Subgroups — #14578149

Order 2432.

1160 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927289	C₂	1	2	yes	maximal, complemented
2	#11927287	C₂	1	2	yes	maximal, complemented
3	#11927280	C₂	1	1	yes	maximal, characteristic, complemented
4	#11927277	C₂	1	1	yes	maximal, characteristic, complemented
5	#11927203	C₂	1	1	yes	maximal, characteristic, complemented
6	#11927200	C₂	1	1	yes	maximal, characteristic, complemented
7	#11927191	C₂	1	1	yes	maximal, characteristic, complemented
8	#11927188	C₂	1	1	yes	maximal, characteristic, complemented
9	#11927188	C₂	1	2	yes	maximal, complemented
10	#11927181	C₂	1	2	yes	maximal, complemented
11	D₄×C₂²⋊D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#11927161	C₂	1	1	yes	maximal, characteristic, complemented
13	#11927159	C₂	1	1	yes	maximal, characteristic, complemented
14	#11927129	C₂	1	2	yes	maximal, complemented
15	#11927129	C₂	1	2	yes	maximal, complemented
16	#11927126	C₂	1	2	yes	maximal, complemented
17	#11927111	C₂	1	1	yes	maximal, characteristic, complemented
18	#11927107	C₂	1	1	yes	maximal, characteristic, complemented
19	#11927103	C₂	1	2	yes	maximal, complemented
20	#11927089	C₂	1	1	yes	maximal, characteristic, complemented
21	#11927074	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#10597382	C₂	1	1	yes	maximal, characteristic, complemented
23	D₄²×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic
25	C₂²×D₄×C₁₉	C₂²	1	2	yes	complemented
26	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
27	C₂²×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
28	C₂×#64543	C₂²	1	2	yes	complemented
29	C₂×#64543	C₂²	1	1	yes	characteristic, complemented
30	C₂×D₄×D₁₉	C₂²	1	1	yes	characteristic, complemented
31	C₂×#64541	C₂²	1	1	yes	characteristic, complemented
32	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
33	C₁₉×#127	C₂²	1	1	yes	characteristic
34	C₁₉×#121	C₂²	1	1	yes	characteristic
35	C₁₉×#121	C₂²	1	1	yes	characteristic, complemented
36	C₁₉×#121	C₂²	1	2	yes	complemented
37	C₁₉×#120	C₂²	1	2	yes	complemented
38	C₁₉×#120	C₂²	1	2	yes	complemented
39	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
40	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
41	#10597399	C₂²	1	2	yes	complemented
42	#10597399	C₂²	1	2	yes	complemented
43	#10597399	C₂²	1	2	yes	complemented
44	#10597399	C₂²	1	2	yes	complemented
45	C₂×C₂²⋊Dic₁₉	C₂²	1	2	yes	complemented
46	C₂×C₂²⋊Dic₁₉	C₂²	1	2	yes	complemented
47	C₂×C₂²⋊Dic₁₉	C₂²	1	2	yes	complemented
48	#10597386	C₂²	1	1	yes	characteristic
49	#10597386	C₂²	1	1	yes	characteristic, complemented
50	#10597385	C₂²	1	1	yes	characteristic
51	#10597385	C₂²	1	2	yes	complemented
52	#10597385	C₂²	1	2	yes	complemented
53	#10597385	C₂²	1	2	yes	complemented
54	#10597385	C₂²	1	2	yes	complemented
55	#10597385	C₂²	1	2	yes	complemented
56	#10597385	C₂²	1	2	yes	complemented
57	#10597385	C₂²	1	2	yes	complemented
58	#10597384	C₂²	1	1	yes	characteristic
59	#10597384	C₂²	1	2	yes	complemented
60	#10597384	C₂²	1	2	yes	complemented
61	#10597384	C₂²	1	2	yes	complemented
62	#10597383	C₂²	1	2	yes	complemented
63	#10597383	C₂²	1	2	yes	complemented
64	#10597383	C₂²	1	2	yes	complemented
65	#10597383	C₂²	1	2	yes	complemented
66	#10597382	C₂²	1	1	yes	characteristic, complemented
