Subgroups — #14577952

Order 2432.

1160 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927290	C₂	1	2	yes	maximal, complemented
2	#11927284	C₂	1	2	yes	maximal, complemented
3	#11927260	C₂	1	1	yes	maximal, characteristic, complemented
4	#11927242	C₂	1	1	yes	maximal, characteristic, complemented
5	#11927229	C₂	1	1	yes	maximal, characteristic, complemented
6	#11927217	C₂	1	2	yes	maximal, complemented
7	#11927212	C₂	1	1	yes	maximal, characteristic, complemented
8	#11927190	C₂	1	1	yes	maximal, characteristic, complemented
9	#11927189	C₂	1	1	yes	maximal, characteristic, complemented
10	#11927182	C₂	1	2	yes	maximal, complemented
11	#11927178	C₂	1	1	yes	maximal, characteristic, complemented
12	#11927168	C₂	1	1	yes	maximal, characteristic, complemented
13	#11927146	C₂	1	2	yes	maximal, complemented
14	#11927145	C₂	1	1	yes	maximal, characteristic, complemented
15	#11927134	C₂	1	2	yes	maximal, complemented
16	#11927125	C₂	1	1	yes	maximal, characteristic, complemented
17	#11927110	C₂	1	1	yes	maximal, characteristic, complemented
18	#11927108	C₂	1	2	yes	maximal, complemented
19	#11927105	C₂	1	2	yes	maximal, complemented
20	#11927054	C₂	1	1	yes	maximal, characteristic, complemented
21	#11927053	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#10597341	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₉×#547	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#41×C₁₉	C₂²	1	2	yes	complemented
25	C₂×#64543	C₂²	1	1	yes	characteristic, complemented
26	C₂×D₄×D₁₉	C₂²	1	2	yes	—
27	C₂×D₄×D₁₉	C₂²	1	1	yes	characteristic, complemented
28	C₂×#64541	C₂²	1	1	yes	characteristic, complemented
29	C₂×#64541	C₂²	1	1	yes	characteristic, complemented
30	C₂²×D₇₆	C₂²	1	1	yes	characteristic
31	C₂²×D₇₆	C₂²	1	2	yes	complemented
32	C₂²×C₄×D₁₉	C₂²	1	1	yes	characteristic, complemented
33	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₁₉×#123	C₂²	1	2	yes	complemented
35	C₁₉×#123	C₂²	1	2	yes	complemented
36	C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	complemented
37	C₁₉×#121	C₂²	1	1	yes	characteristic
38	C₁₉×#121	C₂²	1	1	yes	characteristic, complemented
39	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
40	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
43	#10597393	C₂²	1	2	yes	complemented
44	#10597393	C₂²	1	2	yes	complemented
45	#10597393	C₂²	1	2	yes	complemented
46	#10597392	C₂²	1	2	yes	complemented
47	#10597386	C₂²	1	2	yes	complemented
48	#10597386	C₂²	1	2	yes	complemented
49	#10597386	C₂²	1	1	yes	characteristic, complemented
50	#10597385	C₂²	1	1	yes	characteristic
51	#10597385	C₂²	1	2	yes	complemented
52	#10597384	C₂²	1	1	yes	characteristic, complemented
53	#10597383	C₂²	1	2	yes	—
54	#10597383	C₂²	1	1	yes	characteristic, complemented
55	#10597383	C₂²	1	2	yes	complemented
56	#10597383	C₂²	1	2	yes	complemented
57	#10597383	C₂²	1	2	yes	complemented
58	D₄×Dic₁₉	C₂²	1	2	yes	complemented
59	#10597376	C₂²	1	2	yes	complemented
60	#10597376	C₂²	1	2	yes	complemented
61	#10597376	C₂²	1	2	yes	complemented
62	#10597376	C₂²	1	2	yes	complemented
63	#10597376	C₂²	1	1	yes	characteristic, complemented
64	#10597376	C₂²	1	2	yes	complemented
65	#10597375	C₂²	1	2	yes	—
66	#10597375	C₂²	1	2	yes	complemented
67	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
68	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic, complemented
69	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
