Subgroups — #18088433

Order 4864.

982 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#10597274	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₈×Dic₁₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926306	C₂	1	2	yes	maximal
4	#14561864	C₂	1	2	yes	maximal
5	C₂²×C₁₉×#106	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
7	C₂²×C₄⋊Dic₁₉	C₂²	1	2	yes	—
8	C₂²×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
9	C₂×#10597274	—	2	2	no	—
10	C₂×#10597274	—	2	2	no	—
11	C₂×#10597274	C₄	1	4	yes	complemented
12	C₂×C₈×Dic₁₉	—	2	2	no	—
13	C₂×C₈×Dic₁₉	—	2	2	no	—
14	C₂×C₈×Dic₁₉	C₄	1	4	yes	complemented
15	C₂×C₁₉⋊#95	—	2	4	no	—
16	#11926306	—	2	4	no	—
17	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
19	C₂×C₁₉×#106	—	2	2	no	—
20	C₂×C₁₉×#106	—	2	2	no	—
21	C₂×C₁₉×#106	C₄	1	4	yes	complemented
22	C₂³×C₄×C₁₉	—	2	2	no	—
23	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
24	C₂³×Dic₁₉	—	2	2	no	—
25	C₂³×Dic₁₉	D₄	1	2	yes	—
26	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
27	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
28	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
29	C₂²×C₈×C₁₉	D₄	1	2	yes	—
30	C₂²×C₈×C₁₉	D₄	1	2	yes	—
31	C₂²×C₈×C₁₉	D₄	1	2	yes	—
32	C₂²×C₈×C₁₉	Q₈	1	2	yes	—
33	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
34	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
35	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
36	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
37	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
38	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
39	C₂×C₄⋊Dic₁₉	—	2	2	no	—
40	C₂×C₄⋊Dic₁₉	—	2	2	no	—
41	C₂×C₄⋊Dic₁₉	—	2	2	no	—
42	C₂×C₄⋊Dic₁₉	—	2	2	no	—
43	C₂×C₄⋊Dic₁₉	—	2	2	no	—
44	C₂×C₄⋊Dic₁₉	C₂×C₄	1	4	yes	—
45	C₂×C₄×Dic₁₉	—	2	1	no	—
46	C₂×C₄×Dic₁₉	—	2	1	no	—
47	C₂×C₄×Dic₁₉	—	2	1	no	—
48	C₂×C₄×Dic₁₉	—	2	1	no	—
49	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
50	C₂×C₄×Dic₁₉	Q₈	1	2	yes	—
51	C₂²×C₁₉⋊C₈	—	2	1	no	—
52	C₂²×C₁₉⋊C₈	—	2	1	no	—
53	C₂²×C₁₉⋊C₈	—	2	1	no	—
54	C₂²×C₁₉⋊C₈	—	2	1	no	—
55	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
56	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
57	C₂²×C₁₉⋊C₈	Q₈	1	2	yes	—
58	C₁₉×#106	—	2	8	no	—
59	C₁₉⋊#95	—	4	8	no	—
60	#10597274	—	2	8	no	—
61	C₈×Dic₁₉	—	2	8	no	—
62	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
63	C₂²×C₄×C₁₉	—	2	4	no	—
64	C₂²×C₄×C₁₉	—	4	2	no	—
65	C₂²×C₄×C₁₉	—	4	2	no	—
66	C₂²×C₄×C₁₉	—	4	4	no	—
67	C₂²×C₄×C₁₉	—	4	4	no	—
68	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
76	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
77	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
78	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
79	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
80	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
81	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
82	C₂²×Dic₁₉	—	2	2	no	—
83	C₂²×Dic₁₉	—	2	2	no	—
84	C₂²×Dic₁₉	—	2	4	no	—
85	C₂²×Dic₁₉	—	2	4	no	—
86	C₂²×Dic₁₉	—	4	2	no	—
87	C₂²×Dic₁₉	—	4	2	no	—
88	C₂²×Dic₁₉	—	4	4	no	—
