Subgroups — C₂×C₁₉×#3002 #18066312

Order 4864.

5130 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#41×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₉×#135	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#525	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3002	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₁₉×#452	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₉×#449	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₉×#451	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×#448	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₉×#450	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₉×#447	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₉×#416	C₂	1	2	yes	maximal, complemented
12	C₂²×C₁₉×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#41×C₁₉	—	2	16	no	—
14	C₂²×#41×C₁₉	—	2	1	no	—
15	C₂²×#41×C₁₉	—	2	4	no	—
16	C₂²×#41×C₁₉	—	2	1	no	—
17	C₂²×#41×C₁₉	C₂²	1	2	yes	—
18	C₂²×#41×C₁₉	C₂²	1	2	yes	—
19	C₂²×#41×C₁₉	C₂²	1	8	yes	complemented
20	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic, complemented
21	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
22	C₂³×D₄×C₁₉	—	2	1	no	—
23	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₂⁴×C₄×C₁₉	—	2	1	no	—
25	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#135	—	2	16	no	—
27	C₂×C₁₉×#135	C₂²	1	16	yes	complemented
28	C₂²×Q₁₆×C₁₉	C₂²	1	2	yes	complemented
29	C₂²×SD₁₆×C₁₉	C₂²	1	2	yes	complemented
30	C₂²×SD₁₆×C₁₉	C₂²	1	2	yes	complemented
31	C₂²×D₈×C₁₉	C₂²	1	2	yes	complemented
32	C₂³×C₈×C₁₉	C₂²	1	2	yes	complemented
33	C₁₉×#525	—	2	4	no	—
34	C₁₉×#525	C₂²	1	8	yes	complemented
35	C₂×C₁₉×#123	—	2	1	no	—
36	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
39	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₁₉×#120	—	2	1	no	—
41	C₂×C₄×D₄×C₁₉	—	2	1	no	—
42	C₂×C₄×D₄×C₁₉	—	2	1	no	—
43	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic, complemented
44	C₁₉×#452	C₂²	1	16	yes	complemented
45	C₁₉×#451	C₂²	1	8	yes	complemented
46	C₁₉×#450	C₂²	1	8	yes	complemented
47	C₁₉×#449	C₂²	1	16	yes	complemented
48	C₁₉×#448	C₂²	1	8	yes	complemented
49	C₁₉×#447	C₂²	1	8	yes	complemented
50	C₁₉×#416	C₂²	1	16	yes	complemented
51	C₂×C₁₉×#103	C₂²	1	2	yes	complemented
52	C₂×C₁₉×#103	C₂²	1	2	yes	complemented
53	C₂×C₁₉×#102	C₂²	1	2	yes	complemented
54	C₂×C₁₉×#102	C₂²	1	2	yes	complemented
55	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
56	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
57	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	complemented
58	C₂×C₁₉×C₂²⋊C₈	C₂²	1	8	yes	complemented
59	C₂⁵×C₁₉	—	2	1	no	—
60	C₂⁵×C₁₉	D₄	1	1	yes	characteristic
61	C₂×#41×C₁₉	—	2	16	no	—
62	C₂×#41×C₁₉	—	2	64	no	—
63	C₂×#41×C₁₉	—	2	16	no	—
64	C₂×#41×C₁₉	—	2	64	no	—
65	C₂×#41×C₁₉	—	2	8	no	—
66	C₂×#41×C₁₉	—	2	8	no	—
67	C₂×#41×C₁₉	—	2	8	no	—
68	C₂×#41×C₁₉	—	2	4	no	—
69	C₂×#41×C₁₉	—	2	4	no	—
70	C₂×#41×C₁₉	—	2	8	no	—
71	C₂×#41×C₁₉	—	2	8	no	—
72	C₂×#41×C₁₉	—	2	2	no	—
73	C₂×#41×C₁₉	—	2	8	no	—
74	C₂×#41×C₁₉	D₄	1	16	yes	complemented
75	C₂×#41×C₁₉	C₂³	1	8	yes	—
76	C₂×#41×C₁₉	C₂³	1	8	yes	—
77	C₂×#41×C₁₉	C₂³	1	4	yes	complemented
78	C₂²×Q₈×C₁₉	—	2	8	no	—
79	C₂²×Q₈×C₁₉	—	2	1	no	—
80	C₂²×Q₈×C₁₉	—	2	2	no	—
81	C₂²×Q₈×C₁₉	C₂³	1	4	yes	—
82	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
83	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
84	C₂²×D₄×C₁₉	—	2	16	no	—
85	C₂²×D₄×C₁₉	—	2	2	no	—
86	C₂²×D₄×C₁₉	—	2	2	no	—
87	C₂²×D₄×C₁₉	—	2	8	no	—
88	C₂²×D₄×C₁₉	—	2	8	no	—
89	C₂²×D₄×C₁₉	—	2	1	no	—
90	C₂²×D₄×C₁₉	—	2	1	no	—
91	C₂²×D₄×C₁₉	—	2	1	no	—
92	C₂²×D₄×C₁₉	—	2	1	no	—
93	C₂²×D₄×C₁₉	—	2	2	no	—
94	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
