Subgroups — C₁₉×#33619 #18039578

Order 4864.

636 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#510	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3407	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3067	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#473	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2223	C₂	1	4	yes	maximal, complemented
6	C₁₉×#2222	C₂	1	4	yes	maximal, complemented
7	C₁₉×#2161	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2148	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₉×#362	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#575	—	2	1	no	—
11	C₂×C₁₉×#137	—	2	1	no	—
12	C₂×C₁₉×#135	C₂²	1	1	yes	characteristic
13	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic
15	C₁₉×#510	—	2	2	no	—
16	C₁₉×#510	—	2	2	no	—
17	C₂×C₁₉×Q₃₂	C₂²	1	2	yes	complemented
18	C₂×C₁₉×SD₃₂	C₂²	1	2	yes	complemented
19	C₁₉×#504	—	2	2	no	—
20	C₁₉×#504	C₂²	1	4	yes	—
21	C₂×C₁₉×M₃₂	—	2	2	no	—
22	C₂×C₁₉×M₃₂	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×M₃₂	C₂²	1	1	yes	characteristic
24	C₁₉×#473	—	2	2	no	—
25	C₁₉×#473	C₂²	1	2	yes	—
26	C₁₉×#473	C₂²	1	4	yes	—
27	C₁₉×#472	C₂²	1	2	yes	—
28	C₁₉×#471	—	2	2	no	—
29	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic
31	C₁₉×#413	—	2	1	no	—
32	C₂×C₁₉×#101	—	2	1	no	—
33	C₁₉×#368	C₂²	1	4	yes	complemented
34	C₁₉×#362	C₂²	1	4	yes	complemented
35	C₁₉×#362	C₂²	1	2	yes	complemented
36	C₁₉×#361	C₂²	1	2	yes	complemented
37	C₂×#41×C₁₉	—	2	1	no	—
38	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
39	C₂²×Q₈×C₁₉	—	2	1	no	—
40	C₁₉×#137	—	2	2	no	—
41	C₁₉×#137	—	2	4	no	—
42	C₁₉×#137	—	4	2	no	—
43	C₁₉×#137	—	4	1	no	—
44	C₁₉×AGL(1,ℤ/8)	—	2	2	no	—
45	C₁₉×AGL(1,ℤ/8)	—	4	1	no	—
46	C₁₉×#135	—	2	1	no	—
47	C₁₉×#135	—	2	1	no	—
48	C₁₉×#135	—	2	1	no	—
49	C₁₉×#135	—	2	1	no	—
50	C₁₉×#135	—	4	2	no	—
51	C₂×Q₁₆×C₁₉	—	2	1	no	—
52	C₂×Q₁₆×C₁₉	—	2	1	no	—
53	C₂×Q₁₆×C₁₉	—	2	1	no	—
54	C₂×Q₁₆×C₁₉	—	2	1	no	—
55	C₂×Q₁₆×C₁₉	—	2	1	no	—
56	C₂×Q₁₆×C₁₉	—	4	1	no	—
57	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
58	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
59	C₂×SD₁₆×C₁₉	—	2	1	no	—
60	C₂×SD₁₆×C₁₉	—	4	1	no	—
61	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
62	C₁₉×#131	—	2	1	no	—
63	C₁₉×#131	—	2	1	no	—
64	C₁₉×#131	D₄	1	2	yes	—
65	C₁₉×#131	C₂³	1	2	yes	—
66	C₂×M₁₆×C₁₉	—	2	1	no	—
