Subgroups — C₁₉×#33530 #18039489

Order 4864.

1132 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#575	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3414	C₂	1	2	yes	maximal, complemented
3	C₁₉×#3054	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	C₁₉×#2145	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₉×#349	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#41×C₁₉	—	2	1	no	—
9	C₁₉×#575	—	2	4	no	—
10	C₁₉×#575	—	2	2	no	—
11	C₁₉×#575	C₂²	1	4	yes	—
12	C₂×C₁₉×#137	—	2	2	no	—
13	C₂×C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
14	C₂×C₁₉×#135	—	2	1	no	—
15	C₂×C₁₉×#135	C₂²	1	2	yes	—
16	C₂×C₁₉×#135	C₂²	1	1	yes	characteristic, complemented
17	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#525	—	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×#468	—	2	2	no	—
28	C₁₉×#427	C₂²	1	1	yes	characteristic, complemented
29	C₁₉×#416	—	2	1	no	—
30	C₁₉×#360	C₂²	1	8	yes	complemented
31	C₁₉×#349	C₂²	1	4	yes	complemented
32	C₂×#41×C₁₉	—	2	2	no	—
33	C₂×#41×C₁₉	—	2	4	no	—
34	C₂×#41×C₁₉	—	2	4	no	—
35	C₂×#41×C₁₉	—	2	2	no	—
36	C₂×#41×C₁₉	—	2	1	no	—
37	C₂×#41×C₁₉	—	4	1	no	—
38	C₂×#41×C₁₉	—	4	2	no	—
39	C₂×#41×C₁₉	—	4	2	no	—
40	C₂×#41×C₁₉	—	4	1	no	—
41	C₂²×Q₈×C₁₉	—	2	1	no	—
42	C₂²×D₄×C₁₉	—	2	1	no	—
43	C₂²×D₄×C₁₉	—	4	1	no	—
44	C₂³×C₄×C₁₉	—	4	1	no	—
45	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
46	C₁₉×#137	—	2	8	no	—
47	C₁₉×#137	—	2	8	no	—
48	C₁₉×AGL(1,ℤ/8)	—	2	8	no	—
49	C₁₉×AGL(1,ℤ/8)	—	2	8	no	—
50	C₁₉×#135	—	2	4	no	—
51	C₁₉×#135	—	2	4	no	—
52	C₁₉×#135	—	2	2	no	—
53	C₁₉×#135	—	2	2	no	—
54	C₁₉×#135	—	2	2	no	—
55	C₁₉×#135	—	2	2	no	—
56	C₁₉×#135	D₄	1	4	yes	complemented
57	C₁₉×#135	C₂³	1	4	yes	—
58	C₂×Q₁₆×C₁₉	—	2	1	no	—
59	C₂×Q₁₆×C₁₉	D₄	1	2	yes	complemented
60	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic, complemented
61	C₂×SD₁₆×C₁₉	—	2	2	no	—
62	C₂×SD₁₆×C₁₉	—	2	2	no	—
63	C₂×SD₁₆×C₁₉	—	2	1	no	—
64	C₂×D₈×C₁₉	—	2	1	no	—
65	C₂×D₈×C₁₉	D₄	1	2	yes	complemented
66	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic, complemented
67	C₂×M₁₆×C₁₉	—	2	2	no	—
68	C₂×M₁₆×C₁₉	—	2	2	no	—
69	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
70	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
71	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
72	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
73	C₁₉×#123	—	4	1	no	—
74	C₁₉×C₂²⋊Q₈	—	2	2	no	—
75	C₁₉×#121	—	2	2	no	—
76	C₁₉×#120	—	4	1	no	—
77	C₄×D₄×C₁₉	—	4	2	no	—
78	C₁₉×#117	—	2	1	no	—
79	C₁₉×Q₃₂	—	2	4	no	—
80	C₁₉×SD₃₂	—	2	4	no	—
81	C₁₉×SD₃₂	—	2	4	no	—
82	C₁₉×D₁₆	—	2	4	no	—
