Subgroups — C₂×C₁₉×#3204 #18066707

Order 4864.

2250 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#537	C₂	1	2	yes	maximal, complemented
2	C₁₉×#3204	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₁₉×#481	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₉×#483	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₉×#470	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₉×#469	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#465	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₉×#452	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₉×#449	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₉×#408	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×#41×C₁₉	C₂²	1	2	yes	—
12	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
14	C₂²×SD₁₆×C₁₉	C₂²	1	2	yes	—
15	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#537	—	2	8	no	—
19	C₁₉×#537	C₂²	1	16	yes	complemented
20	C₂×C₁₉×C₂²⋊Q₈	—	2	2	no	—
21	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
23	C₂×C₁₉×#121	—	2	2	no	—
24	C₂×C₁₉×#121	—	2	2	no	—
25	C₂×C₁₉×#121	—	2	2	no	—
26	C₂×C₁₉×#121	C₂²	1	2	yes	—
27	C₂×C₁₉×#121	C₂²	1	2	yes	—
28	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
29	C₁₉×#483	C₂²	1	16	yes	complemented
30	C₁₉×#481	C₂²	1	16	yes	complemented
31	C₁₉×#470	C₂²	1	8	yes	complemented
32	C₁₉×#469	C₂²	1	8	yes	complemented
33	C₁₉×#465	C₂²	1	16	yes	complemented
34	C₁₉×#452	C₂²	1	16	yes	complemented
35	C₁₉×#449	C₂²	1	16	yes	complemented
36	C₂×C₁₉×#106	C₂²	1	2	yes	—
37	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
38	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
39	C₂×C₁₉×#103	C₂²	1	2	yes	—
40	C₂×C₁₉×#103	C₂²	1	2	yes	—
41	C₂×C₁₉×#102	C₂²	1	2	yes	—
42	C₂×C₁₉×#102	C₂²	1	2	yes	—
43	C₁₉×#408	C₂²	1	8	yes	complemented
44	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
45	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
46	C₂×#41×C₁₉	—	2	4	no	—
47	C₂×#41×C₁₉	—	4	2	no	—
48	C₂×#41×C₁₉	—	4	2	no	—
49	C₂×#41×C₁₉	—	4	4	no	—
50	C₂×#41×C₁₉	—	4	4	no	—
51	C₂×#41×C₁₉	D₄	1	4	yes	—
52	C₂×#41×C₁₉	C₂³	1	8	yes	—
53	C₂×#41×C₁₉	C₂³	1	4	yes	—
54	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
55	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
56	C₂²×D₄×C₁₉	—	2	2	no	—
57	C₂²×D₄×C₁₉	—	2	2	no	—
58	C₂²×D₄×C₁₉	—	2	2	no	—
59	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
60	C₂²×D₄×C₁₉	D₄	1	2	yes	—
61	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
62	C₂³×C₄×C₁₉	—	2	2	no	—
63	C₂³×C₄×C₁₉	—	2	2	no	—
64	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
65	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
66	C₂×Q₁₆×C₁₉	—	4	2	no	—
67	C₂×Q₁₆×C₁₉	C₂³	1	4	yes	—
68	C₂×SD₁₆×C₁₉	—	4	4	no	—
69	C₂×SD₁₆×C₁₉	C₂³	1	8	yes	—
70	C₂×D₈×C₁₉	—	4	2	no	—
71	C₂×D₈×C₁₉	C₂³	1	4	yes	—
72	C₂×M₁₆×C₁₉	—	4	2	no	—
73	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
74	C₂²×C₈×C₁₉	—	4	2	no	—
75	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
77	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
79	C₁₉×C₂²⋊Q₈	—	2	16	no	—
80	C₁₉×C₂²⋊Q₈	—	2	4	no	—
81	C₁₉×C₂²⋊Q₈	—	2	4	no	—
82	C₁₉×C₂²⋊Q₈	C₂³	1	8	yes	—
