Subgroups — #18078792

Order 4864.

686 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₄×Dic₁₉	C₂	1	1	yes	maximal, characteristic
2	#14564613	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562134	C₂	1	1	yes	maximal, characteristic, complemented
4	#14562060	C₂	1	1	yes	maximal, characteristic
5	#14561537	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561467	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#3101	C₂	1	1	yes	maximal, characteristic
8	C₂×D₄×Dic₁₉	—	2	1	no	—
9	C₂²×C₄×Dic₁₉	—	2	1	no	—
10	#11926597	C₂²	1	1	yes	characteristic
11	#11926568	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×Dic₁₉	—	2	1	no	—
13	C₄×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
14	C₂²⋊C₄×Dic₁₉	—	2	2	no	—
15	C₄×C₂²⋊Dic₁₉	—	2	1	no	—
16	C₄²×Dic₁₉	C₂²	1	1	yes	characteristic
17	#11926303	—	2	1	no	—
18	#11926303	—	2	1	no	—
19	#11926281	—	2	2	no	—
20	D₄⋊(C₁₉⋊C₈)	—	2	2	no	—
21	C₁₉×#533	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₁₉×#483	—	2	1	no	—
24	C₁₉×#476	C₄	1	2	yes	complemented
25	C₁₉×#461	C₄	1	2	yes	complemented
26	C₁₉×#450	—	2	1	no	—
27	C₄×SD₁₆×C₁₉	—	2	2	no	—
28	C₁₉×#431	C₂²	1	1	yes	characteristic
29	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₉	—	2	1	no	—
31	C₂³×Dic₁₉	—	2	2	no	—
32	C₂×SD₁₆×C₁₉	—	2	2	no	—
33	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
34	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
35	C₁₉×#125	—	2	1	no	—
36	C₁₉×C₂²⋊Q₈	—	2	1	no	—
37	C₁₉×C₂²⋊Q₈	—	2	1	no	—
38	C₄×Q₈×C₁₉	—	2	1	no	—
39	C₄×Q₈×C₁₉	—	2	1	no	—
40	C₄×D₄×C₁₉	—	2	1	no	—
41	C₄×D₄×C₁₉	—	2	1	no	—
42	C₄×D₄×C₁₉	C₂×C₄	1	2	yes	—
43	C₄×D₄×C₁₉	D₄	1	2	yes	—
44	C₁₉×#117	—	2	1	no	—
45	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
46	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
47	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
48	C₂×C₂²⋊Dic₁₉	—	2	2	no	—
49	D₄×Dic₁₉	—	2	8	no	—
50	C₂×C₄⋊Dic₁₉	—	2	1	no	—
51	C₂×C₄×Dic₁₉	—	2	1	no	—
52	C₂×C₄×Dic₁₉	—	2	2	no	—
53	C₂×C₄×Dic₁₉	—	2	1	no	—
54	C₂×C₄×Dic₁₉	—	2	1	no	—
55	C₂×C₄×Dic₁₉	—	4	2	no	—
56	C₂×C₄×Dic₁₉	—	4	2	no	—
57	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
58	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
59	C₂×#64520	—	2	1	no	—
60	C₁₉×#106	—	2	2	no	—
61	C₁₉×C₄⋊C₈	C₂×C₄	1	2	yes	complemented
62	C₁₉×#103	—	2	2	no	—
63	C₁₉×#102	—	2	2	no	—
64	C₁₉×C₂²⋊C₈	—	2	1	no	—
65	C₄×C₈×C₁₉	—	2	1	no	—
66	C₁₉⋊#95	—	2	2	no	—
67	C₁₉⋊#95	D₄	1	2	yes	—
68	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
69	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
70	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
