Subgroups — #14577321

Order 2432.

1328 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927224	C₂	1	2	yes	maximal, complemented
2	#11927222	C₂	1	2	yes	maximal, complemented
3	#11927219	C₂	1	2	yes	maximal, complemented
4	#11927219	C₂	1	2	yes	maximal, complemented
5	#11927191	C₂	1	2	yes	maximal, complemented
6	#11927187	C₂	1	2	yes	maximal, complemented
7	#11927186	C₂	1	2	yes	maximal, complemented
8	#11927183	C₂	1	2	yes	maximal, complemented
9	#11927169	C₂	1	1	yes	maximal, characteristic, complemented
10	#11927132	C₂	1	1	yes	maximal, characteristic, complemented
11	#11927129	C₂	1	2	yes	maximal, complemented
12	#11927102	C₂	1	1	yes	maximal, characteristic, complemented
13	#11927057	C₂	1	1	yes	maximal, characteristic, complemented
14	#11927054	C₂	1	1	yes	maximal, characteristic, complemented
15	#11927053	C₂	1	2	yes	maximal, complemented
16	#120×D₁₉	C₂	1	2	yes	maximal, complemented
17	#11927016	C₂	1	2	yes	maximal, complemented
18	C₂×C₂²⋊C₄×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₉×#538	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁴×D₁₉	C₂²	1	1	yes	characteristic
21	C₂×#64545	C₂²	1	1	yes	characteristic, complemented
22	C₂×#64543	C₂²	1	1	yes	characteristic, complemented
23	C₂×D₄×D₁₉	C₂²	1	2	yes	—
24	C₂×D₄×D₁₉	C₂²	1	2	yes	complemented
25	C₂×D₄×D₁₉	C₂²	1	2	yes	complemented
26	C₂×#64541	C₂²	1	2	yes	complemented
27	C₂²×C₄×D₁₉	C₂²	1	1	yes	characteristic, complemented
28	C₂²×C₄×D₁₉	C₂²	1	1	yes	characteristic, complemented
29	C₁₉×#126	C₂²	1	2	yes	complemented
30	C₁₉×#124	C₂²	1	2	yes	complemented
31	C₁₉×#123	C₂²	1	2	yes	complemented
32	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
33	C₁₉×#121	C₂²	1	2	yes	complemented
34	C₁₉×#121	C₂²	1	1	yes	characteristic, complemented
35	C₁₉×#120	C₂²	1	2	yes	complemented
36	C₄×D₄×C₁₉	C₂²	1	2	yes	complemented
37	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
38	#10597399	C₂²	1	2	yes	complemented
39	C₂×C₂²⋊Dic₁₉	C₂²	1	1	yes	characteristic, complemented
40	#10597392	C₂²	1	1	yes	characteristic, complemented
41	#10597392	C₂²	1	2	yes	complemented
42	#10597385	C₂²	1	2	yes	complemented
43	#10597385	C₂²	1	2	yes	complemented
44	#10597384	C₂²	1	2	yes	complemented
45	#10597384	C₂²	1	1	yes	characteristic, complemented
46	#10597383	C₂²	1	2	yes	—
47	#10597383	C₂²	1	2	yes	—
48	#10597383	C₂²	1	2	yes	complemented
49	#10597383	C₂²	1	2	yes	complemented
50	#10597382	C₂²	1	2	yes	complemented
51	#10597381	C₂²	1	2	yes	complemented
52	D₄×Dic₁₉	C₂²	1	2	yes	complemented
53	#10597376	C₂²	1	1	yes	characteristic, complemented
54	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
55	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
56	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
57	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	1	yes	characteristic
58	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	1	yes	characteristic
59	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	complemented
60	#10597370	C₂²	1	1	yes	characteristic, complemented
61	#10597343	C₂²	1	1	yes	characteristic, complemented
62	#10597343	C₂²	1	2	yes	complemented
63	#10597342	C₂²	1	2	yes	complemented
64	#10597342	C₂²	1	2	yes	complemented
65	#10597342	C₂²	1	2	yes	complemented
66	#10597341	C₂²	1	1	yes	characteristic, complemented
67	#10597340	C₂²	1	2	yes	complemented
