Subgroups — C₁₉×#33856 #18039815

Order 4864.

652 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3416	C₂	1	2	yes	maximal, complemented
2	C₁₉×#3293	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3292	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2248	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2223	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2214	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2213	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2194	C₂	1	2	yes	maximal, complemented
9	C₁₉×#2193	C₂	1	2	yes	maximal, complemented
10	C₁₉×#2178	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#2170	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#578	—	2	1	no	—
13	C₁₉×#578	C₂²	1	2	yes	complemented
14	C₁₉×#576	—	2	1	no	—
15	C₁₉×#576	C₂²	1	2	yes	—
16	C₁₉×#510	—	2	2	no	—
17	C₁₉×#510	C₂²	1	2	yes	—
18	C₁₉×#509	—	2	2	no	—
19	C₁₉×#509	C₂²	1	2	yes	complemented
20	C₁₉×#508	—	2	2	no	—
21	C₁₉×#508	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×SD₃₂	—	2	2	no	—
23	C₂×C₁₉×SD₃₂	C₂²	1	2	yes	complemented
24	C₂×C₁₉×SD₃₂	C₂²	1	2	yes	complemented
25	C₁₉×#504	C₂²	1	2	yes	complemented
26	C₁₉×#494	C₂²	1	1	yes	characteristic, complemented
27	C₁₉×#493	C₂²	1	1	yes	characteristic
28	C₁₉×#473	—	2	1	no	—
29	C₁₉×#473	C₂²	1	2	yes	complemented
30	C₁₉×#472	—	2	1	no	—
31	C₁₉×#472	C₂²	1	2	yes	—
32	C₁₉×#456	—	2	2	no	—
33	C₁₉×#453	—	2	2	no	—
34	C₁₉×#443	C₂²	1	1	yes	characteristic
35	C₁₉×#443	C₂²	1	1	yes	characteristic
36	C₁₉×#443	C₂²	1	1	yes	characteristic, complemented
37	C₁₉×#368	C₂²	1	1	yes	characteristic, complemented
38	C₁₉×#364	C₂²	1	1	yes	characteristic, complemented
39	C₁₉×#362	C₂²	1	2	yes	complemented
40	C₁₉×#361	C₂²	1	2	yes	complemented
41	C₁₉×#359	C₂²	1	1	yes	characteristic
42	C₁₉×#359	C₂²	1	1	yes	characteristic, complemented
43	C₁₉×#350	C₂²	1	2	yes	complemented
44	C₄×C₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
45	C₁₉×2₋¹⁺⁴	—	2	2	no	—
46	C₁₉×H(5,𝔽₂)	—	2	2	no	—
47	C₁₉×#137	—	2	2	no	—
48	C₁₉×#137	—	2	2	no	—
49	C₁₉×#137	—	4	2	no	—
50	C₁₉×#137	—	4	2	no	—
51	C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
52	C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
