Subgroups — #14577589

Order 2432.

1142 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927276	C₂	1	1	yes	maximal, characteristic, complemented
2	#11927266	C₂	1	1	yes	maximal, characteristic, complemented
3	#11927256	C₂	1	2	yes	maximal, complemented
4	#11927223	C₂	1	2	yes	maximal, complemented
5	#11927221	C₂	1	2	yes	maximal, complemented
6	Q₈×C₂²⋊D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#11927204	C₂	1	1	yes	maximal, characteristic, complemented
8	#11927190	C₂	1	1	yes	maximal, characteristic, complemented
9	#11927183	C₂	1	2	yes	maximal, complemented
10	#11927182	C₂	1	1	yes	maximal, characteristic, complemented
11	#11927178	C₂	1	1	yes	maximal, characteristic, complemented
12	#11927164	C₂	1	2	yes	maximal, complemented
13	#11927131	C₂	1	2	yes	maximal, complemented
14	#11927128	C₂	1	2	yes	maximal, complemented
15	#11927090	C₂	1	1	yes	maximal, characteristic, complemented
16	#11927081	C₂	1	1	yes	maximal, characteristic, complemented
17	#11927080	C₂	1	1	yes	maximal, characteristic, complemented
18	#11927075	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#10597393	C₂	1	1	yes	maximal, characteristic, complemented
20	#124×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
21	#11927016	C₂	1	2	yes	maximal, complemented
22	C₄×#64543	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₉×#548	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic, complemented
25	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
26	C₂×Q₈×D₁₉	C₂²	1	1	yes	characteristic, complemented
27	C₂×#64543	C₂²	1	1	yes	characteristic
28	C₂×D₄×D₁₉	C₂²	1	2	yes	—
29	C₂×D₄×D₁₉	C₂²	1	1	yes	characteristic
30	C₂×#64541	C₂²	1	1	yes	characteristic, complemented
31	C₂²×D₇₆	C₂²	1	1	yes	characteristic
32	C₁₉×#124	C₂²	1	1	yes	characteristic, complemented
33	C₁₉×#124	C₂²	1	2	yes	complemented
34	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	complemented
36	C₁₉×#121	C₂²	1	1	yes	characteristic
37	C₁₉×#121	C₂²	1	2	yes	complemented
38	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
39	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
40	C₄×D₄×C₁₉	C₂²	1	2	yes	complemented
41	#10597393	C₂²	1	1	yes	characteristic
42	#10597393	C₂²	1	1	yes	characteristic
43	#10597393	C₂²	1	1	yes	characteristic, complemented
44	#10597393	C₂²	1	2	yes	complemented
45	#10597393	C₂²	1	1	yes	characteristic, complemented
46	#10597393	C₂²	1	2	yes	complemented
47	#10597392	C₂²	1	1	yes	characteristic, complemented
48	#10597392	C₂²	1	2	yes	complemented
49	Q₈×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
50	#10597390	C₂²	1	1	yes	characteristic, complemented
51	#10597390	C₂²	1	2	yes	complemented
52	#10597386	C₂²	1	1	yes	characteristic
53	#10597385	C₂²	1	2	yes	complemented
54	#10597385	C₂²	1	2	yes	complemented
55	#10597385	C₂²	1	2	yes	complemented
56	#10597383	C₂²	1	2	yes	—
57	#10597383	C₂²	1	2	yes	complemented
58	#10597383	C₂²	1	2	yes	complemented
59	#10597382	C₂²	1	1	yes	characteristic, complemented
60	#10597381	C₂²	1	2	yes	complemented
61	D₄×Dic₁₉	C₂²	1	2	yes	complemented
62	D₄×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
63	D₄×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
64	#10597376	C₂²	1	1	yes	characteristic
65	#10597375	C₂²	1	2	yes	complemented
66	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
67	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	—
68	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
