Subgroups — C₂×#14561494 #18072315

Order 4864.

702 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926568	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926410	C₂	1	1	yes	maximal, characteristic
3	#14561494	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₁₉×#431	C₂	1	1	yes	maximal, characteristic
5	C₂²×#64520	—	2	1	no	—
6	C₂²×C₄⋊Dic₁₉	—	2	1	no	—
7	#11926568	—	2	1	no	—
8	#11926568	—	2	1	no	—
9	#11926568	C₄	1	2	yes	complemented
10	#11926568	C₂²	1	2	yes	—
11	C₂×C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
12	C₂×C₄⋊(C₁₉⋊C₈)	C₄	1	2	yes	complemented
13	#11926410	—	2	1	no	—
14	#11926410	—	2	1	no	—
15	#11926410	C₄	1	2	yes	—
16	#11926410	C₂²	1	2	yes	—
17	C₂×C₁₉⋊#95	—	2	1	no	—
18	C₂×C₁₉⋊#95	C₄	1	2	yes	—
19	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#431	—	2	1	no	—
21	C₁₉×#431	—	2	1	no	—
22	C₁₉×#431	C₄	1	2	yes	complemented
23	C₁₉×#431	C₂²	1	2	yes	—
24	C₂×C₁₉×C₄⋊C₈	—	2	1	no	—
25	C₂×C₁₉×C₂²⋊C₈	—	2	1	no	—
26	C₂×C₄×C₈×C₁₉	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	C₂²×C₈×C₁₉	—	2	2	no	—
32	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₉	Q₈	1	1	yes	characteristic
42	C₂×C₄²×C₁₉	Q₈	1	1	yes	characteristic
43	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
44	C₂×C₄⋊Dic₁₉	—	2	2	no	—
45	C₂×C₄⋊Dic₁₉	—	2	2	no	—
46	C₂×C₄⋊Dic₁₉	—	4	2	no	—
47	C₂×C₄⋊Dic₁₉	—	4	2	no	—
48	C₂×#64520	—	2	2	no	—
49	C₂×#64520	—	2	2	no	—
50	C₂×#64520	—	4	2	no	—
51	C₂×#64520	—	4	2	no	—
52	C₂²×C₁₉⋊C₈	—	2	2	no	—
53	C₁₉×C₄⋊C₈	—	2	2	no	—
54	C₁₉×C₄⋊C₈	—	2	2	no	—
55	C₁₉×C₂²⋊C₈	—	2	2	no	—
56	C₁₉×C₂²⋊C₈	—	2	2	no	—
57	C₄×C₈×C₁₉	—	2	2	no	—
58	C₄×C₈×C₁₉	C₂×C₄	1	4	yes	complemented
59	C₁₉⋊#95	—	2	2	no	—
60	C₁₉⋊#95	—	2	2	no	—
61	C₁₉⋊#95	—	2	2	no	—
62	C₁₉⋊#95	C₂×C₄	1	4	yes	—
63	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
64	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
65	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
66	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	4	yes	complemented
67	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₉	—	4	2	no	—
69	C₂²×C₄×C₁₉	—	4	2	no	—
70	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
71	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
72	C₂²×C₄×C₁₉	C₂²⋊C₄	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	C₄⋊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	D₈	1	2	yes	—
86	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	—
87	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	—
88	C₂²×C₄×C₁₉	Q₁₆	1	2	yes	—
89	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
92	C₂²×Dic₁₉	—	2	4	no	—
93	C₂²×Dic₁₉	—	4	4	no	—
94	C₂²×Dic₁₉	—	4	4	no	—
95	C₂²×Dic₁₉	—	4	4	no	—
96	C₂×C₈×C₁₉	—	2	4	no	—
97	C₂×C₈×C₁₉	—	4	4	no	—
98	C₄²×C₁₉	C₄²	1	1	yes	characteristic
99	C₄²×C₁₉	C₄²	1	1	yes	characteristic
100	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
101	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
102	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
103	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
104	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
105	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
106	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
107	C₄²×C₁₉	C₄⋊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	C₂²×C₄	1	1	yes	characteristic
