Subgroups — #14578178

Order 2432.

1056 conjugacy classes of subgroups.

The subgroup lattice has 1016 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927293	C₂	1	1	yes	maximal, characteristic, complemented
2	#11927285	C₂	1	1	yes	maximal, characteristic, complemented
3	#11927285	C₂	1	1	yes	maximal, characteristic, complemented
4	#11927247	C₂	1	1	yes	maximal, characteristic, complemented
5	#11927247	C₂	1	1	yes	maximal, characteristic, complemented
6	#11927245	C₂	1	1	yes	maximal, characteristic, complemented
7	#11927239	C₂	1	1	yes	maximal, characteristic, complemented
8	#11927221	C₂	1	1	yes	maximal, characteristic, complemented
9	#11927219	C₂	1	1	yes	maximal, characteristic, complemented
10	#11927197	C₂	1	1	yes	maximal, characteristic, complemented
11	#11927196	C₂	1	1	yes	maximal, characteristic, complemented
12	#11927187	C₂	1	1	yes	maximal, characteristic, complemented
13	#11927186	C₂	1	1	yes	maximal, characteristic, complemented
14	#11927185	C₂	1	1	yes	maximal, characteristic, complemented
15	#11927185	C₂	1	1	yes	maximal, characteristic, complemented
16	#11927168	C₂	1	1	yes	maximal, characteristic, complemented
17	#11927164	C₂	1	1	yes	maximal, characteristic, complemented
18	#11927142	C₂	1	1	yes	maximal, characteristic, complemented
19	#11927142	C₂	1	1	yes	maximal, characteristic, complemented
20	#11927140	C₂	1	1	yes	maximal, characteristic, complemented
21	#11927134	C₂	1	1	yes	maximal, characteristic, complemented
22	#11927133	C₂	1	1	yes	maximal, characteristic, complemented
23	#11927133	C₂	1	1	yes	maximal, characteristic, complemented
24	#11927130	C₂	1	1	yes	maximal, characteristic, complemented
25	#11927128	C₂	1	1	yes	maximal, characteristic, complemented
26	#11927124	C₂	1	1	yes	maximal, characteristic, complemented
27	#11927105	C₂	1	1	yes	maximal, characteristic, complemented
28	#11927095	C₂	1	1	yes	maximal, characteristic, complemented
29	#11927077	C₂	1	1	yes	maximal, characteristic, complemented
30	#126×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
31	C₁₉×#563	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#64545	C₂²	1	1	yes	characteristic, complemented
33	C₂×#64545	C₂²	1	1	yes	characteristic, complemented
34	C₂×#64545	C₂²	1	1	yes	characteristic, complemented
35	C₂×D₄×D₁₉	C₂²	1	1	yes	characteristic
36	C₂×#64541	C₂²	1	1	yes	characteristic, complemented
37	C₂²×D₇₆	C₂²	1	1	yes	characteristic
38	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
39	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
40	C₁₉×#126	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×#126	C₂²	1	1	yes	characteristic, complemented
44	C₁₉×#125	C₂²	1	1	yes	characteristic, complemented
45	C₁₉×#125	C₂²	1	1	yes	characteristic, complemented
46	C₁₉×#124	C₂²	1	1	yes	characteristic
47	C₁₉×#123	C₂²	1	1	yes	characteristic
48	C₁₉×#123	C₂²	1	1	yes	characteristic
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×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
53	#10597393	C₂²	1	1	yes	characteristic
54	#10597393	C₂²	1	1	yes	characteristic
55	#10597393	C₂²	1	1	yes	characteristic, complemented
56	#10597393	C₂²	1	1	yes	characteristic, complemented
57	#10597392	C₂²	1	1	yes	characteristic, complemented
58	#10597392	C₂²	1	1	yes	characteristic, complemented
59	#10597392	C₂²	1	1	yes	characteristic, complemented
60	#10597392	C₂²	1	1	yes	characteristic, complemented
61	#10597390	C₂²	1	1	yes	characteristic, complemented
62	#10597385	C₂²	1	1	yes	characteristic
63	#10597384	C₂²	1	1	yes	characteristic
64	#10597383	C₂²	1	1	yes	characteristic
65	#10597376	C₂²	1	1	yes	characteristic, complemented
66	#10597375	C₂²	1	1	yes	characteristic
67	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic, complemented
68	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic, complemented
