C₄×D₄	—	19	1	no	—
658	C₄×D₄	—	19	1	no	—
659	C₄×D₄	—	19	1	no	—
660	C₄×D₄	—	19	1	no	—
661	C₄×D₄	—	19	1	no	—
662	C₄×D₄	—	19	1	no	—
663	C₄×D₄	—	19	1	no	—
664	C₄×D₄	—	19	1	no	—
665	C₄×D₄	—	19	1	no	—
666	C₄×D₄	—	19	1	no	—
667	C₄×D₄	—	19	1	no	—
668	C₄×D₄	—	19	1	no	—
669	C₄×D₄	—	19	1	no	—
670	C₄×D₄	—	19	1	no	—
671	C₄×D₄	—	19	1	no	—
672	C₄×D₄	—	19	1	no	—
673	C₄×D₄	—	19	1	no	—
674	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic, complemented
675	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic, complemented
676	#117	—	19	1	no	—
677	#117	—	19	1	no	—
678	#117	—	19	1	no	—
679	#117	—	19	1	no	—
680	#117	—	19	1	no	—
681	#117	—	19	1	no	—
682	#117	—	19	1	no	—
683	#117	—	19	1	no	—
684	#117	—	19	1	no	—
685	C₂×C₄⋊C₄	—	19	1	no	—
686	C₂×C₄⋊C₄	—	19	1	no	—
687	C₂×C₄⋊C₄	—	19	1	no	—
688	C₂×C₄⋊C₄	—	19	1	no	—
689	C₂×C₄⋊C₄	—	19	1	no	—
690	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic, complemented
691	C₂×C₂²⋊C₄	—	19	1	no	—
692	C₂×C₂²⋊C₄	—	19	1	no	—
693	C₂×C₂²⋊C₄	—	19	1	no	—
694	C₂×C₂²⋊C₄	—	19	1	no	—
695	C₂×C₂²⋊C₄	—	19	1	no	—
696	C₂×C₂²⋊C₄	—	19	1	no	—
697	C₂×C₂²⋊C₄	—	19	1	no	—
698	C₂×C₂²⋊C₄	—	19	1	no	—
699	C₂×C₂²⋊C₄	—	19	1	no	—
700	C₂×C₂²⋊C₄	—	19	1	no	—
701	C₂×C₄²	—	19	1	no	—
702	C₁₉	#3513	1	1	yes	characteristic, complemented, Sylow
703	C₂⁴	—	19	1	no	—
704	C₂⁴	—	19	1	no	—
705	C₂⁴	—	19	1	no	—
706	C₂⁴	—	19	1	no	—
707	#41	—	38	4	no	—
708	#41	—	76	2	no	—
709	#41	—	76	2	no	—
710	C₂×Q₈	—	19	1	no	—
711	C₂×Q₈	—	19	1	no	—
712	C₂×Q₈	—	19	1	no	—
713	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
714	C₂×D₄	—	19	1	no	—
715	C₂×D₄	—	19	1	no	—
716	C₂×D₄	—	19	1	no	—
717	C₂×D₄	—	19	1	no	—
718	C₂×D₄	—	19	1	no	—
719	C₂×D₄	—	19	1	no	—
720	C₂×D₄	—	19	1	no	—
721	C₂×D₄	—	19	1	no	—
722	C₂×D₄	—	19	1	no	—
723	C₂×D₄	—	19	1	no	—
724	C₂×D₄	—	19	1	no	—
725	C₂×D₄	—	19	1	no	—
726	C₂×D₄	—	19	1	no	—
727	C₂×D₄	—	19	1	no	—
728	C₂×D₄	—	19	1	no	—
729	C₂×D₄	—	19	1	no	—
730	C₂×D₄	—	19	1	no	—
731	C₂×D₄	—	19	1	no	—
732	C₂×D₄	—	19	1	no	—
733	C₂×D₄	—	19	1	no	—
734	C₂×D₄	—	19	1	no	—
735	C₂×D₄	—	38	4	no	—
736	C₂×D₄	—	38	4	no	—
737	C₂×D₄	—	76	2	no	—
738	C₂×D₄	—	76	2	no	—
739	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
740	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
741	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
742	C₂²×C₄	—	19	1	no	—
743	C₂²×C₄	—	19	1	no	—
744	C₂²×C₄	—	19	1	no	—
745	C₂²×C₄	—	19	1	no	—
746	C₂²×C₄	—	19	1	no	—
747	C₂²×C₄	—	19	1	no	—
748	C₂²×C₄	—	19	1	no	—
749	C₂²×C₄	—	19	1	no	—
750	C₂²×C₄	—	19	1	no	—
751	C₂²×C₄	—	19	1	no	—
752	C₂²×C₄	—	19	1	no	—
753	C₂²×C₄	—	19	1	no	—
754	C₂²×C₄	—	19	1	no	—
755	C₂²×C₄	—	19	1	no	—
756	C₂²×C₄	—	19	1	no	—
757	C₂²×C₄	—	19	1	no	—
758	C₂²×C₄	—	19	1	no	—
759	C₂²×C₄	—	19	1	no	—
760	C₂²×C₄	—	19	1	no	—
761	C₂²×C₄	—	19	1	no	—
