Subgroups — #14577481

Order 2432.

1140 conjugacy classes of subgroups.

The subgroup lattice has 690 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	#11927261	C₂	1	2	yes	maximal, complemented
4	#11927258	C₂	1	1	yes	maximal, characteristic, complemented
5	#11927257	C₂	1	1	yes	maximal, characteristic, complemented
6	#11927247	C₂	1	1	yes	maximal, characteristic, complemented
7	#11927244	C₂	1	1	yes	maximal, characteristic, complemented
8	#11927240	C₂	1	1	yes	maximal, characteristic, complemented
9	#11927212	C₂	1	2	yes	maximal, complemented
10	#11927195	C₂	1	1	yes	maximal, characteristic, complemented
11	#11927194	C₂	1	1	yes	maximal, characteristic, complemented
12	#11927133	C₂	1	2	yes	maximal, complemented
13	#11927126	C₂	1	2	yes	maximal, complemented
14	#11927110	C₂	1	1	yes	maximal, characteristic, complemented
15	#11927110	C₂	1	1	yes	maximal, characteristic, complemented
16	#11927100	C₂	1	1	yes	maximal, characteristic, complemented
17	#11927091	C₂	1	1	yes	maximal, characteristic, complemented
18	#11927053	C₂	1	2	yes	maximal, complemented
19	#11927052	C₂	1	2	yes	maximal, complemented
20	#11927025	C₂	1	1	yes	maximal, characteristic, complemented
21	#11927024	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×D₄×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₉×#553	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#64543	C₂²	1	2	yes	complemented
25	C₂×D₄×D₁₉	C₂²	1	1	yes	characteristic
26	C₂×#64541	C₂²	1	1	yes	characteristic
27	C₂×#64541	C₂²	1	1	yes	characteristic
28	C₂×#64541	C₂²	1	2	yes	complemented
29	C₂²×C₄×D₁₉	C₂²	1	2	yes	—
30	C₁₉×#126	C₂²	1	2	yes	complemented
31	C₁₉×#125	C₂²	1	1	yes	characteristic, complemented
32	C₁₉×#123	C₂²	1	2	yes	complemented
33	C₁₉×#121	C₂²	1	1	yes	characteristic
34	C₁₉×#121	C₂²	1	1	yes	characteristic
35	C₁₉×#121	C₂²	1	2	yes	complemented
36	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
37	C₄×D₄×C₁₉	C₂²	1	2	yes	complemented
38	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
39	C₁₉×#117	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
41	#10597386	C₂²	1	2	yes	—
42	#10597386	C₂²	1	2	yes	—
43	#10597386	C₂²	1	1	yes	characteristic, complemented
44	#10597385	C₂²	1	2	yes	complemented
45	#10597385	C₂²	1	2	yes	complemented
46	#10597384	C₂²	1	1	yes	characteristic
47	#10597384	C₂²	1	1	yes	characteristic
48	#10597384	C₂²	1	1	yes	characteristic
49	#10597383	C₂²	1	2	yes	—
50	#10597383	C₂²	1	2	yes	—
51	#10597382	C₂²	1	2	yes	complemented
52	#10597381	C₂²	1	2	yes	complemented
53	D₄×Dic₁₉	C₂²	1	1	yes	characteristic
54	#10597376	C₂²	1	1	yes	characteristic
55	#10597376	C₂²	1	1	yes	characteristic
56	#10597375	C₂²	1	2	yes	complemented
57	#10597375	C₂²	1	2	yes	complemented
58	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	—
59	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	—
60	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
61	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic, complemented
62	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic, complemented
