Subgroups — #14577478

Order 2432.

1140 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927278	C₂	1	2	yes	maximal, complemented
2	#11927277	C₂	1	2	yes	maximal, complemented
3	#11927265	C₂	1	1	yes	maximal, characteristic, complemented
4	#11927262	C₂	1	1	yes	maximal, characteristic, complemented
5	#11927258	C₂	1	1	yes	maximal, characteristic, complemented
6	#11927257	C₂	1	1	yes	maximal, characteristic, complemented
7	#11927243	C₂	1	2	yes	maximal, complemented
8	#11927239	C₂	1	2	yes	maximal, complemented
9	#11927213	C₂	1	1	yes	maximal, characteristic, complemented
10	#11927212	C₂	1	1	yes	maximal, characteristic, complemented
11	#11927196	C₂	1	1	yes	maximal, characteristic, complemented
12	#11927193	C₂	1	1	yes	maximal, characteristic, complemented
13	#11927129	C₂	1	2	yes	maximal, complemented
14	#11927127	C₂	1	2	yes	maximal, complemented
15	#11927109	C₂	1	2	yes	maximal, complemented
16	#11927096	C₂	1	1	yes	maximal, characteristic, complemented
17	#11927089	C₂	1	1	yes	maximal, characteristic, complemented
18	#11927057	C₂	1	1	yes	maximal, characteristic, complemented
19	#11927055	C₂	1	1	yes	maximal, characteristic, complemented
20	#11927054	C₂	1	1	yes	maximal, characteristic, complemented
21	#11927023	C₂	1	2	yes	maximal, complemented
22	C₂×C₄×C₂²⋊D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₉×#525	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic, complemented
25	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₂²×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
27	C₂×#64545	C₂²	1	1	yes	characteristic, complemented
28	C₂×#64543	C₂²	1	2	yes	—
29	C₂×#64543	C₂²	1	1	yes	characteristic, complemented
30	C₂×#64541	C₂²	1	1	yes	characteristic, complemented
31	C₂²×C₄×D₁₉	C₂²	1	1	yes	characteristic
32	C₁₉×#123	C₂²	1	2	yes	complemented
33	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
34	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₁₉×#121	C₂²	1	1	yes	characteristic
36	C₁₉×#121	C₂²	1	1	yes	characteristic, complemented
37	C₁₉×#120	C₂²	1	2	yes	—
38	C₄×D₄×C₁₉	C₂²	1	2	yes	—
39	C₄×D₄×C₁₉	C₂²	1	2	yes	complemented
40	C₁₉×#117	C₂²	1	1	yes	characteristic, complemented
41	#10597399	C₂²	1	2	yes	—
42	C₂×C₂²⋊Dic₁₉	C₂²	1	1	yes	characteristic
43	#10597392	C₂²	1	1	yes	characteristic, complemented
44	Q₈×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
45	#10597390	C₂²	1	1	yes	characteristic, complemented
46	#10597386	C₂²	1	2	yes	—
47	#10597386	C₂²	1	2	yes	—
48	#10597386	C₂²	1	1	yes	characteristic, complemented
49	#10597385	C₂²	1	2	yes	—
50	#10597385	C₂²	1	2	yes	—
51	#10597385	C₂²	1	2	yes	—
52	#10597385	C₂²	1	2	yes	complemented
53	#10597384	C₂²	1	1	yes	characteristic, complemented
54	#10597384	C₂²	1	2	yes	complemented
55	#10597383	C₂²	1	2	yes	—
56	#10597382	C₂²	1	2	yes	complemented
57	#10597381	C₂²	1	2	yes	complemented
58	D₄×Dic₁₉	C₂²	1	2	yes	—
59	D₄×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
60	#10597376	C₂²	1	1	yes	characteristic
61	#10597376	C₂²	1	1	yes	characteristic, complemented
62	#10597376	C₂²	1	2	yes	complemented
63	#10597375	C₂²	1	2	yes	complemented
64	#10597375	C₂²	1	2	yes	complemented
65	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	—
66	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
67	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