95	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
96	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
97	C₂³×C₄×C₁₉	—	2	16	no	—
98	C₂³×C₄×C₁₉	—	2	1	no	—
99	C₂³×C₄×C₁₉	—	2	2	no	—
100	C₂³×C₄×C₁₉	—	2	8	no	—
101	C₂³×C₄×C₁₉	—	2	8	no	—
102	C₂³×C₄×C₁₉	—	2	2	no	—
103	C₂³×C₄×C₁₉	—	2	1	no	—
104	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
105	C₂³×C₄×C₁₉	D₄	1	4	yes	—
106	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
107	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
108	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
111	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
112	C₁₉×#135	—	2	64	no	—
113	C₂×Q₁₆×C₁₉	—	2	8	no	—
114	C₂×Q₁₆×C₁₉	C₂³	1	8	yes	complemented
115	C₂×SD₁₆×C₁₉	—	2	8	no	—
116	C₂×SD₁₆×C₁₉	—	2	8	no	—
117	C₂×SD₁₆×C₁₉	C₂³	1	8	yes	complemented
118	C₂×SD₁₆×C₁₉	C₂³	1	8	yes	complemented
119	C₂×D₈×C₁₉	—	2	8	no	—
120	C₂×D₈×C₁₉	C₂³	1	8	yes	complemented
121	C₂²×C₈×C₁₉	—	2	8	no	—
122	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
123	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
124	C₂²×C₈×C₁₉	C₂³	1	8	yes	complemented
125	C₁₉×#123	—	2	8	no	—
126	C₁₉×C₂²⋊Q₈	—	2	2	no	—
127	C₁₉×C₂²⋊Q₈	—	2	2	no	—
128	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
129	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	complemented
130	C₁₉×#121	—	2	2	no	—
131	C₁₉×#121	—	2	2	no	—
132	C₁₉×#121	C₂³	1	4	yes	—
133	C₁₉×#121	C₂³	1	4	yes	complemented
134	C₁₉×#120	—	2	8	no	—
135	C₄×D₄×C₁₉	—	2	8	no	—
136	C₄×D₄×C₁₉	—	2	8	no	—
137	C₁₉×#117	—	2	2	no	—
138	C₁₉×#117	C₂³	1	4	yes	complemented
139	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
140	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
141	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
144	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
145	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
146	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
147	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
148	C₂×C₄²×C₁₉	—	2	1	no	—
149	C₁₉×#103	C₂³	1	8	yes	complemented
150	C₁₉×#103	C₂³	1	8	yes	complemented
151	C₁₉×#102	C₂³	1	8	yes	complemented
152	C₁₉×#102	C₂³	1	8	yes	complemented
153	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
154	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
155	C₁₉×C₂²⋊C₈	C₂³	1	8	yes	complemented
156	C₂⁴×C₁₉	—	2	8	no	—
157	C₂⁴×C₁₉	—	2	4	no	—
158	C₂⁴×C₁₉	—	2	4	no	—
159	C₂⁴×C₁₉	—	2	4	no	—
160	C₂⁴×C₁₉	—	2	2	no	—
161	C₂⁴×C₁₉	—	2	1	no	—
162	C₂⁴×C₁₉	—	4	2	no	—
163	C₂⁴×C₁₉	—	4	4	no	—
164	C₂⁴×C₁₉	—	4	4	no	—
165	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
166	C₂⁴×C₁₉	C₂×D₄	1	4	yes	—
167	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
168	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
169	#41×C₁₉	—	2	64	no	—
170	#41×C₁₉	—	2	32	no	—
171	#41×C₁₉	—	2	64	no	—
172	#41×C₁₉	—	2	16	no	—
173	#41×C₁₉	—	2	16	no	—
174	#41×C₁₉	—	2	32	no	—
175	#41×C₁₉	—	2	16	no	—
176	#41×C₁₉	—	2	16	no	—
177	#41×C₁₉	—	4	8	no	—
178	#41×C₁₉	C₂×D₄	1	32	yes	complemented
179	C₂×Q₈×C₁₉	—	2	16	no	—
180	C₂×Q₈×C₁₉	—	2	8	no	—
181	C₂×Q₈×C₁₉	—	2	16	no	—
182	C₂×Q₈×C₁₉	—	2	4	no	—
183	C₂×Q₈×C₁₉	—	2	4	no	—
184	C₂×Q₈×C₁₉	—	2	2	no	—
185	C₂×Q₈×C₁₉	—	2	1	no	—
186	C₂×Q₈×C₁₉	—	2	4	no	—
187	C₂×Q₈×C₁₉	C₂×D₄	1	8	yes	—
188	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
189	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
190	C₂×D₄×C₁₉	—	2	64	no	—
191	C₂×D₄×C₁₉	—	2	16	no	—
192	C₂×D₄×C₁₉	—	2	8	no	—
193	C₂×D₄×C₁₉	—	2	16	no	—
194	C₂×D₄×C₁₉	—	2	16	no	—
195	C₂×D₄×C₁₉	—	2	8	no	—
196	C₂×D₄×C₁₉	—	2	8	no	—
197	C₂×D₄×C₁₉	—	2	16	no	—
198	C₂×D₄×C₁₉	—	2	4	no	—
199	C₂×D₄×C₁₉	—	2	4	no	—
200	C₂×D₄×C₁₉	—	2	4	no	—