83	C₁₉×M₃₂	—	2	2	no	—
84	C₁₉×M₃₂	C₂³	1	4	yes	complemented
85	C₂×C₁₆×C₁₉	—	2	2	no	—
86	C₁₉×#107	—	2	1	no	—
87	C₁₉×#106	C₂³	1	2	yes	complemented
88	C₁₉×#103	—	2	2	no	—
89	C₁₉×#102	—	2	2	no	—
90	C₂⁴×C₁₉	—	4	1	no	—
91	C₂⁴×C₁₉	D₈	1	1	yes	characteristic
92	#41×C₁₉	—	2	8	no	—
93	#41×C₁₉	—	2	4	no	—
94	#41×C₁₉	—	2	4	no	—
95	#41×C₁₉	—	4	4	no	—
96	#41×C₁₉	—	4	4	no	—
97	#41×C₁₉	—	4	4	no	—
98	#41×C₁₉	—	4	4	no	—
99	#41×C₁₉	—	4	4	no	—
100	#41×C₁₉	—	4	2	no	—
101	#41×C₁₉	—	4	2	no	—
102	#41×C₁₉	—	4	1	no	—
103	#41×C₁₉	—	4	1	no	—
104	#41×C₁₉	—	4	1	no	—
105	#41×C₁₉	—	4	1	no	—
106	C₂×Q₈×C₁₉	—	2	4	no	—
107	C₂×Q₈×C₁₉	—	2	2	no	—
108	C₂×Q₈×C₁₉	—	2	1	no	—
109	C₂×Q₈×C₁₉	—	4	1	no	—
110	C₂×Q₈×C₁₉	—	4	2	no	—
111	C₂×D₄×C₁₉	—	2	4	no	—
112	C₂×D₄×C₁₉	—	2	2	no	—
113	C₂×D₄×C₁₉	—	2	1	no	—
114	C₂×D₄×C₁₉	—	4	1	no	—
115	C₂×D₄×C₁₉	—	4	2	no	—
116	C₂×D₄×C₁₉	—	4	4	no	—
117	C₂×D₄×C₁₉	—	4	2	no	—
118	C₂×D₄×C₁₉	—	4	4	no	—
119	C₂×D₄×C₁₉	—	4	2	no	—
120	C₂×D₄×C₁₉	—	4	2	no	—
121	C₂×D₄×C₁₉	—	4	1	no	—
122	C₂²×C₄×C₁₉	—	2	1	no	—
123	C₂²×C₄×C₁₉	—	2	1	no	—
124	C₂²×C₄×C₁₉	—	2	1	no	—
125	C₂²×C₄×C₁₉	—	2	1	no	—
126	C₂²×C₄×C₁₉	—	4	2	no	—
127	C₂²×C₄×C₁₉	—	4	4	no	—
128	C₂²×C₄×C₁₉	—	4	4	no	—
129	C₂²×C₄×C₁₉	—	4	1	no	—
130	C₂²×C₄×C₁₉	—	4	2	no	—
131	C₂²×C₄×C₁₉	—	4	1	no	—
132	C₂²×C₄×C₁₉	D₈	1	2	yes	—
133	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
134	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
136	Q₁₆×C₁₉	—	2	4	no	—
137	Q₁₆×C₁₉	—	2	2	no	—
138	Q₁₆×C₁₉	—	2	2	no	—
139	Q₁₆×C₁₉	C₂×D₄	1	4	yes	—
140	SD₁₆×C₁₉	—	2	8	no	—
141	SD₁₆×C₁₉	—	2	4	no	—
142	SD₁₆×C₁₉	—	2	4	no	—
143	SD₁₆×C₁₉	—	4	2	no	—
144	D₈×C₁₉	—	2	4	no	—
145	D₈×C₁₉	—	2	2	no	—
146	D₈×C₁₉	—	2	2	no	—
147	D₈×C₁₉	C₂×D₄	1	4	yes	—
148	M₁₆×C₁₉	—	2	4	no	—
149	M₁₆×C₁₉	—	2	4	no	—
150	C₂×C₈×C₁₉	—	2	1	no	—
151	C₂×C₈×C₁₉	—	2	1	no	—
152	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
153	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
155	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
156	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
157	C₄⋊C₄×C₁₉	—	2	2	no	—
158	C₄⋊C₄×C₁₉	—	4	2	no	—
159	C₂²⋊C₄×C₁₉	—	4	1	no	—
160	C₂²⋊C₄×C₁₉	—	4	2	no	—
161	C₂²⋊C₄×C₁₉	—	4	2	no	—
162	C₄²×C₁₉	—	4	1	no	—
163	C₁₆×C₁₉	—	2	4	no	—
164	#33530	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
165	C₂³×C₁₉	—	2	1	no	—
166	C₂³×C₁₉	—	2	1	no	—
167	C₂³×C₁₉	—	4	4	no	—
168	C₂³×C₁₉	—	4	2	no	—
169	C₂³×C₁₉	—	4	1	no	—
170	C₂³×C₁₉	—	8	1	no	—
171	C₂³×C₁₉	—	8	4	no	—
172	C₂³×C₁₉	C₂×D₈	1	2	yes	—
173	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
174	Q₈×C₁₉	—	2	4	no	—
175	Q₈×C₁₉	—	4	4	no	—
