Subgroups — D₁₉×#542 #14577005

Order 2432.

1132 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927168	C₂	1	1	yes	maximal, characteristic, complemented
2	#11927167	C₂	1	1	yes	maximal, characteristic, complemented
3	#11927166	C₂	1	1	yes	maximal, characteristic, complemented
4	#11927165	C₂	1	1	yes	maximal, characteristic, complemented
5	#11927164	C₂	1	2	yes	maximal, complemented
6	#11927163	C₂	1	1	yes	maximal, characteristic, complemented
7	#11927162	C₂	1	2	yes	maximal, complemented
8	#11927161	C₂	1	1	yes	maximal, characteristic, complemented
9	#11927160	C₂	1	2	yes	maximal, complemented
10	#11927159	C₂	1	1	yes	maximal, characteristic, complemented
11	#11927158	C₂	1	2	yes	maximal, complemented
12	C₄⋊Q₈×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#126×D₁₉	C₂	1	2	yes	maximal, complemented
14	#124×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#124×D₁₉	C₂	1	2	yes	maximal, complemented
16	#123×D₁₉	C₂	1	2	yes	maximal, complemented
17	C₂²⋊Q₈×D₁₉	C₂	1	2	yes	maximal, complemented
18	C₂²⋊Q₈×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
19	#121×D₁₉	C₂	1	1	yes	maximal, characteristic
20	C₄×Q₈×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×D₄×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
22	#117×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₉×#542	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×Q₈×D₁₉	C₂²	1	1	yes	characteristic
25	C₂×Q₈×D₁₉	C₂²	1	2	yes	—
26	C₂×D₄×D₁₉	C₂²	1	1	yes	characteristic
27	C₂×D₄×D₁₉	C₂²	1	2	yes	—
28	C₂²×C₄×D₁₉	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₁₉	C₂²	1	2	yes	—
30	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₁₉×#126	C₂²	1	2	yes	complemented
32	C₁₉×#124	C₂²	1	2	yes	complemented
33	C₁₉×#124	C₂²	1	1	yes	characteristic, complemented
34	C₁₉×#123	C₂²	1	2	yes	complemented
35	C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	complemented
36	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₁₉×#121	C₂²	1	1	yes	characteristic
38	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
39	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
40	C₁₉×#117	C₂²	1	1	yes	characteristic, complemented
41	#10597393	C₂²	1	2	yes	complemented
42	#10597393	C₂²	1	1	yes	characteristic, complemented
43	#10597392	C₂²	1	2	yes	complemented
44	#10597392	C₂²	1	1	yes	characteristic, complemented
45	Q₈×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
46	#10597390	C₂²	1	2	yes	complemented
47	#10597385	C₂²	1	2	yes	—
48	#10597384	C₂²	1	1	yes	characteristic
49	#10597382	C₂²	1	1	yes	characteristic, complemented
50	#10597382	C₂²	1	2	yes	complemented
51	#10597381	C₂²	1	2	yes	complemented
52	D₄×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
53	#10597376	C₂²	1	1	yes	characteristic
54	#10597375	C₂²	1	2	yes	complemented
55	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
56	#10597372	C₂²	1	1	yes	characteristic, complemented
57	#10597370	C₂²	1	2	yes	complemented
58	#10597370	C₂²	1	1	yes	characteristic, complemented
59	#10597344	C₂²	1	2	yes	complemented
60	#10597344	C₂²	1	2	yes	complemented
61	#10597344	C₂²	1	2	yes	complemented
62	#10597343	C₂²	1	1	yes	characteristic, complemented
63	#10597343	C₂²	1	2	yes	complemented
64	#10597342	C₂²	1	2	yes	complemented
65	#10597342	C₂²	1	2	yes	complemented
