Subgroups — #18081348

Order 4864.

610 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#10597393	C₂	1	1	yes	maximal, characteristic
2	#14563786	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#10597272	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×Q₈⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11926273	C₂	1	1	yes	maximal, characteristic
6	C₂×#11926271	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10597393	C₄	1	1	yes	characteristic
9	C₂×C₄×D₇₆	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×Dic₁₉⋊C₈	—	2	2	no	—
12	C₂×#10597272	—	2	2	no	—
13	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
14	#11926451	C₄	1	1	yes	characteristic
15	#11926445	C₄	1	1	yes	characteristic
16	#11926434	—	2	2	no	—
17	#11926409	C₄	1	1	yes	characteristic
18	C₄×(C₂×D₁₉)⋊C₄	—	2	2	no	—
19	C₄²×Dic₁₉	C₂²	1	1	yes	characteristic
20	Q₈⋊(C₁₉⋊C₈)	—	2	2	no	—
21	#11926273	—	2	2	no	—
22	#11926271	—	2	2	no	—
23	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×Q₈⋊C₈	—	2	2	no	—
27	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂²×D₇₆	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₄×D₁₉	—	2	1	no	—
30	C₂²×C₈×C₁₉	—	2	1	no	—
31	C₂²×C₈×C₁₉	—	2	1	no	—
32	C₄×Q₈×C₁₉	—	2	1	no	—
33	C₄×Q₈×C₁₉	—	2	1	no	—
34	C₄×Q₈×C₁₉	—	2	1	no	—
35	C₄×Q₈×C₁₉	—	2	1	no	—
36	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
37	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₉	—	2	1	no	—
39	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
40	#10597393	—	2	2	no	—
41	#10597393	—	2	2	no	—
42	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
43	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
44	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
45	C₂×C₄⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
49	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
50	C₂²×C₁₉⋊C₈	—	2	1	no	—
51	C₂²×C₁₉⋊C₈	—	2	1	no	—
52	C₄×D₇₆	—	2	1	no	—
53	C₄×D₇₆	—	2	1	no	—
54	C₄×D₇₆	—	2	1	no	—
55	C₄×D₇₆	—	2	1	no	—
56	C₁₉×C₄⋊C₈	—	2	1	no	—
57	C₁₉×C₄⋊C₈	—	2	1	no	—
58	C₄×C₈×C₁₉	—	2	1	no	—
59	C₄×C₈×C₁₉	D₄	1	2	yes	—
60	C₁₉⋊#95	—	2	2	no	—
61	C₁₉⋊#95	—	2	2	no	—
62	#10597272	—	2	8	no	—
63	Dic₁₉⋊C₈	—	4	4	no	—
64	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
65	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
66	C₄×C₁₉⋊C₈	—	2	1	no	—
67	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
68	C₂³×D₁₉	—	2	1	no	—
69	C₂×Q₈×C₁₉	—	2	1	no	—
70	C₂×Q₈×C₁₉	—	2	1	no	—
71	C₂×Q₈×C₁₉	—	2	1	no	—
72	C₂×Q₈×C₁₉	—	2	1	no	—