176	Q₈×C₁₉	—	4	2	no	—
177	Q₈×C₁₉	—	4	1	no	—
178	Q₈×C₁₉	—	4	1	no	—
179	D₄×C₁₉	—	2	4	no	—
180	D₄×C₁₉	—	4	4	no	—
181	D₄×C₁₉	—	4	8	no	—
182	D₄×C₁₉	—	4	4	no	—
183	D₄×C₁₉	—	4	4	no	—
184	D₄×C₁₉	—	4	1	no	—
185	D₄×C₁₉	—	4	1	no	—
186	D₄×C₁₉	—	4	2	no	—
187	D₄×C₁₉	—	8	4	no	—
188	D₄×C₁₉	—	8	1	no	—
189	D₄×C₁₉	—	8	1	no	—
190	C₂×C₄×C₁₉	—	2	1	no	—
191	C₂×C₄×C₁₉	—	2	1	no	—
192	C₂×C₄×C₁₉	—	2	2	no	—
193	C₂×C₄×C₁₉	—	2	2	no	—
194	C₂×C₄×C₁₉	—	2	2	no	—
195	C₂×C₄×C₁₉	—	2	2	no	—
196	C₂×C₄×C₁₉	—	4	8	no	—
197	C₂×C₄×C₁₉	—	4	4	no	—
198	C₂×C₄×C₁₉	—	4	2	no	—
199	C₂×C₄×C₁₉	—	4	4	no	—
200	C₂×C₄×C₁₉	—	4	4	no	—
201	C₂×C₄×C₁₉	—	4	2	no	—
202	C₂×C₄×C₁₉	—	4	1	no	—
203	C₂×C₄×C₁₉	—	8	1	no	—
204	C₂×C₄×C₁₉	—	8	1	no	—
205	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
206	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
207	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
208	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
209	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
210	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
211	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
212	C₈×C₁₉	—	2	2	no	—
213	C₈×C₁₉	#120	1	2	yes	—
214	C₈×C₁₉	C₂²×D₄	1	2	yes	—
215	C₂×#575	C₂×C₁₉	1	1	yes	characteristic, complemented
216	#3414	C₂×C₁₉	1	2	yes	complemented
217	#3054	C₂×C₁₉	1	1	yes	characteristic, complemented
218	#2191	C₂×C₁₉	1	4	yes	complemented
219	#2190	C₂×C₁₉	1	4	yes	complemented
220	#2145	C₂×C₁₉	1	2	yes	complemented
221	C₂×#349	C₂×C₁₉	1	1	yes	characteristic, complemented
222	C₂²×C₁₉	—	2	2	no	—
223	C₂²×C₁₉	—	4	1	no	—
224	C₂²×C₁₉	—	4	2	no	—
225	C₂²×C₁₉	—	4	2	no	—
226	C₂²×C₁₉	—	4	4	no	—
227	C₂²×C₁₉	—	8	1	no	—
228	C₂²×C₁₉	—	8	4	no	—
229	C₂²×C₁₉	—	8	2	no	—
230	C₂²×C₁₉	—	8	8	no	—
231	C₂²×C₁₉	—	8	1	no	—
232	C₂²×C₁₉	#447	1	1	yes	characteristic
233	C₂²×C₁₉	#447	1	1	yes	characteristic
234	C₂²×C₁₉	C₂²×D₈	1	1	yes	characteristic
235	C₄×C₁₉	—	2	2	no	—
236	C₄×C₁₉	—	4	4	no	—
237	C₄×C₁₉	—	8	2	no	—
238	C₄×C₁₉	—	8	1	no	—
239	C₄×C₁₉	#447	1	1	yes	characteristic
240	C₄×C₁₉	#447	1	1	yes	characteristic
241	C₄×C₁₉	C₂×#120	1	1	yes	characteristic
242	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
243	C₂²×#41	—	2	1	no	—
244	#575	—	2	4	no	—
245	#575	—	2	2	no	—
246	#575	C₂²×C₁₉	1	4	yes	—
247	C₂×#137	—	2	2	no	—
248	C₂×AGL(1,ℤ/8)	—	2	2	no	—
249	C₂×#135	—	2	1	no	—
250	C₂×#135	C₂²×C₁₉	1	2	yes	—
251	C₂×#135	C₂²×C₁₉	1	1	yes	characteristic, complemented
252	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
253	#525	—	2	1	no	—
254	#510	—	2	2	no	—
255	#510	C₂²×C₁₉	1	4	yes	complemented
256	#509	—	2	2	no	—