66	#10597342	C₂²	1	2	yes	complemented
67	#10597341	C₂²	1	1	yes	characteristic
68	#10597340	C₂²	1	2	yes	complemented
69	#10597340	C₂²	1	2	yes	complemented
70	#10597339	C₂²	1	1	yes	characteristic, complemented
71	#10597338	C₂²	1	1	yes	characteristic, complemented
72	#10597338	C₂²	1	1	yes	characteristic, complemented
73	C₄⋊C₄×D₁₉	C₂²	1	2	yes	—
74	C₄⋊C₄×D₁₉	C₂²	1	2	yes	—
75	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic
76	C₄⋊C₄×D₁₉	C₂²	1	2	yes	—
77	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic
78	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic
79	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic
80	#10597334	C₂²	1	1	yes	characteristic, complemented
81	#10597334	C₂²	1	2	yes	complemented
82	#10597334	C₂²	1	1	yes	characteristic, complemented
83	#10597333	C₂²	1	1	yes	characteristic, complemented
84	#10597333	C₂²	1	2	yes	complemented
85	#10597332	C₂²	1	2	yes	complemented
86	#10597331	C₂²	1	2	yes	complemented
87	#10597331	C₂²	1	2	yes	complemented
88	#10597331	C₂²	1	2	yes	complemented
89	#10597331	C₂²	1	2	yes	complemented
90	#10597331	C₂²	1	2	yes	complemented
91	#10597331	C₂²	1	2	yes	complemented
92	#10597330	C₂²	1	2	yes	—
93	#10597329	C₂²	1	2	yes	complemented
94	#10597329	C₂²	1	2	yes	complemented
95	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	complemented
96	C₂²⋊C₄×D₁₉	C₂²	1	1	yes	characteristic
97	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	—
98	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	—
99	C₂²⋊C₄×D₁₉	C₂²	1	1	yes	characteristic
100	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	—
101	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	—
102	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	—
103	#10597325	C₂²	1	2	yes	complemented
104	#10597325	C₂²	1	2	yes	complemented
105	#10597325	C₂²	1	2	yes	complemented
106	#10597324	C₂²	1	2	yes	complemented
107	#10597324	C₂²	1	2	yes	complemented
108	#10597324	C₂²	1	2	yes	complemented
109	#10597323	C₂²	1	1	yes	characteristic, complemented
110	#10597323	C₂²	1	1	yes	characteristic, complemented
111	#10597322	C₂²	1	2	yes	complemented
112	#10597321	C₂²	1	2	yes	complemented
113	#10597321	C₂²	1	1	yes	characteristic, complemented
114	C₄×D₇₆	C₂²	1	1	yes	characteristic, complemented
115	#10597318	C₂²	1	1	yes	characteristic, complemented
116	#10597318	C₂²	1	1	yes	characteristic, complemented
117	C₄²×D₁₉	C₂²	1	2	yes	—
118	C₄²×D₁₉	C₂²	1	1	yes	characteristic
119	C₄²×D₁₉	C₂²	1	1	yes	characteristic
120	#10597315	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₃₈	C₂²	1	2	yes	complemented
122	C₄×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₉	C₂³	1	1	yes	characteristic
124	C₂³×D₁₉	C₂³	1	2	yes	—
125	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
126	C₂×Q₈×C₁₉	C₂³	1	2	yes	—
127	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
128	C₂×D₄×C₁₉	C₂³	1	2	yes	—
129	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
134	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
135	C₂²×Dic₁₉	C₂³	1	2	yes	—
136	Q₈×D₁₉	—	2	4	no	—
137	Q₈×D₁₉	—	4	4	no	—
138	D₄×D₁₉	—	2	4	no	—
139	D₄×D₁₉	—	4	4	no	—
140	C₂×D₇₆	C₂³	1	1	yes	characteristic
141	C₂×D₇₆	C₂³	1	2	yes	—
142	C₂×C₄×D₁₉	—	2	4	no	—
143	C₂×C₄×D₁₉	—	4	4	no	—
144	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