67	#10597382	C₂²	1	1	yes	characteristic, complemented
68	#10597382	C₂²	1	2	yes	complemented
69	#10597382	C₂²	1	1	yes	characteristic, complemented
70	#10597382	C₂²	1	1	yes	characteristic, complemented
71	#10597382	C₂²	1	2	yes	complemented
72	#10597382	C₂²	1	1	yes	characteristic, complemented
73	#10597382	C₂²	1	2	yes	complemented
74	#10597382	C₂²	1	2	yes	complemented
75	#10597381	C₂²	1	1	yes	characteristic, complemented
76	#10597381	C₂²	1	2	yes	complemented
77	#10597381	C₂²	1	2	yes	complemented
78	#10597381	C₂²	1	2	yes	complemented
79	#10597381	C₂²	1	2	yes	complemented
80	D₄×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
81	D₄×Dic₁₉	C₂²	1	2	yes	complemented
82	D₄×Dic₁₉	C₂²	1	2	yes	complemented
83	D₄×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
84	#10597376	C₂²	1	1	yes	characteristic, complemented
85	#10597375	C₂²	1	2	yes	complemented
86	#10597375	C₂²	1	2	yes	complemented
87	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic, complemented
88	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic, complemented
89	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
90	#10597372	C₂²	1	1	yes	characteristic, complemented
91	#10597370	C₂²	1	2	yes	complemented
92	#10597370	C₂²	1	1	yes	characteristic, complemented
93	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
94	#10597344	C₂²	1	1	yes	characteristic, complemented
95	#10597343	C₂²	1	1	yes	characteristic, complemented
96	#10597342	C₂²	1	2	yes	complemented
97	#10597339	C₂²	1	1	yes	characteristic, complemented
98	#10597335	C₂²	1	1	yes	characteristic, complemented
99	#10597334	C₂²	1	1	yes	characteristic, complemented
100	#10597333	C₂²	1	1	yes	characteristic, complemented
101	#10597332	C₂²	1	1	yes	characteristic, complemented
102	#10597331	C₂²	1	1	yes	characteristic, complemented
103	#10597331	C₂²	1	2	yes	complemented
104	#10597331	C₂²	1	2	yes	complemented
105	#10597331	C₂²	1	2	yes	complemented
106	#10597331	C₂²	1	2	yes	complemented
107	#10597331	C₂²	1	2	yes	complemented
108	#10597329	C₂²	1	2	yes	complemented
109	#10597329	C₂²	1	2	yes	complemented
110	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	complemented
111	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	complemented
112	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	complemented
113	#10597325	C₂²	1	1	yes	characteristic, complemented
114	#10597325	C₂²	1	2	yes	complemented
115	#10597325	C₂²	1	2	yes	complemented
116	#10597324	C₂²	1	1	yes	characteristic, complemented
117	#10597324	C₂²	1	2	yes	complemented
118	#10597324	C₂²	1	2	yes	complemented
119	#10597321	C₂²	1	1	yes	characteristic, complemented
120	#10597318	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
123	C₂⁴×C₁₉	C₂³	1	2	yes	—
124	C₂⁴×C₁₉	C₂³	1	2	yes	—
125	C₂³×D₁₉	C₂³	1	2	yes	—
126	C₂×D₄×C₁₉	—	4	2	no	—
127	C₂×D₄×C₁₉	—	4	2	no	—
128	C₂×D₄×C₁₉	—	4	4	no	—
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	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
133	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
134	C₂×D₄×C₁₉	C₂³	1	2	yes	—
135	C₂×D₄×C₁₉	C₂³	1	2	yes	—
136	C₂×D₄×C₁₉	C₂³	1	2	yes	—
137	C₂×D₄×C₁₉	C₂³	1	2	yes	—
138	C₂×D₄×C₁₉	C₂³	1	2	yes	—
139	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