53	C₁₉×AGL(1,ℤ/8)	—	4	2	no	—
54	C₁₉×AGL(1,ℤ/8)	—	4	2	no	—
55	C₁₉×#135	—	2	2	no	—
56	C₁₉×#135	—	2	2	no	—
57	C₁₉×#135	—	4	1	no	—
58	C₁₉×#135	—	4	1	no	—
59	C₁₉×#135	D₄	1	1	yes	characteristic
60	C₁₉×#135	C₂³	1	1	yes	characteristic
61	C₁₉×#135	C₂³	1	1	yes	characteristic
62	C₂×Q₁₆×C₁₉	—	2	2	no	—
63	C₂×Q₁₆×C₁₉	—	2	1	no	—
64	C₂×Q₁₆×C₁₉	—	4	1	no	—
65	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
66	C₂×D₈×C₁₉	—	2	2	no	—
67	C₂×D₈×C₁₉	—	2	1	no	—
68	C₂×D₈×C₁₉	—	4	1	no	—
69	C₂×D₈×C₁₉	C₂³	1	2	yes	—
70	C₁₉×#131	—	2	1	no	—
71	C₁₉×#131	—	2	1	no	—
72	C₁₉×#131	C₂³	1	2	yes	—
73	C₁₉×C₄⋊Q₈	—	2	1	no	—
74	C₁₉×#127	—	2	1	no	—
75	C₁₉×Q₃₂	—	2	2	no	—
76	C₁₉×Q₃₂	D₄	1	1	yes	characteristic, complemented
77	C₁₉×SD₃₂	—	2	2	no	—
78	C₁₉×SD₃₂	—	2	2	no	—
79	C₁₉×SD₃₂	—	2	2	no	—
80	C₁₉×SD₃₂	—	2	2	no	—
81	C₁₉×SD₃₂	—	4	2	no	—
82	C₁₉×SD₃₂	D₄	1	1	yes	characteristic, complemented
83	C₁₉×SD₃₂	D₄	1	1	yes	characteristic, complemented
84	C₁₉×D₁₆	—	2	2	no	—
85	C₁₉×D₁₆	D₄	1	1	yes	characteristic, complemented
86	C₁₉×M₃₂	—	2	2	no	—
87	C₁₉×M₃₂	C₂³	1	2	yes	—
88	C₂×C₁₆×C₁₉	—	2	2	no	—
89	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
90	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
91	C₁₉×#108	D₄	1	1	yes	characteristic
92	C₁₉×#108	C₂³	1	1	yes	characteristic
93	C₁₉×#108	C₂³	1	1	yes	characteristic
94	C₁₉×#104	—	2	1	no	—
95	C₁₉×#104	—	2	1	no	—
96	C₁₉×#104	D₄	1	2	yes	—
97	C₁₉×#101	—	2	2	no	—
98	C₁₉×#100	—	2	2	no	—
99	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
100	#41×C₁₉	—	2	1	no	—
101	#41×C₁₉	—	2	1	no	—
102	#41×C₁₉	—	4	2	no	—
103	#41×C₁₉	—	4	2	no	—
104	#41×C₁₉	—	4	2	no	—
105	#41×C₁₉	—	4	2	no	—
106	#41×C₁₉	—	8	2	no	—
107	#41×C₁₉	C₂×D₄	1	2	yes	—
108	C₂×Q₈×C₁₉	—	2	2	no	—
109	C₂×Q₈×C₁₉	—	4	2	no	—
110	C₂×Q₈×C₁₉	—	4	2	no	—
111	C₂×D₄×C₁₉	—	2	2	no	—
112	C₂×D₄×C₁₉	—	4	2	no	—
113	C₂×D₄×C₁₉	—	4	2	no	—
114	C₂×D₄×C₁₉	—	8	1	no	—
115	C₂×D₄×C₁₉	—	8	2	no	—
116	Q₁₆×C₁₉	—	2	2	no	—
117	Q₁₆×C₁₉	—	2	2	no	—
118	Q₁₆×C₁₉	—	4	2	no	—
119	Q₁₆×C₁₉	—	4	2	no	—
120	Q₁₆×C₁₉	—	4	1	no	—
121	Q₁₆×C₁₉	—	4	1	no	—
122	Q₁₆×C₁₉	D₈	1	1	yes	characteristic
123	Q₁₆×C₁₉	C₂×D₄	1	1	yes	characteristic
124	Q₁₆×C₁₉	C₂×D₄	1	1	yes	characteristic
125	SD₁₆×C₁₉	—	2	1	no	—
126	SD₁₆×C₁₉	—	2	1	no	—
