Subgroups — C₁₉×#61100 #18067059

Order 4864.

2616 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3584	C₂	1	4	yes	maximal, complemented
2	C₁₉×#3289	C₂	1	8	yes	maximal, complemented
3	C₁₉×#3288	C₂	1	8	yes	maximal, complemented
4	C₁₉×#3150	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#3067	C₂	1	4	yes	maximal, complemented
6	C₁₉×#3018	C₂	1	4	yes	maximal, complemented
7	C₂×C₁₉×#444	C₂	1	2	yes	maximal, complemented
8	C₁₉×#585	C₂²	1	4	yes	complemented
9	C₁₉×#578	—	2	4	no	—
10	C₁₉×#578	C₂²	1	8	yes	complemented
11	C₁₉×#577	—	2	8	no	—
12	C₁₉×#577	C₂²	1	16	yes	complemented
13	C₁₉×#576	—	2	4	no	—
14	C₁₉×#576	C₂²	1	8	yes	complemented
15	C₁₉×#575	—	2	8	no	—
16	C₁₉×#575	C₂²	1	8	yes	complemented
17	C₂×C₁₉×#135	—	2	8	no	—
18	C₂×C₁₉×#135	C₂²	1	2	yes	—
19	C₂×C₁₉×#135	C₂²	1	4	yes	complemented
20	C₂×C₁₉×#131	C₂²	1	4	yes	complemented
21	C₁₉×#532	C₂²	1	2	yes	complemented
22	C₁₉×#497	C₂²	1	4	yes	complemented
23	C₁₉×#496	C₂²	1	4	yes	complemented
24	C₁₉×#473	C₂²	1	8	yes	complemented
25	C₁₉×#472	C₂²	1	8	yes	complemented
26	C₁₉×#471	C₂²	1	16	yes	complemented
27	C₁₉×#456	C₂²	1	8	yes	complemented
28	C₁₉×#455	C₂²	1	8	yes	complemented
29	C₁₉×#454	C₂²	1	8	yes	complemented
30	C₁₉×#453	C₂²	1	8	yes	complemented
31	C₁₉×#444	C₂²	1	16	yes	complemented
32	C₂×C₁₉×#108	C₂²	1	2	yes	complemented
33	C₂×C₁₉×#104	C₂²	1	4	yes	complemented
34	C₁₉×#413	C₂²	1	4	yes	complemented
35	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic, complemented
36	C₁₉×2₋¹⁺⁴	—	2	8	no	—
37	C₁₉×2₋¹⁺⁴	C₂³	1	8	yes	—
38	C₁₉×H(5,𝔽₂)	—	2	8	no	—
39	C₁₉×H(5,𝔽₂)	—	4	4	no	—
40	C₁₉×H(5,𝔽₂)	C₂³	1	8	yes	—
41	C₂×#41×C₁₉	—	2	16	no	—
42	C₂×#41×C₁₉	—	4	4	no	—
43	C₂×#41×C₁₉	C₂³	1	4	yes	—
44	C₂×#41×C₁₉	C₂³	1	4	yes	—
45	C₁₉×#137	—	2	8	no	—
46	C₁₉×#137	—	2	16	no	—
47	C₁₉×#137	—	2	16	no	—
48	C₁₉×#137	C₂³	1	16	yes	—
49	C₁₉×AGL(1,ℤ/8)	—	2	8	no	—
50	C₁₉×AGL(1,ℤ/8)	—	2	16	no	—
51	C₁₉×AGL(1,ℤ/8)	—	2	16	no	—
52	C₁₉×AGL(1,ℤ/8)	C₂³	1	16	yes	—
53	C₁₉×#135	—	2	16	no	—
54	C₁₉×#135	—	2	8	no	—
55	C₁₉×#135	—	2	16	no	—
56	C₁₉×#135	—	2	8	no	—
57	C₁₉×#135	—	2	4	no	—
58	C₁₉×#135	—	2	4	no	—
59	C₁₉×#135	—	2	4	no	—
60	C₁₉×#135	—	2	4	no	—
61	C₁₉×#135	D₄	1	8	yes	complemented
62	C₁₉×#135	C₂³	1	8	yes	—
63	C₂×Q₁₆×C₁₉	—	2	8	no	—
64	C₂×Q₁₆×C₁₉	D₄	1	2	yes	complemented
65	C₂×Q₁₆×C₁₉	C₂³	1	4	yes	—
66	C₂×SD₁₆×C₁₉	—	2	16	no	—
67	C₂×SD₁₆×C₁₉	D₄	1	4	yes	complemented
68	C₂×SD₁₆×C₁₉	C₂³	1	8	yes	—
69	C₂×D₈×C₁₉	—	2	8	no	—
70	C₂×D₈×C₁₉	D₄	1	2	yes	complemented
71	C₂×D₈×C₁₉	C₂³	1	4	yes	—