70	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	complemented
71	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	complemented
72	#10597372	C₂²	1	2	yes	complemented
73	#10597370	C₂²	1	1	yes	characteristic, complemented
74	#10597344	C₂²	1	2	yes	complemented
75	#10597344	C₂²	1	2	yes	complemented
76	#10597344	C₂²	1	2	yes	complemented
77	#10597343	C₂²	1	1	yes	characteristic, complemented
78	#10597343	C₂²	1	1	yes	characteristic, complemented
79	#10597343	C₂²	1	2	yes	complemented
80	#10597342	C₂²	1	1	yes	characteristic, complemented
81	#10597341	C₂²	1	1	yes	characteristic
82	#10597341	C₂²	1	1	yes	characteristic
83	#10597341	C₂²	1	2	yes	complemented
84	#10597341	C₂²	1	2	yes	complemented
85	#10597341	C₂²	1	1	yes	characteristic, complemented
86	#10597341	C₂²	1	1	yes	characteristic, complemented
87	#10597341	C₂²	1	2	yes	complemented
88	#10597341	C₂²	1	1	yes	characteristic, complemented
89	#10597341	C₂²	1	2	yes	complemented
90	#10597340	C₂²	1	1	yes	characteristic, complemented
91	#10597340	C₂²	1	2	yes	complemented
92	#10597340	C₂²	1	2	yes	complemented
93	#10597340	C₂²	1	2	yes	complemented
94	#10597339	C₂²	1	1	yes	characteristic, complemented
95	#10597338	C₂²	1	1	yes	characteristic, complemented
96	#10597338	C₂²	1	1	yes	characteristic, complemented
97	#10597338	C₂²	1	2	yes	complemented
98	#10597336	C₂²	1	1	yes	characteristic, complemented
99	#10597335	C₂²	1	2	yes	complemented
100	#10597333	C₂²	1	1	yes	characteristic, complemented
101	#10597332	C₂²	1	2	yes	complemented
102	#10597331	C₂²	1	2	yes	complemented
103	#10597330	C₂²	1	1	yes	characteristic, complemented
104	#10597330	C₂²	1	2	yes	complemented
105	#10597330	C₂²	1	2	yes	complemented
106	#10597330	C₂²	1	2	yes	complemented
107	#10597330	C₂²	1	2	yes	complemented
108	#10597329	C₂²	1	1	yes	characteristic, complemented
109	#10597329	C₂²	1	2	yes	complemented
110	#10597329	C₂²	1	2	yes	complemented
111	#10597328	C₂²	1	1	yes	characteristic
112	#10597328	C₂²	1	2	yes	complemented
113	#10597328	C₂²	1	2	yes	complemented
114	#10597328	C₂²	1	2	yes	complemented
115	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	complemented
116	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	complemented
117	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	complemented
118	#10597324	C₂²	1	1	yes	characteristic, complemented
119	#10597321	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₇₆	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₇₆	C₂²	1	1	yes	characteristic, complemented
122	#10597318	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₉	C₂³	1	2	yes	—
124	C₂³×D₁₉	C₂³	1	1	yes	characteristic
125	C₂³×D₁₉	C₂³	1	2	yes	—
126	#41×C₁₉	—	4	4	no	—
127	C₂×Q₈×C₁₉	C₂³	1	2	yes	—
128	C₂×D₄×C₁₉	C₂³	1	2	yes	—
129	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
130	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
131	C₂×D₄×C₁₉	C₂³	1	2	yes	—
132	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
133	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
134	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
135	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
136	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
138	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
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	2	yes	—
145	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
146	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