71	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
72	C₄×C₁₉⋊C₈	—	2	1	no	—
73	C₂⁴×C₁₉	—	2	1	no	—
74	C₂×Q₈×C₁₉	—	2	1	no	—
75	C₂×Q₈×C₁₉	—	2	1	no	—
76	C₂×D₄×C₁₉	—	2	4	no	—
77	C₂×D₄×C₁₉	—	2	1	no	—
78	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
79	C₂²×C₄×C₁₉	—	2	1	no	—
80	C₂²×C₄×C₁₉	—	2	2	no	—
81	C₂²×C₄×C₁₉	—	2	2	no	—
82	C₂²×C₄×C₁₉	—	4	1	no	—
83	C₂²×C₄×C₁₉	—	4	1	no	—
84	C₂²×C₄×C₁₉	—	4	1	no	—
85	C₂²×C₄×C₁₉	—	4	1	no	—
86	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
89	C₂²×Dic₁₉	—	2	1	no	—
90	C₂²×Dic₁₉	—	2	8	no	—
91	C₂²×Dic₁₉	—	2	1	no	—
92	C₂²×Dic₁₉	—	2	2	no	—
93	C₂²×Dic₁₉	—	4	4	no	—
94	C₂²×Dic₁₉	—	4	4	no	—
95	SD₁₆×C₁₉	—	4	4	no	—
96	C₂×C₈×C₁₉	—	2	2	no	—
97	C₄⋊C₄×C₁₉	—	2	1	no	—
98	C₄⋊C₄×C₁₉	—	2	1	no	—
99	C₄⋊C₄×C₁₉	—	2	1	no	—
100	C₄⋊C₄×C₁₉	—	2	1	no	—
101	C₄⋊C₄×C₁₉	—	2	1	no	—
102	C₄⋊C₄×C₁₉	—	4	1	no	—
103	C₄⋊C₄×C₁₉	—	4	1	no	—
104	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
105	C₂²⋊C₄×C₁₉	—	2	2	no	—
106	C₂²⋊C₄×C₁₉	—	2	2	no	—
107	C₂²⋊C₄×C₁₉	—	4	1	no	—
108	C₄²×C₁₉	—	4	1	no	—
109	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
110	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
111	C₄²×C₁₉	#41	1	1	yes	characteristic
112	C₄²×C₁₉	#41	1	1	yes	characteristic
113	C₂²⋊Dic₁₉	—	2	8	no	—
114	C₄⋊Dic₁₉	—	2	4	no	—
115	C₄×Dic₁₉	—	2	4	no	—
116	C₄×Dic₁₉	—	2	1	no	—
117	C₄×Dic₁₉	—	2	1	no	—
118	C₄×Dic₁₉	—	2	1	no	—
119	C₄×Dic₁₉	—	4	2	no	—
120	C₄×Dic₁₉	—	4	4	no	—
121	C₄×Dic₁₉	—	4	1	no	—
122	C₄×Dic₁₉	—	4	1	no	—
123	C₄×Dic₁₉	SD₁₆	1	2	yes	complemented
124	#64520	—	4	1	no	—
125	#64520	—	4	1	no	—
126	C₂×C₁₉⋊C₈	—	4	1	no	—
127	C₂×C₁₉⋊C₈	—	4	1	no	—
128	#9231	—	19	1	no	maximal, Sylow
129	C₂³×C₁₉	—	2	4	no	—
130	C₂³×C₁₉	—	2	2	no	—
131	C₂³×C₁₉	—	4	2	no	—
132	C₂³×C₁₉	—	4	1	no	—
133	C₂³×C₁₉	—	4	1	no	—
134	C₂³×C₁₉	#120	1	1	yes	characteristic
135	Q₈×C₁₉	—	4	2	no	—
136	Q₈×C₁₉	—	8	1	no	—
137	D₄×C₁₉	—	2	4	no	—
138	D₄×C₁₉	—	2	2	no	—
139	D₄×C₁₉	#104	1	4	yes	—
140	C₂×C₄×C₁₉	—	2	2	no	—
141	C₂×C₄×C₁₉	—	2	2	no	—
142	C₂×C₄×C₁₉	—	4	1	no	—
143	C₂×C₄×C₁₉	—	4	1	no	—
144	C₂×C₄×C₁₉	—	4	1	no	—
145	C₂×C₄×C₁₉	—	4	2	no	—
146	C₂×C₄×C₁₉	—	4	2	no	—
147	C₂×C₄×C₁₉	—	4	2	no	—
148	C₂×C₄×C₁₉	—	4	2	no	—
149	C₂×C₄×C₁₉	—	4	1	no	—
150	C₂×C₄×C₁₉	—	4	1	no	—
151	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
153	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
154	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
155	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
156	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
157	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