83	C₁₉×C₂²⋊Q₈	C₂³	1	8	yes	—
84	C₁₉×#121	—	2	16	no	—
85	C₁₉×#121	—	2	16	no	—
86	C₁₉×#121	—	2	16	no	—
87	C₁₉×#121	—	2	4	no	—
88	C₁₉×#121	—	2	4	no	—
89	C₁₉×#121	C₂³	1	8	yes	—
90	C₁₉×#121	C₂³	1	8	yes	—
91	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
92	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
93	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
94	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
95	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
96	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
97	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
98	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
99	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
100	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
101	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
102	C₁₉×#106	C₂³	1	8	yes	—
103	C₁₉×#106	C₂³	1	4	yes	—
104	C₁₉×#106	C₂³	1	4	yes	—
105	C₁₉×#103	C₂³	1	8	yes	—
106	C₁₉×#103	C₂³	1	8	yes	—
107	C₁₉×#102	C₂³	1	8	yes	—
108	C₁₉×#102	C₂³	1	8	yes	—
109	C₁₉×C₂²⋊C₈	C₂³	1	8	yes	—
110	C₁₉×C₂²⋊C₈	C₂³	1	8	yes	—
111	C₂⁴×C₁₉	—	2	2	no	—
112	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
113	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
114	#41×C₁₉	—	4	8	no	—
115	#41×C₁₉	—	4	4	no	—
116	#41×C₁₉	—	4	4	no	—
117	#41×C₁₉	—	4	8	no	—
118	#41×C₁₉	—	4	8	no	—
119	#41×C₁₉	—	4	16	no	—
120	C₂×Q₈×C₁₉	—	2	2	no	—
121	C₂×Q₈×C₁₉	—	2	4	no	—
122	C₂×Q₈×C₁₉	—	2	4	no	—
123	C₂×Q₈×C₁₉	—	4	2	no	—
124	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
125	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
126	C₂×D₄×C₁₉	—	2	8	no	—
127	C₂×D₄×C₁₉	—	2	8	no	—
128	C₂×D₄×C₁₉	—	2	8	no	—
129	C₂×D₄×C₁₉	—	2	2	no	—
130	C₂×D₄×C₁₉	—	2	4	no	—
131	C₂×D₄×C₁₉	—	2	4	no	—
132	C₂×D₄×C₁₉	—	4	4	no	—
133	C₂×D₄×C₁₉	—	4	2	no	—
134	C₂×D₄×C₁₉	—	4	8	no	—
135	C₂×D₄×C₁₉	—	8	4	no	—
136	C₂×D₄×C₁₉	—	8	4	no	—
137	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
138	C₂×D₄×C₁₉	C₂×D₄	1	8	yes	—
139	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
140	C₂²×C₄×C₁₉	—	2	2	no	—
141	C₂²×C₄×C₁₉	—	2	2	no	—
142	C₂²×C₄×C₁₉	—	2	4	no	—
143	C₂²×C₄×C₁₉	—	2	4	no	—
144	C₂²×C₄×C₁₉	—	2	2	no	—
145	C₂²×C₄×C₁₉	—	2	2	no	—
146	C₂²×C₄×C₁₉	—	2	2	no	—
147	C₂²×C₄×C₁₉	—	2	8	no	—
148	C₂²×C₄×C₁₉	—	2	8	no	—
149	C₂²×C₄×C₁₉	—	4	8	no	—
150	C₂²×C₄×C₁₉	—	8	4	no	—
151	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
152	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
153	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
155	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
156	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
157	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
158	Q₁₆×C₁₉	—	4	4	no	—
159	SD₁₆×C₁₉	—	4	8	no	—
160	D₈×C₁₉	—	4	4	no	—
161	M₁₆×C₁₉	—	4	4	no	—
162	C₂×C₈×C₁₉	—	2	4	no	—
163	C₂×C₈×C₁₉	—	2	2	no	—
164	C₂×C₈×C₁₉	—	2	2	no	—
165	C₂×C₈×C₁₉	—	4	4	no	—
166	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
167	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
168	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
169	C₄⋊C₄×C₁₉	—	2	8	no	—
170	C₄⋊C₄×C₁₉	—	2	2	no	—