147	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
148	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
149	C₂²×Dic₁₉	C₂³	1	2	yes	—
150	#64543	—	4	2	no	—
151	D₄×D₁₉	—	4	2	no	—
152	D₄×D₁₉	—	4	4	no	—
153	#64541	—	4	2	no	—
154	#64541	—	4	2	no	—
155	C₂×D₇₆	—	4	2	no	—
156	C₂×D₇₆	—	4	4	no	—
157	C₂×D₇₆	C₂³	1	1	yes	characteristic
158	C₂×D₇₆	C₂³	1	1	yes	characteristic
159	C₂×D₇₆	C₂³	1	2	yes	—
160	C₂×D₇₆	C₂³	1	2	yes	—
161	C₂×D₇₆	C₂³	1	2	yes	—
162	C₂×D₇₆	C₂³	1	2	yes	—
163	C₂×D₇₆	C₂³	1	2	yes	—
164	C₂×D₇₆	C₂³	1	2	yes	—
165	C₂×D₇₆	C₂³	1	1	yes	characteristic
166	C₂×D₇₆	C₂³	1	1	yes	characteristic
167	C₂×C₄×D₁₉	—	4	2	no	—
168	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
169	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
170	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
171	C₂×C₄×D₁₉	C₂³	1	2	yes	—
172	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
173	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
174	C₂×C₄×D₁₉	C₂³	1	2	yes	—
175	C₂×C₄×D₁₉	C₂³	1	2	yes	—
176	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
177	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
178	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
179	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
180	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
181	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
182	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
183	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
184	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
185	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
186	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
187	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
188	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
189	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
190	C₄²×C₁₉	C₂³	1	1	yes	characteristic
191	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
192	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
193	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
194	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
195	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
196	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
203	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
204	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
205	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
206	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
207	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
208	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
209	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
210	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
211	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
212	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
213	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
214	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
215	C₄⋊Dic₁₉	C₂³	1	2	yes	—
216	C₄⋊Dic₁₉	C₂³	1	2	yes	—
217	C₄⋊Dic₁₉	C₂³	1	2	yes	—
218	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
219	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
220	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
221	Dic₁₉⋊C₄	C₂³	1	2	yes	—
222	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
223	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
224	Dic₁₉⋊C₄	C₂³	1	2	yes	—
225	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