68	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
69	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
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
73	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
74	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
75	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
76	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	1	yes	characteristic
77	#10597372	C₂²	1	1	yes	characteristic, complemented
78	#10597370	C₂²	1	1	yes	characteristic
79	#10597370	C₂²	1	1	yes	characteristic, complemented
80	C₂×Dic₁₉⋊C₄	C₂²	1	1	yes	characteristic
81	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	complemented
82	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
83	#10597344	C₂²	1	2	yes	complemented
84	#10597343	C₂²	1	1	yes	characteristic, complemented
85	#10597341	C₂²	1	1	yes	characteristic, complemented
86	#10597340	C₂²	1	2	yes	complemented
87	#10597340	C₂²	1	2	yes	complemented
88	#10597339	C₂²	1	2	yes	complemented
89	#10597339	C₂²	1	1	yes	characteristic, complemented
90	#10597338	C₂²	1	1	yes	characteristic, complemented
91	#10597338	C₂²	1	1	yes	characteristic, complemented
92	C₄⋊C₄×D₁₉	C₂²	1	2	yes	complemented
93	#10597335	C₂²	1	2	yes	complemented
94	#10597334	C₂²	1	1	yes	characteristic, complemented
95	#10597334	C₂²	1	1	yes	characteristic, complemented
96	#10597333	C₂²	1	1	yes	characteristic, complemented
97	#10597333	C₂²	1	2	yes	complemented
98	#10597333	C₂²	1	2	yes	complemented
99	#10597331	C₂²	1	2	yes	—
100	#10597331	C₂²	1	2	yes	—
101	#10597331	C₂²	1	2	yes	complemented
102	#10597331	C₂²	1	2	yes	complemented
103	#10597331	C₂²	1	2	yes	complemented
104	#10597330	C₂²	1	2	yes	—
105	#10597330	C₂²	1	2	yes	—
106	#10597330	C₂²	1	2	yes	complemented
107	#10597329	C₂²	1	2	yes	complemented
108	#10597329	C₂²	1	2	yes	complemented
109	#10597328	C₂²	1	2	yes	—
110	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	—
111	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	complemented
112	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	complemented
113	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	complemented
114	#10597325	C₂²	1	2	yes	complemented
115	#10597325	C₂²	1	2	yes	complemented
116	#10597324	C₂²	1	2	yes	—
117	#10597323	C₂²	1	2	yes	—
118	#10597323	C₂²	1	2	yes	complemented
119	#10597322	C₂²	1	2	yes	complemented
120	#10597321	C₂²	1	2	yes	complemented
121	#10597318	C₂²	1	2	yes	complemented
122	C₄×Dic₃₈	C₂²	1	2	yes	complemented
123	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
124	C₂³×D₁₉	C₂³	1	1	yes	characteristic
125	#41×C₁₉	—	4	2	no	—
126	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
127	C₂×D₄×C₁₉	C₂³	1	2	yes	—
128	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
129	C₂×D₄×C₁₉	C₂³	1	2	yes	—
130	C₂×D₄×C₁₉	C₂³	1	2	yes	—
131	C₂²×C₄×C₁₉	—	4	2	no	—
132	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
133	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
134	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
135	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
136	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
137	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
138	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊D₁₉	—	2	4	no	—
140	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