171	C₄⋊C₄×C₁₉	—	2	2	no	—
172	C₄⋊C₄×C₁₉	—	2	8	no	—
173	C₄⋊C₄×C₁₉	—	2	8	no	—
174	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
175	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
176	C₂²⋊C₄×C₁₉	—	2	8	no	—
177	C₂²⋊C₄×C₁₉	—	2	8	no	—
178	C₂²⋊C₄×C₁₉	—	2	8	no	—
179	C₂²⋊C₄×C₁₉	—	2	8	no	—
180	C₂×#3204	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
181	C₂³×C₁₉	—	2	4	no	—
182	C₂³×C₁₉	—	2	2	no	—
183	C₂³×C₁₉	—	2	4	no	—
184	C₂³×C₁₉	—	2	4	no	—
185	C₂³×C₁₉	—	2	4	no	—
186	C₂³×C₁₉	—	2	4	no	—
187	C₂³×C₁₉	—	4	4	no	—
188	C₂³×C₁₉	—	4	4	no	—
189	C₂³×C₁₉	—	4	4	no	—
190	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
191	C₂³×C₁₉	C₂²×D₄	1	4	yes	—
192	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
193	Q₈×C₁₉	—	2	4	no	—
194	Q₈×C₁₉	—	2	4	no	—
195	Q₈×C₁₉	—	4	4	no	—
196	Q₈×C₁₉	—	4	4	no	—
197	D₄×C₁₉	—	2	4	no	—
198	D₄×C₁₉	—	2	4	no	—
199	D₄×C₁₉	—	4	8	no	—
200	D₄×C₁₉	—	4	4	no	—
201	D₄×C₁₉	—	4	16	no	—
202	D₄×C₁₉	—	4	4	no	—
203	D₄×C₁₉	—	8	8	no	—
204	D₄×C₁₉	—	8	8	no	—
205	C₂×C₄×C₁₉	—	2	4	no	—
206	C₂×C₄×C₁₉	—	2	2	no	—
207	C₂×C₄×C₁₉	—	2	4	no	—
208	C₂×C₄×C₁₉	—	2	8	no	—
209	C₂×C₄×C₁₉	—	2	2	no	—
210	C₂×C₄×C₁₉	—	2	2	no	—
211	C₂×C₄×C₁₉	—	2	4	no	—
212	C₂×C₄×C₁₉	—	2	4	no	—
213	C₂×C₄×C₁₉	—	2	4	no	—
214	C₂×C₄×C₁₉	—	2	4	no	—
215	C₂×C₄×C₁₉	—	2	4	no	—
216	C₂×C₄×C₁₉	—	4	16	no	—
217	C₂×C₄×C₁₉	—	4	4	no	—
218	C₂×C₄×C₁₉	—	4	4	no	—
219	C₂×C₄×C₁₉	—	4	4	no	—
220	C₂×C₄×C₁₉	—	8	8	no	—
221	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
222	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
223	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
225	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
226	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
227	C₈×C₁₉	—	2	4	no	—
228	C₈×C₁₉	—	2	2	no	—
229	C₈×C₁₉	—	2	2	no	—
230	C₂×#537	C₂×C₁₉	1	2	yes	complemented
231	#3204	C₂×C₁₉	1	16	yes	direct product factor
232	C₂×#481	C₂×C₁₉	1	2	yes	complemented
233	C₂×#483	C₂×C₁₉	1	2	yes	complemented
234	C₂×#470	C₂×C₁₉	1	1	yes	characteristic, complemented
235	C₂×#469	C₂×C₁₉	1	1	yes	characteristic, complemented
236	C₂×#465	C₂×C₁₉	1	2	yes	complemented
237	C₂×#452	C₂×C₁₉	1	2	yes	complemented
238	C₂×#449	C₂×C₁₉	1	2	yes	complemented
239	C₂×#408	C₂×C₁₉	1	1	yes	characteristic, complemented
240	C₂²×C₁₉	—	2	4	no	—
241	C₂²×C₁₉	—	2	2	no	—
242	C₂²×C₁₉	—	2	4	no	—
243	C₂²×C₁₉	—	2	4	no	—
244	C₂²×C₁₉	—	2	4	no	—
245	C₂²×C₁₉	—	4	8	no	—
246	C₂²×C₁₉	—	4	4	no	—
247	C₂²×C₁₉	—	4	4	no	—
248	C₂²×C₁₉	—	4	4	no	—
249	C₂²×C₁₉	—	4	4	no	—
250	C₂²×C₁₉	—	8	8	no	—
251	C₂²×C₁₉	#534	1	2	yes	—
252	C₂²×C₁₉	#577	1	4	yes	—
253	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
254	C₄×C₁₉	—	2	4	no	—
255	C₄×C₁₉	—	2	2	no	—
256	C₄×C₁₉	—	4	4	no	—
257	C₄×C₁₉	—	4	4	no	—
258	C₄×C₁₉	—	4	4	no	—
259	C₄×C₁₉	#534	1	2	yes	—
260	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
261	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
262	C₂²×#41	C₂²×C₁₉	1	2	yes	—
263	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
264	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
265	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	—