762	C₂²×C₄	—	19	1	no	—
763	C₂²×C₄	—	19	1	no	—
764	C₂²×C₄	—	76	2	no	—
765	C₂²×C₄	—	76	2	no	—
766	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
767	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
768	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
769	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
770	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
771	C₄⋊C₄	—	19	1	no	—
772	C₄⋊C₄	—	19	1	no	—
773	C₄⋊C₄	—	19	1	no	—
774	C₄⋊C₄	—	19	1	no	—
775	C₄⋊C₄	—	19	1	no	—
776	C₄⋊C₄	—	19	1	no	—
777	C₄⋊C₄	—	19	1	no	—
778	C₄⋊C₄	—	19	1	no	—
779	C₄⋊C₄	—	19	1	no	—
780	C₄⋊C₄	—	19	1	no	—
781	C₄⋊C₄	—	19	1	no	—
782	C₄⋊C₄	—	19	1	no	—
783	C₄⋊C₄	—	19	1	no	—
784	C₄⋊C₄	—	19	1	no	—
785	C₄⋊C₄	—	19	1	no	—
786	C₄⋊C₄	—	19	1	no	—
787	C₄⋊C₄	—	19	1	no	—
788	C₄⋊C₄	—	19	1	no	—
789	C₄⋊C₄	—	19	1	no	—
790	C₄⋊C₄	—	19	1	no	—
791	C₄⋊C₄	—	19	1	no	—
792	C₄⋊C₄	—	19	1	no	—
793	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
794	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
795	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
796	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
797	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
798	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
799	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
800	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
801	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
802	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
803	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
804	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
805	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
806	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
807	C₂²⋊C₄	—	19	1	no	—
808	C₂²⋊C₄	—	19	1	no	—
809	C₂²⋊C₄	—	19	1	no	—
810	C₂²⋊C₄	—	19	1	no	—
811	C₂²⋊C₄	—	19	1	no	—
812	C₂²⋊C₄	—	19	1	no	—
813	C₂²⋊C₄	—	19	1	no	—
814	C₂²⋊C₄	—	19	1	no	—
815	C₂²⋊C₄	—	19	1	no	—
816	C₂²⋊C₄	—	19	1	no	—
817	C₂²⋊C₄	—	19	1	no	—
818	C₂²⋊C₄	—	19	1	no	—
819	C₂²⋊C₄	—	19	1	no	—
820	C₂²⋊C₄	—	19	1	no	—
821	C₂²⋊C₄	—	19	1	no	—
822	C₂²⋊C₄	—	19	1	no	—
823	C₂²⋊C₄	—	19	1	no	—
824	C₂²⋊C₄	—	19	1	no	—
825	C₂²⋊C₄	—	19	1	no	—
826	C₂²⋊C₄	—	19	1	no	—
827	C₂²⋊C₄	—	19	1	no	—
828	C₂²⋊C₄	—	19	1	no	—
829	C₂²⋊C₄	—	19	1	no	—
830	C₂²⋊C₄	—	19	1	no	—
831	C₂²⋊C₄	—	19	1	no	—
832	C₂²⋊C₄	—	19	1	no	—
833	C₂²⋊C₄	—	19	1	no	—
834	C₂²⋊C₄	—	19	1	no	—
835	C₂²⋊C₄	—	19	1	no	—
836	C₂²⋊C₄	—	19	1	no	—
837	C₂²⋊C₄	—	19	1	no	—
838	C₂²⋊C₄	—	19	1	no	—
839	C₂²⋊C₄	—	19	1	no	—
840	C₂²⋊C₄	—	19	1	no	—
841	C₂²⋊C₄	—	19	1	no	—
842	C₂²⋊C₄	—	19	1	no	—
843	C₂²⋊C₄	—	19	1	no	—
844	C₂²⋊C₄	—	19	1	no	—
845	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
846	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