69	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic, complemented
70	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	1	yes	characteristic, complemented
71	#10597344	C₂²	1	1	yes	characteristic, complemented
72	#10597344	C₂²	1	1	yes	characteristic, complemented
73	#10597344	C₂²	1	1	yes	characteristic, complemented
74	#10597344	C₂²	1	1	yes	characteristic, complemented
75	#10597344	C₂²	1	1	yes	characteristic, complemented
76	#10597344	C₂²	1	1	yes	characteristic, complemented
77	#10597344	C₂²	1	1	yes	characteristic, complemented
78	#10597344	C₂²	1	1	yes	characteristic, complemented
79	#10597343	C₂²	1	1	yes	characteristic, complemented
80	#10597343	C₂²	1	1	yes	characteristic, complemented
81	#10597342	C₂²	1	1	yes	characteristic, complemented
82	#10597342	C₂²	1	1	yes	characteristic, complemented
83	#10597342	C₂²	1	1	yes	characteristic, complemented
84	#10597342	C₂²	1	1	yes	characteristic, complemented
85	#10597342	C₂²	1	1	yes	characteristic, complemented
86	#10597341	C₂²	1	1	yes	characteristic
87	#10597341	C₂²	1	1	yes	characteristic
88	#10597341	C₂²	1	1	yes	characteristic
89	#10597341	C₂²	1	1	yes	characteristic
90	#10597341	C₂²	1	1	yes	characteristic
91	#10597341	C₂²	1	1	yes	characteristic
92	#10597341	C₂²	1	1	yes	characteristic, complemented
93	#10597341	C₂²	1	1	yes	characteristic, complemented
94	#10597341	C₂²	1	1	yes	characteristic, complemented
95	#10597341	C₂²	1	1	yes	characteristic, complemented
96	#10597341	C₂²	1	1	yes	characteristic, complemented
97	#10597341	C₂²	1	1	yes	characteristic, complemented
98	#10597341	C₂²	1	1	yes	characteristic, complemented
99	#10597341	C₂²	1	1	yes	characteristic, complemented
100	#10597340	C₂²	1	1	yes	characteristic
101	#10597340	C₂²	1	1	yes	characteristic
102	#10597340	C₂²	1	1	yes	characteristic
103	#10597340	C₂²	1	1	yes	characteristic
104	#10597340	C₂²	1	1	yes	characteristic, complemented
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, complemented
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	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic, complemented
127	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic, complemented
128	C₄⋊C₄×D₁₉	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	#10597335	C₂²	1	1	yes	characteristic, complemented
132	#10597335	C₂²	1	1	yes	characteristic, complemented
133	#10597335	C₂²	1	1	yes	characteristic, complemented
134	#10597333	C₂²	1	1	yes	characteristic, complemented
135	#10597332	C₂²	1	1	yes	characteristic, complemented
136	#10597331	C₂²	1	1	yes	characteristic
137	#10597331	C₂²	1	1	yes	characteristic, complemented
138	#10597331	C₂²	1	1	yes	characteristic, complemented
139	#10597330	C₂²	1	1	yes	characteristic
140	#10597330	C₂²	1	1	yes	characteristic
141	#10597330	C₂²	1	1	yes	characteristic
142	#10597330	C₂²	1	1	yes	characteristic
143	#10597330	C₂²	1	1	yes	characteristic, complemented
144	#10597330	C₂²	1	1	yes	characteristic, complemented
145	#10597330	C₂²	1	1	yes	characteristic, complemented
146	#10597330	C₂²	1	1	yes	characteristic, complemented
147	#10597330	C₂²	1	1	yes	characteristic, complemented
148	#10597330	C₂²	1	1	yes	characteristic, complemented
149	#10597329	C₂²	1	1	yes	characteristic
150	#10597329	C₂²	1	1	yes	characteristic, complemented
151	#10597329	C₂²	1	1	yes	characteristic, complemented
152	#10597329	C₂²	1	1	yes	characteristic, complemented
153	#10597328	C₂²	1	1	yes	characteristic
154	#10597328	C₂²	1	1	yes	characteristic
155	#10597328	C₂²	1	1	yes	characteristic
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, complemented
163	(C₂²⋊D₁₉)⋊C₄	C₂²	1	1	yes	characteristic, complemented
164	(C₂²⋊D₁₉)⋊C₄	C₂²	1	1	yes	characteristic, complemented
165	C₂²⋊C₄×D₁₉	C₂²	1	1	yes	characteristic
166	C₂²⋊C₄×D₁₉	C₂²	1	1	yes	characteristic
167	C₂²⋊C₄×D₁₉	C₂²	1	1	yes	characteristic
