Subgroups — #14577337

Order 2432.

1124 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927255	C₂	1	1	yes	maximal, characteristic, complemented
2	#11927249	C₂	1	1	yes	maximal, characteristic, complemented
3	#11927248	C₂	1	2	yes	maximal, complemented
4	#11927244	C₂	1	1	yes	maximal, characteristic, complemented
5	#11927241	C₂	1	1	yes	maximal, characteristic, complemented
6	#11927239	C₂	1	2	yes	maximal, complemented
7	#11927234	C₂	1	1	yes	maximal, characteristic, complemented
8	#11927231	C₂	1	2	yes	maximal, complemented
9	#11927229	C₂	1	1	yes	maximal, characteristic, complemented
10	#11927194	C₂	1	1	yes	maximal, characteristic, complemented
11	#11927193	C₂	1	2	yes	maximal, complemented
12	#11927171	C₂	1	1	yes	maximal, characteristic, complemented
13	#11927140	C₂	1	2	yes	maximal, complemented
14	#11927137	C₂	1	2	yes	maximal, complemented
15	#11927123	C₂	1	1	yes	maximal, characteristic, complemented
16	#11927054	C₂	1	1	yes	maximal, characteristic, complemented
17	#11927053	C₂	1	1	yes	maximal, characteristic, complemented
18	#11927052	C₂	1	2	yes	maximal, complemented
19	#11927051	C₂	1	2	yes	maximal, complemented
20	#11927025	C₂	1	1	yes	maximal, characteristic, complemented
21	#11927023	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₄⋊C₄×D₁₉	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	—
25	C₂×#64543	C₂²	1	1	yes	characteristic
26	C₂×#64543	C₂²	1	2	yes	—
27	C₂×#64541	C₂²	1	1	yes	characteristic
28	C₂²×C₄×D₁₉	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₁₉	C₂²	1	2	yes	—
30	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₁₉×#123	C₂²	1	2	yes	—
32	C₁₉×#123	C₂²	1	2	yes	complemented
33	C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	complemented
34	C₁₉×#121	C₂²	1	1	yes	characteristic
35	C₁₉×#121	C₂²	1	1	yes	characteristic, complemented
36	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
37	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
40	#10597392	C₂²	1	2	yes	—
41	#10597392	C₂²	1	2	yes	—
42	#10597392	C₂²	1	2	yes	complemented
43	#10597390	C₂²	1	2	yes	complemented
44	#10597385	C₂²	1	1	yes	characteristic
45	#10597385	C₂²	1	2	yes	complemented
46	#10597384	C₂²	1	2	yes	—
47	#10597384	C₂²	1	2	yes	—
48	#10597384	C₂²	1	1	yes	characteristic
49	#10597384	C₂²	1	1	yes	characteristic, complemented
50	#10597383	C₂²	1	1	yes	characteristic
51	#10597383	C₂²	1	2	yes	—
52	#10597381	C₂²	1	2	yes	—
53	#10597381	C₂²	1	2	yes	—
54	#10597381	C₂²	1	2	yes	complemented
55	D₄×Dic₁₉	C₂²	1	2	yes	—
56	D₄×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
57	#10597375	C₂²	1	2	yes	—
58	#10597375	C₂²	1	2	yes	complemented
59	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	—
60	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	—
61	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	—
62	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	—
63	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
64	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