69	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
70	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic, complemented
71	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	complemented
72	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	complemented
73	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	complemented
74	#10597370	C₂²	1	1	yes	characteristic, complemented
75	#10597370	C₂²	1	2	yes	complemented
76	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
77	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
78	#10597344	C₂²	1	2	yes	complemented
79	#10597344	C₂²	1	2	yes	complemented
80	#10597344	C₂²	1	2	yes	complemented
81	#10597342	C₂²	1	2	yes	complemented
82	#10597342	C₂²	1	2	yes	complemented
83	#10597341	C₂²	1	1	yes	characteristic
84	#10597340	C₂²	1	2	yes	complemented
85	#10597340	C₂²	1	2	yes	complemented
86	#10597339	C₂²	1	1	yes	characteristic
87	#10597339	C₂²	1	2	yes	complemented
88	#10597338	C₂²	1	2	yes	complemented
89	#10597338	C₂²	1	1	yes	characteristic, complemented
90	#10597336	C₂²	1	1	yes	characteristic, complemented
91	#10597333	C₂²	1	1	yes	characteristic, complemented
92	#10597333	C₂²	1	1	yes	characteristic, complemented
93	#10597332	C₂²	1	2	yes	complemented
94	#10597332	C₂²	1	2	yes	complemented
95	#10597331	C₂²	1	2	yes	complemented
96	#10597331	C₂²	1	2	yes	complemented
97	#10597331	C₂²	1	2	yes	complemented
98	#10597331	C₂²	1	2	yes	complemented
99	#10597330	C₂²	1	2	yes	—
100	#10597330	C₂²	1	2	yes	complemented
101	#10597330	C₂²	1	2	yes	complemented
102	#10597329	C₂²	1	2	yes	complemented
103	#10597328	C₂²	1	2	yes	—
104	(C₂²⋊D₁₉)⋊C₄	C₂²	1	1	yes	characteristic
105	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	complemented
106	(C₂²⋊D₁₉)⋊C₄	C₂²	1	1	yes	characteristic, complemented
107	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	complemented
108	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	complemented
109	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	complemented
110	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	complemented
111	#10597325	C₂²	1	2	yes	complemented
112	#10597323	C₂²	1	2	yes	complemented
113	#10597323	C₂²	1	1	yes	characteristic, complemented
114	#10597323	C₂²	1	1	yes	characteristic, complemented
115	#10597322	C₂²	1	2	yes	complemented
116	#10597321	C₂²	1	1	yes	characteristic
117	C₄×D₇₆	C₂²	1	2	yes	complemented
118	C₄×D₇₆	C₂²	1	1	yes	characteristic, complemented
119	#10597318	C₂²	1	2	yes	complemented
120	#10597318	C₂²	1	2	yes	complemented
121	C₄²×D₁₉	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₉	C₂³	1	2	yes	—
124	C₂³×D₁₉	C₂³	1	2	yes	—
125	#41×C₁₉	—	4	2	no	—
126	C₂×Q₈×C₁₉	—	4	2	no	—
127	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
128	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
129	C₂×Q₈×C₁₉	C₂³	1	2	yes	—
130	C₂×D₄×C₁₉	C₂³	1	2	yes	—
131	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
132	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
133	C₂×D₄×C₁₉	C₂³	1	2	yes	—
134	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
135	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
136	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
137	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
145	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
146	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
147	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
148	C₂²×Dic₁₉	C₂³	1	2	yes	—