142	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
145	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
146	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
147	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
148	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
149	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
150	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
151	C₂²×Dic₁₉	C₂³	1	2	yes	—
152	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
153	C₂²×Dic₁₉	C₂³	1	2	yes	—
154	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
155	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
156	#64545	—	4	2	no	—
157	#64543	—	2	8	no	—
158	#64543	—	4	2	no	—
159	#64541	—	4	2	no	—
160	C₂×D₇₆	C₂³	1	1	yes	characteristic
161	C₂×D₇₆	C₂³	1	2	yes	—
162	C₂×D₇₆	C₂³	1	2	yes	—
163	C₂×C₄×D₁₉	—	4	2	no	—
164	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
165	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
166	C₂×C₄×D₁₉	C₂³	1	2	yes	—
167	C₂×C₄×D₁₉	C₂³	1	2	yes	—
168	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
169	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
170	C₂×C₄×D₁₉	C₂³	1	2	yes	—
171	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
172	C₂×Dic₃₈	C₂³	1	2	yes	—
173	C₂×Dic₃₈	C₂³	1	2	yes	—
174	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
175	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
176	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
177	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
178	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
179	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
180	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
181	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
182	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
183	C₄²×C₁₉	C₂³	1	2	yes	—
184	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
185	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
186	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
187	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
188	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
189	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
190	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
191	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
192	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
193	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
194	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
195	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
196	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
197	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
198	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
199	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
200	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
201	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
202	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
203	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
204	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
205	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
206	C₄⋊Dic₁₉	C₂³	1	2	yes	—
207	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
208	C₄⋊Dic₁₉	C₂³	1	2	yes	—
209	Dic₁₉⋊C₄	C₂³	1	2	yes	—
210	Dic₁₉⋊C₄	C₂³	1	2	yes	—
211	Dic₁₉⋊C₄	C₂³	1	2	yes	—