73	C₂×Q₈×C₁₉	—	2	1	no	—
74	C₂×Q₈×C₁₉	M₁₆	1	2	yes	—
75	C₂²×C₄×C₁₉	—	2	1	no	—
76	C₂²×C₄×C₁₉	—	2	1	no	—
77	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
80	C₂²×Dic₁₉	—	2	1	no	—
81	C₂²×Dic₁₉	C₂²⋊C₄	1	2	yes	—
82	C₂²×Dic₁₉	C₂²⋊C₄	1	2	yes	—
83	C₂×D₇₆	—	2	1	no	—
84	C₂×D₇₆	—	2	1	no	—
85	C₂×D₇₆	—	2	1	no	—
86	C₂×D₇₆	—	2	1	no	—
87	C₂×D₇₆	—	2	1	no	—
88	C₂×D₇₆	M₁₆	1	2	yes	—
89	C₂×C₄×D₁₉	—	4	1	no	—
90	C₂×C₄×D₁₉	—	4	1	no	—
91	C₂×C₄×D₁₉	—	4	2	no	—
92	C₂×C₄×D₁₉	—	4	2	no	—
93	C₂×C₈×C₁₉	—	2	4	no	—
94	C₂×C₈×C₁₉	—	2	2	no	—
95	C₂×C₈×C₁₉	—	4	1	no	—
96	C₂×C₈×C₁₉	—	4	2	no	—
97	C₄⋊C₄×C₁₉	—	2	1	no	—
98	C₄⋊C₄×C₁₉	—	2	1	no	—
99	C₄⋊C₄×C₁₉	—	4	1	no	—
100	C₄⋊C₄×C₁₉	—	4	1	no	—
101	C₄²×C₁₉	—	4	1	no	—
102	C₄²×C₁₉	—	4	1	no	—
103	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
104	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
105	C₄²×C₁₉	#41	1	1	yes	characteristic
106	C₄²×C₁₉	#41	1	1	yes	characteristic
107	(C₂×D₁₉)⋊C₄	—	2	8	no	—
108	(C₂×D₁₉)⋊C₄	—	4	1	no	—
109	(C₂×D₁₉)⋊C₄	—	4	1	no	—
110	(C₂×D₁₉)⋊C₄	—	4	4	no	—
111	C₄⋊Dic₁₉	—	2	1	no	—
112	C₄⋊Dic₁₉	—	2	1	no	—
113	C₄×Dic₁₉	—	2	1	no	—
114	C₄×Dic₁₉	—	2	1	no	—
115	C₄×Dic₁₉	—	2	1	no	—
116	C₄×Dic₁₉	—	2	1	no	—
117	C₄×Dic₁₉	—	2	2	no	—
118	C₄×Dic₁₉	—	2	2	no	—
119	C₄×Dic₁₉	—	2	4	no	—
120	C₂×C₁₉⋊C₈	—	2	4	no	—
121	C₂×C₁₉⋊C₈	—	2	2	no	—
122	C₂×C₁₉⋊C₈	—	4	1	no	—
123	C₂×C₁₉⋊C₈	—	4	2	no	—
124	#9646	—	19	1	no	maximal, Sylow
125	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
126	C₂²×D₁₉	—	2	2	no	—
127	C₂²×D₁₉	—	4	1	no	—
128	C₂²×D₁₉	—	4	1	no	—
129	C₂²×D₁₉	—	4	2	no	—
130	C₂²×D₁₉	—	4	2	no	—
131	Q₈×C₁₉	—	2	2	no	—
132	Q₈×C₁₉	—	2	2	no	—
133	Q₈×C₁₉	—	4	1	no	—
134	Q₈×C₁₉	—	4	1	no	—
135	C₂×C₄×C₁₉	—	2	2	no	—
136	C₂×C₄×C₁₉	—	2	2	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	2	no	—
141	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
142	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
143	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
144	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
145	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
146	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
147	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
148	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
149	C₂×C₄×C₁₉	#131	1	1	yes	characteristic
150	C₂×C₄×C₁₉	#131	1	1	yes	characteristic
151	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
152	C₂×C₄×C₁₉	#137	1	2	yes	—
153	C₂×Dic₁₉	—	2	2	no	—
154	C₂×Dic₁₉	—	2	2	no	—
155	C₂×Dic₁₉	—	2	2	no	—
156	C₂×Dic₁₉	—	2	2	no	—
