Subgroups — C₂×#14561536 #18072826

Order 4864.

810 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926597	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₄⋊Dic₁₉	C₂	1	1	yes	maximal, characteristic
3	#14561536	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₁₉×#423	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄⋊Dic₁₉	—	2	1	no	—
6	C₂²×C₄×Dic₁₉	—	2	1	no	—
7	#11926597	—	2	1	no	—
8	#11926597	—	2	1	no	—
9	#11926597	C₄	1	2	yes	complemented
10	#11926597	C₂²	1	2	yes	—
11	C₂×C₄⋊(C₁₉⋊C₈)	C₄	1	2	yes	complemented
12	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
13	C₂×C₄×C₁₉⋊C₈	—	2	1	no	—
14	C₄×C₄⋊Dic₁₉	—	2	1	no	—
15	C₄×C₄⋊Dic₁₉	—	2	1	no	—
16	C₄×C₄⋊Dic₁₉	C₄	1	2	yes	—
17	C₄×C₄⋊Dic₁₉	C₂²	1	2	yes	—
18	C₂×C₁₉⋊#95	C₄	1	2	yes	—
19	C₂²×M₁₆×C₁₉	—	2	1	no	—
20	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
21	C₁₉×#423	—	2	1	no	—
22	C₁₉×#423	—	2	1	no	—
23	C₁₉×#423	C₄	1	2	yes	complemented
24	C₁₉×#423	C₂²	1	2	yes	—
25	C₂×C₁₉×C₄⋊C₈	—	2	1	no	—
26	C₂×C₁₉×C₄⋊C₈	C₄	1	2	yes	complemented
27	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
30	C₂³×Dic₁₉	—	2	2	no	—
31	C₂×M₁₆×C₁₉	—	2	2	no	—
32	C₂×M₁₆×C₁₉	—	2	2	no	—
33	C₂×M₁₆×C₁₉	—	4	2	no	—
34	C₂×M₁₆×C₁₉	—	4	2	no	—
35	C₂²×C₈×C₁₉	—	2	2	no	—
36	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
43	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
44	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
45	C₂×C₄²×C₁₉	Q₈	1	1	yes	characteristic
46	C₂×C₄²×C₁₉	Q₈	1	1	yes	characteristic
47	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
48	C₂×C₄⋊Dic₁₉	—	2	8	no	—
49	C₂×C₄⋊Dic₁₉	—	2	2	no	—
50	C₂×C₄⋊Dic₁₉	—	2	2	no	—
51	C₂×C₄×Dic₁₉	—	2	2	no	—
52	C₂×C₄×Dic₁₉	—	2	2	no	—
53	C₂×C₄×Dic₁₉	—	4	2	no	—
54	C₂×C₄×Dic₁₉	—	4	2	no	—
55	C₂²×C₁₉⋊C₈	—	2	2	no	—
56	C₁₉×C₄⋊C₈	—	2	2	no	—
57	C₁₉×C₄⋊C₈	—	2	2	no	—
58	C₁₉×C₄⋊C₈	—	2	2	no	—
59	C₁₉×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
60	C₁₉⋊#95	—	2	2	no	—
61	C₁₉⋊#95	C₂×C₄	1	4	yes	—
62	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
63	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
64	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
65	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	4	yes	complemented
66	C₄×C₁₉⋊C₈	—	2	2	no	—
67	C₄×C₁₉⋊C₈	—	2	2	no	—
68	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₉	—	2	4	no	—
70	C₂²×C₄×C₁₉	—	4	2	no	—
71	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
72	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
73	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₉	D₈	1	2	yes	—
87	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	—
88	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	—
89	C₂²×C₄×C₁₉	Q₁₆	1	2	yes	—
90	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
93	C₂²×Dic₁₉	—	2	8	no	—
94	C₂²×Dic₁₉	—	2	4	no	—
95	C₂²×Dic₁₉	—	4	4	no	—
96	C₂²×Dic₁₉	—	4	4	no	—
97	M₁₆×C₁₉	—	4	4	no	—
98	M₁₆×C₁₉	—	4	2	no	—
99	M₁₆×C₁₉	—	4	2	no	—
100	C₂×C₈×C₁₉	—	2	4	no	—
101	C₂×C₈×C₁₉	—	4	4	no	—
102	C₄²×C₁₉	C₄²	1	1	yes	characteristic
