Subgroups — #18090447

Order 4864.

958 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926440	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926413	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926307	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926306	C₂	1	1	yes	maximal, characteristic
5	C₂×#11926306	C₂	1	1	yes	maximal, characteristic
6	C₂×#11926298	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×#340	C₂	1	1	yes	maximal, characteristic
8	C₂³×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
9	C₂²×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
11	C₂²×Dic₁₉⋊C₄	—	2	1	no	—
12	C₂²×Dic₁₉⋊C₄	—	2	1	no	—
13	C₂²×Dic₁₉⋊C₄	—	2	1	no	—
14	C₂²×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
15	#11926440	—	2	2	no	—
16	#11926440	C₄	1	4	yes	complemented
17	#11926413	—	2	2	no	—
18	#11926413	—	2	2	no	—
19	C₂×C₁₉⋊#95	—	2	1	no	—
20	#11926307	—	2	2	no	—
21	#11926306	—	2	2	no	—
22	#11926306	—	2	2	no	—
23	#11926298	—	2	2	no	—
24	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
25	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
27	C₁₉×#340	—	2	2	no	—
28	C₂³×C₄×C₁₉	—	2	1	no	—
29	C₂³×C₄×C₁₉	—	2	1	no	—
30	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
31	C₂³×Dic₁₉	—	2	1	no	—
32	C₂³×Dic₁₉	—	2	1	no	—
33	C₂³×Dic₁₉	D₄	1	1	yes	characteristic
34	C₂³×Dic₁₉	D₄	1	1	yes	characteristic
35	C₂²×C₈×C₁₉	—	2	1	no	—
36	C₂²×C₈×C₁₉	—	2	1	no	—
37	C₂²×C₈×C₁₉	—	2	1	no	—
38	C₂²×C₈×C₁₉	—	2	1	no	—
39	C₂²×C₈×C₁₉	—	2	1	no	—
40	C₂²×C₈×C₁₉	—	2	1	no	—
41	C₂²×C₈×C₁₉	Q₈	1	2	yes	—
42	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
43	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
44	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
45	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
46	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
47	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
48	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
49	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
50	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
52	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
53	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
54	C₂×C₄⋊Dic₁₉	—	2	1	no	—
55	C₂×C₄⋊Dic₁₉	—	2	1	no	—
56	C₂×C₄⋊Dic₁₉	—	2	1	no	—
57	C₂×C₄⋊Dic₁₉	—	2	1	no	—
58	C₂×C₄⋊Dic₁₉	—	2	1	no	—
59	C₂×C₄⋊Dic₁₉	—	2	1	no	—
60	C₂×C₄⋊Dic₁₉	—	2	1	no	—
61	C₂×C₄⋊Dic₁₉	—	2	1	no	—
62	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
63	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
64	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
65	C₂×C₄⋊Dic₁₉	Q₈	1	2	yes	—
66	C₂×Dic₁₉⋊C₄	—	2	4	no	—
67	C₂×Dic₁₉⋊C₄	—	2	4	no	—
68	C₂×Dic₁₉⋊C₄	—	2	4	no	—
69	C₂×Dic₁₉⋊C₄	—	4	2	no	—
70	C₂×Dic₁₉⋊C₄	—	4	2	no	—
71	C₂×Dic₁₉⋊C₄	—	4	2	no	—
72	C₂×Dic₁₉⋊C₄	—	4	2	no	—
73	C₂×Dic₁₉⋊C₄	—	4	2	no	—
74	C₂×Dic₁₉⋊C₄	—	4	2	no	—
75	C₂×C₄×Dic₁₉	—	2	1	no	—
