Subgroups — C₁₉×#33850 #18039809

Order 4864.

686 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#508	C₂	1	2	yes	maximal, complemented
2	C₁₉×#3287	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3283	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2248	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2217	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2209	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2206	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2189	C₂	1	2	yes	maximal, complemented
9	C₁₉×#2186	C₂	1	2	yes	maximal, complemented
10	C₄×C₁₉×SD₃₂	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×C₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×#135	C₂²	1	2	yes	—
13	C₂×C₁₉×#135	C₂²	1	2	yes	—
14	C₁₉×#550	—	2	1	no	—
15	C₁₉×#547	—	2	1	no	—
16	C₁₉×#508	—	2	8	no	—
17	C₂×C₁₉×Q₃₂	C₂²	1	2	yes	—
18	C₂×C₁₉×SD₃₂	C₂²	1	2	yes	—
19	C₂×C₁₉×SD₃₂	C₂²	1	2	yes	—
20	C₂×C₁₉×SD₃₂	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×D₁₆	C₂²	1	2	yes	—
22	C₂²×C₁₆×C₁₉	C₂²	1	2	yes	—
23	C₁₉×#494	C₂²	1	1	yes	characteristic
24	C₁₉×#493	C₂²	1	1	yes	characteristic
25	C₁₉×#467	C₂²	1	2	yes	—
26	C₁₉×#466	C₂²	1	2	yes	—
27	C₁₉×#461	—	2	1	no	—
28	C₁₉×#460	—	2	1	no	—
29	C₁₉×#452	—	2	2	no	—
30	C₁₉×#449	—	2	2	no	—
31	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
32	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
33	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
34	C₁₉×#367	C₂²	1	1	yes	characteristic
35	C₁₉×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
36	C₁₉×#358	C₂²	1	1	yes	characteristic
37	C₁₉×#358	C₂²	1	2	yes	—
38	C₁₉×#357	C₂²	1	1	yes	characteristic
39	C₁₉×#357	C₂²	1	2	yes	—
40	C₁₉×C₂²⋊C₁₆	C₂²	1	2	yes	—
41	C₄×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
42	C₂×#41×C₁₉	—	2	2	no	—
43	C₂×#41×C₁₉	—	2	2	no	—
44	C₁₉×#135	—	2	4	no	—
45	C₁₉×#135	—	2	4	no	—
46	C₁₉×#135	—	4	2	no	—
47	C₁₉×#135	—	4	2	no	—
48	C₂×Q₁₆×C₁₉	—	2	1	no	—
49	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
50	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
51	C₂×SD₁₆×C₁₉	—	2	2	no	—
52	C₂×SD₁₆×C₁₉	—	2	2	no	—
53	C₂×D₈×C₁₉	—	2	1	no	—
54	C₂×D₈×C₁₉	C₂³	1	2	yes	—
55	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
57	C₁₉×C₄⋊Q₈	—	2	1	no	—
58	C₁₉×#127	—	2	1	no	—
59	C₁₉×#127	—	4	1	no	—
60	C₁₉×#123	—	4	2	no	—
61	C₁₉×C₂²⋊Q₈	—	2	2	no	—
62	C₁₉×#121	—	2	2	no	—
63	C₁₉×#121	—	4	1	no	—
64	C₁₉×#121	—	4	2	no	—
65	C₄×Q₈×C₁₉	—	2	1	no	—
66	C₄×D₄×C₁₉	—	2	1	no	—
67	C₄×D₄×C₁₉	—	4	1	no	—
68	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
70	C₁₉×Q₃₂	—	2	4	no	—
71	C₁₉×SD₃₂	—	2	4	no	—
72	C₁₉×SD₃₂	—	4	2	no	—
73	C₁₉×SD₃₂	D₄	1	4	yes	complemented
74	C₁₉×D₁₆	—	2	4	no	—