63	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
64	#10597372	C₂²	1	1	yes	characteristic, complemented
65	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic, complemented
66	#10597344	C₂²	1	2	yes	complemented
67	#10597344	C₂²	1	2	yes	complemented
68	#10597342	C₂²	1	2	yes	—
69	#10597342	C₂²	1	2	yes	—
70	#10597342	C₂²	1	2	yes	complemented
71	#10597341	C₂²	1	1	yes	characteristic
72	#10597341	C₂²	1	1	yes	characteristic
73	#10597341	C₂²	1	1	yes	characteristic
74	#10597341	C₂²	1	2	yes	complemented
75	#10597340	C₂²	1	2	yes	complemented
76	#10597340	C₂²	1	2	yes	complemented
77	#10597339	C₂²	1	2	yes	—
78	#10597339	C₂²	1	1	yes	characteristic
79	#10597339	C₂²	1	2	yes	complemented
80	#10597338	C₂²	1	1	yes	characteristic
81	#10597338	C₂²	1	1	yes	characteristic
82	#10597338	C₂²	1	1	yes	characteristic, complemented
83	#10597338	C₂²	1	1	yes	characteristic, complemented
84	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic
85	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic, complemented
86	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic, complemented
87	#10597334	C₂²	1	1	yes	characteristic, complemented
88	#10597334	C₂²	1	1	yes	characteristic, complemented
89	#10597334	C₂²	1	1	yes	characteristic, complemented
90	#10597333	C₂²	1	2	yes	complemented
91	#10597333	C₂²	1	2	yes	complemented
92	#10597333	C₂²	1	2	yes	complemented
93	#10597331	C₂²	1	2	yes	—
94	#10597331	C₂²	1	2	yes	—
95	#10597331	C₂²	1	1	yes	characteristic, complemented
96	#10597331	C₂²	1	1	yes	characteristic, complemented
97	#10597331	C₂²	1	2	yes	complemented
98	#10597331	C₂²	1	2	yes	complemented
99	#10597330	C₂²	1	1	yes	characteristic
100	#10597330	C₂²	1	1	yes	characteristic
101	#10597330	C₂²	1	2	yes	complemented
102	#10597330	C₂²	1	2	yes	complemented
103	#10597329	C₂²	1	2	yes	complemented
104	#10597329	C₂²	1	2	yes	complemented
105	#10597328	C₂²	1	2	yes	—
106	#10597328	C₂²	1	2	yes	—
107	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	—
108	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	—
109	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	complemented
110	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	complemented
111	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	—
112	#10597325	C₂²	1	2	yes	complemented
113	#10597324	C₂²	1	2	yes	complemented
114	#10597323	C₂²	1	2	yes	complemented
115	#10597321	C₂²	1	2	yes	complemented
116	C₄×D₇₆	C₂²	1	2	yes	—
117	C₄×D₇₆	C₂²	1	1	yes	characteristic
118	C₄×D₇₆	C₂²	1	1	yes	characteristic, complemented
119	#10597318	C₂²	1	2	yes	complemented
120	C₄²×D₁₉	C₂²	1	1	yes	characteristic
121	#10597316	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₃₈	C₂²	1	2	yes	complemented
123	C₂³×D₁₉	C₂³	1	2	yes	—
124	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
125	C₂×D₄×C₁₉	C₂³	1	2	yes	—
126	C₂×D₄×C₁₉	C₂³	1	2	yes	—
127	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
131	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