68	#10597340	C₂²	1	2	yes	complemented
69	#10597340	C₂²	1	2	yes	complemented
70	#10597339	C₂²	1	2	yes	complemented
71	#10597339	C₂²	1	2	yes	complemented
72	#10597338	C₂²	1	1	yes	characteristic, complemented
73	#10597338	C₂²	1	1	yes	characteristic, complemented
74	#10597338	C₂²	1	2	yes	complemented
75	#10597331	C₂²	1	2	yes	complemented
76	#10597331	C₂²	1	2	yes	complemented
77	#10597330	C₂²	1	2	yes	complemented
78	#10597330	C₂²	1	2	yes	complemented
79	#10597329	C₂²	1	2	yes	complemented
80	#10597329	C₂²	1	2	yes	complemented
81	#10597329	C₂²	1	2	yes	complemented
82	#10597329	C₂²	1	2	yes	complemented
83	#10597329	C₂²	1	2	yes	complemented
84	#10597328	C₂²	1	2	yes	—
85	#10597328	C₂²	1	2	yes	—
86	#10597328	C₂²	1	2	yes	complemented
87	#10597328	C₂²	1	2	yes	complemented
88	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	complemented
89	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	complemented
90	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	complemented
91	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	—
92	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	complemented
93	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	complemented
94	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	complemented
95	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	complemented
96	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	complemented
97	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	complemented
98	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	complemented
99	#10597325	C₂²	1	2	yes	complemented
100	#10597325	C₂²	1	2	yes	complemented
101	#10597325	C₂²	1	2	yes	complemented
102	#10597324	C₂²	1	2	yes	complemented
103	C₄×D₇₆	C₂²	1	2	yes	complemented
104	C₄×D₇₆	C₂²	1	2	yes	complemented
105	#10597318	C₂²	1	2	yes	complemented
106	#10597318	C₂²	1	2	yes	complemented
107	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
108	C₂³×D₁₉	—	2	4	no	—
109	C₂³×D₁₉	—	4	2	no	—
110	C₂³×D₁₉	—	4	2	no	—
111	C₂³×D₁₉	C₂³	1	1	yes	characteristic
112	C₂³×D₁₉	C₂³	1	2	yes	—
113	C₂³×D₁₉	C₂³	1	2	yes	—
114	C₂³×D₁₉	C₂³	1	2	yes	—
115	C₂³×D₁₉	C₂³	1	1	yes	characteristic
116	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic, complemented
117	C₂×D₄×C₁₉	C₂³	1	2	yes	—
118	C₂×D₄×C₁₉	C₂³	1	2	yes	—
119	C₂×D₄×C₁₉	C₂³	1	2	yes	—
120	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic, complemented
121	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
122	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
123	C₂²×C₄×C₁₉	C₂³	1	2	yes	complemented
124	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
125	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
126	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
127	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
128	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
129	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	complemented
131	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
132	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
133	C₂²×Dic₁₉	C₂³	1	2	yes	complemented
134	#64545	—	4	2	no	—
135	#64543	—	4	2	no	—
136	D₄×D₁₉	—	2	8	no	—
137	D₄×D₁₉	—	4	4	no	—
138	D₄×D₁₉	—	4	4	no	—
139	#64541	—	4	4	no	—
140	C₂×D₇₆	C₂³	1	2	yes	—
141	C₂×D₇₆	C₂³	1	2	yes	—
142	C₂×D₇₆	C₂³	1	2	yes	—