847	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
848	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
849	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
850	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
851	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
852	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
853	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
854	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
855	C₄²	—	19	1	no	—
856	C₄²	—	19	1	no	—
857	C₄²	—	19	1	no	—
858	C₄²	—	19	1	no	—
859	C₄²	—	19	1	no	—
860	C₄²	—	19	1	no	—
861	C₄²	—	19	1	no	—
862	C₄²	—	19	1	no	—
863	C₄²	—	19	1	no	—
864	C₄²	—	19	1	no	—
865	C₄²	C₂²×D₁₉	1	1	yes	characteristic
866	C₄²	C₂²×D₁₉	1	1	yes	characteristic
867	C₂³	—	19	1	no	—
868	C₂³	—	19	1	no	—
869	C₂³	—	19	1	no	—
870	C₂³	—	19	1	no	—
871	C₂³	—	19	1	no	—
872	C₂³	—	19	1	no	—
873	C₂³	—	38	2	no	—
874	C₂³	—	38	2	no	—
875	C₂³	—	38	2	no	—
876	C₂³	—	38	2	no	—
877	C₂³	—	38	2	no	—
878	C₂³	—	38	2	no	—
879	C₂³	—	76	1	no	—
880	C₂³	—	76	1	no	—
881	C₂³	—	76	1	no	—
882	C₂³	—	76	1	no	—
883	C₂³	—	76	1	no	—
884	C₂³	—	76	1	no	—
885	C₂³	C₂³×D₁₉	1	1	yes	characteristic
886	C₂³	C₂³×D₁₉	1	1	yes	characteristic
887	C₂³	C₂³×D₁₉	1	1	yes	characteristic
888	Q₈	—	4	1	no	—
889	Q₈	—	38	2	no	—
890	Q₈	—	76	1	no	—
891	Q₈	—	76	1	no	—
892	D₄	—	2	2	no	—
893	D₄	—	2	2	no	—
894	D₄	—	4	1	no	—
895	D₄	—	19	4	no	—
896	D₄	—	38	2	no	—
897	D₄	—	38	2	no	—
898	D₄	—	38	2	no	—
899	D₄	—	38	2	no	—
900	D₄	—	38	2	no	—
901	D₄	—	38	2	no	—
902	D₄	—	38	2	no	—
903	D₄	—	38	2	no	—
904	D₄	—	38	2	no	—
905	D₄	—	38	2	no	—
906	D₄	—	76	1	no	—
907	D₄	—	76	1	no	—
908	D₄	—	76	1	no	—
909	D₄	—	76	1	no	—
910	D₄	—	76	1	no	—
911	D₄	—	76	1	no	—
912	D₄	—	76	1	no	—
913	D₄	—	76	1	no	—
914	D₄	—	76	1	no	—
915	D₄	—	76	1	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	4	1	no	—
918	C₂×C₄	—	4	1	no	—
919	C₂×C₄	—	4	1	no	—
920	C₂×C₄	—	4	1	no	—
921	C₂×C₄	—	19	1	no	—
922	C₂×C₄	—	19	1	no	—
923	C₂×C₄	—	19	1	no	—
924	C₂×C₄	—	19	1	no	—
925	C₂×C₄	—	19	1	no	—
926	C₂×C₄	—	19	1	no	—
927	C₂×C₄	—	19	1	no	—
928	C₂×C₄	—	19	1	no	—
929	C₂×C₄	—	19	1	no	—
930	C₂×C₄	—	19	1	no	—
931	C₂×C₄	—	38	2	no	—
932	C₂×C₄	—	38	2	no	—
933	C₂×C₄	—	38	2	no	—
934	C₂×C₄	—	38	2	no	—
935	C₂×C₄	—	38	2	no	—
936	C₂×C₄	—	38	2	no	—
937	C₂×C₄	—	38	2	no	—
938	C₂×C₄	—	76	1	no	—
939	C₂×C₄	—	76	1	no	—
940	C₂×C₄	—	76	1	no	—
941	C₂×C₄	—	76	1	no	—
942	C₂×C₄	—	76	1	no	—
943	C₂×C₄	—	76	1	no	—
944	C₂×C₄	—	76	1	no	—
945	C₂×C₄	—	76	1	no	—
946	C₂×C₄	—	76	1	no	—
947	C₂×C₄	—	76	1	no	—
948	C₂×C₄	—	76	1	no	—
949	C₂×C₄	—	76	1	no	—
950	C₂×C₄	—	76	1	no	—
951	C₂×C₄	—	76	1	no	—
952	C₂×C₄	—	76	1	no	—
953	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
954	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