266	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
267	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
268	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
269	#537	—	2	8	no	—
270	#537	C₂²×C₁₉	1	16	yes	complemented
271	C₂×C₂²⋊Q₈	—	2	2	no	—
272	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
273	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
274	C₂×#121	—	2	2	no	—
275	C₂×#121	—	2	2	no	—
276	C₂×#121	—	2	2	no	—
277	C₂×#121	C₂²×C₁₉	1	2	yes	—
278	C₂×#121	C₂²×C₁₉	1	2	yes	—
279	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
280	#483	C₂²×C₁₉	1	16	yes	complemented
281	#481	C₂²×C₁₉	1	16	yes	complemented
282	#470	C₂²×C₁₉	1	8	yes	complemented
283	#469	C₂²×C₁₉	1	8	yes	complemented
284	#465	C₂²×C₁₉	1	16	yes	complemented
285	#452	C₂²×C₁₉	1	16	yes	complemented
286	#449	C₂²×C₁₉	1	16	yes	complemented
287	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
288	C₂×#106	C₂²×C₁₉	1	2	yes	—
289	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
290	C₂×#103	C₂²×C₁₉	1	2	yes	—
291	C₂×#103	C₂²×C₁₉	1	2	yes	—
292	C₂×#102	C₂²×C₁₉	1	2	yes	—
293	C₂×#102	C₂²×C₁₉	1	2	yes	—
294	#408	C₂²×C₁₉	1	8	yes	complemented
295	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
296	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
297	C₂×C₁₉	—	4	4	no	—
298	C₂×C₁₉	—	4	2	no	—
299	C₂×C₁₉	—	8	4	no	—
300	C₂×C₁₉	#3204	1	4	yes	direct product factor
301	C₂×C₁₉	C₂×#534	1	1	yes	characteristic
302	C₂×C₁₉	C₂×#577	1	2	yes	—
303	C₂×#41	—	2	4	no	—
304	C₂×#41	—	4	2	no	—
305	C₂×#41	—	4	2	no	—
306	C₂×#41	—	4	4	no	—
307	C₂×#41	—	4	4	no	—
308	C₂×#41	D₄×C₁₉	1	4	yes	—
309	C₂×#41	C₂³×C₁₉	1	8	yes	—
310	C₂×#41	C₂³×C₁₉	1	4	yes	—
311	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
312	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
313	C₂²×D₄	—	2	2	no	—
314	C₂²×D₄	—	2	2	no	—
315	C₂²×D₄	—	2	2	no	—
316	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
317	C₂²×D₄	D₄×C₁₉	1	2	yes	—
318	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
319	C₂³×C₄	—	2	2	no	—
320	C₂³×C₄	—	2	2	no	—
321	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
322	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
323	C₂×Q₁₆	—	4	2	no	—
324	C₂×Q₁₆	C₂³×C₁₉	1	4	yes	—
325	C₂×SD₁₆	—	4	4	no	—
326	C₂×SD₁₆	C₂³×C₁₉	1	8	yes	—
327	C₂×D₈	—	4	2	no	—
328	C₂×D₈	C₂³×C₁₉	1	4	yes	—
329	C₂×M₁₆	—	4	2	no	—
330	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
331	C₂²×C₈	—	4	2	no	—
332	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
333	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
334	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
335	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
336	C₂²⋊Q₈	—	2	16	no	—
337	C₂²⋊Q₈	—	2	4	no	—
338	C₂²⋊Q₈	—	2	4	no	—
339	C₂²⋊Q₈	C₂³×C₁₉	1	8	yes	—
340	C₂²⋊Q₈	C₂³×C₁₉	1	8	yes	—
341	#121	—	2	16	no	—
342	#121	—	2	16	no	—
343	#121	—	2	16	no	—
344	#121	—	2	4	no	—
345	#121	—	2	4	no	—
346	#121	C₂³×C₁₉	1	8	yes	—
347	#121	C₂³×C₁₉	1	8	yes	—
348	C₂×C₄⋊C₄	—	2	2	no	—
349	C₂×C₄⋊C₄	—	2	4	no	—
350	C₂×C₄⋊C₄	—	2	2	no	—
351	C₂×C₄⋊C₄	—	2	2	no	—
352	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
