Subgroups — C₂×#14561500 #18072379

Order 4864.

678 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926601	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926412	C₂	1	1	yes	maximal, characteristic
3	#14561500	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
5	#11926601	—	2	1	no	—
6	#11926601	—	2	1	no	—
7	#11926601	C₄	1	2	yes	complemented
8	#11926601	C₂²	1	2	yes	—
9	C₂×C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
10	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
11	C₂×#10597260	C₄	1	2	yes	complemented
12	#11926412	—	2	1	no	—
13	#11926412	—	2	1	no	—
14	#11926412	C₄	1	2	yes	—
15	#11926412	C₂²	1	2	yes	—
16	C₂×C₁₉⋊#95	—	2	1	no	—
17	C₂×C₁₉⋊#95	—	2	1	no	—
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	C₄×M₁₆×C₁₉	—	2	1	no	—
22	C₄×M₁₆×C₁₉	—	2	1	no	—
23	C₄×M₁₆×C₁₉	C₄	1	2	yes	complemented
24	C₄×M₁₆×C₁₉	C₂²	1	2	yes	—
25	C₂×C₁₉×#97	—	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	C₂×M₁₆×C₁₉	—	2	8	no	—
32	C₂×M₁₆×C₁₉	—	2	2	no	—
33	C₂×M₁₆×C₁₉	—	2	2	no	—
34	C₂²×C₈×C₁₉	—	2	2	no	—
35	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
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	D₄	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	Q₈	1	1	yes	characteristic
45	C₂×C₄²×C₁₉	Q₈	1	1	yes	characteristic
46	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
47	C₂²×C₁₉⋊C₈	—	2	2	no	—
48	C₁₉×#97	—	2	2	no	—
49	C₁₉×#97	—	2	2	no	—
50	C₄×C₈×C₁₉	—	2	2	no	—
51	C₄×C₈×C₁₉	C₂×C₄	1	4	yes	complemented
52	C₁₉⋊#95	—	2	2	no	—
53	C₁₉⋊#95	—	2	2	no	—
54	C₁₉⋊#95	—	2	2	no	—
55	C₁₉⋊#95	—	2	2	no	—
56	C₁₉⋊#95	—	2	2	no	—
57	C₁₉⋊#95	C₂×C₄	1	4	yes	—
58	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
59	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
60	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
61	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
62	#10597260	—	2	2	no	—
63	#10597260	C₂×C₄	1	4	yes	complemented
64	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₉	—	2	4	no	—
66	C₂²×C₄×C₁₉	—	4	2	no	—
67	C₂²×C₄×C₁₉	—	4	2	no	—
68	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
69	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
70	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
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	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	C₄⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₉	C₄⋊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	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
86	C₂²×Dic₁₉	—	2	4	no	—
87	C₂²×Dic₁₉	—	4	4	no	—
88	C₂²×Dic₁₉	—	4	4	no	—
89	C₂²×Dic₁₉	—	4	4	no	—
90	M₁₆×C₁₉	—	2	8	no	—
91	M₁₆×C₁₉	—	2	8	no	—
92	C₂×C₈×C₁₉	—	2	8	no	—
93	C₂×C₈×C₁₉	—	2	4	no	—
94	C₄²×C₁₉	C₄²	1	1	yes	characteristic
95	C₄²×C₁₉	C₄²	1	1	yes	characteristic
96	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
97	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
98	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
99	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
100	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
101	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
102	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
103	C₄²×C₁₉	C₄⋊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	C₂²×C₄	1	1	yes	characteristic
107	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
108	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
109	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
110	C₂×C₁₉⋊C₈	—	2	4	no	—
111	C₂×C₁₉⋊C₈	—	4	4	no	—
112	C₂×#1288	—	19	1	no	maximal, Sylow
113	C₂³×C₁₉	—	2	2	no	—
114	C₂³×C₁₉	—	2	2	no	—
115	C₂³×C₁₉	#95	1	1	yes	characteristic
116	C₂³×C₁₉	#95	1	1	yes	characteristic
117	C₂³×C₁₉	#104	1	4	yes	—
118	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
119	C₂×C₄×C₁₉	—	2	2	no	—
120	C₂×C₄×C₁₉	—	2	2	no	—
121	C₂×C₄×C₁₉	—	2	2	no	—
122	C₂×C₄×C₁₉	—	2	2	no	—
123	C₂×C₄×C₁₉	—	2	2	no	—
124	C₂×C₄×C₁₉	—	2	2	no	—
125	C₂×C₄×C₁₉	—	2	2	no	—
126	C₂×C₄×C₁₉	—	2	2	no	—
127	C₂×C₄×C₁₉	—	2	2	no	—
128	C₂×C₄×C₁₉	—	2	2	no	—
129	C₂×C₄×C₁₉	—	4	1	no	—
130	C₂×C₄×C₁₉	—	4	1	no	—
131	C₂×C₄×C₁₉	—	4	1	no	—
132	C₂×C₄×C₁₉	—	4	1	no	—
133	C₂×C₄×C₁₉	—	4	1	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	#95	1	1	yes	characteristic