201	C₂×D₄×C₁₉	—	2	4	no	—
202	C₂×D₄×C₁₉	—	2	2	no	—
203	C₂×D₄×C₁₉	—	2	4	no	—
204	C₂×D₄×C₁₉	—	2	4	no	—
205	C₂×D₄×C₁₉	—	2	1	no	—
206	C₂×D₄×C₁₉	—	4	4	no	—
207	C₂×D₄×C₁₉	—	4	4	no	—
208	C₂×D₄×C₁₉	—	4	4	no	—
209	C₂×D₄×C₁₉	C₂×D₄	1	8	yes	—
210	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
211	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
212	C₂²×C₄×C₁₉	—	2	8	no	—
213	C₂²×C₄×C₁₉	—	2	64	no	—
214	C₂²×C₄×C₁₉	—	2	16	no	—
215	C₂²×C₄×C₁₉	—	2	4	no	—
216	C₂²×C₄×C₁₉	—	2	4	no	—
217	C₂²×C₄×C₁₉	—	2	2	no	—
218	C₂²×C₄×C₁₉	—	2	4	no	—
219	C₂²×C₄×C₁₉	—	2	16	no	—
220	C₂²×C₄×C₁₉	—	2	4	no	—
221	C₂²×C₄×C₁₉	—	2	16	no	—
222	C₂²×C₄×C₁₉	—	2	8	no	—
223	C₂²×C₄×C₁₉	—	2	8	no	—
224	C₂²×C₄×C₁₉	—	2	4	no	—
225	C₂²×C₄×C₁₉	—	2	4	no	—
226	C₂²×C₄×C₁₉	—	2	16	no	—
227	C₂²×C₄×C₁₉	—	2	1	no	—
228	C₂²×C₄×C₁₉	—	2	1	no	—
229	C₂²×C₄×C₁₉	—	2	1	no	—
230	C₂²×C₄×C₁₉	—	2	4	no	—
231	C₂²×C₄×C₁₉	—	4	4	no	—
232	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
235	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
236	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
237	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
238	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
239	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
240	C₂²×C₄×C₁₉	C₂×D₄	1	8	yes	—
241	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
246	Q₁₆×C₁₉	—	2	16	no	—
247	SD₁₆×C₁₉	—	2	16	no	—
248	SD₁₆×C₁₉	—	2	16	no	—
249	D₈×C₁₉	—	2	16	no	—
250	C₂×C₈×C₁₉	—	2	4	no	—
251	C₂×C₈×C₁₉	—	2	4	no	—
252	C₂×C₈×C₁₉	—	2	16	no	—
253	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
254	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
255	C₄⋊C₄×C₁₉	—	2	4	no	—
256	C₄⋊C₄×C₁₉	—	2	4	no	—
257	C₄⋊C₄×C₁₉	—	2	1	no	—
258	C₄⋊C₄×C₁₉	—	2	1	no	—
259	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
260	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
261	C₂²⋊C₄×C₁₉	—	2	4	no	—
262	C₂²⋊C₄×C₁₉	—	2	4	no	—
263	C₂²⋊C₄×C₁₉	—	2	4	no	—
264	C₂²⋊C₄×C₁₉	—	2	4	no	—
265	C₂²⋊C₄×C₁₉	—	2	4	no	—
266	C₄²×C₁₉	—	2	4	no	—
267	C₂×#3002	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
268	C₂³×C₁₉	—	2	2	no	—
269	C₂³×C₁₉	—	2	2	no	—
270	C₂³×C₁₉	—	2	2	no	—
271	C₂³×C₁₉	—	2	2	no	—
272	C₂³×C₁₉	—	2	16	no	—
273	C₂³×C₁₉	—	2	8	no	—
274	C₂³×C₁₉	—	2	2	no	—
275	C₂³×C₁₉	—	2	8	no	—
276	C₂³×C₁₉	—	2	2	no	—
277	C₂³×C₁₉	—	2	8	no	—
278	C₂³×C₁₉	—	2	2	no	—
279	C₂³×C₁₉	—	2	4	no	—
280	C₂³×C₁₉	—	2	2	no	—
281	C₂³×C₁₉	—	4	4	no	—
282	C₂³×C₁₉	—	4	16	no	—
283	C₂³×C₁₉	—	4	32	no	—
284	C₂³×C₁₉	—	4	8	no	—
285	C₂³×C₁₉	—	4	4	no	—
286	C₂³×C₁₉	—	4	8	no	—
287	C₂³×C₁₉	—	4	4	no	—
288	C₂³×C₁₉	—	4	2	no	—
289	C₂³×C₁₉	—	4	2	no	—
290	C₂³×C₁₉	—	4	2	no	—
291	C₂³×C₁₉	#120	1	4	yes	—
292	C₂³×C₁₉	#135	1	4	yes	complemented
293	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
294	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
295	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
296	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
297	Q₈×C₁₉	—	2	16	no	—
298	Q₈×C₁₉	—	2	8	no	—
299	Q₈×C₁₉	—	2	4	no	—
300	Q₈×C₁₉	—	2	4	no	—
301	Q₈×C₁₉	—	4	2	no	—
302	Q₈×C₁₉	C₂²×D₄	1	8	yes	—
303	D₄×C₁₉	—	2	32	no	—
304	D₄×C₁₉	—	2	16	no	—
305	D₄×C₁₉	—	2	32	no	—
306	D₄×C₁₉	—	2	8	no	—
307	D₄×C₁₉	—	2	4	no	—
308	D₄×C₁₉	—	2	4	no	—
309	D₄×C₁₉	—	4	8	no	—
310	D₄×C₁₉	—	4	8	no	—
311	D₄×C₁₉	—	4	8	no	—
312	D₄×C₁₉	—	4	2	no	—
313	D₄×C₁₉	C₂²×D₄	1	8	yes	—
314	C₂×C₄×C₁₉	—	2	16	no	—
315	C₂×C₄×C₁₉	—	2	32	no	—
316	C₂×C₄×C₁₉	—	2	2	no	—
317	C₂×C₄×C₁₉	—	2	8	no	—
318	C₂×C₄×C₁₉	—	2	2	no	—
319	C₂×C₄×C₁₉	—	2	8	no	—
320	C₂×C₄×C₁₉	—	2	4	no	—
321	C₂×C₄×C₁₉	—	2	8	no	—
322	C₂×C₄×C₁₉	—	2	32	no	—
323	C₂×C₄×C₁₉	—	2	4	no	—
324	C₂×C₄×C₁₉	—	2	4	no	—
325	C₂×C₄×C₁₉	—	2	8	no	—
326	C₂×C₄×C₁₉	—	2	4	no	—