158	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
159	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
160	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
161	C₂×Dic₁₉	—	2	2	no	—
162	C₂×Dic₁₉	—	2	2	no	—
163	C₂×Dic₁₉	—	2	2	no	—
164	C₂×Dic₁₉	—	2	2	no	—
165	C₂×Dic₁₉	—	2	4	no	—
166	C₂×Dic₁₉	—	4	16	no	—
167	C₂×Dic₁₉	—	4	1	no	—
168	C₂×Dic₁₉	—	4	2	no	—
169	C₂×Dic₁₉	—	4	2	no	—
170	C₂×Dic₁₉	—	4	1	no	—
171	C₈×C₁₉	—	4	2	no	—
172	C₁₉⋊C₈	—	8	1	no	—
173	C₁₉⋊C₈	—	8	1	no	—
174	#3101	D₁₉	1	1	yes	characteristic
175	C₄²×D₄	—	19	1	no	—
176	#1994	—	19	1	no	—
177	#1503	—	19	1	no	—
178	#1486	—	19	1	no	—
179	#1303	—	19	1	no	—
180	#1276	—	19	1	no	—
181	C₂²×C₁₉	—	2	1	no	—
182	C₂²×C₁₉	—	2	1	no	—
183	C₂²×C₁₉	—	2	4	no	—
184	C₂²×C₁₉	—	4	4	no	—
185	C₂²×C₁₉	—	4	4	no	—
186	C₂²×C₁₉	—	4	2	no	—
187	C₂²×C₁₉	—	4	2	no	—
188	C₂²×C₁₉	#386	1	1	yes	characteristic
189	C₂²×C₁₉	#450	1	1	yes	characteristic
190	C₂²×C₁₉	#452	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	—	4	2	no	—
195	C₄×C₁₉	—	8	1	no	—
196	C₄×C₁₉	—	8	1	no	—
197	C₄×C₁₉	C₂×#104	1	2	yes	—
198	C₄×C₁₉	C₄×SD₁₆	1	1	yes	characteristic
199	C₄×C₁₉	#440	1	1	yes	characteristic
200	C₄×C₁₉	#461	1	1	yes	characteristic
201	C₄×C₁₉	#463	1	1	yes	characteristic
202	Dic₁₉	—	2	4	no	—
203	Dic₁₉	—	4	2	no	—
204	Dic₁₉	—	4	4	no	—
205	#533	C₂×D₁₉	1	1	yes	characteristic
206	C₂×C₄×D₄	—	38	1	no	—
207	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
208	C₂²×C₄²	—	38	1	no	—
209	#483	—	2	1	no	—
210	#476	Dic₁₉	1	2	yes	complemented
211	#461	Dic₁₉	1	2	yes	complemented
212	#450	—	2	1	no	—
213	C₄×SD₁₆	—	2	2	no	—
214	#431	—	19	1	no	—
215	#431	C₂×D₁₉	1	1	yes	characteristic
216	#423	—	19	1	no	—
217	C₄×C₄⋊C₄	—	19	1	no	—
218	C₄×C₄⋊C₄	—	38	1	no	—
219	C₄×C₂²⋊C₄	—	38	2	no	—
220	C₄×C₂²⋊C₄	—	38	1	no	—
221	C₄³	—	19	1	no	—
222	#339	—	38	1	no	—
223	#339	—	38	1	no	—
224	#328	—	38	2	no	—
225	D₄⋊C₈	—	38	2	no	—
226	C₂×C₁₉	—	2	1	no	—
227	C₂×C₁₉	—	2	1	no	—
228	C₂×C₁₉	—	4	4	no	—
229	C₂×C₁₉	#1877	1	1	yes	characteristic
230	C₂×C₁₉	#1896	1	1	yes	characteristic
231	C₂×C₁₉	#1906	1	1	yes	characteristic
232	C₂²×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
233	C₂³×C₄	—	2	1	no	—
234	C₂³×C₄	—	38	2	no	—
235	C₂×SD₁₆	—	2	2	no	—
236	C₂×M₁₆	—	38	1	no	—
237	C₄⋊Q₈	C₂×Dic₁₉	1	1	yes	characteristic, complemented
238	C₄⋊Q₈	C₂×Dic₁₉	1	1	yes	characteristic, complemented
239	#125	—	2	1	no	—
240	C₂²⋊Q₈	—	2	1	no	—
241	C₂²⋊Q₈	—	2	1	no	—
242	C₄×Q₈	—	2	1	no	—
243	C₄×Q₈	—	2	1	no	—
244	C₄×D₄	—	2	1	no	—
245	C₄×D₄	—	2	1	no	—
246	C₄×D₄	—	38	8	no	—
247	C₄×D₄	C₂×Dic₁₉	1	2	yes	—
248	C₄×D₄	C₂²⋊D₁₉	1	2	yes	—