138	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
139	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
140	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
141	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
142	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
143	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
144	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂×Dic₁₉	—	4	4	no	—
150	C₂×Dic₁₉	—	4	4	no	—
151	C₂×Dic₁₉	—	4	4	no	—
152	C₂×Dic₁₉	—	8	8	no	—
153	C₈×C₁₉	—	2	8	no	—
154	C₁₉⋊C₈	—	4	4	no	—
155	C₂×#432	—	19	1	no	—
156	C₂×C₄×M₁₆	D₁₉	1	1	yes	characteristic
157	C₂×#383	—	19	1	no	—
158	#1288	—	19	4	no	—
159	C₂²×C₁₉	—	2	8	no	—
160	C₂²×C₁₉	—	2	1	no	—
161	C₂²×C₁₉	—	2	1	no	—
162	C₂²×C₁₉	—	2	1	no	—
163	C₂²×C₁₉	—	2	1	no	—
164	C₂²×C₁₉	H(3,ℤ/4)	1	2	yes	—
165	C₂²×C₁₉	#339	1	2	yes	—
166	C₂²×C₁₉	#339	1	2	yes	—
167	C₂²×C₁₉	#344	1	2	yes	—
168	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
169	C₂²×C₁₉	C₂×#104	1	2	yes	—
170	C₄×C₁₉	—	2	1	no	—
171	C₄×C₁₉	—	2	1	no	—
172	C₄×C₁₉	—	2	1	no	—
173	C₄×C₁₉	—	2	1	no	—
174	C₄×C₁₉	—	2	1	no	—
175	C₄×C₁₉	—	2	1	no	—
176	C₄×C₁₉	—	2	1	no	—
177	C₄×C₁₉	—	2	1	no	—
178	C₄×C₁₉	—	2	1	no	—
179	C₄×C₁₉	—	2	1	no	—
180	C₄×C₁₉	—	2	1	no	—
181	C₄×C₁₉	—	2	1	no	—
182	Dic₁₉	—	8	4	no	—
183	C₂²×M₁₆	—	2	1	no	—
184	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
185	#432	—	19	2	no	—
186	#432	—	19	2	no	—
187	#432	—	38	1	no	—
188	#432	—	38	1	no	—
189	C₂×C₄⋊C₈	—	38	1	no	—
190	C₂×C₂²⋊C₈	—	38	1	no	—
191	C₄×M₁₆	—	2	1	no	—
192	C₄×M₁₆	—	2	1	no	—
193	C₄×M₁₆	Dic₁₉	1	2	yes	complemented
194	C₄×M₁₆	C₂×D₁₉	1	2	yes	—
195	C₂×#97	—	2	1	no	—
196	C₂×#97	—	19	2	no	—
197	C₂×C₄×C₈	Dic₁₉	1	2	yes	complemented
198	#383	—	19	2	no	—
199	#383	—	19	2	no	—
200	#383	—	38	1	no	—
201	#383	—	38	1	no	—
202	C₂×#95	—	19	2	no	—
203	C₂×#95	—	38	1	no	—
204	C₂×#95	—	38	1	no	—
205	C₂×C₁₉	—	2	2	no	—
206	C₂×C₁₉	—	2	2	no	—
207	C₂×C₁₉	#1288	1	4	yes	complemented
208	C₂×C₁₉	C₂×H(3,ℤ/4)	1	1	yes	characteristic
209	C₂×C₁₉	C₂×#339	1	1	yes	characteristic
210	C₂×C₁₉	C₂×#344	1	1	yes	characteristic
211	C₂³×C₄	—	38	2	no	—
212	C₂³×C₄	C₄×D₁₉	1	1	yes	characteristic
213	C₂³×C₄	D₇₆	1	1	yes	characteristic
214	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
215	C₂×M₁₆	—	2	8	no	—
216	C₂×M₁₆	—	2	2	no	—
217	C₂×M₁₆	—	2	2	no	—
218	C₂²×C₈	—	2	2	no	—
219	C₂²×C₈	—	38	2	no	—
220	C₂×C₄²	Dic₃₈	1	1	yes	characteristic
221	C₂×C₄²	Dic₃₈	1	1	yes	characteristic
222	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
223	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
224	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
225	C₂×C₄²	D₇₆	1	1	yes	characteristic
226	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
227	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
228	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
229	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
230	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
231	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
232	C₄⋊C₈	—	38	2	no	—
233	C₄⋊C₈	—	38	2	no	—
234	C₂²⋊C₈	—	38	2	no	—
235	C₂²⋊C₈	—	38	2	no	—
236	#97	—	2	2	no	—
237	#97	—	2	2	no	—
238	#97	—	19	4	no	—
239	#97	—	38	2	no	—
240	C₄×C₈	—	2	2	no	—
241	C₄×C₈	C₂×Dic₁₉	1	4	yes	complemented
242	#95	—	19	4	no	—
243	#95	—	38	2	no	—
244	#95	—	38	2	no	—
245	#95	—	38	2	no	—
246	#95	—	38	2	no	—
247	#95	—	38	2	no	—
248	C₁₉	C₂×#1288	1	1	yes	characteristic, complemented, Sylow
249	C₂⁴	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
250	C₂²×C₄	—	2	4	no	—
251	C₂²×C₄	—	4	2	no	—
252	C₂²×C₄	—	4	2	no	—
253	C₂²×C₄	—	38	4	no	—
254	C₂²×C₄	—	76	4	no	—
255	C₂²×C₄	—	76	4	no	—
256	C₂²×C₄	—	76	4	no	—
257	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
258	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
259	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
260	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
261	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
262	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
263	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
264	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
265	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
266	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