75	C₂×C₁₆×C₁₉	—	2	4	no	—
76	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
77	C₂×C₁₆×C₁₉	C₂³	1	2	yes	—
78	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
79	C₁₉×#107	C₂³	1	1	yes	characteristic
80	C₁₉×#107	C₂³	1	1	yes	characteristic
81	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
82	C₁₉×#103	—	2	1	no	—
83	C₁₉×#103	—	2	2	no	—
84	C₁₉×#102	—	2	1	no	—
85	C₁₉×#102	—	2	2	no	—
86	C₁₉×C₂²⋊C₈	D₄	1	2	yes	—
87	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
88	#41×C₁₉	—	4	4	no	—
89	#41×C₁₉	—	4	4	no	—
90	#41×C₁₉	—	8	2	no	—
91	#41×C₁₉	—	8	2	no	—
92	C₂×Q₈×C₁₉	—	2	1	no	—
93	C₂×Q₈×C₁₉	—	2	2	no	—
94	C₂×D₄×C₁₉	—	2	1	no	—
95	C₂×D₄×C₁₉	—	2	2	no	—
96	C₂×D₄×C₁₉	—	4	2	no	—
97	C₂×D₄×C₁₉	—	4	2	no	—
98	C₂×D₄×C₁₉	—	4	2	no	—
99	C₂×D₄×C₁₉	—	4	1	no	—
100	C₂×D₄×C₁₉	—	4	1	no	—
101	C₂×D₄×C₁₉	D₈	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	—	4	1	no	—
103	C₂²×C₄×C₁₉	—	4	2	no	—
104	C₂²×C₄×C₁₉	—	4	2	no	—
105	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
106	Q₁₆×C₁₉	—	2	2	no	—
107	Q₁₆×C₁₉	—	2	1	no	—
108	Q₁₆×C₁₉	—	2	2	no	—
109	Q₁₆×C₁₉	—	8	1	no	—
110	Q₁₆×C₁₉	C₂×D₄	1	2	yes	—
111	SD₁₆×C₁₉	—	4	4	no	—
112	SD₁₆×C₁₉	—	4	4	no	—
113	D₈×C₁₉	—	2	2	no	—
114	D₈×C₁₉	—	2	1	no	—
115	D₈×C₁₉	—	2	2	no	—
116	D₈×C₁₉	—	8	1	no	—
117	D₈×C₁₉	C₂×D₄	1	2	yes	—
118	C₂×C₈×C₁₉	—	2	2	no	—
119	C₂×C₈×C₁₉	—	2	2	no	—
120	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
121	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
123	C₄⋊C₄×C₁₉	—	2	1	no	—
124	C₄⋊C₄×C₁₉	—	2	1	no	—
125	C₄⋊C₄×C₁₉	—	4	1	no	—
126	C₄⋊C₄×C₁₉	—	4	2	no	—
127	C₄⋊C₄×C₁₉	—	4	1	no	—
128	C₄⋊C₄×C₁₉	—	4	1	no	—
129	C₄⋊C₄×C₁₉	D₈	1	1	yes	characteristic
130	C₂²⋊C₄×C₁₉	—	4	2	no	—
131	C₂²⋊C₄×C₁₉	—	4	1	no	—
132	C₂²⋊C₄×C₁₉	—	4	2	no	—
133	C₂²⋊C₄×C₁₉	D₈	1	2	yes	—
134	C₄²×C₁₉	—	4	1	no	—
135	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
136	C₁₆×C₁₉	—	2	2	no	—
137	C₁₆×C₁₉	—	2	1	no	—
138	C₁₆×C₁₉	C₂×D₄	1	2	yes	—
139	#33850	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
140	C₂³×C₁₉	—	4	1	no	—
141	C₂³×C₁₉	—	4	2	no	—
142	C₂³×C₁₉	C₂×D₈	1	2	yes	—
143	Q₈×C₁₉	—	2	2	no	—
144	Q₈×C₁₉	—	4	1	no	—
145	Q₈×C₁₉	—	4	2	no	—
146	Q₈×C₁₉	—	4	2	no	—
147	D₄×C₁₉	—	2	2	no	—
148	D₄×C₁₉	—	2	2	no	—
149	D₄×C₁₉	—	4	2	no	—
150	D₄×C₁₉	—	4	1	no	—
151	D₄×C₁₉	—	4	2	no	—
152	D₄×C₁₉	—	8	4	no	—
153	D₄×C₁₉	—	8	4	no	—
154	D₄×C₁₉	—	8	2	no	—
155	D₄×C₁₉	—	16	1	no	—
156	D₄×C₁₉	—	16	2	no	—
157	C₂×C₄×C₁₉	—	2	2	no	—
158	C₂×C₄×C₁₉	—	2	2	no	—
159	C₂×C₄×C₁₉	—	4	1	no	—
160	C₂×C₄×C₁₉	—	4	1	no	—
161	C₂×C₄×C₁₉	—	4	1	no	—
162	C₂×C₄×C₁₉	—	4	2	no	—
163	C₂×C₄×C₁₉	—	8	4	no	—
164	C₂×C₄×C₁₉	—	8	4	no	—
165	C₂×C₄×C₁₉	—	8	2	no	—
166	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