226	Dic₁₉⋊C₄	C₂³	1	2	yes	—
227	C₄×Dic₁₉	C₂³	1	2	yes	—
228	C₄×Dic₁₉	C₂³	1	2	yes	—
229	C₄×Dic₁₉	C₂³	1	2	yes	—
230	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
231	C₂³×C₁₉	C₂⁴	1	2	yes	—
232	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
233	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
234	C₂²×D₁₉	—	2	2	no	—
235	C₂²×D₁₉	—	2	4	no	—
236	C₂²×D₁₉	—	4	1	no	—
237	C₂²×D₁₉	—	4	1	no	—
238	C₂²×D₁₉	—	4	2	no	—
239	C₂²×D₁₉	—	4	2	no	—
240	C₂²×D₁₉	—	4	2	no	—
241	C₂²×D₁₉	—	4	2	no	—
242	C₂²×D₁₉	—	4	2	no	—
243	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
244	C₂²×D₁₉	C₂⁴	1	2	yes	—
245	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
246	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
247	C₂²×D₁₉	C₂⁴	1	2	yes	—
248	Q₈×C₁₉	—	4	2	no	—
249	D₄×C₁₉	—	2	4	no	—
250	D₄×C₁₉	—	2	2	no	—
251	D₄×C₁₉	—	2	2	no	—
252	D₄×C₁₉	—	4	2	no	—
253	C₂×C₄×C₁₉	—	2	4	no	—
254	C₂×C₄×C₁₉	—	2	2	no	—
255	C₂×C₄×C₁₉	—	2	2	no	—
256	C₂×C₄×C₁₉	—	4	2	no	—
257	C₂×C₄×C₁₉	—	4	2	no	—
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	2	yes	—
262	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
263	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
264	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
265	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
266	C₂²⋊D₁₉	—	2	2	no	—
267	C₂²⋊D₁₉	—	4	2	no	—
268	C₂²⋊D₁₉	—	4	1	no	—
269	C₂²⋊D₁₉	—	4	1	no	—
270	C₂²⋊D₁₉	—	4	2	no	—
271	C₂²⋊D₁₉	—	4	2	no	—
272	C₂²⋊D₁₉	—	4	2	no	—
273	C₂²⋊D₁₉	—	4	2	no	—
274	C₂²⋊D₁₉	—	4	2	no	—
275	C₂²⋊D₁₉	—	4	2	no	—
276	C₂²⋊D₁₉	—	4	1	no	—
277	C₂×Dic₁₉	—	4	1	no	—
278	C₂×Dic₁₉	—	4	2	no	—
279	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
280	C₂×Dic₁₉	C₂⁴	1	2	yes	—
281	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
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	D₇₆	—	2	2	no	—
287	D₇₆	—	2	2	no	—
288	D₇₆	—	4	2	no	—
289	D₇₆	—	4	2	no	—
290	D₇₆	—	4	2	no	—
291	D₇₆	—	4	2	no	—
292	D₇₆	—	4	2	no	—
293	D₇₆	—	4	1	no	—
294	D₇₆	—	4	1	no	—
295	D₇₆	—	4	2	no	—
296	C₄×D₁₉	—	2	2	no	—
297	C₄×D₁₉	—	2	2	no	—
298	C₄×D₁₉	—	2	2	no	—
299	C₄×D₁₉	—	4	1	no	—
300	C₄×D₁₉	—	4	1	no	—
301	C₄×D₁₉	—	4	2	no	—
302	C₄×D₁₉	—	4	2	no	—
303	C₄×D₁₉	—	4	2	no	—
304	Dic₃₈	—	2	2	no	—
305	Dic₃₈	—	4	1	no	—
306	#3542	—	19	1	no	maximal, Sylow
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	2	no	—
312	C₂²×C₁₉	—	2	1	no	—
313	C₂²×C₁₉	—	2	1	no	—
314	C₂²×C₁₉	—	2	2	no	—
315	C₂²×C₁₉	H(5,𝔽₂)	1	2	yes	—
316	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
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	2	no	—
322	C₂×D₁₉	—	2	2	no	—
323	C₂×D₁₉	—	2	1	no	—
324	C₂×D₁₉	—	2	1	no	—
325	C₂×D₁₉	—	2	2	no	—
326	C₂×D₁₉	—	2	1	no	—
327	C₂×D₁₉	—	2	2	no	—
328	C₂×D₁₉	—	2	1	no	—
329	C₂×D₁₉	—	2	1	no	—
330	C₂×D₁₉	—	2	1	no	—
331	C₂×D₁₉	—	2	2	no	—
332	C₂×D₁₉	—	4	4	no	—
333	C₂×D₁₉	—	8	4	no	—
334	C₂×D₁₉	—	8	4	no	—
335	C₄×C₁₉	—	2	1	no	—
336	C₄×C₁₉	—	2	1	no	—
337	C₄×C₁₉	—	2	2	no	—
338	C₄×C₁₉	—	2	2	no	—
339	C₄×C₁₉	—	2	2	no	—
340	C₄×C₁₉	—	2	1	no	—
341	C₄×C₁₉	—	2	1	no	—
342	C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
343	Dic₁₉	—	2	2	no	—
344	Dic₁₉	—	2	1	no	—
345	Dic₁₉	—	2	1	no	—
346	Dic₁₉	—	2	1	no	—
347	Dic₁₉	—	2	1	no	—
348	Dic₁₉	—	2	2	no	—
349	Dic₁₉	—	2	1	no	—
350	#562	—	19	2	no	—
351	#560	—	19	2	no	—
352	#555	—	19	1	no	—
353	#553	—	19	1	no	—
354	#552	—	19	1	no	—
355	#551	—	19	2	no	—
356	#550	—	19	1	no	—
357	#547	D₁₉	1	1	yes	characteristic, complemented
358	#546	—	19	2	no	—
359	#546	—	19	1	no	—