127	SD₁₆×C₁₉	—	4	2	no	—
128	SD₁₆×C₁₉	—	4	2	no	—
129	SD₁₆×C₁₉	—	4	2	no	—
130	SD₁₆×C₁₉	—	4	2	no	—
131	SD₁₆×C₁₉	D₈	1	2	yes	—
132	D₈×C₁₉	—	2	2	no	—
133	D₈×C₁₉	—	2	2	no	—
134	D₈×C₁₉	—	4	2	no	—
135	D₈×C₁₉	—	4	2	no	—
136	D₈×C₁₉	—	4	1	no	—
137	D₈×C₁₉	—	4	1	no	—
138	D₈×C₁₉	D₈	1	1	yes	characteristic
139	D₈×C₁₉	C₂×D₄	1	1	yes	characteristic
140	D₈×C₁₉	C₂×D₄	1	1	yes	characteristic
141	M₁₆×C₁₉	—	2	2	no	—
142	M₁₆×C₁₉	—	2	1	no	—
143	M₁₆×C₁₉	—	2	1	no	—
144	M₁₆×C₁₉	—	4	1	no	—
145	M₁₆×C₁₉	—	4	1	no	—
146	M₁₆×C₁₉	C₂×D₄	1	2	yes	—
147	C₂×C₈×C₁₉	—	2	2	no	—
148	C₂×C₈×C₁₉	—	4	1	no	—
149	C₂×C₈×C₁₉	—	4	1	no	—
150	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
151	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
152	C₄⋊C₄×C₁₉	—	8	1	no	—
153	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₁₆×C₁₉	—	2	2	no	—
155	C₁₆×C₁₉	—	2	1	no	—
156	C₁₆×C₁₉	C₂×D₄	1	1	yes	characteristic
157	C₁₆×C₁₉	C₂×D₄	1	1	yes	characteristic
158	#33856	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
159	C₂³×C₁₉	—	4	2	no	—
160	C₂³×C₁₉	—	8	2	no	—
161	Q₈×C₁₉	—	2	1	no	—
162	Q₈×C₁₉	—	2	1	no	—
163	Q₈×C₁₉	—	4	2	no	—
164	Q₈×C₁₉	—	4	2	no	—
165	Q₈×C₁₉	—	8	2	no	—
166	Q₈×C₁₉	C₂×D₈	1	2	yes	—
167	D₄×C₁₉	—	2	2	no	—
168	D₄×C₁₉	—	2	1	no	—
169	D₄×C₁₉	—	2	1	no	—
170	D₄×C₁₉	—	4	1	no	—
171	D₄×C₁₉	—	4	1	no	—
172	D₄×C₁₉	—	4	2	no	—
173	D₄×C₁₉	—	4	2	no	—
174	D₄×C₁₉	—	8	2	no	—
175	D₄×C₁₉	—	8	2	no	—
176	D₄×C₁₉	—	8	2	no	—
177	D₄×C₁₉	—	16	2	no	—
178	D₄×C₁₉	C₂×D₈	1	2	yes	—
179	C₂×C₄×C₁₉	—	2	1	no	—
180	C₂×C₄×C₁₉	—	2	2	no	—
181	C₂×C₄×C₁₉	—	4	1	no	—
182	C₂×C₄×C₁₉	—	4	1	no	—
183	C₂×C₄×C₁₉	—	4	2	no	—
184	C₂×C₄×C₁₉	—	8	2	no	—
185	C₂×C₄×C₁₉	—	8	2	no	—
186	C₂×C₄×C₁₉	—	8	2	no	—
187	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
188	C₈×C₁₉	—	2	2	no	—
189	C₈×C₁₉	—	4	1	no	—
190	C₈×C₁₉	—	4	1	no	—
191	C₈×C₁₉	C₂×D₈	1	1	yes	characteristic
192	C₈×C₁₉	C₂×D₈	1	1	yes	characteristic
193	C₈×C₁₉	C₂²×D₄	1	1	yes	characteristic
194	C₈×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
195	#3416	C₂×C₁₉	1	2	yes	complemented
196	#3293	C₂×C₁₉	1	1	yes	characteristic, complemented
197	#3292	C₂×C₁₉	1	1	yes	characteristic, complemented
198	#2248	C₂×C₁₉	1	1	yes	characteristic, complemented