143	C₂×D₇₆	C₂³	1	1	yes	characteristic, complemented
144	C₂×C₄×D₁₉	—	4	2	no	—
145	C₂×C₄×D₁₉	—	4	2	no	—
146	C₂×C₄×D₁₉	C₂³	1	2	yes	—
147	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₁₉	C₂³	1	2	yes	—
150	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₁₉	C₂³	1	2	yes	—
153	C₂×C₄×D₁₉	C₂³	1	2	yes	—
154	C₂×C₄×D₁₉	C₂³	1	2	yes	—
155	C₂×C₄×D₁₉	C₂³	1	2	yes	complemented
156	C₂×C₄×D₁₉	C₂³	1	2	yes	complemented
157	C₂×Dic₃₈	C₂³	1	2	yes	complemented
158	C₂×Dic₃₈	C₂³	1	1	yes	characteristic, complemented
159	C₄⋊C₄×C₁₉	C₂³	1	2	yes	complemented
160	C₄⋊C₄×C₁₉	C₂³	1	2	yes	complemented
161	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic, complemented
162	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic, complemented
163	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
164	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
165	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
166	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
167	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
168	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	complemented
169	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	complemented
170	C₄²×C₁₉	C₂³	1	2	yes	complemented
171	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
172	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
173	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
174	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
175	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
176	C₂²⋊Dic₁₉	C₂³	1	2	yes	complemented
177	C₂²⋊Dic₁₉	C₂³	1	2	yes	complemented
178	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
179	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
180	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
181	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
182	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
183	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
184	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
185	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
186	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
187	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	complemented
189	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	complemented
190	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	complemented
191	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	complemented
192	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic, complemented
193	C₄⋊Dic₁₉	C₂³	1	2	yes	complemented
194	C₄⋊Dic₁₉	C₂³	1	2	yes	complemented
195	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic, complemented
196	Dic₁₉⋊C₄	C₂³	1	2	yes	complemented
197	Dic₁₉⋊C₄	C₂³	1	2	yes	complemented
198	Dic₁₉⋊C₄	C₂³	1	2	yes	complemented
199	Dic₁₉⋊C₄	C₂³	1	2	yes	complemented
200	Dic₁₉⋊C₄	C₂³	1	2	yes	complemented
201	Dic₁₉⋊C₄	C₂³	1	2	yes	complemented
202	C₄×Dic₁₉	C₂³	1	2	yes	complemented
203	C₄×Dic₁₉	C₂³	1	2	yes	complemented
204	C₄×Dic₁₉	C₂³	1	2	yes	complemented
205	C₂³×C₁₉	—	2	2	no	—
206	C₂³×C₁₉	—	4	1	no	—
207	C₂³×C₁₉	—	4	1	no	—
208	C₂³×C₁₉	C₂⁴	1	2	yes	—
209	C₂³×C₁₉	C₂⁴	1	2	yes	—
210	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
211	C₂²×D₁₉	—	2	2	no	—
212	C₂²×D₁₉	—	2	2	no	—
213	C₂²×D₁₉	—	2	2	no	—
214	C₂²×D₁₉	—	2	4	no	—
215	C₂²×D₁₉	—	2	4	no	—