76	C₂×C₄×Dic₁₉	—	2	1	no	—
77	C₂×C₄×Dic₁₉	—	2	1	no	—
78	C₂×C₄×Dic₁₉	—	2	1	no	—
79	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
80	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
81	C₂²×C₁₉⋊C₈	—	2	1	no	—
82	C₂²×C₁₉⋊C₈	—	2	1	no	—
83	C₂²×C₁₉⋊C₈	—	2	1	no	—
84	C₂²×C₁₉⋊C₈	—	2	1	no	—
85	C₂²×C₁₉⋊C₈	—	2	1	no	—
86	C₂²×C₁₉⋊C₈	—	2	1	no	—
87	C₂²×C₁₉⋊C₈	Q₈	1	2	yes	—
88	C₁₉⋊#95	—	2	4	no	—
89	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	—	2	2	no	—
91	C₂²×C₄×C₁₉	—	2	2	no	—
92	C₂²×C₄×C₁₉	—	4	1	no	—
93	C₂²×C₄×C₁₉	—	4	1	no	—
94	C₂²×C₄×C₁₉	—	4	1	no	—
95	C₂²×C₄×C₁₉	—	4	1	no	—
96	C₂²×C₄×C₁₉	—	4	1	no	—
97	C₂²×C₄×C₁₉	—	4	1	no	—
98	C₂²×C₄×C₁₉	—	4	1	no	—
99	C₂²×C₄×C₁₉	—	4	1	no	—
100	C₂²×C₄×C₁₉	—	4	1	no	—
101	C₂²×C₄×C₁₉	—	4	1	no	—
102	C₂²×C₄×C₁₉	—	4	1	no	—
103	C₂²×C₄×C₁₉	—	4	1	no	—
104	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
110	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
111	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
112	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
113	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
114	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
115	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
116	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
117	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
118	C₂²×Dic₁₉	—	2	1	no	—
119	C₂²×Dic₁₉	—	2	1	no	—
120	C₂²×Dic₁₉	—	2	1	no	—
121	C₂²×Dic₁₉	—	2	1	no	—
122	C₂²×Dic₁₉	—	2	1	no	—
123	C₂²×Dic₁₉	—	2	1	no	—
124	C₂²×Dic₁₉	—	2	1	no	—
125	C₂²×Dic₁₉	—	2	1	no	—
126	C₂²×Dic₁₉	—	2	2	no	—
127	C₂²×Dic₁₉	—	2	2	no	—
128	C₂²×Dic₁₉	—	2	2	no	—
129	C₂²×Dic₁₉	—	2	2	no	—
130	C₂²×Dic₁₉	—	4	1	no	—
131	C₂²×Dic₁₉	—	4	1	no	—
132	C₂²×Dic₁₉	—	4	1	no	—
133	C₂²×Dic₁₉	—	4	1	no	—
134	C₂²×Dic₁₉	—	4	1	no	—
135	C₂²×Dic₁₉	—	4	1	no	—
136	C₂²×Dic₁₉	—	4	1	no	—
137	C₂²×Dic₁₉	—	4	1	no	—
138	C₂²×Dic₁₉	—	4	1	no	—
139	C₂²×Dic₁₉	—	4	1	no	—
140	C₂²×Dic₁₉	C₂²⋊C₄	1	2	yes	—
141	C₂²×Dic₁₉	C₂²⋊C₄	1	2	yes	—
142	C₂²×Dic₁₉	D₈	1	2	yes	—
143	C₂²×Dic₁₉	SD₁₆	1	2	yes	—
144	C₂²×Dic₁₉	SD₁₆	1	2	yes	—
145	C₂²×Dic₁₉	Q₁₆	1	2	yes	—
146	C₂×C₈×C₁₉	—	2	2	no	—
147	C₂×C₈×C₁₉	—	2	2	no	—
148	C₂×C₈×C₁₉	—	2	2	no	—
149	C₂×C₈×C₁₉	—	4	1	no	—
150	C₂×C₈×C₁₉	—	4	1	no	—
151	C₂×C₈×C₁₉	—	4	1	no	—
152	C₂×C₈×C₁₉	—	4	1	no	—
153	C₄⋊C₄×C₁₉	—	2	2	no	—
154	C₄⋊C₄×C₁₉	—	2	2	no	—
155	C₄⋊C₄×C₁₉	—	2	2	no	—
156	C₄⋊C₄×C₁₉	—	2	2	no	—
157	C₄⋊C₄×C₁₉	—	4	1	no	—
158	C₄⋊C₄×C₁₉	—	4	1	no	—
159	C₄⋊C₄×C₁₉	—	4	1	no	—
160	C₄⋊C₄×C₁₉	—	4	1	no	—
161	C₄⋊Dic₁₉	—	2	2	no	—
162	C₄⋊Dic₁₉	—	2	2	no	—
163	C₄⋊Dic₁₉	—	2	2	no	—
164	C₄⋊Dic₁₉	—	2	2	no	—
165	C₄⋊Dic₁₉	—	2	2	no	—
166	C₄⋊Dic₁₉	—	4	1	no	—
167	C₄⋊Dic₁₉	—	4	1	no	—
168	C₄⋊Dic₁₉	C₄⋊C₄	1	4	yes	complemented
169	Dic₁₉⋊C₄	—	4	8	no	—
170	Dic₁₉⋊C₄	—	4	8	no	—
171	Dic₁₉⋊C₄	—	4	8	no	—
172	C₄×Dic₁₉	—	2	2	no	—
173	C₄×Dic₁₉	—	2	2	no	—
174	C₄×Dic₁₉	—	2	2	no	—
175	C₄×Dic₁₉	—	2	2	no	—
176	C₂×C₁₉⋊C₈	—	2	2	no	—
