Subgroups — C₁₉×#33533 #18039492

Order 4864.

1102 conjugacy classes of subgroups.

The subgroup lattice has 438 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	1	yes	maximal, characteristic, complemented
2	C₁₉×#3414	C₂	1	2	yes	maximal, complemented
3	C₁₉×#3060	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2191	C₂	1	4	yes	maximal, complemented
5	C₁₉×#2190	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₉×#360	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2115	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#585	—	2	1	no	—
9	C₁₉×#578	—	2	2	no	—
10	C₁₉×#577	—	2	4	no	—
11	C₁₉×#576	—	2	2	no	—
12	C₁₉×#575	—	2	1	no	—
13	C₁₉×#575	C₂²	1	4	yes	—
14	C₂×C₁₉×#135	—	2	2	no	—
15	C₂×C₁₉×#135	C₂²	1	2	yes	—
16	C₂×C₁₉×#135	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic
18	C₁₉×#537	—	2	1	no	—
19	C₁₉×#510	—	2	2	no	—
20	C₁₉×#510	C₂²	1	4	yes	complemented
21	C₁₉×#509	—	2	2	no	—
22	C₁₉×#509	C₂²	1	4	yes	complemented
23	C₁₉×#508	—	2	4	no	—
24	C₂×C₁₉×M₃₂	C₂²	1	2	yes	complemented
25	C₁₉×#470	C₂²	1	2	yes	complemented
26	C₁₉×#469	C₂²	1	2	yes	complemented
27	C₁₉×#465	—	2	2	no	—
28	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic, complemented
29	C₁₉×#417	—	2	1	no	—
30	C₁₉×#360	C₂²	1	8	yes	complemented
31	C₁₉×#349	C₂²	1	4	yes	complemented
32	C₁₉×2₋¹⁺⁴	—	2	4	no	—
33	C₁₉×2₋¹⁺⁴	—	4	1	no	—
34	C₁₉×H(5,𝔽₂)	—	2	4	no	—
35	C₁₉×H(5,𝔽₂)	—	4	2	no	—
36	C₁₉×H(5,𝔽₂)	—	4	1	no	—
37	C₂×#41×C₁₉	—	2	4	no	—
38	C₂×#41×C₁₉	—	2	2	no	—
39	C₂×#41×C₁₉	—	2	1	no	—
40	C₂×#41×C₁₉	—	4	4	no	—
41	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
42	C₁₉×#137	—	2	4	no	—
43	C₁₉×#137	—	2	8	no	—
44	C₁₉×AGL(1,ℤ/8)	—	2	4	no	—
45	C₁₉×AGL(1,ℤ/8)	—	2	8	no	—
46	C₁₉×#135	—	2	4	no	—
47	C₁₉×#135	—	2	4	no	—
48	C₁₉×#135	—	2	2	no	—
49	C₁₉×#135	—	2	4	no	—
50	C₁₉×#135	—	2	2	no	—
51	C₁₉×#135	—	2	2	no	—
52	C₁₉×#135	—	2	2	no	—
53	C₁₉×#135	D₄	1	4	yes	complemented
54	C₁₉×#135	C₂³	1	4	yes	—
55	C₂×Q₁₆×C₁₉	—	2	2	no	—
56	C₂×Q₁₆×C₁₉	D₄	1	2	yes	complemented
57	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
58	C₂×SD₁₆×C₁₉	—	2	4	no	—
59	C₂×SD₁₆×C₁₉	—	2	2	no	—
60	C₂×SD₁₆×C₁₉	—	2	1	no	—
61	C₂×D₈×C₁₉	—	2	2	no	—
62	C₂×D₈×C₁₉	D₄	1	2	yes	complemented
63	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
64	C₁₉×#131	—	2	2	no	—
65	C₁₉×#131	—	2	2	no	—
66	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