65	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
66	#10597372	C₂²	1	2	yes	—
67	#10597372	C₂²	1	1	yes	characteristic, complemented
68	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
69	#10597370	C₂²	1	1	yes	characteristic
70	#10597370	C₂²	1	1	yes	characteristic, complemented
71	#10597370	C₂²	1	2	yes	complemented
72	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	—
73	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	complemented
74	#10597344	C₂²	1	2	yes	complemented
75	#10597343	C₂²	1	1	yes	characteristic
76	#10597343	C₂²	1	1	yes	characteristic, complemented
77	#10597342	C₂²	1	2	yes	—
78	#10597342	C₂²	1	2	yes	—
79	#10597342	C₂²	1	1	yes	characteristic
80	#10597340	C₂²	1	1	yes	characteristic
81	#10597339	C₂²	1	2	yes	—
82	#10597339	C₂²	1	2	yes	—
83	#10597338	C₂²	1	1	yes	characteristic
84	#10597338	C₂²	1	1	yes	characteristic, complemented
85	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic
86	C₄⋊C₄×D₁₉	C₂²	1	2	yes	—
87	C₄⋊C₄×D₁₉	C₂²	1	2	yes	—
88	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic
89	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic
90	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic
91	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic, complemented
92	#10597336	C₂²	1	2	yes	complemented
93	#10597336	C₂²	1	1	yes	characteristic, complemented
94	#10597335	C₂²	1	2	yes	complemented
95	#10597335	C₂²	1	2	yes	complemented
96	#10597335	C₂²	1	2	yes	complemented
97	#10597335	C₂²	1	2	yes	complemented
98	#10597334	C₂²	1	1	yes	characteristic, complemented
99	#10597333	C₂²	1	1	yes	characteristic, complemented
100	#10597333	C₂²	1	2	yes	complemented
101	#10597330	C₂²	1	2	yes	—
102	#10597330	C₂²	1	2	yes	—
103	#10597330	C₂²	1	1	yes	characteristic
104	#10597329	C₂²	1	1	yes	characteristic
105	#10597329	C₂²	1	2	yes	—
106	#10597329	C₂²	1	2	yes	complemented
107	#10597328	C₂²	1	1	yes	characteristic
108	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	—
109	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	—
110	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	—
111	#10597325	C₂²	1	2	yes	complemented
112	#10597325	C₂²	1	2	yes	complemented
113	#10597325	C₂²	1	2	yes	complemented
114	#10597324	C₂²	1	1	yes	characteristic
115	#10597324	C₂²	1	2	yes	complemented
116	#10597324	C₂²	1	2	yes	complemented
117	#10597323	C₂²	1	2	yes	—
118	#10597323	C₂²	1	2	yes	complemented
119	C₄×D₇₆	C₂²	1	1	yes	characteristic
120	#10597318	C₂²	1	1	yes	characteristic
121	#10597316	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₉	C₂³	1	1	yes	characteristic
124	#41×C₁₉	—	4	4	no	—
125	C₂×Q₈×C₁₉	C₂³	1	2	yes	—
126	C₂×D₄×C₁₉	C₂³	1	2	yes	—
127	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
128	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
129	C₂×D₄×C₁₉	C₂³	1	2	yes	—
130	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
132	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