955	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
956	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
957	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
958	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
959	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
960	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
961	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
962	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
963	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
964	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
965	C₂²	—	2	1	no	—
966	C₂²	—	2	1	no	—
967	C₂²	—	2	1	no	—
968	C₂²	—	2	1	no	—
969	C₂²	—	2	1	no	—
970	C₂²	—	2	1	no	—
971	C₂²	—	2	1	no	—
972	C₂²	—	2	1	no	—
973	C₂²	—	19	2	no	—
974	C₂²	—	19	2	no	—
975	C₂²	—	38	1	no	—
976	C₂²	—	38	1	no	—
977	C₂²	—	38	1	no	—
978	C₂²	—	38	1	no	—
979	C₂²	—	38	1	no	—
980	C₂²	—	38	1	no	—
981	C₂²	—	38	1	no	—
982	C₂²	—	38	1	no	—
983	C₂²	—	38	1	no	—
984	C₂²	—	38	1	no	—
985	C₂²	—	38	1	no	—
986	C₂²	—	38	1	no	—
987	C₂²	—	38	1	no	—
988	C₂²	—	38	1	no	—
989	C₂²	—	38	1	no	—
990	C₂²	—	38	1	no	—
991	C₂²	—	76	4	no	—
992	C₂²	—	76	4	no	—
993	C₂²	—	152	2	no	—
994	C₂²	—	152	2	no	—
995	C₂²	#41×D₁₉	1	2	yes	—
996	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
997	C₄	—	2	1	no	—
998	C₄	—	2	1	no	—
999	C₄	—	2	1	no	—
1000	C₄	—	2	1	no	—
1001	C₄	—	2	1	no	—
1002	C₄	—	2	1	no	—
1003	C₄	—	2	1	no	—
1004	C₄	—	2	1	no	—
1005	C₄	—	2	1	no	—
1006	C₄	—	2	1	no	—
1007	C₄	—	2	1	no	—
1008	C₄	—	2	1	no	—
1009	C₄	—	19	2	no	—
1010	C₄	—	38	1	no	—
1011	C₄	—	38	1	no	—
1012	C₄	—	38	1	no	—
1013	C₄	—	38	1	no	—
1014	C₄	—	38	1	no	—
1015	C₄	—	38	1	no	—
1016	C₄	—	38	1	no	—
1017	C₄	—	38	1	no	—
1018	C₄	—	38	1	no	—
1019	C₂	—	2	2	no	—
1020	C₂	—	4	1	no	—
1021	C₂	—	4	1	no	—
1022	C₂	—	38	2	no	—
1023	C₂	—	38	2	no	—
1024	C₂	—	76	1	no	—
1025	C₂	—	76	1	no	—
1026	C₂	—	76	1	no	—
1027	C₂	—	76	1	no	—
1028	C₂	C₂×#41×D₁₉	1	1	yes	characteristic
1029	C₂	H(5,𝔽₂)×D₁₉	1	1	yes	characteristic
1030	C₂	#11927381	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₁₉×#539	C₂
hypercenter	#539	D₁₉
hypocenter	C₁₉	#3513
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ #539

Complements

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

N	H ≅ G/N	type
1. #11927278	C₂	semidirect
2. #11927248	C₂	semidirect
3. #11927247	C₂	semidirect
4. #11927245	C₂	semidirect
5. #11927237	C₂	semidirect
6. #11927226	C₂	semidirect
7. #11927221	C₂	semidirect
8. #11927219	C₂	semidirect
9. #11927217	C₂	semidirect
10. #11927217	C₂	semidirect
11. #11927196	C₂	semidirect
12. #11927186	C₂	semidirect
13. #11927186	C₂	semidirect
14. #11927186	C₂	semidirect
15. #11927185	C₂	semidirect
16. #11927178	C₂	semidirect
17. #11927164	C₂	semidirect