140	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
141	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₁₉	—	4	4	no	—
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	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
152	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
153	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
154	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
155	C₂²×Dic₁₉	C₂³	1	2	yes	—
156	C₂²×Dic₁₉	C₂³	1	2	yes	—
157	C₂²×Dic₁₉	C₂³	1	2	yes	—
158	C₂²×Dic₁₉	C₂³	1	2	yes	—
159	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
160	#64543	—	4	2	no	—
161	#64543	—	4	4	no	—
162	D₄×D₁₉	—	4	2	no	—
163	#64541	—	4	2	no	—
164	C₂×D₇₆	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×Dic₃₈	—	4	2	no	—
169	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
170	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
171	C₂×Dic₃₈	C₂³	1	2	yes	—
172	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
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	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
177	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
178	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
179	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
180	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
181	C₄²×C₁₉	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
183	C₂²⋊Dic₁₉	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	2	yes	—
188	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
189	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
190	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
191	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
192	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
193	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
194	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
195	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
196	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
197	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
198	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
199	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
200	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
201	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
202	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
203	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
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	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
210	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
211	C₄⋊Dic₁₉	C₂³	1	2	yes	—
212	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
213	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
214	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
220	Dic₁₉⋊C₄	C₂³	1	2	yes	—
221	Dic₁₉⋊C₄	C₂³	1	2	yes	—
222	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
223	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
224	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
225	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
226	C₄×Dic₁₉	C₂³	1	2	yes	—
227	C₄×Dic₁₉	C₂³	1	2	yes	—
228	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
229	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