199	#2223	C₂×C₁₉	1	2	yes	complemented
200	#2214	C₂×C₁₉	1	1	yes	characteristic, complemented
201	#2213	C₂×C₁₉	1	1	yes	characteristic, complemented
202	#2194	C₂×C₁₉	1	2	yes	complemented
203	#2193	C₂×C₁₉	1	2	yes	complemented
204	#2178	C₂×C₁₉	1	1	yes	characteristic, complemented
205	#2170	C₂×C₁₉	1	1	yes	characteristic, complemented
206	C₂²×C₁₉	—	2	2	no	—
207	C₂²×C₁₉	—	4	1	no	—
208	C₂²×C₁₉	—	4	1	no	—
209	C₂²×C₁₉	—	8	2	no	—
210	C₂²×C₁₉	—	16	2	no	—
211	C₂²×C₁₉	—	32	2	no	—
212	C₂²×C₁₉	#576	1	1	yes	characteristic
213	C₄×C₁₉	—	2	2	no	—
214	C₄×C₁₉	—	2	2	no	—
215	C₄×C₁₉	—	4	1	no	—
216	C₄×C₁₉	—	4	1	no	—
217	C₄×C₁₉	—	8	2	no	—
218	C₄×C₁₉	D₄²	1	1	yes	characteristic
219	C₄×C₁₉	C₂²×D₈	1	1	yes	characteristic
220	#578	—	2	1	no	—
221	#578	C₂²×C₁₉	1	2	yes	complemented
222	#576	—	2	1	no	—
223	#576	C₂²×C₁₉	1	2	yes	—
224	#510	—	2	2	no	—
225	#510	C₂²×C₁₉	1	2	yes	—
226	#509	—	2	2	no	—
227	#509	C₂²×C₁₉	1	2	yes	complemented
228	#508	—	2	2	no	—
229	#508	C₂²×C₁₉	1	1	yes	characteristic
230	C₂×SD₃₂	—	2	2	no	—
231	C₂×SD₃₂	C₂²×C₁₉	1	2	yes	complemented
232	C₂×SD₃₂	C₂²×C₁₉	1	2	yes	complemented
233	#504	C₂²×C₁₉	1	2	yes	complemented
234	#494	C₂²×C₁₉	1	1	yes	characteristic, complemented
235	#493	C₂²×C₁₉	1	1	yes	characteristic
236	#473	—	2	1	no	—
237	#473	C₂²×C₁₉	1	2	yes	complemented
238	#472	—	2	1	no	—
239	#472	C₂²×C₁₉	1	2	yes	—
240	#456	—	2	2	no	—
241	#453	—	2	2	no	—
242	#443	C₂²×C₁₉	1	1	yes	characteristic
243	#443	C₂²×C₁₉	1	1	yes	characteristic
244	#443	C₂²×C₁₉	1	1	yes	characteristic, complemented
245	#368	C₂²×C₁₉	1	1	yes	characteristic, complemented
246	#364	C₂²×C₁₉	1	1	yes	characteristic, complemented
247	#362	C₂²×C₁₉	1	2	yes	complemented
248	#361	C₂²×C₁₉	1	2	yes	complemented
249	#359	C₂²×C₁₉	1	1	yes	characteristic
250	#359	C₂²×C₁₉	1	1	yes	characteristic, complemented
251	#350	C₂²×C₁₉	1	2	yes	complemented
252	C₄×C₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
253	C₂×C₁₉	—	2	1	no	—
254	C₂×C₁₉	—	4	2	no	—
255	C₂×C₁₉	—	8	1	no	—
256	C₂×C₁₉	—	8	1	no	—
257	C₂×C₁₉	—	16	2	no	—
258	C₂×C₁₉	D₄×D₈	1	1	yes	characteristic
259	2₋¹⁺⁴	—	2	2	no	—
260	H(5,𝔽₂)	—	2	2	no	—
261	#137	—	2	2	no	—
262	#137	—	2	2	no	—
263	#137	—	4	2	no	—
264	#137	—	4	2	no	—
265	AGL(1,ℤ/8)	—	2	2	no	—
