Subgroups — C₄×#11926306 #18087719

Order 4864.

1182 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₄⋊Dic₁₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926306	C₂	1	4	yes	maximal
4	C₂×C₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
5	C₂³×C₁₉⋊C₈	C₂²	1	2	yes	—
6	C₂²×C₄⋊Dic₁₉	C₂²	1	2	yes	—
7	C₂²×C₄×Dic₁₉	—	2	1	no	—
8	C₂×C₄×C₁₉⋊C₈	—	2	2	no	—
9	C₂×C₄×C₁₉⋊C₈	—	2	2	no	—
10	C₂×C₄×C₁₉⋊C₈	C₄	1	4	yes	complemented
11	C₄×C₄⋊Dic₁₉	—	2	2	no	—
12	C₄×C₄⋊Dic₁₉	C₄	1	4	yes	complemented
13	C₂×C₁₉⋊#95	—	2	1	no	—
14	#11926306	C₄	1	16	yes	direct product factor
15	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
16	C₂²×C₄²×C₁₉	—	2	1	no	—
17	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
18	C₄×C₄⋊C₄×C₁₉	—	2	2	no	—
19	C₄×C₄⋊C₄×C₁₉	C₄	1	4	yes	complemented
20	C₂×C₁₉×#95	—	2	1	no	—
21	C₂³×C₄×C₁₉	—	2	2	no	—
22	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
23	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
24	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
25	C₂³×Dic₁₉	—	2	2	no	—
26	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
27	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
28	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	8	yes	—
29	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
30	C₂×C₄²×C₁₉	—	2	4	no	—
31	C₂×C₄²×C₁₉	—	4	2	no	—
32	C₂×C₄²×C₁₉	—	4	2	no	—
33	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
34	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
35	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
36	C₂×C₄²×C₁₉	D₄	1	2	yes	—
37	C₂×C₄²×C₁₉	D₄	1	2	yes	—
38	C₂×C₄²×C₁₉	Q₈	1	2	yes	—
39	C₂×C₄⋊Dic₁₉	—	2	2	no	—
40	C₂×C₄⋊Dic₁₉	—	2	4	no	—
41	C₂×C₄⋊Dic₁₉	C₂×C₄	1	8	yes	—
42	C₂×C₄⋊Dic₁₉	C₂×C₄	1	4	yes	—
43	C₂×C₄×Dic₁₉	—	2	4	no	—
44	C₂×C₄×Dic₁₉	—	4	2	no	—
45	C₂×C₄×Dic₁₉	—	4	2	no	—
46	C₂²×C₁₉⋊C₈	—	2	2	no	—
47	C₂²×C₁₉⋊C₈	—	2	2	no	—
48	C₂²×C₁₉⋊C₈	—	2	4	no	—
49	C₂²×C₁₉⋊C₈	C₂×C₄	1	8	yes	—
50	C₂²×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
51	C₁₉×#95	—	2	4	no	—
52	C₁₉⋊#95	—	2	4	no	—
53	C₄×C₁₉⋊C₈	—	2	8	no	—
54	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
55	C₂²×C₄×C₁₉	—	2	4	no	—
56	C₂²×C₄×C₁₉	—	2	4	no	—
57	C₂²×C₄×C₁₉	—	2	8	no	—
58	C₂²×C₄×C₁₉	—	4	2	no	—
59	C₂²×C₄×C₁₉	—	4	2	no	—
60	C₂²×C₄×C₁₉	—	4	4	no	—
61	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
62	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
63	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
64	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
65	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
66	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
67	C₂²×C₄×C₁₉	D₈	1	2	yes	—
