Subgroups — C₁₉×#23915 #18029874

Order 4864.

1886 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3487	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#535	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#454	C₂	1	2	yes	maximal, complemented
4	C₁₉×#3003	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2002	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1897	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1888	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1785	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₉×2₋¹⁺⁴	C₂²	1	1	yes	characteristic, complemented
10	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
11	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	4	yes	—
13	C₁₉×#550	—	2	4	no	—
14	C₁₉×#548	—	2	4	no	—
15	C₁₉×#535	—	2	2	no	—
16	C₁₉×#535	—	2	8	no	—
17	C₁₉×#535	C₂²	1	2	yes	complemented
18	C₂×C₁₉×#127	C₂²	1	2	yes	—
19	C₂×C₁₉×#124	C₂²	1	2	yes	—
20	C₁₉×#525	—	2	2	no	—
21	C₁₉×#525	C₂²	1	2	yes	—
22	C₂×C₁₉×#121	—	2	2	no	—
23	C₂×C₁₉×#120	—	2	2	no	—
24	C₁₉×#519	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
26	C₁₉×#454	—	2	8	no	—
27	C₁₉×#450	—	2	4	no	—
28	C₁₉×#447	—	2	4	no	—
29	C₂×C₁₉×#104	C₂²	1	4	yes	complemented
30	C₁₉×#418	C₂²	1	4	yes	—
31	C₂×C₁₉×#101	C₂²	1	2	yes	complemented
32	C₂×C₁₉×#100	C₂²	1	2	yes	complemented
33	C₁₉×#407	C₂²	1	2	yes	—
34	C₁₉×#339	C₂²	1	4	yes	complemented
35	C₂⁵×C₁₉	—	2	1	no	—
36	C₁₉×2₋¹⁺⁴	—	2	4	no	—
37	C₁₉×2₋¹⁺⁴	—	4	2	no	—
38	C₂×#41×C₁₉	—	2	4	no	—
39	C₂×#41×C₁₉	—	2	2	no	—
40	C₂×#41×C₁₉	—	2	2	no	—
41	C₂×#41×C₁₉	—	2	4	no	—
42	C₂×#41×C₁₉	—	4	2	no	—
43	C₂×#41×C₁₉	C₂³	1	2	yes	—
44	C₂²×Q₈×C₁₉	—	2	2	no	—
45	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₁₉	—	2	4	no	—
47	C₂²×D₄×C₁₉	—	2	4	no	—
48	C₂²×D₄×C₁₉	—	2	1	no	—
49	C₂²×D₄×C₁₉	—	2	4	no	—
50	C₂²×D₄×C₁₉	—	4	2	no	—
51	C₂²×D₄×C₁₉	D₄	1	2	yes	—
52	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
53	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
54	C₂³×C₄×C₁₉	D₄	1	2	yes	—
55	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
56	C₁₉×AGL(1,ℤ/8)	—	2	8	no	—
57	C₁₉×AGL(1,ℤ/8)	—	4	4	no	—
58	C₂×SD₁₆×C₁₉	—	2	4	no	—
59	C₂×D₈×C₁₉	—	2	4	no	—
60	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
61	C₁₉×#127	—	2	4	no	—
62	C₁₉×#127	—	2	4	no	—
63	C₁₉×#127	—	2	2	no	—
64	C₁₉×#127	—	2	4	no	—
65	C₁₉×#124	—	2	4	no	—
66	C₁₉×#124	—	2	4	no	—
67	C₁₉×#124	—	2	2	no	—
68	C₁₉×#124	D₄	1	8	yes	complemented
69	C₁₉×#123	—	2	2	no	—
70	C₁₉×C₂²⋊Q₈	—	2	4	no	—
71	C₁₉×C₂²⋊Q₈	D₄	1	4	yes	complemented
72	C₁₉×#121	—	2	16	no	—
73	C₁₉×#121	—	2	4	no	—
74	C₁₉×#121	—	2	8	no	—
75	C₁₉×#121	—	2	4	no	—
76	C₁₉×#121	D₄	1	4	yes	complemented