149	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
150	Q₈×D₁₉	—	4	2	no	—
151	#64543	—	2	4	no	—
152	D₄×D₁₉	—	2	8	no	—
153	D₄×D₁₉	—	4	2	no	—
154	#64541	—	4	2	no	—
155	C₂×D₇₆	—	4	2	no	—
156	C₂×D₇₆	C₂³	1	1	yes	characteristic
157	C₂×D₇₆	C₂³	1	1	yes	characteristic
158	C₂×D₇₆	C₂³	1	2	yes	—
159	C₂×D₇₆	C₂³	1	2	yes	—
160	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
161	C₂×C₄×D₁₉	C₂³	1	2	yes	—
162	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
163	C₂×C₄×D₁₉	C₂³	1	2	yes	—
164	C₂×C₄×D₁₉	C₂³	1	2	yes	—
165	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
166	C₂×C₄×D₁₉	C₂³	1	2	yes	—
167	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
168	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
169	C₂×Dic₃₈	C₂³	1	2	yes	—
170	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
171	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
172	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
173	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
174	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
175	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
176	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
177	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
178	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
179	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
180	C₄²×C₁₉	C₂³	1	1	yes	characteristic
181	C₄²×C₁₉	C₂³	1	2	yes	—
182	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
183	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
184	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
185	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
186	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
187	C₂²⋊Dic₁₉	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	2	yes	—
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	2	yes	—
196	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
197	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
198	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
199	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
200	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
201	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
202	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
203	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
204	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
205	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
206	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
207	C₄⋊Dic₁₉	C₂³	1	2	yes	—
208	C₄⋊Dic₁₉	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	2	yes	—
213	Dic₁₉⋊C₄	C₂³	1	2	yes	—
214	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
215	Dic₁₉⋊C₄	C₂³	1	2	yes	—
216	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
217	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
218	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
224	C₄×Dic₁₉	C₂³	1	2	yes	—
225	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
226	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
227	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
228	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
229	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
230	C₂³×C₁₉	C₂⁴	1	2	yes	—
231	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
232	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
233	C₂²×D₁₉	—	2	4	no	—
234	C₂²×D₁₉	—	2	4	no	—
235	C₂²×D₁₉	—	4	2	no	—
236	C₂²×D₁₉	—	4	2	no	—