353	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
354	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
355	C₂×C₂²⋊C₄	—	2	2	no	—
356	C₂×C₂²⋊C₄	—	2	2	no	—
357	C₂×C₂²⋊C₄	—	2	2	no	—
358	C₂×C₂²⋊C₄	—	2	2	no	—
359	#106	C₂³×C₁₉	1	8	yes	—
360	#106	C₂³×C₁₉	1	4	yes	—
361	#106	C₂³×C₁₉	1	4	yes	—
362	#103	C₂³×C₁₉	1	8	yes	—
363	#103	C₂³×C₁₉	1	8	yes	—
364	#102	C₂³×C₁₉	1	8	yes	—
365	#102	C₂³×C₁₉	1	8	yes	—
366	C₂²⋊C₈	C₂³×C₁₉	1	8	yes	—
367	C₂²⋊C₈	C₂³×C₁₉	1	8	yes	—
368	C₁₉	C₂×#3204	1	1	yes	characteristic, direct product factor, Sylow
369	C₂⁴	—	2	2	no	—
370	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
371	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
372	#41	—	4	8	no	—
373	#41	—	4	4	no	—
374	#41	—	4	4	no	—
375	#41	—	4	8	no	—
376	#41	—	4	8	no	—
377	#41	—	4	16	no	—
378	C₂×Q₈	—	2	2	no	—
379	C₂×Q₈	—	2	4	no	—
380	C₂×Q₈	—	2	4	no	—
381	C₂×Q₈	—	4	2	no	—
382	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
383	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
384	C₂×D₄	—	2	8	no	—
385	C₂×D₄	—	2	8	no	—
386	C₂×D₄	—	2	8	no	—
387	C₂×D₄	—	2	2	no	—
388	C₂×D₄	—	2	4	no	—
389	C₂×D₄	—	2	4	no	—
390	C₂×D₄	—	4	4	no	—
391	C₂×D₄	—	4	2	no	—
392	C₂×D₄	—	4	8	no	—
393	C₂×D₄	—	8	4	no	—
394	C₂×D₄	—	8	4	no	—
395	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
396	C₂×D₄	C₂×D₄×C₁₉	1	8	yes	—
397	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	4	no	—
401	C₂²×C₄	—	2	4	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	8	no	—
406	C₂²×C₄	—	2	8	no	—
407	C₂²×C₄	—	4	8	no	—
408	C₂²×C₄	—	8	4	no	—
409	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
410	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
411	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
412	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
413	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
414	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
415	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
416	Q₁₆	—	4	4	no	—
417	SD₁₆	—	4	8	no	—
418	D₈	—	4	4	no	—
419	M₁₆	—	4	4	no	—
420	C₂×C₈	—	2	4	no	—
421	C₂×C₈	—	2	2	no	—
422	C₂×C₈	—	2	2	no	—
423	C₂×C₈	—	4	4	no	—
424	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
425	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
426	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
427	C₄⋊C₄	—	2	8	no	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	2	8	no	—
431	C₄⋊C₄	—	2	8	no	—
432	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
433	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
434	C₂²⋊C₄	—	2	8	no	—
435	C₂²⋊C₄	—	2	8	no	—
436	C₂²⋊C₄	—	2	8	no	—
437	C₂²⋊C₄	—	2	8	no	—
438	C₂³	—	2	4	no	—
439	C₂³	—	2	2	no	—
440	C₂³	—	2	4	no	—
441	C₂³	—	2	4	no	—
442	C₂³	—	2	4	no	—
443	C₂³	—	2	4	no	—
444	C₂³	—	4	4	no	—
445	C₂³	—	4	4	no	—
446	C₂³	—	4	4	no	—
447	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
448	C₂³	C₂²×D₄×C₁₉	1	4	yes	—
449	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
450	Q₈	—	2	4	no	—
451	Q₈	—	2	4	no	—
452	Q₈	—	4	4	no	—
453	Q₈	—	4	4	no	—
454	D₄	—	2	4	no	—
455	D₄	—	2	4	no	—
456	D₄	—	4	8	no	—
457	D₄	—	4	4	no	—
458	D₄	—	4	16	no	—
459	D₄	—	4	4	no	—