216	C₂²×D₁₉	—	2	4	no	—
217	C₂²×D₁₉	—	2	4	no	—
218	C₂²×D₁₉	—	2	4	no	—
219	C₂²×D₁₉	—	4	2	no	—
220	C₂²×D₁₉	—	4	2	no	—
221	C₂²×D₁₉	—	4	1	no	—
222	C₂²×D₁₉	—	4	1	no	—
223	C₂²×D₁₉	—	4	2	no	—
224	C₂²×D₁₉	—	4	2	no	—
225	C₂²×D₁₉	—	4	16	no	—
226	C₂²×D₁₉	#41	1	4	yes	complemented
227	C₂²×D₁₉	C₂⁴	1	2	yes	—
228	C₂²×D₁₉	C₂⁴	1	2	yes	—
229	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
230	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
231	Q₈×C₁₉	—	4	1	no	—
232	D₄×C₁₉	—	2	4	no	—
233	D₄×C₁₉	—	4	2	no	—
234	D₄×C₁₉	—	4	2	no	—
235	D₄×C₁₉	—	4	1	no	—
236	C₂×C₄×C₁₉	—	4	1	no	—
237	C₂×C₄×C₁₉	—	4	1	no	—
238	C₂×C₄×C₁₉	—	4	2	no	—
239	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
240	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
241	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
242	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
243	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
245	C₂²⋊D₁₉	—	2	4	no	—
246	C₂²⋊D₁₉	—	2	4	no	—
247	C₂²⋊D₁₉	—	2	4	no	—
248	C₂²⋊D₁₉	—	2	4	no	—
249	C₂²⋊D₁₉	—	4	2	no	—
250	C₂²⋊D₁₉	—	4	2	no	—
251	C₂²⋊D₁₉	—	4	2	no	—
252	C₂×Dic₁₉	—	4	1	no	—
253	C₂×Dic₁₉	—	4	1	no	—
254	C₂×Dic₁₉	—	4	2	no	—
255	C₂×Dic₁₉	C₂⁴	1	2	yes	—
256	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
257	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
258	C₂×Dic₁₉	C₂⁴	1	2	yes	—
259	C₂×Dic₁₉	C₂⁴	1	2	yes	—
260	C₂×Dic₁₉	C₂⁴	1	2	yes	—
261	D₇₆	—	2	4	no	—
262	D₇₆	—	2	4	no	—
263	D₇₆	—	2	4	no	—
264	D₇₆	—	4	1	no	—
265	C₄×D₁₉	—	2	4	no	—
266	C₄×D₁₉	—	2	4	no	—
267	C₄×D₁₉	—	2	2	no	—
268	C₄×D₁₉	—	2	2	no	—
269	C₄×D₁₉	—	4	2	no	—
270	C₄×D₁₉	—	4	1	no	—
271	C₄×D₁₉	—	4	1	no	—
272	C₄×D₁₉	—	4	2	no	—
273	C₄×D₁₉	—	4	2	no	—
274	C₄×D₁₉	—	4	2	no	—
275	C₄×D₁₉	—	4	2	no	—
276	Dic₃₈	—	4	2	no	—
277	Dic₃₈	—	4	1	no	—
278	#3490	—	19	1	no	maximal, Sylow
279	C₂²×C₁₉	—	2	1	no	—
280	C₂²×C₁₉	—	2	1	no	—
281	C₂²×C₁₉	—	2	2	no	—
282	C₂²×C₁₉	—	2	2	no	—
283	C₂²×C₁₉	—	2	2	no	—
284	C₂²×C₁₉	—	2	2	no	—
285	C₂²×C₁₉	—	2	2	no	—
286	C₂²×C₁₉	—	2	2	no	—
287	C₂²×C₁₉	—	4	4	no	—
288	C₂²×C₁₉	C₂×#41	1	2	yes	—
289	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
290	C₂×D₁₉	—	2	8	no	—
291	C₂×D₁₉	—	2	1	no	—
292	C₂×D₁₉	—	2	1	no	—
293	C₂×D₁₉	—	2	1	no	—
294	C₂×D₁₉	—	2	1	no	—
295	C₂×D₁₉	—	2	2	no	—
296	C₂×D₁₉	—	2	2	no	—
297	C₂×D₁₉	—	2	2	no	—
298	C₂×D₁₉	—	2	2	no	—
299	C₂×D₁₉	—	2	2	no	—
300	C₂×D₁₉	—	4	4	no	—
301	C₂×D₁₉	—	4	8	no	—
302	C₂×D₁₉	—	4	8	no	—
303	C₂×D₁₉	—	8	4	no	—
304	C₂×D₁₉	C₂×#41	1	4	yes	—
305	C₂×D₁₉	H(5,𝔽₂)	1	2	yes	—
306	C₂×D₁₉	H(5,𝔽₂)	1	2	yes	—
307	C₄×C₁₉	—	2	2	no	—
308	C₄×C₁₉	—	2	1	no	—
309	C₄×C₁₉	—	2	2	no	—
310	C₄×C₁₉	—	2	2	no	—
311	C₄×C₁₉	—	2	1	no	—
312	C₄×C₁₉	—	2	2	no	—
313	Dic₁₉	—	2	2	no	—
314	Dic₁₉	—	2	2	no	—
315	Dic₁₉	—	2	2	no	—
316	Dic₁₉	—	2	2	no	—
317	Dic₁₉	—	2	1	no	—
318	Dic₁₉	—	2	1	no	—
319	#551	—	19	2	no	—
320	#551	—	19	2	no	—
321	#551	—	19	2	no	—
322	#551	—	19	2	no	—
323	#546	—	19	2	no	—
324	#546	—	19	2	no	—
325	#546	—	19	2	no	—
326	#546	—	19	2	no	—
327	#543	—	19	1	no	—
328	#538	—	19	2	no	—
329	#538	—	19	1	no	—
330	#538	D₁₉	1	1	yes	characteristic, complemented
331	#534	—	19	1	no	—
332	#525	—	19	1	no	—
333	#525	—	19	1	no	—
334	#525	—	19	2	no	—
335	C₂×#120	—	19	2	no	—
336	#518	—	19	2	no	—
337	C₂²×C₂²⋊C₄	—	19	1	no	—
338	C₂×C₁₉	—	2	2	no	—
339	C₂×C₁₉	—	4	2	no	—
340	C₂×C₁₉	—	4	2	no	—
341	C₂×C₁₉	C₂²×#41	1	1	yes	characteristic