257	#509	C₂²×C₁₉	1	4	yes	complemented
258	#508	—	2	4	no	—
259	C₂×M₃₂	C₂²×C₁₉	1	2	yes	complemented
260	#470	C₂²×C₁₉	1	2	yes	complemented
261	#469	C₂²×C₁₉	1	2	yes	complemented
262	#468	—	2	2	no	—
263	#427	C₂²×C₁₉	1	1	yes	characteristic, complemented
264	#416	—	2	1	no	—
265	#360	C₂²×C₁₉	1	8	yes	complemented
266	#349	C₂²×C₁₉	1	4	yes	complemented
267	C₂×C₁₉	—	2	1	no	—
268	C₂×C₁₉	—	2	1	no	—
269	C₂×C₁₉	—	2	1	no	—
270	C₂×C₁₉	—	4	2	no	—
271	C₂×C₁₉	—	8	4	no	—
272	C₂×C₁₉	—	16	1	no	—
273	C₂×C₁₉	C₂×#447	1	1	yes	characteristic
274	C₂×#41	—	2	2	no	—
275	C₂×#41	—	2	4	no	—
276	C₂×#41	—	2	2	no	—
277	C₂×#41	—	2	4	no	—
278	C₂×#41	—	2	1	no	—
279	C₂×#41	—	4	1	no	—
280	C₂×#41	—	4	2	no	—
281	C₂×#41	—	4	2	no	—
282	C₂×#41	—	4	1	no	—
283	C₂²×Q₈	—	2	1	no	—
284	C₂²×D₄	—	2	1	no	—
285	C₂²×D₄	—	4	1	no	—
286	C₂³×C₄	—	4	1	no	—
287	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
288	#137	—	2	8	no	—
289	#137	—	2	8	no	—
290	AGL(1,ℤ/8)	—	2	8	no	—
291	AGL(1,ℤ/8)	—	2	8	no	—
292	#135	—	2	4	no	—
293	#135	—	2	4	no	—
294	#135	—	2	2	no	—
295	#135	—	2	2	no	—
296	#135	—	2	2	no	—
297	#135	—	2	2	no	—
298	#135	D₄×C₁₉	1	4	yes	complemented
299	#135	C₂³×C₁₉	1	4	yes	—
300	C₂×Q₁₆	—	2	1	no	—
301	C₂×Q₁₆	D₄×C₁₉	1	2	yes	complemented
302	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic, complemented
303	C₂×SD₁₆	—	2	2	no	—
304	C₂×SD₁₆	—	2	2	no	—
305	C₂×SD₁₆	—	2	1	no	—
306	C₂×D₈	—	2	1	no	—
307	C₂×D₈	D₄×C₁₉	1	2	yes	complemented
308	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic, complemented
309	C₂×M₁₆	—	2	2	no	—
310	C₂×M₁₆	—	2	2	no	—
311	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
312	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
313	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
314	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
315	#123	—	4	1	no	—
316	C₂²⋊Q₈	—	2	2	no	—
317	#121	—	2	2	no	—
318	#120	—	4	1	no	—
319	C₄×D₄	—	4	2	no	—
320	#117	—	2	1	no	—
321	Q₃₂	—	2	4	no	—
322	SD₃₂	—	2	4	no	—
323	SD₃₂	—	2	4	no	—
324	D₁₆	—	2	4	no	—
325	M₃₂	—	2	2	no	—
326	M₃₂	C₂³×C₁₉	1	4	yes	complemented
327	C₂×C₁₆	—	2	2	no	—
328	#107	—	2	1	no	—
329	#106	C₂³×C₁₉	1	2	yes	complemented
330	#103	—	2	2	no	—
331	#102	—	2	2	no	—
332	C₁₉	#33530	1	1	yes	characteristic, direct product factor, Sylow
333	C₂⁴	—	4	1	no	—
334	C₂⁴	D₈×C₁₉	1	1	yes	characteristic
335	#41	—	2	8	no	—
336	#41	—	2	4	no	—
337	#41	—	2	4	no	—
338	#41	—	4	4	no	—
339	#41	—	4	4	no	—
340	#41	—	4	4	no	—
341	#41	—	4	4	no	—
342	#41	—	4	4	no	—
343	#41	—	4	2	no	—
344	#41	—	4	2	no	—
345	#41	—	4	1	no	—
346	#41	—	4	1	no	—
347	#41	—	4	1	no	—