237	C₂²×D₁₉	—	4	2	no	—
238	C₂²×D₁₉	—	4	2	no	—
239	C₂²×D₁₉	C₂⁴	1	2	yes	—
240	C₂²×D₁₉	C₂⁴	1	2	yes	—
241	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
242	Q₈×C₁₉	—	2	2	no	—
243	Q₈×C₁₉	—	2	2	no	—
244	Q₈×C₁₉	—	4	2	no	—
245	D₄×C₁₉	—	2	4	no	—
246	D₄×C₁₉	—	2	2	no	—
247	D₄×C₁₉	—	2	2	no	—
248	D₄×C₁₉	—	4	2	no	—
249	C₂×C₄×C₁₉	—	2	2	no	—
250	C₂×C₄×C₁₉	—	2	2	no	—
251	C₂×C₄×C₁₉	—	4	2	no	—
252	C₂×C₄×C₁₉	—	4	2	no	—
253	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
255	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
256	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
257	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
258	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
259	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
260	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
261	C₂²⋊D₁₉	—	2	2	no	—
262	C₂²⋊D₁₉	—	2	4	no	—
263	C₂²⋊D₁₉	—	4	2	no	—
264	C₂²⋊D₁₉	—	4	2	no	—
265	C₂²⋊D₁₉	—	4	2	no	—
266	C₂²⋊D₁₉	—	4	2	no	—
267	C₂²⋊D₁₉	#41	1	4	yes	complemented
268	C₂×Dic₁₉	—	2	2	no	—
269	C₂×Dic₁₉	—	2	2	no	—
270	C₂×Dic₁₉	—	4	1	no	—
271	C₂×Dic₁₉	—	4	1	no	—
272	C₂×Dic₁₉	—	4	2	no	—
273	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
274	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
275	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
276	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
277	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
278	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
279	C₂×Dic₁₉	C₂⁴	1	2	yes	—
280	C₂×Dic₁₉	C₂⁴	1	2	yes	—
281	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
282	D₇₆	—	2	4	no	—
283	D₇₆	—	2	2	no	—
284	D₇₆	—	2	2	no	—
285	D₇₆	—	4	2	no	—
286	C₄×D₁₉	—	2	2	no	—
287	C₄×D₁₉	—	2	2	no	—
288	C₄×D₁₉	—	2	4	no	—
289	C₄×D₁₉	—	4	1	no	—
290	C₄×D₁₉	—	4	2	no	—
291	C₄×D₁₉	—	4	2	no	—
292	C₄×D₁₉	—	4	2	no	—
293	Dic₃₈	—	2	2	no	—
294	Dic₃₈	—	2	2	no	—
295	Dic₃₈	—	4	2	no	—
296	#3514	—	19	1	no	maximal, Sylow
297	C₂²×C₁₉	—	2	1	no	—
298	C₂²×C₁₉	—	2	1	no	—
299	C₂²×C₁₉	—	2	1	no	—
300	C₂²×C₁₉	—	2	2	no	—
301	C₂²×C₁₉	—	2	1	no	—
302	C₂²×C₁₉	—	2	2	no	—
303	C₂²×C₁₉	—	2	1	no	—
304	C₂²×C₁₉	—	2	2	no	—
305	C₂²×C₁₉	C₂×#41	1	2	yes	—
306	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
307	C₂×D₁₉	—	2	1	no	—
308	C₂×D₁₉	—	2	1	no	—
309	C₂×D₁₉	—	2	2	no	—
310	C₂×D₁₉	—	2	2	no	—
311	C₂×D₁₉	—	2	2	no	—
312	C₂×D₁₉	—	2	2	no	—
313	C₂×D₁₉	—	2	2	no	—
314	C₂×D₁₉	—	2	2	no	—
315	C₂×D₁₉	—	8	4	no	—
316	C₂×D₁₉	—	8	4	no	—
317	C₂×D₁₉	C₂×#41	1	2	yes	—
318	C₄×C₁₉	—	2	1	no	—
319	C₄×C₁₉	—	2	2	no	—
320	C₄×C₁₉	—	2	2	no	—
321	C₄×C₁₉	—	2	1	no	—
322	C₄×C₁₉	—	2	1	no	—
323	C₄×C₁₉	—	2	2	no	—
324	C₄×C₁₉	—	2	1	no	—
325	C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
326	Dic₁₉	—	2	1	no	—
327	Dic₁₉	—	2	1	no	—
328	Dic₁₉	—	2	2	no	—
329	Dic₁₉	—	2	1	no	—
330	Dic₁₉	—	2	1	no	—
331	Dic₁₉	—	2	2	no	—
332	Dic₁₉	—	2	1	no	—
333	Dic₁₉	—	2	1	no	—
334	Dic₁₉	C₂×#41	1	2	yes	—
335	#559	—	19	1	no	—
336	#556	—	19	1	no	—
337	#555	—	19	2	no	—
338	#551	—	19	2	no	—
339	#551	—	19	2	no	—
340	D₄×Q₈	—	19	1	no	—
341	#548	—	19	1	no	—
342	#548	D₁₉	1	1	yes	characteristic, complemented
343	#546	—	19	1	no	—
344	#546	—	19	2	no	—
345	#546	—	19	1	no	—
346	D₄²	—	19	1	no	—
347	#542	—	19	2	no	—
348	#538	—	19	2	no	—
349	#538	—	19	2	no	—
350	#532	—	19	1	no	—
351	#529	—	19	1	no	—
352	#529	—	19	1	no	—
353	#529	—	19	1	no	—
354	C₂×#124	—	19	1	no	—
355	C₂×#124	—	19	1	no	—
356	#518	—	19	2	no	—
357	C₄×#41	—	19	1	no	—
358	C₂×C₁₉	—	2	2	no	—
359	C₂×C₁₉	—	4	2	no	—