145	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₁₉	C₂³	1	2	yes	—
147	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₁₉	C₂³	1	2	yes	—
150	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₁₉	C₂³	1	2	yes	—
152	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₁₉	C₂³	1	2	yes	—
155	C₂×C₄×D₁₉	C₂³	1	2	yes	—
156	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
157	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
158	C₂×Dic₃₈	C₂³	1	2	yes	—
159	C₂×Dic₃₈	C₂³	1	2	yes	—
160	C₂×Dic₃₈	C₂³	1	2	yes	—
161	C₂×Dic₃₈	C₂³	1	2	yes	—
162	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
163	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
164	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
165	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
166	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
167	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
168	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
169	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
170	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
171	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
172	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
173	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
174	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
175	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
176	C₄²×C₁₉	C₂³	1	1	yes	characteristic
177	C₄²×C₁₉	C₂³	1	1	yes	characteristic
178	C₄²×C₁₉	C₂³	1	2	yes	—
179	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
180	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
181	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
182	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
183	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
184	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
185	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
186	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
187	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
189	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
190	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
191	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
192	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
193	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
194	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
195	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
196	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
197	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
198	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
199	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
200	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
201	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
202	C₄⋊Dic₁₉	C₂³	1	2	yes	—
203	C₄⋊Dic₁₉	C₂³	1	2	yes	—
204	C₄⋊Dic₁₉	C₂³	1	2	yes	—
205	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
206	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
207	Dic₁₉⋊C₄	C₂³	1	2	yes	—
208	Dic₁₉⋊C₄	C₂³	1	2	yes	—
209	Dic₁₉⋊C₄	C₂³	1	2	yes	—
210	Dic₁₉⋊C₄	C₂³	1	2	yes	—
211	Dic₁₉⋊C₄	C₂³	1	2	yes	—
212	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
213	Dic₁₉⋊C₄	C₂³	1	2	yes	—
214	Dic₁₉⋊C₄	C₂³	1	2	yes	—