67	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
68	C₂²×C₈×C₁₉	D₄	1	2	yes	—
69	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
70	C₁₉×C₂²⋊Q₈	—	2	2	no	—
71	C₁₉×C₂²⋊Q₈	—	4	1	no	—
72	C₁₉×#121	—	2	2	no	—
73	C₁₉×#121	—	4	1	no	—
74	C₁₉×#121	—	4	2	no	—
75	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
76	C₁₉×Q₃₂	—	2	4	no	—
77	C₁₉×SD₃₂	—	2	4	no	—
78	C₁₉×SD₃₂	—	2	4	no	—
79	C₁₉×D₁₆	—	2	4	no	—
80	C₁₉×M₃₂	—	2	2	no	—
81	C₁₉×M₃₂	C₂³	1	4	yes	—
82	C₂×C₁₆×C₁₉	—	2	2	no	—
83	C₁₉×#106	—	2	1	no	—
84	C₁₉×#106	C₂³	1	2	yes	—
85	C₁₉×#103	—	2	2	no	—
86	C₁₉×#102	—	2	2	no	—
87	#41×C₁₉	—	2	2	no	—
88	#41×C₁₉	—	2	2	no	—
89	#41×C₁₉	—	2	8	no	—
90	#41×C₁₉	—	2	4	no	—
91	#41×C₁₉	—	2	4	no	—
92	#41×C₁₉	—	4	4	no	—
93	#41×C₁₉	—	4	8	no	—
94	#41×C₁₉	—	4	4	no	—
95	#41×C₁₉	—	4	4	no	—
96	#41×C₁₉	—	4	4	no	—
97	#41×C₁₉	—	4	2	no	—
98	#41×C₁₉	—	4	2	no	—
99	#41×C₁₉	—	4	2	no	—
100	#41×C₁₉	—	4	2	no	—
101	C₂×Q₈×C₁₉	—	2	4	no	—
102	C₂×Q₈×C₁₉	—	2	2	no	—
103	C₂×Q₈×C₁₉	—	2	1	no	—
104	C₂×Q₈×C₁₉	—	4	4	no	—
105	C₂×Q₈×C₁₉	D₈	1	1	yes	characteristic
106	C₂×D₄×C₁₉	—	2	4	no	—
107	C₂×D₄×C₁₉	—	2	2	no	—
108	C₂×D₄×C₁₉	—	2	1	no	—
109	C₂×D₄×C₁₉	—	4	8	no	—
110	C₂×D₄×C₁₉	—	4	4	no	—
111	C₂×D₄×C₁₉	—	4	4	no	—
112	C₂×D₄×C₁₉	—	4	2	no	—
113	C₂×D₄×C₁₉	—	4	1	no	—
114	C₂×D₄×C₁₉	—	4	2	no	—
115	C₂×D₄×C₁₉	D₈	1	2	yes	—
116	C₂×D₄×C₁₉	D₈	1	1	yes	characteristic
117	C₂²×C₄×C₁₉	—	4	4	no	—
118	C₂²×C₄×C₁₉	—	4	2	no	—
119	C₂²×C₄×C₁₉	—	4	1	no	—
120	C₂²×C₄×C₁₉	—	4	1	no	—
121	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
123	Q₁₆×C₁₉	—	2	4	no	—
124	Q₁₆×C₁₉	—	2	2	no	—
125	Q₁₆×C₁₉	—	2	2	no	—
126	Q₁₆×C₁₉	C₂×D₄	1	4	yes	—
127	SD₁₆×C₁₉	—	2	8	no	—
128	SD₁₆×C₁₉	—	2	4	no	—
129	SD₁₆×C₁₉	—	2	4	no	—
130	SD₁₆×C₁₉	—	4	1	no	—
131	SD₁₆×C₁₉	—	4	1	no	—
132	D₈×C₁₉	—	2	4	no	—
133	D₈×C₁₉	—	2	2	no	—
134	D₈×C₁₉	—	2	2	no	—
135	D₈×C₁₉	C₂×D₄	1	4	yes	—
136	M₁₆×C₁₉	—	2	2	no	—
137	M₁₆×C₁₉	—	2	4	no	—
138	C₂×C₈×C₁₉	—	2	2	no	—
139	C₂×C₈×C₁₉	—	2	2	no	—
140	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
141	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
142	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
143	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
144	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
145	C₄⋊C₄×C₁₉	—	2	2	no	—
146	C₄⋊C₄×C₁₉	—	4	1	no	—
147	C₄⋊C₄×C₁₉	—	4	2	no	—
148	C₂²⋊C₄×C₁₉	—	4	2	no	—
149	C₂²⋊C₄×C₁₉	—	4	2	no	—
150	C₁₆×C₁₉	—	2	4	no	—