133	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
136	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
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	2	yes	—
142	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
143	C₂²×Dic₁₉	C₂³	1	2	yes	—
144	C₂²×Dic₁₉	C₂³	1	2	yes	—
145	#64543	—	4	4	no	—
146	D₄×D₁₉	—	2	4	no	—
147	#64541	—	2	4	no	—
148	#64541	—	2	4	no	—
149	#64541	—	4	4	no	—
150	C₂×D₇₆	C₂³	1	1	yes	characteristic
151	C₂×D₇₆	C₂³	1	1	yes	characteristic
152	C₂×D₇₆	C₂³	1	1	yes	characteristic
153	C₂×D₇₆	C₂³	1	2	yes	—
154	C₂×D₇₆	C₂³	1	2	yes	—
155	C₂×D₇₆	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₁₉	—	4	4	no	—
157	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
160	C₂×C₄×D₁₉	C₂³	1	2	yes	—
161	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
162	C₂×C₄×D₁₉	C₂³	1	2	yes	—
163	C₂×C₄×D₁₉	C₂³	1	2	yes	—
164	C₂×C₄×D₁₉	C₂³	1	2	yes	—
165	C₂×C₄×D₁₉	C₂³	1	2	yes	—
166	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
167	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
168	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
169	C₂×Dic₃₈	C₂³	1	2	yes	—
170	C₂×Dic₃₈	C₂³	1	2	yes	—
171	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
172	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
173	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
174	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
175	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
176	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
181	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
182	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
183	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
184	C₄²×C₁₉	C₂³	1	2	yes	—
185	C₄²×C₁₉	C₂³	1	1	yes	characteristic
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	2	yes	—
192	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
193	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
194	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
195	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
201	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
202	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
203	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
204	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
205	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
206	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
207	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
208	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
209	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
210	C₄⋊Dic₁₉	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	2	yes	—
216	Dic₁₉⋊C₄	C₂³	1	2	yes	—
217	Dic₁₉⋊C₄	C₂³	1	2	yes	—
218	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
219	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
220	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
221	C₄×Dic₁₉	C₂³	1	2	yes	—
222	C₄×Dic₁₉	C₂³	1	2	yes	—
223	C₄×Dic₁₉	C₂³	1	2	yes	—
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	C₂³×C₁₉	C₂⁴	1	2	yes	—