111	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
112	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
113	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
114	C₄⋊Dic₁₉	—	4	4	no	—
115	C₄⋊Dic₁₉	—	4	2	no	—
116	C₄⋊Dic₁₉	—	4	2	no	—
117	#64520	—	4	4	no	—
118	#64520	—	4	2	no	—
119	#64520	—	4	2	no	—
120	C₂×C₁₉⋊C₈	—	2	4	no	—
121	C₂×C₁₉⋊C₈	—	4	4	no	—
122	C₂×#1286	—	19	1	no	maximal, Sylow
123	C₂³×C₁₉	—	2	2	no	—
124	C₂³×C₁₉	—	2	2	no	—
125	C₂³×C₁₉	#95	1	1	yes	characteristic
126	C₂³×C₁₉	#95	1	1	yes	characteristic
127	C₂³×C₁₉	#102	1	2	yes	—
128	C₂³×C₁₉	#103	1	2	yes	—
129	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
130	C₂×C₄×C₁₉	—	2	2	no	—
131	C₂×C₄×C₁₉	—	2	2	no	—
132	C₂×C₄×C₁₉	—	2	2	no	—
133	C₂×C₄×C₁₉	—	2	2	no	—
134	C₂×C₄×C₁₉	—	4	1	no	—
135	C₂×C₄×C₁₉	—	4	1	no	—
136	C₂×C₄×C₁₉	—	4	1	no	—
137	C₂×C₄×C₁₉	—	4	1	no	—
138	C₂×C₄×C₁₉	—	4	1	no	—
139	C₂×C₄×C₁₉	—	4	1	no	—
140	C₂×C₄×C₁₉	—	4	1	no	—
141	C₂×C₄×C₁₉	—	4	1	no	—
142	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
143	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
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	#102	1	2	yes	—
149	C₂×C₄×C₁₉	#102	1	2	yes	—
150	C₂×C₄×C₁₉	#102	1	2	yes	—
151	C₂×C₄×C₁₉	#103	1	2	yes	—
152	C₂×C₄×C₁₉	#103	1	2	yes	—
153	C₂×C₄×C₁₉	#103	1	2	yes	—
154	C₂×C₄×C₁₉	#106	1	2	yes	—
155	C₂×C₄×C₁₉	#106	1	2	yes	—
156	C₂×C₄×C₁₉	#107	1	2	yes	—
157	C₂×C₄×C₁₉	#107	1	2	yes	—
158	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
159	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
165	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
166	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
167	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
168	C₂×Dic₁₉	—	4	4	no	—
169	C₂×Dic₁₉	—	4	4	no	—
170	C₂×Dic₁₉	—	4	4	no	—
171	C₂×Dic₁₉	—	8	8	no	—
172	C₈×C₁₉	—	4	4	no	—
173	C₁₉⋊C₈	—	4	4	no	—
174	C₂×#431	D₁₉	1	1	yes	characteristic
175	C₂×#423	—	19	1	no	—
176	C₂×#382	—	19	1	no	—
177	#1286	—	19	4	no	—
178	C₂²×C₁₉	—	2	4	no	—
179	C₂²×C₁₉	—	2	4	no	—
180	C₂²×C₁₉	—	2	1	no	—
181	C₂²×C₁₉	—	2	1	no	—
182	C₂²×C₁₉	—	2	1	no	—
183	C₂²×C₁₉	—	2	1	no	—
184	C₂²×C₁₉	H(3,ℤ/4)	1	2	yes	—
185	C₂²×C₁₉	#340	1	2	yes	—
186	C₂²×C₁₉	#340	1	2	yes	—
187	C₂²×C₁₉	#344	1	2	yes	—
188	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
189	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
190	C₂²×C₁₉	C₂×#103	1	1	yes	characteristic
191	C₄×C₁₉	—	2	1	no	—
192	C₄×C₁₉	—	2	1	no	—
193	C₄×C₁₉	—	2	1	no	—
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	#340	1	2	yes	—
200	C₄×C₁₉	#340	1	2	yes	—
201	C₄×C₁₉	C₂×#102	1	1	yes	characteristic
202	C₄×C₁₉	C₂×#103	1	1	yes	characteristic
203	C₄×C₁₉	C₂×#106	1	1	yes	characteristic
204	C₄×C₁₉	C₂×#107	1	1	yes	characteristic
205	Dic₁₉	—	8	4	no	—
206	C₂²×M₁₆	—	38	1	no	—
207	C₂²×C₄⋊C₄	—	38	1	no	—
208	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
209	#431	—	2	1	no	—
210	#431	—	2	1	no	—
211	#431	Dic₁₉	1	2	yes	complemented
212	#431	C₂×D₁₉	1	2	yes	—
213	#423	—	19	2	no	—
214	#423	—	19	2	no	—
215	#423	—	38	1	no	—
216	#423	—	38	1	no	—
217	C₂×C₄⋊C₈	—	2	1	no	—
218	C₂×C₄⋊C₈	—	19	2	no	—
219	C₂×C₄⋊C₈	—	38	1	no	—
220	C₂×C₂²⋊C₈	—	2	1	no	—
221	C₂×C₄×C₈	Dic₁₉	1	2	yes	complemented
222	#382	—	19	2	no	—
223	#382	—	19	2	no	—
224	#382	—	38	1	no	—
225	#382	—	38	1	no	—
226	C₂×#95	—	19	2	no	—
227	C₂×#95	—	38	1	no	—
228	C₂×C₁₉	—	2	1	no	—
229	C₂×C₁₉	—	2	2	no	—