151	#33533	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
152	C₂³×C₁₉	—	4	4	no	—
153	C₂³×C₁₉	—	4	2	no	—
154	C₂³×C₁₉	—	4	1	no	—
155	C₂³×C₁₉	C₂×D₈	1	2	yes	—
156	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
157	Q₈×C₁₉	—	2	2	no	—
158	Q₈×C₁₉	—	2	4	no	—
159	Q₈×C₁₉	—	4	4	no	—
160	Q₈×C₁₉	—	4	2	no	—
161	Q₈×C₁₉	—	4	1	no	—
162	Q₈×C₁₉	—	4	1	no	—
163	D₄×C₁₉	—	2	4	no	—
164	D₄×C₁₉	—	2	4	no	—
165	D₄×C₁₉	—	2	2	no	—
166	D₄×C₁₉	—	4	4	no	—
167	D₄×C₁₉	—	4	8	no	—
168	D₄×C₁₉	—	4	4	no	—
169	D₄×C₁₉	—	4	4	no	—
170	D₄×C₁₉	—	4	1	no	—
171	D₄×C₁₉	—	4	1	no	—
172	D₄×C₁₉	—	4	2	no	—
173	D₄×C₁₉	—	8	2	no	—
174	D₄×C₁₉	—	16	2	no	—
175	C₂×C₄×C₁₉	—	2	2	no	—
176	C₂×C₄×C₁₉	—	2	2	no	—
177	C₂×C₄×C₁₉	—	4	8	no	—
178	C₂×C₄×C₁₉	—	4	4	no	—
179	C₂×C₄×C₁₉	—	4	2	no	—
180	C₂×C₄×C₁₉	—	4	4	no	—
181	C₂×C₄×C₁₉	—	4	4	no	—
182	C₂×C₄×C₁₉	—	4	2	no	—
183	C₂×C₄×C₁₉	—	4	1	no	—
184	C₂×C₄×C₁₉	—	8	2	no	—
185	C₂×C₄×C₁₉	—	16	1	no	—
186	C₂×C₄×C₁₉	#120	1	2	yes	—
187	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
188	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
189	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
190	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
191	C₈×C₁₉	—	2	2	no	—
192	C₈×C₁₉	#120	1	1	yes	characteristic
193	C₈×C₁₉	#120	1	1	yes	characteristic
194	C₈×C₁₉	C₂²×D₄	1	2	yes	—
195	#3584	C₂×C₁₉	1	1	yes	characteristic, complemented
196	#3414	C₂×C₁₉	1	2	yes	complemented
197	#3060	C₂×C₁₉	1	1	yes	characteristic, complemented
198	#2191	C₂×C₁₉	1	4	yes	complemented
199	#2190	C₂×C₁₉	1	4	yes	complemented
200	C₂×#360	C₂×C₁₉	1	2	yes	complemented
201	#2115	C₂×C₁₉	1	1	yes	characteristic, complemented
202	C₂²×C₁₉	—	2	2	no	—
203	C₂²×C₁₉	—	4	1	no	—
204	C₂²×C₁₉	—	4	2	no	—
205	C₂²×C₁₉	—	4	4	no	—
206	C₂²×C₁₉	—	8	1	no	—
207	C₂²×C₁₉	—	8	1	no	—
208	C₂²×C₁₉	—	8	1	no	—
209	C₂²×C₁₉	—	16	2	no	—
210	C₂²×C₁₉	—	16	4	no	—
211	C₂²×C₁₉	#447	1	2	yes	—
212	C₂²×C₁₉	C₂²×D₈	1	1	yes	characteristic
213	C₄×C₁₉	—	2	2	no	—
214	C₄×C₁₉	—	4	4	no	—
215	C₄×C₁₉	—	8	2	no	—
216	C₄×C₁₉	—	8	1	no	—
217	C₄×C₁₉	#447	1	2	yes	—
218	C₄×C₁₉	C₂×#120	1	1	yes	characteristic
219	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
220	#585	—	2	1	no	—
221	#578	—	2	2	no	—
222	#577	—	2	4	no	—
223	#576	—	2	2	no	—
224	#575	—	2	1	no	—
225	#575	C₂²×C₁₉	1	4	yes	—
226	C₂×#135	—	2	2	no	—
227	C₂×#135	C₂²×C₁₉	1	2	yes	—
228	C₂×#135	C₂²×C₁₉	1	1	yes	characteristic, complemented