133	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
134	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
136	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
138	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
142	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
143	C₂²×Dic₁₉	C₂³	1	2	yes	—
144	C₂²×Dic₁₉	C₂³	1	2	yes	—
145	C₂²×Dic₁₉	C₂³	1	2	yes	—
146	#64543	—	2	4	no	—
147	#64543	—	4	4	no	—
148	#64541	—	2	4	no	—
149	C₂×D₇₆	C₂³	1	1	yes	characteristic
150	C₂×D₇₆	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₁₉	—	2	4	no	—
152	C₂×C₄×D₁₉	—	4	4	no	—
153	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₁₉	C₂³	1	2	yes	—
158	C₂×C₄×D₁₉	C₂³	1	2	yes	—
159	C₂×C₄×D₁₉	C₂³	1	2	yes	—
160	C₂×C₄×D₁₉	C₂³	1	2	yes	—
161	C₂×C₄×D₁₉	C₂³	1	2	yes	—
162	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
163	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
164	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
165	C₂×Dic₃₈	C₂³	1	2	yes	—
166	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
167	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
168	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
169	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
170	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
171	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
172	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
173	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
174	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
175	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
176	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
177	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
178	C₄²×C₁₉	C₂³	1	1	yes	characteristic
179	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
180	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
181	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
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	1	yes	characteristic
187	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
188	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
189	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
190	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
191	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
192	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
193	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
194	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
195	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
196	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
197	C₄⋊Dic₁₉	C₂³	1	2	yes	—
198	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
199	C₄⋊Dic₁₉	C₂³	1	2	yes	—
200	C₄⋊Dic₁₉	C₂³	1	2	yes	—
201	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
202	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
203	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
204	C₄⋊Dic₁₉	C₂³	1	2	yes	—
205	Dic₁₉⋊C₄	C₂³	1	2	yes	—