229	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
230	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
231	C₂²×D₁₉	—	2	4	no	—
232	C₂²×D₁₉	—	4	2	no	—
233	C₂²×D₁₉	—	4	2	no	—
234	C₂²×D₁₉	C₂⁴	1	2	yes	—
235	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
236	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
237	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
238	D₄×C₁₉	—	2	2	no	—
239	D₄×C₁₉	—	4	2	no	—
240	D₄×C₁₉	—	4	2	no	—
241	D₄×C₁₉	—	4	1	no	—
242	C₂×C₄×C₁₉	—	2	2	no	—
243	C₂×C₄×C₁₉	—	2	2	no	—
244	C₂×C₄×C₁₉	—	4	2	no	—
245	C₂×C₄×C₁₉	—	4	2	no	—
246	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
247	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
251	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
252	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
253	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
254	C₂²⋊D₁₉	—	2	2	no	—
255	C₂²⋊D₁₉	—	2	2	no	—
256	C₂²⋊D₁₉	—	2	2	no	—
257	C₂²⋊D₁₉	—	2	2	no	—
258	C₂²⋊D₁₉	—	2	4	no	—
259	C₂²⋊D₁₉	—	2	2	no	—
260	C₂²⋊D₁₉	—	2	2	no	—
261	C₂²⋊D₁₉	—	4	2	no	—
262	C₂²⋊D₁₉	—	4	2	no	—
263	C₂²⋊D₁₉	—	4	2	no	—
264	C₂²⋊D₁₉	—	4	2	no	—
265	C₂×Dic₁₉	—	2	4	no	—
266	C₂×Dic₁₉	—	4	2	no	—
267	C₂×Dic₁₉	C₂⁴	1	2	yes	—
268	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
269	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
270	C₂×Dic₁₉	C₂⁴	1	2	yes	—
271	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
272	C₂×Dic₁₉	C₂⁴	1	2	yes	—
273	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
274	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
275	D₇₆	—	2	2	no	—
276	D₇₆	—	2	2	no	—
277	D₇₆	—	2	2	no	—
278	D₇₆	—	4	2	no	—
279	D₇₆	—	4	1	no	—
280	D₇₆	—	4	2	no	—
281	C₄×D₁₉	—	2	2	no	—
282	C₄×D₁₉	—	2	2	no	—
283	C₄×D₁₉	—	2	2	no	—
284	C₄×D₁₉	—	2	4	no	—
285	C₄×D₁₉	—	4	2	no	—
286	C₄×D₁₉	—	4	2	no	—
287	C₄×D₁₉	—	4	1	no	—
288	C₄×D₁₉	—	4	2	no	—
289	C₄×D₁₉	—	4	2	no	—
290	C₄×D₁₉	#41	1	4	yes	complemented
291	Dic₃₈	—	2	2	no	—
292	Dic₃₈	—	2	2	no	—
293	Dic₃₈	—	2	4	no	—
294	Dic₃₈	—	4	2	no	—
295	#3506	—	19	1	no	maximal, Sylow
296	C₂²×C₁₉	—	2	1	no	—
297	C₂²×C₁₉	—	2	1	no	—
298	C₂²×C₁₉	—	2	2	no	—
299	C₂²×C₁₉	—	2	2	no	—
300	C₂²×C₁₉	—	2	1	no	—
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	C₂⁵	1	1	yes	characteristic
306	C₂×D₁₉	—	2	1	no	—
307	C₂×D₁₉	—	2	1	no	—
308	C₂×D₁₉	—	2	1	no	—
309	C₂×D₁₉	—	2	1	no	—
310	C₂×D₁₉	—	2	2	no	—
311	C₂×D₁₉	—	2	2	no	—
312	C₂×D₁₉	—	2	1	no	—
313	C₂×D₁₉	—	2	1	no	—
314	C₂×D₁₉	—	2	1	no	—
315	C₂×D₁₉	—	2	1	no	—
316	C₂×D₁₉	—	2	2	no	—
317	C₂×D₁₉	—	4	8	no	—
318	C₂×D₁₉	C₂×#41	1	2	yes	—
319	C₄×C₁₉	—	2	1	no	—
320	C₄×C₁₉	—	2	1	no	—
321	C₄×C₁₉	—	2	2	no	—
322	C₄×C₁₉	—	2	1	no	—
323	C₄×C₁₉	—	2	2	no	—
324	C₄×C₁₉	—	2	2	no	—
325	C₄×C₁₉	—	2	1	no	—
326	C₄×C₁₉	C₂×#41	1	2	yes	—
327	Dic₁₉	—	2	1	no	—
328	Dic₁₉	—	2	1	no	—
329	Dic₁₉	—	2	2	no	—
330	Dic₁₉	—	2	2	no	—
331	Dic₁₉	—	2	1	no	—
332	Dic₁₉	—	2	2	no	—
333	Dic₁₉	C₂×#41	1	2	yes	—
334	Dic₁₉	H(5,𝔽₂)	1	2	yes	—
335	#559	—	19	2	no	—
336	#559	—	19	2	no	—
337	#556	—	19	2	no	—
338	#555	—	19	1	no	—
339	#555	—	19	1	no	—