360	#546	—	19	1	no	—
361	D₄²	—	19	1	no	—
362	#542	—	19	1	no	—
363	#540	—	19	2	no	—
364	#540	—	19	1	no	—
365	#538	—	19	2	no	—
366	#537	—	19	1	no	—
367	#535	—	19	2	no	—
368	#535	—	19	1	no	—
369	#534	—	19	2	no	—
370	#525	—	19	1	no	—
371	#525	—	19	1	no	—
372	C₂×#121	—	19	1	no	—
373	C₂×C₁₉	—	2	2	no	—
374	C₂×C₁₉	—	4	2	no	—
375	C₂×C₁₉	—	4	1	no	—
376	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
377	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
378	C₂×C₁₉	#585	1	1	yes	characteristic
379	D₁₉	—	4	1	no	—
380	D₁₉	—	4	1	no	—
381	D₁₉	—	4	2	no	—
382	D₁₉	—	4	1	no	—
383	D₁₉	—	4	2	no	—
384	C₂×#41	—	19	1	no	—
385	C₂×#41	—	19	1	no	—
386	C₂×#41	—	19	1	no	—
387	C₂×#41	C₂×D₁₉	1	2	yes	complemented
388	C₂²×D₄	—	19	2	no	—
389	C₂²×D₄	—	19	1	no	—
390	C₂²×D₄	—	19	2	no	—
391	C₂²×D₄	—	19	1	no	—
392	C₂³×C₄	—	19	1	no	—
393	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
394	#127	—	19	2	no	—
395	#127	—	19	2	no	—
396	#127	—	19	1	no	—
397	#126	—	19	2	no	—
398	#126	—	19	2	no	—
399	#126	—	19	2	no	—
400	#125	—	19	1	no	—
401	#125	—	19	2	no	—
402	#124	—	19	2	no	—
403	#124	—	19	2	no	—
404	#124	—	19	2	no	—
405	#124	—	19	2	no	—
406	#124	—	19	1	no	—
407	#123	—	19	2	no	—
408	#123	—	19	2	no	—
409	#123	—	19	1	no	—
410	#123	—	19	2	no	—
411	#123	—	19	2	no	—
412	#123	—	19	2	no	—
413	#123	—	19	1	no	—
414	#123	—	19	2	no	—
415	#123	—	19	2	no	—
416	#123	—	19	2	no	—
417	#123	C₂×D₁₉	1	2	yes	complemented
418	#123	C₂×D₁₉	1	2	yes	complemented
419	C₂²⋊Q₈	—	19	2	no	—
420	C₂²⋊Q₈	—	19	1	no	—
421	C₂²⋊Q₈	—	19	1	no	—
422	C₂²⋊Q₈	—	19	1	no	—
423	C₂²⋊Q₈	—	19	1	no	—
424	C₂²⋊Q₈	—	19	2	no	—
425	C₂²⋊Q₈	—	19	1	no	—
426	C₂²⋊Q₈	C₂×D₁₉	1	2	yes	complemented
427	#121	—	19	1	no	—
428	#121	—	19	1	no	—
429	#121	—	19	2	no	—
430	#121	—	19	2	no	—
431	#121	—	19	2	no	—
432	#121	—	19	1	no	—
433	#121	—	19	2	no	—
434	#121	—	19	2	no	—
435	#121	—	19	2	no	—
436	#121	—	19	1	no	—
437	#121	—	19	1	no	—
438	#121	—	19	2	no	—
439	#121	—	19	1	no	—
440	#121	—	19	1	no	—
441	#121	—	19	2	no	—
442	#121	—	19	2	no	—
443	#121	—	19	2	no	—
444	#121	—	19	1	no	—
445	#121	—	19	1	no	—
446	#121	—	19	2	no	—
447	#121	—	19	2	no	—
448	#121	—	19	2	no	—
449	#121	—	19	2	no	—
450	#121	C₂×D₁₉	1	1	yes	characteristic
451	#121	C₂×D₁₉	1	1	yes	characteristic, complemented
452	#120	—	19	2	no	—
453	#120	—	19	2	no	—
454	#120	—	19	1	no	—
455	#120	—	19	2	no	—
456	#120	—	19	2	no	—
457	#120	—	19	1	no	—
458	#120	—	19	2	no	—
459	#120	—	19	2	no	—
460	#120	—	19	2	no	—
461	C₄×Q₈	—	19	1	no	—
462	C₄×D₄	—	19	2	no	—
463	C₄×D₄	—	19	1	no	—
464	C₄×D₄	—	19	1	no	—
465	C₄×D₄	—	19	2	no	—
466	C₄×D₄	—	19	1	no	—
467	C₄×D₄	—	19	2	no	—
468	C₄×D₄	—	19	2	no	—
469	C₄×D₄	—	19	1	no	—
470	C₄×D₄	—	19	1	no	—
471	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic, complemented
472	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic, complemented
473	#117	—	19	2	no	—
474	#117	—	19	1	no	—
475	#117	—	19	1	no	—
476	#117	—	19	2	no	—
477	#117	—	19	1	no	—
478	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic, complemented
479	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic, complemented
480	C₂×C₂²⋊C₄	—	19	2	no	—
481	C₂×C₂²⋊C₄	—	19	2	no	—
482	C₂×C₂²⋊C₄	—	19	2	no	—
483	C₁₉	#3542	1	1	yes	characteristic, complemented, Sylow
484	C₂⁴	—	19	2	no	—
485	C₂⁴	—	19	1	no	—
486	C₂⁴	—	19	2	no	—
487	#41	—	4	4	no	—
488	#41	—	76	2	no	—
489	#41	—	76	2	no	—
490	#41	—	76	2	no	—
491	C₂×Q₈	—	19	1	no	—
492	C₂×Q₈	—	19	1	no	—
493	C₂×Q₈	C₂²×D₁₉	1	2	yes	—