167	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
168	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
169	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
170	C₈×C₁₉	—	2	2	no	—
171	C₈×C₁₉	—	2	1	no	—
172	C₈×C₁₉	C₂²×D₄	1	1	yes	characteristic
173	C₈×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
174	C₂×#508	C₂×C₁₉	1	2	yes	complemented
175	#3287	C₂×C₁₉	1	1	yes	characteristic, complemented
176	#3283	C₂×C₁₉	1	1	yes	characteristic, complemented
177	#2248	C₂×C₁₉	1	1	yes	characteristic, complemented
178	#2217	C₂×C₁₉	1	2	yes	complemented
179	#2209	C₂×C₁₉	1	1	yes	characteristic, complemented
180	#2206	C₂×C₁₉	1	1	yes	characteristic, complemented
181	#2189	C₂×C₁₉	1	2	yes	complemented
182	#2186	C₂×C₁₉	1	2	yes	complemented
183	C₄×SD₃₂	C₂×C₁₉	1	1	yes	characteristic, complemented
184	D₄×C₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
185	C₂²×C₁₉	—	2	2	no	—
186	C₂²×C₁₉	—	2	2	no	—
187	C₂²×C₁₉	—	2	2	no	—
188	C₂²×C₁₉	—	4	2	no	—
189	C₂²×C₁₉	—	8	1	no	—
190	C₂²×C₁₉	—	8	1	no	—
191	C₂²×C₁₉	—	8	2	no	—
192	C₂²×C₁₉	—	8	2	no	—
193	C₂²×C₁₉	—	8	2	no	—
194	C₂²×C₁₉	C₂²×D₈	1	1	yes	characteristic
195	C₄×C₁₉	—	2	1	no	—
196	C₄×C₁₉	—	2	2	no	—
197	C₄×C₁₉	—	4	2	no	—
198	C₄×C₁₉	—	8	1	no	—
199	C₄×C₁₉	—	8	1	no	—
200	C₄×C₁₉	—	8	2	no	—
201	C₄×C₁₉	#508	1	2	yes	complemented
202	C₄×C₁₉	D₄²	1	1	yes	characteristic
203	C₄×C₁₉	#576	1	1	yes	characteristic
204	C₂×#135	C₂²×C₁₉	1	2	yes	—
205	C₂×#135	C₂²×C₁₉	1	2	yes	—
206	#550	—	2	1	no	—
207	#547	—	2	1	no	—
208	#508	—	2	8	no	—
209	C₂×Q₃₂	C₂²×C₁₉	1	2	yes	—
210	C₂×SD₃₂	C₂²×C₁₉	1	2	yes	—
211	C₂×SD₃₂	C₂²×C₁₉	1	2	yes	—
212	C₂×SD₃₂	C₂²×C₁₉	1	1	yes	characteristic
213	C₂×D₁₆	C₂²×C₁₉	1	2	yes	—
214	C₂²×C₁₆	C₂²×C₁₉	1	2	yes	—
215	#494	C₂²×C₁₉	1	1	yes	characteristic
216	#493	C₂²×C₁₉	1	1	yes	characteristic
217	#467	C₂²×C₁₉	1	2	yes	—
218	#466	C₂²×C₁₉	1	2	yes	—
219	#461	—	2	1	no	—
220	#460	—	2	1	no	—
221	#452	—	2	2	no	—
222	#449	—	2	2	no	—
223	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
224	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
225	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
226	#367	C₂²×C₁₉	1	1	yes	characteristic
227	C₄⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic
228	#358	C₂²×C₁₉	1	1	yes	characteristic
229	#358	C₂²×C₁₉	1	2	yes	—
230	#357	C₂²×C₁₉	1	1	yes	characteristic
231	#357	C₂²×C₁₉	1	2	yes	—
232	C₂²⋊C₁₆	C₂²×C₁₉	1	2	yes	—
233	C₄×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
234	C₂×C₁₉	—	4	2	no	—
235	C₂×C₁₉	—	8	2	no	—
236	C₂×C₁₉	—	16	2	no	—
237	C₂×C₁₉	D₄×D₈	1	1	yes	characteristic
238	C₂×C₁₉	C₂×#508	1	1	yes	characteristic
239	C₂×C₁₉	#3416	1	1	yes	characteristic
240	C₂×#41	—	2	2	no	—
241	C₂×#41	—	2	2	no	—