215	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
216	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
217	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
218	Dic₁₉⋊C₄	C₂³	1	2	yes	—
219	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
220	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
221	C₄×Dic₁₉	C₂³	1	2	yes	—
222	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
223	C₄×Dic₁₉	C₂³	1	2	yes	—
224	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
225	C₄×Dic₁₉	C₂³	1	2	yes	—
226	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
227	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
228	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
229	C₂³×C₁₉	C₂⁴	1	2	yes	—
230	C₂²×D₁₉	—	2	2	no	—
231	C₂²×D₁₉	—	2	4	no	—
232	C₂²×D₁₉	—	2	4	no	—
233	C₂²×D₁₉	—	2	2	no	—
234	C₂²×D₁₉	—	2	2	no	—
235	C₂²×D₁₉	—	2	4	no	—
236	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
237	C₂²×D₁₉	C₂⁴	1	2	yes	—
238	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
239	Q₈×C₁₉	—	2	2	no	—
240	Q₈×C₁₉	—	4	2	no	—
241	D₄×C₁₉	—	2	2	no	—
242	D₄×C₁₉	—	4	2	no	—
243	C₂×C₄×C₁₉	—	2	2	no	—
244	C₂×C₄×C₁₉	—	4	2	no	—
245	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
246	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
247	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
250	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
251	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
252	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
253	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
254	C₂²⋊D₁₉	—	2	4	no	—
255	C₂²⋊D₁₉	—	4	2	no	—
256	C₂²⋊D₁₉	—	4	2	no	—
257	C₂×Dic₁₉	—	2	2	no	—
258	C₂×Dic₁₉	—	4	2	no	—
259	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
260	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
261	C₂×Dic₁₉	C₂⁴	1	2	yes	—
262	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
263	C₂×Dic₁₉	C₂⁴	1	2	yes	—
264	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
265	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
266	C₂×Dic₁₉	C₂⁴	1	2	yes	—
267	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
268	D₇₆	—	2	2	no	—
269	D₇₆	—	4	2	no	—
270	C₄×D₁₉	—	2	2	no	—
271	C₄×D₁₉	—	2	4	no	—
272	C₄×D₁₉	—	2	2	no	—
273	C₄×D₁₉	—	2	4	no	—
274	C₄×D₁₉	—	2	4	no	—
275	C₄×D₁₉	—	2	2	no	—
276	C₄×D₁₉	—	2	2	no	—
277	C₄×D₁₉	—	2	2	no	—
278	C₄×D₁₉	—	2	2	no	—
279	C₄×D₁₉	—	2	2	no	—
280	C₄×D₁₉	—	4	2	no	—
281	C₄×D₁₉	—	4	2	no	—
282	C₄×D₁₉	#41	1	4	yes	—
283	Dic₃₈	—	2	2	no	—
284	Dic₃₈	—	2	4	no	—
285	Dic₃₈	—	4	2	no	—
286	Dic₃₈	—	4	2	no	—
287	Dic₃₈	—	4	2	no	—
288	C₂×#542	—	19	1	no	maximal, Sylow
289	C₂²×C₁₉	—	2	1	no	—
290	C₂²×C₁₉	—	2	2	no	—
291	C₂²×C₁₉	—	2	2	no	—
292	C₂²×C₁₉	—	2	1	no	—
293	C₂²×C₁₉	—	2	1	no	—
294	C₂²×C₁₉	—	2	2	no	—
295	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
296	C₂×D₁₉	—	2	1	no	—
297	C₂×D₁₉	—	2	2	no	—
298	C₂×D₁₉	—	2	2	no	—
299	C₂×D₁₉	—	2	1	no	—
300	C₂×D₁₉	—	2	1	no	—
301	C₂×D₁₉	—	2	2	no	—
302	C₂×D₁₉	—	4	4	no	—
303	C₂×D₁₉	—	4	8	no	—
304	C₂×D₁₉	C₂×#41	1	2	yes	—
305	C₂×D₁₉	H(5,𝔽₂)	1	2	yes	—
306	C₂×D₁₉	2₋¹⁺⁴	1	2	yes	—
307	C₄×C₁₉	—	2	2	no	—
308	C₄×C₁₉	—	2	1	no	—
309	C₄×C₁₉	—	2	1	no	—
310	C₄×C₁₉	—	2	2	no	—
311	C₄×C₁₉	—	2	2	no	—
312	C₄×C₁₉	—	2	1	no	—
313	C₄×C₁₉	—	2	1	no	—
314	C₄×C₁₉	—	2	1	no	—
315	C₄×C₁₉	C₂×#41	1	2	yes	—
316	Dic₁₉	—	2	2	no	—