77	C₁₉×#120	—	2	16	no	—
78	C₁₉×#120	—	2	4	no	—
79	C₁₉×#120	—	2	2	no	—
80	C₄×Q₈×C₁₉	—	2	4	no	—
81	C₄×D₄×C₁₉	—	2	8	no	—
82	C₄×D₄×C₁₉	—	2	4	no	—
83	C₁₉×#117	—	2	2	no	—
84	C₁₉×#117	—	2	4	no	—
85	C₁₉×#117	C₂³	1	2	yes	—
86	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
87	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
88	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
89	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
90	C₁₉×#104	—	2	8	no	—
91	C₁₉×#102	—	2	8	no	—
92	C₁₉×#101	—	2	4	no	—
93	C₁₉×#100	—	4	2	no	—
94	C₁₉×C₂²⋊C₈	—	2	4	no	—
95	C₂⁴×C₁₉	—	2	4	no	—
96	C₂⁴×C₁₉	—	2	2	no	—
97	C₂⁴×C₁₉	—	4	2	no	—
98	C₂⁴×C₁₉	—	4	2	no	—
99	C₂⁴×C₁₉	—	8	4	no	—
100	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
101	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
102	#41×C₁₉	—	2	4	no	—
103	#41×C₁₉	—	2	4	no	—
104	#41×C₁₉	—	4	16	no	—
105	#41×C₁₉	—	4	4	no	—
106	#41×C₁₉	—	4	8	no	—
107	#41×C₁₉	—	4	4	no	—
108	C₂×Q₈×C₁₉	—	2	2	no	—
109	C₂×Q₈×C₁₉	—	2	2	no	—
110	C₂×Q₈×C₁₉	—	2	2	no	—
111	C₂×Q₈×C₁₉	—	4	8	no	—
112	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
113	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
114	C₂×D₄×C₁₉	—	2	4	no	—
115	C₂×D₄×C₁₉	—	2	2	no	—
116	C₂×D₄×C₁₉	—	2	4	no	—
117	C₂×D₄×C₁₉	—	2	2	no	—
118	C₂×D₄×C₁₉	—	2	8	no	—
119	C₂×D₄×C₁₉	—	2	16	no	—
120	C₂×D₄×C₁₉	—	2	4	no	—
121	C₂×D₄×C₁₉	—	2	4	no	—
122	C₂×D₄×C₁₉	—	2	4	no	—
123	C₂×D₄×C₁₉	—	2	2	no	—
124	C₂×D₄×C₁₉	—	2	2	no	—
125	C₂×D₄×C₁₉	—	2	2	no	—
126	C₂×D₄×C₁₉	—	2	4	no	—
127	C₂×D₄×C₁₉	—	2	2	no	—
128	C₂×D₄×C₁₉	—	4	16	no	—
129	C₂×D₄×C₁₉	—	4	2	no	—
130	C₂×D₄×C₁₉	—	4	2	no	—
131	C₂×D₄×C₁₉	—	4	2	no	—
132	C₂×D₄×C₁₉	—	8	8	no	—
133	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
134	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
135	C₂²×C₄×C₁₉	—	2	2	no	—
136	C₂²×C₄×C₁₉	—	2	2	no	—
137	C₂²×C₄×C₁₉	—	2	4	no	—
138	C₂²×C₄×C₁₉	—	2	2	no	—
139	C₂²×C₄×C₁₉	—	2	4	no	—
140	C₂²×C₄×C₁₉	—	2	4	no	—
141	C₂²×C₄×C₁₉	—	2	2	no	—
142	C₂²×C₄×C₁₉	—	4	2	no	—
143	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
146	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
147	SD₁₆×C₁₉	—	4	8	no	—
148	D₈×C₁₉	—	4	8	no	—
149	M₁₆×C₁₉	—	2	4	no	—
150	M₁₆×C₁₉	—	2	4	no	—
151	C₂×C₈×C₁₉	—	2	4	no	—
152	C₄⋊C₄×C₁₉	—	2	4	no	—
153	C₄⋊C₄×C₁₉	—	2	4	no	—
154	C₄⋊C₄×C₁₉	—	2	4	no	—
155	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
156	C₂²⋊C₄×C₁₉	—	2	4	no	—
157	C₂²⋊C₄×C₁₉	—	2	8	no	—
158	C₂²⋊C₄×C₁₉	—	2	4	no	—
159	C₂²⋊C₄×C₁₉	—	2	2	no	—
160	C₂²⋊C₄×C₁₉	—	2	16	no	—
161	C₂²⋊C₄×C₁₉	—	2	4	no	—
162	C₄²×C₁₉	—	2	4	no	—
163	C₄²×C₁₉	—	2	2	no	—
164	C₄²×C₁₉	—	2	2	no	—
165	C₄²×C₁₉	C₂×D₄	1	4	yes	—