206	Dic₁₉⋊C₄	C₂³	1	2	yes	—
207	Dic₁₉⋊C₄	C₂³	1	2	yes	—
208	Dic₁₉⋊C₄	C₂³	1	2	yes	—
209	Dic₁₉⋊C₄	C₂³	1	2	yes	—
210	Dic₁₉⋊C₄	C₂³	1	2	yes	—
211	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
212	Dic₁₉⋊C₄	C₂³	1	2	yes	—
213	Dic₁₉⋊C₄	C₂³	1	2	yes	—
214	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
215	Dic₁₉⋊C₄	C₂³	1	2	yes	—
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	C₄×Dic₁₉	C₂³	1	2	yes	—
223	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
224	C₄×Dic₁₉	C₂³	1	2	yes	—
225	C₄×Dic₁₉	C₂³	1	2	yes	—
226	C₄×Dic₁₉	C₂³	1	2	yes	—
227	C₄×Dic₁₉	C₂³	1	2	yes	—
228	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
229	C₂³×C₁₉	C₂⁴	1	2	yes	—
230	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
231	C₂²×D₁₉	—	2	2	no	—
232	C₂²×D₁₉	—	2	2	no	—
233	C₂²×D₁₉	—	2	2	no	—
234	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
235	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
236	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
237	Q₈×C₁₉	—	4	2	no	—
238	D₄×C₁₉	—	2	4	no	—
239	D₄×C₁₉	—	2	2	no	—
240	D₄×C₁₉	—	2	2	no	—
241	D₄×C₁₉	—	4	2	no	—
242	C₂×C₄×C₁₉	—	2	4	no	—
243	C₂×C₄×C₁₉	—	2	2	no	—
244	C₂×C₄×C₁₉	—	2	2	no	—
245	C₂×C₄×C₁₉	—	4	2	no	—
246	C₂×C₄×C₁₉	—	4	2	no	—
247	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
250	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
251	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
252	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
253	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
254	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
255	C₂²⋊D₁₉	—	2	2	no	—
256	C₂²⋊D₁₉	—	2	2	no	—
257	C₂²⋊D₁₉	—	2	4	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	C₂×Dic₁₉	—	2	4	no	—
263	C₂×Dic₁₉	—	2	2	no	—
264	C₂×Dic₁₉	—	2	4	no	—
265	C₂×Dic₁₉	—	4	2	no	—
266	C₂×Dic₁₉	C₂⁴	1	2	yes	—
267	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
268	C₂×Dic₁₉	C₂⁴	1	2	yes	—
269	C₂×Dic₁₉	C₂⁴	1	2	yes	—
270	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
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	C₄×D₁₉	—	2	2	no	—
278	C₄×D₁₉	—	2	2	no	—
279	C₄×D₁₉	—	2	2	no	—
280	C₄×D₁₉	—	2	2	no	—
281	C₄×D₁₉	—	4	2	no	—
282	C₄×D₁₉	—	4	2	no	—
283	C₄×D₁₉	—	4	2	no	—
284	C₄×D₁₉	—	4	2	no	—
285	C₄×D₁₉	—	4	2	no	—
286	C₄×D₁₉	#41	1	4	yes	complemented
287	Dic₃₈	—	2	2	no	—
288	Dic₃₈	—	2	2	no	—
289	Dic₃₈	—	4	2	no	—
290	#3492	—	19	1	no	maximal, Sylow
291	C₂²×C₁₉	—	2	1	no	—
292	C₂²×C₁₉	—	2	1	no	—
293	C₂²×C₁₉	—	2	2	no	—
294	C₂²×C₁₉	—	2	1	no	—
295	C₂²×C₁₉	—	2	2	no	—
296	C₂²×C₁₉	—	2	1	no	—
297	C₂²×C₁₉	—	2	1	no	—
298	C₂²×C₁₉	—	2	2	no	—
299	C₂²×C₁₉	H(5,𝔽₂)	1	2	yes	—
300	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
301	C₂×D₁₉	—	2	8	no	—
302	C₂×D₁₉	—	2	1	no	—
303	C₂×D₁₉	—	2	1	no	—
304	C₂×D₁₉	—	2	1	no	—
305	C₂×D₁₉	—	2	1	no	—
306	C₂×D₁₉	—	2	1	no	—
307	C₂×D₁₉	—	2	1	no	—
308	C₂×D₁₉	—	2	1	no	—
309	C₂×D₁₉	C₂×#41	1	2	yes	—
310	C₂×D₁₉	2₋¹⁺⁴	1	2	yes	—
311	C₄×C₁₉	—	2	1	no	—
312	C₄×C₁₉	—	2	1	no	—
313	C₄×C₁₉	—	2	2	no	—