266	AGL(1,ℤ/8)	—	2	2	no	—
267	AGL(1,ℤ/8)	—	4	2	no	—
268	AGL(1,ℤ/8)	—	4	2	no	—
269	#135	—	2	2	no	—
270	#135	—	2	2	no	—
271	#135	—	4	1	no	—
272	#135	—	4	1	no	—
273	#135	D₄×C₁₉	1	1	yes	characteristic
274	#135	C₂³×C₁₉	1	1	yes	characteristic
275	#135	C₂³×C₁₉	1	1	yes	characteristic
276	C₂×Q₁₆	—	2	2	no	—
277	C₂×Q₁₆	—	2	1	no	—
278	C₂×Q₁₆	—	4	1	no	—
279	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
280	C₂×D₈	—	2	2	no	—
281	C₂×D₈	—	2	1	no	—
282	C₂×D₈	—	4	1	no	—
283	C₂×D₈	C₂³×C₁₉	1	2	yes	—
284	#131	—	2	1	no	—
285	#131	—	2	1	no	—
286	#131	C₂³×C₁₉	1	2	yes	—
287	C₄⋊Q₈	—	2	1	no	—
288	#127	—	2	1	no	—
289	Q₃₂	—	2	2	no	—
290	Q₃₂	D₄×C₁₉	1	1	yes	characteristic, complemented
291	SD₃₂	—	2	2	no	—
292	SD₃₂	—	2	2	no	—
293	SD₃₂	—	2	2	no	—
294	SD₃₂	—	2	2	no	—
295	SD₃₂	—	4	2	no	—
296	SD₃₂	D₄×C₁₉	1	1	yes	characteristic, complemented
297	SD₃₂	D₄×C₁₉	1	1	yes	characteristic, complemented
298	D₁₆	—	2	2	no	—
299	D₁₆	D₄×C₁₉	1	1	yes	characteristic, complemented
300	M₃₂	—	2	2	no	—
301	M₃₂	C₂³×C₁₉	1	2	yes	—
302	C₂×C₁₆	—	2	2	no	—
303	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
304	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
305	#108	D₄×C₁₉	1	1	yes	characteristic
306	#108	C₂³×C₁₉	1	1	yes	characteristic
307	#108	C₂³×C₁₉	1	1	yes	characteristic
308	#104	—	2	1	no	—
309	#104	—	2	1	no	—
310	#104	D₄×C₁₉	1	2	yes	—
311	#101	—	2	2	no	—
312	#100	—	2	2	no	—
313	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
314	C₁₉	#33856	1	1	yes	characteristic, direct product factor, Sylow
315	#41	—	2	1	no	—
316	#41	—	2	1	no	—
317	#41	—	4	2	no	—
318	#41	—	4	2	no	—
319	#41	—	4	2	no	—
320	#41	—	4	2	no	—
321	#41	—	8	2	no	—
322	#41	C₂×D₄×C₁₉	1	2	yes	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	4	2	no	—
325	C₂×Q₈	—	4	2	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	4	2	no	—
328	C₂×D₄	—	4	2	no	—
329	C₂×D₄	—	8	1	no	—
330	C₂×D₄	—	8	2	no	—
331	Q₁₆	—	2	2	no	—
332	Q₁₆	—	2	2	no	—
333	Q₁₆	—	4	2	no	—
334	Q₁₆	—	4	2	no	—
335	Q₁₆	—	4	1	no	—
336	Q₁₆	—	4	1	no	—
337	Q₁₆	D₈×C₁₉	1	1	yes	characteristic
338	Q₁₆	C₂×D₄×C₁₉	1	1	yes	characteristic
339	Q₁₆	C₂×D₄×C₁₉	1	1	yes	characteristic
340	SD₁₆	—	2	1	no	—
341	SD₁₆	—	2	1	no	—
342	SD₁₆	—	4	2	no	—