68	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	—
69	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	—
70	C₂²×C₄×C₁₉	Q₁₆	1	2	yes	—
71	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
74	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
78	C₂²×C₄×C₁₉	#41	1	4	yes	—
79	C₂²×Dic₁₉	—	2	4	no	—
80	C₂²×Dic₁₉	—	2	8	no	—
81	C₂²×Dic₁₉	—	4	2	no	—
82	C₂²×Dic₁₉	—	4	2	no	—
83	C₂²×Dic₁₉	—	4	4	no	—
84	C₄⋊C₄×C₁₉	—	2	4	no	—
85	C₄⋊C₄×C₁₉	—	2	8	no	—
86	C₄⋊C₄×C₁₉	C₄²	1	8	yes	complemented
87	C₄²×C₁₉	—	4	8	no	—
88	C₄²×C₁₉	C₄²	1	4	yes	—
89	C₄²×C₁₉	C₂²⋊C₄	1	4	yes	—
90	C₄²×C₁₉	C₄⋊C₄	1	4	yes	—
91	C₄²×C₁₉	C₄⋊C₄	1	4	yes	—
92	C₄⋊Dic₁₉	—	2	4	no	—
93	C₄⋊Dic₁₉	—	2	8	no	—
94	C₄⋊Dic₁₉	C₄²	1	8	yes	complemented
95	C₄×Dic₁₉	—	4	8	no	—
96	C₂×C₁₉⋊C₈	—	2	4	no	—
97	C₂×C₁₉⋊C₈	—	2	4	no	—
98	C₂×C₁₉⋊C₈	—	2	8	no	—
99	C₂×C₁₉⋊C₈	—	2	8	no	—
100	C₂×C₁₉⋊C₈	C₄²	1	8	yes	complemented
101	C₄×#340	—	19	1	no	maximal, Sylow
102	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
103	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
104	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
105	C₂³×C₁₉	C₄×D₄	1	4	yes	—
106	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
107	C₂³×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
108	C₂³×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
109	C₂³×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
110	C₂³×C₁₉	#135	1	4	yes	—
111	C₂×C₄×C₁₉	—	2	4	no	—
112	C₂×C₄×C₁₉	—	2	4	no	—
113	C₂×C₄×C₁₉	—	2	4	no	—
114	C₂×C₄×C₁₉	—	2	8	no	—
115	C₂×C₄×C₁₉	—	4	4	no	—
116	C₂×C₄×C₁₉	—	4	4	no	—
117	C₂×C₄×C₁₉	—	4	8	no	—
118	C₂×C₄×C₁₉	—	4	8	no	—
119	C₂×C₄×C₁₉	#95	1	4	yes	—
120	C₂×C₄×C₁₉	#95	1	4	yes	—
121	C₂×C₄×C₁₉	#102	1	4	yes	—
122	C₂×C₄×C₁₉	#102	1	4	yes	—
123	C₂×C₄×C₁₉	#103	1	4	yes	—
124	C₂×C₄×C₁₉	#103	1	4	yes	—
125	C₂×C₄×C₁₉	#106	1	4	yes	—
126	C₂×C₄×C₁₉	#107	1	4	yes	—
127	C₂×C₄×C₁₉	C₂×C₄²	1	2	yes	—
128	C₂×C₄×C₁₉	C₂×C₄²	1	2	yes	—
129	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
130	C₂×C₄×C₁₉	C₂×C₄²	1	2	yes	—
131	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
132	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
133	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
134	C₂×C₄×C₁₉	#117	1	2	yes	—
135	C₂×C₄×C₁₉	#117	1	2	yes	—
136	C₂×C₄×C₁₉	#117	1	2	yes	—
137	C₂×C₄×C₁₉	C₄×D₄	1	4	yes	—
138	C₂×C₄×C₁₉	C₄×D₄	1	4	yes	—
139	C₂×C₄×C₁₉	C₄×Q₈	1	4	yes	—
140	C₂×Dic₁₉	—	2	8	no	—
141	C₂×Dic₁₉	—	4	4	no	—
142	C₂×Dic₁₉	—	4	4	no	—
143	C₂×Dic₁₉	—	4	8	no	—
144	C₂×Dic₁₉	—	4	8	no	—
145	C₁₉⋊C₈	—	2	8	no	—
146	C₂²×C₄×C₈	—	19	1	no	—
147	C₂×C₄×C₄⋊C₄	—	19	1	no	—
148	C₂×C₄×C₄⋊C₄	D₁₉	1	1	yes	characteristic
149	C₂×#340	—	19	4	no	—
150	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