342	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
343	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
344	D₁₉	—	2	2	no	—
345	D₁₉	—	2	2	no	—
346	D₁₉	—	2	4	no	—
347	D₁₉	—	4	2	no	—
348	C₂⁵	—	19	1	no	—
349	C₂×#41	—	19	1	no	—
350	C₂×#41	—	19	1	no	—
351	C₂×#41	—	19	2	no	—
352	C₂²×D₄	—	19	2	no	—
353	C₂²×D₄	—	19	2	no	—
354	C₂²×D₄	—	19	2	no	—
355	C₂³×C₄	—	19	1	no	—
356	C₂³×C₄	—	19	1	no	—
357	#126	—	19	2	no	—
358	#126	—	19	2	no	—
359	#126	—	19	2	no	—
360	#126	C₂×D₁₉	1	2	yes	complemented
361	#124	—	19	2	no	—
362	#124	—	19	2	no	—
363	#124	—	19	2	no	—
364	#124	C₂×D₁₉	1	2	yes	complemented
365	#123	—	19	2	no	—
366	#123	—	19	2	no	—
367	#123	—	19	2	no	—
368	#123	—	19	2	no	—
369	#123	—	19	2	no	—
370	#123	—	19	2	no	—
371	#123	—	19	2	no	—
372	#123	—	19	2	no	—
373	#123	—	19	2	no	—
374	#123	C₂×D₁₉	1	2	yes	complemented
375	C₂²⋊Q₈	—	19	1	no	—
376	C₂²⋊Q₈	—	19	2	no	—
377	C₂²⋊Q₈	—	19	1	no	—
378	C₂²⋊Q₈	—	19	2	no	—
379	C₂²⋊Q₈	—	19	1	no	—
380	C₂²⋊Q₈	—	19	2	no	—
381	C₂²⋊Q₈	—	19	2	no	—
382	C₂²⋊Q₈	—	19	2	no	—
383	C₂²⋊Q₈	—	19	2	no	—
384	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
385	#121	—	19	2	no	—
386	#121	—	19	2	no	—
387	#121	—	19	2	no	—
388	#121	—	19	1	no	—
389	#121	—	19	1	no	—
390	#121	—	19	1	no	—
391	#121	—	19	2	no	—
392	#121	—	19	2	no	—
393	#121	C₂×D₁₉	1	2	yes	complemented
394	#121	C₂×D₁₉	1	1	yes	characteristic, complemented
395	#120	—	19	2	no	—
396	#120	—	19	2	no	—
397	#120	—	19	2	no	—
398	#120	—	19	2	no	—
399	#120	—	19	2	no	—
400	#120	—	19	2	no	—
401	#120	—	19	2	no	—
402	#120	—	19	2	no	—
403	#120	—	19	2	no	—
404	#120	C₂×D₁₉	1	2	yes	complemented
405	C₄×D₄	—	19	2	no	—
406	C₄×D₄	—	19	2	no	—
407	C₄×D₄	—	19	2	no	—
408	C₄×D₄	—	19	2	no	—
409	C₄×D₄	—	19	2	no	—
410	C₄×D₄	—	19	2	no	—
411	C₄×D₄	—	19	2	no	—
412	C₄×D₄	—	19	2	no	—
413	C₄×D₄	—	19	2	no	—
414	C₄×D₄	—	19	2	no	—
415	C₄×D₄	—	19	2	no	—
416	C₄×D₄	C₂×D₁₉	1	2	yes	complemented
417	#117	—	19	2	no	—
418	#117	—	19	1	no	—
419	#117	—	19	1	no	—
420	#117	—	19	2	no	—
421	#117	—	19	2	no	—
422	C₂×C₂²⋊C₄	—	19	1	no	—
423	C₂×C₂²⋊C₄	—	19	1	no	—
424	C₂×C₂²⋊C₄	—	19	1	no	—
425	C₂×C₂²⋊C₄	—	19	2	no	—
426	C₂×C₂²⋊C₄	—	19	2	no	—
427	C₂×C₂²⋊C₄	—	19	2	no	—
428	C₂×C₂²⋊C₄	—	19	2	no	—
429	C₂×C₂²⋊C₄	—	19	2	no	—
430	C₂×C₂²⋊C₄	—	19	2	no	—
431	C₂×C₂²⋊C₄	—	19	2	no	—
432	C₂×C₂²⋊C₄	—	19	2	no	—
433	C₂×C₂²⋊C₄	—	19	2	no	—
434	C₂×C₂²⋊C₄	C₂×D₁₉	1	1	yes	characteristic, complemented
435	C₁₉	#3490	1	1	yes	characteristic, complemented, Sylow
436	C₂⁴	—	19	1	no	—
437	C₂⁴	—	19	1	no	—
438	C₂⁴	—	19	2	no	—
439	C₂⁴	—	19	2	no	—
440	C₂⁴	—	19	2	no	—
441	C₂⁴	—	38	4	no	—
442	C₂⁴	—	76	2	no	—
443	C₂⁴	—	76	2	no	—
444	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
445	#41	—	76	4	no	—
446	#41	—	76	2	no	—
447	#41	—	76	2	no	—
448	C₂×Q₈	—	19	1	no	—
449	C₂×Q₈	—	19	2	no	—
450	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic, complemented
451	C₂×D₄	—	19	2	no	—
452	C₂×D₄	—	19	2	no	—
453	C₂×D₄	—	19	2	no	—
454	C₂×D₄	—	19	2	no	—
455	C₂×D₄	—	19	2	no	—
456	C₂×D₄	—	19	2	no	—
457	C₂×D₄	—	19	2	no	—
458	C₂×D₄	—	19	2	no	—
459	C₂×D₄	—	19	2	no	—
460	C₂×D₄	—	19	2	no	—
461	C₂×D₄	—	19	1	no	—
462	C₂×D₄	—	38	8	no	—
463	C₂×D₄	—	76	4	no	—
464	C₂×D₄	—	76	4	no	—
465	C₂×D₄	C₂²×D₁₉	1	2	yes	—
466	C₂×D₄	C₂²×D₁₉	1	2	yes	—
467	C₂×D₄	C₂²×D₁₉	1	2	yes	—
468	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic, complemented