249	#117	—	2	1	no	—
250	C₂×C₄⋊C₄	—	38	1	no	—
251	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
252	C₂×C₂²⋊C₄	—	2	1	no	—
253	C₂×C₂²⋊C₄	—	38	2	no	—
254	C₂×C₄²	—	19	1	no	—
255	C₂×C₄²	—	19	1	no	—
256	C₂×C₄²	—	38	1	no	—
257	C₂×C₄²	—	38	2	no	—
258	C₂×C₄²	—	38	1	no	—
259	C₂×C₄²	—	38	1	no	—
260	C₂×C₄²	—	76	2	no	—
261	C₂×C₄²	—	76	2	no	—
262	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
263	#106	—	2	2	no	—
264	C₄⋊C₈	—	38	1	no	—
265	C₄⋊C₈	—	38	1	no	—
266	C₄⋊C₈	—	38	1	no	—
267	C₄⋊C₈	C₂×Dic₁₉	1	2	yes	complemented
268	#103	—	2	2	no	—
269	#102	—	2	2	no	—
270	C₂²⋊C₈	—	2	1	no	—
271	C₂²⋊C₈	—	38	1	no	—
272	C₄×C₈	—	2	1	no	—
273	C₄×C₈	—	38	1	no	—
274	#95	—	19	2	no	—
275	#95	—	38	2	no	—
276	C₁₉	#9231	1	1	yes	characteristic, complemented, Sylow
277	C₂⁴	—	2	1	no	—
278	C₂×Q₈	—	2	1	no	—
279	C₂×Q₈	—	2	1	no	—
280	C₂×D₄	—	2	4	no	—
281	C₂×D₄	—	2	1	no	—
282	C₂×D₄	C₂²⋊Dic₁₉	1	2	yes	—
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	4	1	no	—
287	C₂²×C₄	—	4	1	no	—
288	C₂²×C₄	—	4	1	no	—
289	C₂²×C₄	—	4	1	no	—
290	C₂²×C₄	—	38	1	no	—
291	C₂²×C₄	—	38	8	no	—
292	C₂²×C₄	—	38	2	no	—
293	C₂²×C₄	—	38	1	no	—
294	C₂²×C₄	—	76	4	no	—
295	C₂²×C₄	—	76	4	no	—
296	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
297	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
298	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
299	SD₁₆	—	4	4	no	—
300	M₁₆	—	76	1	no	—
301	M₁₆	—	76	1	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	76	1	no	—
304	C₂×C₈	—	76	1	no	—
305	C₄⋊C₄	—	2	1	no	—
306	C₄⋊C₄	—	2	1	no	—
307	C₄⋊C₄	—	2	1	no	—
308	C₄⋊C₄	—	2	1	no	—
309	C₄⋊C₄	—	2	1	no	—
310	C₄⋊C₄	—	4	1	no	—
311	C₄⋊C₄	—	4	1	no	—
312	C₄⋊C₄	—	38	4	no	—
313	C₄⋊C₄	C₂²⋊Dic₁₉	1	2	yes	—
314	C₂²⋊C₄	—	2	2	no	—
315	C₂²⋊C₄	—	2	2	no	—
316	C₂²⋊C₄	—	4	1	no	—
317	C₂²⋊C₄	—	38	8	no	—
318	C₄²	—	4	1	no	—
319	C₄²	—	19	2	no	—
320	C₄²	—	38	4	no	—
321	C₄²	—	38	1	no	—
322	C₄²	—	38	1	no	—
323	C₄²	—	38	1	no	—
324	C₄²	—	76	2	no	—
325	C₄²	—	76	4	no	—
326	C₄²	—	76	1	no	—
327	C₄²	—	76	1	no	—
328	C₄²	#64543	1	1	yes	characteristic
329	C₄²	#64543	1	1	yes	characteristic
330	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
331	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
332	C₂³	—	2	4	no	—
333	C₂³	—	2	2	no	—
334	C₂³	—	4	2	no	—
335	C₂³	—	4	1	no	—
336	C₂³	—	4	1	no	—
337	C₂³	#10597383	1	1	yes	characteristic
338	Q₈	—	4	2	no	—
339	Q₈	—	8	1	no	—
340	D₄	—	2	4	no	—
341	D₄	—	2	2	no	—
342	D₄	#10597294	1	4	yes	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	38	2	no	—
355	C₂×C₄	—	38	2	no	—
356	C₂×C₄	—	38	2	no	—
357	C₂×C₄	—	38	2	no	—