317	Dic₁₉	—	2	1	no	—
318	Dic₁₉	—	2	1	no	—
319	Dic₁₉	—	2	2	no	—
320	Dic₁₉	—	2	2	no	—
321	Dic₁₉	—	2	1	no	—
322	Dic₁₉	—	2	1	no	—
323	Dic₁₉	—	2	1	no	—
324	Dic₁₉	C₂×#41	1	2	yes	—
325	#542	—	19	1	no	—
326	#542	—	19	2	no	—
327	#542	—	19	2	no	—
328	#542	—	19	1	no	—
329	#542	—	19	2	no	—
330	#542	—	19	2	no	—
331	#542	—	19	1	no	—
332	#542	—	19	1	no	—
333	#542	—	19	1	no	—
334	#542	—	19	1	no	—
335	#542	—	19	1	no	—
336	#542	D₁₉	1	1	yes	characteristic, direct product factor
337	C₂×C₄⋊Q₈	—	19	1	no	—
338	C₂×#126	—	19	2	no	—
339	C₂×#124	—	19	1	no	—
340	C₂×#124	—	19	2	no	—
341	C₂×#123	—	19	2	no	—
342	C₂×C₂²⋊Q₈	—	19	2	no	—
343	C₂×C₂²⋊Q₈	—	19	1	no	—
344	C₂×#121	—	19	1	no	—
345	C₂×C₄×Q₈	—	19	1	no	—
346	C₂×C₄×D₄	—	19	1	no	—
347	C₂×#117	—	19	1	no	—
348	C₂×C₁₉	—	4	1	no	—
349	C₂×C₁₉	—	4	2	no	—
350	C₂×C₁₉	C₂²×#41	1	1	yes	characteristic
351	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
352	C₂×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
353	D₁₉	—	4	1	no	—
354	D₁₉	—	4	2	no	—
355	D₁₉	#542	1	4	yes	direct product factor
356	C₂²×Q₈	—	19	1	no	—
357	C₂²×Q₈	—	19	2	no	—
358	C₂²×D₄	—	19	1	no	—
359	C₂²×D₄	—	19	2	no	—
360	C₂³×C₄	—	19	1	no	—
361	C₂³×C₄	—	19	2	no	—
362	C₄⋊Q₈	—	19	2	no	—
363	C₄⋊Q₈	—	19	2	no	—
364	C₄⋊Q₈	—	19	1	no	—
365	C₄⋊Q₈	—	19	1	no	—
366	C₄⋊Q₈	—	19	1	no	—
367	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
368	#126	—	19	2	no	—
369	#126	—	19	2	no	—
370	#126	—	19	2	no	—
371	#126	—	19	2	no	—
372	#126	—	19	2	no	—
373	#126	—	19	2	no	—
374	#126	—	19	2	no	—
375	#126	C₂×D₁₉	1	2	yes	complemented
376	#124	—	19	1	no	—
377	#124	—	19	2	no	—
378	#124	—	19	1	no	—
379	#124	—	19	2	no	—
380	#124	—	19	2	no	—
381	#124	—	19	2	no	—
382	#124	—	19	2	no	—
383	#124	—	19	2	no	—
384	#124	—	19	2	no	—
385	#124	—	19	2	no	—
386	#124	—	19	1	no	—
387	#124	—	19	2	no	—
388	#124	C₂×D₁₉	1	1	yes	characteristic, complemented
389	#124	C₂×D₁₉	1	2	yes	complemented
390	#123	—	19	2	no	—
391	#123	—	19	2	no	—
392	#123	—	19	2	no	—
393	#123	—	19	2	no	—
394	#123	—	19	2	no	—
395	#123	—	19	2	no	—
396	#123	—	19	2	no	—
397	#123	C₂×D₁₉	1	2	yes	complemented
398	C₂²⋊Q₈	—	19	2	no	—
399	C₂²⋊Q₈	—	19	1	no	—
400	C₂²⋊Q₈	—	19	2	no	—
401	C₂²⋊Q₈	—	19	1	no	—
402	C₂²⋊Q₈	—	19	2	no	—
403	C₂²⋊Q₈	—	19	2	no	—
404	C₂²⋊Q₈	—	19	2	no	—
405	C₂²⋊Q₈	—	19	2	no	—
406	C₂²⋊Q₈	—	19	1	no	—
407	C₂²⋊Q₈	—	19	2	no	—
408	C₂²⋊Q₈	—	19	2	no	—
409	C₂²⋊Q₈	—	19	2	no	—
410	C₂²⋊Q₈	C₂×D₁₉	1	2	yes	complemented
411	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
412	#121	—	19	1	no	—
413	#121	—	19	2	no	—
414	#121	—	19	1	no	—
415	#121	—	19	1	no	—
416	#121	—	19	2	no	—
417	#121	C₂×D₁₉	1	1	yes	characteristic
418	C₄×Q₈	—	19	1	no	—
419	C₄×Q₈	—	19	2	no	—
420	C₄×Q₈	—	19	1	no	—
421	C₄×Q₈	—	19	2	no	—
422	C₄×Q₈	—	19	1	no	—
423	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
424	C₄×D₄	—	19	1	no	—
425	C₄×D₄	—	19	2	no	—
426	C₄×D₄	—	19	1	no	—
427	C₄×D₄	—	19	2	no	—
428	C₄×D₄	—	19	1	no	—
429	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic, complemented
430	#117	—	19	1	no	—
431	#117	—	19	1	no	—
432	#117	—	19	1	no	—
433	#117	—	19	1	no	—
434	#117	—	19	1	no	—
435	#117	—	19	1	no	—
436	#117	—	19	1	no	—
437	#117	C₂×D₁₉	1	1	yes	characteristic, complemented
438	C₂×C₄⋊C₄	—	19	1	no	—
439	C₂×C₄⋊C₄	—	19	1	no	—
440	C₂×C₄⋊C₄	—	19	1	no	—
441	C₂×C₄⋊C₄	—	19	1	no	—