67	C₂×M₁₆×C₁₉	—	2	1	no	—
68	C₂×M₁₆×C₁₉	—	2	1	no	—
69	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
70	C₂²×C₈×C₁₉	—	2	1	no	—
71	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
72	C₁₉×Q₃₂	—	2	4	no	—
73	C₁₉×SD₃₂	—	2	4	no	—
74	C₁₉×M₃₂	—	2	1	no	—
75	C₁₉×M₃₂	—	2	4	no	—
76	C₁₉×M₃₂	D₄	1	2	yes	—
77	C₁₉×M₃₂	D₄	1	2	yes	—
78	C₁₉×M₃₂	C₂³	1	2	yes	—
79	C₂×C₁₆×C₁₉	—	2	1	no	—
80	C₂×C₁₆×C₁₉	—	2	4	no	—
81	C₂×C₁₆×C₁₉	C₂³	1	2	yes	—
82	C₁₉×#108	—	2	1	no	—
83	C₁₉×#108	—	2	1	no	—
84	C₁₉×#108	C₂³	1	2	yes	—
85	C₁₉×#108	C₂³	1	2	yes	—
86	C₁₉×#101	—	2	4	no	—
87	C₁₉×#101	—	2	2	no	—
88	C₁₉×#100	—	2	2	no	—
89	#41×C₁₉	—	2	1	no	—
90	#41×C₁₉	—	2	1	no	—
91	#41×C₁₉	—	4	1	no	—
92	#41×C₁₉	—	4	1	no	—
93	#41×C₁₉	—	4	1	no	—
94	#41×C₁₉	—	4	1	no	—
95	#41×C₁₉	D₈	1	2	yes	—
96	#41×C₁₉	C₂×D₄	1	2	yes	—
97	C₂×Q₈×C₁₉	—	2	1	no	—
98	C₂×Q₈×C₁₉	—	2	2	no	—
99	C₂×Q₈×C₁₉	—	4	1	no	—
100	C₂×Q₈×C₁₉	—	4	1	no	—
101	C₂×Q₈×C₁₉	—	4	1	no	—
102	C₂×Q₈×C₁₉	—	4	1	no	—
103	C₂×Q₈×C₁₉	—	4	1	no	—
104	C₂×Q₈×C₁₉	D₈	1	1	yes	characteristic
105	C₂×D₄×C₁₉	—	2	1	no	—
106	C₂×D₄×C₁₉	—	2	1	no	—
107	C₂×D₄×C₁₉	—	4	1	no	—
108	C₂×D₄×C₁₉	D₈	1	1	yes	characteristic
109	C₂²×C₄×C₁₉	—	2	1	no	—
110	C₂²×C₄×C₁₉	—	4	1	no	—
111	C₂²×C₄×C₁₉	—	4	1	no	—
112	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
113	Q₁₆×C₁₉	—	2	2	no	—
114	Q₁₆×C₁₉	—	2	1	no	—
115	Q₁₆×C₁₉	—	2	2	no	—
116	Q₁₆×C₁₉	—	2	1	no	—
117	Q₁₆×C₁₉	—	4	4	no	—
118	Q₁₆×C₁₉	—	4	2	no	—
119	Q₁₆×C₁₉	—	4	1	no	—
120	Q₁₆×C₁₉	—	4	1	no	—
121	SD₁₆×C₁₉	—	4	2	no	—
122	SD₁₆×C₁₉	—	4	4	no	—
123	SD₁₆×C₁₉	—	4	2	no	—
124	SD₁₆×C₁₉	—	4	1	no	—
125	SD₁₆×C₁₉	—	4	1	no	—
126	D₈×C₁₉	—	2	1	no	—
127	D₈×C₁₉	—	2	1	no	—
128	D₈×C₁₉	—	4	2	no	—
129	M₁₆×C₁₉	—	2	1	no	—
130	M₁₆×C₁₉	—	2	2	no	—
131	M₁₆×C₁₉	—	2	2	no	—
132	M₁₆×C₁₉	—	2	2	no	—
133	M₁₆×C₁₉	—	2	2	no	—
134	M₁₆×C₁₉	—	4	1	no	—
135	M₁₆×C₁₉	—	4	1	no	—
136	M₁₆×C₁₉	C₂×D₄	1	2	yes	—
137	C₂×C₈×C₁₉	—	2	1	no	—
138	C₂×C₈×C₁₉	—	2	2	no	—
139	C₂×C₈×C₁₉	—	2	2	no	—
140	C₂×C₈×C₁₉	—	4	1	no	—
141	C₂×C₈×C₁₉	—	4	1	no	—
142	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
145	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
146	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
147	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
148	C₁₆×C₁₉	—	2	2	no	—
149	C₁₆×C₁₉	C₂×D₄	1	4	yes	—
150	#33619	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