327	C₂×C₄×C₁₉	—	2	4	no	—
328	C₂×C₄×C₁₉	—	2	2	no	—
329	C₂×C₄×C₁₉	—	2	2	no	—
330	C₂×C₄×C₁₉	—	2	2	no	—
331	C₂×C₄×C₁₉	—	4	2	no	—
332	C₂×C₄×C₁₉	—	4	2	no	—
333	C₂×C₄×C₁₉	—	4	2	no	—
334	C₂×C₄×C₁₉	—	4	8	no	—
335	C₂×C₄×C₁₉	#120	1	4	yes	—
336	C₂×C₄×C₁₉	#120	1	8	yes	—
337	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
338	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
339	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
340	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
341	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
342	C₂×C₄×C₁₉	C₂²×D₄	1	8	yes	—
343	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
344	C₈×C₁₉	—	2	4	no	—
345	C₈×C₁₉	—	2	4	no	—
346	C₂³×#41	C₂×C₁₉	1	1	yes	characteristic, complemented
347	C₂²×#135	C₂×C₁₉	1	2	yes	complemented
348	C₂×#525	C₂×C₁₉	1	1	yes	characteristic, complemented
349	#3002	C₂×C₁₉	1	16	yes	direct product factor
350	C₂×#452	C₂×C₁₉	1	2	yes	complemented
351	C₂×#449	C₂×C₁₉	1	2	yes	complemented
352	C₂×#451	C₂×C₁₉	1	1	yes	characteristic, complemented
353	C₂×#448	C₂×C₁₉	1	1	yes	characteristic, complemented
354	C₂×#450	C₂×C₁₉	1	1	yes	characteristic, complemented
355	C₂×#447	C₂×C₁₉	1	1	yes	characteristic, complemented
356	C₂×#416	C₂×C₁₉	1	2	yes	complemented
357	C₂²×C₂²⋊C₈	C₂×C₁₉	1	1	yes	characteristic, complemented
358	C₂²×C₁₉	—	2	2	no	—
359	C₂²×C₁₉	—	2	8	no	—
360	C₂²×C₁₉	—	2	8	no	—
361	C₂²×C₁₉	—	2	2	no	—
362	C₂²×C₁₉	—	2	2	no	—
363	C₂²×C₁₉	—	2	2	no	—
364	C₂²×C₁₉	—	2	2	no	—
365	C₂²×C₁₉	—	2	8	no	—
366	C₂²×C₁₉	—	2	2	no	—
367	C₂²×C₁₉	—	2	2	no	—
368	C₂²×C₁₉	—	4	16	no	—
369	C₂²×C₁₉	—	4	32	no	—
370	C₂²×C₁₉	—	4	4	no	—
371	C₂²×C₁₉	—	4	16	no	—
372	C₂²×C₁₉	—	4	4	no	—
373	C₂²×C₁₉	—	4	4	no	—
374	C₂²×C₁₉	—	4	2	no	—
375	C₂²×C₁₉	—	4	2	no	—
376	C₂²×C₁₉	—	4	2	no	—
377	C₂²×C₁₉	—	8	4	no	—
378	C₂²×C₁₉	C₂×#120	1	4	yes	—
379	C₂²×C₁₉	C₂×#120	1	2	yes	—
380	C₂²×C₁₉	C₂×#135	1	2	yes	—
381	C₂²×C₁₉	C₂×#135	1	4	yes	complemented
382	C₂²×C₁₉	#575	1	2	yes	—
383	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
384	C₄×C₁₉	—	2	2	no	—
385	C₄×C₁₉	—	2	8	no	—
386	C₄×C₁₉	—	2	2	no	—
387	C₄×C₁₉	—	4	2	no	—
388	C₄×C₁₉	—	4	2	no	—
389	C₄×C₁₉	—	4	2	no	—
390	C₄×C₁₉	C₂×#120	1	4	yes	—
391	C₄×C₁₉	C₂×#120	1	2	yes	—
392	C₄×C₁₉	C₂³×D₄	1	2	yes	—
393	C₂²×#41	—	2	16	no	—
394	C₂²×#41	—	2	1	no	—
395	C₂²×#41	—	2	1	no	—
396	C₂²×#41	—	2	4	no	—
397	C₂²×#41	C₂²×C₁₉	1	2	yes	—
398	C₂²×#41	C₂²×C₁₉	1	2	yes	—
399	C₂²×#41	C₂²×C₁₉	1	8	yes	complemented
400	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic, complemented
401	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
402	C₂³×D₄	—	2	1	no	—
403	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
404	C₂⁴×C₄	—	2	1	no	—
405	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
406	C₂×#135	—	2	16	no	—
407	C₂×#135	C₂²×C₁₉	1	16	yes	complemented
408	C₂²×Q₁₆	C₂²×C₁₉	1	2	yes	complemented
409	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	complemented
410	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	complemented
411	C₂²×D₈	C₂²×C₁₉	1	2	yes	complemented
412	C₂³×C₈	C₂²×C₁₉	1	2	yes	complemented
413	#525	—	2	4	no	—
414	#525	C₂²×C₁₉	1	8	yes	complemented
415	C₂×#123	—	2	1	no	—
416	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
417	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
418	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
419	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic, complemented
420	C₂×#120	—	2	1	no	—
421	C₂×C₄×D₄	—	2	1	no	—
422	C₂×C₄×D₄	—	2	1	no	—
423	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic, complemented
424	#452	C₂²×C₁₉	1	16	yes	complemented
425	#451	C₂²×C₁₉	1	8	yes	complemented
426	#450	C₂²×C₁₉	1	8	yes	complemented