469	C₂²×C₄	—	19	1	no	—
470	C₂²×C₄	—	19	1	no	—
471	C₂²×C₄	—	19	2	no	—
472	C₂²×C₄	—	19	2	no	—
473	C₂²×C₄	—	19	1	no	—
474	C₂²×C₄	—	19	1	no	—
475	C₂²×C₄	—	19	2	no	—
476	C₂²×C₄	—	19	1	no	—
477	C₂²×C₄	—	19	1	no	—
478	C₂²×C₄	—	19	2	no	—
479	C₂²×C₄	—	19	2	no	—
480	C₂²×C₄	—	19	2	no	—
481	C₂²×C₄	—	19	2	no	—
482	C₂²×C₄	—	19	2	no	—
483	C₂²×C₄	—	76	2	no	—
484	C₂²×C₄	—	76	2	no	—
485	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
486	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
487	C₂²×C₄	C₂²×D₁₉	1	2	yes	complemented
488	C₄⋊C₄	—	19	2	no	—
489	C₄⋊C₄	—	19	2	no	—
490	C₄⋊C₄	—	19	2	no	—
491	C₄⋊C₄	—	19	2	no	—
492	C₄⋊C₄	—	19	2	no	—
493	C₄⋊C₄	—	19	2	no	—
494	C₄⋊C₄	—	19	2	no	—
495	C₄⋊C₄	—	19	1	no	—
496	C₄⋊C₄	—	19	1	no	—
497	C₄⋊C₄	—	19	2	no	—
498	C₄⋊C₄	C₂²×D₁₉	1	2	yes	complemented
499	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic, complemented
500	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic, complemented
501	C₄⋊C₄	C₂²×D₁₉	1	2	yes	complemented
502	C₂²⋊C₄	—	19	2	no	—
503	C₂²⋊C₄	—	19	2	no	—
504	C₂²⋊C₄	—	19	2	no	—
505	C₂²⋊C₄	—	19	2	no	—
506	C₂²⋊C₄	—	19	2	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	—	19	2	no	—
512	C₂²⋊C₄	—	19	2	no	—
513	C₂²⋊C₄	—	19	2	no	—
514	C₂²⋊C₄	—	19	2	no	—
515	C₂²⋊C₄	—	19	2	no	—
516	C₂²⋊C₄	—	19	2	no	—
517	C₂²⋊C₄	—	19	2	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	2	no	—
523	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
524	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
525	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
526	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
527	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
528	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	complemented
529	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	complemented
530	C₄²	—	19	2	no	—
531	C₄²	—	19	2	no	—
532	C₄²	—	19	2	no	—
533	C₄²	C₂²×D₁₉	1	2	yes	complemented
534	C₂³	—	2	2	no	—
535	C₂³	—	4	1	no	—
536	C₂³	—	4	1	no	—
537	C₂³	—	19	2	no	—
538	C₂³	—	19	1	no	—
539	C₂³	—	19	1	no	—
540	C₂³	—	19	4	no	—
541	C₂³	—	19	2	no	—
542	C₂³	—	38	2	no	—
543	C₂³	—	38	2	no	—
544	C₂³	—	38	4	no	—
545	C₂³	—	38	4	no	—
546	C₂³	—	38	4	no	—
547	C₂³	—	38	4	no	—
548	C₂³	—	38	4	no	—
549	C₂³	—	38	2	no	—
550	C₂³	—	76	1	no	—
551	C₂³	—	76	1	no	—
552	C₂³	—	76	2	no	—
553	C₂³	—	76	2	no	—
554	C₂³	—	76	2	no	—
555	C₂³	—	76	2	no	—
556	C₂³	—	76	16	no	—
557	C₂³	C₂³×D₁₉	1	2	yes	—
558	C₂³	C₂³×D₁₉	1	2	yes	—
559	C₂³	C₂³×D₁₉	1	1	yes	characteristic
560	Q₈	—	4	1	no	—
561	Q₈	—	76	1	no	—
562	Q₈	—	76	2	no	—
563	D₄	—	2	4	no	—
564	D₄	—	4	2	no	—
565	D₄	—	4	2	no	—
566	D₄	—	4	1	no	—
567	D₄	—	38	4	no	—
568	D₄	—	38	4	no	—
569	D₄	—	38	4	no	—
570	D₄	—	38	4	no	—
571	D₄	—	38	4	no	—
572	D₄	—	38	4	no	—
573	D₄	—	38	4	no	—
574	D₄	—	76	1	no	—
575	D₄	—	76	2	no	—
576	D₄	—	76	2	no	—
577	D₄	—	76	2	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	2	no	—
581	C₂×C₄	—	19	2	no	—
582	C₂×C₄	—	19	1	no	—
583	C₂×C₄	—	19	1	no	—
584	C₂×C₄	—	19	2	no	—
585	C₂×C₄	—	19	2	no	—
586	C₂×C₄	—	19	2	no	—
587	C₂×C₄	—	38	4	no	—
588	C₂×C₄	—	38	2	no	—
589	C₂×C₄	—	38	2	no	—
590	C₂×C₄	—	38	4	no	—
591	C₂×C₄	—	76	2	no	—
592	C₂×C₄	—	76	1	no	—
593	C₂×C₄	—	76	1	no	—
594	C₂×C₄	—	76	2	no	—
595	C₂×C₄	—	76	2	no	—
596	C₂×C₄	—	76	2	no	—
597	C₂×C₄	—	76	2	no	—
598	C₂×C₄	—	76	1	no	—
599	C₂×C₄	—	76	1	no	—