166	#23915	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
167	C₂³×C₁₉	—	2	1	no	—
168	C₂³×C₁₉	—	2	1	no	—
169	C₂³×C₁₉	—	2	4	no	—
170	C₂³×C₁₉	—	2	2	no	—
171	C₂³×C₁₉	—	2	2	no	—
172	C₂³×C₁₉	—	2	2	no	—
173	C₂³×C₁₉	—	2	2	no	—
174	C₂³×C₁₉	—	4	2	no	—
175	C₂³×C₁₉	—	4	4	no	—
176	C₂³×C₁₉	—	4	8	no	—
177	C₂³×C₁₉	—	4	8	no	—
178	C₂³×C₁₉	—	4	2	no	—
179	C₂³×C₁₉	—	4	2	no	—
180	C₂³×C₁₉	—	8	8	no	—
181	C₂³×C₁₉	—	8	8	no	—
182	C₂³×C₁₉	—	8	8	no	—
183	C₂³×C₁₉	#120	1	2	yes	—
184	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
185	Q₈×C₁₉	—	2	8	no	—
186	Q₈×C₁₉	—	2	4	no	—
187	Q₈×C₁₉	—	4	4	no	—
188	D₄×C₁₉	—	2	4	no	—
189	D₄×C₁₉	—	2	8	no	—
190	D₄×C₁₉	—	4	8	no	—
191	D₄×C₁₉	—	4	8	no	—
192	D₄×C₁₉	—	4	4	no	—
193	D₄×C₁₉	—	4	2	no	—
194	D₄×C₁₉	—	4	2	no	—
195	D₄×C₁₉	—	4	4	no	—
196	D₄×C₁₉	—	4	4	no	—
197	D₄×C₁₉	—	8	4	no	—
198	D₄×C₁₉	—	8	8	no	—
199	D₄×C₁₉	—	8	16	no	—
200	C₂×C₄×C₁₉	—	2	1	no	—
201	C₂×C₄×C₁₉	—	2	2	no	—
202	C₂×C₄×C₁₉	—	2	1	no	—
203	C₂×C₄×C₁₉	—	2	2	no	—
204	C₂×C₄×C₁₉	—	2	8	no	—
205	C₂×C₄×C₁₉	—	2	4	no	—
206	C₂×C₄×C₁₉	—	2	4	no	—
207	C₂×C₄×C₁₉	—	2	2	no	—
208	C₂×C₄×C₁₉	—	4	8	no	—
209	C₂×C₄×C₁₉	—	4	8	no	—
210	C₂×C₄×C₁₉	—	4	4	no	—
211	C₂×C₄×C₁₉	—	4	4	no	—
212	C₂×C₄×C₁₉	#120	1	4	yes	—
213	C₂×C₄×C₁₉	#120	1	2	yes	—
214	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
215	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
216	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
217	C₈×C₁₉	—	4	4	no	—
218	#3487	C₂×C₁₉	1	1	yes	characteristic, complemented
219	C₂×#535	C₂×C₁₉	1	1	yes	characteristic, complemented
220	C₂×#454	C₂×C₁₉	1	2	yes	complemented
221	#3003	C₂×C₁₉	1	2	yes	complemented
222	#2002	C₂×C₁₉	1	4	yes	complemented
223	#1897	C₂×C₁₉	1	2	yes	complemented
224	#1888	C₂×C₁₉	1	2	yes	complemented
225	#1785	C₂×C₁₉	1	1	yes	characteristic, complemented
226	C₂²×C₁₉	—	2	2	no	—
227	C₂²×C₁₉	—	2	2	no	—
228	C₂²×C₁₉	—	2	4	no	—
229	C₂²×C₁₉	—	4	2	no	—
230	C₂²×C₁₉	—	4	2	no	—
231	C₂²×C₁₉	—	4	4	no	—
232	C₂²×C₁₉	—	4	8	no	—
233	C₂²×C₁₉	—	4	2	no	—
234	C₂²×C₁₉	—	4	2	no	—
235	C₂²×C₁₉	—	4	4	no	—
236	C₂²×C₁₉	—	4	4	no	—
237	C₂²×C₁₉	—	4	4	no	—
238	C₂²×C₁₉	—	8	2	no	—
239	C₂²×C₁₉	—	8	4	no	—
240	C₂²×C₁₉	—	8	16	no	—
241	C₂²×C₁₉	—	8	4	no	—
242	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
243	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
244	C₂²×C₁₉	#534	1	1	yes	characteristic
245	C₄×C₁₉	—	2	2	no	—
246	C₄×C₁₉	—	2	4	no	—
247	C₄×C₁₉	—	4	4	no	—
248	C₄×C₁₉	—	4	2	no	—
249	C₄×C₁₉	—	4	4	no	—
250	C₄×C₁₉	D₄²	1	4	yes	—
251	C₂×2₋¹⁺⁴	C₂²×C₁₉	1	1	yes	characteristic, complemented
252	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
253	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