157	C₂×Dic₁₉	—	2	2	no	—
158	C₂×Dic₁₉	—	4	1	no	—
159	C₂×Dic₁₉	—	4	2	no	—
160	C₂×Dic₁₉	#104	1	4	yes	—
161	D₇₆	—	2	2	no	—
162	D₇₆	—	2	2	no	—
163	D₇₆	—	4	1	no	—
164	D₇₆	—	4	1	no	—
165	C₄×D₁₉	—	8	2	no	—
166	C₄×D₁₉	—	8	1	no	—
167	C₄×D₁₉	—	8	1	no	—
168	C₈×C₁₉	—	2	4	no	—
169	C₈×C₁₉	—	8	1	no	—
170	C₁₉⋊C₈	—	2	4	no	—
171	C₁₉⋊C₈	—	8	1	no	—
172	C₄×#124	—	19	1	no	—
173	#1842	—	19	1	no	—
174	C₄×#97	—	19	1	no	—
175	C₂×Q₈⋊C₈	—	19	1	no	—
176	C₂×Q₈⋊C₈	D₁₉	1	1	yes	characteristic, complemented
177	C₂×D₄⋊C₈	—	19	1	no	—
178	C₂×D₄⋊C₈	—	19	1	no	—
179	C₂²×C₁₉	#390	1	1	yes	characteristic
180	C₂²×C₁₉	#407	1	1	yes	characteristic
181	C₂²×C₁₉	#408	1	1	yes	characteristic
182	C₂²×C₁₉	#417	1	2	yes	—
183	C₂²×C₁₉	C₂×#104	1	2	yes	—
184	C₂×D₁₉	—	4	2	no	—
185	C₂×D₁₉	—	4	4	no	—
186	C₂×D₁₉	—	8	1	no	—
187	C₂×D₁₉	—	8	1	no	—
188	C₂×D₁₉	—	8	2	no	—
189	C₄×C₁₉	—	2	1	no	—
190	C₄×C₁₉	—	2	1	no	—
191	C₄×C₁₉	—	4	2	no	—
192	C₄×C₁₉	—	8	1	no	—
193	C₄×C₁₉	#435	1	1	yes	characteristic
194	C₄×C₁₉	#435	1	1	yes	characteristic
195	C₄×C₁₉	#435	1	1	yes	characteristic
196	C₄×C₁₉	#435	1	1	yes	characteristic
197	C₄×C₁₉	#489	1	2	yes	—
198	C₄×C₁₉	#496	1	1	yes	characteristic
199	C₄×C₁₉	#497	1	1	yes	characteristic
200	Dic₁₉	—	2	4	no	—
201	Dic₁₉	—	4	2	no	—
202	Dic₁₉	—	8	1	no	—
203	C₂×#124	—	19	1	no	—
204	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
205	C₂×C₄×D₄	—	19	1	no	—
206	C₂×C₄⋊C₈	—	19	1	no	—
207	C₂×C₄⋊C₈	—	38	2	no	—
208	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
209	C₂×#97	—	38	2	no	—
210	C₂×C₄×C₈	—	19	1	no	—
211	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
212	#391	—	19	1	no	—
213	#390	—	19	1	no	—
214	#388	—	38	2	no	—
215	#382	—	19	1	no	—
216	C₄×C₂²⋊C₄	—	38	2	no	—
217	C₄³	—	19	1	no	—
218	Q₈⋊C₈	—	2	2	no	—
219	Q₈⋊C₈	—	38	2	no	—
220	D₄⋊C₈	—	38	2	no	—
221	D₄⋊C₈	—	38	2	no	—
222	C₂×C₁₉	#1483	1	2	yes	—
223	C₂×C₁₉	#1489	1	2	yes	—
224	C₂×C₁₉	#1955	1	1	yes	characteristic
225	C₂×C₁₉	#1959	1	1	yes	characteristic
226	C₂×C₁₉	#1962	1	1	yes	characteristic
227	D₁₉	—	8	2	no	—
228	C₂²×Q₈	C₄×D₁₉	1	1	yes	characteristic
229	C₂²×D₄	—	19	1	no	—
230	C₂³×C₄	—	38	1	no	—
231	C₂²×C₈	—	2	1	no	—
232	C₂²×C₈	—	2	1	no	—
233	C₂²×C₈	—	38	1	no	—
234	C₂²×C₈	—	38	1	no	—
235	#124	—	38	2	no	—
236	#124	—	38	2	no	—
237	C₄×Q₈	—	2	1	no	—
238	C₄×Q₈	—	2	1	no	—
239	C₄×Q₈	—	2	1	no	—
240	C₄×Q₈	—	2	1	no	—
241	C₄×D₄	—	38	1	no	—
242	C₄×D₄	—	38	1	no	—
243	C₄×D₄	—	38	1	no	—
244	C₄×D₄	—	38	1	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	—	19	1	no	—