230	C₂×C₁₉	—	2	1	no	—
231	C₂×C₁₉	#1286	1	4	yes	complemented
232	C₂×C₁₉	C₂×H(3,ℤ/4)	1	1	yes	characteristic
233	C₂×C₁₉	C₂×#340	1	1	yes	characteristic
234	C₂×C₁₉	C₂×#344	1	1	yes	characteristic
235	C₂³×C₄	—	38	2	no	—
236	C₂³×C₄	C₄×D₁₉	1	1	yes	characteristic
237	C₂³×C₄	D₇₆	1	1	yes	characteristic
238	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
239	C₂×M₁₆	—	38	2	no	—
240	C₂×M₁₆	—	38	2	no	—
241	C₂×M₁₆	—	76	2	no	—
242	C₂×M₁₆	—	76	2	no	—
243	C₂²×C₈	—	2	2	no	—
244	C₂²×C₈	—	38	2	no	—
245	C₂×C₄⋊C₄	—	38	2	no	—
246	C₂×C₄⋊C₄	—	38	2	no	—
247	C₂×C₄⋊C₄	—	76	2	no	—
248	C₂×C₄⋊C₄	—	76	2	no	—
249	C₂×C₄²	Dic₃₈	1	1	yes	characteristic
250	C₂×C₄²	Dic₃₈	1	1	yes	characteristic
251	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
252	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
253	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
254	C₂×C₄²	D₇₆	1	1	yes	characteristic
255	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
256	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
257	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
258	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
259	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
260	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
261	C₄⋊C₈	—	2	2	no	—
262	C₄⋊C₈	—	2	2	no	—
263	C₄⋊C₈	—	19	4	no	—
264	C₄⋊C₈	—	38	2	no	—
265	C₄⋊C₈	—	38	2	no	—
266	C₄⋊C₈	—	38	2	no	—
267	C₂²⋊C₈	—	2	2	no	—
268	C₂²⋊C₈	—	2	2	no	—
269	C₄×C₈	—	2	2	no	—
270	C₄×C₈	C₂×Dic₁₉	1	4	yes	complemented
271	#95	—	19	4	no	—
272	#95	—	38	2	no	—
273	#95	—	38	2	no	—
274	#95	—	38	2	no	—
275	C₁₉	C₂×#1286	1	1	yes	characteristic, complemented, Sylow
276	C₂⁴	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
277	C₂²×C₄	—	4	2	no	—
278	C₂²×C₄	—	4	2	no	—
279	C₂²×C₄	—	38	4	no	—
280	C₂²×C₄	—	76	4	no	—
281	C₂²×C₄	—	76	4	no	—
282	C₂²×C₄	—	76	4	no	—
283	C₂²×C₄	#64516	1	2	yes	—
284	C₂²×C₄	#64516	1	2	yes	—
285	C₂²×C₄	D₁₅₂	1	2	yes	—
286	C₂²×C₄	Dic₇₆	1	2	yes	—
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	C₂²⋊Dic₁₉	1	1	yes	characteristic
301	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
302	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
303	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
304	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
305	M₁₆	—	76	4	no	—
306	M₁₆	—	76	2	no	—
307	M₁₆	—	76	2	no	—
308	C₂×C₈	—	2	4	no	—
309	C₂×C₈	—	4	4	no	—
310	C₂×C₈	—	38	4	no	—
311	C₂×C₈	—	76	4	no	—
312	C₄⋊C₄	—	76	4	no	—
313	C₄⋊C₄	—	76	2	no	—
314	C₄⋊C₄	—	76	2	no	—
315	C₄²	C₄×Dic₁₉	1	1	yes	characteristic
316	C₄²	C₄×Dic₁₉	1	1	yes	characteristic
317	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
318	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
319	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
320	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
321	C₄²	C₄⋊Dic₁₉	1	1	yes	characteristic
322	C₄²	C₄⋊Dic₁₉	1	1	yes	characteristic
323	C₄²	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
324	C₄²	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
325	C₄²	C₂²⋊Dic₁₉	1	1	yes	characteristic
326	C₄²	C₂²⋊Dic₁₉	1	1	yes	characteristic
327	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
328	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
329	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
330	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