427	#449	C₂²×C₁₉	1	16	yes	complemented
428	#448	C₂²×C₁₉	1	8	yes	complemented
429	#447	C₂²×C₁₉	1	8	yes	complemented
430	#416	C₂²×C₁₉	1	16	yes	complemented
431	C₂×#103	C₂²×C₁₉	1	2	yes	complemented
432	C₂×#103	C₂²×C₁₉	1	2	yes	complemented
433	C₂×#102	C₂²×C₁₉	1	2	yes	complemented
434	C₂×#102	C₂²×C₁₉	1	2	yes	complemented
435	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
436	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
437	C₂×C₂²⋊C₈	C₂²×C₁₉	1	8	yes	complemented
438	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	complemented
439	C₂×C₁₉	—	2	4	no	—
440	C₂×C₁₉	—	2	4	no	—
441	C₂×C₁₉	—	4	2	no	—
442	C₂×C₁₉	—	4	8	no	—
443	C₂×C₁₉	—	8	2	no	—
444	C₂×C₁₉	#3002	1	4	yes	direct product factor
445	C₂×C₁₉	C₂²×#120	1	1	yes	characteristic
446	C₂×C₁₉	C₂²×#135	1	1	yes	characteristic
447	C₂×C₁₉	C₂×#575	1	1	yes	characteristic
448	C₂⁵	—	2	1	no	—
449	C₂⁵	D₄×C₁₉	1	1	yes	characteristic
450	C₂×#41	—	2	16	no	—
451	C₂×#41	—	2	64	no	—
452	C₂×#41	—	2	16	no	—
453	C₂×#41	—	2	64	no	—
454	C₂×#41	—	2	8	no	—
455	C₂×#41	—	2	8	no	—
456	C₂×#41	—	2	8	no	—
457	C₂×#41	—	2	4	no	—
458	C₂×#41	—	2	4	no	—
459	C₂×#41	—	2	8	no	—
460	C₂×#41	—	2	8	no	—
461	C₂×#41	—	2	2	no	—
462	C₂×#41	—	2	8	no	—
463	C₂×#41	D₄×C₁₉	1	16	yes	complemented
464	C₂×#41	C₂³×C₁₉	1	8	yes	—
465	C₂×#41	C₂³×C₁₉	1	8	yes	—
466	C₂×#41	C₂³×C₁₉	1	4	yes	complemented
467	C₂²×Q₈	—	2	8	no	—
468	C₂²×Q₈	—	2	1	no	—
469	C₂²×Q₈	—	2	2	no	—
470	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
471	C₂²×Q₈	C₂³×C₁₉	1	4	yes	—
472	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
473	C₂²×D₄	—	2	16	no	—
474	C₂²×D₄	—	2	2	no	—
475	C₂²×D₄	—	2	2	no	—
476	C₂²×D₄	—	2	8	no	—
477	C₂²×D₄	—	2	8	no	—
478	C₂²×D₄	—	2	1	no	—
479	C₂²×D₄	—	2	1	no	—
480	C₂²×D₄	—	2	1	no	—
481	C₂²×D₄	—	2	1	no	—
482	C₂²×D₄	—	2	2	no	—
483	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
484	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
485	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
486	C₂³×C₄	—	2	16	no	—
487	C₂³×C₄	—	2	1	no	—
488	C₂³×C₄	—	2	2	no	—
489	C₂³×C₄	—	2	2	no	—
490	C₂³×C₄	—	2	8	no	—
491	C₂³×C₄	—	2	8	no	—
492	C₂³×C₄	—	2	1	no	—
493	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
494	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
495	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
496	C₂³×C₄	D₄×C₁₉	1	4	yes	—
497	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
498	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
499	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
500	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
501	#135	—	2	64	no	—
502	C₂×Q₁₆	—	2	8	no	—
503	C₂×Q₁₆	C₂³×C₁₉	1	8	yes	complemented
504	C₂×SD₁₆	—	2	8	no	—
505	C₂×SD₁₆	—	2	8	no	—
506	C₂×SD₁₆	C₂³×C₁₉	1	8	yes	complemented
507	C₂×SD₁₆	C₂³×C₁₉	1	8	yes	complemented
508	C₂×D₈	—	2	8	no	—
509	C₂×D₈	C₂³×C₁₉	1	8	yes	complemented
510	C₂²×C₈	—	2	8	no	—
511	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
512	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
513	C₂²×C₈	C₂³×C₁₉	1	8	yes	complemented
514	#123	—	2	8	no	—
515	C₂²⋊Q₈	—	2	2	no	—
516	C₂²⋊Q₈	—	2	2	no	—
517	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
518	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	complemented
519	#121	—	2	2	no	—
520	#121	—	2	2	no	—
521	#121	C₂³×C₁₉	1	4	yes	—
522	#121	C₂³×C₁₉	1	4	yes	complemented
523	#120	—	2	8	no	—
524	C₄×D₄	—	2	8	no	—
525	C₄×D₄	—	2	8	no	—
526	#117	—	2	2	no	—
527	#117	C₂³×C₁₉	1	4	yes	complemented
528	C₂×C₄⋊C₄	—	2	1	no	—
529	C₂×C₄⋊C₄	—	2	1	no	—
530	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
531	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
532	C₂×C₂²⋊C₄	—	2	1	no	—
533	C₂×C₂²⋊C₄	—	2	1	no	—