442	C₂×C₄⋊C₄	—	19	2	no	—
443	C₂×C₄⋊C₄	—	19	2	no	—
444	C₂×C₄⋊C₄	—	19	2	no	—
445	C₂×C₂²⋊C₄	—	19	1	no	—
446	C₂×C₂²⋊C₄	—	19	1	no	—
447	C₂×C₂²⋊C₄	—	19	2	no	—
448	C₂×C₂²⋊C₄	—	19	2	no	—
449	C₂×C₂²⋊C₄	—	19	2	no	—
450	C₂×C₂²⋊C₄	—	19	2	no	—
451	C₂×C₂²⋊C₄	—	19	2	no	—
452	C₂×C₄²	—	19	1	no	—
453	C₂×C₄²	—	19	1	no	—
454	C₂×C₄²	—	19	2	no	—
455	C₁₉	C₂×#542	1	1	yes	characteristic, complemented, Sylow
456	C₂⁴	—	19	1	no	—
457	C₂⁴	—	19	2	no	—
458	C₂×Q₈	—	19	2	no	—
459	C₂×Q₈	—	19	1	no	—
460	C₂×Q₈	—	19	2	no	—
461	C₂×Q₈	—	19	2	no	—
462	C₂×Q₈	—	19	2	no	—
463	C₂×Q₈	—	38	4	no	—
464	C₂×Q₈	—	76	4	no	—
465	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
466	C₂×Q₈	C₂²×D₁₉	1	2	yes	—
467	C₂×D₄	—	19	2	no	—
468	C₂×D₄	—	19	2	no	—
469	C₂×D₄	—	19	2	no	—
470	C₂×D₄	—	19	1	no	—
471	C₂×D₄	—	19	2	no	—
472	C₂×D₄	—	38	4	no	—
473	C₂×D₄	—	76	4	no	—
474	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
475	C₂×D₄	C₂²×D₁₉	1	2	yes	—
476	C₂²×C₄	—	19	1	no	—
477	C₂²×C₄	—	19	1	no	—
478	C₂²×C₄	—	19	2	no	—
479	C₂²×C₄	—	19	1	no	—
480	C₂²×C₄	—	19	1	no	—
481	C₂²×C₄	—	19	2	no	—
482	C₂²×C₄	—	19	1	no	—
483	C₂²×C₄	—	19	1	no	—
484	C₂²×C₄	—	19	2	no	—
485	C₂²×C₄	—	19	1	no	—
486	C₂²×C₄	—	19	2	no	—
487	C₂²×C₄	—	19	1	no	—
488	C₂²×C₄	—	19	1	no	—
489	C₂²×C₄	—	19	2	no	—
490	C₂²×C₄	—	19	2	no	—
491	C₂²×C₄	—	38	4	no	—
492	C₂²×C₄	—	76	4	no	—
493	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
494	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
495	C₄⋊C₄	—	19	1	no	—
496	C₄⋊C₄	—	19	1	no	—
497	C₄⋊C₄	—	19	1	no	—
498	C₄⋊C₄	—	19	1	no	—
499	C₄⋊C₄	—	19	2	no	—
500	C₄⋊C₄	—	19	2	no	—
501	C₄⋊C₄	—	19	2	no	—
502	C₄⋊C₄	—	19	2	no	—
503	C₄⋊C₄	—	19	2	no	—
504	C₄⋊C₄	—	19	2	no	—
505	C₄⋊C₄	—	19	2	no	—
506	C₄⋊C₄	—	19	2	no	—
507	C₄⋊C₄	—	19	1	no	—
508	C₄⋊C₄	—	19	1	no	—
509	C₄⋊C₄	—	19	1	no	—
510	C₄⋊C₄	—	19	1	no	—
511	C₄⋊C₄	—	19	2	no	—
512	C₄⋊C₄	—	19	2	no	—
513	C₄⋊C₄	—	19	2	no	—
514	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
515	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
516	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
517	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
518	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
519	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
520	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
521	C₂²⋊C₄	—	19	1	no	—
522	C₂²⋊C₄	—	19	1	no	—
523	C₂²⋊C₄	—	19	2	no	—
524	C₂²⋊C₄	—	19	2	no	—
525	C₂²⋊C₄	—	19	2	no	—
526	C₂²⋊C₄	—	19	2	no	—
527	C₂²⋊C₄	—	19	2	no	—
528	C₂²⋊C₄	—	19	1	no	—
529	C₂²⋊C₄	—	19	1	no	—
530	C₂²⋊C₄	—	19	1	no	—
531	C₂²⋊C₄	—	19	1	no	—
532	C₂²⋊C₄	—	19	2	no	—
533	C₂²⋊C₄	—	19	2	no	—
534	C₂²⋊C₄	—	19	2	no	—
535	C₂²⋊C₄	—	19	2	no	—
536	C₂²⋊C₄	—	19	2	no	—
537	C₂²⋊C₄	—	19	2	no	—
538	C₂²⋊C₄	—	19	2	no	—
539	C₂²⋊C₄	—	19	2	no	—
540	C₂²⋊C₄	—	19	2	no	—
541	C₂²⋊C₄	—	19	2	no	—
542	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
543	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
544	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
545	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
546	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
547	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
548	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
549	C₄²	—	19	1	no	—
550	C₄²	—	19	1	no	—
551	C₄²	—	19	1	no	—
552	C₄²	—	19	1	no	—