72	C₁₉×#131	—	2	4	no	—
73	C₁₉×#131	—	2	4	no	—
74	C₁₉×#131	C₂³	1	8	yes	—
75	C₁₉×#131	C₂³	1	8	yes	—
76	C₂×M₁₆×C₁₉	—	2	4	no	—
77	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
78	C₂²×C₈×C₁₉	—	2	4	no	—
79	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
80	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
81	C₁₉×#127	C₂³	1	2	yes	—
82	C₁₉×#124	C₂³	1	4	yes	—
83	C₁₉×#121	—	4	2	no	—
84	C₄×D₄×C₁₉	—	4	2	no	—
85	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
86	C₁₉×#108	C₂³	1	8	yes	—
87	C₁₉×#104	C₂³	1	16	yes	—
88	C₁₉×#101	C₂³	1	8	yes	—
89	C₁₉×#100	C₂³	1	8	yes	—
90	C₁₉×#97	C₂³	1	4	yes	—
91	#41×C₁₉	—	2	4	no	—
92	#41×C₁₉	—	2	4	no	—
93	#41×C₁₉	—	2	16	no	—
94	#41×C₁₉	—	2	16	no	—
95	#41×C₁₉	—	2	8	no	—
96	#41×C₁₉	—	2	8	no	—
97	#41×C₁₉	—	4	8	no	—
98	#41×C₁₉	—	4	8	no	—
99	#41×C₁₉	—	4	16	no	—
100	#41×C₁₉	—	4	8	no	—
101	#41×C₁₉	C₂×D₄	1	8	yes	—
102	#41×C₁₉	C₂⁴	1	8	yes	—
103	C₂×Q₈×C₁₉	—	2	16	no	—
104	C₂×Q₈×C₁₉	—	4	4	no	—
105	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
106	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
107	C₂×D₄×C₁₉	—	2	4	no	—
108	C₂×D₄×C₁₉	—	2	16	no	—
109	C₂×D₄×C₁₉	—	2	4	no	—
110	C₂×D₄×C₁₉	—	4	2	no	—
111	C₂×D₄×C₁₉	—	4	8	no	—
112	C₂×D₄×C₁₉	—	4	4	no	—
113	C₂×D₄×C₁₉	—	4	16	no	—
114	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
115	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
116	C₂²×C₄×C₁₉	—	2	4	no	—
117	C₂²×C₄×C₁₉	—	2	1	no	—
118	C₂²×C₄×C₁₉	—	2	4	no	—
119	C₂²×C₄×C₁₉	—	4	8	no	—
120	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
121	Q₁₆×C₁₉	—	2	16	no	—
122	Q₁₆×C₁₉	—	2	4	no	—
123	Q₁₆×C₁₉	—	2	4	no	—
124	Q₁₆×C₁₉	C₂×D₄	1	8	yes	—
125	SD₁₆×C₁₉	—	2	16	no	—
126	SD₁₆×C₁₉	—	2	16	no	—
127	SD₁₆×C₁₉	—	2	8	no	—
128	SD₁₆×C₁₉	—	2	8	no	—
129	SD₁₆×C₁₉	C₂×D₄	1	16	yes	—
130	D₈×C₁₉	—	2	16	no	—
131	D₈×C₁₉	—	2	4	no	—
132	D₈×C₁₉	—	2	4	no	—
133	D₈×C₁₉	C₂×D₄	1	8	yes	—
134	M₁₆×C₁₉	—	2	4	no	—
135	M₁₆×C₁₉	—	2	8	no	—
136	M₁₆×C₁₉	—	2	8	no	—
137	M₁₆×C₁₉	C₂⁴	1	8	yes	—
138	C₂×C₈×C₁₉	—	2	4	no	—
139	C₂×C₈×C₁₉	—	2	8	no	—
140	C₂×C₈×C₁₉	—	2	8	no	—
141	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
142	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
143	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
144	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
145	C₄⋊C₄×C₁₉	—	4	2	no	—
146	C₂²⋊C₄×C₁₉	—	4	4	no	—
147	C₄²×C₁₉	—	2	1	no	—
148	C₄²×C₁₉	C₂⁴	1	2	yes	—
149	#61100	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
150	C₂³×C₁₉	—	2	4	no	—