177	C₂×C₁₉⋊C₈	—	2	2	no	—
178	C₂×C₁₉⋊C₈	—	2	2	no	—
179	C₂×C₁₉⋊C₈	—	4	1	no	—
180	C₂×C₁₉⋊C₈	—	4	1	no	—
181	C₂×C₁₉⋊C₈	—	4	1	no	—
182	C₂×C₁₉⋊C₈	—	4	1	no	—
183	#11207	—	19	1	no	maximal, Sylow
184	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
185	C₂³×C₁₉	#120	1	1	yes	characteristic
186	C₂³×C₁₉	#121	1	1	yes	characteristic
187	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
188	C₂³×C₁₉	#123	1	1	yes	characteristic
189	C₂³×C₁₉	#124	1	1	yes	characteristic
190	C₂³×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
191	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
192	C₂³×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
193	C₂³×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
194	C₂³×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
195	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
196	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
197	C₂³×C₁₉	#137	1	1	yes	characteristic
198	C₂³×C₁₉	#137	1	1	yes	characteristic
199	C₂×C₄×C₁₉	—	4	2	no	—
200	C₂×C₄×C₁₉	—	4	2	no	—
201	C₂×C₄×C₁₉	—	4	2	no	—
202	C₂×C₄×C₁₉	—	4	2	no	—
203	C₂×C₄×C₁₉	—	4	2	no	—
204	C₂×C₄×C₁₉	—	4	2	no	—
205	C₂×C₄×C₁₉	—	8	1	no	—
206	C₂×C₄×C₁₉	—	8	1	no	—
207	C₂×C₄×C₁₉	—	8	1	no	—
208	C₂×C₄×C₁₉	—	8	1	no	—
209	C₂×C₄×C₁₉	—	8	1	no	—
210	C₂×C₄×C₁₉	—	8	1	no	—
211	C₂×C₄×C₁₉	—	8	1	no	—
212	C₂×C₄×C₁₉	—	8	1	no	—
213	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
214	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
215	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
216	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
217	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
218	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
219	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
220	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
221	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
222	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
223	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
224	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
225	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
226	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
227	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
228	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
229	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
230	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
231	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
232	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
233	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
234	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
235	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
236	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
237	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
238	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