168	C₂²⋊C₄×D₁₉	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	#10597325	C₂²	1	1	yes	characteristic, complemented
172	#10597325	C₂²	1	1	yes	characteristic, complemented
173	#10597325	C₂²	1	1	yes	characteristic, complemented
174	#10597323	C₂²	1	1	yes	characteristic, complemented
175	#10597322	C₂²	1	1	yes	characteristic, complemented
176	#10597322	C₂²	1	1	yes	characteristic, complemented
177	#10597322	C₂²	1	1	yes	characteristic, complemented
178	#10597321	C₂²	1	1	yes	characteristic, complemented
179	#10597320	C₂²	1	1	yes	characteristic, complemented
180	C₄×D₇₆	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	C₄×D₇₆	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	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
191	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
192	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
193	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
194	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
195	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
196	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
197	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
199	C₂×C₂²⋊D₁₉	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	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
205	#64545	—	4	2	no	—
206	#64545	—	4	2	no	—
207	#64545	—	4	2	no	—
208	D₄×D₁₉	—	4	2	no	—
209	#64541	—	4	2	no	—
210	C₂×D₇₆	—	4	2	no	—
211	C₂×D₇₆	C₂³	1	1	yes	characteristic
212	C₂×D₇₆	C₂³	1	1	yes	characteristic
213	C₂×D₇₆	C₂³	1	1	yes	characteristic
214	C₂×D₇₆	C₂³	1	1	yes	characteristic
215	C₂×D₇₆	C₂³	1	1	yes	characteristic
216	C₂×D₇₆	C₂³	1	1	yes	characteristic
217	C₂×D₇₆	C₂³	1	1	yes	characteristic
218	C₂×D₇₆	C₂³	1	1	yes	characteristic
219	C₂×D₇₆	C₂³	1	1	yes	characteristic
220	C₂×D₇₆	C₂³	1	1	yes	characteristic
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×C₄×D₁₉	C₂³	1	1	yes	characteristic
230	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
231	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
232	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
233	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
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×Dic₃₈	C₂³	1	1	yes	characteristic
249	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
250	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
251	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
252	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
253	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
254	C₄⋊C₄×C₁₉	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	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
267	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
268	C₂²⋊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	C₄²×C₁₉	C₂³	1	1	yes	characteristic
277	C₄²×C₁₉	C₂³	1	1	yes	characteristic
278	C₄²×C₁₉	C₂³	1	1	yes	characteristic
279	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
280	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
281	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
282	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
283	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
284	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
285	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
286	(C₂×D₁₉)⋊C₄	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	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
349	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
350	C₂²×D₁₉	—	2	2	no	—
351	C₂²×D₁₉	—	4	1	no	—
352	C₂²×D₁₉	—	4	1	no	—
353	C₂²×D₁₉	—	4	1	no	—
354	C₂²×D₁₉	—	4	1	no	—
355	C₂²×D₁₉	—	4	1	no	—
356	C₂²×D₁₉	—	4	1	no	—
357	C₂²×D₁₉	—	4	1	no	—
358	C₂²×D₁₉	—	4	1	no	—
359	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
360	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
361	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