89	C₂²×Dic₁₉	—	4	4	no	—
90	C₂²×Dic₁₉	C₄⋊C₄	1	4	yes	—
91	C₂²×Dic₁₉	SD₁₆	1	8	yes	—
92	C₂×C₈×C₁₉	C₄²	1	4	yes	—
93	C₂×C₈×C₁₉	C₂²⋊C₄	1	4	yes	—
94	C₂×C₈×C₁₉	C₂²⋊C₄	1	4	yes	—
95	C₂×C₈×C₁₉	C₂²⋊C₄	1	4	yes	—
96	C₂×C₈×C₁₉	C₄⋊C₄	1	4	yes	—
97	C₂×C₈×C₁₉	C₄⋊C₄	1	4	yes	—
98	C₂×C₈×C₁₉	C₄⋊C₄	1	4	yes	—
99	C₄⋊C₄×C₁₉	—	2	4	no	—
100	C₄⋊C₄×C₁₉	—	2	4	no	—
101	C₄⋊C₄×C₁₉	—	4	2	no	—
102	C₄⋊C₄×C₁₉	—	4	2	no	—
103	C₄⋊Dic₁₉	—	2	4	no	—
104	C₄⋊Dic₁₉	—	2	4	no	—
105	C₄⋊Dic₁₉	—	4	2	no	—
106	C₄⋊Dic₁₉	—	4	2	no	—
107	C₄×Dic₁₉	—	2	2	no	—
108	C₄×Dic₁₉	—	2	2	no	—
109	C₄×Dic₁₉	—	2	2	no	—
110	C₄×Dic₁₉	—	2	2	no	—
111	C₂×C₁₉⋊C₈	—	2	2	no	—
112	C₂×C₁₉⋊C₈	—	2	2	no	—
113	C₂×C₁₉⋊C₈	—	2	2	no	—
114	C₂×C₁₉⋊C₈	—	2	2	no	—
115	C₂×C₁₉⋊C₈	—	2	2	no	—
116	C₂×C₁₉⋊C₈	—	2	2	no	—
117	C₂×C₁₉⋊C₈	C₄⋊C₄	1	4	yes	—
118	#10861	—	19	1	no	maximal, Sylow
119	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
120	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
121	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
122	C₂³×C₁₉	#121	1	1	yes	characteristic
123	C₂³×C₁₉	#121	1	1	yes	characteristic
124	C₂³×C₁₉	#127	1	1	yes	characteristic
125	C₂³×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
126	C₂³×C₁₉	C₂×SD₁₆	1	4	yes	—
127	C₂³×C₁₉	#135	1	4	yes	—
128	C₂×C₄×C₁₉	—	4	4	no	—
129	C₂×C₄×C₁₉	—	4	8	no	—
130	C₂×C₄×C₁₉	—	8	4	no	—
131	C₂×C₄×C₁₉	—	8	2	no	—
132	C₂×C₄×C₁₉	—	8	2	no	—
133	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
134	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
135	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
136	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
137	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
138	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
139	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
140	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
141	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
142	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
143	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
144	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
145	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
146	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
147	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
148	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
149	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
150	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
151	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
152	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
153	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
154	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
155	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
156	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
157	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
158	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
159	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
160	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
161	C₂×Dic₁₉	—	2	4	no	—