151	C₂³×C₁₉	—	2	4	no	—
152	C₂³×C₁₉	—	4	8	no	—
153	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
154	Q₈×C₁₉	—	2	4	no	—
155	Q₈×C₁₉	—	2	8	no	—
156	Q₈×C₁₉	—	4	8	no	—
157	Q₈×C₁₉	C₂²×D₄	1	8	yes	—
158	D₄×C₁₉	—	2	8	no	—
159	D₄×C₁₉	—	2	8	no	—
160	D₄×C₁₉	—	2	4	no	—
161	D₄×C₁₉	—	2	8	no	—
162	D₄×C₁₉	—	4	16	no	—
163	D₄×C₁₉	—	4	8	no	—
164	D₄×C₁₉	—	4	8	no	—
165	D₄×C₁₉	—	8	4	no	—
166	D₄×C₁₉	C₂²×D₄	1	8	yes	—
167	C₂×C₄×C₁₉	—	2	4	no	—
168	C₂×C₄×C₁₉	—	2	8	no	—
169	C₂×C₄×C₁₉	—	2	8	no	—
170	C₂×C₄×C₁₉	—	2	2	no	—
171	C₂×C₄×C₁₉	—	2	4	no	—
172	C₂×C₄×C₁₉	—	4	8	no	—
173	C₂×C₄×C₁₉	—	4	16	no	—
174	C₂×C₄×C₁₉	—	4	4	no	—
175	C₂×C₄×C₁₉	—	4	4	no	—
176	C₂×C₄×C₁₉	—	8	1	no	—
177	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
178	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
179	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
180	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
181	C₈×C₁₉	—	2	8	no	—
182	C₈×C₁₉	C₂²×D₄	1	4	yes	—
183	C₈×C₁₉	C₂²×D₄	1	4	yes	—
184	#3584	C₂×C₁₉	1	4	yes	complemented
185	#3289	C₂×C₁₉	1	8	yes	complemented
186	#3288	C₂×C₁₉	1	8	yes	complemented
187	#3150	C₂×C₁₉	1	1	yes	characteristic, complemented
188	#3067	C₂×C₁₉	1	4	yes	complemented
189	#3018	C₂×C₁₉	1	4	yes	complemented
190	C₂×#444	C₂×C₁₉	1	2	yes	complemented
191	C₂²×C₁₉	—	2	8	no	—
192	C₂²×C₁₉	—	4	1	no	—
193	C₂²×C₁₉	—	4	4	no	—
194	C₂²×C₁₉	—	8	4	no	—
195	C₂²×C₁₉	—	8	4	no	—
196	C₂²×C₁₉	—	16	8	no	—
197	C₂²×C₁₉	D₄²	1	2	yes	—
198	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
199	C₄×C₁₉	—	2	8	no	—
200	C₄×C₁₉	—	4	2	no	—
201	C₄×C₁₉	—	4	4	no	—
202	C₄×C₁₉	D₄²	1	1	yes	characteristic
203	C₄×C₁₉	D₄²	1	1	yes	characteristic
204	C₄×C₁₉	C₂³×D₄	1	2	yes	—
205	#585	C₂²×C₁₉	1	4	yes	complemented
206	#578	—	2	4	no	—
207	#578	C₂²×C₁₉	1	8	yes	complemented
208	#577	—	2	8	no	—
209	#577	C₂²×C₁₉	1	16	yes	complemented
210	#576	—	2	4	no	—
211	#576	C₂²×C₁₉	1	8	yes	complemented
212	#575	—	2	8	no	—
213	#575	C₂²×C₁₉	1	8	yes	complemented
214	C₂×#135	—	2	8	no	—
215	C₂×#135	C₂²×C₁₉	1	2	yes	—
216	C₂×#135	C₂²×C₁₉	1	4	yes	complemented
217	C₂×#131	C₂²×C₁₉	1	4	yes	complemented
218	#532	C₂²×C₁₉	1	2	yes	complemented
219	#497	C₂²×C₁₉	1	4	yes	complemented
220	#496	C₂²×C₁₉	1	4	yes	complemented
221	#473	C₂²×C₁₉	1	8	yes	complemented
222	#472	C₂²×C₁₉	1	8	yes	complemented
223	#471	C₂²×C₁₉	1	16	yes	complemented
224	#456	C₂²×C₁₉	1	8	yes	complemented
225	#455	C₂²×C₁₉	1	8	yes	complemented
226	#454	C₂²×C₁₉	1	8	yes	complemented
227	#453	C₂²×C₁₉	1	8	yes	complemented