314	C₄×C₁₉	—	2	2	no	—
315	C₄×C₁₉	—	2	2	no	—
316	C₄×C₁₉	—	2	1	no	—
317	C₄×C₁₉	—	2	1	no	—
318	C₄×C₁₉	C₂×#41	1	2	yes	—
319	Dic₁₉	—	2	1	no	—
320	Dic₁₉	—	2	2	no	—
321	Dic₁₉	—	2	1	no	—
322	Dic₁₉	—	2	1	no	—
323	Dic₁₉	—	2	2	no	—
324	Dic₁₉	—	2	2	no	—
325	Dic₁₉	—	2	2	no	—
326	Dic₁₉	—	2	1	no	—
327	Dic₁₉	C₂×#41	1	2	yes	—
328	#554	—	19	1	no	—
329	#554	—	19	2	no	—
330	#554	—	19	1	no	—
331	#553	—	19	2	no	—
332	#553	—	19	1	no	—
333	#553	—	19	1	no	—
334	#552	—	19	2	no	—
335	#552	—	19	1	no	—
336	#552	—	19	1	no	—
337	#547	—	19	2	no	—
338	#547	—	19	1	no	—
339	#547	D₁₉	1	1	yes	characteristic, complemented
340	#544	—	19	1	no	—
341	#539	—	19	2	no	—
342	#539	—	19	2	no	—
343	#537	—	19	1	no	—
344	#525	—	19	2	no	—
345	#525	—	19	2	no	—
346	#525	—	19	1	no	—
347	#525	—	19	1	no	—
348	#520	—	19	1	no	—
349	#520	—	19	1	no	—
350	C₂²×C₄⋊C₄	—	19	1	no	—
351	C₂×C₁₉	—	2	2	no	—
352	C₂×C₁₉	—	4	2	no	—
353	C₂×C₁₉	—	4	1	no	—
354	C₂×C₁₉	C₂²×#41	1	1	yes	characteristic
355	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
356	C₂×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
357	D₁₉	—	2	2	no	—
358	D₁₉	—	2	2	no	—
359	D₁₉	—	4	1	no	—
360	C₂×#41	—	19	1	no	—
361	C₂×#41	—	19	2	no	—
362	C₂×#41	—	19	1	no	—
363	C₂×#41	C₂×D₁₉	1	2	yes	—
364	C₂³×C₄	—	19	1	no	—
365	C₂³×C₄	—	19	2	no	—
366	C₄⋊Q₈	—	19	2	no	—
367	C₄⋊Q₈	—	19	1	no	—
368	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
369	#126	—	19	2	no	—
370	#126	—	19	2	no	—
371	#126	—	19	2	no	—
372	#126	—	19	2	no	—
373	#125	—	19	2	no	—
374	#125	—	19	2	no	—
375	#125	—	19	2	no	—
376	#125	—	19	2	no	—
377	#125	—	19	2	no	—
378	#125	—	19	1	no	—
379	#125	—	19	1	no	—
380	#123	—	19	2	no	—
381	#123	—	19	2	no	—
382	#123	—	19	2	no	—
383	#123	—	19	2	no	—
384	#123	—	19	2	no	—
385	#123	—	19	1	no	—
386	#123	—	19	1	no	—
387	#123	—	19	2	no	—
388	#123	—	19	2	no	—
389	#123	C₂×D₁₉	1	2	yes	—
390	#123	C₂×D₁₉	1	2	yes	complemented
391	C₂²⋊Q₈	—	19	2	no	—
392	C₂²⋊Q₈	—	19	2	no	—
393	C₂²⋊Q₈	—	19	2	no	—
394	C₂²⋊Q₈	—	19	1	no	—
395	C₂²⋊Q₈	—	19	1	no	—
396	C₂²⋊Q₈	—	19	2	no	—
397	C₂²⋊Q₈	—	19	2	no	—
398	C₂²⋊Q₈	—	19	1	no	—
399	C₂²⋊Q₈	—	19	2	no	—
400	C₂²⋊Q₈	—	19	1	no	—
401	C₂²⋊Q₈	—	19	1	no	—
402	C₂²⋊Q₈	—	19	1	no	—
403	C₂²⋊Q₈	—	19	2	no	—
404	C₂²⋊Q₈	—	19	2	no	—
405	C₂²⋊Q₈	C₂×D₁₉	1	2	yes	complemented
406	#121	—	19	2	no	—
407	#121	—	19	2	no	—
408	#121	—	19	1	no	—
409	#121	—	19	1	no	—
410	#121	—	19	1	no	—
411	#121	—	19	2	no	—
412	#121	—	19	2	no	—
413	#121	—	19	2	no	—
414	#121	—	19	1	no	—
415	#121	C₂×D₁₉	1	1	yes	characteristic
416	#121	C₂×D₁₉	1	1	yes	characteristic, complemented
417	#120	—	19	2	no	—
418	#120	—	19	1	no	—
419	#120	—	19	1	no	—
420	C₄×Q₈	—	19	2	no	—
421	C₄×Q₈	—	19	1	no	—
422	C₄×Q₈	—	19	1	no	—
423	C₄×D₄	—	19	2	no	—
424	C₄×D₄	—	19	1	no	—
425	C₄×D₄	—	19	2	no	—
426	C₄×D₄	—	19	2	no	—
427	C₄×D₄	—	19	2	no	—
428	C₄×D₄	—	19	1	no	—
429	C₄×D₄	—	19	2	no	—
430	C₄×D₄	—	19	2	no	—
431	C₄×D₄	—	19	1	no	—
432	C₄×D₄	—	19	2	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	C₂×D₁₉	1	1	yes	characteristic