162	C₂×Dic₁₉	—	2	4	no	—
163	C₂×Dic₁₉	—	2	8	no	—
164	C₂×Dic₁₉	—	2	8	no	—
165	C₂×Dic₁₉	—	4	4	no	—
166	C₂×Dic₁₉	—	4	8	no	—
167	C₂×Dic₁₉	—	8	4	no	—
168	C₂×Dic₁₉	—	8	2	no	—
169	C₂×Dic₁₉	—	8	2	no	—
170	C₂×Dic₁₉	#106	1	8	yes	complemented
171	C₈×C₁₉	#95	1	8	yes	complemented
172	C₁₉⋊C₈	—	2	4	no	—
173	C₂²×#106	—	19	1	no	—
174	C₂²×#106	D₁₉	1	1	yes	characteristic
175	C₂²×C₄×C₈	—	19	1	no	—
176	C₂×#340	—	19	2	no	—
177	C₄⋊#95	—	19	2	no	—
178	C₂²×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
179	C₂²×C₁₉	#380	1	1	yes	characteristic
180	C₂²×C₁₉	#384	1	1	yes	characteristic
181	C₂²×C₁₉	#389	1	1	yes	characteristic
182	C₂²×C₁₉	#389	1	1	yes	characteristic
183	C₂²×C₁₉	#390	1	1	yes	characteristic
184	C₂²×C₁₉	#390	1	1	yes	characteristic
185	C₂²×C₁₉	C₂×#106	1	2	yes	—
186	C₂²×C₁₉	#427	1	2	yes	—
187	C₂²×C₁₉	C₄×SD₁₆	1	4	yes	—
188	C₂²×C₁₉	C₄×SD₁₆	1	4	yes	—
189	C₂²×C₁₉	#465	1	4	yes	—
190	C₂²×C₁₉	#465	1	4	yes	—
191	C₂²×C₁₉	#492	1	2	yes	—
192	C₂²×C₁₉	#495	1	2	yes	—
193	C₂²×C₁₉	#498	1	2	yes	—
194	C₂²×C₁₉	#499	1	2	yes	—
195	C₄×C₁₉	—	8	4	no	—
196	C₄×C₁₉	C₂×#95	1	1	yes	characteristic
197	C₄×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
198	C₄×C₁₉	#380	1	1	yes	characteristic
199	C₄×C₁₉	#382	1	1	yes	characteristic
200	C₄×C₁₉	#389	1	1	yes	characteristic
201	C₄×C₁₉	#389	1	1	yes	characteristic
202	C₄×C₁₉	#391	1	1	yes	characteristic
203	C₄×C₁₉	#391	1	1	yes	characteristic
204	Dic₁₉	—	2	8	no	—
205	Dic₁₉	—	8	4	no	—
206	C₂³×C₈	—	19	1	no	—
207	C₂³×C₈	C₂×D₁₉	1	1	yes	characteristic
208	C₂²×C₄⋊C₄	—	19	2	no	—
209	C₂²×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
210	C₂²×C₄²	—	19	1	no	—
211	C₂×#106	—	2	2	no	—
212	C₂×#106	—	2	2	no	—
213	C₂×#106	—	19	4	no	—
214	C₂×#106	—	38	2	no	—
215	C₂×#106	—	38	2	no	—
216	C₂×#106	Dic₁₉	1	4	yes	complemented
217	C₂×C₄×C₈	—	19	4	no	—
218	C₂×C₄×C₈	—	38	2	no	—
219	C₂×C₄×C₈	—	38	2	no	—
220	C₂×#95	—	38	4	no	—
221	#340	—	38	4	no	—
222	C₂×C₁₉	C₄⋊#95	1	1	yes	characteristic
223	C₂×C₁₉	C₄×#106	1	2	yes	—
224	C₂×C₁₉	#1807	1	2	yes	—
225	C₂×C₁₉	#1844	1	1	yes	characteristic
226	C₂×C₁₉	#1846	1	1	yes	characteristic
227	C₂×C₁₉	#1941	1	2	yes	—
228	C₂×C₁₉	#1941	1	2	yes	—
229	C₂×C₁₉	#1968	1	2	yes	—
230	C₂×C₁₉	#1968	1	2	yes	—
231	C₂³×C₄	—	2	2	no	—
232	C₂³×C₄	—	19	2	no	—
233	C₂³×C₄	—	38	2	no	—
234	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
235	C₂²×C₈	—	19	2	no	—
236	C₂²×C₈	—	19	2	no	—
237	C₂²×C₈	—	19	2	no	—
238	C₂²×C₈	—	38	1	no	—
239	C₂²×C₈	—	38	1	no	—
240	C₂²×C₈	—	38	1	no	—
241	C₂²×C₈	—	38	1	no	—
242	C₂²×C₈	Dic₃₈	1	2	yes	—
243	C₂²×C₈	C₄×D₁₉	1	2	yes	—
244	C₂²×C₈	C₄×D₁₉	1	2	yes	—
245	C₂²×C₈	D₇₆	1	2	yes	—
246	C₂²×C₈	C₂×Dic₁₉	1	2	yes	—
247	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
248	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	—	2	2	no	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	—	19	4	no	—
255	C₂×C₄⋊C₄	—	38	2	no	—
256	C₂×C₄⋊C₄	—	38	2	no	—
257	C₂×C₄⋊C₄	—	38	2	no	—
258	C₂×C₄⋊C₄	—	38	2	no	—
259	C₂×C₄⋊C₄	—	38	2	no	—
260	C₂×C₄⋊C₄	C₂×Dic₁₉	1	4	yes	—
261	C₂×C₄²	—	19	2	no	—
262	C₂×C₄²	—	19	2	no	—
263	C₂×C₄²	—	38	1	no	—