18. #11927146	C₂	semidirect
19. #11927142	C₂	semidirect
20. #11927133	C₂	semidirect
21. #11927127	C₂	semidirect
22. #11927079	C₂	semidirect
23. #11927077	C₂	semidirect
24. #11927057	C₂	semidirect
25. #11927053	C₂	semidirect
26. C₂×#10597340	C₂	semidirect
27. #123×D₁₉	C₂	semidirect
28. #11927025	C₂	semidirect
29. #11927016	C₂	semidirect
30. C₄×D₄×D₁₉	C₂	semidirect
31. C₁₉×#539	C₂	semidirect
32. C₂×#64545	C₂²	semidirect
37. C₂×#64541	C₂²	semidirect
39. C₂²×C₄×D₁₉	C₂²	semidirect
40. C₂²×C₄×D₁₉	C₂²	semidirect
41. C₁₉×#126	C₂²	semidirect
42. C₁₉×#126	C₂²	semidirect
43. C₁₉×#125	C₂²	semidirect
44. C₁₉×#125	C₂²	semidirect
45. C₁₉×#123	C₂²	semidirect
46. C₁₉×#123	C₂²	semidirect
47. C₁₉×#123	C₂²	semidirect
48. C₁₉×#123	C₂²	semidirect
49. C₁₉×C₂²⋊Q₈	C₂²	semidirect
50. C₁₉×C₂²⋊Q₈	C₂²	semidirect
51. C₁₉×C₂²⋊Q₈	C₂²	semidirect
53. C₄×D₄×C₁₉	C₂²	semidirect
54. C₄×D₄×C₁₉	C₂²	semidirect
55. C₂×C₄⋊C₄×C₁₉	C₂²	semidirect
56. #10597393	C₂²	semidirect
57. #10597392	C₂²	semidirect
58. #10597390	C₂²	semidirect
60. #10597385	C₂²	semidirect
61. #10597385	C₂²	semidirect
62. #10597385	C₂²	semidirect
65. #10597381	C₂²	semidirect
66. D₄×Dic₁₉	C₂²	semidirect
67. D₄×Dic₁₉	C₂²	semidirect
68. #10597376	C₂²	semidirect
69. #10597375	C₂²	semidirect
72. C₄×C₂²⋊D₁₉	C₂²	semidirect
73. C₄×C₂²⋊D₁₉	C₂²	semidirect
74. C₄×C₂²⋊D₁₉	C₂²	semidirect
75. C₄×C₂²⋊D₁₉	C₂²	semidirect
76. C₄×C₂²⋊D₁₉	C₂²	semidirect
77. C₂×(C₂×D₁₉)⋊C₄	C₂²	semidirect
78. C₂×(C₂×D₁₉)⋊C₄	C₂²	semidirect
79. C₂×(C₂×D₁₉)⋊C₄	C₂²	semidirect
80. C₂×(C₂×D₁₉)⋊C₄	C₂²	semidirect
81. #10597372	C₂²	semidirect
82. C₂×Dic₁₉⋊C₄	C₂²	semidirect
83. #10597344	C₂²	semidirect
84. #10597344	C₂²	semidirect
85. #10597344	C₂²	semidirect
86. #10597344	C₂²	semidirect
87. #10597344	C₂²	semidirect
88. #10597344	C₂²	semidirect
89. #10597343	C₂²	semidirect
90. #10597343	C₂²	semidirect
91. #10597342	C₂²	semidirect
92. #10597342	C₂²	semidirect
93. #10597342	C₂²	semidirect
94. #10597342	C₂²	semidirect
95. #10597342	C₂²	semidirect
98. #10597341	C₂²	semidirect
99. #10597341	C₂²	semidirect
100. #10597341	C₂²	semidirect
101. #10597341	C₂²	semidirect
105. #10597340	C₂²	semidirect
106. #10597340	C₂²	semidirect
107. #10597340	C₂²	semidirect
108. #10597340	C₂²	semidirect
109. #10597340	C₂²	semidirect
110. #10597340	C₂²	semidirect
111. #10597340	C₂²	semidirect
112. #10597340	C₂²	semidirect
113. #10597340	C₂²	semidirect
114. #10597340	C₂²	semidirect
115. #10597340	C₂²	semidirect
117. #10597339	C₂²	semidirect
118. #10597339	C₂²	semidirect
119. #10597339	C₂²	semidirect
120. #10597339	C₂²	semidirect
121. #10597339	C₂²	semidirect
122. #10597339	C₂²	semidirect
123. #10597339	C₂²	semidirect
124. #10597338	C₂²	semidirect
125. #10597338	C₂²	semidirect
126. #10597338	C₂²	semidirect