340	#553	—	19	1	no	—
341	#553	—	19	1	no	—
342	#553	—	19	1	no	—
343	#553	D₁₉	1	1	yes	characteristic, complemented
344	#550	—	19	2	no	—
345	#547	—	19	1	no	—
346	#547	—	19	1	no	—
347	#538	—	19	2	no	—
348	#538	—	19	2	no	—
349	#535	—	19	1	no	—
350	#535	—	19	1	no	—
351	#533	—	19	1	no	—
352	#532	—	19	1	no	—
353	#525	—	19	2	no	—
354	#525	—	19	2	no	—
355	#520	—	19	1	no	—
356	#520	—	19	1	no	—
357	C₂×C₄×D₄	—	19	1	no	—
358	C₂×C₁₉	—	4	2	no	—
359	C₂×C₁₉	—	4	1	no	—
360	C₂×C₁₉	—	4	1	no	—
361	C₂×C₁₉	C₂²×#41	1	1	yes	characteristic
362	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
363	C₂×C₁₉	#585	1	1	yes	characteristic
364	D₁₉	—	2	2	no	—
365	D₁₉	—	4	1	no	—
366	D₁₉	—	4	1	no	—
367	D₁₉	—	4	2	no	—
368	C₂×#41	—	19	2	no	—
369	C₂×#41	—	19	1	no	—
370	C₂×#41	—	19	1	no	—
371	C₂×#41	—	19	2	no	—
372	C₂²×D₄	—	19	1	no	—
373	C₂³×C₄	—	19	2	no	—
374	C₄⋊Q₈	—	19	1	no	—
375	C₄⋊Q₈	—	19	1	no	—
376	C₄⋊Q₈	—	19	1	no	—
377	#127	—	19	2	no	—
378	#127	—	19	2	no	—
379	#127	—	19	1	no	—
380	#126	—	19	2	no	—
381	#126	—	19	2	no	—
382	#126	—	19	2	no	—
383	#126	C₂×D₁₉	1	2	yes	complemented
384	#125	—	19	1	no	—
385	#125	C₂×D₁₉	1	1	yes	characteristic, complemented
386	#124	—	19	2	no	—
387	#124	—	19	1	no	—
388	#124	—	19	1	no	—
389	#124	—	19	2	no	—
390	#124	—	19	2	no	—
391	#124	—	19	2	no	—
392	#124	—	19	2	no	—
393	#124	—	19	2	no	—
394	#123	—	19	2	no	—
395	#123	—	19	2	no	—
396	#123	—	19	2	no	—
397	#123	—	19	2	no	—
398	#123	—	19	2	no	—
399	#123	—	19	2	no	—
400	#123	—	19	2	no	—
401	#123	C₂×D₁₉	1	2	yes	complemented
402	C₂²⋊Q₈	—	19	2	no	—
403	C₂²⋊Q₈	—	19	2	no	—
404	C₂²⋊Q₈	—	19	2	no	—
405	C₂²⋊Q₈	—	19	2	no	—
406	#121	—	19	1	no	—
407	#121	—	19	1	no	—
408	#121	—	19	1	no	—
409	#121	—	19	2	no	—
410	#121	—	19	2	no	—
411	#121	—	19	1	no	—
412	#121	—	19	1	no	—
413	#121	—	19	1	no	—
414	#121	—	19	1	no	—
415	#121	—	19	1	no	—
416	#121	—	19	2	no	—
417	#121	—	19	1	no	—
418	#121	—	19	1	no	—
419	#121	—	19	2	no	—
420	#121	—	19	2	no	—
421	#121	C₂×D₁₉	1	1	yes	characteristic
422	#121	C₂×D₁₉	1	1	yes	characteristic
423	#121	C₂×D₁₉	1	2	yes	complemented
424	#120	—	19	2	no	—
425	#120	—	19	2	no	—
426	#120	—	19	2	no	—
427	#120	—	19	2	no	—
428	C₄×Q₈	—	19	2	no	—
429	C₄×Q₈	—	19	2	no	—
430	C₄×Q₈	—	19	2	no	—
431	C₄×Q₈	—	19	2	no	—
432	C₄×D₄	—	19	1	no	—
433	C₄×D₄	—	19	2	no	—
434	C₄×D₄	—	19	2	no	—
435	C₄×D₄	—	19	2	no	—
436	C₄×D₄	—	19	2	no	—
437	C₄×D₄	—	19	1	no	—
438	C₄×D₄	—	19	1	no	—
439	C₄×D₄	—	19	1	no	—
440	C₄×D₄	—	19	2	no	—
441	C₄×D₄	—	19	2	no	—
442	C₄×D₄	—	19	2	no	—
443	C₄×D₄	—	19	2	no	—
444	C₄×D₄	—	19	2	no	—
445	C₄×D₄	—	19	2	no	—
446	C₄×D₄	—	19	1	no	—
447	C₄×D₄	—	19	2	no	—
448	C₄×D₄	—	19	1	no	—
449	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
450	C₄×D₄	C₂×D₁₉	1	2	yes	complemented
451	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic, complemented
452	#117	—	19	1	no	—
453	#117	—	19	1	no	—
454	#117	—	19	1	no	—
455	#117	—	19	1	no	—
456	#117	—	19	1	no	—
457	#117	—	19	2	no	—
458	#117	—	19	2	no	—
459	#117	C₂×D₁₉	1	1	yes	characteristic, complemented
460	C₂×C₄⋊C₄	—	19	1	no	—