362	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
363	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
364	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
365	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
366	Q₈×C₁₉	—	4	1	no	—
367	Q₈×C₁₉	—	4	1	no	—
368	Q₈×C₁₉	—	4	1	no	—
369	D₄×C₁₉	—	4	1	no	—
370	C₂×C₄×C₁₉	—	4	1	no	—
371	C₂×C₄×C₁₉	—	4	1	no	—
372	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
373	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
374	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
375	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
376	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
377	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
378	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
379	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
380	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
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	C₂²⋊D₁₉	—	2	2	no	—
386	C₂²⋊D₁₉	—	4	1	no	—
387	C₂²⋊D₁₉	—	4	1	no	—
388	C₂²⋊D₁₉	—	4	1	no	—
389	C₂²⋊D₁₉	—	4	1	no	—
390	C₂²⋊D₁₉	—	4	1	no	—
391	C₂²⋊D₁₉	—	4	1	no	—
392	C₂²⋊D₁₉	—	4	1	no	—
393	C₂×Dic₁₉	—	4	1	no	—
394	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
395	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
396	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
397	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
398	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
399	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
400	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
401	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
402	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
403	D₇₆	—	2	2	no	—
404	D₇₆	—	2	2	no	—
405	D₇₆	—	2	2	no	—
406	D₇₆	—	2	2	no	—
407	D₇₆	—	2	2	no	—
408	D₇₆	—	4	1	no	—
409	D₇₆	—	4	1	no	—
410	D₇₆	—	4	1	no	—
411	D₇₆	—	4	1	no	—
412	D₇₆	—	4	1	no	—
413	D₇₆	—	4	1	no	—
414	D₇₆	—	4	1	no	—
415	D₇₆	—	4	1	no	—
416	D₇₆	—	4	1	no	—
417	D₇₆	—	4	1	no	—
418	D₇₆	—	4	1	no	—
419	D₇₆	—	4	1	no	—
420	D₇₆	—	4	1	no	—
421	C₄×D₁₉	—	2	2	no	—
422	C₄×D₁₉	—	2	2	no	—
423	C₄×D₁₉	—	4	1	no	—
424	C₄×D₁₉	—	4	1	no	—
425	C₄×D₁₉	—	4	1	no	—
426	C₄×D₁₉	—	4	1	no	—
427	C₄×D₁₉	—	4	1	no	—
428	C₄×D₁₉	—	4	1	no	—
429	C₄×D₁₉	—	4	1	no	—
430	C₄×D₁₉	—	4	1	no	—
431	C₄×D₁₉	—	4	1	no	—
432	C₄×D₁₉	—	4	1	no	—
433	C₄×D₁₉	—	4	1	no	—
434	C₄×D₁₉	—	4	1	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	Dic₃₈	—	4	1	no	—
441	Dic₃₈	—	4	1	no	—
442	#3560	—	19	1	no	maximal, Sylow
443	C₂²×C₁₉	—	2	1	no	—
444	C₂²×C₁₉	—	2	1	no	—
445	C₂²×C₁₉	—	2	1	no	—
446	C₂²×C₁₉	—	2	1	no	—
447	C₂²×C₁₉	—	2	1	no	—
448	C₂²×C₁₉	—	2	1	no	—
449	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
450	C₂×D₁₉	—	2	1	no	—
451	C₂×D₁₉	—	2	1	no	—
452	C₂×D₁₉	—	2	1	no	—
453	C₂×D₁₉	—	2	1	no	—
454	C₂×D₁₉	—	2	1	no	—
455	C₂×D₁₉	—	2	1	no	—
456	C₂×D₁₉	—	2	1	no	—
457	C₂×D₁₉	—	2	1	no	—
458	C₂×D₁₉	—	2	1	no	—
459	C₂×D₁₉	—	2	1	no	—
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	—	8	2	no	—
471	C₂×D₁₉	—	8	2	no	—
472	C₂×D₁₉	—	8	2	no	—
473	C₂×D₁₉	H(5,𝔽₂)	1	2	yes	—
474	C₄×C₁₉	—	2	1	no	—
475	C₄×C₁₉	—	2	1	no	—
476	C₄×C₁₉	—	2	1	no	—
477	C₄×C₁₉	—	2	1	no	—
478	C₄×C₁₉	—	2	1	no	—
479	C₄×C₁₉	—	2	1	no	—
480	C₄×C₁₉	—	2	1	no	—
481	C₄×C₁₉	—	2	1	no	—
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	Dic₁₉	—	2	1	no	—
488	Dic₁₉	—	2	1	no	—
489	Dic₁₉	—	2	1	no	—
490	Dic₁₉	—	2	1	no	—
491	Dic₁₉	—	2	1	no	—
492	Dic₁₉	—	2	1	no	—
493	Dic₁₉	—	2	1	no	—
494	Dic₁₉	—	2	1	no	—
495	Dic₁₉	—	2	1	no	—
496	#563	—	19	1	no	—
497	#563	D₁₉	1	1	yes	characteristic, complemented
498	#560	—	19	1	no	—
499	#560	—	19	1	no	—
500	#553	—	19	1	no	—
501	#553	—	19	1	no	—
502	#553	—	19	1	no	—
503	#553	—	19	1	no	—
504	#551	—	19	1	no	—
505	#551	—	19	1	no	—
506	#547	—	19	1	no	—
507	#547	—	19	1	no	—
508	#546	—	19	1	no	—
509	#546	—	19	1	no	—