600	C₂×C₄	—	76	2	no	—
601	C₂×C₄	C₂³×D₁₉	1	2	yes	—
602	C₂×C₄	C₂³×D₁₉	1	2	yes	—
603	C₂×C₄	C₂³×D₁₉	1	2	yes	—
604	C₂×C₄	C₂³×D₁₉	1	2	yes	—
605	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
606	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
607	C₂²	—	2	1	no	—
608	C₂²	—	2	1	no	—
609	C₂²	—	2	2	no	—
610	C₂²	—	2	2	no	—
611	C₂²	—	2	2	no	—
612	C₂²	—	2	2	no	—
613	C₂²	—	2	2	no	—
614	C₂²	—	2	2	no	—
615	C₂²	—	4	4	no	—
616	C₂²	—	19	4	no	—
617	C₂²	—	19	2	no	—
618	C₂²	—	19	2	no	—
619	C₂²	—	38	8	no	—
620	C₂²	—	38	1	no	—
621	C₂²	—	38	1	no	—
622	C₂²	—	38	1	no	—
623	C₂²	—	38	1	no	—
624	C₂²	—	38	2	no	—
625	C₂²	—	38	2	no	—
626	C₂²	—	38	2	no	—
627	C₂²	—	38	2	no	—
628	C₂²	—	38	2	no	—
629	C₂²	—	76	4	no	—
630	C₂²	—	76	8	no	—
631	C₂²	—	76	8	no	—
632	C₂²	—	152	4	no	—
633	C₂²	#41×D₁₉	1	2	yes	—
634	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
635	C₄	—	2	2	no	—
636	C₄	—	2	2	no	—
637	C₄	—	2	1	no	—
638	C₄	—	2	1	no	—
639	C₄	—	2	2	no	—
640	C₄	—	2	2	no	—
641	C₄	—	38	2	no	—
642	C₄	—	38	1	no	—
643	C₄	—	38	1	no	—
644	C₄	—	38	2	no	—
645	C₄	—	38	2	no	—
646	C₄	—	38	2	no	—
647	C₂	—	2	2	no	—
648	C₂	—	4	2	no	—
649	C₂	—	4	2	no	—
650	C₂	—	38	2	no	—
651	C₂	—	38	2	no	—
652	C₂	—	38	4	no	—
653	C₂	—	76	2	no	—
654	C₂	C₂×#41×D₁₉	1	1	yes	characteristic
655	C₂	H(5,𝔽₂)×D₁₉	1	1	yes	characteristic
656	C₂	H(5,𝔽₂)×D₁₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₁₉×#538	C₂
hypercenter	#538	D₁₉
hypocenter	C₁₉	#3490
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ #538

Complements

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

N	H ≅ G/N	type
1. #11927224	C₂	semidirect
2. #11927222	C₂	semidirect
3. #11927219	C₂	semidirect
4. #11927219	C₂	semidirect
5. #11927191	C₂	semidirect
6. #11927187	C₂	semidirect
7. #11927186	C₂	semidirect
8. #11927183	C₂	semidirect
9. #11927169	C₂	semidirect
10. #11927132	C₂	semidirect
11. #11927129	C₂	semidirect
12. #11927102	C₂	semidirect
13. #11927057	C₂	semidirect
14. #11927054	C₂	semidirect
15. #11927053	C₂	semidirect
16. #120×D₁₉	C₂	semidirect
17. #11927016	C₂	semidirect
18. C₂×C₂²⋊C₄×D₁₉	C₂	semidirect
19. C₁₉×#538	C₂	semidirect
21. C₂×#64545	C₂²	semidirect
22. C₂×#64543	C₂²	semidirect
24. C₂×D₄×D₁₉	C₂²	semidirect
25. C₂×D₄×D₁₉	C₂²	semidirect
26. C₂×#64541	C₂²	semidirect
27. C₂²×C₄×D₁₉	C₂²	semidirect
28. C₂²×C₄×D₁₉	C₂²	semidirect
29. C₁₉×#126	C₂²	semidirect
30. C₁₉×#124	C₂²	semidirect
31. C₁₉×#123	C₂²	semidirect
32. C₁₉×C₂²⋊Q₈	C₂²	semidirect
33. C₁₉×#121	C₂²	semidirect
34. C₁₉×#121	C₂²	semidirect
35. C₁₉×#120	C₂²	semidirect
36. C₄×D₄×C₁₉	C₂²	semidirect
37. C₂×C₂²⋊C₄×C₁₉	C₂²	semidirect
38. #10597399	C₂²	semidirect
39. C₂×C₂²⋊Dic₁₉	C₂²	semidirect
40. #10597392	C₂²	semidirect
41. #10597392	C₂²	semidirect
42. #10597385	C₂²	semidirect
43. #10597385	C₂²	semidirect
44. #10597384	C₂²	semidirect
45. #10597384	C₂²	semidirect
48. #10597383	C₂²	semidirect
49. #10597383	C₂²	semidirect
50. #10597382	C₂²	semidirect
51. #10597381	C₂²	semidirect
52. D₄×Dic₁₉	C₂²	semidirect
53. #10597376	C₂²	semidirect
54. C₄×C₂²⋊D₁₉	C₂²	semidirect
55. C₄×C₂²⋊D₁₉	C₂²	semidirect
56. C₄×C₂²⋊D₁₉	C₂²	semidirect
59. C₂×(C₂×D₁₉)⋊C₄	C₂²	semidirect
60. #10597370	C₂²	semidirect
61. #10597343	C₂²	semidirect
62. #10597343	C₂²	semidirect
63. #10597342	C₂²	semidirect
64. #10597342	C₂²	semidirect