212	Dic₁₉⋊C₄	C₂³	1	2	yes	—
213	Dic₁₉⋊C₄	C₂³	1	2	yes	—
214	Dic₁₉⋊C₄	C₂³	1	2	yes	—
215	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
216	Dic₁₉⋊C₄	C₂³	1	2	yes	—
217	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
218	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
219	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
220	Dic₁₉⋊C₄	C₂³	1	2	yes	—
221	C₄×Dic₁₉	C₂³	1	2	yes	—
222	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
223	C₄×Dic₁₉	C₂³	1	2	yes	—
224	C₄×Dic₁₉	C₂³	1	2	yes	—
225	C₄×Dic₁₉	C₂³	1	2	yes	—
226	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
227	C₄×Dic₁₉	C₂³	1	2	yes	—
228	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
229	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
230	C₂³×C₁₉	—	2	2	no	—
231	C₂³×C₁₉	—	4	1	no	—
232	C₂³×C₁₉	—	4	1	no	—
233	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
234	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
235	C₂³×C₁₉	C₂⁴	1	2	yes	—
236	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
237	C₂²×D₁₉	—	2	2	no	—
238	C₂²×D₁₉	—	4	1	no	—
239	C₂²×D₁₉	—	4	1	no	—
240	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
241	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
242	C₂²×D₁₉	C₂⁴	1	2	yes	—
243	Q₈×C₁₉	—	2	2	no	—
244	D₄×C₁₉	—	2	4	no	—
245	D₄×C₁₉	—	2	2	no	—
246	D₄×C₁₉	—	4	2	no	—
247	D₄×C₁₉	—	4	2	no	—
248	C₂×C₄×C₁₉	—	2	2	no	—
249	C₂×C₄×C₁₉	—	2	2	no	—
250	C₂×C₄×C₁₉	—	2	2	no	—
251	C₂×C₄×C₁₉	—	4	1	no	—
252	C₂×C₄×C₁₉	—	4	1	no	—
253	C₂×C₄×C₁₉	—	4	1	no	—
254	C₂×C₄×C₁₉	—	4	2	no	—
255	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
256	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
257	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
258	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
259	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
260	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
261	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
262	C₂²⋊D₁₉	—	2	4	no	—
263	C₂²⋊D₁₉	—	2	4	no	—
264	C₂²⋊D₁₉	—	2	2	no	—
265	C₂²⋊D₁₉	—	2	2	no	—
266	C₂²⋊D₁₉	—	2	2	no	—
267	C₂²⋊D₁₉	—	2	2	no	—
268	C₂²⋊D₁₉	—	4	2	no	—
269	C₂²⋊D₁₉	—	4	2	no	—
270	C₂²⋊D₁₉	—	4	2	no	—
271	C₂²⋊D₁₉	—	4	2	no	—
272	C₂²⋊D₁₉	—	4	2	no	—
273	C₂×Dic₁₉	—	2	4	no	—
274	C₂×Dic₁₉	—	4	1	no	—
275	C₂×Dic₁₉	—	4	2	no	—
276	C₂×Dic₁₉	—	4	1	no	—
277	C₂×Dic₁₉	#41	1	4	yes	complemented
278	C₂×Dic₁₉	C₂⁴	1	2	yes	—
279	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
280	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
281	C₂×Dic₁₉	C₂⁴	1	2	yes	—
282	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
283	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
284	C₂×Dic₁₉	C₂⁴	1	2	yes	—
285	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
286	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
287	D₇₆	—	2	2	no	—
288	D₇₆	—	4	2	no	—
289	D₇₆	—	4	2	no	—
290	C₄×D₁₉	—	2	2	no	—
291	C₄×D₁₉	—	2	2	no	—
292	C₄×D₁₉	—	2	4	no	—
293	C₄×D₁₉	—	4	1	no	—
294	C₄×D₁₉	—	4	1	no	—
295	C₄×D₁₉	—	4	2	no	—
296	C₄×D₁₉	—	4	2	no	—
297	Dic₃₈	—	2	2	no	—
298	Dic₃₈	—	2	4	no	—
299	Dic₃₈	—	4	2	no	—
300	#3506	—	19	1	no	maximal, Sylow
301	C₂²×C₁₉	—	2	1	no	—
302	C₂²×C₁₉	—	2	1	no	—
303	C₂²×C₁₉	—	2	2	no	—
304	C₂²×C₁₉	—	2	1	no	—
305	C₂²×C₁₉	—	2	1	no	—
306	C₂²×C₁₉	—	2	2	no	—
307	C₂²×C₁₉	—	2	1	no	—
308	C₂²×C₁₉	—	2	1	no	—
309	C₂²×C₁₉	—	2	2	no	—
310	C₂²×C₁₉	—	2	1	no	—