239	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
240	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
241	C₂×Dic₁₉	—	2	2	no	—
242	C₂×Dic₁₉	—	2	2	no	—
243	C₂×Dic₁₉	—	2	2	no	—
244	C₂×Dic₁₉	—	2	2	no	—
245	C₂×Dic₁₉	—	2	2	no	—
246	C₂×Dic₁₉	—	2	2	no	—
247	C₂×Dic₁₉	—	2	2	no	—
248	C₂×Dic₁₉	—	2	2	no	—
249	C₂×Dic₁₉	—	2	2	no	—
250	C₂×Dic₁₉	—	2	2	no	—
251	C₂×Dic₁₉	—	2	2	no	—
252	C₂×Dic₁₉	—	2	2	no	—
253	C₂×Dic₁₉	—	2	4	no	—
254	C₂×Dic₁₉	—	4	2	no	—
255	C₂×Dic₁₉	—	4	2	no	—
256	C₂×Dic₁₉	—	4	2	no	—
257	C₂×Dic₁₉	—	4	2	no	—
258	C₂×Dic₁₉	—	4	2	no	—
259	C₂×Dic₁₉	—	4	2	no	—
260	C₂×Dic₁₉	—	4	2	no	—
261	C₂×Dic₁₉	—	4	2	no	—
262	C₂×Dic₁₉	—	4	2	no	—
263	C₂×Dic₁₉	—	8	1	no	—
264	C₂×Dic₁₉	—	8	1	no	—
265	C₂×Dic₁₉	—	8	1	no	—
266	C₂×Dic₁₉	—	8	1	no	—
267	C₂×Dic₁₉	#102	1	4	yes	—
268	C₂×Dic₁₉	#103	1	4	yes	—
269	C₈×C₁₉	—	4	2	no	—
270	C₁₉⋊C₈	—	4	2	no	—
271	C₂×#389	—	19	1	no	—
272	C₂×#384	—	19	1	no	—
273	C₂×#340	—	19	1	no	—
274	C₂×#340	—	19	1	no	—
275	C₂×#340	—	19	1	no	—
276	C₂×#340	D₁₉	1	1	yes	characteristic
277	C₂×#336	—	19	1	no	—
278	C₂²×C₁₉	#380	1	1	yes	characteristic
279	C₂²×C₁₉	#386	1	1	yes	characteristic
280	C₂²×C₁₉	#391	1	1	yes	characteristic
281	C₂²×C₁₉	#394	1	1	yes	characteristic
282	C₂²×C₁₉	#395	1	1	yes	characteristic
283	C₂²×C₁₉	#398	1	1	yes	characteristic
284	C₂²×C₁₉	#400	1	1	yes	characteristic
285	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
286	C₂²×C₁₉	C₂×#103	1	1	yes	characteristic
287	C₂²×C₁₉	#417	1	1	yes	characteristic
288	C₂²×C₁₉	#417	1	1	yes	characteristic
289	C₂²×C₁₉	#447	1	1	yes	characteristic
290	C₂²×C₁₉	#448	1	1	yes	characteristic
291	C₂²×C₁₉	#450	1	1	yes	characteristic
292	C₂²×C₁₉	#451	1	1	yes	characteristic
293	C₂²×C₁₉	#459	1	1	yes	characteristic
294	C₂²×C₁₉	#460	1	1	yes	characteristic
295	C₂²×C₁₉	#461	1	1	yes	characteristic
296	C₂²×C₁₉	#462	1	1	yes	characteristic
297	C₂²×C₁₉	#474	1	1	yes	characteristic
298	C₂²×C₁₉	#475	1	1	yes	characteristic
299	C₂²×C₁₉	#476	1	1	yes	characteristic
300	C₂²×C₁₉	#477	1	1	yes	characteristic
301	C₂²×C₁₉	#480	1	1	yes	characteristic
302	C₂²×C₁₉	#481	1	1	yes	characteristic
303	C₂²×C₁₉	#483	1	1	yes	characteristic
304	C₂²×C₁₉	#484	1	1	yes	characteristic
305	C₂²×C₁₉	#486	1	1	yes	characteristic
306	C₂²×C₁₉	#487	1	1	yes	characteristic
307	C₂²×C₁₉	#490	1	1	yes	characteristic
308	C₂²×C₁₉	#491	1	1	yes	characteristic
309	C₂²×C₁₉	#498	1	1	yes	characteristic
310	C₂²×C₁₉	#500	1	1	yes	characteristic
311	C₂²×C₁₉	#501	1	1	yes	characteristic
312	C₂²×C₁₉	#501	1	1	yes	characteristic
313	C₄×C₁₉	—	8	2	no	—
314	C₄×C₁₉	—	8	2	no	—
315	C₄×C₁₉	#387	1	1	yes	characteristic
316	C₄×C₁₉	#387	1	1	yes	characteristic
317	C₄×C₁₉	#389	1	1	yes	characteristic
318	C₄×C₁₉	#389	1	1	yes	characteristic
319	C₄×C₁₉	#396	1	1	yes	characteristic
320	C₄×C₁₉	#396	1	1	yes	characteristic
321	C₄×C₁₉	#398	1	1	yes	characteristic