228	#444	C₂²×C₁₉	1	16	yes	complemented
229	C₂×#108	C₂²×C₁₉	1	2	yes	complemented
230	C₂×#104	C₂²×C₁₉	1	4	yes	complemented
231	#413	C₂²×C₁₉	1	4	yes	complemented
232	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic, complemented
233	C₂×C₁₉	—	2	1	no	—
234	C₂×C₁₉	—	2	2	no	—
235	C₂×C₁₉	—	4	8	no	—
236	C₂×C₁₉	—	8	4	no	—
237	C₂×C₁₉	C₂×D₄²	1	1	yes	characteristic
238	2₋¹⁺⁴	—	2	8	no	—
239	2₋¹⁺⁴	C₂³×C₁₉	1	8	yes	—
240	H(5,𝔽₂)	—	2	8	no	—
241	H(5,𝔽₂)	—	4	4	no	—
242	H(5,𝔽₂)	C₂³×C₁₉	1	8	yes	—
243	C₂×#41	—	2	16	no	—
244	C₂×#41	—	4	4	no	—
245	C₂×#41	C₂³×C₁₉	1	4	yes	—
246	C₂×#41	C₂³×C₁₉	1	4	yes	—
247	#137	—	2	8	no	—
248	#137	—	2	16	no	—
249	#137	—	2	16	no	—
250	#137	C₂³×C₁₉	1	16	yes	—
251	AGL(1,ℤ/8)	—	2	8	no	—
252	AGL(1,ℤ/8)	—	2	16	no	—
253	AGL(1,ℤ/8)	—	2	16	no	—
254	AGL(1,ℤ/8)	C₂³×C₁₉	1	16	yes	—
255	#135	—	2	16	no	—
256	#135	—	2	8	no	—
257	#135	—	2	16	no	—
258	#135	—	2	8	no	—
259	#135	—	2	4	no	—
260	#135	—	2	4	no	—
261	#135	—	2	4	no	—
262	#135	—	2	4	no	—
263	#135	D₄×C₁₉	1	8	yes	complemented
264	#135	C₂³×C₁₉	1	8	yes	—
265	C₂×Q₁₆	—	2	8	no	—
266	C₂×Q₁₆	D₄×C₁₉	1	2	yes	complemented
267	C₂×Q₁₆	C₂³×C₁₉	1	4	yes	—
268	C₂×SD₁₆	—	2	16	no	—
269	C₂×SD₁₆	D₄×C₁₉	1	4	yes	complemented
270	C₂×SD₁₆	C₂³×C₁₉	1	8	yes	—
271	C₂×D₈	—	2	8	no	—
272	C₂×D₈	D₄×C₁₉	1	2	yes	complemented
273	C₂×D₈	C₂³×C₁₉	1	4	yes	—
274	#131	—	2	4	no	—
275	#131	—	2	4	no	—
276	#131	C₂³×C₁₉	1	8	yes	—
277	#131	C₂³×C₁₉	1	8	yes	—
278	C₂×M₁₆	—	2	4	no	—
279	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
280	C₂²×C₈	—	2	4	no	—
281	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
282	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
283	#127	C₂³×C₁₉	1	2	yes	—
284	#124	C₂³×C₁₉	1	4	yes	—
285	#121	—	4	2	no	—
286	C₄×D₄	—	4	2	no	—
287	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
288	#108	C₂³×C₁₉	1	8	yes	—
289	#104	C₂³×C₁₉	1	16	yes	—
290	#101	C₂³×C₁₉	1	8	yes	—
291	#100	C₂³×C₁₉	1	8	yes	—
292	#97	C₂³×C₁₉	1	4	yes	—
293	C₁₉	#61100	1	1	yes	characteristic, direct product factor, Sylow
294	#41	—	2	4	no	—
295	#41	—	2	4	no	—
296	#41	—	2	16	no	—
297	#41	—	2	16	no	—
298	#41	—	2	8	no	—
299	#41	—	2	8	no	—
300	#41	—	4	8	no	—
301	#41	—	4	8	no	—
302	#41	—	4	16	no	—
303	#41	—	4	8	no	—
304	#41	C₂×D₄×C₁₉	1	8	yes	—
305	#41	C₂⁴×C₁₉	1	8	yes	—
306	C₂×Q₈	—	2	16	no	—
307	C₂×Q₈	—	4	4	no	—
308	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
309	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
310	C₂×D₄	—	2	4	no	—
311	C₂×D₄	—	2	16	no	—
312	C₂×D₄	—	2	4	no	—