510	#546	—	19	1	no	—
511	#546	—	19	1	no	—
512	#542	—	19	1	no	—
513	#542	—	19	1	no	—
514	#539	—	19	1	no	—
515	#539	—	19	1	no	—
516	#539	—	19	1	no	—
517	#538	—	19	1	no	—
518	#538	—	19	1	no	—
519	#538	—	19	1	no	—
520	#538	—	19	1	no	—
521	#538	—	19	1	no	—
522	#537	—	19	1	no	—
523	#534	—	19	1	no	—
524	#532	—	19	1	no	—
525	#529	—	19	1	no	—
526	C₂×#126	—	19	1	no	—
527	C₂×C₁₉	—	4	1	no	—
528	C₂×C₁₉	—	4	1	no	—
529	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
530	C₂×C₁₉	#585	1	1	yes	characteristic
531	C₂×C₁₉	#585	1	1	yes	characteristic
532	D₁₉	—	2	2	no	—
533	D₁₉	—	4	1	no	—
534	D₁₉	—	4	1	no	—
535	D₁₉	—	4	1	no	—
536	D₁₉	—	4	1	no	—
537	D₁₉	—	4	1	no	—
538	D₁₉	—	4	1	no	—
539	C₂×#41	—	19	1	no	—
540	C₂×#41	—	19	1	no	—
541	C₂×#41	—	19	1	no	—
542	C₂×#41	—	19	1	no	—
543	C₂²×D₄	—	19	1	no	—
544	C₂²×D₄	—	19	1	no	—
545	C₄⋊Q₈	—	19	1	no	—
546	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
547	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
548	#127	—	19	1	no	—
549	#126	—	19	1	no	—
550	#126	—	19	1	no	—
551	#126	—	19	1	no	—
552	#126	—	19	1	no	—
553	#126	—	19	1	no	—
554	#126	—	19	1	no	—
555	#126	—	19	1	no	—
556	#126	—	19	1	no	—
557	#126	—	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	C₂×D₁₉	1	1	yes	characteristic, complemented
564	#126	C₂×D₁₉	1	1	yes	characteristic, complemented
565	#126	C₂×D₁₉	1	1	yes	characteristic, complemented
566	#126	C₂×D₁₉	1	1	yes	characteristic, complemented
567	#125	—	19	1	no	—
568	#125	—	19	1	no	—
569	#125	—	19	1	no	—
570	#125	C₂×D₁₉	1	1	yes	characteristic, complemented
571	#125	C₂×D₁₉	1	1	yes	characteristic, complemented
572	#124	—	19	1	no	—
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	#124	C₂×D₁₉	1	1	yes	characteristic
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	—	19	1	no	—
603	#123	C₂×D₁₉	1	1	yes	characteristic
604	#123	C₂×D₁₉	1	1	yes	characteristic
605	C₂²⋊Q₈	—	19	1	no	—
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	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
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	—	19	1	no	—
636	#121	—	19	1	no	—
637	#121	—	19	1	no	—
638	#121	—	19	1	no	—
639	#121	—	19	1	no	—
640	#121	—	19	1	no	—
641	#121	—	19	1	no	—
642	#121	—	19	1	no	—
643	#121	—	19	1	no	—
644	#121	—	19	1	no	—
645	#121	—	19	1	no	—
646	#121	—	19	1	no	—
647	#120	—	19	1	no	—
648	#120	—	19	1	no	—
649	#120	—	19	1	no	—
650	#120	—	19	1	no	—
651	#120	—	19	1	no	—
652	#120	—	19	1	no	—
653	#120	—	19	1	no	—
654	#120	—	19	1	no	—
655	#120	—	19	1	no	—
656	#120	—	19	1	no	—
657	C₄×Q₈	—	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	—	19	1	no	—
675	C₄×D₄	—	19	1	no	—
676	C₄×D₄	—	19	1	no	—
677	#117	—	19	1	no	—
678	#117	—	19	1	no	—
679	#117	—	19	1	no	—
680	#117	—	19	1	no	—
681	C₂×C₄⋊C₄	—	19	1	no	—
682	C₂×C₄⋊C₄	—	19	1	no	—
683	C₂×C₄⋊C₄	—	19	1	no	—
684	C₂×C₄⋊C₄	—	19	1	no	—
685	C₂×C₄⋊C₄	—	19	1	no	—
686	C₂×C₂²⋊C₄	—	19	1	no	—
687	C₂×C₂²⋊C₄	—	19	1	no	—
688	C₂×C₂²⋊C₄	—	19	1	no	—
689	C₂×C₂²⋊C₄	—	19	1	no	—
690	C₂×C₂²⋊C₄	—	19	1	no	—
691	C₂×C₂²⋊C₄	—	19	1	no	—
692	C₂×C₂²⋊C₄	—	19	1	no	—
693	C₂×C₄²	—	19	1	no	—
694	C₁₉	#3560	1	1	yes	characteristic, complemented, Sylow
695	C₂⁴	—	19	1	no	—
696	C₂⁴	—	19	1	no	—
697	C₂⁴	—	19	1	no	—
698	#41	—	76	2	no	—
699	#41	—	76	2	no	—
700	#41	—	76	2	no	—
701	#41	—	76	2	no	—
702	C₂×Q₈	—	19	1	no	—
703	C₂×Q₈	—	19	1	no	—
704	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
705	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
706	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
707	C₂×D₄	—	19	1	no	—
708	C₂×D₄	—	19	1	no	—
709	C₂×D₄	—	19	1	no	—
710	C₂×D₄	—	19	1	no	—
711	C₂×D₄	—	19	1	no	—
712	C₂×D₄	—	19	1	no	—
713	C₂×D₄	—	19	1	no	—
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	—	76	2	no	—
734	C₂×D₄	—	76	2	no	—
735	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
736	C₂²×C₄	—	19	1	no	—
737	C₂²×C₄	—	19	1	no	—