247	C₂×C₄⋊C₄	C₄×D₁₉	1	1	yes	characteristic
248	C₂×C₂²⋊C₄	—	38	2	no	—
249	C₂×C₂²⋊C₄	—	38	2	no	—
250	C₂×C₂²⋊C₄	—	38	1	no	—
251	C₂×C₄²	—	2	1	no	—
252	C₂×C₄²	—	19	1	no	—
253	C₂×C₄²	—	19	1	no	—
254	C₂×C₄²	—	19	2	no	—
255	C₂×C₄²	—	19	2	no	—
256	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
257	C₄⋊C₈	—	2	1	no	—
258	C₄⋊C₈	—	2	1	no	—
259	C₄⋊C₈	—	38	1	no	—
260	C₄⋊C₈	—	38	1	no	—
261	C₄⋊C₈	—	76	4	no	—
262	#97	—	38	8	no	—
263	C₄×C₈	—	2	1	no	—
264	C₄×C₈	—	19	2	no	—
265	C₄×C₈	—	38	1	no	—
266	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
267	#95	—	38	2	no	—
268	#95	—	38	2	no	—
269	C₁₉	#9646	1	1	yes	characteristic, complemented, Sylow
270	C₂⁴	—	38	1	no	—
271	C₂×Q₈	—	2	1	no	—
272	C₂×Q₈	—	2	1	no	—
273	C₂×Q₈	—	2	1	no	—
274	C₂×Q₈	—	2	1	no	—
275	C₂×Q₈	—	2	1	no	—
276	C₂×Q₈	#64515	1	2	yes	—
277	C₂×D₄	—	19	2	no	—
278	C₂×D₄	—	38	1	no	—
279	C₂×D₄	—	38	1	no	—
280	C₂×D₄	—	38	1	no	—
281	C₂×D₄	—	38	1	no	—
282	C₂×D₄	—	38	1	no	—
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	—	2	1	no	—
285	C₂²×C₄	—	19	2	no	—
286	C₂²×C₄	—	19	2	no	—
287	C₂²×C₄	—	38	1	no	—
288	C₂²×C₄	—	76	1	no	—
289	C₂²×C₄	—	76	1	no	—
290	C₂²×C₄	—	76	2	no	—
291	C₂²×C₄	—	76	2	no	—
292	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
293	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
294	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
295	C₂×C₈	—	2	4	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	4	1	no	—
298	C₂×C₈	—	4	2	no	—
299	C₂×C₈	—	38	4	no	—
300	C₂×C₈	—	38	2	no	—
301	C₂×C₈	—	76	1	no	—
302	C₂×C₈	—	76	2	no	—
303	C₄⋊C₄	—	2	1	no	—
304	C₄⋊C₄	—	2	1	no	—
305	C₄⋊C₄	—	4	1	no	—
306	C₄⋊C₄	—	4	1	no	—
307	C₄⋊C₄	—	38	1	no	—
308	C₄⋊C₄	—	38	1	no	—
309	C₂²⋊C₄	—	38	8	no	—
310	C₂²⋊C₄	—	76	4	no	—
311	C₂²⋊C₄	—	76	1	no	—
312	C₂²⋊C₄	—	76	1	no	—
313	C₄²	—	4	1	no	—
314	C₄²	—	4	1	no	—
315	C₄²	—	38	4	no	—
316	C₄²	—	38	1	no	—
317	C₄²	—	38	1	no	—
318	C₄²	—	38	1	no	—
319	C₄²	—	38	1	no	—
320	C₄²	—	38	2	no	—
321	C₄²	—	38	2	no	—
322	C₄²	#64541	1	1	yes	characteristic
323	C₄²	D₄×D₁₉	1	1	yes	characteristic
324	C₄²	#64543	1	1	yes	characteristic
325	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
326	C₂³	—	38	2	no	—
327	C₂³	—	76	2	no	—
328	C₂³	—	76	2	no	—
329	C₂³	—	76	1	no	—
330	C₂³	—	76	1	no	—
331	C₂³	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
332	Q₈	—	2	2	no	—
333	Q₈	—	2	2	no	—
334	Q₈	—	4	1	no	—
335	Q₈	—	4	1	no	—
336	D₄	—	38	2	no	—
337	D₄	—	38	2	no	—
338	D₄	—	76	1	no	—
339	D₄	—	76	1	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	2	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	19	4	no	—