230	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
231	C₂³×C₁₉	—	2	4	no	—
232	C₂³×C₁₉	—	4	2	no	—
233	C₂³×C₁₉	—	4	2	no	—
234	C₂³×C₁₉	—	4	2	no	—
235	C₂³×C₁₉	—	4	2	no	—
236	C₂³×C₁₉	—	4	2	no	—
237	C₂³×C₁₉	C₂⁴	1	2	yes	—
238	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
239	C₂³×C₁₉	C₂⁴	1	2	yes	—
240	C₂³×C₁₉	C₂⁴	1	2	yes	—
241	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
242	C₂²×D₁₉	—	4	2	no	—
243	C₂²×D₁₉	—	4	2	no	—
244	C₂²×D₁₉	—	4	2	no	—
245	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
246	C₂²×D₁₉	C₂⁴	1	2	yes	—
247	D₄×C₁₉	—	2	4	no	—
248	D₄×C₁₉	—	2	2	no	—
249	D₄×C₁₉	—	2	2	no	—
250	D₄×C₁₉	—	2	2	no	—
251	D₄×C₁₉	—	2	2	no	—
252	D₄×C₁₉	—	4	2	no	—
253	D₄×C₁₉	—	4	2	no	—
254	D₄×C₁₉	—	4	2	no	—
255	D₄×C₁₉	—	4	2	no	—
256	D₄×C₁₉	—	4	2	no	—
257	C₂×C₄×C₁₉	—	2	2	no	—
258	C₂×C₄×C₁₉	—	2	2	no	—
259	C₂×C₄×C₁₉	—	4	2	no	—
260	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
261	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
262	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
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	4	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	C₂²⋊D₁₉	—	4	2	no	—
274	C₂²⋊D₁₉	—	4	1	no	—
275	C₂²⋊D₁₉	—	4	2	no	—
276	C₂²⋊D₁₉	—	4	2	no	—
277	C₂×Dic₁₉	—	2	2	no	—
278	C₂×Dic₁₉	—	4	2	no	—
279	C₂×Dic₁₉	—	4	2	no	—
280	C₂×Dic₁₉	—	4	2	no	—
281	C₂×Dic₁₉	—	4	1	no	—
282	C₂×Dic₁₉	—	4	2	no	—
283	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
284	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
285	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
286	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
287	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
288	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
289	C₂×Dic₁₉	C₂⁴	1	2	yes	—
290	C₂×Dic₁₉	C₂⁴	1	2	yes	—
291	C₂×Dic₁₉	C₂⁴	1	2	yes	—
292	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
293	D₇₆	—	2	2	no	—
294	C₄×D₁₉	—	2	2	no	—
295	C₄×D₁₉	—	4	2	no	—
296	C₄×D₁₉	—	4	2	no	—
297	Dic₃₈	—	2	2	no	—
298	Dic₃₈	—	2	2	no	—
299	Dic₃₈	—	4	2	no	—
300	Dic₃₈	—	4	1	no	—
301	Dic₃₈	—	4	2	no	—
302	#3558	—	19	1	no	maximal, Sylow
303	C₂²×C₁₉	—	2	1	no	—
304	C₂²×C₁₉	—	2	1	no	—
305	C₂²×C₁₉	—	2	2	no	—
306	C₂²×C₁₉	—	2	2	no	—
307	C₂²×C₁₉	—	2	2	no	—
308	C₂²×C₁₉	—	2	1	no	—
309	C₂²×C₁₉	—	2	2	no	—
310	C₂²×C₁₉	—	2	2	no	—
311	C₂²×C₁₉	—	2	1	no	—
312	C₂²×C₁₉	—	2	2	no	—
313	C₂²×C₁₉	—	2	2	no	—
314	C₂²×C₁₉	—	2	1	no	—
315	C₂²×C₁₉	—	2	2	no	—
316	C₂²×C₁₉	—	2	2	no	—
317	C₂²×C₁₉	—	8	4	no	—
318	C₂²×C₁₉	—	8	4	no	—
319	C₂²×C₁₉	H(5,𝔽₂)	1	2	yes	—
320	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
321	C₂×D₁₉	—	2	1	no	—
322	C₂×D₁₉	—	2	2	no	—
323	C₂×D₁₉	—	2	2	no	—
324	C₂×D₁₉	—	2	1	no	—
325	C₂×D₁₉	—	2	2	no	—
326	C₂×D₁₉	—	2	1	no	—
327	C₂×D₁₉	—	8	4	no	—
328	C₄×C₁₉	—	2	1	no	—
329	C₄×C₁₉	—	2	2	no	—
330	C₄×C₁₉	—	2	1	no	—
331	C₄×C₁₉	—	2	1	no	—
332	C₄×C₁₉	—	2	1	no	—
333	C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
334	Dic₁₉	—	2	2	no	—
335	Dic₁₉	—	2	2	no	—
336	Dic₁₉	—	2	1	no	—
337	Dic₁₉	—	2	2	no	—
338	Dic₁₉	—	2	1	no	—
339	Dic₁₉	—	2	1	no	—
340	Dic₁₉	—	2	1	no	—
341	Dic₁₉	—	2	1	no	—
342	Dic₁₉	—	2	1	no	—
343	Dic₁₉	—	2	1	no	—
344	#562	—	19	2	no	—
345	H(3,𝔽₄)	—	19	2	no	—
346	#559	—	19	1	no	—
347	#559	—	19	1	no	—