461	C₂×C₄⋊C₄	—	19	1	no	—
462	C₂×C₄⋊C₄	—	19	1	no	—
463	C₂×C₄⋊C₄	—	19	1	no	—
464	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic, complemented
465	C₂×C₂²⋊C₄	—	19	2	no	—
466	C₂×C₄²	—	19	1	no	—
467	C₁₉	#3506	1	1	yes	characteristic, complemented, Sylow
468	C₂⁴	—	19	2	no	—
469	#41	—	38	4	no	—
470	#41	—	38	4	no	—
471	#41	—	76	4	no	—
472	#41	—	76	4	no	—
473	C₂×Q₈	—	19	1	no	—
474	C₂×Q₈	—	19	1	no	—
475	C₂×Q₈	—	19	2	no	—
476	C₂×Q₈	—	19	2	no	—
477	C₂×D₄	—	19	1	no	—
478	C₂×D₄	—	19	1	no	—
479	C₂×D₄	—	19	2	no	—
480	C₂×D₄	—	19	1	no	—
481	C₂×D₄	—	19	1	no	—
482	C₂×D₄	—	19	1	no	—
483	C₂×D₄	—	19	1	no	—
484	C₂×D₄	—	19	2	no	—
485	C₂×D₄	—	19	2	no	—
486	C₂×D₄	—	19	2	no	—
487	C₂×D₄	—	19	2	no	—
488	C₂×D₄	—	19	1	no	—
489	C₂×D₄	—	19	1	no	—
490	C₂×D₄	—	19	1	no	—
491	C₂×D₄	—	19	2	no	—
492	C₂×D₄	—	19	1	no	—
493	C₂×D₄	—	19	2	no	—
494	C₂×D₄	—	38	4	no	—
495	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
496	C₂×D₄	C₂²×D₁₉	1	2	yes	—
497	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
498	C₂×D₄	C₂²×D₁₉	1	2	yes	—
499	C₂²×C₄	—	19	1	no	—
500	C₂²×C₄	—	19	2	no	—
501	C₂²×C₄	—	19	2	no	—
502	C₂²×C₄	—	19	1	no	—
503	C₂²×C₄	—	19	1	no	—
504	C₂²×C₄	—	19	1	no	—
505	C₂²×C₄	—	19	2	no	—
506	C₂²×C₄	—	19	1	no	—
507	C₂²×C₄	—	19	2	no	—
508	C₂²×C₄	—	19	2	no	—
509	C₂²×C₄	—	19	2	no	—
510	C₂²×C₄	—	19	2	no	—
511	C₂²×C₄	—	76	4	no	—
512	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
513	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
514	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
515	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
516	C₄⋊C₄	—	19	2	no	—
517	C₄⋊C₄	—	19	2	no	—
518	C₄⋊C₄	—	19	2	no	—
519	C₄⋊C₄	—	19	1	no	—
520	C₄⋊C₄	—	19	1	no	—
521	C₄⋊C₄	—	19	2	no	—
522	C₄⋊C₄	—	19	2	no	—
523	C₄⋊C₄	—	19	2	no	—
524	C₄⋊C₄	—	19	2	no	—
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	C₂²×D₁₉	1	1	yes	characteristic
531	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
532	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
533	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
534	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
535	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
536	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
537	C₂²⋊C₄	—	19	2	no	—
538	C₂²⋊C₄	—	19	2	no	—
539	C₂²⋊C₄	—	19	2	no	—
540	C₂²⋊C₄	—	19	2	no	—
541	C₂²⋊C₄	—	19	1	no	—
542	C₂²⋊C₄	—	19	1	no	—
543	C₂²⋊C₄	—	19	2	no	—
544	C₂²⋊C₄	—	19	2	no	—
545	C₂²⋊C₄	—	19	2	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	1	no	—
552	C₂²⋊C₄	—	19	1	no	—
553	C₂²⋊C₄	—	19	2	no	—
554	C₂²⋊C₄	—	19	2	no	—
555	C₂²⋊C₄	—	19	1	no	—
556	C₂²⋊C₄	—	19	1	no	—
557	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
558	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
559	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
560	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
561	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
562	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
563	C₄²	—	19	1	no	—
564	C₄²	—	19	1	no	—
565	C₄²	—	19	1	no	—
566	C₄²	—	19	2	no	—