151	C₂²×C₁₉	C₄×C₂²⋊C₄	1	2	yes	—
152	C₂²×C₁₉	C₄×C₂²⋊C₄	1	2	yes	—
153	C₂²×C₁₉	C₄×C₄⋊C₄	1	2	yes	—
154	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
155	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
156	C₂²×C₁₉	C₂×#103	1	1	yes	characteristic
157	C₂²×C₁₉	C₂×#103	1	1	yes	characteristic
158	C₂²×C₁₉	#416	1	2	yes	—
159	C₂²×C₁₉	#416	1	2	yes	—
160	C₂²×C₁₉	C₂×#106	1	1	yes	characteristic
161	C₂²×C₁₉	C₂×#107	1	1	yes	characteristic
162	C₂²×C₁₉	#427	1	2	yes	—
163	C₂²×C₁₉	C₄×D₈	1	4	yes	—
164	C₂²×C₁₉	C₄×SD₁₆	1	4	yes	—
165	C₂²×C₁₉	C₄×SD₁₆	1	4	yes	—
166	C₂²×C₁₉	C₄×Q₁₆	1	4	yes	—
167	C₄×C₁₉	—	2	4	no	—
168	C₄×C₁₉	—	4	8	no	—
169	C₄×C₁₉	#340	1	8	yes	complemented
170	C₄×C₁₉	C₄³	1	1	yes	characteristic
171	C₄×C₁₉	#376	1	1	yes	characteristic
172	C₄×C₁₉	C₄×C₂²⋊C₄	1	2	yes	—
173	C₄×C₁₉	C₄×C₄⋊C₄	1	2	yes	—
174	C₄×C₁₉	C₄×C₄⋊C₄	1	2	yes	—
175	Dic₁₉	—	4	8	no	—
176	C₂³×C₈	—	19	2	no	—
177	C₂²×C₄⋊C₄	—	19	2	no	—
178	C₂²×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
179	C₂²×C₄²	—	2	1	no	—
180	C₂²×C₄²	—	38	1	no	—
181	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
182	C₂×C₄×C₈	—	19	4	no	—
183	C₂×C₄×C₈	—	38	2	no	—
184	C₂×C₄×C₈	—	38	2	no	—
185	C₄×C₄⋊C₄	—	2	2	no	—
186	C₄×C₄⋊C₄	—	19	4	no	—
187	C₄×C₄⋊C₄	—	38	2	no	—
188	C₄×C₄⋊C₄	Dic₁₉	1	4	yes	complemented
189	C₂×#95	—	2	1	no	—
190	C₂×#95	—	38	1	no	—
191	#340	—	19	16	no	—
192	C₂×C₁₉	C₄×#95	1	1	yes	characteristic
193	C₂×C₁₉	C₂×#340	1	1	yes	characteristic
194	C₂×C₁₉	#1735	1	1	yes	characteristic
195	C₂×C₁₉	C₄×#102	1	2	yes	—
196	C₂×C₁₉	C₄×#102	1	2	yes	—
197	C₂×C₁₉	C₄×#103	1	2	yes	—
198	C₂×C₁₉	C₄×#103	1	2	yes	—
199	C₂×C₁₉	C₄×#106	1	2	yes	—
200	C₂×C₁₉	C₄×#107	1	2	yes	—
201	C₂³×C₄	—	2	2	no	—
202	C₂³×C₄	—	38	2	no	—
203	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
204	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
205	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
206	C₂²×C₈	—	19	8	no	—
207	C₂²×C₈	—	19	4	no	—
208	C₂²×C₈	—	38	2	no	—
209	C₂²×C₈	—	38	4	no	—
210	C₂²×C₈	—	38	2	no	—
211	C₂×C₄⋊C₄	—	2	4	no	—
212	C₂×C₄⋊C₄	—	2	2	no	—
213	C₂×C₄⋊C₄	—	19	8	no	—
214	C₂×C₄⋊C₄	—	19	4	no	—
215	C₂×C₄⋊C₄	—	38	2	no	—
216	C₂×C₄⋊C₄	—	38	4	no	—
217	C₂×C₄⋊C₄	C₄×D₁₉	1	8	yes	—
218	C₂×C₄⋊C₄	C₂×Dic₁₉	1	4	yes	—
219	C₂×C₄²	—	2	4	no	—
220	C₂×C₄²	—	4	2	no	—
221	C₂×C₄²	—	4	2	no	—
222	C₂×C₄²	—	38	4	no	—
223	C₂×C₄²	—	76	2	no	—
224	C₂×C₄²	—	76	2	no	—
225	C₂×C₄²	Dic₃₈	1	2	yes	—
226	C₂×C₄²	C₄×D₁₉	1	2	yes	—
227	C₂×C₄²	C₄×D₁₉	1	2	yes	—
228	C₂×C₄²	D₇₆	1	2	yes	—
229	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
230	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
231	C₄×C₈	—	38	8	no	—
232	#95	—	2	4	no	—
233	#95	—	38	4	no	—