322	C₄×C₁₉	#398	1	1	yes	characteristic
323	Dic₁₉	—	2	4	no	—
324	Dic₁₉	—	2	4	no	—
325	Dic₁₉	—	4	4	no	—
326	Dic₁₉	—	8	2	no	—
327	C₂³×C₈	—	19	1	no	—
328	C₂³×C₈	C₂×D₁₉	1	1	yes	characteristic
329	C₂²×C₄⋊C₄	—	19	1	no	—
330	C₂²×C₄⋊C₄	—	19	1	no	—
331	C₂²×C₄⋊C₄	—	38	1	no	—
332	C₂²×C₄⋊C₄	—	38	1	no	—
333	C₂²×C₄⋊C₄	—	38	1	no	—
334	C₂²×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
335	C₂²×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
336	C₂²×C₄²	—	19	1	no	—
337	#389	—	19	4	no	—
338	#389	—	38	2	no	—
339	#384	—	38	2	no	—
340	#384	—	38	2	no	—
341	C₂×#95	—	38	1	no	—
342	#340	—	2	2	no	—
343	#340	—	38	2	no	—
344	#340	—	38	2	no	—
345	#340	—	38	2	no	—
346	#336	—	38	2	no	—
347	C₂×C₁₉	#1441	1	1	yes	characteristic
348	C₂×C₁₉	#1802	1	1	yes	characteristic
349	C₂×C₁₉	#1803	1	1	yes	characteristic
350	C₂×C₁₉	#1872	1	1	yes	characteristic
351	C₂×C₁₉	#1874	1	1	yes	characteristic
352	C₂×C₁₉	#1990	1	1	yes	characteristic
353	C₂×C₁₉	#1992	1	1	yes	characteristic
354	C₂×C₁₉	#2041	1	1	yes	characteristic
355	C₂×C₁₉	#2043	1	1	yes	characteristic
356	C₂×C₁₉	#2057	1	1	yes	characteristic
357	C₂×C₁₉	#2058	1	1	yes	characteristic
358	C₂×C₁₉	#2083	1	1	yes	characteristic
359	C₂×C₁₉	#2084	1	1	yes	characteristic
360	C₂×C₁₉	#2099	1	1	yes	characteristic
361	C₂×C₁₉	#2100	1	1	yes	characteristic
362	C₂³×C₄	—	2	1	no	—
363	C₂³×C₄	—	2	1	no	—
364	C₂³×C₄	—	19	1	no	—
365	C₂³×C₄	—	19	1	no	—
366	C₂³×C₄	—	38	1	no	—
367	C₂³×C₄	—	38	1	no	—
368	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
369	C₂²×C₈	—	2	1	no	—
370	C₂²×C₈	—	2	1	no	—
371	C₂²×C₈	—	2	1	no	—
372	C₂²×C₈	—	2	1	no	—
373	C₂²×C₈	—	2	1	no	—
374	C₂²×C₈	—	2	1	no	—
375	C₂²×C₈	—	19	2	no	—
376	C₂²×C₈	—	38	1	no	—
377	C₂²×C₈	—	38	1	no	—
378	C₂²×C₈	—	38	1	no	—
379	C₂²×C₈	—	38	1	no	—
380	C₂²×C₈	—	38	1	no	—
381	C₂²×C₈	—	38	1	no	—
382	C₂²×C₈	Dic₃₈	1	2	yes	—
383	C₂×C₄⋊C₄	—	2	1	no	—
384	C₂×C₄⋊C₄	—	2	1	no	—
385	C₂×C₄⋊C₄	—	2	1	no	—
386	C₂×C₄⋊C₄	—	2	1	no	—
387	C₂×C₄⋊C₄	—	2	1	no	—
388	C₂×C₄⋊C₄	—	2	1	no	—
389	C₂×C₄⋊C₄	—	2	1	no	—
390	C₂×C₄⋊C₄	—	2	1	no	—
391	C₂×C₄⋊C₄	—	2	1	no	—
392	C₂×C₄⋊C₄	—	2	1	no	—
393	C₂×C₄⋊C₄	—	19	2	no	—
394	C₂×C₄⋊C₄	—	19	2	no	—
395	C₂×C₄⋊C₄	—	19	2	no	—
396	C₂×C₄⋊C₄	—	19	2	no	—
397	C₂×C₄⋊C₄	—	38	1	no	—
398	C₂×C₄⋊C₄	—	38	1	no	—
399	C₂×C₄⋊C₄	—	38	1	no	—
400	C₂×C₄⋊C₄	—	38	1	no	—
401	C₂×C₄⋊C₄	—	38	1	no	—
402	C₂×C₄⋊C₄	—	38	1	no	—
403	C₂×C₄⋊C₄	—	38	1	no	—
404	C₂×C₄⋊C₄	—	38	4	no	—
405	C₂×C₄⋊C₄	—	38	4	no	—
406	C₂×C₄⋊C₄	—	38	4	no	—
407	C₂×C₄⋊C₄	—	38	1	no	—
408	C₂×C₄⋊C₄	—	76	2	no	—
409	C₂×C₄⋊C₄	—	76	2	no	—
410	C₂×C₄⋊C₄	—	76	2	no	—
411	C₂×C₄⋊C₄	—	76	2	no	—
412	C₂×C₄⋊C₄	—	76	2	no	—
413	C₂×C₄⋊C₄	—	76	2	no	—
414	C₂×C₄⋊C₄	C₄×D₁₉	1	2	yes	—
415	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
416	C₂×C₄²	—	19	2	no	—
417	C₂×C₄²	—	19	2	no	—
418	C₂×C₄²	—	38	1	no	—
419	C₂×C₄²	—	38	1	no	—
420	C₂×C₄²	—	38	1	no	—
421	C₂×C₄²	—	38	1	no	—
422	#95	—	38	4	no	—