103	C₄²×C₁₉	C₄²	1	1	yes	characteristic
104	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
105	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
106	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
107	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
108	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
109	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
110	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
111	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
112	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
113	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
114	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
115	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
116	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
117	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
118	C₄⋊Dic₁₉	—	2	8	no	—
119	C₄⋊Dic₁₉	—	2	8	no	—
120	C₄×Dic₁₉	—	4	4	no	—
121	C₄×Dic₁₉	—	4	2	no	—
122	C₄×Dic₁₉	—	4	2	no	—
123	C₂×C₁₉⋊C₈	—	2	4	no	—
124	C₂×C₁₉⋊C₈	—	4	4	no	—
125	C₂×#1303	—	19	1	no	maximal, Sylow
126	C₂³×C₁₉	—	2	2	no	—
127	C₂³×C₁₉	—	2	2	no	—
128	C₂³×C₁₉	#95	1	1	yes	characteristic
129	C₂³×C₁₉	#95	1	1	yes	characteristic
130	C₂³×C₁₉	#102	1	2	yes	—
131	C₂³×C₁₉	#103	1	2	yes	—
132	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
133	C₂×C₄×C₁₉	—	2	2	no	—
134	C₂×C₄×C₁₉	—	2	2	no	—
135	C₂×C₄×C₁₉	—	2	2	no	—
136	C₂×C₄×C₁₉	—	2	2	no	—
137	C₂×C₄×C₁₉	—	2	2	no	—
138	C₂×C₄×C₁₉	—	2	2	no	—
139	C₂×C₄×C₁₉	—	2	2	no	—
140	C₂×C₄×C₁₉	—	4	1	no	—
141	C₂×C₄×C₁₉	—	4	1	no	—
142	C₂×C₄×C₁₉	—	4	1	no	—
143	C₂×C₄×C₁₉	—	4	1	no	—
144	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
145	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
146	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
147	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
148	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
149	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
150	C₂×C₄×C₁₉	#102	1	2	yes	—
151	C₂×C₄×C₁₉	#102	1	2	yes	—
152	C₂×C₄×C₁₉	#102	1	2	yes	—
153	C₂×C₄×C₁₉	#103	1	2	yes	—
154	C₂×C₄×C₁₉	#103	1	2	yes	—
155	C₂×C₄×C₁₉	#103	1	2	yes	—
156	C₂×C₄×C₁₉	#104	1	4	yes	—
157	C₂×C₄×C₁₉	#106	1	2	yes	—
158	C₂×C₄×C₁₉	#106	1	2	yes	—
159	C₂×C₄×C₁₉	#107	1	2	yes	—
160	C₂×C₄×C₁₉	#107	1	2	yes	—
161	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
162	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
168	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
169	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
170	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
171	C₂×Dic₁₉	—	2	8	no	—
172	C₂×Dic₁₉	—	4	16	no	—
173	C₂×Dic₁₉	—	4	4	no	—
174	C₂×Dic₁₉	—	4	4	no	—
175	C₈×C₁₉	—	4	4	no	—
176	C₁₉⋊C₈	—	4	4	no	—
177	C₂×#431	—	19	1	no	—
178	C₂×#423	D₁₉	1	1	yes	characteristic
179	C₂×C₄×C₄⋊C₄	—	19	1	no	—
180	#1303	—	19	4	no	—
181	C₂²×C₁₉	—	2	4	no	—
182	C₂²×C₁₉	—	2	4	no	—
183	C₂²×C₁₉	—	2	1	no	—
184	C₂²×C₁₉	—	2	1	no	—
185	C₂²×C₁₉	—	2	1	no	—
186	C₂²×C₁₉	—	2	1	no	—