534	C₂×C₂²⋊C₄	—	2	1	no	—
535	C₂×C₂²⋊C₄	—	2	1	no	—
536	C₂×C₂²⋊C₄	—	2	1	no	—
537	C₂×C₄²	—	2	1	no	—
538	#103	C₂³×C₁₉	1	8	yes	complemented
539	#103	C₂³×C₁₉	1	8	yes	complemented
540	#102	C₂³×C₁₉	1	8	yes	complemented
541	#102	C₂³×C₁₉	1	8	yes	complemented
542	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
543	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
544	C₂²⋊C₈	C₂³×C₁₉	1	8	yes	complemented
545	C₁₉	C₂×#3002	1	1	yes	characteristic, direct product factor, Sylow
546	C₂⁴	—	2	8	no	—
547	C₂⁴	—	2	4	no	—
548	C₂⁴	—	2	4	no	—
549	C₂⁴	—	2	4	no	—
550	C₂⁴	—	2	2	no	—
551	C₂⁴	—	2	1	no	—
552	C₂⁴	—	4	2	no	—
553	C₂⁴	—	4	4	no	—
554	C₂⁴	—	4	4	no	—
555	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
556	C₂⁴	C₂×D₄×C₁₉	1	4	yes	—
557	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
558	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
559	#41	—	2	64	no	—
560	#41	—	2	32	no	—
561	#41	—	2	64	no	—
562	#41	—	2	16	no	—
563	#41	—	2	16	no	—
564	#41	—	2	32	no	—
565	#41	—	2	16	no	—
566	#41	—	2	16	no	—
567	#41	—	4	8	no	—
568	#41	C₂×D₄×C₁₉	1	32	yes	complemented
569	C₂×Q₈	—	2	16	no	—
570	C₂×Q₈	—	2	8	no	—
571	C₂×Q₈	—	2	16	no	—
572	C₂×Q₈	—	2	4	no	—
573	C₂×Q₈	—	2	4	no	—
574	C₂×Q₈	—	2	2	no	—
575	C₂×Q₈	—	2	1	no	—
576	C₂×Q₈	—	2	4	no	—
577	C₂×Q₈	C₂×D₄×C₁₉	1	8	yes	—
578	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
579	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
580	C₂×D₄	—	2	64	no	—
581	C₂×D₄	—	2	16	no	—
582	C₂×D₄	—	2	8	no	—
583	C₂×D₄	—	2	16	no	—
584	C₂×D₄	—	2	16	no	—
585	C₂×D₄	—	2	8	no	—
586	C₂×D₄	—	2	8	no	—
587	C₂×D₄	—	2	16	no	—
588	C₂×D₄	—	2	4	no	—
589	C₂×D₄	—	2	4	no	—
590	C₂×D₄	—	2	4	no	—
591	C₂×D₄	—	2	4	no	—
592	C₂×D₄	—	2	2	no	—
593	C₂×D₄	—	2	4	no	—
594	C₂×D₄	—	2	4	no	—
595	C₂×D₄	—	2	1	no	—
596	C₂×D₄	—	4	4	no	—
597	C₂×D₄	—	4	4	no	—
598	C₂×D₄	—	4	4	no	—
599	C₂×D₄	C₂×D₄×C₁₉	1	8	yes	—
600	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
601	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
602	C₂²×C₄	—	2	8	no	—
603	C₂²×C₄	—	2	64	no	—
604	C₂²×C₄	—	2	16	no	—
605	C₂²×C₄	—	2	4	no	—
606	C₂²×C₄	—	2	4	no	—
607	C₂²×C₄	—	2	2	no	—
608	C₂²×C₄	—	2	4	no	—
609	C₂²×C₄	—	2	16	no	—
610	C₂²×C₄	—	2	4	no	—
611	C₂²×C₄	—	2	16	no	—
612	C₂²×C₄	—	2	8	no	—
613	C₂²×C₄	—	2	8	no	—
614	C₂²×C₄	—	2	4	no	—
615	C₂²×C₄	—	2	4	no	—
616	C₂²×C₄	—	2	16	no	—
617	C₂²×C₄	—	2	1	no	—
618	C₂²×C₄	—	2	1	no	—
619	C₂²×C₄	—	2	1	no	—
620	C₂²×C₄	—	2	4	no	—
621	C₂²×C₄	—	4	4	no	—
622	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
623	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
624	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
625	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
626	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
627	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
628	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
629	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
630	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
631	C₂²×C₄	C₂×D₄×C₁₉	1	8	yes	—
632	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
633	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
634	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
635	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
636	Q₁₆	—	2	16	no	—
637	SD₁₆	—	2	16	no	—
638	SD₁₆	—	2	16	no	—
639	D₈	—	2	16	no	—
640	C₂×C₈	—	2	4	no	—
641	C₂×C₈	—	2	4	no	—
642	C₂×C₈	—	2	16	no	—
643	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
644	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
645	C₄⋊C₄	—	2	4	no	—
646	C₄⋊C₄	—	2	4	no	—
647	C₄⋊C₄	—	2	1	no	—
648	C₄⋊C₄	—	2	1	no	—
649	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