151	C₂³×C₁₉	—	2	1	no	—
152	C₂³×C₁₉	—	4	1	no	—
153	C₂³×C₁₉	#135	1	1	yes	characteristic
154	Q₈×C₁₉	—	2	1	no	—
155	Q₈×C₁₉	—	4	1	no	—
156	Q₈×C₁₉	—	4	2	no	—
157	Q₈×C₁₉	—	4	2	no	—
158	Q₈×C₁₉	—	4	1	no	—
159	Q₈×C₁₉	—	8	1	no	—
160	Q₈×C₁₉	—	8	1	no	—
161	Q₈×C₁₉	C₂×D₈	1	2	yes	—
162	D₄×C₁₉	—	2	2	no	—
163	D₄×C₁₉	—	2	2	no	—
164	D₄×C₁₉	—	2	1	no	—
165	D₄×C₁₉	—	4	1	no	—
166	D₄×C₁₉	—	4	1	no	—
167	D₄×C₁₉	—	8	1	no	—
168	D₄×C₁₉	—	8	1	no	—
169	D₄×C₁₉	C₂×D₈	1	2	yes	—
170	C₂×C₄×C₁₉	—	2	1	no	—
171	C₂×C₄×C₁₉	—	2	2	no	—
172	C₂×C₄×C₁₉	—	2	2	no	—
173	C₂×C₄×C₁₉	—	4	1	no	—
174	C₂×C₄×C₁₉	—	4	2	no	—
175	C₂×C₄×C₁₉	—	8	1	no	—
176	C₂×C₄×C₁₉	—	8	1	no	—
177	C₂×C₄×C₁₉	—	8	1	no	—
178	C₂×C₄×C₁₉	—	8	1	no	—
179	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
180	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
181	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
182	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
183	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
184	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
185	C₈×C₁₉	—	2	2	no	—
186	C₈×C₁₉	—	4	2	no	—
187	C₈×C₁₉	—	4	2	no	—
188	C₈×C₁₉	#121	1	1	yes	characteristic
189	C₈×C₁₉	#121	1	1	yes	characteristic
190	C₈×C₁₉	C₂²×D₄	1	1	yes	characteristic
191	C₈×C₁₉	C₂×#41	1	1	yes	characteristic
192	C₂×#510	C₂×C₁₉	1	1	yes	characteristic, complemented
193	#3407	C₂×C₁₉	1	1	yes	characteristic, complemented
194	#3067	C₂×C₁₉	1	1	yes	characteristic
195	C₂×#473	C₂×C₁₉	1	1	yes	characteristic, complemented
196	#2223	C₂×C₁₉	1	4	yes	complemented
197	#2222	C₂×C₁₉	1	4	yes	complemented
198	#2161	C₂×C₁₉	1	1	yes	characteristic, complemented
199	#2148	C₂×C₁₉	1	1	yes	characteristic, complemented
200	C₂×#362	C₂×C₁₉	1	1	yes	characteristic, complemented
201	C₂²×C₁₉	—	2	2	no	—
202	C₂²×C₁₉	—	4	1	no	—
203	C₂²×C₁₉	—	8	1	no	—
204	C₂²×C₁₉	—	8	1	no	—
205	C₂²×C₁₉	—	16	1	no	—
206	C₂²×C₁₉	#466	1	1	yes	characteristic
207	C₂²×C₁₉	#466	1	1	yes	characteristic
208	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
209	C₄×C₁₉	—	2	2	no	—
210	C₄×C₁₉	—	8	1	no	—
211	C₄×C₁₉	—	8	2	no	—
212	C₄×C₁₉	#466	1	1	yes	characteristic
213	C₄×C₁₉	#466	1	1	yes	characteristic
214	C₄×C₁₉	C₂×#121	1	1	yes	characteristic
215	C₄×C₁₉	C₂²×D₈	1	1	yes	characteristic
216	#575	—	2	1	no	—
217	C₂×#137	—	2	1	no	—
218	C₂×#135	C₂²×C₁₉	1	1	yes	characteristic
219	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