187	C₂²×C₁₉	#339	1	2	yes	—
188	C₂²×C₁₉	#340	1	2	yes	—
189	C₂²×C₁₉	#340	1	2	yes	—
190	C₂²×C₁₉	#344	1	2	yes	—
191	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
192	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
193	C₂²×C₁₉	C₂×#103	1	1	yes	characteristic
194	C₄×C₁₉	—	2	1	no	—
195	C₄×C₁₉	—	2	1	no	—
196	C₄×C₁₉	—	2	1	no	—
197	C₄×C₁₉	—	2	1	no	—
198	C₄×C₁₉	—	2	1	no	—
199	C₄×C₁₉	—	2	1	no	—
200	C₄×C₁₉	#339	1	2	yes	—
201	C₄×C₁₉	#340	1	2	yes	—
202	C₄×C₁₉	#340	1	2	yes	—
203	C₄×C₁₉	C₂×#102	1	1	yes	characteristic
204	C₄×C₁₉	C₂×#103	1	1	yes	characteristic
205	C₄×C₁₉	C₂×#104	1	2	yes	—
206	C₄×C₁₉	C₂×#106	1	1	yes	characteristic
207	C₄×C₁₉	C₂×#107	1	1	yes	characteristic
208	Dic₁₉	—	4	8	no	—
209	C₂²×M₁₆	—	2	1	no	—
210	C₂²×C₄⋊C₄	—	38	1	no	—
211	C₂²×C₄²	—	38	1	no	—
212	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
213	#431	—	19	2	no	—
214	#431	—	19	2	no	—
215	#431	—	38	1	no	—
216	#431	—	38	1	no	—
217	#423	—	2	1	no	—
218	#423	—	2	1	no	—
219	#423	Dic₁₉	1	2	yes	complemented
220	#423	C₂×D₁₉	1	2	yes	—
221	C₂×C₄⋊C₈	—	2	1	no	—
222	C₂×C₄⋊C₈	—	19	2	no	—
223	C₂×C₄⋊C₈	Dic₁₉	1	2	yes	complemented
224	C₂×C₂²⋊C₈	—	38	1	no	—
225	C₂×C₄×C₈	—	38	1	no	—
226	C₄×C₄⋊C₄	—	19	2	no	—
227	C₄×C₄⋊C₄	—	19	2	no	—
228	C₄×C₄⋊C₄	—	38	1	no	—
229	C₄×C₄⋊C₄	—	38	1	no	—
230	C₂×#95	—	19	2	no	—
231	C₂×C₁₉	—	2	1	no	—
232	C₂×C₁₉	—	2	2	no	—
233	C₂×C₁₉	—	2	1	no	—
234	C₂×C₁₉	#1303	1	4	yes	complemented
235	C₂×C₁₉	C₂×#339	1	1	yes	characteristic
236	C₂×C₁₉	C₂×#340	1	1	yes	characteristic
237	C₂×C₁₉	C₂×#344	1	1	yes	characteristic
238	C₂³×C₄	—	38	2	no	—
239	C₂³×C₄	C₄×D₁₉	1	1	yes	characteristic
240	C₂³×C₄	D₇₆	1	1	yes	characteristic
241	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
242	C₂×M₁₆	—	2	2	no	—
243	C₂×M₁₆	—	2	2	no	—
244	C₂×M₁₆	—	4	2	no	—
245	C₂×M₁₆	—	4	2	no	—
246	C₂²×C₈	—	2	2	no	—
247	C₂²×C₈	—	38	2	no	—
248	C₂×C₄⋊C₄	—	38	8	no	—
249	C₂×C₄⋊C₄	—	38	2	no	—
250	C₂×C₄⋊C₄	—	38	2	no	—
251	C₂×C₄²	—	38	2	no	—
252	C₂×C₄²	—	38	2	no	—
253	C₂×C₄²	—	76	2	no	—
254	C₂×C₄²	—	76	2	no	—
255	C₂×C₄²	Dic₃₈	1	1	yes	characteristic
256	C₂×C₄²	Dic₃₈	1	1	yes	characteristic
257	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
258	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
259	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
260	C₂×C₄²	D₇₆	1	1	yes	characteristic
261	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
262	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
263	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
264	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
265	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
266	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
267	C₄⋊C₈	—	2	2	no	—
268	C₄⋊C₈	—	2	2	no	—
269	C₄⋊C₈	—	2	2	no	—
270	C₄⋊C₈	—	19	4	no	—
271	C₄⋊C₈	—	38	2	no	—
272	C₄⋊C₈	C₂×Dic₁₉	1	4	yes	complemented
273	C₂²⋊C₈	—	38	2	no	—
274	C₂²⋊C₈	—	38	2	no	—
275	C₄×C₈	—	38	2	no	—
276	C₄×C₈	—	38	2	no	—
277	#95	—	19	4	no	—
278	#95	—	38	2	no	—
279	C₁₉	C₂×#1303	1	1	yes	characteristic, complemented, Sylow