439	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic, complemented
440	#117	—	19	1	no	—
441	#117	—	19	2	no	—
442	#117	—	19	1	no	—
443	#117	—	19	1	no	—
444	#117	—	19	2	no	—
445	#117	—	19	2	no	—
446	#117	—	19	1	no	—
447	C₂×C₄⋊C₄	—	19	2	no	—
448	C₂×C₄⋊C₄	—	19	1	no	—
449	C₂×C₄⋊C₄	—	19	2	no	—
450	C₂×C₄⋊C₄	—	19	1	no	—
451	C₂×C₄⋊C₄	—	19	1	no	—
452	C₂×C₄⋊C₄	—	19	2	no	—
453	C₂×C₄⋊C₄	—	19	2	no	—
454	C₂×C₄⋊C₄	—	19	1	no	—
455	C₂×C₄⋊C₄	—	19	1	no	—
456	C₂×C₄⋊C₄	—	19	1	no	—
457	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
458	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic, complemented
459	C₁₉	#3492	1	1	yes	characteristic, complemented, Sylow
460	C₂⁴	—	19	1	no	—
461	#41	—	4	4	no	—
462	#41	—	38	4	no	—
463	#41	—	38	4	no	—
464	#41	—	76	4	no	—
465	C₂×Q₈	—	19	1	no	—
466	C₂×Q₈	—	19	1	no	—
467	C₂×Q₈	—	19	2	no	—
468	C₂×Q₈	C₂²×D₁₉	1	2	yes	—
469	C₂×D₄	—	19	1	no	—
470	C₂×D₄	—	19	2	no	—
471	C₂×D₄	—	19	1	no	—
472	C₂×D₄	—	19	2	no	—
473	C₂×D₄	—	19	1	no	—
474	C₂×D₄	—	19	1	no	—
475	C₂×D₄	—	19	2	no	—
476	C₂×D₄	—	19	1	no	—
477	C₂×D₄	—	19	1	no	—
478	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
479	C₂×D₄	C₂²×D₁₉	1	2	yes	—
480	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
481	C₂×D₄	C₂²×D₁₉	1	2	yes	—
482	C₂²×C₄	—	19	1	no	—
483	C₂²×C₄	—	19	2	no	—
484	C₂²×C₄	—	19	1	no	—
485	C₂²×C₄	—	19	2	no	—
486	C₂²×C₄	—	19	2	no	—
487	C₂²×C₄	—	19	1	no	—
488	C₂²×C₄	—	19	1	no	—
489	C₂²×C₄	—	19	1	no	—
490	C₂²×C₄	—	19	1	no	—
491	C₂²×C₄	—	19	2	no	—
492	C₂²×C₄	—	19	2	no	—
493	C₂²×C₄	—	19	2	no	—
494	C₂²×C₄	—	19	2	no	—
495	C₂²×C₄	—	19	2	no	—
496	C₂²×C₄	—	38	4	no	—
497	C₂²×C₄	—	76	4	no	—
498	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
499	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
500	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
501	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
502	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
503	C₄⋊C₄	—	19	2	no	—
504	C₄⋊C₄	—	19	2	no	—
505	C₄⋊C₄	—	19	2	no	—
506	C₄⋊C₄	—	19	2	no	—
507	C₄⋊C₄	—	19	1	no	—
508	C₄⋊C₄	—	19	2	no	—
509	C₄⋊C₄	—	19	2	no	—
510	C₄⋊C₄	—	19	2	no	—
511	C₄⋊C₄	—	19	1	no	—
512	C₄⋊C₄	—	19	2	no	—
513	C₄⋊C₄	—	19	2	no	—
514	C₄⋊C₄	—	19	1	no	—
515	C₄⋊C₄	—	19	2	no	—
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	1	no	—
522	C₄⋊C₄	—	19	2	no	—
523	C₄⋊C₄	—	19	1	no	—
524	C₄⋊C₄	—	19	2	no	—
525	C₄⋊C₄	—	19	2	no	—
526	C₄⋊C₄	—	19	2	no	—
527	C₄⋊C₄	—	19	1	no	—
528	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
529	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
530	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
531	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
532	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
533	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
534	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
535	C₂²⋊C₄	—	19	2	no	—
536	C₂²⋊C₄	—	19	1	no	—
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	2	no	—