343	SD₁₆	—	4	2	no	—
344	SD₁₆	—	4	2	no	—
345	SD₁₆	—	4	2	no	—
346	SD₁₆	D₈×C₁₉	1	2	yes	—
347	D₈	—	2	2	no	—
348	D₈	—	2	2	no	—
349	D₈	—	4	2	no	—
350	D₈	—	4	2	no	—
351	D₈	—	4	1	no	—
352	D₈	—	4	1	no	—
353	D₈	D₈×C₁₉	1	1	yes	characteristic
354	D₈	C₂×D₄×C₁₉	1	1	yes	characteristic
355	D₈	C₂×D₄×C₁₉	1	1	yes	characteristic
356	M₁₆	—	2	2	no	—
357	M₁₆	—	2	1	no	—
358	M₁₆	—	2	1	no	—
359	M₁₆	—	4	1	no	—
360	M₁₆	—	4	1	no	—
361	M₁₆	C₂×D₄×C₁₉	1	2	yes	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	4	1	no	—
364	C₂×C₈	—	4	1	no	—
365	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
366	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
367	C₄⋊C₄	—	8	1	no	—
368	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
369	C₁₆	—	2	2	no	—
370	C₁₆	—	2	1	no	—
371	C₁₆	C₂×D₄×C₁₉	1	1	yes	characteristic
372	C₁₆	C₂×D₄×C₁₉	1	1	yes	characteristic
373	C₂³	—	4	2	no	—
374	C₂³	—	8	2	no	—
375	Q₈	—	2	1	no	—
376	Q₈	—	2	1	no	—
377	Q₈	—	4	2	no	—
378	Q₈	—	4	2	no	—
379	Q₈	—	8	2	no	—
380	Q₈	C₂×D₈×C₁₉	1	2	yes	—
381	D₄	—	2	2	no	—
382	D₄	—	2	1	no	—
383	D₄	—	2	1	no	—
384	D₄	—	4	1	no	—
385	D₄	—	4	1	no	—
386	D₄	—	4	2	no	—
387	D₄	—	4	2	no	—
388	D₄	—	8	2	no	—
389	D₄	—	8	2	no	—
390	D₄	—	8	2	no	—
391	D₄	—	16	2	no	—
392	D₄	C₂×D₈×C₁₉	1	2	yes	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	8	2	no	—
399	C₂×C₄	—	8	2	no	—
400	C₂×C₄	—	8	2	no	—
401	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
402	C₈	—	2	2	no	—
403	C₈	—	4	1	no	—
404	C₈	—	4	1	no	—
405	C₈	C₂×D₈×C₁₉	1	1	yes	characteristic
406	C₈	C₂×D₈×C₁₉	1	1	yes	characteristic
407	C₈	C₂²×D₄×C₁₉	1	1	yes	characteristic
408	C₈	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
409	C₂²	—	2	2	no	—
410	C₂²	—	4	1	no	—
411	C₂²	—	4	1	no	—
412	C₂²	—	8	2	no	—
413	C₂²	—	16	2	no	—
414	C₂²	—	32	2	no	—
415	C₂²	C₁₉×#576	1	1	yes	characteristic
416	C₄	—	2	2	no	—
417	C₄	—	2	2	no	—
418	C₄	—	4	1	no	—
419	C₄	—	4	1	no	—
420	C₄	—	8	2	no	—
421	C₄	D₄²×C₁₉	1	1	yes	characteristic
422	C₄	C₂²×D₈×C₁₉	1	1	yes	characteristic
423	C₂	—	2	1	no	—
424	C₂	—	4	2	no	—
425	C₂	—	8	1	no	—
426	C₂	—	8	1	no	—
427	C₂	—	16	2	no	—
428	C₂	D₄×D₈×C₁₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₉	D₄×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₉