738	C₂²×C₄	—	19	1	no	—
739	C₂²×C₄	—	19	1	no	—
740	C₂²×C₄	—	19	1	no	—
741	C₂²×C₄	—	19	1	no	—
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	C₂²×D₁₉	1	1	yes	characteristic
757	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
758	C₄⋊C₄	—	19	1	no	—
759	C₄⋊C₄	—	19	1	no	—
760	C₄⋊C₄	—	19	1	no	—
761	C₄⋊C₄	—	19	1	no	—
762	C₄⋊C₄	—	19	1	no	—
763	C₄⋊C₄	—	19	1	no	—
764	C₄⋊C₄	—	19	1	no	—
765	C₄⋊C₄	—	19	1	no	—
766	C₄⋊C₄	—	19	1	no	—
767	C₄⋊C₄	—	19	1	no	—
768	C₄⋊C₄	—	19	1	no	—
769	C₄⋊C₄	—	19	1	no	—
770	C₄⋊C₄	—	19	1	no	—
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	C₂²×D₁₉	1	1	yes	characteristic
781	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
782	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
783	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
784	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
785	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
786	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
787	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
788	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
789	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
790	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
791	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
792	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
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	C₂²⋊C₄	—	19	1	no	—
797	C₂²⋊C₄	—	19	1	no	—
798	C₂²⋊C₄	—	19	1	no	—
799	C₂²⋊C₄	—	19	1	no	—
800	C₂²⋊C₄	—	19	1	no	—
801	C₂²⋊C₄	—	19	1	no	—
802	C₂²⋊C₄	—	19	1	no	—
803	C₂²⋊C₄	—	19	1	no	—
804	C₂²⋊C₄	—	19	1	no	—
805	C₂²⋊C₄	—	19	1	no	—
806	C₂²⋊C₄	—	19	1	no	—
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	C₂²×D₁₉	1	1	yes	characteristic
837	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
838	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
839	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
840	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
841	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
842	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
843	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
844	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
845	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
846	C₄²	—	19	1	no	—
847	C₄²	—	19	1	no	—
848	C₄²	—	19	1	no	—
849	C₄²	—	19	1	no	—
850	C₄²	—	19	1	no	—
851	C₄²	—	19	1	no	—
852	C₄²	—	19	1	no	—
853	C₄²	C₂²×D₁₉	1	1	yes	characteristic
854	C₄²	C₂²×D₁₉	1	1	yes	characteristic
855	C₄²	C₂²×D₁₉	1	1	yes	characteristic
856	C₂³	—	19	1	no	—
857	C₂³	—	19	1	no	—
858	C₂³	—	19	1	no	—
859	C₂³	—	19	1	no	—
860	C₂³	—	19	1	no	—
861	C₂³	—	19	1	no	—
862	C₂³	—	19	1	no	—
863	C₂³	—	38	2	no	—
864	C₂³	—	76	1	no	—
865	C₂³	—	76	1	no	—
866	C₂³	—	76	1	no	—
867	C₂³	—	76	1	no	—
868	C₂³	—	76	1	no	—
869	C₂³	—	76	1	no	—
870	C₂³	—	76	1	no	—
871	C₂³	—	76	1	no	—
872	C₂³	C₂³×D₁₉	1	1	yes	characteristic
873	C₂³	C₂³×D₁₉	1	1	yes	characteristic
874	Q₈	—	4	1	no	—
875	Q₈	—	4	1	no	—
876	Q₈	—	4	1	no	—
877	Q₈	—	76	1	no	—
878	Q₈	—	76	1	no	—
879	D₄	—	4	1	no	—
880	D₄	—	38	2	no	—
881	D₄	—	38	2	no	—
882	D₄	—	38	2	no	—
883	D₄	—	38	2	no	—
884	D₄	—	38	2	no	—
885	D₄	—	38	2	no	—
886	D₄	—	76	1	no	—
887	D₄	—	76	1	no	—
888	D₄	—	76	1	no	—
889	D₄	—	76	1	no	—
890	D₄	—	76	1	no	—
891	D₄	—	76	1	no	—
892	D₄	—	76	1	no	—
893	D₄	—	76	1	no	—
894	D₄	—	76	1	no	—
895	D₄	—	76	1	no	—
896	D₄	—	76	1	no	—
897	D₄	—	76	1	no	—
898	D₄	—	76	1	no	—
899	D₄	—	76	1	no	—
900	D₄	—	76	1	no	—
901	D₄	—	76	1	no	—
902	D₄	—	76	1	no	—
903	D₄	—	76	1	no	—
904	D₄	—	76	1	no	—
905	D₄	—	76	1	no	—
906	C₂×C₄	—	4	1	no	—
907	C₂×C₄	—	4	1	no	—
908	C₂×C₄	—	19	1	no	—
909	C₂×C₄	—	19	1	no	—
910	C₂×C₄	—	19	1	no	—
911	C₂×C₄	—	19	1	no	—
912	C₂×C₄	—	19	1	no	—
913	C₂×C₄	—	19	1	no	—
914	C₂×C₄	—	19	1	no	—
915	C₂×C₄	—	19	1	no	—
916	C₂×C₄	—	19	1	no	—
917	C₂×C₄	—	38	2	no	—
918	C₂×C₄	—	38	2	no	—