311	C₂²×C₁₉	—	2	1	no	—
312	C₂²×C₁₉	—	4	4	no	—
313	C₂²×C₁₉	C₂×#41	1	2	yes	—
314	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
315	C₂×D₁₉	—	2	2	no	—
316	C₂×D₁₉	—	2	1	no	—
317	C₂×D₁₉	—	2	1	no	—
318	C₂×D₁₉	—	2	1	no	—
319	C₂×D₁₉	—	2	1	no	—
320	C₂×D₁₉	—	2	2	no	—
321	C₂×D₁₉	—	2	1	no	—
322	C₂×D₁₉	—	2	2	no	—
323	C₂×D₁₉	—	2	1	no	—
324	C₂×D₁₉	—	4	4	no	—
325	C₄×C₁₉	—	2	2	no	—
326	C₄×C₁₉	—	2	1	no	—
327	C₄×C₁₉	—	2	1	no	—
328	C₄×C₁₉	—	2	2	no	—
329	C₄×C₁₉	—	2	1	no	—
330	C₄×C₁₉	—	2	2	no	—
331	C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
332	Dic₁₉	—	2	2	no	—
333	Dic₁₉	—	2	2	no	—
334	Dic₁₉	—	2	1	no	—
335	Dic₁₉	—	2	1	no	—
336	Dic₁₉	—	2	1	no	—
337	Dic₁₉	—	2	2	no	—
338	Dic₁₉	—	2	1	no	—
339	Dic₁₉	C₂×#41	1	2	yes	—
340	Dic₁₉	C₂×#41	1	2	yes	—
341	#559	—	19	2	no	—
342	#559	—	19	2	no	—
343	#556	—	19	1	no	—
344	#556	—	19	1	no	—
345	#555	—	19	1	no	—
346	#555	—	19	1	no	—
347	#553	—	19	2	no	—
348	#553	—	19	2	no	—
349	#550	—	19	1	no	—
350	#550	—	19	1	no	—
351	#547	—	19	1	no	—
352	#547	—	19	1	no	—
353	#538	—	19	2	no	—
354	#538	—	19	2	no	—
355	#535	—	19	2	no	—
356	#533	—	19	1	no	—
357	#532	—	19	1	no	—
358	#525	—	19	1	no	—
359	#525	—	19	1	no	—
360	#525	—	19	1	no	—
361	#525	D₁₉	1	1	yes	characteristic, complemented
362	#520	—	19	2	no	—
363	C₂×C₄×D₄	—	19	1	no	—
364	C₂×C₁₉	—	2	2	no	—
365	C₂×C₁₉	—	4	2	no	—
366	C₂×C₁₉	—	4	1	no	—
367	C₂×C₁₉	—	4	1	no	—
368	C₂×C₁₉	C₂²×#41	1	1	yes	characteristic
369	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
370	C₂×C₁₉	#585	1	1	yes	characteristic
371	D₁₉	—	4	2	no	—
372	D₁₉	—	4	1	no	—
373	D₁₉	—	4	1	no	—
374	C₂×#41	—	19	1	no	—
375	C₂×#41	—	19	2	no	—
376	C₂×#41	—	19	1	no	—
377	C₂×#41	—	19	1	no	—
378	C₂×#41	C₂×D₁₉	1	1	yes	characteristic, complemented
379	C₂²×D₄	—	19	1	no	—
380	C₂³×C₄	—	19	1	no	—
381	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
382	C₄⋊Q₈	—	19	1	no	—
383	C₄⋊Q₈	—	19	1	no	—
384	C₄⋊Q₈	—	19	1	no	—
385	#127	—	19	2	no	—
386	#127	—	19	2	no	—
387	#127	—	19	1	no	—
388	#126	—	19	2	no	—
389	#126	—	19	2	no	—
390	#126	—	19	2	no	—
391	#126	—	19	2	no	—
392	#125	—	19	2	no	—
393	#124	—	19	2	no	—
394	#124	—	19	2	no	—
395	#124	—	19	2	no	—
396	#124	—	19	2	no	—
397	#124	—	19	2	no	—
398	#124	—	19	2	no	—
399	#124	—	19	2	no	—
400	#123	—	19	2	no	—
401	#123	—	19	2	no	—
402	#123	—	19	2	no	—
403	#123	—	19	2	no	—
404	#123	—	19	2	no	—
405	#123	—	19	2	no	—
406	#123	—	19	2	no	—
407	#123	C₂×D₁₉	1	2	yes	complemented
408	C₂²⋊Q₈	—	19	1	no	—
409	C₂²⋊Q₈	—	19	1	no	—
410	C₂²⋊Q₈	—	19	1	no	—
411	C₂²⋊Q₈	—	19	1	no	—
412	C₂²⋊Q₈	—	19	2	no	—
413	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
414	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
415	#121	—	19	1	no	—
416	#121	—	19	2	no	—
417	#121	—	19	2	no	—
418	#121	—	19	2	no	—
419	#121	—	19	2	no	—
420	#121	—	19	2	no	—
421	#121	—	19	1	no	—
422	#121	—	19	1	no	—
423	#121	—	19	2	no	—
424	#121	—	19	1	no	—
425	#121	—	19	2	no	—
426	#121	—	19	2	no	—
427	#121	—	19	2	no	—
428	#121	C₂×D₁₉	1	1	yes	characteristic
429	#121	C₂×D₁₉	1	1	yes	characteristic, complemented
430	#120	—	19	2	no	—
431	#120	—	19	2	no	—
432	#120	—	19	2	no	—
433	#120	C₂×D₁₉	1	2	yes	—
434	C₄×Q₈	—	19	1	no	—
435	C₄×Q₈	—	19	2	no	—
436	C₄×Q₈	—	19	1	no	—
437	C₄×Q₈	—	19	2	no	—
438	C₄×Q₈	—	19	2	no	—
439	C₄×D₄	—	19	2	no	—
440	C₄×D₄	—	19	1	no	—
441	C₄×D₄	—	19	1	no	—
442	C₄×D₄	—	19	1	no	—
443	C₄×D₄	—	19	1	no	—