543	C₂²⋊C₄	—	19	2	no	—
544	C₂²⋊C₄	—	19	1	no	—
545	C₂²⋊C₄	—	19	1	no	—
546	C₂²⋊C₄	—	19	2	no	—
547	C₂²⋊C₄	—	19	2	no	—
548	C₂²⋊C₄	—	19	1	no	—
549	C₂²⋊C₄	—	19	1	no	—
550	C₂²⋊C₄	—	19	2	no	—
551	C₂²⋊C₄	—	19	1	no	—
552	C₂²⋊C₄	—	19	1	no	—
553	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
554	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
555	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
556	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
557	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
558	C₄²	—	19	2	no	—
559	C₄²	—	19	2	no	—
560	C₄²	—	19	2	no	—
561	C₄²	—	19	2	no	—
562	C₄²	—	19	2	no	—
563	C₄²	—	19	1	no	—
564	C₄²	C₂²×D₁₉	1	1	yes	characteristic
565	C₂³	—	19	1	no	—
566	C₂³	—	19	1	no	—
567	C₂³	—	19	1	no	—
568	C₂³	—	38	2	no	—
569	C₂³	—	38	2	no	—
570	C₂³	—	38	2	no	—
571	C₂³	C₂³×D₁₉	1	1	yes	characteristic
572	C₂³	C₂³×D₁₉	1	2	yes	—
573	C₂³	C₂³×D₁₉	1	1	yes	characteristic
574	Q₈	—	4	2	no	—
575	Q₈	—	38	2	no	—
576	Q₈	—	38	2	no	—
577	Q₈	—	76	2	no	—
578	D₄	—	2	2	no	—
579	D₄	—	2	4	no	—
580	D₄	—	2	2	no	—
581	D₄	—	4	2	no	—
582	D₄	—	38	2	no	—
583	D₄	—	38	2	no	—
584	D₄	—	38	2	no	—
585	D₄	—	38	2	no	—
586	D₄	—	38	4	no	—
587	D₄	—	38	2	no	—
588	D₄	—	38	4	no	—
589	D₄	—	38	2	no	—
590	D₄	—	76	2	no	—
591	C₂×C₄	—	2	4	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	4	2	no	—
595	C₂×C₄	—	4	2	no	—
596	C₂×C₄	—	19	1	no	—
597	C₂×C₄	—	19	4	no	—
598	C₂×C₄	—	19	1	no	—
599	C₂×C₄	—	19	2	no	—
600	C₂×C₄	—	19	1	no	—
601	C₂×C₄	—	19	2	no	—
602	C₂×C₄	—	19	2	no	—
603	C₂×C₄	—	19	1	no	—
604	C₂×C₄	—	19	1	no	—
605	C₂×C₄	—	19	2	no	—
606	C₂×C₄	—	38	2	no	—
607	C₂×C₄	—	38	2	no	—
608	C₂×C₄	—	38	2	no	—
609	C₂×C₄	—	38	4	no	—
610	C₂×C₄	—	38	4	no	—
611	C₂×C₄	—	38	2	no	—
612	C₂×C₄	—	38	2	no	—
613	C₂×C₄	—	76	2	no	—
614	C₂×C₄	—	76	2	no	—
615	C₂×C₄	—	76	2	no	—
616	C₂×C₄	—	76	2	no	—
617	C₂×C₄	—	76	2	no	—
618	C₂×C₄	—	76	2	no	—
619	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
620	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
621	C₂×C₄	C₂³×D₁₉	1	2	yes	—
622	C₂×C₄	C₂³×D₁₉	1	2	yes	—
623	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
624	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
625	C₂×C₄	C₂³×D₁₉	1	2	yes	—
626	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
627	C₂²	—	2	1	no	—
628	C₂²	—	2	1	no	—
629	C₂²	—	2	1	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	2	1	no	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	1	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	19	2	no	—
636	C₂²	—	19	2	no	—
637	C₂²	—	38	8	no	—
638	C₂²	—	38	1	no	—
639	C₂²	—	38	1	no	—
640	C₂²	—	38	1	no	—
641	C₂²	—	38	1	no	—
642	C₂²	—	38	1	no	—
643	C₂²	—	38	1	no	—
644	C₂²	—	38	1	no	—
645	C₂²	#10597430	1	2	yes	—
646	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
647	C₄	—	2	1	no	—
648	C₄	—	2	1	no	—
649	C₄	—	2	2	no	—
650	C₄	—	2	2	no	—
651	C₄	—	2	1	no	—
652	C₄	—	2	2	no	—
653	C₄	—	2	1	no	—
654	C₄	—	19	2	no	—
655	C₄	—	38	1	no	—
656	C₄	—	38	2	no	—