242	#135	—	2	4	no	—
243	#135	—	2	4	no	—
244	#135	—	4	2	no	—
245	#135	—	4	2	no	—
246	C₂×Q₁₆	—	2	1	no	—
247	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
248	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
249	C₂×SD₁₆	—	2	2	no	—
250	C₂×SD₁₆	—	2	2	no	—
251	C₂×D₈	—	2	1	no	—
252	C₂×D₈	C₂³×C₁₉	1	2	yes	—
253	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
254	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
255	C₄⋊Q₈	—	2	1	no	—
256	#127	—	2	1	no	—
257	#127	—	4	1	no	—
258	#123	—	4	2	no	—
259	C₂²⋊Q₈	—	2	2	no	—
260	#121	—	2	2	no	—
261	#121	—	4	1	no	—
262	#121	—	4	2	no	—
263	C₄×Q₈	—	2	1	no	—
264	C₄×D₄	—	2	1	no	—
265	C₄×D₄	—	4	1	no	—
266	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
267	C₂×C₄⋊C₄	—	4	1	no	—
268	Q₃₂	—	2	4	no	—
269	SD₃₂	—	2	4	no	—
270	SD₃₂	—	4	2	no	—
271	SD₃₂	D₄×C₁₉	1	4	yes	complemented
272	D₁₆	—	2	4	no	—
273	C₂×C₁₆	—	2	4	no	—
274	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
275	C₂×C₁₆	C₂³×C₁₉	1	2	yes	—
276	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
277	#107	C₂³×C₁₉	1	1	yes	characteristic
278	#107	C₂³×C₁₉	1	1	yes	characteristic
279	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
280	#103	—	2	1	no	—
281	#103	—	2	2	no	—
282	#102	—	2	1	no	—
283	#102	—	2	2	no	—
284	C₂²⋊C₈	D₄×C₁₉	1	2	yes	—
285	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
286	C₁₉	#33850	1	1	yes	characteristic, direct product factor, Sylow
287	#41	—	4	4	no	—
288	#41	—	4	4	no	—
289	#41	—	8	2	no	—
290	#41	—	8	2	no	—
291	C₂×Q₈	—	2	1	no	—
292	C₂×Q₈	—	2	2	no	—
293	C₂×D₄	—	2	1	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	4	2	no	—
296	C₂×D₄	—	4	2	no	—
297	C₂×D₄	—	4	2	no	—
298	C₂×D₄	—	4	1	no	—
299	C₂×D₄	—	4	1	no	—
300	C₂×D₄	D₈×C₁₉	1	1	yes	characteristic
301	C₂²×C₄	—	4	1	no	—
302	C₂²×C₄	—	4	2	no	—
303	C₂²×C₄	—	4	2	no	—
304	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
305	Q₁₆	—	2	2	no	—
306	Q₁₆	—	2	1	no	—
307	Q₁₆	—	2	2	no	—
308	Q₁₆	—	8	1	no	—
309	Q₁₆	C₂×D₄×C₁₉	1	2	yes	—
310	SD₁₆	—	4	4	no	—
311	SD₁₆	—	4	4	no	—
312	D₈	—	2	2	no	—
313	D₈	—	2	1	no	—
314	D₈	—	2	2	no	—
315	D₈	—	8	1	no	—
316	D₈	C₂×D₄×C₁₉	1	2	yes	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
320	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
321	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	—	2	1	no	—
324	C₄⋊C₄	—	4	1	no	—
325	C₄⋊C₄	—	4	2	no	—
326	C₄⋊C₄	—	4	1	no	—
327	C₄⋊C₄	—	4	1	no	—
328	C₄⋊C₄	D₈×C₁₉	1	1	yes	characteristic
329	C₂²⋊C₄	—	4	2	no	—
330	C₂²⋊C₄	—	4	1	no	—
331	C₂²⋊C₄	—	4	2	no	—
332	C₂²⋊C₄	D₈×C₁₉	1	2	yes	—
333	C₄²	—	4	1	no	—
334	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
335	C₁₆	—	2	2	no	—
336	C₁₆	—	2	1	no	—
337	C₁₆	C₂×D₄×C₁₉	1	2	yes	—