254	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	4	yes	—
255	#550	—	2	4	no	—
256	#548	—	2	4	no	—
257	#535	—	2	2	no	—
258	#535	—	2	8	no	—
259	#535	C₂²×C₁₉	1	2	yes	complemented
260	C₂×#127	C₂²×C₁₉	1	2	yes	—
261	C₂×#124	C₂²×C₁₉	1	2	yes	—
262	#525	—	2	2	no	—
263	#525	C₂²×C₁₉	1	2	yes	—
264	C₂×#121	—	2	2	no	—
265	C₂×#120	—	2	2	no	—
266	#519	C₂²×C₁₉	1	1	yes	characteristic, complemented
267	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
268	#454	—	2	8	no	—
269	#450	—	2	4	no	—
270	#447	—	2	4	no	—
271	C₂×#104	C₂²×C₁₉	1	4	yes	complemented
272	#418	C₂²×C₁₉	1	4	yes	—
273	C₂×#101	C₂²×C₁₉	1	2	yes	complemented
274	C₂×#100	C₂²×C₁₉	1	2	yes	complemented
275	#407	C₂²×C₁₉	1	2	yes	—
276	#339	C₂²×C₁₉	1	4	yes	complemented
277	C₂×C₁₉	—	2	1	no	—
278	C₂×C₁₉	—	2	1	no	—
279	C₂×C₁₉	—	4	2	no	—
280	C₂×C₁₉	—	8	2	no	—
281	C₂×C₁₉	—	8	2	no	—
282	C₂×C₁₉	—	8	4	no	—
283	C₂×C₁₉	#2403	1	1	yes	characteristic
284	C₂×C₁₉	#3021	1	2	yes	—
285	C₂⁵	—	2	1	no	—
286	2₋¹⁺⁴	—	2	4	no	—
287	2₋¹⁺⁴	—	4	2	no	—
288	C₂×#41	—	2	4	no	—
289	C₂×#41	—	2	2	no	—
290	C₂×#41	—	2	2	no	—
291	C₂×#41	—	2	4	no	—
292	C₂×#41	—	4	2	no	—
293	C₂×#41	C₂³×C₁₉	1	2	yes	—
294	C₂²×Q₈	—	2	2	no	—
295	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
296	C₂²×D₄	—	2	4	no	—
297	C₂²×D₄	—	2	4	no	—
298	C₂²×D₄	—	2	1	no	—
299	C₂²×D₄	—	2	4	no	—
300	C₂²×D₄	—	4	2	no	—
301	C₂²×D₄	D₄×C₁₉	1	2	yes	—
302	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
303	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
304	C₂³×C₄	D₄×C₁₉	1	2	yes	—
305	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
306	AGL(1,ℤ/8)	—	2	8	no	—
307	AGL(1,ℤ/8)	—	4	4	no	—
308	C₂×SD₁₆	—	2	4	no	—
309	C₂×D₈	—	2	4	no	—
310	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
311	#127	—	2	4	no	—
312	#127	—	2	4	no	—
313	#127	—	2	2	no	—
314	#127	—	2	4	no	—
315	#124	—	2	4	no	—
316	#124	—	2	4	no	—
317	#124	—	2	2	no	—
318	#124	D₄×C₁₉	1	8	yes	complemented
319	#123	—	2	2	no	—
320	C₂²⋊Q₈	—	2	4	no	—
321	C₂²⋊Q₈	D₄×C₁₉	1	4	yes	complemented
322	#121	—	2	16	no	—
323	#121	—	2	4	no	—
324	#121	—	2	8	no	—
325	#121	—	2	4	no	—
326	#121	D₄×C₁₉	1	4	yes	complemented
327	#120	—	2	16	no	—
328	#120	—	2	4	no	—
329	#120	—	2	2	no	—
330	C₄×Q₈	—	2	4	no	—
331	C₄×D₄	—	2	8	no	—
332	C₄×D₄	—	2	4	no	—
333	#117	—	2	2	no	—
334	#117	—	2	4	no	—
335	#117	C₂³×C₁₉	1	2	yes	—
336	C₂×C₄⋊C₄	—	2	1	no	—
337	C₂×C₂²⋊C₄	—	2	1	no	—
338	C₂×C₂²⋊C₄	—	2	4	no	—
339	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
340	#104	—	2	8	no	—
341	#102	—	2	8	no	—
342	#101	—	2	4	no	—
343	#100	—	4	2	no	—
344	C₂²⋊C₈	—	2	4	no	—
345	C₁₉	#23915	1	1	yes	characteristic, direct product factor, Sylow