553	C₄²	—	19	1	no	—
554	C₄²	—	19	1	no	—
555	C₄²	—	19	2	no	—
556	C₄²	—	19	2	no	—
557	C₄²	—	19	2	no	—
558	C₄²	C₂²×D₁₉	1	1	yes	characteristic
559	C₄²	C₂²×D₁₉	1	1	yes	characteristic
560	C₄²	C₂²×D₁₉	1	2	yes	—
561	C₂³	—	19	1	no	—
562	C₂³	—	19	1	no	—
563	C₂³	—	19	2	no	—
564	C₂³	—	38	2	no	—
565	C₂³	—	38	4	no	—
566	C₂³	—	38	4	no	—
567	C₂³	—	38	2	no	—
568	C₂³	—	38	2	no	—
569	C₂³	—	38	4	no	—
570	C₂³	C₂³×D₁₉	1	1	yes	characteristic
571	C₂³	C₂³×D₁₉	1	2	yes	—
572	Q₈	—	2	2	no	—
573	Q₈	—	4	2	no	—
574	Q₈	—	38	4	no	—
575	Q₈	—	38	2	no	—
576	Q₈	—	76	2	no	—
577	Q₈	—	76	2	no	—
578	Q₈	—	76	2	no	—
579	D₄	—	2	2	no	—
580	D₄	—	4	2	no	—
581	D₄	—	38	4	no	—
582	D₄	—	38	2	no	—
583	D₄	—	76	2	no	—
584	D₄	—	76	2	no	—
585	D₄	—	76	2	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	4	2	no	—
588	C₂×C₄	—	19	1	no	—
589	C₂×C₄	—	19	4	no	—
590	C₂×C₄	—	19	1	no	—
591	C₂×C₄	—	19	1	no	—
592	C₂×C₄	—	19	2	no	—
593	C₂×C₄	—	19	1	no	—
594	C₂×C₄	—	19	1	no	—
595	C₂×C₄	—	19	2	no	—
596	C₂×C₄	—	19	1	no	—
597	C₂×C₄	—	19	2	no	—
598	C₂×C₄	—	38	2	no	—
599	C₂×C₄	—	38	2	no	—
600	C₂×C₄	—	38	2	no	—
601	C₂×C₄	—	38	4	no	—
602	C₂×C₄	—	38	4	no	—
603	C₂×C₄	—	38	4	no	—
604	C₂×C₄	—	38	2	no	—
605	C₂×C₄	—	38	2	no	—
606	C₂×C₄	—	38	2	no	—
607	C₂×C₄	—	38	2	no	—
608	C₂×C₄	—	38	2	no	—
609	C₂×C₄	—	76	2	no	—
610	C₂×C₄	—	76	2	no	—
611	C₂×C₄	—	76	2	no	—
612	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
613	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
614	C₂×C₄	C₂³×D₁₉	1	2	yes	—
615	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
616	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
617	C₂×C₄	C₂³×D₁₉	1	2	yes	—
618	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
619	C₂×C₄	C₂³×D₁₉	1	2	yes	—
620	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
621	C₂²	—	2	1	no	—
622	C₂²	—	2	2	no	—
623	C₂²	—	2	2	no	—
624	C₂²	—	2	1	no	—
625	C₂²	—	2	1	no	—
626	C₂²	—	2	2	no	—
627	C₂²	—	19	2	no	—
628	C₂²	—	19	2	no	—
629	C₂²	—	19	2	no	—
630	C₂²	—	38	1	no	—
631	C₂²	—	38	2	no	—
632	C₂²	—	38	2	no	—
633	C₂²	—	38	1	no	—
634	C₂²	—	38	1	no	—
635	C₂²	—	38	2	no	—
636	C₂²	—	76	4	no	—
637	C₂²	—	76	8	no	—
638	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
639	C₄	—	2	1	no	—
640	C₄	—	2	2	no	—
641	C₄	—	2	1	no	—
642	C₄	—	2	2	no	—
643	C₄	—	2	2	no	—
644	C₄	—	2	1	no	—
645	C₄	—	2	1	no	—
646	C₄	—	2	1	no	—
647	C₄	—	19	2	no	—
648	C₄	—	38	1	no	—
649	C₄	—	38	2	no	—
650	C₄	—	38	1	no	—
651	C₄	—	38	2	no	—
652	C₄	—	38	2	no	—
653	C₄	—	38	1	no	—
654	C₄	—	38	1	no	—
655	C₄	—	38	1	no	—
656	C₄	#41×D₁₉	1	2	yes	—
657	C₂	—	4	1	no	—
658	C₂	—	4	2	no	—
659	C₂	—	19	4	no	—
660	C₂	—	76	1	no	—
661	C₂	—	76	2	no	—
662	C₂	C₂×#41×D₁₉	1	1	yes	characteristic
663	C₂	H(5,𝔽₂)×D₁₉	1	1	yes	characteristic
664	C₂	2₋¹⁺⁴×D₁₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₁₉×#542	C₂
prime radical	#121×D₁₉	C₂
hypercenter	#542	D₁₉
hypocenter	C₁₉	C₂×#542
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ #542

Complements

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

N	H ≅ G/N	type
1. #11927168	C₂	semidirect
2. #11927167	C₂	semidirect
3. #11927166	C₂	semidirect
4. #11927165	C₂	semidirect
5. #11927164	C₂	semidirect
6. #11927163	C₂	semidirect
7. #11927162	C₂	semidirect
8. #11927161	C₂	semidirect
9. #11927160	C₂	semidirect
10. #11927159	C₂	semidirect