229	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic
230	#537	—	2	1	no	—
231	#510	—	2	2	no	—
232	#510	C₂²×C₁₉	1	4	yes	complemented
233	#509	—	2	2	no	—
234	#509	C₂²×C₁₉	1	4	yes	complemented
235	#508	—	2	4	no	—
236	C₂×M₃₂	C₂²×C₁₉	1	2	yes	complemented
237	#470	C₂²×C₁₉	1	2	yes	complemented
238	#469	C₂²×C₁₉	1	2	yes	complemented
239	#465	—	2	2	no	—
240	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic, complemented
241	#417	—	2	1	no	—
242	#360	C₂²×C₁₉	1	8	yes	complemented
243	#349	C₂²×C₁₉	1	4	yes	complemented
244	C₂×C₁₉	—	2	1	no	—
245	C₂×C₁₉	—	2	2	no	—
246	C₂×C₁₉	—	4	2	no	—
247	C₂×C₁₉	—	8	4	no	—
248	C₂×C₁₉	—	16	1	no	—
249	C₂×C₁₉	C₂×#447	1	1	yes	characteristic
250	2₋¹⁺⁴	—	2	4	no	—
251	2₋¹⁺⁴	—	4	1	no	—
252	H(5,𝔽₂)	—	2	4	no	—
253	H(5,𝔽₂)	—	4	2	no	—
254	H(5,𝔽₂)	—	4	1	no	—
255	C₂×#41	—	2	4	no	—
256	C₂×#41	—	2	2	no	—
257	C₂×#41	—	2	1	no	—
258	C₂×#41	—	4	4	no	—
259	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
260	#137	—	2	4	no	—
261	#137	—	2	8	no	—
262	AGL(1,ℤ/8)	—	2	4	no	—
263	AGL(1,ℤ/8)	—	2	8	no	—
264	#135	—	2	4	no	—
265	#135	—	2	4	no	—
266	#135	—	2	2	no	—
267	#135	—	2	4	no	—
268	#135	—	2	2	no	—
269	#135	—	2	2	no	—
270	#135	—	2	2	no	—
271	#135	D₄×C₁₉	1	4	yes	complemented
272	#135	C₂³×C₁₉	1	4	yes	—
273	C₂×Q₁₆	—	2	2	no	—
274	C₂×Q₁₆	D₄×C₁₉	1	2	yes	complemented
275	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
276	C₂×SD₁₆	—	2	4	no	—
277	C₂×SD₁₆	—	2	2	no	—
278	C₂×SD₁₆	—	2	1	no	—
279	C₂×D₈	—	2	2	no	—
280	C₂×D₈	D₄×C₁₉	1	2	yes	complemented
281	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
282	#131	—	2	2	no	—
283	#131	—	2	2	no	—
284	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
285	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
286	C₂²×C₈	D₄×C₁₉	1	2	yes	—
287	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
288	C₂²⋊Q₈	—	2	2	no	—
289	C₂²⋊Q₈	—	4	1	no	—
290	#121	—	2	2	no	—
291	#121	—	4	1	no	—
292	#121	—	4	2	no	—
293	C₂×C₄⋊C₄	—	2	1	no	—
294	Q₃₂	—	2	4	no	—
295	SD₃₂	—	2	4	no	—
296	SD₃₂	—	2	4	no	—
297	D₁₆	—	2	4	no	—
298	M₃₂	—	2	2	no	—
299	M₃₂	C₂³×C₁₉	1	4	yes	—
300	C₂×C₁₆	—	2	2	no	—
301	#106	—	2	1	no	—
302	#106	C₂³×C₁₉	1	2	yes	—
303	#103	—	2	2	no	—
304	#102	—	2	2	no	—
305	C₁₉	#33533	1	1	yes	characteristic, direct product factor, Sylow
306	#41	—	2	2	no	—
307	#41	—	2	2	no	—
308	#41	—	2	8	no	—
309	#41	—	2	4	no	—
310	#41	—	2	4	no	—
311	#41	—	4	4	no	—