346	C₂⁴	—	2	4	no	—
347	C₂⁴	—	2	2	no	—
348	C₂⁴	—	4	2	no	—
349	C₂⁴	—	4	2	no	—
350	C₂⁴	—	8	4	no	—
351	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
352	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
353	#41	—	2	4	no	—
354	#41	—	2	4	no	—
355	#41	—	4	16	no	—
356	#41	—	4	4	no	—
357	#41	—	4	8	no	—
358	#41	—	4	4	no	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	2	2	no	—
361	C₂×Q₈	—	2	2	no	—
362	C₂×Q₈	—	4	8	no	—
363	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
364	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
365	C₂×D₄	—	2	4	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	2	4	no	—
368	C₂×D₄	—	2	2	no	—
369	C₂×D₄	—	2	8	no	—
370	C₂×D₄	—	2	16	no	—
371	C₂×D₄	—	2	4	no	—
372	C₂×D₄	—	2	4	no	—
373	C₂×D₄	—	2	4	no	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	2	4	no	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	—	4	16	no	—
380	C₂×D₄	—	4	2	no	—
381	C₂×D₄	—	4	2	no	—
382	C₂×D₄	—	4	2	no	—
383	C₂×D₄	—	8	8	no	—
384	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
385	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	4	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	4	no	—
391	C₂²×C₄	—	2	4	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	4	2	no	—
394	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
395	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
396	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
397	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
398	SD₁₆	—	4	8	no	—
399	D₈	—	4	8	no	—
400	M₁₆	—	2	4	no	—
401	M₁₆	—	2	4	no	—
402	C₂×C₈	—	2	4	no	—
403	C₄⋊C₄	—	2	4	no	—
404	C₄⋊C₄	—	2	4	no	—
405	C₄⋊C₄	—	2	4	no	—
406	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
407	C₂²⋊C₄	—	2	4	no	—
408	C₂²⋊C₄	—	2	8	no	—
409	C₂²⋊C₄	—	2	4	no	—
410	C₂²⋊C₄	—	2	2	no	—
411	C₂²⋊C₄	—	2	16	no	—
412	C₂²⋊C₄	—	2	4	no	—
413	C₄²	—	2	4	no	—
414	C₄²	—	2	2	no	—
415	C₄²	—	2	2	no	—
416	C₄²	C₂×D₄×C₁₉	1	4	yes	—
417	C₂³	—	2	1	no	—
418	C₂³	—	2	1	no	—
419	C₂³	—	2	2	no	—
420	C₂³	—	2	4	no	—
421	C₂³	—	2	2	no	—
422	C₂³	—	2	2	no	—
423	C₂³	—	2	2	no	—
424	C₂³	—	4	2	no	—
425	C₂³	—	4	4	no	—
426	C₂³	—	4	8	no	—
427	C₂³	—	4	8	no	—
428	C₂³	—	4	2	no	—
429	C₂³	—	4	2	no	—
430	C₂³	—	8	8	no	—
431	C₂³	—	8	8	no	—
432	C₂³	—	8	8	no	—
433	C₂³	C₁₉×#120	1	2	yes	—
434	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
435	Q₈	—	2	8	no	—
436	Q₈	—	2	4	no	—
437	Q₈	—	4	4	no	—
438	D₄	—	2	4	no	—
439	D₄	—	2	8	no	—
440	D₄	—	4	8	no	—
441	D₄	—	4	8	no	—
442	D₄	—	4	4	no	—
443	D₄	—	4	2	no	—
444	D₄	—	4	2	no	—
445	D₄	—	4	4	no	—
446	D₄	—	4	4	no	—
447	D₄	—	8	4	no	—
448	D₄	—	8	16	no	—