423	C₁₉	#11207	1	1	yes	characteristic, complemented, Sylow
424	C₂⁴	D₄×D₁₉	1	1	yes	characteristic
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	4	1	no	—
428	C₂²×C₄	—	4	1	no	—
429	C₂²×C₄	—	4	1	no	—
430	C₂²×C₄	—	4	1	no	—
431	C₂²×C₄	—	4	1	no	—
432	C₂²×C₄	—	4	1	no	—
433	C₂²×C₄	—	4	1	no	—
434	C₂²×C₄	—	4	1	no	—
435	C₂²×C₄	—	4	1	no	—
436	C₂²×C₄	—	4	1	no	—
437	C₂²×C₄	—	4	1	no	—
438	C₂²×C₄	—	4	1	no	—
439	C₂²×C₄	—	19	2	no	—
440	C₂²×C₄	—	19	2	no	—
441	C₂²×C₄	—	19	2	no	—
442	C₂²×C₄	—	19	2	no	—
443	C₂²×C₄	—	19	2	no	—
444	C₂²×C₄	—	19	2	no	—
445	C₂²×C₄	—	38	1	no	—
446	C₂²×C₄	—	38	1	no	—
447	C₂²×C₄	—	38	1	no	—
448	C₂²×C₄	—	38	1	no	—
449	C₂²×C₄	—	38	1	no	—
450	C₂²×C₄	—	38	1	no	—
451	C₂²×C₄	—	38	1	no	—
452	C₂²×C₄	—	38	1	no	—
453	C₂²×C₄	—	38	2	no	—
454	C₂²×C₄	—	38	2	no	—
455	C₂²×C₄	—	38	2	no	—
456	C₂²×C₄	—	38	2	no	—
457	C₂²×C₄	—	76	1	no	—
458	C₂²×C₄	—	76	1	no	—
459	C₂²×C₄	—	76	1	no	—
460	C₂²×C₄	—	76	1	no	—
461	C₂²×C₄	—	76	1	no	—
462	C₂²×C₄	—	76	1	no	—
463	C₂²×C₄	—	76	1	no	—
464	C₂²×C₄	—	76	1	no	—
465	C₂²×C₄	—	76	1	no	—
466	C₂²×C₄	—	76	1	no	—
467	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
468	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
469	C₂²×C₄	#64541	1	1	yes	characteristic
470	C₂²×C₄	#64541	1	1	yes	characteristic
471	C₂²×C₄	#64541	1	1	yes	characteristic
472	C₂²×C₄	#64541	1	1	yes	characteristic
473	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
474	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
475	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
476	C₂²×C₄	#64543	1	1	yes	characteristic
477	C₂²×C₄	#64543	1	1	yes	characteristic
478	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
479	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
480	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
481	C₂×C₈	—	2	2	no	—
482	C₂×C₈	—	2	2	no	—
483	C₂×C₈	—	2	2	no	—
484	C₂×C₈	—	4	1	no	—
485	C₂×C₈	—	4	1	no	—
486	C₂×C₈	—	4	1	no	—
487	C₂×C₈	—	4	1	no	—
488	C₂×C₈	—	38	2	no	—
489	C₂×C₈	—	38	2	no	—
490	C₂×C₈	—	38	2	no	—
491	C₂×C₈	—	76	1	no	—
492	C₂×C₈	—	76	1	no	—
493	C₂×C₈	—	76	1	no	—
494	C₂×C₈	—	76	1	no	—
495	C₄⋊C₄	—	2	2	no	—
496	C₄⋊C₄	—	2	2	no	—
497	C₄⋊C₄	—	2	2	no	—
498	C₄⋊C₄	—	2	2	no	—
499	C₄⋊C₄	—	4	1	no	—
500	C₄⋊C₄	—	4	1	no	—
501	C₄⋊C₄	—	4	1	no	—
502	C₄⋊C₄	—	4	1	no	—
503	C₄⋊C₄	—	19	4	no	—
504	C₄⋊C₄	—	38	2	no	—
505	C₄⋊C₄	—	38	2	no	—
506	C₄⋊C₄	—	38	2	no	—
507	C₄⋊C₄	—	38	2	no	—
508	C₄⋊C₄	—	38	2	no	—
509	C₄⋊C₄	—	76	8	no	—
510	C₄⋊C₄	—	76	8	no	—
511	C₄⋊C₄	—	76	8	no	—
512	C₄⋊C₄	—	76	1	no	—
513	C₄⋊C₄	—	76	1	no	—
514	C₄²	—	38	2	no	—
515	C₄²	—	38	2	no	—
516	C₄²	—	38	2	no	—
517	C₄²	—	38	2	no	—
518	C₂³	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
519	C₂³	#10597329	1	1	yes	characteristic
520	C₂³	#10597330	1	1	yes	characteristic
521	C₂³	#10597331	1	1	yes	characteristic
522	C₂³	#10597334	1	1	yes	characteristic
523	C₂³	#10597342	1	1	yes	characteristic