264	C₂×C₄²	—	38	1	no	—
265	C₂×C₄²	—	38	1	no	—
266	C₂×C₄²	—	38	1	no	—
267	#106	—	2	8	no	—
268	#106	—	38	8	no	—
269	C₄×C₈	—	38	8	no	—
270	#95	—	76	8	no	—
271	C₁₉	#10861	1	1	yes	characteristic, complemented, Sylow
272	C₂⁴	D₄×D₁₉	1	1	yes	characteristic
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	4	2	no	—
275	C₂²×C₄	—	4	2	no	—
276	C₂²×C₄	—	4	4	no	—
277	C₂²×C₄	—	4	4	no	—
278	C₂²×C₄	—	19	4	no	—
279	C₂²×C₄	—	19	8	no	—
280	C₂²×C₄	—	38	2	no	—
281	C₂²×C₄	—	38	2	no	—
282	C₂²×C₄	—	38	4	no	—
283	C₂²×C₄	—	38	4	no	—
284	C₂²×C₄	—	76	2	no	—
285	C₂²×C₄	—	76	2	no	—
286	C₂²×C₄	—	76	4	no	—
287	C₂²×C₄	—	76	4	no	—
288	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
289	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
290	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
291	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
292	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
293	C₂²×C₄	#64543	1	1	yes	characteristic
294	C₂²×C₄	#64543	1	1	yes	characteristic
295	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
296	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
297	C₂²×C₄	#64545	1	1	yes	characteristic
298	C₂²×C₄	#64545	1	1	yes	characteristic
299	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
300	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
301	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
302	C₂×C₈	—	19	4	no	—
303	C₂×C₈	—	38	2	no	—
304	C₂×C₈	—	38	2	no	—
305	C₂×C₈	—	38	2	no	—
306	C₂×C₈	—	38	2	no	—
307	C₂×C₈	—	38	2	no	—
308	C₂×C₈	—	38	2	no	—
309	C₂×C₈	C₄×Dic₁₉	1	4	yes	—
310	C₂×C₈	Dic₁₉⋊C₄	1	4	yes	—
311	C₂×C₈	Dic₁₉⋊C₄	1	4	yes	—
312	C₂×C₈	C₄⋊Dic₁₉	1	4	yes	—
313	C₂×C₈	(C₂×D₁₉)⋊C₄	1	4	yes	—
314	C₂×C₈	(C₂×D₁₉)⋊C₄	1	4	yes	—
315	C₂×C₈	C₂²⋊Dic₁₉	1	4	yes	—
316	C₄⋊C₄	—	2	4	no	—
317	C₄⋊C₄	—	2	4	no	—
318	C₄⋊C₄	—	4	2	no	—
319	C₄⋊C₄	—	4	2	no	—
320	C₄⋊C₄	—	38	4	no	—
321	C₄⋊C₄	—	38	4	no	—
322	C₄⋊C₄	—	76	2	no	—
323	C₄⋊C₄	—	76	2	no	—
324	C₄²	—	38	2	no	—
325	C₄²	—	38	2	no	—
326	C₄²	—	38	2	no	—
327	C₄²	—	38	2	no	—
328	C₂³	#10597334	1	1	yes	characteristic
329	C₂³	C₄⋊C₄×D₁₉	1	1	yes	characteristic
330	C₂³	#10597339	1	1	yes	characteristic
331	C₂³	#10597341	1	1	yes	characteristic
332	C₂³	SD₁₆×D₁₉	1	4	yes	—
333	C₂³	#10597362	1	4	yes	—
334	C₂³	D₄×Dic₁₉	1	1	yes	characteristic
335	C₂³	#10597384	1	1	yes	characteristic
336	C₂³	#10597386	1	1	yes	characteristic
337	C₂×C₄	—	4	8	no	—
338	C₂×C₄	—	4	4	no	—
339	C₂×C₄	—	8	2	no	—
340	C₂×C₄	—	8	2	no	—
341	C₂×C₄	—	8	4	no	—
342	C₂×C₄	—	19	8	no	—
343	C₂×C₄	—	38	4	no	—
344	C₂×C₄	—	38	4	no	—
345	C₂×C₄	—	38	8	no	—
346	C₂×C₄	—	38	8	no	—
347	C₂×C₄	—	76	8	no	—
348	C₂×C₄	—	76	4	no	—
349	C₂×C₄	—	152	2	no	—
350	C₂×C₄	—	152	2	no	—
351	C₂×C₄	—	152	4	no	—
352	C₂×C₄	#10597333	1	1	yes	characteristic
353	C₂×C₄	#10597333	1	1	yes	characteristic
354	C₂×C₄	#10597334	1	1	yes	characteristic
355	C₂×C₄	#10597336	1	1	yes	characteristic
356	C₂×C₄	#10597336	1	1	yes	characteristic
357	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
358	C₂×C₄	#10597338	1	1	yes	characteristic
359	C₂×C₄	#10597338	1	1	yes	characteristic