234	C₁₉	C₄×#340	1	1	yes	characteristic, complemented, Sylow
235	C₂⁴	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
236	C₂²×C₄	—	2	4	no	—
237	C₂²×C₄	—	2	4	no	—
238	C₂²×C₄	—	2	8	no	—
239	C₂²×C₄	—	4	2	no	—
240	C₂²×C₄	—	4	2	no	—
241	C₂²×C₄	—	4	4	no	—
242	C₂²×C₄	—	38	4	no	—
243	C₂²×C₄	—	38	8	no	—
244	C₂²×C₄	—	76	2	no	—
245	C₂²×C₄	—	76	2	no	—
246	C₂²×C₄	—	76	4	no	—
247	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
248	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
249	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
250	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
251	C₂²×C₄	#64525	1	2	yes	—
252	C₂²×C₄	#64526	1	2	yes	—
253	C₂²×C₄	#64527	1	2	yes	—
254	C₂²×C₄	#64528	1	2	yes	—
255	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
256	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
257	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
258	C₂²×C₄	C₂×C₄×D₁₉	1	4	yes	—
259	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
260	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
261	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
262	C₂²×C₄	#64541	1	4	yes	—
263	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
264	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
265	C₂×C₈	—	19	8	no	—
266	C₂×C₈	—	38	4	no	—
267	C₂×C₈	—	38	8	no	—
268	C₂×C₈	—	38	4	no	—
269	C₂×C₈	—	38	8	no	—
270	C₄⋊C₄	—	2	4	no	—
271	C₄⋊C₄	—	2	8	no	—
272	C₄⋊C₄	—	19	8	no	—
273	C₄⋊C₄	—	38	4	no	—
274	C₄⋊C₄	—	38	8	no	—
275	C₄⋊C₄	C₄×Dic₁₉	1	8	yes	complemented
276	C₄²	—	4	8	no	—
277	C₄²	—	76	8	no	—
278	C₄²	C₄×Dic₁₉	1	4	yes	—
279	C₄²	Dic₁₉⋊C₄	1	4	yes	—
280	C₄²	C₄⋊Dic₁₉	1	4	yes	—
281	C₄²	(C₂×D₁₉)⋊C₄	1	4	yes	—
282	C₂³	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
283	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
284	C₂³	C₄×C₂²⋊D₁₉	1	4	yes	—
285	C₂³	C₂×#64525	1	1	yes	characteristic
286	C₂³	C₂×#64526	1	1	yes	characteristic
287	C₂³	C₂×#64527	1	1	yes	characteristic
288	C₂³	C₂×#64528	1	1	yes	characteristic
289	C₂³	#10597396	1	4	yes	—
290	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
291	C₂×C₄	—	2	4	no	—
292	C₂×C₄	—	2	4	no	—
293	C₂×C₄	—	2	4	no	—
294	C₂×C₄	—	2	8	no	—
295	C₂×C₄	—	4	4	no	—
296	C₂×C₄	—	4	4	no	—
297	C₂×C₄	—	4	8	no	—
298	C₂×C₄	—	4	8	no	—
299	C₂×C₄	—	38	8	no	—
300	C₂×C₄	—	76	4	no	—
301	C₂×C₄	—	76	4	no	—
302	C₂×C₄	—	76	8	no	—
303	C₂×C₄	—	76	8	no	—
304	C₂×C₄	#10597264	1	4	yes	—
305	C₂×C₄	#10597265	1	4	yes	—
306	C₂×C₄	#10597266	1	4	yes	—
307	C₂×C₄	#10597267	1	4	yes	—
308	C₂×C₄	C₁₉⋊#95	1	4	yes	—
309	C₂×C₄	C₁₉⋊#95	1	4	yes	—
310	C₂×C₄	#10597289	1	4	yes	—
311	C₂×C₄	#10597292	1	4	yes	—
312	C₂×C₄	C₄×Dic₃₈	1	4	yes	—
313	C₂×C₄	C₄²×D₁₉	1	2	yes	—