331	C₂³	—	2	2	no	—
332	C₂³	—	2	2	no	—
333	C₂³	#10597273	1	2	yes	—
334	C₂³	#10597278	1	2	yes	—
335	C₂³	C₁₉⋊#95	1	1	yes	characteristic
336	C₂³	C₁₉⋊#95	1	1	yes	characteristic
337	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	76	4	no	—
351	C₂×C₄	—	76	4	no	—
352	C₂×C₄	—	76	4	no	—
353	C₂×C₄	—	152	8	no	—
354	C₂×C₄	#10597273	1	2	yes	—
355	C₂×C₄	#10597273	1	2	yes	—
356	C₂×C₄	#10597273	1	2	yes	—
357	C₂×C₄	#10597274	1	2	yes	—
358	C₂×C₄	#10597274	1	2	yes	—
359	C₂×C₄	#10597275	1	2	yes	—
360	C₂×C₄	#10597275	1	2	yes	—
361	C₂×C₄	#10597278	1	2	yes	—
362	C₂×C₄	#10597278	1	2	yes	—
363	C₂×C₄	#10597278	1	2	yes	—
364	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
365	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
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	C₂×#64516	1	1	yes	characteristic
371	C₂×C₄	C₂×#64516	1	1	yes	characteristic
372	C₂×C₄	C₂×D₁₅₂	1	1	yes	characteristic
373	C₂×C₄	C₂×Dic₇₆	1	1	yes	characteristic
374	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
375	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
376	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
377	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
378	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
379	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
380	C₈	—	4	4	no	—
381	C₈	—	76	4	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	2	4	no	—
387	C₂²	—	2	4	no	—
388	C₂²	#11926300	1	2	yes	—
389	C₂²	#11926307	1	2	yes	—
390	C₂²	#11926307	1	2	yes	—
391	C₂²	#11926315	1	2	yes	—
392	C₂²	C₂×C₁₉⋊#95	1	1	yes	characteristic
393	C₂²	C₂×#10597278	1	1	yes	characteristic
394	C₂²	C₂×#10597273	1	1	yes	characteristic
395	C₄	—	2	1	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	2	1	no	—
399	C₄	—	2	1	no	—
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	152	4	no	—
404	C₄	#11926307	1	2	yes	—
405	C₄	#11926307	1	2	yes	—
406	C₄	C₂×#10597278	1	1	yes	characteristic
407	C₄	C₂×#10597273	1	1	yes	characteristic
408	C₄	C₂×#10597274	1	1	yes	characteristic
409	C₄	C₂×#10597275	1	1	yes	characteristic
410	C₂	—	2	1	no	—
411	C₂	—	2	1	no	—
412	C₂	—	2	2	no	—
413	C₂	#14561494	1	4	yes	direct product factor
414	C₂	C₂×#11926300	1	1	yes	characteristic
415	C₂	C₂×#11926307	1	1	yes	characteristic
416	C₂	C₂×#11926315	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₁₉⋊#95
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#431	C₂
socle	C₂³×C₁₉	#95
prime radical	C₂⁴×C₁₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#431	D₁₉
hypocenter	C₁₉	C₂×#1286
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#431

Complements

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

N	H ≅ G/N	type
3. #14561494	C₂	direct (N × H)
9. #11926568	C₄	semidirect
12. C₂×C₄⋊(C₁₉⋊C₈)	C₄	semidirect
22. C₁₉×#431	C₄	semidirect
26. C₂×C₄×C₈×C₁₉	C₄	semidirect
58. C₄×C₈×C₁₉	C₂×C₄	semidirect
66. C₄⋊(C₁₉⋊C₈)	C₂×C₄	semidirect
211. #431	Dic₁₉	semidirect
221. C₂×C₄×C₈	Dic₁₉	semidirect
231. C₂×C₁₉	#1286	semidirect
270. C₄×C₈	C₂×Dic₁₉	semidirect
275. C₁₉	C₂×#1286	semidirect
413. C₂	#14561494	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×#11926568	2
C₂×#11926410	2
#14561494	2
C₂×C₁₉×#431	2
C₂×#1286	19

Subgroups — C2×#14561494 #18072315

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14561494 #18072315