220	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic
221	#510	—	2	2	no	—
222	#510	—	2	2	no	—
223	C₂×Q₃₂	C₂²×C₁₉	1	2	yes	complemented
224	C₂×SD₃₂	C₂²×C₁₉	1	2	yes	complemented
225	#504	—	2	2	no	—
226	#504	C₂²×C₁₉	1	4	yes	—
227	C₂×M₃₂	—	2	2	no	—
228	C₂×M₃₂	C₂²×C₁₉	1	1	yes	characteristic
229	C₂×M₃₂	C₂²×C₁₉	1	1	yes	characteristic
230	#473	—	2	2	no	—
231	#473	C₂²×C₁₉	1	2	yes	—
232	#473	C₂²×C₁₉	1	4	yes	—
233	#472	C₂²×C₁₉	1	2	yes	—
234	#471	—	2	2	no	—
235	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic
236	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic
237	#413	—	2	1	no	—
238	C₂×#101	—	2	1	no	—
239	#368	C₂²×C₁₉	1	4	yes	complemented
240	#362	C₂²×C₁₉	1	4	yes	complemented
241	#362	C₂²×C₁₉	1	2	yes	complemented
242	#361	C₂²×C₁₉	1	2	yes	complemented
243	C₂×C₁₉	—	2	1	no	—
244	C₂×C₁₉	—	2	1	no	—
245	C₂×C₁₉	—	2	1	no	—
246	C₂×C₁₉	—	4	2	no	—
247	C₂×C₁₉	—	16	1	no	—
248	C₂×C₁₉	C₂×#466	1	1	yes	characteristic
249	C₂×#41	—	2	1	no	—
250	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
251	C₂²×Q₈	—	2	1	no	—
252	#137	—	2	4	no	—
253	#137	—	2	2	no	—
254	#137	—	4	2	no	—
255	#137	—	4	1	no	—
256	AGL(1,ℤ/8)	—	2	2	no	—
257	AGL(1,ℤ/8)	—	4	1	no	—
258	#135	—	2	1	no	—
259	#135	—	2	1	no	—
260	#135	—	2	1	no	—
261	#135	—	2	1	no	—
262	#135	—	4	2	no	—
263	C₂×Q₁₆	—	2	1	no	—
264	C₂×Q₁₆	—	2	1	no	—
265	C₂×Q₁₆	—	2	1	no	—
266	C₂×Q₁₆	—	2	1	no	—
267	C₂×Q₁₆	—	2	1	no	—
268	C₂×Q₁₆	—	4	1	no	—
269	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
270	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
271	C₂×SD₁₆	—	2	1	no	—
272	C₂×SD₁₆	—	4	1	no	—
273	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
274	#131	—	2	1	no	—
275	#131	—	2	1	no	—
276	#131	D₄×C₁₉	1	2	yes	—
277	#131	C₂³×C₁₉	1	2	yes	—
278	C₂×M₁₆	—	2	1	no	—
279	C₂×M₁₆	—	2	1	no	—
280	C₂×M₁₆	—	2	1	no	—
281	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
282	C₂²×C₈	—	2	1	no	—
283	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
284	Q₃₂	—	2	4	no	—
285	SD₃₂	—	2	4	no	—
286	M₃₂	—	2	1	no	—
287	M₃₂	—	2	4	no	—
288	M₃₂	D₄×C₁₉	1	2	yes	—
289	M₃₂	D₄×C₁₉	1	2	yes	—
290	M₃₂	C₂³×C₁₉	1	2	yes	—
291	C₂×C₁₆	—	2	1	no	—
292	C₂×C₁₆	—	2	4	no	—
293	C₂×C₁₆	C₂³×C₁₉	1	2	yes	—
294	#108	—	2	1	no	—
295	#108	—	2	1	no	—
296	#108	C₂³×C₁₉	1	2	yes	—
297	#108	C₂³×C₁₉	1	2	yes	—
298	#101	—	2	4	no	—
299	#101	—	2	2	no	—