494	C₂×D₄	—	19	1	no	—
495	C₂×D₄	—	19	2	no	—
496	C₂×D₄	—	19	2	no	—
497	C₂×D₄	—	19	2	no	—
498	C₂×D₄	—	19	1	no	—
499	C₂×D₄	—	19	1	no	—
500	C₂×D₄	—	19	2	no	—
501	C₂×D₄	—	19	2	no	—
502	C₂×D₄	—	19	2	no	—
503	C₂×D₄	—	19	1	no	—
504	C₂×D₄	—	19	2	no	—
505	C₂×D₄	—	19	1	no	—
506	C₂×D₄	—	19	1	no	—
507	C₂×D₄	—	19	1	no	—
508	C₂×D₄	—	19	1	no	—
509	C₂×D₄	—	19	2	no	—
510	C₂×D₄	—	19	2	no	—
511	C₂×D₄	—	19	2	no	—
512	C₂×D₄	—	19	2	no	—
513	C₂×D₄	—	19	2	no	—
514	C₂×D₄	—	19	2	no	—
515	C₂×D₄	—	76	2	no	—
516	C₂×D₄	—	76	4	no	—
517	C₂×D₄	—	76	2	no	—
518	C₂×D₄	—	76	4	no	—
519	C₂×D₄	C₂²×D₁₉	1	2	yes	—
520	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
521	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
522	C₂×D₄	C₂²×D₁₉	1	2	yes	—
523	C₂²×C₄	—	19	1	no	—
524	C₂²×C₄	—	19	2	no	—
525	C₂²×C₄	—	19	1	no	—
526	C₂²×C₄	—	19	1	no	—
527	C₂²×C₄	—	19	1	no	—
528	C₂²×C₄	—	19	2	no	—
529	C₂²×C₄	—	19	2	no	—
530	C₂²×C₄	—	19	1	no	—
531	C₂²×C₄	—	19	2	no	—
532	C₂²×C₄	—	19	1	no	—
533	C₂²×C₄	—	76	2	no	—
534	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
535	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
536	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
537	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
538	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
539	C₄⋊C₄	—	19	1	no	—
540	C₄⋊C₄	—	19	1	no	—
541	C₄⋊C₄	—	19	1	no	—
542	C₄⋊C₄	—	19	1	no	—
543	C₄⋊C₄	—	19	2	no	—
544	C₄⋊C₄	—	19	2	no	—
545	C₄⋊C₄	—	19	2	no	—
546	C₄⋊C₄	—	19	1	no	—
547	C₄⋊C₄	—	19	1	no	—
548	C₄⋊C₄	—	19	2	no	—
549	C₄⋊C₄	—	19	2	no	—
550	C₄⋊C₄	—	19	2	no	—
551	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
552	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
553	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
554	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
555	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
556	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
557	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
558	C₂²⋊C₄	—	19	2	no	—
559	C₂²⋊C₄	—	19	1	no	—
560	C₂²⋊C₄	—	19	1	no	—
561	C₂²⋊C₄	—	19	2	no	—
562	C₂²⋊C₄	—	19	2	no	—
563	C₂²⋊C₄	—	19	1	no	—
564	C₂²⋊C₄	—	19	2	no	—
565	C₂²⋊C₄	—	19	2	no	—
566	C₂²⋊C₄	—	19	2	no	—
567	C₂²⋊C₄	—	19	2	no	—
568	C₂²⋊C₄	—	19	2	no	—
569	C₂²⋊C₄	—	19	2	no	—
570	C₂²⋊C₄	—	19	2	no	—
571	C₂²⋊C₄	—	19	2	no	—
572	C₂²⋊C₄	—	19	2	no	—
573	C₂²⋊C₄	—	19	1	no	—
574	C₂²⋊C₄	—	19	2	no	—
575	C₂²⋊C₄	—	19	1	no	—
576	C₂²⋊C₄	—	19	1	no	—
577	C₂²⋊C₄	—	19	2	no	—
578	C₂²⋊C₄	—	19	1	no	—
579	C₂²⋊C₄	—	19	2	no	—
580	C₂²⋊C₄	—	19	1	no	—
581	C₂²⋊C₄	—	19	2	no	—
582	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
583	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
584	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
585	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
586	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
587	C₄²	—	19	2	no	—
588	C₄²	—	19	2	no	—
589	C₄²	—	19	1	no	—
590	C₄²	—	19	2	no	—
591	C₄²	C₂²×D₁₉	1	1	yes	characteristic
592	C₂³	—	19	2	no	—
593	C₂³	—	19	1	no	—
594	C₂³	—	19	1	no	—
595	C₂³	—	19	1	no	—
596	C₂³	—	19	2	no	—
597	C₂³	—	38	2	no	—
598	C₂³	—	38	4	no	—
599	C₂³	—	76	1	no	—
600	C₂³	—	76	1	no	—
601	C₂³	—	76	2	no	—
602	C₂³	—	76	2	no	—
603	C₂³	—	76	2	no	—
604	C₂³	—	76	2	no	—
605	C₂³	—	76	2	no	—
606	C₂³	C₂³×D₁₉	1	2	yes	—
607	C₂³	C₂³×D₁₉	1	1	yes	characteristic
608	C₂³	C₂³×D₁₉	1	1	yes	characteristic
609	Q₈	—	4	2	no	—
610	Q₈	—	38	2	no	—
611	Q₈	—	76	1	no	—
612	D₄	—	2	4	no	—