127. #10597338	C₂²	semidirect
128. #10597338	C₂²	semidirect
129. C₄⋊C₄×D₁₉	C₂²	semidirect
130. C₄⋊C₄×D₁₉	C₂²	semidirect
131. C₄⋊C₄×D₁₉	C₂²	semidirect
132. C₄⋊C₄×D₁₉	C₂²	semidirect
133. #10597335	C₂²	semidirect
134. #10597335	C₂²	semidirect
135. #10597335	C₂²	semidirect
136. #10597333	C₂²	semidirect
137. #10597333	C₂²	semidirect
138. #10597333	C₂²	semidirect
139. #10597332	C₂²	semidirect
140. #10597332	C₂²	semidirect
141. #10597331	C₂²	semidirect
142. #10597331	C₂²	semidirect
143. #10597331	C₂²	semidirect
144. #10597331	C₂²	semidirect
145. #10597331	C₂²	semidirect
148. #10597330	C₂²	semidirect
149. #10597330	C₂²	semidirect
150. #10597330	C₂²	semidirect
151. #10597330	C₂²	semidirect
152. #10597329	C₂²	semidirect
153. #10597329	C₂²	semidirect
154. #10597329	C₂²	semidirect
155. #10597329	C₂²	semidirect
158. #10597328	C₂²	semidirect
159. #10597328	C₂²	semidirect
160. #10597328	C₂²	semidirect
161. #10597328	C₂²	semidirect
164. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
165. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
166. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
167. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
168. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
169. C₂²⋊C₄×D₁₉	C₂²	semidirect
170. C₂²⋊C₄×D₁₉	C₂²	semidirect
171. C₂²⋊C₄×D₁₉	C₂²	semidirect
172. C₂²⋊C₄×D₁₉	C₂²	semidirect
173. C₂²⋊C₄×D₁₉	C₂²	semidirect
174. C₂²⋊C₄×D₁₉	C₂²	semidirect
175. #10597325	C₂²	semidirect
176. #10597324	C₂²	semidirect
177. #10597324	C₂²	semidirect
178. #10597323	C₂²	semidirect
179. #10597322	C₂²	semidirect
180. #10597321	C₂²	semidirect
181. C₄×D₇₆	C₂²	semidirect
182. C₄×D₇₆	C₂²	semidirect
183. C₄×D₇₆	C₂²	semidirect
184. #10597318	C₂²	semidirect
185. #10597318	C₂²	semidirect
186. C₄²×D₁₉	C₂²	semidirect
402. C₂²⋊D₁₉	#41	semidirect
523. #539	D₁₉	semidirect
566. #126	C₂×D₁₉	semidirect
567. #126	C₂×D₁₉	semidirect
571. #125	C₂×D₁₉	semidirect
572. #125	C₂×D₁₉	semidirect
602. #123	C₂×D₁₉	semidirect
603. #123	C₂×D₁₉	semidirect
604. #123	C₂×D₁₉	semidirect
605. #123	C₂×D₁₉	semidirect
616. C₂²⋊Q₈	C₂×D₁₉	semidirect
617. C₂²⋊Q₈	C₂×D₁₉	semidirect
618. C₂²⋊Q₈	C₂×D₁₉	semidirect
674. C₄×D₄	C₂×D₁₉	semidirect
675. C₄×D₄	C₂×D₁₉	semidirect
690. C₂×C₄⋊C₄	C₂×D₁₉	semidirect
702. C₁₉	#3513	semidirect

Maximal subgroups

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

subgroup	index
#11927278	2
#11927248	2
#11927247	2
#11927245	2
#11927237	2
#11927226	2
#11927221	2
#11927219	2
#11927217	2
#11927196	2
#11927186	2
#11927185	2
#11927178	2
#11927164	2
#11927146	2
#11927142	2
#11927133	2
#11927127	2
#11927079	2
#11927077	2
#11927057	2
#11927053	2
C₂×#10597340	2
#123×D₁₉	2
#11927025	2
#11927016	2
C₄×D₄×D₁₉	2
C₁₉×#539	2
#3513	19