300	#100	—	2	2	no	—
301	C₁₉	#33619	1	1	yes	characteristic, direct product factor, Sylow
302	#41	—	2	1	no	—
303	#41	—	2	1	no	—
304	#41	—	4	1	no	—
305	#41	—	4	1	no	—
306	#41	—	4	1	no	—
307	#41	—	4	1	no	—
308	#41	D₈×C₁₉	1	2	yes	—
309	#41	C₂×D₄×C₁₉	1	2	yes	—
310	C₂×Q₈	—	2	1	no	—
311	C₂×Q₈	—	2	2	no	—
312	C₂×Q₈	—	4	1	no	—
313	C₂×Q₈	—	4	1	no	—
314	C₂×Q₈	—	4	1	no	—
315	C₂×Q₈	—	4	1	no	—
316	C₂×Q₈	—	4	1	no	—
317	C₂×Q₈	D₈×C₁₉	1	1	yes	characteristic
318	C₂×D₄	—	2	1	no	—
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	—	4	1	no	—
321	C₂×D₄	D₈×C₁₉	1	1	yes	characteristic
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	4	1	no	—
324	C₂²×C₄	—	4	1	no	—
325	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
326	Q₁₆	—	2	2	no	—
327	Q₁₆	—	2	1	no	—
328	Q₁₆	—	2	2	no	—
329	Q₁₆	—	2	1	no	—
330	Q₁₆	—	4	4	no	—
331	Q₁₆	—	4	2	no	—
332	Q₁₆	—	4	1	no	—
333	Q₁₆	—	4	1	no	—
334	SD₁₆	—	4	2	no	—
335	SD₁₆	—	4	4	no	—
336	SD₁₆	—	4	2	no	—
337	SD₁₆	—	4	1	no	—
338	SD₁₆	—	4	1	no	—
339	D₈	—	2	1	no	—
340	D₈	—	2	1	no	—
341	D₈	—	4	2	no	—
342	M₁₆	—	2	1	no	—
343	M₁₆	—	2	2	no	—
344	M₁₆	—	2	2	no	—
345	M₁₆	—	2	2	no	—
346	M₁₆	—	2	2	no	—
347	M₁₆	—	4	1	no	—
348	M₁₆	—	4	1	no	—
349	M₁₆	C₂×D₄×C₁₉	1	2	yes	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	4	1	no	—
354	C₂×C₈	—	4	1	no	—
355	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
356	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
357	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
358	C₂×C₈	#41×C₁₉	1	1	yes	characteristic
359	C₂×C₈	#41×C₁₉	1	1	yes	characteristic
360	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
361	C₁₆	—	2	2	no	—
362	C₁₆	C₂×D₄×C₁₉	1	4	yes	—
363	C₂³	—	2	1	no	—
364	C₂³	—	4	1	no	—
365	C₂³	C₁₉×#135	1	1	yes	characteristic
366	Q₈	—	2	1	no	—
367	Q₈	—	4	1	no	—
368	Q₈	—	4	2	no	—
369	Q₈	—	4	2	no	—
370	Q₈	—	4	1	no	—
371	Q₈	—	8	1	no	—
372	Q₈	—	8	1	no	—
373	Q₈	C₂×D₈×C₁₉	1	2	yes	—
374	D₄	—	2	2	no	—
375	D₄	—	2	2	no	—
376	D₄	—	2	1	no	—
377	D₄	—	4	1	no	—
378	D₄	—	4	1	no	—
379	D₄	—	8	1	no	—
380	D₄	—	8	1	no	—
381	D₄	C₂×D₈×C₁₉	1	2	yes	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	8	1	no	—
388	C₂×C₄	—	8	1	no	—
389	C₂×C₄	—	8	1	no	—
390	C₂×C₄	—	8	1	no	—
391	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
392	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
393	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