919	C₂×C₄	—	76	1	no	—
920	C₂×C₄	—	76	1	no	—
921	C₂×C₄	—	76	1	no	—
922	C₂×C₄	—	76	1	no	—
923	C₂×C₄	—	76	1	no	—
924	C₂×C₄	—	76	1	no	—
925	C₂×C₄	—	76	1	no	—
926	C₂×C₄	—	76	1	no	—
927	C₂×C₄	—	76	1	no	—
928	C₂×C₄	—	76	1	no	—
929	C₂×C₄	—	76	1	no	—
930	C₂×C₄	—	76	1	no	—
931	C₂×C₄	—	76	1	no	—
932	C₂×C₄	—	76	1	no	—
933	C₂×C₄	—	76	1	no	—
934	C₂×C₄	—	76	1	no	—
935	C₂×C₄	—	76	1	no	—
936	C₂×C₄	—	76	1	no	—
937	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
938	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
939	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
940	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
941	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
942	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
943	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
944	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
945	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
946	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
947	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
948	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
949	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
950	C₂²	—	2	1	no	—
951	C₂²	—	2	1	no	—
952	C₂²	—	2	1	no	—
953	C₂²	—	2	1	no	—
954	C₂²	—	2	1	no	—
955	C₂²	—	2	1	no	—
956	C₂²	—	19	2	no	—
957	C₂²	—	38	1	no	—
958	C₂²	—	38	1	no	—
959	C₂²	—	38	1	no	—
960	C₂²	—	38	1	no	—
961	C₂²	—	38	1	no	—
962	C₂²	—	38	1	no	—
963	C₂²	—	38	1	no	—
964	C₂²	—	38	1	no	—
965	C₂²	—	38	1	no	—
966	C₂²	—	38	1	no	—
967	C₂²	—	38	1	no	—
968	C₂²	—	38	1	no	—
969	C₂²	—	38	1	no	—
970	C₂²	—	38	1	no	—
971	C₂²	—	38	1	no	—
972	C₂²	—	38	1	no	—
973	C₂²	—	38	1	no	—
974	C₂²	—	38	1	no	—
975	C₂²	—	38	1	no	—
976	C₂²	—	38	1	no	—
977	C₂²	—	152	2	no	—
978	C₂²	—	152	2	no	—
979	C₂²	—	152	2	no	—
980	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
981	C₄	—	2	1	no	—
982	C₄	—	2	1	no	—
983	C₄	—	2	1	no	—
984	C₄	—	2	1	no	—
985	C₄	—	2	1	no	—
986	C₄	—	2	1	no	—
987	C₄	—	2	1	no	—
988	C₄	—	2	1	no	—
989	C₄	—	2	1	no	—
990	C₄	—	2	1	no	—
991	C₄	—	2	1	no	—
992	C₄	—	2	1	no	—
993	C₄	—	2	1	no	—
994	C₄	—	38	1	no	—
995	C₄	—	38	1	no	—
996	C₄	—	38	1	no	—
997	C₄	—	38	1	no	—
998	C₄	—	38	1	no	—
999	C₄	—	38	1	no	—
1000	C₄	—	38	1	no	—
1001	C₄	—	38	1	no	—
1002	C₄	—	38	1	no	—
1003	C₂	—	4	1	no	—
1004	C₂	—	4	1	no	—
1005	C₂	—	38	2	no	—
1006	C₂	—	76	1	no	—
1007	C₂	—	76	1	no	—
1008	C₂	—	76	1	no	—
1009	C₂	—	76	1	no	—
1010	C₂	—	76	1	no	—
1011	C₂	—	76	1	no	—
1012	C₂	H(5,𝔽₂)×D₁₉	1	1	yes	characteristic
1013	C₂	#11927381	1	1	yes	characteristic
1014	C₂	#11927381	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₁₉×#563	C₂
hypercenter	#563	D₁₉
hypocenter	C₁₉	#3560
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ #563

Complements

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

N	H ≅ G/N	type
1. #11927293	C₂	semidirect
2. #11927285	C₂	semidirect
3. #11927285	C₂	semidirect
4. #11927247	C₂	semidirect
5. #11927247	C₂	semidirect
6. #11927245	C₂	semidirect
7. #11927239	C₂	semidirect
8. #11927221	C₂	semidirect
9. #11927219	C₂	semidirect
10. #11927197	C₂	semidirect
11. #11927196	C₂	semidirect
12. #11927187	C₂	semidirect
13. #11927186	C₂	semidirect
14. #11927185	C₂	semidirect
15. #11927185	C₂	semidirect
16. #11927168	C₂	semidirect
17. #11927164	C₂	semidirect
18. #11927142	C₂	semidirect
19. #11927142	C₂	semidirect
20. #11927140	C₂	semidirect
21. #11927134	C₂	semidirect
22. #11927133	C₂	semidirect
23. #11927133	C₂	semidirect
24. #11927130	C₂	semidirect
25. #11927128	C₂	semidirect
26. #11927124	C₂	semidirect
27. #11927105	C₂	semidirect
28. #11927095	C₂	semidirect
29. #11927077	C₂	semidirect
30. #126×D₁₉	C₂	semidirect
31. C₁₉×#563	C₂	semidirect
32. C₂×#64545	C₂²	semidirect
33. C₂×#64545	C₂²	semidirect
34. C₂×#64545	C₂²	semidirect
36. C₂×#64541	C₂²	semidirect
38. C₁₉×C₄⋊Q₈	C₂²	semidirect