567	C₄²	—	19	2	no	—
568	C₄²	—	19	2	no	—
569	C₄²	—	19	2	no	—
570	C₄²	—	19	2	no	—
571	C₄²	C₂²×D₁₉	1	1	yes	characteristic
572	C₄²	C₂²×D₁₉	1	2	yes	—
573	C₂³	—	19	1	no	—
574	C₂³	—	19	2	no	—
575	C₂³	—	19	1	no	—
576	C₂³	—	19	1	no	—
577	C₂³	—	38	4	no	—
578	C₂³	—	76	2	no	—
579	C₂³	—	76	2	no	—
580	C₂³	C₂³×D₁₉	1	2	yes	—
581	C₂³	C₂³×D₁₉	1	1	yes	characteristic
582	C₂³	C₂³×D₁₉	1	1	yes	characteristic
583	Q₈	—	38	2	no	—
584	Q₈	—	38	2	no	—
585	Q₈	—	38	4	no	—
586	Q₈	—	76	2	no	—
587	D₄	—	2	2	no	—
588	D₄	—	4	2	no	—
589	D₄	—	4	1	no	—
590	D₄	—	4	2	no	—
591	D₄	—	38	2	no	—
592	D₄	—	38	2	no	—
593	D₄	—	38	4	no	—
594	D₄	—	38	2	no	—
595	D₄	—	38	2	no	—
596	D₄	—	38	2	no	—
597	D₄	—	38	2	no	—
598	D₄	—	38	2	no	—
599	D₄	—	38	2	no	—
600	D₄	—	38	2	no	—
601	D₄	—	76	2	no	—
602	D₄	—	76	1	no	—
603	D₄	—	76	2	no	—
604	D₄	—	76	2	no	—
605	D₄	—	76	2	no	—
606	D₄	—	76	2	no	—
607	D₄	—	76	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	4	2	no	—
611	C₂×C₄	—	4	2	no	—
612	C₂×C₄	—	19	1	no	—
613	C₂×C₄	—	19	1	no	—
614	C₂×C₄	—	19	4	no	—
615	C₂×C₄	—	19	2	no	—
616	C₂×C₄	—	19	1	no	—
617	C₂×C₄	—	19	1	no	—
618	C₂×C₄	—	19	1	no	—
619	C₂×C₄	—	19	2	no	—
620	C₂×C₄	—	19	2	no	—
621	C₂×C₄	—	38	2	no	—
622	C₂×C₄	—	38	4	no	—
623	C₂×C₄	—	38	4	no	—
624	C₂×C₄	—	38	2	no	—
625	C₂×C₄	—	38	2	no	—
626	C₂×C₄	—	76	2	no	—
627	C₂×C₄	—	76	2	no	—
628	C₂×C₄	—	76	2	no	—
629	C₂×C₄	—	76	2	no	—
630	C₂×C₄	—	76	1	no	—
631	C₂×C₄	—	76	2	no	—
632	C₂×C₄	C₂³×D₁₉	1	2	yes	—
633	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
634	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
635	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
636	C₂×C₄	C₂³×D₁₉	1	2	yes	—
637	C₂×C₄	C₂³×D₁₉	1	2	yes	—
638	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
639	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
640	C₂²	—	2	1	no	—
641	C₂²	—	2	1	no	—
642	C₂²	—	2	2	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	2	1	no	—
646	C₂²	—	2	1	no	—
647	C₂²	—	2	1	no	—
648	C₂²	—	2	2	no	—
649	C₂²	—	19	2	no	—
650	C₂²	—	38	1	no	—
651	C₂²	—	38	1	no	—
652	C₂²	—	38	1	no	—
653	C₂²	—	38	1	no	—
654	C₂²	—	38	2	no	—
655	C₂²	—	38	2	no	—
656	C₂²	—	38	1	no	—
657	C₂²	—	38	1	no	—
658	C₂²	—	38	1	no	—
659	C₂²	—	38	1	no	—
660	C₂²	—	38	2	no	—
661	C₂²	—	76	8	no	—
662	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
663	C₄	—	2	1	no	—
664	C₄	—	2	1	no	—
665	C₄	—	2	1	no	—
666	C₄	—	2	2	no	—
667	C₄	—	2	2	no	—
668	C₄	—	2	1	no	—
669	C₄	—	2	2	no	—
670	C₄	—	19	2	no	—
671	C₄	—	19	2	no	—
672	C₄	—	38	1	no	—
673	C₄	—	38	1	no	—
674	C₄	—	38	2	no	—
675	C₄	—	38	2	no	—
676	C₄	—	38	1	no	—
677	C₄	—	38	2	no	—
678	C₄	#41×D₁₉	1	2	yes	—
679	C₂	—	4	2	no	—
680	C₂	—	4	1	no	—
681	C₂	—	4	1	no	—
682	C₂	—	38	2	no	—
683	C₂	—	76	2	no	—
684	C₂	—	76	1	no	—
685	C₂	—	76	1	no	—
686	C₂	C₂×#41×D₁₉	1	1	yes	characteristic
687	C₂	H(5,𝔽₂)×D₁₉	1	1	yes	characteristic
688	C₂	#11927380	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₁₉×#553	C₂
hypercenter	#553	D₁₉
hypocenter	C₁₉	#3506
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ #553