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₁₉×#443 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3416	C₂	semidirect
2. C₁₉×#3293	C₂	semidirect
3. C₁₉×#3292	C₂	semidirect
4. C₁₉×#2248	C₂	semidirect
5. C₁₉×#2223	C₂	semidirect
6. C₁₉×#2214	C₂	semidirect
7. C₁₉×#2213	C₂	semidirect
8. C₁₉×#2194	C₂	semidirect
9. C₁₉×#2193	C₂	semidirect
10. C₁₉×#2178	C₂	semidirect
11. C₁₉×#2170	C₂	semidirect
13. C₁₉×#578	C₂²	semidirect
19. C₁₉×#509	C₂²	semidirect
23. C₂×C₁₉×SD₃₂	C₂²	semidirect
24. C₂×C₁₉×SD₃₂	C₂²	semidirect
25. C₁₉×#504	C₂²	semidirect
26. C₁₉×#494	C₂²	semidirect
29. C₁₉×#473	C₂²	semidirect
36. C₁₉×#443	C₂²	semidirect
37. C₁₉×#368	C₂²	semidirect
38. C₁₉×#364	C₂²	semidirect
39. C₁₉×#362	C₂²	semidirect
40. C₁₉×#361	C₂²	semidirect
42. C₁₉×#359	C₂²	semidirect
43. C₁₉×#350	C₂²	semidirect
44. C₄×C₁₆×C₁₉	C₂²	semidirect
76. C₁₉×Q₃₂	D₄	semidirect
82. C₁₉×SD₃₂	D₄	semidirect
83. C₁₉×SD₃₂	D₄	semidirect
85. C₁₉×D₁₆	D₄	semidirect
158. #33856	C₁₉	direct (N × H)
195. #3416	C₂×C₁₉	semidirect
196. #3293	C₂×C₁₉	semidirect
197. #3292	C₂×C₁₉	semidirect
198. #2248	C₂×C₁₉	semidirect
199. #2223	C₂×C₁₉	semidirect
200. #2214	C₂×C₁₉	semidirect
201. #2213	C₂×C₁₉	semidirect
202. #2194	C₂×C₁₉	semidirect
203. #2193	C₂×C₁₉	semidirect
204. #2178	C₂×C₁₉	semidirect
205. #2170	C₂×C₁₉	semidirect
221. #578	C₂²×C₁₉	semidirect
227. #509	C₂²×C₁₉	semidirect
231. C₂×SD₃₂	C₂²×C₁₉	semidirect
232. C₂×SD₃₂	C₂²×C₁₉	semidirect
233. #504	C₂²×C₁₉	semidirect
234. #494	C₂²×C₁₉	semidirect
237. #473	C₂²×C₁₉	semidirect
244. #443	C₂²×C₁₉	semidirect
245. #368	C₂²×C₁₉	semidirect
246. #364	C₂²×C₁₉	semidirect
247. #362	C₂²×C₁₉	semidirect
248. #361	C₂²×C₁₉	semidirect
250. #359	C₂²×C₁₉	semidirect
251. #350	C₂²×C₁₉	semidirect
252. C₄×C₁₆	C₂²×C₁₉	semidirect
290. Q₃₂	D₄×C₁₉	semidirect
296. SD₃₂	D₄×C₁₉	semidirect
297. SD₃₂	D₄×C₁₉	semidirect
299. D₁₆	D₄×C₁₉	semidirect
314. C₁₉	#33856	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×#3416	2
C₁₉×#3293	2
C₁₉×#3292	2
C₁₉×#2248	2
C₁₉×#2223	2
C₁₉×#2214	2
C₁₉×#2213	2
C₁₉×#2194	2
C₁₉×#2193	2
C₁₉×#2178	2
C₁₉×#2170	2
#33856	19

Subgroups — C19×#33856 #18039815

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#33856 #18039815