650	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	—	2	4	no	—
653	C₂²⋊C₄	—	2	4	no	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	—	2	4	no	—
656	C₄²	—	2	4	no	—
657	C₂³	—	2	2	no	—
658	C₂³	—	2	2	no	—
659	C₂³	—	2	2	no	—
660	C₂³	—	2	2	no	—
661	C₂³	—	2	16	no	—
662	C₂³	—	2	8	no	—
663	C₂³	—	2	2	no	—
664	C₂³	—	2	8	no	—
665	C₂³	—	2	2	no	—
666	C₂³	—	2	8	no	—
667	C₂³	—	2	2	no	—
668	C₂³	—	2	4	no	—
669	C₂³	—	2	2	no	—
670	C₂³	—	4	4	no	—
671	C₂³	—	4	16	no	—
672	C₂³	—	4	32	no	—
673	C₂³	—	4	8	no	—
674	C₂³	—	4	4	no	—
675	C₂³	—	4	8	no	—
676	C₂³	—	4	4	no	—
677	C₂³	—	4	2	no	—
678	C₂³	—	4	2	no	—
679	C₂³	—	4	2	no	—
680	C₂³	C₁₉×#120	1	4	yes	—
681	C₂³	C₁₉×#135	1	4	yes	complemented
682	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
683	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
684	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
685	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
686	Q₈	—	2	16	no	—
687	Q₈	—	2	8	no	—
688	Q₈	—	2	4	no	—
689	Q₈	—	2	4	no	—
690	Q₈	—	4	2	no	—
691	Q₈	C₂²×D₄×C₁₉	1	8	yes	—
692	D₄	—	2	32	no	—
693	D₄	—	2	16	no	—
694	D₄	—	2	32	no	—
695	D₄	—	2	8	no	—
696	D₄	—	2	4	no	—
697	D₄	—	2	4	no	—
698	D₄	—	4	8	no	—
699	D₄	—	4	8	no	—
700	D₄	—	4	8	no	—
701	D₄	—	4	2	no	—
702	D₄	C₂²×D₄×C₁₉	1	8	yes	—
703	C₂×C₄	—	2	16	no	—
704	C₂×C₄	—	2	32	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	8	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	8	no	—
709	C₂×C₄	—	2	4	no	—
710	C₂×C₄	—	2	8	no	—
711	C₂×C₄	—	2	32	no	—
712	C₂×C₄	—	2	4	no	—
713	C₂×C₄	—	2	4	no	—
714	C₂×C₄	—	2	8	no	—
715	C₂×C₄	—	2	4	no	—
716	C₂×C₄	—	2	4	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	4	2	no	—
721	C₂×C₄	—	4	2	no	—
722	C₂×C₄	—	4	2	no	—
723	C₂×C₄	—	4	8	no	—
724	C₂×C₄	C₁₉×#120	1	4	yes	—
725	C₂×C₄	C₁₉×#120	1	8	yes	—
726	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
727	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
728	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
729	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
730	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
731	C₂×C₄	C₂²×D₄×C₁₉	1	8	yes	—
732	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
733	C₈	—	2	4	no	—
734	C₈	—	2	4	no	—
735	C₂²	—	2	2	no	—
736	C₂²	—	2	8	no	—
737	C₂²	—	2	8	no	—
738	C₂²	—	2	2	no	—
739	C₂²	—	2	2	no	—
740	C₂²	—	2	2	no	—
741	C₂²	—	2	2	no	—
742	C₂²	—	2	8	no	—
743	C₂²	—	2	2	no	—
744	C₂²	—	2	2	no	—
745	C₂²	—	4	16	no	—
746	C₂²	—	4	32	no	—
747	C₂²	—	4	4	no	—
748	C₂²	—	4	16	no	—
749	C₂²	—	4	4	no	—
750	C₂²	—	4	4	no	—
751	C₂²	—	4	2	no	—
752	C₂²	—	4	2	no	—
753	C₂²	—	4	2	no	—
754	C₂²	—	8	4	no	—
755	C₂²	C₂×C₁₉×#120	1	4	yes	—
756	C₂²	C₂×C₁₉×#120	1	2	yes	—
757	C₂²	C₂×C₁₉×#135	1	2	yes	—
758	C₂²	C₂×C₁₉×#135	1	4	yes	complemented
759	C₂²	C₁₉×#575	1	2	yes	—
760	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
761	C₄	—	2	2	no	—
762	C₄	—	2	8	no	—
763	C₄	—	2	2	no	—
764	C₄	—	4	2	no	—
765	C₄	—	4	2	no	—
766	C₄	—	4	2	no	—
767	C₄	C₂×C₁₉×#120	1	4	yes	—
768	C₄	C₂×C₁₉×#120	1	2	yes	—
769	C₄	C₂³×D₄×C₁₉	1	2	yes	—
770	C₂	—	2	4	no	—
771	C₂	—	2	4	no	—
772	C₂	—	4	2	no	—
773	C₂	—	4	8	no	—
774	C₂	—	8	2	no	—
775	C₂	C₁₉×#3002	1	4	yes	direct product factor
776	C₂	C₂²×C₁₉×#120	1	1	yes	characteristic
777	C₂	C₂²×C₁₉×#135	1	1	yes	characteristic
778	C₂	C₂×C₁₉×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
socle	C₂³×C₁₉	C₂²×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ C₂⁴×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×#41×C₁₉	C₂	semidirect
2. C₂²×C₁₉×#135	C₂	semidirect
3. C₂×C₁₉×#525	C₂	semidirect
4. C₁₉×#3002	C₂	direct (N × H)
5. C₂×C₁₉×#452	C₂	semidirect
6. C₂×C₁₉×#449	C₂	semidirect
7. C₂×C₁₉×#451	C₂	semidirect
8. C₂×C₁₉×#448	C₂	semidirect