312	#41	—	4	8	no	—
313	#41	—	4	4	no	—
314	#41	—	4	4	no	—
315	#41	—	4	4	no	—
316	#41	—	4	2	no	—
317	#41	—	4	2	no	—
318	#41	—	4	2	no	—
319	#41	—	4	2	no	—
320	C₂×Q₈	—	2	4	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	1	no	—
323	C₂×Q₈	—	4	4	no	—
324	C₂×Q₈	D₈×C₁₉	1	1	yes	characteristic
325	C₂×D₄	—	2	4	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	—	4	8	no	—
329	C₂×D₄	—	4	4	no	—
330	C₂×D₄	—	4	4	no	—
331	C₂×D₄	—	4	2	no	—
332	C₂×D₄	—	4	1	no	—
333	C₂×D₄	—	4	2	no	—
334	C₂×D₄	D₈×C₁₉	1	2	yes	—
335	C₂×D₄	D₈×C₁₉	1	1	yes	characteristic
336	C₂²×C₄	—	4	4	no	—
337	C₂²×C₄	—	4	2	no	—
338	C₂²×C₄	—	4	1	no	—
339	C₂²×C₄	—	4	1	no	—
340	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
341	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
342	Q₁₆	—	2	4	no	—
343	Q₁₆	—	2	2	no	—
344	Q₁₆	—	2	2	no	—
345	Q₁₆	C₂×D₄×C₁₉	1	4	yes	—
346	SD₁₆	—	2	8	no	—
347	SD₁₆	—	2	4	no	—
348	SD₁₆	—	2	4	no	—
349	SD₁₆	—	4	1	no	—
350	SD₁₆	—	4	1	no	—
351	D₈	—	2	4	no	—
352	D₈	—	2	2	no	—
353	D₈	—	2	2	no	—
354	D₈	C₂×D₄×C₁₉	1	4	yes	—
355	M₁₆	—	2	2	no	—
356	M₁₆	—	2	4	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
360	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
361	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
362	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
363	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	4	1	no	—
366	C₄⋊C₄	—	4	2	no	—
367	C₂²⋊C₄	—	4	2	no	—
368	C₂²⋊C₄	—	4	2	no	—
369	C₁₆	—	2	4	no	—
370	C₂³	—	4	4	no	—
371	C₂³	—	4	2	no	—
372	C₂³	—	4	1	no	—
373	C₂³	C₂×D₈×C₁₉	1	2	yes	—
374	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
375	Q₈	—	2	2	no	—
376	Q₈	—	2	4	no	—
377	Q₈	—	4	4	no	—
378	Q₈	—	4	2	no	—
379	Q₈	—	4	1	no	—
380	Q₈	—	4	1	no	—
381	D₄	—	2	4	no	—
382	D₄	—	2	2	no	—
383	D₄	—	2	4	no	—
384	D₄	—	4	4	no	—
385	D₄	—	4	8	no	—
386	D₄	—	4	4	no	—
387	D₄	—	4	4	no	—
388	D₄	—	4	2	no	—
389	D₄	—	4	1	no	—
390	D₄	—	4	1	no	—
391	D₄	—	8	2	no	—
392	D₄	—	16	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	4	8	no	—
396	C₂×C₄	—	4	4	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	4	no	—
399	C₂×C₄	—	4	4	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	8	2	no	—
403	C₂×C₄	—	16	1	no	—
404	C₂×C₄	C₁₉×#120	1	2	yes	—
405	C₂×C₄	C₂×D₈×C₁₉	1	2	yes	—
406	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
407	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