444	C₄×D₄	—	19	1	no	—
445	C₄×D₄	—	19	1	no	—
446	C₄×D₄	—	19	1	no	—
447	C₄×D₄	—	19	1	no	—
448	C₄×D₄	—	19	1	no	—
449	C₄×D₄	—	19	2	no	—
450	C₄×D₄	—	19	2	no	—
451	C₄×D₄	—	19	2	no	—
452	C₄×D₄	—	19	2	no	—
453	C₄×D₄	—	19	1	no	—
454	C₄×D₄	—	19	2	no	—
455	C₄×D₄	—	19	2	no	—
456	C₄×D₄	—	19	2	no	—
457	C₄×D₄	—	19	2	no	—
458	C₄×D₄	C₂×D₁₉	1	2	yes	—
459	C₄×D₄	C₂×D₁₉	1	2	yes	complemented
460	#117	—	19	1	no	—
461	#117	—	19	1	no	—
462	#117	—	19	1	no	—
463	#117	—	19	2	no	—
464	#117	—	19	2	no	—
465	#117	—	19	2	no	—
466	#117	C₂×D₁₉	1	1	yes	characteristic, complemented
467	C₂×C₄⋊C₄	—	19	1	no	—
468	C₂×C₄⋊C₄	—	19	2	no	—
469	C₂×C₄⋊C₄	—	19	2	no	—
470	C₂×C₂²⋊C₄	—	19	1	no	—
471	C₂×C₂²⋊C₄	—	19	1	no	—
472	C₂×C₄²	—	19	1	no	—
473	C₁₉	#3506	1	1	yes	characteristic, complemented, Sylow
474	C₂⁴	—	19	1	no	—
475	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
476	#41	—	4	2	no	—
477	#41	—	38	8	no	—
478	#41	—	76	2	no	—
479	#41	—	76	2	no	—
480	#41	—	76	2	no	—
481	C₂×Q₈	—	19	2	no	—
482	C₂×Q₈	—	19	1	no	—
483	C₂×Q₈	—	19	2	no	—
484	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
485	C₂×D₄	—	19	2	no	—
486	C₂×D₄	—	19	1	no	—
487	C₂×D₄	—	19	1	no	—
488	C₂×D₄	—	19	1	no	—
489	C₂×D₄	—	19	1	no	—
490	C₂×D₄	—	19	2	no	—
491	C₂×D₄	—	19	2	no	—
492	C₂×D₄	—	19	2	no	—
493	C₂×D₄	—	19	2	no	—
494	C₂×D₄	—	19	2	no	—
495	C₂×D₄	—	19	2	no	—
496	C₂×D₄	—	19	1	no	—
497	C₂×D₄	—	19	2	no	—
498	C₂×D₄	—	19	2	no	—
499	C₂×D₄	—	38	4	no	—
500	C₂×D₄	C₂²×D₁₉	1	2	yes	—
501	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
502	C₂×D₄	C₂²×D₁₉	1	2	yes	—
503	C₂×D₄	C₂²×D₁₉	1	2	yes	—
504	C₂²×C₄	—	4	2	no	—
505	C₂²×C₄	—	19	1	no	—
506	C₂²×C₄	—	19	2	no	—
507	C₂²×C₄	—	19	1	no	—
508	C₂²×C₄	—	19	1	no	—
509	C₂²×C₄	—	19	2	no	—
510	C₂²×C₄	—	19	2	no	—
511	C₂²×C₄	—	19	1	no	—
512	C₂²×C₄	—	19	1	no	—
513	C₂²×C₄	—	19	2	no	—
514	C₂²×C₄	—	19	2	no	—
515	C₂²×C₄	—	19	1	no	—
516	C₂²×C₄	—	19	1	no	—
517	C₂²×C₄	—	76	2	no	—
518	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
519	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
520	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
521	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
522	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
523	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
524	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
525	C₄⋊C₄	—	19	1	no	—
526	C₄⋊C₄	—	19	1	no	—
527	C₄⋊C₄	—	19	2	no	—
528	C₄⋊C₄	—	19	1	no	—
529	C₄⋊C₄	—	19	1	no	—
530	C₄⋊C₄	—	19	2	no	—
531	C₄⋊C₄	—	19	2	no	—
532	C₄⋊C₄	—	19	2	no	—
533	C₄⋊C₄	—	19	2	no	—
534	C₄⋊C₄	—	19	2	no	—
535	C₄⋊C₄	—	19	2	no	—
536	C₄⋊C₄	—	19	2	no	—
537	C₄⋊C₄	—	19	2	no	—
538	C₄⋊C₄	—	19	1	no	—
539	C₄⋊C₄	—	19	1	no	—
540	C₄⋊C₄	—	19	2	no	—
541	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
542	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
543	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
544	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
545	C₂²⋊C₄	—	19	1	no	—
546	C₂²⋊C₄	—	19	1	no	—
547	C₂²⋊C₄	—	19	1	no	—
548	C₂²⋊C₄	—	19	1	no	—
549	C₂²⋊C₄	—	19	2	no	—
550	C₂²⋊C₄	—	19	2	no	—
551	C₂²⋊C₄	—	19	2	no	—
552	C₂²⋊C₄	—	19	2	no	—
553	C₂²⋊C₄	—	19	2	no	—
554	C₂²⋊C₄	—	19	1	no	—
555	C₂²⋊C₄	—	19	1	no	—
556	C₂²⋊C₄	—	19	1	no	—
557	C₂²⋊C₄	—	19	1	no	—
558	C₂²⋊C₄	—	19	2	no	—
559	C₂²⋊C₄	—	19	2	no	—
560	C₂²⋊C₄	—	19	2	no	—
561	C₂²⋊C₄	—	19	2	no	—
562	C₂²⋊C₄	—	19	2	no	—