9. C₂×C₁₉×#450	C₂	semidirect
10. C₂×C₁₉×#447	C₂	semidirect
11. C₂×C₁₉×#416	C₂	semidirect
12. C₂²×C₁₉×C₂²⋊C₈	C₂	semidirect
19. C₂²×#41×C₁₉	C₂²	semidirect
20. C₂²×#41×C₁₉	C₂²	semidirect
27. C₂×C₁₉×#135	C₂²	semidirect
28. C₂²×Q₁₆×C₁₉	C₂²	semidirect
29. C₂²×SD₁₆×C₁₉	C₂²	semidirect
30. C₂²×SD₁₆×C₁₉	C₂²	semidirect
31. C₂²×D₈×C₁₉	C₂²	semidirect
32. C₂³×C₈×C₁₉	C₂²	semidirect
34. C₁₉×#525	C₂²	semidirect
37. C₂×C₁₉×C₂²⋊Q₈	C₂²	semidirect
39. C₂×C₁₉×#121	C₂²	semidirect
43. C₂×C₁₉×#117	C₂²	semidirect
44. C₁₉×#452	C₂²	semidirect
45. C₁₉×#451	C₂²	semidirect
46. C₁₉×#450	C₂²	semidirect
47. C₁₉×#449	C₂²	semidirect
48. C₁₉×#448	C₂²	semidirect
49. C₁₉×#447	C₂²	semidirect
50. C₁₉×#416	C₂²	semidirect
51. C₂×C₁₉×#103	C₂²	semidirect
52. C₂×C₁₉×#103	C₂²	semidirect
53. C₂×C₁₉×#102	C₂²	semidirect
54. C₂×C₁₉×#102	C₂²	semidirect
57. C₂×C₁₉×C₂²⋊C₈	C₂²	semidirect
58. C₂×C₁₉×C₂²⋊C₈	C₂²	semidirect
74. C₂×#41×C₁₉	D₄	semidirect
77. C₂×#41×C₁₉	C₂³	semidirect
114. C₂×Q₁₆×C₁₉	C₂³	semidirect
117. C₂×SD₁₆×C₁₉	C₂³	semidirect
118. C₂×SD₁₆×C₁₉	C₂³	semidirect
120. C₂×D₈×C₁₉	C₂³	semidirect
124. C₂²×C₈×C₁₉	C₂³	semidirect
129. C₁₉×C₂²⋊Q₈	C₂³	semidirect
133. C₁₉×#121	C₂³	semidirect
138. C₁₉×#117	C₂³	semidirect
149. C₁₉×#103	C₂³	semidirect
150. C₁₉×#103	C₂³	semidirect
151. C₁₉×#102	C₂³	semidirect
152. C₁₉×#102	C₂³	semidirect
155. C₁₉×C₂²⋊C₈	C₂³	semidirect
178. #41×C₁₉	C₂×D₄	semidirect
267. C₂×#3002	C₁₉	direct (N × H)
292. C₂³×C₁₉	#135	semidirect
346. C₂³×#41	C₂×C₁₉	semidirect
347. C₂²×#135	C₂×C₁₉	semidirect
348. C₂×#525	C₂×C₁₉	semidirect
349. #3002	C₂×C₁₉	direct (N × H)
350. C₂×#452	C₂×C₁₉	semidirect
351. C₂×#449	C₂×C₁₉	semidirect
352. C₂×#451	C₂×C₁₉	semidirect
353. C₂×#448	C₂×C₁₉	semidirect
354. C₂×#450	C₂×C₁₉	semidirect
355. C₂×#447	C₂×C₁₉	semidirect
356. C₂×#416	C₂×C₁₉	semidirect
357. C₂²×C₂²⋊C₈	C₂×C₁₉	semidirect
381. C₂²×C₁₉	C₂×#135	semidirect
399. C₂²×#41	C₂²×C₁₉	semidirect
400. C₂²×#41	C₂²×C₁₉	semidirect
407. C₂×#135	C₂²×C₁₉	semidirect
408. C₂²×Q₁₆	C₂²×C₁₉	semidirect
409. C₂²×SD₁₆	C₂²×C₁₉	semidirect
410. C₂²×SD₁₆	C₂²×C₁₉	semidirect
411. C₂²×D₈	C₂²×C₁₉	semidirect
412. C₂³×C₈	C₂²×C₁₉	semidirect
414. #525	C₂²×C₁₉	semidirect
417. C₂×C₂²⋊Q₈	C₂²×C₁₉	semidirect
419. C₂×#121	C₂²×C₁₉	semidirect
423. C₂×#117	C₂²×C₁₉	semidirect
424. #452	C₂²×C₁₉	semidirect
425. #451	C₂²×C₁₉	semidirect
426. #450	C₂²×C₁₉	semidirect
427. #449	C₂²×C₁₉	semidirect
428. #448	C₂²×C₁₉	semidirect
429. #447	C₂²×C₁₉	semidirect
430. #416	C₂²×C₁₉	semidirect
431. C₂×#103	C₂²×C₁₉	semidirect
432. C₂×#103	C₂²×C₁₉	semidirect
433. C₂×#102	C₂²×C₁₉	semidirect
434. C₂×#102	C₂²×C₁₉	semidirect
437. C₂×C₂²⋊C₈	C₂²×C₁₉	semidirect
438. C₂×C₂²⋊C₈	C₂²×C₁₉	semidirect
444. C₂×C₁₉	#3002	direct (N × H)
463. C₂×#41	D₄×C₁₉	semidirect
466. C₂×#41	C₂³×C₁₉	semidirect
503. C₂×Q₁₆	C₂³×C₁₉	semidirect
506. C₂×SD₁₆	C₂³×C₁₉	semidirect
507. C₂×SD₁₆	C₂³×C₁₉	semidirect
509. C₂×D₈	C₂³×C₁₉	semidirect
513. C₂²×C₈	C₂³×C₁₉	semidirect
518. C₂²⋊Q₈	C₂³×C₁₉	semidirect
522. #121	C₂³×C₁₉	semidirect
527. #117	C₂³×C₁₉	semidirect
538. #103	C₂³×C₁₉	semidirect
539. #103	C₂³×C₁₉	semidirect
540. #102	C₂³×C₁₉	semidirect
541. #102	C₂³×C₁₉	semidirect
544. C₂²⋊C₈	C₂³×C₁₉	semidirect
545. C₁₉	C₂×#3002	direct (N × H)
568. #41	C₂×D₄×C₁₉	semidirect
681. C₂³	C₁₉×#135	semidirect
758. C₂²	C₂×C₁₉×#135	semidirect
775. C₂	C₁₉×#3002	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#41×C₁₉	2
C₂²×C₁₉×#135	2
C₂×C₁₉×#525	2
C₁₉×#3002	2
C₂×C₁₉×#452	2
C₂×C₁₉×#449	2
C₂×C₁₉×#451	2
C₂×C₁₉×#448	2
C₂×C₁₉×#450	2
C₂×C₁₉×#447	2
C₂×C₁₉×#416	2
C₂²×C₁₉×C₂²⋊C₈	2
C₂×#3002	19

Subgroups — C2×C19×#3002 #18066312

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#3002 #18066312