348	#41	—	4	1	no	—
349	C₂×Q₈	—	2	4	no	—
350	C₂×Q₈	—	2	2	no	—
351	C₂×Q₈	—	2	1	no	—
352	C₂×Q₈	—	4	1	no	—
353	C₂×Q₈	—	4	2	no	—
354	C₂×D₄	—	2	4	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	1	no	—
357	C₂×D₄	—	4	1	no	—
358	C₂×D₄	—	4	2	no	—
359	C₂×D₄	—	4	4	no	—
360	C₂×D₄	—	4	2	no	—
361	C₂×D₄	—	4	4	no	—
362	C₂×D₄	—	4	2	no	—
363	C₂×D₄	—	4	2	no	—
364	C₂×D₄	—	4	1	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	4	2	no	—
370	C₂²×C₄	—	4	4	no	—
371	C₂²×C₄	—	4	4	no	—
372	C₂²×C₄	—	4	1	no	—
373	C₂²×C₄	—	4	2	no	—
374	C₂²×C₄	—	4	1	no	—
375	C₂²×C₄	D₈×C₁₉	1	2	yes	—
376	C₂²×C₄	D₈×C₁₉	1	1	yes	characteristic
377	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
378	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
379	Q₁₆	—	2	4	no	—
380	Q₁₆	—	2	2	no	—
381	Q₁₆	—	2	2	no	—
382	Q₁₆	C₂×D₄×C₁₉	1	4	yes	—
383	SD₁₆	—	2	8	no	—
384	SD₁₆	—	2	4	no	—
385	SD₁₆	—	2	4	no	—
386	SD₁₆	—	4	2	no	—
387	D₈	—	2	4	no	—
388	D₈	—	2	2	no	—
389	D₈	—	2	2	no	—
390	D₈	C₂×D₄×C₁₉	1	4	yes	—
391	M₁₆	—	2	4	no	—
392	M₁₆	—	2	4	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
396	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
397	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
398	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
399	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	4	2	no	—
402	C₂²⋊C₄	—	4	1	no	—
403	C₂²⋊C₄	—	4	2	no	—
404	C₂²⋊C₄	—	4	2	no	—
405	C₄²	—	4	1	no	—
406	C₁₆	—	2	4	no	—
407	C₂³	—	2	1	no	—
408	C₂³	—	2	1	no	—
409	C₂³	—	4	4	no	—
410	C₂³	—	4	2	no	—
411	C₂³	—	4	1	no	—
412	C₂³	—	8	1	no	—
413	C₂³	—	8	4	no	—
414	C₂³	C₂×D₈×C₁₉	1	2	yes	—
415	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
416	Q₈	—	2	4	no	—
417	Q₈	—	4	4	no	—
418	Q₈	—	4	2	no	—
419	Q₈	—	4	1	no	—
420	Q₈	—	4	1	no	—
421	D₄	—	2	4	no	—
422	D₄	—	4	4	no	—
423	D₄	—	4	8	no	—
424	D₄	—	4	4	no	—
425	D₄	—	4	4	no	—
426	D₄	—	4	2	no	—
427	D₄	—	4	1	no	—
428	D₄	—	4	1	no	—
429	D₄	—	8	4	no	—
430	D₄	—	8	1	no	—
431	D₄	—	8	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	4	8	no	—
439	C₂×C₄	—	4	4	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	4	no	—
442	C₂×C₄	—	4	4	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	8	1	no	—
446	C₂×C₄	—	8	1	no	—
447	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
448	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
449	C₂×C₄	C₂×D₈×C₁₉	1	2	yes	—
450	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
451	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
452	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
453	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