267	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
268	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
269	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
270	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
271	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
272	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
273	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
274	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
275	M₁₆	—	2	8	no	—
276	M₁₆	—	2	8	no	—
277	C₂×C₈	—	2	8	no	—
278	C₂×C₈	—	2	4	no	—
279	C₂×C₈	—	38	4	no	—
280	C₂×C₈	—	76	4	no	—
281	C₄²	C₄×Dic₁₉	1	1	yes	characteristic
282	C₄²	C₄×Dic₁₉	1	1	yes	characteristic
283	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
284	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
285	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
286	C₄²	Dic₁₉⋊C₄	1	1	yes	characteristic
287	C₄²	C₄⋊Dic₁₉	1	1	yes	characteristic
288	C₄²	C₄⋊Dic₁₉	1	1	yes	characteristic
289	C₄²	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
290	C₄²	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
291	C₄²	C₂²⋊Dic₁₉	1	1	yes	characteristic
292	C₄²	C₂²⋊Dic₁₉	1	1	yes	characteristic
293	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
294	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
295	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
296	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
297	C₂³	—	2	2	no	—
298	C₂³	—	2	2	no	—
299	C₂³	#10597262	1	4	yes	—
300	C₂³	C₁₉⋊#95	1	1	yes	characteristic
301	C₂³	C₁₉⋊#95	1	1	yes	characteristic
302	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	4	1	no	—
314	C₂×C₄	—	4	1	no	—
315	C₂×C₄	—	4	1	no	—
316	C₂×C₄	—	4	1	no	—
317	C₂×C₄	—	4	1	no	—
318	C₂×C₄	—	4	1	no	—
319	C₂×C₄	—	4	1	no	—
320	C₂×C₄	—	4	1	no	—
321	C₂×C₄	—	76	4	no	—
322	C₂×C₄	—	76	4	no	—
323	C₂×C₄	—	76	4	no	—
324	C₂×C₄	—	152	8	no	—
325	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
326	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
327	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
328	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
329	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
330	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
331	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
332	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
333	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
334	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
335	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
336	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
337	C₈	—	2	8	no	—
338	C₈	—	76	4	no	—
339	C₂²	—	2	1	no	—
340	C₂²	—	2	1	no	—
341	C₂²	—	2	1	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	2	8	no	—
344	C₂²	#11926301	1	2	yes	—
345	C₂²	#11926304	1	2	yes	—
346	C₂²	#11926304	1	2	yes	—
347	C₂²	#11926315	1	2	yes	—
348	C₂²	C₂×C₁₉⋊#95	1	1	yes	characteristic
349	C₂²	C₂×#10597262	1	2	yes	—
350	C₄	—	2	1	no	—
351	C₄	—	2	1	no	—
352	C₄	—	2	1	no	—
353	C₄	—	2	1	no	—
354	C₄	—	2	1	no	—
355	C₄	—	2	1	no	—
356	C₄	—	2	1	no	—
357	C₄	—	2	1	no	—
358	C₄	—	2	1	no	—
359	C₄	—	2	1	no	—
360	C₄	—	2	1	no	—
361	C₄	—	2	1	no	—
362	C₄	—	152	4	no	—
363	C₂	—	2	2	no	—
364	C₂	—	2	2	no	—
365	C₂	#14561500	1	4	yes	direct product factor
366	C₂	C₂×#11926301	1	1	yes	characteristic
367	C₂	C₂×#11926304	1	1	yes	characteristic
368	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×C₄×M₁₆×C₁₉	C₂
socle	C₂³×C₁₉	#95
prime radical	C₂⁴×C₁₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×C₄×M₁₆	D₁₉
hypocenter	C₁₉	C₂×#1288
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
3. #14561500	C₂	direct (N × H)
7. #11926601	C₄	semidirect
11. C₂×#10597260	C₄	semidirect
23. C₄×M₁₆×C₁₉	C₄	semidirect
26. C₂×C₄×C₈×C₁₉	C₄	semidirect
51. C₄×C₈×C₁₉	C₂×C₄	semidirect
63. #10597260	C₂×C₄	semidirect
193. C₄×M₁₆	Dic₁₉	semidirect
197. C₂×C₄×C₈	Dic₁₉	semidirect
207. C₂×C₁₉	#1288	semidirect
241. C₄×C₈	C₂×Dic₁₉	semidirect
248. C₁₉	C₂×#1288	semidirect
365. C₂	#14561500	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×#11926601	2
C₂×#11926412	2
#14561500	2
C₂×C₄×M₁₆×C₁₉	2
C₂×#1288	19

Subgroups — C2×#14561500 #18072379

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14561500 #18072379