65. #10597342	C₂²	semidirect
66. #10597341	C₂²	semidirect
67. #10597340	C₂²	semidirect
68. #10597340	C₂²	semidirect
69. #10597340	C₂²	semidirect
70. #10597339	C₂²	semidirect
71. #10597339	C₂²	semidirect
72. #10597338	C₂²	semidirect
73. #10597338	C₂²	semidirect
74. #10597338	C₂²	semidirect
75. #10597331	C₂²	semidirect
76. #10597331	C₂²	semidirect
77. #10597330	C₂²	semidirect
78. #10597330	C₂²	semidirect
79. #10597329	C₂²	semidirect
80. #10597329	C₂²	semidirect
81. #10597329	C₂²	semidirect
82. #10597329	C₂²	semidirect
83. #10597329	C₂²	semidirect
86. #10597328	C₂²	semidirect
87. #10597328	C₂²	semidirect
88. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
89. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
90. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
92. C₂²⋊C₄×D₁₉	C₂²	semidirect
93. C₂²⋊C₄×D₁₉	C₂²	semidirect
94. C₂²⋊C₄×D₁₉	C₂²	semidirect
95. C₂²⋊C₄×D₁₉	C₂²	semidirect
96. C₂²⋊C₄×D₁₉	C₂²	semidirect
97. C₂²⋊C₄×D₁₉	C₂²	semidirect
98. C₂²⋊C₄×D₁₉	C₂²	semidirect
99. #10597325	C₂²	semidirect
100. #10597325	C₂²	semidirect
101. #10597325	C₂²	semidirect
102. #10597324	C₂²	semidirect
103. C₄×D₇₆	C₂²	semidirect
104. C₄×D₇₆	C₂²	semidirect
105. #10597318	C₂²	semidirect
106. #10597318	C₂²	semidirect
116. C₂×Q₈×C₁₉	C₂³	semidirect
120. C₂×D₄×C₁₉	C₂³	semidirect
123. C₂²×C₄×C₁₉	C₂³	semidirect
130. C₂×C₂²⋊D₁₉	C₂³	semidirect
133. C₂²×Dic₁₉	C₂³	semidirect
143. C₂×D₇₆	C₂³	semidirect
155. C₂×C₄×D₁₉	C₂³	semidirect
156. C₂×C₄×D₁₉	C₂³	semidirect
157. C₂×Dic₃₈	C₂³	semidirect
158. C₂×Dic₃₈	C₂³	semidirect
159. C₄⋊C₄×C₁₉	C₂³	semidirect
160. C₄⋊C₄×C₁₉	C₂³	semidirect
161. C₄⋊C₄×C₁₉	C₂³	semidirect
162. C₄⋊C₄×C₁₉	C₂³	semidirect
168. C₂²⋊C₄×C₁₉	C₂³	semidirect
169. C₂²⋊C₄×C₁₉	C₂³	semidirect
170. C₄²×C₁₉	C₂³	semidirect
176. C₂²⋊Dic₁₉	C₂³	semidirect
177. C₂²⋊Dic₁₉	C₂³	semidirect
188. (C₂×D₁₉)⋊C₄	C₂³	semidirect
189. (C₂×D₁₉)⋊C₄	C₂³	semidirect
190. (C₂×D₁₉)⋊C₄	C₂³	semidirect
191. (C₂×D₁₉)⋊C₄	C₂³	semidirect
192. C₄⋊Dic₁₉	C₂³	semidirect
193. C₄⋊Dic₁₉	C₂³	semidirect
194. C₄⋊Dic₁₉	C₂³	semidirect
195. C₄⋊Dic₁₉	C₂³	semidirect
196. Dic₁₉⋊C₄	C₂³	semidirect
197. Dic₁₉⋊C₄	C₂³	semidirect
198. Dic₁₉⋊C₄	C₂³	semidirect
199. Dic₁₉⋊C₄	C₂³	semidirect
200. Dic₁₉⋊C₄	C₂³	semidirect
201. Dic₁₉⋊C₄	C₂³	semidirect
202. C₄×Dic₁₉	C₂³	semidirect
203. C₄×Dic₁₉	C₂³	semidirect
204. C₄×Dic₁₉	C₂³	semidirect
226. C₂²×D₁₉	#41	semidirect
330. #538	D₁₉	semidirect
360. #126	C₂×D₁₉	semidirect
364. #124	C₂×D₁₉	semidirect
374. #123	C₂×D₁₉	semidirect
384. C₂²⋊Q₈	C₂×D₁₉	semidirect
393. #121	C₂×D₁₉	semidirect
394. #121	C₂×D₁₉	semidirect
404. #120	C₂×D₁₉	semidirect
416. C₄×D₄	C₂×D₁₉	semidirect
434. C₂×C₂²⋊C₄	C₂×D₁₉	semidirect
435. C₁₉	#3490	semidirect
450. C₂×Q₈	C₂²×D₁₉	semidirect
468. C₂×D₄	C₂²×D₁₉	semidirect
487. C₂²×C₄	C₂²×D₁₉	semidirect
498. C₄⋊C₄	C₂²×D₁₉	semidirect
499. C₄⋊C₄	C₂²×D₁₉	semidirect
500. C₄⋊C₄	C₂²×D₁₉	semidirect
501. C₄⋊C₄	C₂²×D₁₉	semidirect
528. C₂²⋊C₄	C₂²×D₁₉	semidirect
529. C₂²⋊C₄	C₂²×D₁₉	semidirect
533. C₄²	C₂²×D₁₉	semidirect

Maximal subgroups

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

subgroup	index
#11927224	2
#11927222	2
#11927219	2
#11927191	2
#11927187	2
#11927186	2
#11927183	2
#11927169	2
#11927132	2
#11927129	2
#11927102	2
#11927057	2
#11927054	2
#11927053	2
#120×D₁₉	2
#11927016	2
C₂×C₂²⋊C₄×D₁₉	2
C₁₉×#538	2
#3490	19