563	C₂²⋊C₄	—	19	2	no	—
564	C₂²⋊C₄	—	19	2	no	—
565	C₂²⋊C₄	—	19	2	no	—
566	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
567	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
568	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
569	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
570	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
571	C₄²	—	19	1	no	—
572	C₄²	—	19	1	no	—
573	C₄²	—	19	1	no	—
574	C₄²	—	19	1	no	—
575	C₄²	—	19	2	no	—
576	C₄²	—	19	2	no	—
577	C₄²	—	19	2	no	—
578	C₄²	—	19	2	no	—
579	C₄²	—	19	2	no	—
580	C₄²	C₂²×D₁₉	1	2	yes	—
581	C₂³	—	2	2	no	—
582	C₂³	—	4	1	no	—
583	C₂³	—	4	1	no	—
584	C₂³	—	19	1	no	—
585	C₂³	—	19	1	no	—
586	C₂³	—	19	2	no	—
587	C₂³	—	38	2	no	—
588	C₂³	—	76	1	no	—
589	C₂³	—	76	1	no	—
590	C₂³	C₂³×D₁₉	1	1	yes	characteristic
591	C₂³	C₂³×D₁₉	1	1	yes	characteristic
592	C₂³	C₂³×D₁₉	1	2	yes	—
593	C₂³	C₂³×D₁₉	1	1	yes	characteristic
594	Q₈	—	2	2	no	—
595	Q₈	—	38	4	no	—
596	Q₈	—	38	2	no	—
597	Q₈	—	76	2	no	—
598	D₄	—	2	4	no	—
599	D₄	—	2	2	no	—
600	D₄	—	4	2	no	—
601	D₄	—	4	2	no	—
602	D₄	—	38	2	no	—
603	D₄	—	38	2	no	—
604	D₄	—	38	2	no	—
605	D₄	—	38	2	no	—
606	D₄	—	38	4	no	—
607	D₄	—	38	4	no	—
608	D₄	—	38	2	no	—
609	D₄	—	76	2	no	—
610	D₄	—	76	2	no	—
611	D₄	—	76	2	no	—
612	D₄	—	76	2	no	—
613	D₄	—	76	2	no	—
614	D₄	—	76	2	no	—
615	D₄	—	76	2	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	—	4	2	no	—
623	C₂×C₄	—	19	4	no	—
624	C₂×C₄	—	19	1	no	—
625	C₂×C₄	—	19	1	no	—
626	C₂×C₄	—	19	2	no	—
627	C₂×C₄	—	19	1	no	—
628	C₂×C₄	—	19	2	no	—
629	C₂×C₄	—	19	1	no	—
630	C₂×C₄	—	19	1	no	—
631	C₂×C₄	—	19	1	no	—
632	C₂×C₄	—	19	2	no	—
633	C₂×C₄	—	38	4	no	—
634	C₂×C₄	—	38	4	no	—
635	C₂×C₄	—	38	2	no	—
636	C₂×C₄	—	38	2	no	—
637	C₂×C₄	—	76	1	no	—
638	C₂×C₄	—	76	1	no	—
639	C₂×C₄	—	76	2	no	—
640	C₂×C₄	—	76	2	no	—
641	C₂×C₄	—	76	1	no	—
642	C₂×C₄	—	76	2	no	—
643	C₂×C₄	—	76	1	no	—
644	C₂×C₄	C₂³×D₁₉	1	2	yes	—
645	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
646	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
647	C₂×C₄	C₂³×D₁₉	1	2	yes	—
648	C₂×C₄	C₂³×D₁₉	1	2	yes	—
649	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
650	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
651	C₂²	—	2	1	no	—
652	C₂²	—	2	1	no	—
653	C₂²	—	2	2	no	—
654	C₂²	—	2	1	no	—
655	C₂²	—	2	1	no	—
656	C₂²	—	2	1	no	—
657	C₂²	—	2	1	no	—
658	C₂²	—	2	2	no	—
659	C₂²	—	2	1	no	—
660	C₂²	—	2	2	no	—
661	C₂²	—	2	1	no	—
662	C₂²	—	4	4	no	—
663	C₂²	—	38	2	no	—
664	C₂²	—	38	1	no	—
665	C₂²	—	38	1	no	—
666	C₂²	—	38	1	no	—
667	C₂²	—	38	1	no	—
668	C₂²	—	38	2	no	—
669	C₂²	—	38	2	no	—
670	C₂²	—	38	1	no	—
671	C₂²	—	38	1	no	—
672	C₂²	—	76	4	no	—
673	C₂²	#41×D₁₉	1	2	yes	—
674	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
675	C₄	—	2	2	no	—
676	C₄	—	2	1	no	—
677	C₄	—	2	1	no	—
678	C₄	—	2	1	no	—
679	C₄	—	2	2	no	—
680	C₄	—	2	2	no	—
681	C₄	—	19	2	no	—
682	C₄	—	19	2	no	—
683	C₄	—	38	2	no	—
684	C₄	—	38	1	no	—
685	C₄	—	38	1	no	—
686	C₄	—	38	2	no	—
687	C₄	—	38	1	no	—
688	C₄	—	38	1	no	—
689	C₄	—	38	2	no	—
690	C₄	#10597430	1	2	yes	—
691	C₂	—	2	2	no	—
692	C₂	—	4	1	no	—
693	C₂	—	4	1	no	—
694	C₂	—	4	2	no	—
695	C₂	—	76	1	no	—
696	C₂	—	76	1	no	—
697	C₂	—	76	2	no	—
698	C₂	C₂×#41×D₁₉	1	1	yes	characteristic
699	C₂	C₂×#10597430	1	1	yes	characteristic
700	C₂	#11927380	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₁₉×#525	C₂
hypercenter	#525	D₁₉