657	C₄	—	38	1	no	—
658	C₄	—	38	2	no	—
659	C₄	—	38	2	no	—
660	C₄	—	38	1	no	—
661	C₄	—	38	1	no	—
662	C₄	—	38	2	no	—
663	C₄	#41×D₁₉	1	2	yes	—
664	C₂	—	2	2	no	—
665	C₂	—	4	1	no	—
666	C₂	—	4	2	no	—
667	C₂	—	38	2	no	—
668	C₂	—	38	2	no	—
669	C₂	—	76	1	no	—
670	C₂	C₂×#41×D₁₉	1	1	yes	characteristic
671	C₂	C₂×#10597430	1	1	yes	characteristic
672	C₂	2₋¹⁺⁴×D₁₉	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	#3492
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. #11927255	C₂	semidirect
2. #11927249	C₂	semidirect
3. #11927248	C₂	semidirect
4. #11927244	C₂	semidirect
5. #11927241	C₂	semidirect
6. #11927239	C₂	semidirect
7. #11927234	C₂	semidirect
8. #11927231	C₂	semidirect
9. #11927229	C₂	semidirect
10. #11927194	C₂	semidirect
11. #11927193	C₂	semidirect
12. #11927171	C₂	semidirect
13. #11927140	C₂	semidirect
14. #11927137	C₂	semidirect
15. #11927123	C₂	semidirect
16. #11927054	C₂	semidirect
17. #11927053	C₂	semidirect
18. #11927052	C₂	semidirect
19. #11927051	C₂	semidirect
20. #11927025	C₂	semidirect
21. #11927023	C₂	semidirect
22. C₂×C₄⋊C₄×D₁₉	C₂	semidirect
23. C₁₉×#547	C₂	semidirect
30. C₁₉×C₄⋊Q₈	C₂²	semidirect
32. C₁₉×#123	C₂²	semidirect
33. C₁₉×C₂²⋊Q₈	C₂²	semidirect
35. C₁₉×#121	C₂²	semidirect
37. C₄×D₄×C₁₉	C₂²	semidirect
39. C₂×C₄⋊C₄×C₁₉	C₂²	semidirect
42. #10597392	C₂²	semidirect
43. #10597390	C₂²	semidirect
45. #10597385	C₂²	semidirect
49. #10597384	C₂²	semidirect
54. #10597381	C₂²	semidirect
56. D₄×Dic₁₉	C₂²	semidirect
58. #10597375	C₂²	semidirect
65. C₄×C₂²⋊D₁₉	C₂²	semidirect
67. #10597372	C₂²	semidirect
70. #10597370	C₂²	semidirect
71. #10597370	C₂²	semidirect
73. C₂×Dic₁₉⋊C₄	C₂²	semidirect
74. #10597344	C₂²	semidirect
76. #10597343	C₂²	semidirect
84. #10597338	C₂²	semidirect
91. C₄⋊C₄×D₁₉	C₂²	semidirect
92. #10597336	C₂²	semidirect
93. #10597336	C₂²	semidirect
94. #10597335	C₂²	semidirect
95. #10597335	C₂²	semidirect
96. #10597335	C₂²	semidirect
97. #10597335	C₂²	semidirect
98. #10597334	C₂²	semidirect
99. #10597333	C₂²	semidirect
100. #10597333	C₂²	semidirect
106. #10597329	C₂²	semidirect
111. #10597325	C₂²	semidirect
112. #10597325	C₂²	semidirect
113. #10597325	C₂²	semidirect
115. #10597324	C₂²	semidirect
116. #10597324	C₂²	semidirect
118. #10597323	C₂²	semidirect
121. #10597316	C₂²	semidirect
122. C₄×Dic₃₈	C₂²	semidirect
286. C₄×D₁₉	#41	semidirect
339. #547	D₁₉	semidirect
368. C₄⋊Q₈	C₂×D₁₉	semidirect
390. #123	C₂×D₁₉	semidirect
405. C₂²⋊Q₈	C₂×D₁₉	semidirect
416. #121	C₂×D₁₉	semidirect
439. C₄×D₄	C₂×D₁₉	semidirect
458. C₂×C₄⋊C₄	C₂×D₁₉	semidirect
459. C₁₉	#3492	semidirect

Maximal subgroups

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

subgroup	index
#11927255	2
#11927249	2
#11927248	2
#11927244	2
#11927241	2
#11927239	2
#11927234	2
#11927231	2
#11927229	2
#11927194	2
#11927193	2
#11927171	2
#11927140	2
#11927137	2
#11927123	2
#11927054	2
#11927053	2
#11927052	2
#11927051	2
#11927025	2
#11927023	2
C₂×C₄⋊C₄×D₁₉	2
C₁₉×#547	2
#3492	19