11. #11927158	C₂	semidirect
12. C₄⋊Q₈×D₁₉	C₂	semidirect
13. #126×D₁₉	C₂	semidirect
14. #124×D₁₉	C₂	semidirect
15. #124×D₁₉	C₂	semidirect
16. #123×D₁₉	C₂	semidirect
17. C₂²⋊Q₈×D₁₉	C₂	semidirect
18. C₂²⋊Q₈×D₁₉	C₂	semidirect
20. C₄×Q₈×D₁₉	C₂	semidirect
21. C₄×D₄×D₁₉	C₂	semidirect
22. #117×D₁₉	C₂	semidirect
23. C₁₉×#542	C₂	semidirect
30. C₁₉×C₄⋊Q₈	C₂²	semidirect
31. C₁₉×#126	C₂²	semidirect
32. C₁₉×#124	C₂²	semidirect
33. C₁₉×#124	C₂²	semidirect
34. C₁₉×#123	C₂²	semidirect
35. C₁₉×C₂²⋊Q₈	C₂²	semidirect
36. C₁₉×C₂²⋊Q₈	C₂²	semidirect
38. C₄×Q₈×C₁₉	C₂²	semidirect
39. C₄×D₄×C₁₉	C₂²	semidirect
40. C₁₉×#117	C₂²	semidirect
41. #10597393	C₂²	semidirect
42. #10597393	C₂²	semidirect
43. #10597392	C₂²	semidirect
44. #10597392	C₂²	semidirect
45. Q₈×Dic₁₉	C₂²	semidirect
46. #10597390	C₂²	semidirect
49. #10597382	C₂²	semidirect
50. #10597382	C₂²	semidirect
51. #10597381	C₂²	semidirect
52. D₄×Dic₁₉	C₂²	semidirect
54. #10597375	C₂²	semidirect
55. C₄×C₂²⋊D₁₉	C₂²	semidirect
56. #10597372	C₂²	semidirect
57. #10597370	C₂²	semidirect
58. #10597370	C₂²	semidirect
59. #10597344	C₂²	semidirect
60. #10597344	C₂²	semidirect
61. #10597344	C₂²	semidirect
62. #10597343	C₂²	semidirect
63. #10597343	C₂²	semidirect
64. #10597342	C₂²	semidirect
65. #10597342	C₂²	semidirect
66. #10597342	C₂²	semidirect
68. #10597340	C₂²	semidirect
69. #10597340	C₂²	semidirect
70. #10597339	C₂²	semidirect
71. #10597338	C₂²	semidirect
72. #10597338	C₂²	semidirect
80. #10597334	C₂²	semidirect
81. #10597334	C₂²	semidirect
82. #10597334	C₂²	semidirect
83. #10597333	C₂²	semidirect
84. #10597333	C₂²	semidirect
85. #10597332	C₂²	semidirect
86. #10597331	C₂²	semidirect
87. #10597331	C₂²	semidirect
88. #10597331	C₂²	semidirect
89. #10597331	C₂²	semidirect
90. #10597331	C₂²	semidirect
91. #10597331	C₂²	semidirect
93. #10597329	C₂²	semidirect
94. #10597329	C₂²	semidirect
95. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
103. #10597325	C₂²	semidirect
104. #10597325	C₂²	semidirect
105. #10597325	C₂²	semidirect
106. #10597324	C₂²	semidirect
107. #10597324	C₂²	semidirect
108. #10597324	C₂²	semidirect
109. #10597323	C₂²	semidirect
110. #10597323	C₂²	semidirect
111. #10597322	C₂²	semidirect
112. #10597321	C₂²	semidirect
113. #10597321	C₂²	semidirect
114. C₄×D₇₆	C₂²	semidirect
115. #10597318	C₂²	semidirect
116. #10597318	C₂²	semidirect
120. #10597315	C₂²	semidirect
121. C₄×Dic₃₈	C₂²	semidirect
122. C₄×Dic₃₈	C₂²	semidirect
336. #542	D₁₉	direct (N × H)
355. D₁₉	#542	direct (N × H)
367. C₄⋊Q₈	C₂×D₁₉	semidirect
375. #126	C₂×D₁₉	semidirect
388. #124	C₂×D₁₉	semidirect
389. #124	C₂×D₁₉	semidirect
397. #123	C₂×D₁₉	semidirect
410. C₂²⋊Q₈	C₂×D₁₉	semidirect
411. C₂²⋊Q₈	C₂×D₁₉	semidirect
423. C₄×Q₈	C₂×D₁₉	semidirect
429. C₄×D₄	C₂×D₁₉	semidirect
437. #117	C₂×D₁₉	semidirect
455. C₁₉	C₂×#542	semidirect

Maximal subgroups

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

subgroup	index
#11927168	2
#11927167	2
#11927166	2
#11927165	2
#11927164	2
#11927163	2
#11927162	2
#11927161	2
#11927160	2
#11927159	2
#11927158	2
C₄⋊Q₈×D₁₉	2
#126×D₁₉	2
#124×D₁₉	2
#123×D₁₉	2
C₂²⋊Q₈×D₁₉	2
#121×D₁₉	2
C₄×Q₈×D₁₉	2
C₄×D₄×D₁₉	2
#117×D₁₉	2
C₁₉×#542	2
C₂×#542	19

Subgroups — D19×#542 #14577005

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₉×#542 #14577005