613	D₄	—	2	2	no	—
614	D₄	—	2	2	no	—
615	D₄	—	4	2	no	—
616	D₄	—	38	2	no	—
617	D₄	—	38	2	no	—
618	D₄	—	38	2	no	—
619	D₄	—	76	2	no	—
620	D₄	—	76	2	no	—
621	D₄	—	76	2	no	—
622	D₄	—	76	2	no	—
623	D₄	—	76	2	no	—
624	D₄	—	76	2	no	—
625	D₄	—	76	1	no	—
626	D₄	—	76	1	no	—
627	D₄	—	76	2	no	—
628	D₄	—	76	2	no	—
629	D₄	—	76	1	no	—
630	D₄	—	76	1	no	—
631	D₄	—	76	2	no	—
632	D₄	—	76	2	no	—
633	D₄	—	76	2	no	—
634	D₄	—	76	2	no	—
635	D₄	—	76	1	no	—
636	D₄	—	76	2	no	—
637	C₂×C₄	—	2	4	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	4	2	no	—
641	C₂×C₄	—	4	2	no	—
642	C₂×C₄	—	19	1	no	—
643	C₂×C₄	—	19	2	no	—
644	C₂×C₄	—	19	1	no	—
645	C₂×C₄	—	19	1	no	—
646	C₂×C₄	—	19	2	no	—
647	C₂×C₄	—	19	1	no	—
648	C₂×C₄	—	19	1	no	—
649	C₂×C₄	—	38	2	no	—
650	C₂×C₄	—	38	2	no	—
651	C₂×C₄	—	38	2	no	—
652	C₂×C₄	—	76	1	no	—
653	C₂×C₄	—	76	1	no	—
654	C₂×C₄	—	76	2	no	—
655	C₂×C₄	—	76	2	no	—
656	C₂×C₄	—	76	2	no	—
657	C₂×C₄	—	76	1	no	—
658	C₂×C₄	—	76	2	no	—
659	C₂×C₄	C₂³×D₁₉	1	2	yes	—
660	C₂×C₄	C₂³×D₁₉	1	2	yes	—
661	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
662	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
663	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
664	C₂×C₄	C₂³×D₁₉	1	2	yes	—
665	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
666	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
667	C₂²	—	2	1	no	—
668	C₂²	—	2	1	no	—
669	C₂²	—	2	1	no	—
670	C₂²	—	2	2	no	—
671	C₂²	—	2	1	no	—
672	C₂²	—	2	2	no	—
673	C₂²	—	2	1	no	—
674	C₂²	—	2	2	no	—
675	C₂²	—	38	2	no	—
676	C₂²	—	38	1	no	—
677	C₂²	—	38	1	no	—
678	C₂²	—	38	1	no	—
679	C₂²	—	38	2	no	—
680	C₂²	—	38	1	no	—
681	C₂²	—	38	1	no	—
682	C₂²	—	38	1	no	—
683	C₂²	—	38	2	no	—
684	C₂²	—	38	2	no	—
685	C₂²	—	38	2	no	—
686	C₂²	—	38	1	no	—
687	C₂²	—	38	1	no	—
688	C₂²	—	38	1	no	—
689	C₂²	—	38	2	no	—
690	C₂²	—	76	4	no	—
691	C₂²	—	152	4	no	—
692	C₂²	—	152	4	no	—
693	C₂²	#10597430	1	2	yes	—
694	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
695	C₄	—	2	2	no	—
696	C₄	—	2	2	no	—
697	C₄	—	2	1	no	—
698	C₄	—	2	2	no	—
699	C₄	—	2	1	no	—
700	C₄	—	2	1	no	—
701	C₄	—	2	1	no	—
702	C₄	—	38	1	no	—
703	C₄	—	38	1	no	—
704	C₄	—	38	1	no	—
705	C₄	—	38	1	no	—
706	C₄	—	38	2	no	—
707	C₄	—	38	2	no	—
708	C₄	—	38	1	no	—
709	C₄	#10597435	1	2	yes	—
710	C₂	—	2	2	no	—
711	C₂	—	4	2	no	—
712	C₂	—	4	1	no	—
713	C₂	—	76	1	no	—
714	C₂	—	76	1	no	—
715	C₂	—	76	2	no	—
716	C₂	—	76	1	no	—
717	C₂	—	76	2	no	—
718	C₂	C₂×#10597430	1	1	yes	characteristic
719	C₂	C₂×#10597435	1	1	yes	characteristic
720	C₂	#11927381	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₁₉×#547	C₂
hypercenter	#547	D₁₉
hypocenter	C₁₉	#3542
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ #547

Complements

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

N	H ≅ G/N	type
1. #11927290	C₂	semidirect
2. #11927284	C₂	semidirect
3. #11927260	C₂	semidirect
4. #11927242	C₂	semidirect
5. #11927229	C₂	semidirect
6. #11927217	C₂	semidirect
7. #11927212	C₂	semidirect
8. #11927190	C₂	semidirect
9. #11927189	C₂	semidirect
10. #11927182	C₂	semidirect
11. #11927178	C₂	semidirect
12. #11927168	C₂	semidirect
13. #11927146	C₂	semidirect
14. #11927145	C₂	semidirect
15. #11927134	C₂	semidirect
16. #11927125	C₂	semidirect
17. #11927110	C₂	semidirect
18. #11927108	C₂	semidirect
19. #11927105	C₂	semidirect
20. #11927054	C₂	semidirect
21. #11927053	C₂	semidirect
22. C₂×#10597341	C₂	semidirect
23. C₁₉×#547	C₂	semidirect
24. C₂×#41×C₁₉	C₂²	semidirect