348	#548	—	19	1	no	—
349	#548	—	19	1	no	—
350	#546	—	19	2	no	—
351	#546	—	19	1	no	—
352	#546	—	19	1	no	—
353	#546	—	19	2	no	—
354	D₄²	—	19	1	no	—
355	D₄²	D₁₉	1	1	yes	characteristic, complemented
356	#542	—	19	1	no	—
357	#542	—	19	1	no	—
358	#538	—	19	2	no	—
359	#538	—	19	2	no	—
360	#538	—	19	2	no	—
361	#535	—	19	1	no	—
362	#535	—	19	1	no	—
363	#534	—	19	2	no	—
364	#532	—	19	1	no	—
365	#529	—	19	1	no	—
366	C₂×#124	—	19	1	no	—
367	C₂×C₁₉	—	2	2	no	—
368	C₂×C₁₉	—	4	2	no	—
369	C₂×C₁₉	—	4	2	no	—
370	C₂×C₁₉	—	4	1	no	—
371	C₂×C₁₉	—	4	2	no	—
372	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
373	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
374	C₂×C₁₉	#585	1	1	yes	characteristic
375	D₁₉	—	4	2	no	—
376	D₁₉	—	4	1	no	—
377	C₂×#41	—	19	2	no	—
378	C₂×#41	—	19	1	no	—
379	C₂×#41	—	19	1	no	—
380	C₂²×Q₈	—	19	1	no	—
381	C₂²×D₄	—	19	2	no	—
382	C₂²×D₄	—	19	1	no	—
383	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
384	C₂²×D₄	C₂×D₁₉	1	2	yes	complemented
385	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic, complemented
386	C₄⋊Q₈	—	19	1	no	—
387	#127	—	19	1	no	—
388	#127	—	19	1	no	—
389	#127	C₂×D₁₉	1	1	yes	characteristic
390	#126	—	19	1	no	—
391	#126	—	19	1	no	—
392	#126	—	19	2	no	—
393	#126	—	19	2	no	—
394	#125	—	19	1	no	—
395	#124	—	19	1	no	—
396	#124	—	19	1	no	—
397	#124	—	19	2	no	—
398	#124	—	19	1	no	—
399	#124	—	19	1	no	—
400	#124	—	19	2	no	—
401	#124	—	19	1	no	—
402	#124	—	19	2	no	—
403	#124	—	19	2	no	—
404	#124	—	19	1	no	—
405	#124	—	19	2	no	—
406	#124	—	19	2	no	—
407	#124	—	19	2	no	—
408	#124	—	19	2	no	—
409	#124	—	19	2	no	—
410	#124	—	19	1	no	—
411	#123	—	19	1	no	—
412	#123	—	19	2	no	—
413	#123	—	19	2	no	—
414	#123	—	19	2	no	—
415	#123	—	19	2	no	—
416	#123	—	19	2	no	—
417	#123	—	19	2	no	—
418	#123	—	19	1	no	—
419	#123	—	19	2	no	—
420	#123	—	19	2	no	—
421	C₂²⋊Q₈	—	19	1	no	—
422	C₂²⋊Q₈	—	19	2	no	—
423	C₂²⋊Q₈	—	19	2	no	—
424	C₂²⋊Q₈	—	19	1	no	—
425	C₂²⋊Q₈	—	19	1	no	—
426	C₂²⋊Q₈	—	19	2	no	—
427	C₂²⋊Q₈	—	19	2	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	2	no	—
437	#121	—	19	2	no	—
438	#121	—	19	2	no	—
439	#121	—	19	2	no	—
440	#121	—	19	1	no	—
441	#121	C₂×D₁₉	1	1	yes	characteristic
442	#121	C₂×D₁₉	1	1	yes	characteristic, complemented
443	#121	C₂×D₁₉	1	2	yes	complemented
444	#120	—	19	2	no	—
445	#120	—	19	2	no	—
446	#120	—	19	2	no	—
447	#120	—	19	2	no	—
448	#120	—	19	2	no	—
449	#120	—	19	2	no	—
450	#120	—	19	2	no	—
451	#120	—	19	2	no	—
452	#120	C₂×D₁₉	1	2	yes	complemented
453	#120	C₂×D₁₉	1	2	yes	complemented
454	C₄×Q₈	—	19	1	no	—
455	C₄×Q₈	—	19	1	no	—
456	C₄×Q₈	—	19	1	no	—
457	C₄×D₄	—	19	1	no	—
458	C₄×D₄	—	19	2	no	—
459	C₄×D₄	—	19	2	no	—
460	C₄×D₄	—	19	1	no	—
461	C₄×D₄	—	19	1	no	—
462	C₄×D₄	—	19	1	no	—
463	C₄×D₄	—	19	2	no	—
464	C₄×D₄	—	19	1	no	—
465	C₄×D₄	—	19	2	no	—
466	C₄×D₄	—	19	2	no	—
467	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic, complemented
468	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic, complemented
469	#117	—	19	1	no	—
470	#117	—	19	1	no	—
471	C₂×C₂²⋊C₄	—	19	2	no	—
472	C₂×C₂²⋊C₄	—	19	2	no	—
473	C₂×C₂²⋊C₄	—	19	2	no	—
474	C₂×C₂²⋊C₄	—	19	2	no	—
475	C₂×C₄²	—	19	1	no	—
476	C₁₉	#3558	1	1	yes	characteristic, complemented, Sylow
477	C₂⁴	—	19	2	no	—
478	C₂⁴	C₂²×D₁₉	1	2	yes	—