338	C₂³	—	4	1	no	—
339	C₂³	—	4	2	no	—
340	C₂³	C₂×D₈×C₁₉	1	2	yes	—
341	Q₈	—	2	2	no	—
342	Q₈	—	4	1	no	—
343	Q₈	—	4	2	no	—
344	Q₈	—	4	2	no	—
345	D₄	—	2	2	no	—
346	D₄	—	2	2	no	—
347	D₄	—	4	2	no	—
348	D₄	—	4	1	no	—
349	D₄	—	4	2	no	—
350	D₄	—	8	4	no	—
351	D₄	—	8	4	no	—
352	D₄	—	8	2	no	—
353	D₄	—	16	1	no	—
354	D₄	—	16	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	8	4	no	—
362	C₂×C₄	—	8	4	no	—
363	C₂×C₄	—	8	2	no	—
364	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
365	C₂×C₄	C₂×D₈×C₁₉	1	2	yes	—
366	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
367	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
368	C₈	—	2	2	no	—
369	C₈	—	2	1	no	—
370	C₈	C₂²×D₄×C₁₉	1	1	yes	characteristic
371	C₈	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
372	C₂²	—	2	2	no	—
373	C₂²	—	2	2	no	—
374	C₂²	—	2	2	no	—
375	C₂²	—	4	2	no	—
376	C₂²	—	8	1	no	—
377	C₂²	—	8	1	no	—
378	C₂²	—	8	2	no	—
379	C₂²	—	8	2	no	—
380	C₂²	—	8	2	no	—
381	C₂²	C₂²×D₈×C₁₉	1	1	yes	characteristic
382	C₄	—	2	2	no	—
383	C₄	—	2	1	no	—
384	C₄	—	4	2	no	—
385	C₄	—	8	2	no	—
386	C₄	—	8	1	no	—
387	C₄	—	8	1	no	—
388	C₄	C₁₉×#508	1	2	yes	complemented
389	C₄	D₄²×C₁₉	1	1	yes	characteristic
390	C₄	C₁₉×#576	1	1	yes	characteristic
391	C₂	—	4	2	no	—
392	C₂	—	8	2	no	—
393	C₂	—	16	2	no	—
394	C₂	D₄×D₈×C₁₉	1	1	yes	characteristic
395	C₂	C₂×C₁₉×#508	1	1	yes	characteristic
396	C₂	C₁₉×#3416	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₉
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄×D₄×C₁₉ ◁ C₈×D₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#508	C₂	semidirect
2. C₁₉×#3287	C₂	semidirect
3. C₁₉×#3283	C₂	semidirect
4. C₁₉×#2248	C₂	semidirect
5. C₁₉×#2217	C₂	semidirect
6. C₁₉×#2209	C₂	semidirect
7. C₁₉×#2206	C₂	semidirect
8. C₁₉×#2189	C₂	semidirect
9. C₁₉×#2186	C₂	semidirect
10. C₄×C₁₉×SD₃₂	C₂	semidirect
11. D₄×C₁₆×C₁₉	C₂	semidirect
73. C₁₉×SD₃₂	D₄	semidirect
139. #33850	C₁₉	direct (N × H)
174. C₂×#508	C₂×C₁₉	semidirect
175. #3287	C₂×C₁₉	semidirect
176. #3283	C₂×C₁₉	semidirect
177. #2248	C₂×C₁₉	semidirect
178. #2217	C₂×C₁₉	semidirect
179. #2209	C₂×C₁₉	semidirect
180. #2206	C₂×C₁₉	semidirect
181. #2189	C₂×C₁₉	semidirect
182. #2186	C₂×C₁₉	semidirect
183. C₄×SD₃₂	C₂×C₁₉	semidirect
184. D₄×C₁₆	C₂×C₁₉	semidirect
201. C₄×C₁₉	#508	semidirect
271. SD₃₂	D₄×C₁₉	semidirect
286. C₁₉	#33850	direct (N × H)
388. C₄	C₁₉×#508	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#508	2
C₁₉×#3287	2
C₁₉×#3283	2
C₁₉×#2248	2
C₁₉×#2217	2
C₁₉×#2209	2
C₁₉×#2206	2
C₁₉×#2189	2
C₁₉×#2186	2
C₄×C₁₉×SD₃₂	2
D₄×C₁₆×C₁₉	2
#33850	19

Subgroups — C19×#33850 #18039809

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#33850 #18039809