25. C₂×#64543	C₂²	semidirect
27. C₂×D₄×D₁₉	C₂²	semidirect
28. C₂×#64541	C₂²	semidirect
29. C₂×#64541	C₂²	semidirect
31. C₂²×D₇₆	C₂²	semidirect
32. C₂²×C₄×D₁₉	C₂²	semidirect
33. C₁₉×C₄⋊Q₈	C₂²	semidirect
34. C₁₉×#123	C₂²	semidirect
35. C₁₉×#123	C₂²	semidirect
36. C₁₉×C₂²⋊Q₈	C₂²	semidirect
38. C₁₉×#121	C₂²	semidirect
39. C₄×D₄×C₁₉	C₂²	semidirect
40. C₄×D₄×C₁₉	C₂²	semidirect
41. C₂×C₄⋊C₄×C₁₉	C₂²	semidirect
42. C₂×C₄⋊C₄×C₁₉	C₂²	semidirect
43. #10597393	C₂²	semidirect
44. #10597393	C₂²	semidirect
45. #10597393	C₂²	semidirect
46. #10597392	C₂²	semidirect
47. #10597386	C₂²	semidirect
48. #10597386	C₂²	semidirect
49. #10597386	C₂²	semidirect
51. #10597385	C₂²	semidirect
52. #10597384	C₂²	semidirect
54. #10597383	C₂²	semidirect
55. #10597383	C₂²	semidirect
56. #10597383	C₂²	semidirect
57. #10597383	C₂²	semidirect
58. D₄×Dic₁₉	C₂²	semidirect
59. #10597376	C₂²	semidirect
60. #10597376	C₂²	semidirect
61. #10597376	C₂²	semidirect
62. #10597376	C₂²	semidirect
63. #10597376	C₂²	semidirect
64. #10597376	C₂²	semidirect
66. #10597375	C₂²	semidirect
68. C₄×C₂²⋊D₁₉	C₂²	semidirect
69. C₄×C₂²⋊D₁₉	C₂²	semidirect
70. C₂×(C₂×D₁₉)⋊C₄	C₂²	semidirect
71. C₂×(C₂×D₁₉)⋊C₄	C₂²	semidirect
72. #10597372	C₂²	semidirect
73. #10597370	C₂²	semidirect
74. #10597344	C₂²	semidirect
75. #10597344	C₂²	semidirect
76. #10597344	C₂²	semidirect
77. #10597343	C₂²	semidirect
78. #10597343	C₂²	semidirect
79. #10597343	C₂²	semidirect
80. #10597342	C₂²	semidirect
83. #10597341	C₂²	semidirect
84. #10597341	C₂²	semidirect
85. #10597341	C₂²	semidirect
86. #10597341	C₂²	semidirect
87. #10597341	C₂²	semidirect
88. #10597341	C₂²	semidirect
89. #10597341	C₂²	semidirect
90. #10597340	C₂²	semidirect
91. #10597340	C₂²	semidirect
92. #10597340	C₂²	semidirect
93. #10597340	C₂²	semidirect
94. #10597339	C₂²	semidirect
95. #10597338	C₂²	semidirect
96. #10597338	C₂²	semidirect
97. #10597338	C₂²	semidirect
98. #10597336	C₂²	semidirect
99. #10597335	C₂²	semidirect
100. #10597333	C₂²	semidirect
101. #10597332	C₂²	semidirect
102. #10597331	C₂²	semidirect
103. #10597330	C₂²	semidirect
104. #10597330	C₂²	semidirect
105. #10597330	C₂²	semidirect
106. #10597330	C₂²	semidirect
107. #10597330	C₂²	semidirect
108. #10597329	C₂²	semidirect
109. #10597329	C₂²	semidirect
110. #10597329	C₂²	semidirect
112. #10597328	C₂²	semidirect
113. #10597328	C₂²	semidirect
114. #10597328	C₂²	semidirect
115. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
116. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
117. C₂²⋊C₄×D₁₉	C₂²	semidirect
118. #10597324	C₂²	semidirect
119. #10597321	C₂²	semidirect
120. C₄×D₇₆	C₂²	semidirect
121. C₄×D₇₆	C₂²	semidirect
122. #10597318	C₂²	semidirect
357. #547	D₁₉	semidirect
387. C₂×#41	C₂×D₁₉	semidirect
393. C₄⋊Q₈	C₂×D₁₉	semidirect
417. #123	C₂×D₁₉	semidirect
418. #123	C₂×D₁₉	semidirect
426. C₂²⋊Q₈	C₂×D₁₉	semidirect
451. #121	C₂×D₁₉	semidirect
471. C₄×D₄	C₂×D₁₉	semidirect
472. C₄×D₄	C₂×D₁₉	semidirect
478. C₂×C₄⋊C₄	C₂×D₁₉	semidirect
479. C₂×C₄⋊C₄	C₂×D₁₉	semidirect
483. C₁₉	#3542	semidirect

Maximal subgroups

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

subgroup	index
#11927290	2
#11927284	2
#11927260	2
#11927242	2
#11927229	2
#11927217	2
#11927212	2
#11927190	2
#11927189	2
#11927182	2
#11927178	2
#11927168	2
#11927146	2
#11927145	2
#11927134	2
#11927125	2
#11927110	2
#11927108	2
#11927105	2
#11927054	2
#11927053	2
C₂×#10597341	2
C₁₉×#547	2
#3542	19