479	C₂⁴	C₂²×D₁₉	1	2	yes	—
480	#41	—	76	2	no	—
481	#41	—	76	4	no	—
482	#41	—	76	2	no	—
483	C₂×Q₈	—	19	1	no	—
484	C₂×Q₈	—	19	1	no	—
485	C₂×Q₈	—	19	1	no	—
486	C₂×Q₈	—	19	2	no	—
487	C₂×Q₈	—	19	2	no	—
488	C₂×Q₈	—	76	2	no	—
489	C₂×D₄	—	4	2	no	—
490	C₂×D₄	—	4	2	no	—
491	C₂×D₄	—	4	4	no	—
492	C₂×D₄	—	19	2	no	—
493	C₂×D₄	—	19	1	no	—
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	2	no	—
499	C₂×D₄	—	19	2	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	—	76	2	no	—
505	C₂×D₄	—	76	4	no	—
506	C₂×D₄	C₂²×D₁₉	1	2	yes	—
507	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
508	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
509	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
510	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
511	C₂×D₄	C₂²×D₁₉	1	2	yes	—
512	C₂×D₄	C₂²×D₁₉	1	2	yes	—
513	C₂×D₄	C₂²×D₁₉	1	2	yes	—
514	C₂×D₄	C₂²×D₁₉	1	2	yes	—
515	C₂×D₄	C₂²×D₁₉	1	2	yes	—
516	C₂²×C₄	—	19	1	no	—
517	C₂²×C₄	—	19	1	no	—
518	C₂²×C₄	—	19	2	no	—
519	C₂²×C₄	—	19	2	no	—
520	C₂²×C₄	—	19	2	no	—
521	C₂²×C₄	—	19	2	no	—
522	C₂²×C₄	—	19	1	no	—
523	C₂²×C₄	—	19	2	no	—
524	C₂²×C₄	—	19	2	no	—
525	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
526	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
527	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
528	C₄⋊C₄	—	19	1	no	—
529	C₄⋊C₄	—	19	1	no	—
530	C₄⋊C₄	—	19	1	no	—
531	C₄⋊C₄	—	19	1	no	—
532	C₄⋊C₄	—	19	2	no	—
533	C₄⋊C₄	—	19	2	no	—
534	C₄⋊C₄	—	19	1	no	—
535	C₄⋊C₄	—	19	2	no	—
536	C₄⋊C₄	—	19	2	no	—
537	C₄⋊C₄	—	19	1	no	—
538	C₄⋊C₄	—	19	1	no	—
539	C₄⋊C₄	—	19	1	no	—
540	C₄⋊C₄	—	19	1	no	—
541	C₄⋊C₄	—	19	1	no	—
542	C₄⋊C₄	—	19	2	no	—
543	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
544	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
545	C₂²⋊C₄	—	19	1	no	—
546	C₂²⋊C₄	—	19	2	no	—
547	C₂²⋊C₄	—	19	2	no	—
548	C₂²⋊C₄	—	19	2	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	2	no	—
555	C₂²⋊C₄	—	19	2	no	—
556	C₂²⋊C₄	—	19	1	no	—
557	C₂²⋊C₄	—	19	1	no	—
558	C₂²⋊C₄	—	19	1	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	1	no	—
564	C₂²⋊C₄	—	19	2	no	—
565	C₂²⋊C₄	—	19	1	no	—
566	C₂²⋊C₄	—	19	1	no	—
567	C₂²⋊C₄	—	19	1	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	C₂²×D₁₉	1	2	yes	—
573	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
574	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
575	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
576	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
577	C₄²	—	19	1	no	—
578	C₄²	—	19	1	no	—
579	C₄²	—	19	1	no	—
580	C₄²	—	19	1	no	—
581	C₄²	—	19	1	no	—
582	C₄²	—	19	2	no	—
583	C₄²	—	19	2	no	—
584	C₄²	C₂²×D₁₉	1	1	yes	characteristic
585	C₂³	—	2	4	no	—
586	C₂³	—	4	2	no	—
587	C₂³	—	4	2	no	—
588	C₂³	—	4	2	no	—
589	C₂³	—	4	2	no	—
590	C₂³	—	4	2	no	—
591	C₂³	—	19	1	no	—
592	C₂³	—	19	2	no	—
593	C₂³	—	76	2	no	—
594	C₂³	—	76	2	no	—
595	C₂³	—	76	2	no	—
596	C₂³	C₂³×D₁₉	1	2	yes	—
597	C₂³	C₂³×D₁₉	1	1	yes	characteristic
598	C₂³	C₂³×D₁₉	1	2	yes	—
599	C₂³	C₂³×D₁₉	1	2	yes	—
600	C₂³	C₂³×D₁₉	1	1	yes	characteristic
601	Q₈	—	38	2	no	—
602	Q₈	—	38	2	no	—
603	Q₈	—	76	2	no	—
604	Q₈	—	76	2	no	—
605	Q₈	—	76	1	no	—
606	D₄	—	2	2	no	—
607	D₄	—	2	4	no	—
608	D₄	—	2	2	no	—
609	D₄	—	2	2	no	—
610	D₄	—	2	2	no	—
611	D₄	—	4	2	no	—
612	D₄	—	4	2	no	—