280	C₂⁴	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	4	2	no	—
283	C₂²×C₄	—	38	8	no	—
284	C₂²×C₄	—	38	4	no	—
285	C₂²×C₄	—	76	4	no	—
286	C₂²×C₄	—	76	4	no	—
287	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
288	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
289	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
290	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
291	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
292	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
293	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
294	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
295	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
296	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
297	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
298	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
299	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
300	C₂²×C₄	#64525	1	2	yes	—
301	C₂²×C₄	#64526	1	2	yes	—
302	C₂²×C₄	#64527	1	2	yes	—
303	C₂²×C₄	#64528	1	2	yes	—
304	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
305	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
306	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
307	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
308	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
309	M₁₆	—	4	2	no	—
310	M₁₆	—	4	2	no	—
311	M₁₆	—	4	4	no	—
312	C₂×C₈	—	2	4	no	—
313	C₂×C₈	—	4	4	no	—
314	C₂×C₈	—	38	4	no	—
315	C₂×C₈	—	76	4	no	—
316	C₄⋊C₄	—	38	8	no	—
317	C₄⋊C₄	—	38	8	no	—
318	C₄²	—	76	2	no	—
319	C₄²	—	76	2	no	—
320	C₄²	—	76	4	no	—
321	C₄²	C₄×Dic₁₉	1	1	yes	characteristic
322	C₄²	C₄×Dic₁₉	1	1	yes	characteristic
323	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
324	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
325	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
326	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
327	C₄²	C₄⋊Dic₁₉	1	1	yes	characteristic
328	C₄²	C₄⋊Dic₁₉	1	1	yes	characteristic
329	C₄²	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
330	C₄²	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
331	C₄²	C₂²⋊Dic₁₉	1	1	yes	characteristic
332	C₄²	C₂²⋊Dic₁₉	1	1	yes	characteristic
333	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
334	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
335	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
336	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
337	C₂³	—	2	2	no	—
338	C₂³	—	2	2	no	—
339	C₂³	#10597266	1	2	yes	—
340	C₂³	#10597267	1	2	yes	—
341	C₂³	C₁₉⋊#95	1	1	yes	characteristic
342	C₂³	C₁₉⋊#95	1	1	yes	characteristic
343	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	38	8	no	—
356	C₂×C₄	—	76	16	no	—
357	C₂×C₄	—	76	4	no	—
358	C₂×C₄	—	76	4	no	—
359	C₂×C₄	#10597264	1	2	yes	—
360	C₂×C₄	#10597264	1	2	yes	—
361	C₂×C₄	#10597265	1	2	yes	—
362	C₂×C₄	#10597265	1	2	yes	—
363	C₂×C₄	#10597266	1	2	yes	—
364	C₂×C₄	#10597267	1	2	yes	—
365	C₂×C₄	#10597282	1	4	yes	—