347	C₂×C₄	—	38	2	no	—
348	C₂×C₄	—	38	2	no	—
349	C₂×C₄	—	38	2	no	—
350	C₂×C₄	—	38	2	no	—
351	C₂×C₄	—	38	2	no	—
352	C₂×C₄	—	76	2	no	—
353	C₂×C₄	—	76	1	no	—
354	C₂×C₄	—	152	2	no	—
355	C₂×C₄	—	152	1	no	—
356	C₂×C₄	—	152	1	no	—
357	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
358	C₂×C₄	#10597330	1	1	yes	characteristic
359	C₂×C₄	#10597331	1	1	yes	characteristic
360	C₂×C₄	C₂×#64515	1	1	yes	characteristic
361	C₂×C₄	#10597347	1	1	yes	characteristic
362	C₂×C₄	M₁₆×D₁₉	1	1	yes	characteristic
363	C₂×C₄	#10597353	1	1	yes	characteristic
364	C₂×C₄	#10597360	1	2	yes	—
365	C₂×C₄	#10597364	1	2	yes	—
366	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
367	C₂×C₄	#10597385	1	1	yes	characteristic
368	C₂×C₄	#10597386	1	1	yes	characteristic
369	C₈	—	2	4	no	—
370	C₈	—	8	1	no	—
371	C₈	—	38	4	no	—
372	C₈	—	152	1	no	—
373	C₂²	—	76	4	no	—
374	C₂²	—	76	2	no	—
375	C₂²	—	152	1	no	—
376	C₂²	—	152	1	no	—
377	C₂²	—	152	2	no	—
378	C₂²	#11926444	1	1	yes	characteristic
379	C₂²	#11926506	1	1	yes	characteristic
380	C₂²	#11926509	1	1	yes	characteristic
381	C₂²	#11926544	1	2	yes	—
382	C₂²	#104×D₁₉	1	2	yes	—
383	C₄	—	2	1	no	—
384	C₄	—	2	1	no	—
385	C₄	—	4	2	no	—
386	C₄	—	8	1	no	—
387	C₄	—	38	4	no	—
388	C₄	—	76	2	no	—
389	C₄	—	152	1	no	—
390	C₄	#11926612	1	1	yes	characteristic
391	C₄	#11926613	1	1	yes	characteristic
392	C₄	#11926615	1	1	yes	characteristic
393	C₄	#11926618	1	1	yes	characteristic
394	C₄	#11926905	1	2	yes	—
395	C₄	#11926930	1	1	yes	characteristic
396	C₄	#11926937	1	1	yes	characteristic
397	C₂	—	152	2	no	—
398	C₂	#14562047	1	2	yes	—
399	C₂	#14562073	1	2	yes	—
400	C₂	#14564431	1	1	yes	characteristic
401	C₂	#14564448	1	1	yes	characteristic
402	C₂	#14564461	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×Q₈⋊C₈	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂²×D₇₆	C₂×C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×Q₈⋊C₈	D₁₉
hypocenter	C₁₉	#9646
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×Q₈⋊C₈

Complements

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

N	H ≅ G/N	type
2. #14563786	C₂	semidirect
3. C₄×#10597272	C₂	semidirect
4. C₂×Q₈⋊(C₁₉⋊C₈)	C₂	semidirect
7. C₂×C₁₉×Q₈⋊C₈	C₂	semidirect
176. C₂×Q₈⋊C₈	D₁₉	semidirect
269. C₁₉	#9646	semidirect

Maximal subgroups

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

subgroup	index
C₄×#10597393	2
#14563786	2
C₄×#10597272	2
C₂×Q₈⋊(C₁₉⋊C₈)	2
C₂×#11926273	2
C₂×#11926271	2
C₂×C₁₉×Q₈⋊C₈	2
#9646	19