524	C₂³	D₈×D₁₉	1	1	yes	characteristic
525	C₂³	#10597357	1	1	yes	characteristic
526	C₂³	SD₁₆×D₁₉	1	1	yes	characteristic
527	C₂³	SD₁₆×D₁₉	1	1	yes	characteristic
528	C₂³	#10597360	1	1	yes	characteristic
529	C₂³	#10597361	1	1	yes	characteristic
530	C₂³	Q₁₆×D₁₉	1	1	yes	characteristic
531	C₂³	#10597364	1	1	yes	characteristic
532	C₂³	#10597383	1	1	yes	characteristic
533	C₂×C₄	—	4	2	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	4	2	no	—
536	C₂×C₄	—	4	2	no	—
537	C₂×C₄	—	4	2	no	—
538	C₂×C₄	—	4	2	no	—
539	C₂×C₄	—	8	1	no	—
540	C₂×C₄	—	8	1	no	—
541	C₂×C₄	—	8	1	no	—
542	C₂×C₄	—	8	1	no	—
543	C₂×C₄	—	8	1	no	—
544	C₂×C₄	—	8	1	no	—
545	C₂×C₄	—	8	1	no	—
546	C₂×C₄	—	8	1	no	—
547	C₂×C₄	—	19	4	no	—
548	C₂×C₄	—	19	4	no	—
549	C₂×C₄	—	38	2	no	—
550	C₂×C₄	—	38	2	no	—
551	C₂×C₄	—	38	2	no	—
552	C₂×C₄	—	38	2	no	—
553	C₂×C₄	—	38	2	no	—
554	C₂×C₄	—	38	2	no	—
555	C₂×C₄	—	38	2	no	—
556	C₂×C₄	—	38	2	no	—
557	C₂×C₄	—	38	2	no	—
558	C₂×C₄	—	38	2	no	—
559	C₂×C₄	—	38	2	no	—
560	C₂×C₄	—	38	2	no	—
561	C₂×C₄	—	38	4	no	—
562	C₂×C₄	—	76	2	no	—
563	C₂×C₄	—	76	2	no	—
564	C₂×C₄	—	76	2	no	—
565	C₂×C₄	—	76	2	no	—
566	C₂×C₄	—	76	2	no	—
567	C₂×C₄	—	76	2	no	—
568	C₂×C₄	—	76	2	no	—
569	C₂×C₄	—	76	2	no	—
570	C₂×C₄	—	76	2	no	—
571	C₂×C₄	—	152	1	no	—
572	C₂×C₄	—	152	1	no	—
573	C₂×C₄	—	152	1	no	—
574	C₂×C₄	—	152	1	no	—
575	C₂×C₄	C₄×Dic₃₈	1	1	yes	characteristic
576	C₂×C₄	#10597316	1	1	yes	characteristic
577	C₂×C₄	#10597318	1	1	yes	characteristic
578	C₂×C₄	#10597322	1	1	yes	characteristic
579	C₂×C₄	#10597324	1	1	yes	characteristic
580	C₂×C₄	#10597324	1	1	yes	characteristic
581	C₂×C₄	#10597325	1	1	yes	characteristic
582	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
583	C₂×C₄	#10597329	1	1	yes	characteristic
584	C₂×C₄	#10597330	1	1	yes	characteristic
585	C₂×C₄	#10597330	1	1	yes	characteristic
586	C₂×C₄	#10597330	1	1	yes	characteristic
587	C₂×C₄	#10597333	1	1	yes	characteristic
588	C₂×C₄	#10597334	1	1	yes	characteristic
589	C₂×C₄	#10597335	1	1	yes	characteristic
590	C₂×C₄	#10597335	1	1	yes	characteristic
591	C₂×C₄	#10597335	1	1	yes	characteristic
592	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
593	C₂×C₄	#10597342	1	1	yes	characteristic
594	C₂×C₄	#10597342	1	1	yes	characteristic
595	C₂×C₄	#10597342	1	1	yes	characteristic
596	C₂×C₄	#10597342	1	1	yes	characteristic
597	C₂×C₄	#10597370	1	1	yes	characteristic
598	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
599	C₂×C₄	#10597375	1	1	yes	characteristic
600	C₂×C₄	#10597384	1	1	yes	characteristic
601	C₂×C₄	#10597385	1	1	yes	characteristic
602	C₂×C₄	#10597390	1	1	yes	characteristic
603	C₈	—	4	2	no	—
604	C₈	—	76	2	no	—
605	C₂²	#11926403	1	1	yes	characteristic
606	C₂²	#11926420	1	1	yes	characteristic
607	C₂²	#11926448	1	1	yes	characteristic
608	C₂²	#11926459	1	1	yes	characteristic
609	C₂²	#11926464	1	1	yes	characteristic
610	C₂²	#11926478	1	1	yes	characteristic