449	D₄	—	8	8	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	8	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	4	8	no	—
459	C₂×C₄	—	4	8	no	—
460	C₂×C₄	—	4	4	no	—
461	C₂×C₄	—	4	4	no	—
462	C₂×C₄	C₁₉×#120	1	4	yes	—
463	C₂×C₄	C₁₉×#120	1	2	yes	—
464	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
465	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
466	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
467	C₈	—	4	4	no	—
468	C₂²	—	2	2	no	—
469	C₂²	—	2	2	no	—
470	C₂²	—	2	4	no	—
471	C₂²	—	4	2	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	4	4	no	—
474	C₂²	—	4	8	no	—
475	C₂²	—	4	2	no	—
476	C₂²	—	4	2	no	—
477	C₂²	—	4	4	no	—
478	C₂²	—	4	4	no	—
479	C₂²	—	4	4	no	—
480	C₂²	—	8	2	no	—
481	C₂²	—	8	4	no	—
482	C₂²	—	8	16	no	—
483	C₂²	—	8	4	no	—
484	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
485	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
486	C₂²	C₁₉×#534	1	1	yes	characteristic
487	C₄	—	2	2	no	—
488	C₄	—	2	4	no	—
489	C₄	—	4	4	no	—
490	C₄	—	4	2	no	—
491	C₄	—	4	4	no	—
492	C₄	D₄²×C₁₉	1	4	yes	—
493	C₂	—	2	1	no	—
494	C₂	—	2	1	no	—
495	C₂	—	4	2	no	—
496	C₂	—	8	2	no	—
497	C₂	—	8	4	no	—
498	C₂	—	8	2	no	—
499	C₂	C₁₉×#2403	1	1	yes	characteristic
500	C₂	C₁₉×#3021	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3487	C₂	semidirect
2. C₂×C₁₉×#535	C₂	semidirect
3. C₂×C₁₉×#454	C₂	semidirect
4. C₁₉×#3003	C₂	semidirect
5. C₁₉×#2002	C₂	semidirect
6. C₁₉×#1897	C₂	semidirect
7. C₁₉×#1888	C₂	semidirect
8. C₁₉×#1785	C₂	semidirect
9. C₂×C₁₉×2₋¹⁺⁴	C₂²	semidirect
17. C₁₉×#535	C₂²	semidirect
24. C₁₉×#519	C₂²	semidirect
29. C₂×C₁₉×#104	C₂²	semidirect
31. C₂×C₁₉×#101	C₂²	semidirect
32. C₂×C₁₉×#100	C₂²	semidirect
34. C₁₉×#339	C₂²	semidirect
68. C₁₉×#124	D₄	semidirect
71. C₁₉×C₂²⋊Q₈	D₄	semidirect
76. C₁₉×#121	D₄	semidirect
166. #23915	C₁₉	direct (N × H)
218. #3487	C₂×C₁₉	semidirect
219. C₂×#535	C₂×C₁₉	semidirect
220. C₂×#454	C₂×C₁₉	semidirect
221. #3003	C₂×C₁₉	semidirect
222. #2002	C₂×C₁₉	semidirect
223. #1897	C₂×C₁₉	semidirect
224. #1888	C₂×C₁₉	semidirect
225. #1785	C₂×C₁₉	semidirect
251. C₂×2₋¹⁺⁴	C₂²×C₁₉	semidirect
259. #535	C₂²×C₁₉	semidirect
266. #519	C₂²×C₁₉	semidirect
271. C₂×#104	C₂²×C₁₉	semidirect
273. C₂×#101	C₂²×C₁₉	semidirect
274. C₂×#100	C₂²×C₁₉	semidirect
276. #339	C₂²×C₁₉	semidirect
318. #124	D₄×C₁₉	semidirect
321. C₂²⋊Q₈	D₄×C₁₉	semidirect
326. #121	D₄×C₁₉	semidirect
345. C₁₉	#23915	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×#3487	2
C₂×C₁₉×#535	2
C₂×C₁₉×#454	2
C₁₉×#3003	2
C₁₉×#2002	2
C₁₉×#1897	2
C₁₉×#1888	2
C₁₉×#1785	2
#23915	19

Subgroups — C19×#23915 #18029874

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23915 #18029874