613	D₄	—	4	2	no	—
614	D₄	—	4	2	no	—
615	D₄	—	4	2	no	—
616	D₄	—	38	2	no	—
617	D₄	—	38	4	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	2	no	—
626	D₄	—	76	1	no	—
627	D₄	—	76	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	4	2	no	—
631	C₂×C₄	—	19	1	no	—
632	C₂×C₄	—	19	1	no	—
633	C₂×C₄	—	19	1	no	—
634	C₂×C₄	—	19	1	no	—
635	C₂×C₄	—	19	1	no	—
636	C₂×C₄	—	19	2	no	—
637	C₂×C₄	—	19	2	no	—
638	C₂×C₄	—	19	2	no	—
639	C₂×C₄	—	19	1	no	—
640	C₂×C₄	—	19	1	no	—
641	C₂×C₄	—	38	2	no	—
642	C₂×C₄	—	38	2	no	—
643	C₂×C₄	—	76	2	no	—
644	C₂×C₄	—	76	2	no	—
645	C₂×C₄	—	76	2	no	—
646	C₂×C₄	—	76	2	no	—
647	C₂×C₄	—	76	2	no	—
648	C₂×C₄	—	76	2	no	—
649	C₂×C₄	—	76	1	no	—
650	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
651	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
652	C₂×C₄	C₂³×D₁₉	1	2	yes	—
653	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
654	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
655	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
656	C₂²	—	2	1	no	—
657	C₂²	—	2	1	no	—
658	C₂²	—	2	1	no	—
659	C₂²	—	2	2	no	—
660	C₂²	—	2	2	no	—
661	C₂²	—	2	2	no	—
662	C₂²	—	2	2	no	—
663	C₂²	—	2	1	no	—
664	C₂²	—	2	2	no	—
665	C₂²	—	2	2	no	—
666	C₂²	—	2	2	no	—
667	C₂²	—	2	2	no	—
668	C₂²	—	2	1	no	—
669	C₂²	—	2	2	no	—
670	C₂²	—	8	4	no	—
671	C₂²	—	8	4	no	—
672	C₂²	—	38	1	no	—
673	C₂²	—	38	2	no	—
674	C₂²	—	38	2	no	—
675	C₂²	—	38	1	no	—
676	C₂²	—	38	2	no	—
677	C₂²	—	38	1	no	—
678	C₂²	—	152	4	no	—
679	C₂²	#10597430	1	2	yes	—
680	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
681	C₄	—	2	1	no	—
682	C₄	—	2	1	no	—
683	C₄	—	2	1	no	—
684	C₄	—	2	2	no	—
685	C₄	—	2	1	no	—
686	C₄	—	38	1	no	—
687	C₄	—	38	1	no	—
688	C₄	—	38	1	no	—
689	C₄	—	38	1	no	—
690	C₄	—	38	2	no	—
691	C₄	—	38	2	no	—
692	C₄	—	38	2	no	—
693	C₄	—	38	1	no	—
694	C₄	—	38	1	no	—
695	C₄	—	38	1	no	—
696	C₄	#10597430	1	2	yes	—
697	C₂	—	2	2	no	—
698	C₂	—	4	1	no	—
699	C₂	—	4	2	no	—
700	C₂	—	4	2	no	—
701	C₂	—	4	2	no	—
702	C₂	—	76	1	no	—
703	C₂	—	76	2	no	—
704	C₂	C₂×#10597430	1	1	yes	characteristic
705	C₂	C₂×#10597430	1	1	yes	characteristic
706	C₂	#11927379	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	D₄²×C₁₉	C₂
hypercenter	D₄²	D₁₉
hypocenter	C₁₉	#3558
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ D₄²

Complements

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

N	H ≅ G/N	type
1. #11927289	C₂	semidirect
2. #11927287	C₂	semidirect
3. #11927280	C₂	semidirect
4. #11927277	C₂	semidirect
5. #11927203	C₂	semidirect
6. #11927200	C₂	semidirect
7. #11927191	C₂	semidirect
8. #11927188	C₂	semidirect
9. #11927188	C₂	semidirect
10. #11927181	C₂	semidirect
11. D₄×C₂²⋊D₁₉	C₂	semidirect
12. #11927161	C₂	semidirect
13. #11927159	C₂	semidirect
14. #11927129	C₂	semidirect
15. #11927129	C₂	semidirect
16. #11927126	C₂	semidirect
17. #11927111	C₂	semidirect
18. #11927107	C₂	semidirect
19. #11927103	C₂	semidirect
20. #11927089	C₂	semidirect
21. #11927074	C₂	semidirect
22. C₂×#10597382	C₂	semidirect
23. D₄²×C₁₉	C₂	semidirect
25. C₂²×D₄×C₁₉	C₂²	semidirect
26. C₂²×D₄×C₁₉	C₂²	semidirect
27. C₂²×C₂²⋊D₁₉	C₂²	semidirect
28. C₂×#64543	C₂²	semidirect
29. C₂×#64543	C₂²	semidirect
30. C₂×D₄×D₁₉	C₂²	semidirect
31. C₂×#64541	C₂²	semidirect
32. C₂²×Dic₃₈	C₂²	semidirect