611	C₂²	#11926485	1	1	yes	characteristic
612	C₂²	#102×D₁₉	1	1	yes	characteristic
613	C₂²	#103×D₁₉	1	1	yes	characteristic
614	C₂²	#11926542	1	1	yes	characteristic
615	C₂²	#11926544	1	1	yes	characteristic
616	C₂²	#11926676	1	1	yes	characteristic
617	C₂²	#11926681	1	1	yes	characteristic
618	C₂²	#11926693	1	1	yes	characteristic
619	C₂²	#11926698	1	1	yes	characteristic
620	C₂²	#11926738	1	1	yes	characteristic
621	C₂²	#11926743	1	1	yes	characteristic
622	C₂²	#11926748	1	1	yes	characteristic
623	C₂²	#11926753	1	1	yes	characteristic
624	C₂²	#11926823	1	1	yes	characteristic
625	C₂²	#11926828	1	1	yes	characteristic
626	C₂²	#11926833	1	1	yes	characteristic
627	C₂²	#11926838	1	1	yes	characteristic
628	C₂²	#11926856	1	1	yes	characteristic
629	C₂²	#11926861	1	1	yes	characteristic
630	C₂²	#11926873	1	1	yes	characteristic
631	C₂²	#11926878	1	1	yes	characteristic
632	C₂²	#11926889	1	1	yes	characteristic
633	C₂²	#11926893	1	1	yes	characteristic
634	C₂²	#11926907	1	1	yes	characteristic
635	C₂²	#11926911	1	1	yes	characteristic
636	C₂²	#11926941	1	1	yes	characteristic
637	C₂²	#11926948	1	1	yes	characteristic
638	C₂²	#11926951	1	1	yes	characteristic
639	C₂²	#11926952	1	1	yes	characteristic
640	C₄	—	8	2	no	—
641	C₄	—	8	2	no	—
642	C₄	—	38	4	no	—
643	C₄	—	38	4	no	—
644	C₄	—	76	4	no	—
645	C₄	—	152	2	no	—
646	C₄	#11926426	1	1	yes	characteristic
647	C₄	#11926428	1	1	yes	characteristic
648	C₄	#11926439	1	1	yes	characteristic
649	C₄	#11926441	1	1	yes	characteristic
650	C₄	#11926467	1	1	yes	characteristic
651	C₄	#11926468	1	1	yes	characteristic
652	C₄	#11926475	1	1	yes	characteristic
653	C₄	#11926478	1	1	yes	characteristic
654	C₂	#14561886	1	1	yes	characteristic
655	C₂	#14563634	1	1	yes	characteristic
656	C₂	#14563639	1	1	yes	characteristic
657	C₂	#14563939	1	1	yes	characteristic
658	C₂	#14563949	1	1	yes	characteristic
659	C₂	#14564594	1	1	yes	characteristic
660	C₂	#14564602	1	1	yes	characteristic
661	C₂	#14564867	1	1	yes	characteristic
662	C₂	#14564879	1	1	yes	characteristic
663	C₂	#14564961	1	1	yes	characteristic
664	C₂	#14564966	1	1	yes	characteristic
665	C₂	#14565110	1	1	yes	characteristic
666	C₂	#14565115	1	1	yes	characteristic
667	C₂	#14565195	1	1	yes	characteristic
668	C₂	#14565200	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	D₄×D₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#340	C₂
socle, prime radical	C₂⁴×C₁₉	C₂×D₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#340	D₁₉
hypocenter	C₁₉	#11207
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂×#340

Complements

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

N	H ≅ G/N	type
16. #11926440	C₄	semidirect
168. C₄⋊Dic₁₉	C₄⋊C₄	semidirect
423. C₁₉	#11207	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926440	2
C₂×#11926413	2
C₂×#11926307	2
C₂×#11926306	2
C₂×#11926298	2
C₂×C₁₉×#340	2
#11207	19