313	C₂×D₄	—	4	2	no	—
314	C₂×D₄	—	4	8	no	—
315	C₂×D₄	—	4	4	no	—
316	C₂×D₄	—	4	16	no	—
317	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
318	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
319	C₂²×C₄	—	2	4	no	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	2	4	no	—
322	C₂²×C₄	—	4	8	no	—
323	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
324	Q₁₆	—	2	16	no	—
325	Q₁₆	—	2	4	no	—
326	Q₁₆	—	2	4	no	—
327	Q₁₆	C₂×D₄×C₁₉	1	8	yes	—
328	SD₁₆	—	2	16	no	—
329	SD₁₆	—	2	16	no	—
330	SD₁₆	—	2	8	no	—
331	SD₁₆	—	2	8	no	—
332	SD₁₆	C₂×D₄×C₁₉	1	16	yes	—
333	D₈	—	2	16	no	—
334	D₈	—	2	4	no	—
335	D₈	—	2	4	no	—
336	D₈	C₂×D₄×C₁₉	1	8	yes	—
337	M₁₆	—	2	4	no	—
338	M₁₆	—	2	8	no	—
339	M₁₆	—	2	8	no	—
340	M₁₆	C₂⁴×C₁₉	1	8	yes	—
341	C₂×C₈	—	2	4	no	—
342	C₂×C₈	—	2	8	no	—
343	C₂×C₈	—	2	8	no	—
344	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
345	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
346	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
347	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
348	C₄⋊C₄	—	4	2	no	—
349	C₂²⋊C₄	—	4	4	no	—
350	C₄²	—	2	1	no	—
351	C₄²	C₂⁴×C₁₉	1	2	yes	—
352	C₂³	—	2	4	no	—
353	C₂³	—	2	4	no	—
354	C₂³	—	4	8	no	—
355	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
356	Q₈	—	2	4	no	—
357	Q₈	—	2	8	no	—
358	Q₈	—	4	8	no	—
359	Q₈	C₂²×D₄×C₁₉	1	8	yes	—
360	D₄	—	2	8	no	—
361	D₄	—	2	8	no	—
362	D₄	—	2	4	no	—
363	D₄	—	2	8	no	—
364	D₄	—	4	16	no	—
365	D₄	—	4	8	no	—
366	D₄	—	4	8	no	—
367	D₄	—	8	4	no	—
368	D₄	C₂²×D₄×C₁₉	1	8	yes	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	8	no	—
371	C₂×C₄	—	2	8	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	4	8	no	—
375	C₂×C₄	—	4	16	no	—
376	C₂×C₄	—	4	4	no	—
377	C₂×C₄	—	4	4	no	—
378	C₂×C₄	—	8	1	no	—
379	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
380	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
381	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
382	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
383	C₈	—	2	8	no	—
384	C₈	C₂²×D₄×C₁₉	1	4	yes	—
385	C₈	C₂²×D₄×C₁₉	1	4	yes	—
386	C₂²	—	2	8	no	—
387	C₂²	—	4	1	no	—
388	C₂²	—	4	4	no	—
389	C₂²	—	8	4	no	—
390	C₂²	—	8	4	no	—
391	C₂²	—	16	8	no	—
392	C₂²	D₄²×C₁₉	1	2	yes	—
393	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
394	C₄	—	2	8	no	—
395	C₄	—	4	2	no	—
396	C₄	—	4	4	no	—
397	C₄	D₄²×C₁₉	1	1	yes	characteristic
398	C₄	D₄²×C₁₉	1	1	yes	characteristic
399	C₄	C₂³×D₄×C₁₉	1	2	yes	—
400	C₂	—	2	1	no	—
401	C₂	—	2	2	no	—
402	C₂	—	4	8	no	—