366	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
367	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
368	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
369	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
370	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
371	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
372	C₂×C₄	#10597289	1	2	yes	—
373	C₂×C₄	#10597289	1	2	yes	—
374	C₂×C₄	#10597292	1	2	yes	—
375	C₂×C₄	#10597292	1	2	yes	—
376	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
377	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
378	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
379	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
380	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
381	C₂×C₄	C₂×#64525	1	1	yes	characteristic
382	C₂×C₄	C₂×#64526	1	1	yes	characteristic
383	C₂×C₄	C₂×#64527	1	1	yes	characteristic
384	C₂×C₄	C₂×#64528	1	1	yes	characteristic
385	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
386	C₈	—	4	4	no	—
387	C₈	—	76	4	no	—
388	C₂²	—	2	4	no	—
389	C₂²	—	2	4	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	2	1	no	—
393	C₂²	—	2	1	no	—
394	C₂²	#11926305	1	2	yes	—
395	C₂²	#11926306	1	2	yes	—
396	C₂²	#11926306	1	2	yes	—
397	C₂²	#11926315	1	2	yes	—
398	C₂²	C₂×C₁₉⋊#95	1	1	yes	characteristic
399	C₂²	C₂×#10597266	1	1	yes	characteristic
400	C₂²	C₂×#10597267	1	1	yes	characteristic
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	2	1	no	—
407	C₄	—	76	8	no	—
408	C₄	#11926305	1	2	yes	—
409	C₄	#11926306	1	2	yes	—
410	C₄	#11926306	1	2	yes	—
411	C₄	C₂×#10597289	1	1	yes	characteristic
412	C₄	C₂×#10597292	1	1	yes	characteristic
413	C₄	C₂×#10597282	1	2	yes	—
414	C₄	C₂×#10597265	1	1	yes	characteristic
415	C₄	C₂×#10597264	1	1	yes	characteristic
416	C₂	—	2	1	no	—
417	C₂	—	2	1	no	—
418	C₂	—	2	2	no	—
419	C₂	#14561536	1	4	yes	direct product factor
420	C₂	C₂×#11926305	1	1	yes	characteristic
421	C₂	C₂×#11926306	1	1	yes	characteristic
422	C₂	C₂×#11926315	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²⋊Dic₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#423	C₂
socle	C₂³×C₁₉	#95
prime radical	C₂⁴×C₁₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#423	D₁₉
hypocenter	C₁₉	C₂×#1303
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂×#423

Complements

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

N	H ≅ G/N	type
3. #14561536	C₂	direct (N × H)
9. #11926597	C₄	semidirect
11. C₂×C₄⋊(C₁₉⋊C₈)	C₄	semidirect
23. C₁₉×#423	C₄	semidirect
26. C₂×C₁₉×C₄⋊C₈	C₄	semidirect
59. C₁₉×C₄⋊C₈	C₂×C₄	semidirect
65. C₄⋊(C₁₉⋊C₈)	C₂×C₄	semidirect
219. #423	Dic₁₉	semidirect
223. C₂×C₄⋊C₈	Dic₁₉	semidirect
234. C₂×C₁₉	#1303	semidirect
272. C₄⋊C₈	C₂×Dic₁₉	semidirect
279. C₁₉	C₂×#1303	semidirect
419. C₂	#14561536	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#11926597	2
C₂×C₄×C₄⋊Dic₁₉	2
#14561536	2
C₂×C₁₉×#423	2
C₂×#1303	19

Subgroups — C2×#14561536 #18072826

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14561536 #18072826