358	C₂×C₄	—	38	4	no	—
359	C₂×C₄	—	76	16	no	—
360	C₂×C₄	—	76	1	no	—
361	C₂×C₄	—	76	2	no	—
362	C₂×C₄	—	76	2	no	—
363	C₂×C₄	—	76	1	no	—
364	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
365	C₂×C₄	#10597360	1	1	yes	characteristic
366	C₂×C₄	#10597361	1	1	yes	characteristic
367	C₂×C₄	#10597362	1	1	yes	characteristic
368	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
369	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
370	C₂×C₄	#10597381	1	1	yes	characteristic
371	C₂×C₄	#10597385	1	1	yes	characteristic
372	C₂×C₄	#10597385	1	1	yes	characteristic
373	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
374	C₈	—	4	2	no	—
375	C₈	—	152	1	no	—
376	C₈	—	152	1	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	2	1	no	—
379	C₂²	—	2	4	no	—
380	C₂²	—	4	4	no	—
381	C₂²	—	4	4	no	—
382	C₂²	—	4	2	no	—
383	C₂²	—	4	2	no	—
384	C₂²	#11926424	1	1	yes	characteristic
385	C₂²	#11926693	1	1	yes	characteristic
386	C₂²	#11926703	1	1	yes	characteristic
387	C₄	—	2	1	no	—
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	4	2	no	—
391	C₄	—	8	1	no	—
392	C₄	—	8	1	no	—
393	C₄	—	38	4	no	—
394	C₄	—	76	4	no	—
395	C₄	—	76	2	no	—
396	C₄	C₂×#10597294	1	2	yes	—
397	C₄	SD₁₆×Dic₁₉	1	1	yes	characteristic
398	C₄	#11926645	1	1	yes	characteristic
399	C₄	#11926747	1	1	yes	characteristic
400	C₄	#11926761	1	1	yes	characteristic
401	C₂	—	2	1	no	—
402	C₂	—	2	1	no	—
403	C₂	—	4	4	no	—
404	C₂	#14563971	1	1	yes	characteristic
405	C₂	#14564079	1	1	yes	characteristic
406	C₂	#14564138	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#10597385
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#3101	C₂
socle	C₂²×C₁₉	#386
prime radical	C₂²×D₄×C₁₉	D₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#3101	D₁₉
hypocenter	C₁₉	#9231
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3101

Complements

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

N	H ≅ G/N	type
2. #14564613	C₂	semidirect
3. #14562134	C₂	semidirect
5. #14561537	C₂	semidirect
6. #14561467	C₂	semidirect
24. C₁₉×#476	C₄	semidirect
25. C₁₉×#461	C₄	semidirect
33. C₁₉×C₄⋊Q₈	C₂×C₄	semidirect
34. C₁₉×C₄⋊Q₈	C₂×C₄	semidirect
61. C₁₉×C₄⋊C₈	C₂×C₄	semidirect
123. C₄×Dic₁₉	SD₁₆	semidirect
210. #476	Dic₁₉	semidirect
211. #461	Dic₁₉	semidirect
237. C₄⋊Q₈	C₂×Dic₁₉	semidirect
238. C₄⋊Q₈	C₂×Dic₁₉	semidirect
267. C₄⋊C₈	C₂×Dic₁₉	semidirect
276. C₁₉	#9231	semidirect

Maximal subgroups

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

subgroup	index
C₄×D₄×Dic₁₉	2
#14564613	2
#14562134	2
#14562060	2
#14561537	2
#14561467	2
C₁₉×#3101	2
#9231	19