454	C₈	—	2	2	no	—
455	C₈	C₁₉×#120	1	2	yes	—
456	C₈	C₂²×D₄×C₁₉	1	2	yes	—
457	C₂²	—	2	2	no	—
458	C₂²	—	4	1	no	—
459	C₂²	—	4	2	no	—
460	C₂²	—	4	2	no	—
461	C₂²	—	4	4	no	—
462	C₂²	—	8	1	no	—
463	C₂²	—	8	4	no	—
464	C₂²	—	8	2	no	—
465	C₂²	—	8	8	no	—
466	C₂²	—	8	1	no	—
467	C₂²	C₁₉×#447	1	1	yes	characteristic
468	C₂²	C₁₉×#447	1	1	yes	characteristic
469	C₂²	C₂²×D₈×C₁₉	1	1	yes	characteristic
470	C₄	—	2	2	no	—
471	C₄	—	4	4	no	—
472	C₄	—	8	2	no	—
473	C₄	—	8	1	no	—
474	C₄	C₁₉×#447	1	1	yes	characteristic
475	C₄	C₁₉×#447	1	1	yes	characteristic
476	C₄	C₂×C₁₉×#120	1	1	yes	characteristic
477	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
478	C₂	—	2	1	no	—
479	C₂	—	2	1	no	—
480	C₂	—	2	1	no	—
481	C₂	—	4	2	no	—
482	C₂	—	8	4	no	—
483	C₂	—	16	1	no	—
484	C₂	C₂×C₁₉×#447	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₉	#447
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₉
socle	C₂×C₁₉	C₂×#447
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂²×M₁₆×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#575	C₂	semidirect
2. C₁₉×#3414	C₂	semidirect
3. C₁₉×#3054	C₂	semidirect
4. C₁₉×#2191	C₂	semidirect
5. C₁₉×#2190	C₂	semidirect
6. C₁₉×#2145	C₂	semidirect
7. C₂×C₁₉×#349	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. C₁₉×#427	C₂²	semidirect
30. C₁₉×#360	C₂²	semidirect
31. C₁₉×#349	C₂²	semidirect
56. C₁₉×#135	D₄	semidirect
59. C₂×Q₁₆×C₁₉	D₄	semidirect
60. C₂×Q₁₆×C₁₉	C₂³	semidirect
65. C₂×D₈×C₁₉	D₄	semidirect
66. C₂×D₈×C₁₉	C₂³	semidirect
84. C₁₉×M₃₂	C₂³	semidirect
87. C₁₉×#106	C₂³	semidirect
164. #33530	C₁₉	direct (N × H)
215. C₂×#575	C₂×C₁₉	semidirect
216. #3414	C₂×C₁₉	semidirect
217. #3054	C₂×C₁₉	semidirect
218. #2191	C₂×C₁₉	semidirect
219. #2190	C₂×C₁₉	semidirect
220. #2145	C₂×C₁₉	semidirect
221. C₂×#349	C₂×C₁₉	semidirect
251. C₂×#135	C₂²×C₁₉	semidirect
255. #510	C₂²×C₁₉	semidirect
257. #509	C₂²×C₁₉	semidirect
259. C₂×M₃₂	C₂²×C₁₉	semidirect
260. #470	C₂²×C₁₉	semidirect
261. #469	C₂²×C₁₉	semidirect
263. #427	C₂²×C₁₉	semidirect
265. #360	C₂²×C₁₉	semidirect
266. #349	C₂²×C₁₉	semidirect
298. #135	D₄×C₁₉	semidirect
301. C₂×Q₁₆	D₄×C₁₉	semidirect
302. C₂×Q₁₆	C₂³×C₁₉	semidirect
307. C₂×D₈	D₄×C₁₉	semidirect
308. C₂×D₈	C₂³×C₁₉	semidirect
326. M₃₂	C₂³×C₁₉	semidirect
329. #106	C₂³×C₁₉	semidirect
332. C₁₉	#33530	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#575	2
C₁₉×#3414	2
C₁₉×#3054	2
C₁₉×#2191	2
C₁₉×#2190	2
C₁₉×#2145	2
C₂×C₁₉×#349	2
#33530	19

Subgroups — C19×#33530 #18039489

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#33530 #18039489