460	D₄	—	8	8	no	—
461	D₄	—	8	8	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	8	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	2	4	no	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	4	16	no	—
474	C₂×C₄	—	4	4	no	—
475	C₂×C₄	—	4	4	no	—
476	C₂×C₄	—	4	4	no	—
477	C₂×C₄	—	8	8	no	—
478	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
479	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
480	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
481	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
482	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
483	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
484	C₈	—	2	4	no	—
485	C₈	—	2	2	no	—
486	C₈	—	2	2	no	—
487	C₂²	—	2	4	no	—
488	C₂²	—	2	2	no	—
489	C₂²	—	2	4	no	—
490	C₂²	—	2	4	no	—
491	C₂²	—	2	4	no	—
492	C₂²	—	4	8	no	—
493	C₂²	—	4	4	no	—
494	C₂²	—	4	4	no	—
495	C₂²	—	4	4	no	—
496	C₂²	—	4	4	no	—
497	C₂²	—	8	8	no	—
498	C₂²	C₁₉×#534	1	2	yes	—
499	C₂²	C₁₉×#577	1	4	yes	—
500	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
501	C₄	—	2	4	no	—
502	C₄	—	2	2	no	—
503	C₄	—	4	4	no	—
504	C₄	—	4	4	no	—
505	C₄	—	4	4	no	—
506	C₄	C₁₉×#534	1	2	yes	—
507	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
508	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
509	C₂	—	4	4	no	—
510	C₂	—	4	2	no	—
511	C₂	—	8	4	no	—
512	C₂	C₁₉×#3204	1	4	yes	direct product factor
513	C₂	C₂×C₁₉×#534	1	1	yes	characteristic
514	C₂	C₂×C₁₉×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂²×#41×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#537	C₂	semidirect
2. C₁₉×#3204	C₂	direct (N × H)
3. C₂×C₁₉×#481	C₂	semidirect
4. C₂×C₁₉×#483	C₂	semidirect
5. C₂×C₁₉×#470	C₂	semidirect
6. C₂×C₁₉×#469	C₂	semidirect
7. C₂×C₁₉×#465	C₂	semidirect
8. C₂×C₁₉×#452	C₂	semidirect
9. C₂×C₁₉×#449	C₂	semidirect
10. C₂×C₁₉×#408	C₂	semidirect
19. C₁₉×#537	C₂²	semidirect
29. C₁₉×#483	C₂²	semidirect
30. C₁₉×#481	C₂²	semidirect
31. C₁₉×#470	C₂²	semidirect
32. C₁₉×#469	C₂²	semidirect
33. C₁₉×#465	C₂²	semidirect
34. C₁₉×#452	C₂²	semidirect
35. C₁₉×#449	C₂²	semidirect
43. C₁₉×#408	C₂²	semidirect
180. C₂×#3204	C₁₉	direct (N × H)
230. C₂×#537	C₂×C₁₉	semidirect
231. #3204	C₂×C₁₉	direct (N × H)
232. C₂×#481	C₂×C₁₉	semidirect
233. C₂×#483	C₂×C₁₉	semidirect
234. C₂×#470	C₂×C₁₉	semidirect
235. C₂×#469	C₂×C₁₉	semidirect
236. C₂×#465	C₂×C₁₉	semidirect
237. C₂×#452	C₂×C₁₉	semidirect
238. C₂×#449	C₂×C₁₉	semidirect
239. C₂×#408	C₂×C₁₉	semidirect
270. #537	C₂²×C₁₉	semidirect
280. #483	C₂²×C₁₉	semidirect
281. #481	C₂²×C₁₉	semidirect
282. #470	C₂²×C₁₉	semidirect
283. #469	C₂²×C₁₉	semidirect
284. #465	C₂²×C₁₉	semidirect
285. #452	C₂²×C₁₉	semidirect
286. #449	C₂²×C₁₉	semidirect
294. #408	C₂²×C₁₉	semidirect
300. C₂×C₁₉	#3204	direct (N × H)
368. C₁₉	C₂×#3204	direct (N × H)
512. C₂	C₁₉×#3204	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×#537	2
C₁₉×#3204	2
C₂×C₁₉×#481	2
C₂×C₁₉×#483	2
C₂×C₁₉×#470	2
C₂×C₁₉×#469	2
C₂×C₁₉×#465	2
C₂×C₁₉×#452	2
C₂×C₁₉×#449	2
C₂×C₁₉×#408	2
C₂×#3204	19

Subgroups — C2×C19×#3204 #18066707

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#3204 #18066707