hypocenter	C₁₉	#3506
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ #525

Complements

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

N	H ≅ G/N	type
1. #11927278	C₂	semidirect
2. #11927277	C₂	semidirect
3. #11927265	C₂	semidirect
4. #11927262	C₂	semidirect
5. #11927258	C₂	semidirect
6. #11927257	C₂	semidirect
7. #11927243	C₂	semidirect
8. #11927239	C₂	semidirect
9. #11927213	C₂	semidirect
10. #11927212	C₂	semidirect
11. #11927196	C₂	semidirect
12. #11927193	C₂	semidirect
13. #11927129	C₂	semidirect
14. #11927127	C₂	semidirect
15. #11927109	C₂	semidirect
16. #11927096	C₂	semidirect
17. #11927089	C₂	semidirect
18. #11927057	C₂	semidirect
19. #11927055	C₂	semidirect
20. #11927054	C₂	semidirect
21. #11927023	C₂	semidirect
22. C₂×C₄×C₂²⋊D₁₉	C₂	semidirect
23. C₁₉×#525	C₂	semidirect
24. C₂×#41×C₁₉	C₂²	semidirect
27. C₂×#64545	C₂²	semidirect
29. C₂×#64543	C₂²	semidirect
30. C₂×#64541	C₂²	semidirect
32. C₁₉×#123	C₂²	semidirect
34. C₁₉×C₂²⋊Q₈	C₂²	semidirect
36. C₁₉×#121	C₂²	semidirect
39. C₄×D₄×C₁₉	C₂²	semidirect
40. C₁₉×#117	C₂²	semidirect
43. #10597392	C₂²	semidirect
44. Q₈×Dic₁₉	C₂²	semidirect
45. #10597390	C₂²	semidirect
48. #10597386	C₂²	semidirect
52. #10597385	C₂²	semidirect
53. #10597384	C₂²	semidirect
54. #10597384	C₂²	semidirect
56. #10597382	C₂²	semidirect
57. #10597381	C₂²	semidirect
59. D₄×Dic₁₉	C₂²	semidirect
61. #10597376	C₂²	semidirect
62. #10597376	C₂²	semidirect
63. #10597375	C₂²	semidirect
64. #10597375	C₂²	semidirect
74. C₄×C₂²⋊D₁₉	C₂²	semidirect
75. C₄×C₂²⋊D₁₉	C₂²	semidirect
77. #10597372	C₂²	semidirect
79. #10597370	C₂²	semidirect
81. C₂×Dic₁₉⋊C₄	C₂²	semidirect
83. #10597344	C₂²	semidirect
84. #10597343	C₂²	semidirect
85. #10597341	C₂²	semidirect
86. #10597340	C₂²	semidirect
87. #10597340	C₂²	semidirect
88. #10597339	C₂²	semidirect
89. #10597339	C₂²	semidirect
90. #10597338	C₂²	semidirect
91. #10597338	C₂²	semidirect
92. C₄⋊C₄×D₁₉	C₂²	semidirect
93. #10597335	C₂²	semidirect
94. #10597334	C₂²	semidirect
95. #10597334	C₂²	semidirect
96. #10597333	C₂²	semidirect
97. #10597333	C₂²	semidirect
98. #10597333	C₂²	semidirect
101. #10597331	C₂²	semidirect
102. #10597331	C₂²	semidirect
103. #10597331	C₂²	semidirect
106. #10597330	C₂²	semidirect
107. #10597329	C₂²	semidirect
108. #10597329	C₂²	semidirect
111. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
112. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
113. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
114. #10597325	C₂²	semidirect
115. #10597325	C₂²	semidirect
118. #10597323	C₂²	semidirect
119. #10597322	C₂²	semidirect
120. #10597321	C₂²	semidirect
121. #10597318	C₂²	semidirect
122. C₄×Dic₃₈	C₂²	semidirect
277. C₂×Dic₁₉	#41	semidirect
361. #525	D₁₉	semidirect
378. C₂×#41	C₂×D₁₉	semidirect
407. #123	C₂×D₁₉	semidirect
414. C₂²⋊Q₈	C₂×D₁₉	semidirect
429. #121	C₂×D₁₉	semidirect
459. C₄×D₄	C₂×D₁₉	semidirect
466. #117	C₂×D₁₉	semidirect
473. C₁₉	#3506	semidirect

Maximal subgroups

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

subgroup	index
#11927278	2
#11927277	2
#11927265	2
#11927262	2
#11927258	2
#11927257	2
#11927243	2
#11927239	2
#11927213	2
#11927212	2
#11927196	2
#11927193	2
#11927129	2
#11927127	2
#11927109	2
#11927096	2
#11927089	2
#11927057	2
#11927055	2
#11927054	2
#11927023	2
C₂×C₄×C₂²⋊D₁₉	2
C₁₉×#525	2
#3506	19