394	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
395	C₂×C₄	C₁₉×#135	1	1	yes	characteristic
396	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
397	C₈	—	2	2	no	—
398	C₈	—	4	2	no	—
399	C₈	—	4	2	no	—
400	C₈	C₁₉×#121	1	1	yes	characteristic
401	C₈	C₁₉×#121	1	1	yes	characteristic
402	C₈	C₂²×D₄×C₁₉	1	1	yes	characteristic
403	C₈	C₂×#41×C₁₉	1	1	yes	characteristic
404	C₂²	—	2	2	no	—
405	C₂²	—	4	1	no	—
406	C₂²	—	8	1	no	—
407	C₂²	—	8	1	no	—
408	C₂²	—	16	1	no	—
409	C₂²	C₁₉×#466	1	1	yes	characteristic
410	C₂²	C₁₉×#466	1	1	yes	characteristic
411	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
412	C₄	—	2	2	no	—
413	C₄	—	8	1	no	—
414	C₄	—	8	2	no	—
415	C₄	C₁₉×#466	1	1	yes	characteristic
416	C₄	C₁₉×#466	1	1	yes	characteristic
417	C₄	C₂×C₁₉×#121	1	1	yes	characteristic
418	C₄	C₂²×D₈×C₁₉	1	1	yes	characteristic
419	C₂	—	2	1	no	—
420	C₂	—	2	1	no	—
421	C₂	—	2	1	no	—
422	C₂	—	4	2	no	—
423	C₂	—	16	1	no	—
424	C₂	C₂×C₁₉×#466	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₉	C₂×#466
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₉
prime radical	C₁₉×#3067	C₂
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. C₂×C₁₉×#510	C₂	semidirect
2. C₁₉×#3407	C₂	semidirect
4. C₂×C₁₉×#473	C₂	semidirect
5. C₁₉×#2223	C₂	semidirect
6. C₁₉×#2222	C₂	semidirect
7. C₁₉×#2161	C₂	semidirect
8. C₁₉×#2148	C₂	semidirect
9. C₂×C₁₉×#362	C₂	semidirect
17. C₂×C₁₉×Q₃₂	C₂²	semidirect
18. C₂×C₁₉×SD₃₂	C₂²	semidirect
33. C₁₉×#368	C₂²	semidirect
34. C₁₉×#362	C₂²	semidirect
35. C₁₉×#362	C₂²	semidirect
36. C₁₉×#361	C₂²	semidirect
150. #33619	C₁₉	direct (N × H)
192. C₂×#510	C₂×C₁₉	semidirect
193. #3407	C₂×C₁₉	semidirect
195. C₂×#473	C₂×C₁₉	semidirect
196. #2223	C₂×C₁₉	semidirect
197. #2222	C₂×C₁₉	semidirect
198. #2161	C₂×C₁₉	semidirect
199. #2148	C₂×C₁₉	semidirect
200. C₂×#362	C₂×C₁₉	semidirect
223. C₂×Q₃₂	C₂²×C₁₉	semidirect
224. C₂×SD₃₂	C₂²×C₁₉	semidirect
239. #368	C₂²×C₁₉	semidirect
240. #362	C₂²×C₁₉	semidirect
241. #362	C₂²×C₁₉	semidirect
242. #361	C₂²×C₁₉	semidirect
301. C₁₉	#33619	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×#510	2
C₁₉×#3407	2
C₁₉×#3067	2
C₂×C₁₉×#473	2
C₁₉×#2223	2
C₁₉×#2222	2
C₁₉×#2161	2
C₁₉×#2148	2
C₂×C₁₉×#362	2
#33619	19

Subgroups — C19×#33619 #18039578

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#33619 #18039578