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. #11927261	C₂	semidirect
4. #11927258	C₂	semidirect
5. #11927257	C₂	semidirect
6. #11927247	C₂	semidirect
7. #11927244	C₂	semidirect
8. #11927240	C₂	semidirect
9. #11927212	C₂	semidirect
10. #11927195	C₂	semidirect
11. #11927194	C₂	semidirect
12. #11927133	C₂	semidirect
13. #11927126	C₂	semidirect
14. #11927110	C₂	semidirect
15. #11927110	C₂	semidirect
16. #11927100	C₂	semidirect
17. #11927091	C₂	semidirect
18. #11927053	C₂	semidirect
19. #11927052	C₂	semidirect
20. #11927025	C₂	semidirect
21. #11927024	C₂	semidirect
22. C₄×D₄×D₁₉	C₂	semidirect
23. C₁₉×#553	C₂	semidirect
24. C₂×#64543	C₂²	semidirect
28. C₂×#64541	C₂²	semidirect
30. C₁₉×#126	C₂²	semidirect
31. C₁₉×#125	C₂²	semidirect
32. C₁₉×#123	C₂²	semidirect
35. C₁₉×#121	C₂²	semidirect
37. C₄×D₄×C₁₉	C₂²	semidirect
38. C₄×D₄×C₁₉	C₂²	semidirect
39. C₁₉×#117	C₂²	semidirect
40. C₂×C₄⋊C₄×C₁₉	C₂²	semidirect
43. #10597386	C₂²	semidirect
44. #10597385	C₂²	semidirect
45. #10597385	C₂²	semidirect
51. #10597382	C₂²	semidirect
52. #10597381	C₂²	semidirect
56. #10597375	C₂²	semidirect
57. #10597375	C₂²	semidirect
60. C₄×C₂²⋊D₁₉	C₂²	semidirect
61. C₄×C₂²⋊D₁₉	C₂²	semidirect
62. C₄×C₂²⋊D₁₉	C₂²	semidirect
63. C₄×C₂²⋊D₁₉	C₂²	semidirect
64. #10597372	C₂²	semidirect
65. C₂×C₄⋊Dic₁₉	C₂²	semidirect
66. #10597344	C₂²	semidirect
67. #10597344	C₂²	semidirect
70. #10597342	C₂²	semidirect
74. #10597341	C₂²	semidirect
75. #10597340	C₂²	semidirect
76. #10597340	C₂²	semidirect
79. #10597339	C₂²	semidirect
82. #10597338	C₂²	semidirect
83. #10597338	C₂²	semidirect
85. C₄⋊C₄×D₁₉	C₂²	semidirect
86. C₄⋊C₄×D₁₉	C₂²	semidirect
87. #10597334	C₂²	semidirect
88. #10597334	C₂²	semidirect
89. #10597334	C₂²	semidirect
90. #10597333	C₂²	semidirect
91. #10597333	C₂²	semidirect
92. #10597333	C₂²	semidirect
95. #10597331	C₂²	semidirect
96. #10597331	C₂²	semidirect
97. #10597331	C₂²	semidirect
98. #10597331	C₂²	semidirect
101. #10597330	C₂²	semidirect
102. #10597330	C₂²	semidirect
103. #10597329	C₂²	semidirect
104. #10597329	C₂²	semidirect
109. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
110. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
112. #10597325	C₂²	semidirect
113. #10597324	C₂²	semidirect
114. #10597323	C₂²	semidirect
115. #10597321	C₂²	semidirect
118. C₄×D₇₆	C₂²	semidirect
119. #10597318	C₂²	semidirect
121. #10597316	C₂²	semidirect
122. C₄×Dic₃₈	C₂²	semidirect
290. C₄×D₁₉	#41	semidirect
343. #553	D₁₉	semidirect
383. #126	C₂×D₁₉	semidirect
385. #125	C₂×D₁₉	semidirect
401. #123	C₂×D₁₉	semidirect
423. #121	C₂×D₁₉	semidirect
450. C₄×D₄	C₂×D₁₉	semidirect
451. C₄×D₄	C₂×D₁₉	semidirect
459. #117	C₂×D₁₉	semidirect
464. C₂×C₄⋊C₄	C₂×D₁₉	semidirect
467. 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
#11927261	2
#11927258	2
#11927257	2
#11927247	2
#11927244	2
#11927240	2
#11927212	2
#11927195	2
#11927194	2
#11927133	2
#11927126	2
#11927110	2
#11927100	2
#11927091	2
#11927053	2
#11927052	2
#11927025	2
#11927024	2
C₄×D₄×D₁₉	2
C₁₉×#553	2
#3506	19