408	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
409	C₈	—	2	2	no	—
410	C₈	C₁₉×#120	1	1	yes	characteristic
411	C₈	C₁₉×#120	1	1	yes	characteristic
412	C₈	C₂²×D₄×C₁₉	1	2	yes	—
413	C₂²	—	2	2	no	—
414	C₂²	—	4	1	no	—
415	C₂²	—	4	2	no	—
416	C₂²	—	4	4	no	—
417	C₂²	—	8	1	no	—
418	C₂²	—	8	1	no	—
419	C₂²	—	8	1	no	—
420	C₂²	—	16	2	no	—
421	C₂²	—	16	4	no	—
422	C₂²	C₁₉×#447	1	2	yes	—
423	C₂²	C₂²×D₈×C₁₉	1	1	yes	characteristic
424	C₄	—	2	2	no	—
425	C₄	—	4	4	no	—
426	C₄	—	8	2	no	—
427	C₄	—	8	1	no	—
428	C₄	C₁₉×#447	1	2	yes	—
429	C₄	C₂×C₁₉×#120	1	1	yes	characteristic
430	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
431	C₂	—	2	1	no	—
432	C₂	—	2	2	no	—
433	C₂	—	4	2	no	—
434	C₂	—	8	4	no	—
435	C₂	—	16	1	no	—
436	C₂	C₂×C₁₉×#447	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₉	C₂×#447
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₉
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₁₉×#131 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3584	C₂	semidirect
2. C₁₉×#3414	C₂	semidirect
3. C₁₉×#3060	C₂	semidirect
4. C₁₉×#2191	C₂	semidirect
5. C₁₉×#2190	C₂	semidirect
6. C₂×C₁₉×#360	C₂	semidirect
7. C₁₉×#2115	C₂	semidirect
16. C₂×C₁₉×#135	C₂²	semidirect
20. C₁₉×#510	C₂²	semidirect
22. C₁₉×#509	C₂²	semidirect
24. C₂×C₁₉×M₃₂	C₂²	semidirect
25. C₁₉×#470	C₂²	semidirect
26. C₁₉×#469	C₂²	semidirect
28. C₂×C₁₉×#106	C₂²	semidirect
30. C₁₉×#360	C₂²	semidirect
31. C₁₉×#349	C₂²	semidirect
53. C₁₉×#135	D₄	semidirect
56. C₂×Q₁₆×C₁₉	D₄	semidirect
62. C₂×D₈×C₁₉	D₄	semidirect
151. #33533	C₁₉	direct (N × H)
195. #3584	C₂×C₁₉	semidirect
196. #3414	C₂×C₁₉	semidirect
197. #3060	C₂×C₁₉	semidirect
198. #2191	C₂×C₁₉	semidirect
199. #2190	C₂×C₁₉	semidirect
200. C₂×#360	C₂×C₁₉	semidirect
201. #2115	C₂×C₁₉	semidirect
228. C₂×#135	C₂²×C₁₉	semidirect
232. #510	C₂²×C₁₉	semidirect
234. #509	C₂²×C₁₉	semidirect
236. C₂×M₃₂	C₂²×C₁₉	semidirect
237. #470	C₂²×C₁₉	semidirect
238. #469	C₂²×C₁₉	semidirect
240. C₂×#106	C₂²×C₁₉	semidirect
242. #360	C₂²×C₁₉	semidirect
243. #349	C₂²×C₁₉	semidirect
271. #135	D₄×C₁₉	semidirect
274. C₂×Q₁₆	D₄×C₁₉	semidirect
280. C₂×D₈	D₄×C₁₉	semidirect
305. C₁₉	#33533	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×#3414	2
C₁₉×#3060	2
C₁₉×#2191	2
C₁₉×#2190	2
C₂×C₁₉×#360	2
C₁₉×#2115	2
#33533	19

Subgroups — C19×#33533 #18039492

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#33533 #18039492