39. C₁₉×C₄⋊Q₈	C₂²	semidirect
40. C₁₉×#126	C₂²	semidirect
41. C₁₉×#126	C₂²	semidirect
42. C₁₉×#126	C₂²	semidirect
43. C₁₉×#126	C₂²	semidirect
44. C₁₉×#125	C₂²	semidirect
45. C₁₉×#125	C₂²	semidirect
49. C₁₉×C₂²⋊Q₈	C₂²	semidirect
50. C₁₉×C₂²⋊Q₈	C₂²	semidirect
51. C₁₉×C₂²⋊Q₈	C₂²	semidirect
52. C₁₉×C₂²⋊Q₈	C₂²	semidirect
55. #10597393	C₂²	semidirect
56. #10597393	C₂²	semidirect
57. #10597392	C₂²	semidirect
58. #10597392	C₂²	semidirect
59. #10597392	C₂²	semidirect
60. #10597392	C₂²	semidirect
61. #10597390	C₂²	semidirect
65. #10597376	C₂²	semidirect
67. C₄×C₂²⋊D₁₉	C₂²	semidirect
68. C₄×C₂²⋊D₁₉	C₂²	semidirect
69. C₄×C₂²⋊D₁₉	C₂²	semidirect
70. C₂×(C₂×D₁₉)⋊C₄	C₂²	semidirect
71. #10597344	C₂²	semidirect
72. #10597344	C₂²	semidirect
73. #10597344	C₂²	semidirect
74. #10597344	C₂²	semidirect
75. #10597344	C₂²	semidirect
76. #10597344	C₂²	semidirect
77. #10597344	C₂²	semidirect
78. #10597344	C₂²	semidirect
79. #10597343	C₂²	semidirect
80. #10597343	C₂²	semidirect
81. #10597342	C₂²	semidirect
82. #10597342	C₂²	semidirect
83. #10597342	C₂²	semidirect
84. #10597342	C₂²	semidirect
85. #10597342	C₂²	semidirect
92. #10597341	C₂²	semidirect
93. #10597341	C₂²	semidirect
94. #10597341	C₂²	semidirect
95. #10597341	C₂²	semidirect
96. #10597341	C₂²	semidirect
97. #10597341	C₂²	semidirect
98. #10597341	C₂²	semidirect
99. #10597341	C₂²	semidirect
104. #10597340	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
116. #10597339	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. C₄⋊C₄×D₁₉	C₂²	semidirect
127. C₄⋊C₄×D₁₉	C₂²	semidirect
128. C₄⋊C₄×D₁₉	C₂²	semidirect
129. C₄⋊C₄×D₁₉	C₂²	semidirect
130. C₄⋊C₄×D₁₉	C₂²	semidirect
131. #10597335	C₂²	semidirect
132. #10597335	C₂²	semidirect
133. #10597335	C₂²	semidirect
134. #10597333	C₂²	semidirect
135. #10597332	C₂²	semidirect
137. #10597331	C₂²	semidirect
138. #10597331	C₂²	semidirect
143. #10597330	C₂²	semidirect
144. #10597330	C₂²	semidirect
145. #10597330	C₂²	semidirect
146. #10597330	C₂²	semidirect
147. #10597330	C₂²	semidirect
148. #10597330	C₂²	semidirect
150. #10597329	C₂²	semidirect
151. #10597329	C₂²	semidirect
152. #10597329	C₂²	semidirect
158. #10597328	C₂²	semidirect
159. #10597328	C₂²	semidirect
160. #10597328	C₂²	semidirect
161. #10597328	C₂²	semidirect
162. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
163. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
164. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
168. C₂²⋊C₄×D₁₉	C₂²	semidirect
169. C₂²⋊C₄×D₁₉	C₂²	semidirect
170. C₂²⋊C₄×D₁₉	C₂²	semidirect
171. #10597325	C₂²	semidirect
172. #10597325	C₂²	semidirect
173. #10597325	C₂²	semidirect
174. #10597323	C₂²	semidirect
175. #10597322	C₂²	semidirect
176. #10597322	C₂²	semidirect
177. #10597322	C₂²	semidirect
178. #10597321	C₂²	semidirect
179. #10597320	C₂²	semidirect
180. C₄×D₇₆	C₂²	semidirect
181. C₄×D₇₆	C₂²	semidirect
182. C₄×D₇₆	C₂²	semidirect
183. C₄×D₇₆	C₂²	semidirect
184. C₄×D₇₆	C₂²	semidirect
185. #10597318	C₂²	semidirect
186. C₄²×D₁₉	C₂²	semidirect
497. #563	D₁₉	semidirect
546. C₄⋊Q₈	C₂×D₁₉	semidirect
547. C₄⋊Q₈	C₂×D₁₉	semidirect
563. #126	C₂×D₁₉	semidirect
564. #126	C₂×D₁₉	semidirect
565. #126	C₂×D₁₉	semidirect
566. #126	C₂×D₁₉	semidirect
570. #125	C₂×D₁₉	semidirect
571. #125	C₂×D₁₉	semidirect
616. C₂²⋊Q₈	C₂×D₁₉	semidirect
617. C₂²⋊Q₈	C₂×D₁₉	semidirect
618. C₂²⋊Q₈	C₂×D₁₉	semidirect
619. C₂²⋊Q₈	C₂×D₁₉	semidirect
694. C₁₉	#3560	semidirect

Maximal subgroups

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

subgroup	index
#11927293	2
#11927285	2
#11927247	2
#11927245	2
#11927239	2
#11927221	2
#11927219	2
#11927197	2
#11927196	2
#11927187	2
#11927186	2
#11927185	2
#11927168	2
#11927164	2
#11927142	2
#11927140	2
#11927134	2
#11927133	2
#11927130	2
#11927128	2
#11927124	2
#11927105	2
#11927095	2
#11927077	2
#126×D₁₉	2
C₁₉×#563	2
#3560	19