403	C₂	—	8	4	no	—
404	C₂	C₂×D₄²×C₁₉	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₉	D₄²
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
socle	C₂×C₁₉	C₂×D₄²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3584	C₂	semidirect
2. C₁₉×#3289	C₂	semidirect
3. C₁₉×#3288	C₂	semidirect
4. C₁₉×#3150	C₂	semidirect
5. C₁₉×#3067	C₂	semidirect
6. C₁₉×#3018	C₂	semidirect
7. C₂×C₁₉×#444	C₂	semidirect
8. C₁₉×#585	C₂²	semidirect
10. C₁₉×#578	C₂²	semidirect
12. C₁₉×#577	C₂²	semidirect
14. C₁₉×#576	C₂²	semidirect
16. C₁₉×#575	C₂²	semidirect
19. C₂×C₁₉×#135	C₂²	semidirect
20. C₂×C₁₉×#131	C₂²	semidirect
21. C₁₉×#532	C₂²	semidirect
22. C₁₉×#497	C₂²	semidirect
23. C₁₉×#496	C₂²	semidirect
24. C₁₉×#473	C₂²	semidirect
25. C₁₉×#472	C₂²	semidirect
26. C₁₉×#471	C₂²	semidirect
27. C₁₉×#456	C₂²	semidirect
28. C₁₉×#455	C₂²	semidirect
29. C₁₉×#454	C₂²	semidirect
30. C₁₉×#453	C₂²	semidirect
31. C₁₉×#444	C₂²	semidirect
32. C₂×C₁₉×#108	C₂²	semidirect
33. C₂×C₁₉×#104	C₂²	semidirect
34. C₁₉×#413	C₂²	semidirect
35. C₂×C₁₉×#97	C₂²	semidirect
61. C₁₉×#135	D₄	semidirect
64. C₂×Q₁₆×C₁₉	D₄	semidirect
67. C₂×SD₁₆×C₁₉	D₄	semidirect
70. C₂×D₈×C₁₉	D₄	semidirect
149. #61100	C₁₉	direct (N × H)
184. #3584	C₂×C₁₉	semidirect
185. #3289	C₂×C₁₉	semidirect
186. #3288	C₂×C₁₉	semidirect
187. #3150	C₂×C₁₉	semidirect
188. #3067	C₂×C₁₉	semidirect
189. #3018	C₂×C₁₉	semidirect
190. C₂×#444	C₂×C₁₉	semidirect
205. #585	C₂²×C₁₉	semidirect
207. #578	C₂²×C₁₉	semidirect
209. #577	C₂²×C₁₉	semidirect
211. #576	C₂²×C₁₉	semidirect
213. #575	C₂²×C₁₉	semidirect
216. C₂×#135	C₂²×C₁₉	semidirect
217. C₂×#131	C₂²×C₁₉	semidirect
218. #532	C₂²×C₁₉	semidirect
219. #497	C₂²×C₁₉	semidirect
220. #496	C₂²×C₁₉	semidirect
221. #473	C₂²×C₁₉	semidirect
222. #472	C₂²×C₁₉	semidirect
223. #471	C₂²×C₁₉	semidirect
224. #456	C₂²×C₁₉	semidirect
225. #455	C₂²×C₁₉	semidirect
226. #454	C₂²×C₁₉	semidirect
227. #453	C₂²×C₁₉	semidirect
228. #444	C₂²×C₁₉	semidirect
229. C₂×#108	C₂²×C₁₉	semidirect
230. C₂×#104	C₂²×C₁₉	semidirect
231. #413	C₂²×C₁₉	semidirect
232. C₂×#97	C₂²×C₁₉	semidirect
263. #135	D₄×C₁₉	semidirect
266. C₂×Q₁₆	D₄×C₁₉	semidirect
269. C₂×SD₁₆	D₄×C₁₉	semidirect
272. C₂×D₈	D₄×C₁₉	semidirect
293. C₁₉	#61100	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#3584	2
C₁₉×#3289	2
C₁₉×#3288	2
C₁₉×#3150	2
C₁₉×#3067	2
C₁₉×#3018	2
C₂×C₁₉×#444	2
#61100	19

Subgroups — C19×#61100 #18067059

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#61100 #18067059