35. C₁₉×#121	C₂²	semidirect
36. C₁₉×#121	C₂²	semidirect
37. C₁₉×#120	C₂²	semidirect
38. C₁₉×#120	C₂²	semidirect
39. C₄×D₄×C₁₉	C₂²	semidirect
40. C₄×D₄×C₁₉	C₂²	semidirect
41. #10597399	C₂²	semidirect
42. #10597399	C₂²	semidirect
43. #10597399	C₂²	semidirect
44. #10597399	C₂²	semidirect
45. C₂×C₂²⋊Dic₁₉	C₂²	semidirect
46. C₂×C₂²⋊Dic₁₉	C₂²	semidirect
47. C₂×C₂²⋊Dic₁₉	C₂²	semidirect
49. #10597386	C₂²	semidirect
51. #10597385	C₂²	semidirect
52. #10597385	C₂²	semidirect
53. #10597385	C₂²	semidirect
54. #10597385	C₂²	semidirect
55. #10597385	C₂²	semidirect
56. #10597385	C₂²	semidirect
57. #10597385	C₂²	semidirect
59. #10597384	C₂²	semidirect
60. #10597384	C₂²	semidirect
61. #10597384	C₂²	semidirect
62. #10597383	C₂²	semidirect
63. #10597383	C₂²	semidirect
64. #10597383	C₂²	semidirect
65. #10597383	C₂²	semidirect
66. #10597382	C₂²	semidirect
67. #10597382	C₂²	semidirect
68. #10597382	C₂²	semidirect
69. #10597382	C₂²	semidirect
70. #10597382	C₂²	semidirect
71. #10597382	C₂²	semidirect
72. #10597382	C₂²	semidirect
73. #10597382	C₂²	semidirect
74. #10597382	C₂²	semidirect
75. #10597381	C₂²	semidirect
76. #10597381	C₂²	semidirect
77. #10597381	C₂²	semidirect
78. #10597381	C₂²	semidirect
79. #10597381	C₂²	semidirect
80. D₄×Dic₁₉	C₂²	semidirect
81. D₄×Dic₁₉	C₂²	semidirect
82. D₄×Dic₁₉	C₂²	semidirect
83. D₄×Dic₁₉	C₂²	semidirect
84. #10597376	C₂²	semidirect
85. #10597375	C₂²	semidirect
86. #10597375	C₂²	semidirect
87. C₄×C₂²⋊D₁₉	C₂²	semidirect
88. C₄×C₂²⋊D₁₉	C₂²	semidirect
89. C₄×C₂²⋊D₁₉	C₂²	semidirect
90. #10597372	C₂²	semidirect
91. #10597370	C₂²	semidirect
92. #10597370	C₂²	semidirect
93. C₂×C₄×Dic₁₉	C₂²	semidirect
94. #10597344	C₂²	semidirect
95. #10597343	C₂²	semidirect
96. #10597342	C₂²	semidirect
97. #10597339	C₂²	semidirect
98. #10597335	C₂²	semidirect
99. #10597334	C₂²	semidirect
100. #10597333	C₂²	semidirect
101. #10597332	C₂²	semidirect
102. #10597331	C₂²	semidirect
103. #10597331	C₂²	semidirect
104. #10597331	C₂²	semidirect
105. #10597331	C₂²	semidirect
106. #10597331	C₂²	semidirect
107. #10597331	C₂²	semidirect
108. #10597329	C₂²	semidirect
109. #10597329	C₂²	semidirect
110. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
111. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
112. C₂²⋊C₄×D₁₉	C₂²	semidirect
113. #10597325	C₂²	semidirect
114. #10597325	C₂²	semidirect
115. #10597325	C₂²	semidirect
116. #10597324	C₂²	semidirect
117. #10597324	C₂²	semidirect
118. #10597324	C₂²	semidirect
119. #10597321	C₂²	semidirect
120. #10597318	C₂²	semidirect
121. C₄×Dic₃₈	C₂²	semidirect
122. C₄×Dic₃₈	C₂²	semidirect
355. D₄²	D₁₉	semidirect
384. C₂²×D₄	C₂×D₁₉	semidirect
385. C₂²×D₄	C₂×D₁₉	semidirect
442. #121	C₂×D₁₉	semidirect
443. #121	C₂×D₁₉	semidirect
452. #120	C₂×D₁₉	semidirect
453. #120	C₂×D₁₉	semidirect
467. C₄×D₄	C₂×D₁₉	semidirect
468. C₄×D₄	C₂×D₁₉	semidirect
476. C₁₉	#3558	semidirect

Maximal subgroups

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

subgroup	index
#11927289	2
#11927287	2
#11927280	2
#11927277	2
#11927203	2
#11927200	2
#11927191	2
#11927188	2
#11927181	2
D₄×C₂²⋊D₁₉	2
#11927161	2
#11927159	2
#11927129	2
#11927126	2
#11927111	2
#11927107	2
#11927103	2
#11927089	2
#11927074	2
C₂×#10597382	2
D₄²×C₁₉	2
#3558	19