360	C₂×C₄	#10597339	1	1	yes	characteristic
361	C₂×C₄	#10597341	1	1	yes	characteristic
362	C₂×C₄	#10597343	1	1	yes	characteristic
363	C₂×C₄	#10597343	1	1	yes	characteristic
364	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
365	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
366	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
367	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
368	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
369	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
370	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
371	C₂×C₄	#10597382	1	1	yes	characteristic
372	C₂×C₄	#10597384	1	1	yes	characteristic
373	C₂×C₄	#10597390	1	1	yes	characteristic
374	C₂×C₄	Q₈×Dic₁₉	1	1	yes	characteristic
375	C₂×C₄	Q₈×Dic₁₉	1	1	yes	characteristic
376	C₂×C₄	#10597392	1	1	yes	characteristic
377	C₂×C₄	#10597392	1	1	yes	characteristic
378	C₂×C₄	#10597393	1	1	yes	characteristic
379	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
380	C₈	—	38	4	no	—
381	C₈	C₁₉⋊#95	1	8	yes	complemented
382	C₂²	C₄⋊C₄×Dic₁₉	1	1	yes	characteristic
383	C₂²	#11926401	1	1	yes	characteristic
384	C₂²	#11926413	1	1	yes	characteristic
385	C₂²	#11926440	1	1	yes	characteristic
386	C₂²	#11926443	1	1	yes	characteristic
387	C₂²	#11926445	1	1	yes	characteristic
388	C₂²	#11926447	1	1	yes	characteristic
389	C₂²	#106×D₁₉	1	2	yes	—
390	C₂²	#11926579	1	2	yes	—
391	C₂²	#11926631	1	4	yes	—
392	C₂²	SD₁₆×Dic₁₉	1	4	yes	—
393	C₂²	#11926770	1	4	yes	—
394	C₂²	#11926774	1	4	yes	—
395	C₂²	#11926915	1	2	yes	—
396	C₂²	#11926925	1	2	yes	—
397	C₂²	#11926941	1	2	yes	—
398	C₂²	#11926944	1	2	yes	—
399	C₄	—	8	4	no	—
400	C₄	—	38	8	no	—
401	C₄	—	152	4	no	—
402	C₄	C₂×C₁₉⋊#95	1	1	yes	characteristic
403	C₄	C₄⋊C₄×Dic₁₉	1	1	yes	characteristic
404	C₄	#11926401	1	1	yes	characteristic
405	C₄	#11926409	1	1	yes	characteristic
406	C₄	#11926440	1	1	yes	characteristic
407	C₄	#11926443	1	1	yes	characteristic
408	C₄	#11926449	1	1	yes	characteristic
409	C₄	#11926451	1	1	yes	characteristic
410	C₂	#14561864	1	1	yes	characteristic
411	C₂	#106×Dic₁₉	1	2	yes	—
412	C₂	#14563657	1	2	yes	—
413	C₂	#14563790	1	1	yes	characteristic
414	C₂	#14563796	1	1	yes	characteristic
415	C₂	#14564361	1	2	yes	—
416	C₂	#14564364	1	2	yes	—
417	C₂	#14564487	1	2	yes	—
418	C₂	#14564491	1	2	yes	—

	subgroup	G/H
center	C₂⁴	D₄×D₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂²×C₁₉×#106	C₂
socle, prime radical	C₂⁴×C₁₉	C₂×D₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂²×#106	D₁₉
hypocenter	C₁₉	#10861
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂²×#106

Complements

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

N	H ≅ G/N	type
11. C₂×#10597274	C₄	semidirect
14. C₂×C₈×Dic₁₉	C₄	semidirect
21. C₂×C₁₉×#106	C₄	semidirect
170. C₂×Dic₁₉	#106	semidirect
171. C₈×C₁₉	#95	semidirect
216. C₂×#106	Dic₁₉	semidirect
271. C₁₉	#10861	semidirect
381. C₈	C₁₉⋊#95	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#10597274	2
C₂²×C₈×Dic₁₉	2
C₂×#11926306	2
#14561864	2
C₂²×C₁₉×#106	2
#10861	19