314	C₂×C₄	C₄²×D₁₉	1	2	yes	—
315	C₂×C₄	#10597318	1	2	yes	—
316	C₂×C₄	#10597318	1	2	yes	—
317	C₂×C₄	C₄×D₇₆	1	4	yes	—
318	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
319	C₂×C₄	C₂×C₄×Dic₁₉	1	2	yes	—
320	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
321	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
322	C₂×C₄	#10597372	1	2	yes	—
323	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
324	C₂×C₄	C₄×C₂²⋊D₁₉	1	4	yes	—
325	C₈	—	38	8	no	—
326	C₂²	C₂×C₁₉⋊#95	1	1	yes	characteristic
327	C₂²	C₄×C₂²⋊Dic₁₉	1	2	yes	—
328	C₂²	C₄×(C₂×D₁₉)⋊C₄	1	2	yes	—
329	C₂²	C₄×Dic₁₉⋊C₄	1	2	yes	—
330	C₂²	C₂×#10597266	1	1	yes	characteristic
331	C₂²	C₂×#10597289	1	1	yes	characteristic
332	C₂²	C₂×#10597267	1	1	yes	characteristic
333	C₂²	C₂×#10597292	1	1	yes	characteristic
334	C₂²	#11926538	1	2	yes	—
335	C₂²	#11926540	1	2	yes	—
336	C₂²	C₂×#10597265	1	1	yes	characteristic
337	C₂²	C₂×#10597264	1	1	yes	characteristic
338	C₂²	#11926580	1	2	yes	—
339	C₂²	C₄×#64525	1	4	yes	—
340	C₂²	C₄×#64526	1	4	yes	—
341	C₂²	C₄×#64527	1	4	yes	—
342	C₂²	C₄×#64528	1	4	yes	—
343	C₄	—	2	4	no	—
344	C₄	—	4	8	no	—
345	C₄	—	76	8	no	—
346	C₄	#11926306	1	8	yes	direct product factor
347	C₄	C₄²×Dic₁₉	1	1	yes	characteristic
348	C₄	#11926390	1	1	yes	characteristic
349	C₄	C₄×(C₂×D₁₉)⋊C₄	1	2	yes	—
350	C₄	C₄×C₄⋊Dic₁₉	1	2	yes	—
351	C₄	C₄×Dic₁₉⋊C₄	1	2	yes	—
352	C₂	C₄×C₁₉⋊#95	1	1	yes	characteristic
353	C₂	C₂×#11926306	1	1	yes	characteristic
354	C₂	#14563351	1	1	yes	characteristic
355	C₂	C₄×#10597289	1	2	yes	—
356	C₂	C₄×#10597266	1	2	yes	—
357	C₂	C₄×#10597292	1	2	yes	—
358	C₂	C₄×#10597267	1	2	yes	—
359	C₂	C₄×#10597265	1	2	yes	—
360	C₂	C₄×#10597264	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄	C₂²⋊D₁₉
commutator	C₄×C₁₉	C₄³
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₄×C₄⋊C₄×C₁₉	C₂
socle, prime radical	C₂⁴×C₁₉	C₂×D₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×C₄×C₄⋊C₄	D₁₉
hypocenter	C₁₉	C₄×#340
LCS	G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³×C₄ ◁ C₂²×C₄² ◁ C₂×C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
10. C₂×C₄×C₁₉⋊C₈	C₄	semidirect
12. C₄×C₄⋊Dic₁₉	C₄	semidirect
14. #11926306	C₄	direct (N × H)
19. C₄×C₄⋊C₄×C₁₉	C₄	semidirect
86. C₄⋊C₄×C₁₉	C₄²	semidirect
94. C₄⋊Dic₁₉	C₄²	semidirect
100. C₂×C₁₉⋊C₈	C₄²	semidirect
169. C₄×C₁₉	#340	semidirect
188. C₄×C₄⋊C₄	Dic₁₉	semidirect
234. C₁₉	C₄×#340	semidirect
275. C₄⋊C₄	C₄×Dic₁₉	semidirect
346. C₄	#11926306	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄×C₁₉⋊C₈	2
C₂×C₄×C₄⋊Dic₁₉	2
C₂×#11926306	2
C₂×C₄×C₄⋊C₄×C₁₉	2
C₄×#340	19

Subgroups — C4×#11926306 #18087719

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11926306 #18087719