360	C₂×C₁₉	—	4	1	no	—
361	C₂×C₁₉	C₂²×#41	1	1	yes	characteristic
362	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
363	C₂×C₁₉	#585	1	1	yes	characteristic
364	D₁₉	—	2	2	no	—
365	D₁₉	—	4	2	no	—
366	D₁₉	—	4	2	no	—
367	C₂×#41	—	19	1	no	—
368	C₂×#41	—	19	1	no	—
369	C₂×#41	C₂×D₁₉	1	1	yes	characteristic, complemented
370	C₂²×Q₈	—	19	1	no	—
371	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
372	C₂²×D₄	—	19	2	no	—
373	C₂²×D₄	—	19	1	no	—
374	C₂²×D₄	—	19	1	no	—
375	C₄⋊Q₈	—	19	1	no	—
376	C₄⋊Q₈	—	19	2	no	—
377	#127	—	19	1	no	—
378	#126	—	19	2	no	—
379	#126	—	19	2	no	—
380	#126	—	19	2	no	—
381	#126	—	19	2	no	—
382	#126	—	19	2	no	—
383	#125	—	19	1	no	—
384	#124	—	19	1	no	—
385	#124	—	19	1	no	—
386	#124	—	19	1	no	—
387	#124	—	19	2	no	—
388	#124	—	19	1	no	—
389	#124	—	19	2	no	—
390	#124	—	19	1	no	—
391	#124	—	19	2	no	—
392	#124	—	19	2	no	—
393	#124	—	19	2	no	—
394	#124	—	19	2	no	—
395	#124	—	19	1	no	—
396	#124	C₂×D₁₉	1	1	yes	characteristic, complemented
397	#124	C₂×D₁₉	1	2	yes	complemented
398	#123	—	19	2	no	—
399	#123	—	19	2	no	—
400	#123	—	19	2	no	—
401	#123	—	19	2	no	—
402	#123	—	19	2	no	—
403	#123	—	19	2	no	—
404	#123	—	19	2	no	—
405	C₂²⋊Q₈	—	19	1	no	—
406	C₂²⋊Q₈	—	19	2	no	—
407	C₂²⋊Q₈	—	19	1	no	—
408	C₂²⋊Q₈	—	19	2	no	—
409	C₂²⋊Q₈	—	19	2	no	—
410	C₂²⋊Q₈	—	19	2	no	—
411	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
412	C₂²⋊Q₈	C₂×D₁₉	1	2	yes	complemented
413	#121	—	19	2	no	—
414	#121	—	19	2	no	—
415	#121	—	19	2	no	—
416	#121	—	19	1	no	—
417	#121	—	19	1	no	—
418	#121	—	19	2	no	—
419	#121	—	19	2	no	—
420	#121	—	19	2	no	—
421	#121	C₂×D₁₉	1	1	yes	characteristic
422	#121	C₂×D₁₉	1	2	yes	complemented
423	#120	—	19	2	no	—
424	#120	—	19	2	no	—
425	#120	—	19	2	no	—
426	#120	—	19	2	no	—
427	C₄×Q₈	—	19	1	no	—
428	C₄×Q₈	—	19	1	no	—
429	C₄×Q₈	—	19	1	no	—
430	C₄×Q₈	—	19	1	no	—
431	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
432	C₄×D₄	—	19	1	no	—
433	C₄×D₄	—	19	2	no	—
434	C₄×D₄	—	19	1	no	—
435	C₄×D₄	—	19	1	no	—
436	C₄×D₄	—	19	1	no	—
437	C₄×D₄	—	19	2	no	—
438	C₄×D₄	—	19	2	no	—
439	C₄×D₄	—	19	2	no	—
440	C₄×D₄	—	19	2	no	—
441	C₄×D₄	—	19	1	no	—
442	C₄×D₄	—	19	1	no	—
443	C₄×D₄	—	19	1	no	—
444	C₄×D₄	—	19	2	no	—
445	C₄×D₄	—	19	2	no	—
446	C₄×D₄	—	19	2	no	—
447	C₄×D₄	—	19	1	no	—
448	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic, complemented
449	C₄×D₄	C₂×D₁₉	1	2	yes	complemented
450	#117	—	19	1	no	—
451	#117	—	19	2	no	—
452	#117	—	19	1	no	—
453	#117	—	19	1	no	—
454	#117	—	19	2	no	—
455	#117	—	19	2	no	—
456	#117	—	19	2	no	—
457	C₂×C₂²⋊C₄	—	19	2	no	—
458	C₂×C₂²⋊C₄	—	19	2	no	—
459	C₂×C₂²⋊C₄	—	19	2	no	—
460	C₂×C₂²⋊C₄	—	19	2	no	—
461	C₂×C₂²⋊C₄	—	19	2	no	—
462	C₂×C₂²⋊C₄	—	19	2	no	—
463	C₂×C₄²	—	19	1	no	—
464	C₂×C₄²	—	19	1	no	—
465	C₂×C₄²	—	19	1	no	—
466	C₁₉	#3514	1	1	yes	characteristic, complemented, Sylow
467	C₂⁴	—	19	2	no	—
468	C₂⁴	—	19	2	no	—
469	#41	—	4	2	no	—
470	#41	—	38	4	no	—
471	#41	—	76	2	no	—
472	C₂×Q₈	—	4	2	no	—
473	C₂×Q₈	—	19	1	no	—
474	C₂×Q₈	—	19	1	no	—
475	C₂×Q₈	—	19	2	no	—
476	C₂×Q₈	—	76	2	no	—
477	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
478	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
479	C₂×Q₈	C₂²×D₁₉	1	2	yes	—
480	C₂×D₄	—	19	1	no	—
481	C₂×D₄	—	19	1	no	—
482	C₂×D₄	—	19	2	no	—
483	C₂×D₄	—	19	2	no	—
484	C₂×D₄	—	19	2	no	—
485	C₂×D₄	—	19	2	no	—
486	C₂×D₄	—	19	2	no	—
487	C₂×D₄	—	19	2	no	—
488	C₂×D₄	—	19	1	no	—
489	C₂×D₄	—	19	1	no	—
490	C₂×D₄	—	19	2	no	—
491	C₂×D₄	—	38	8	no	—
492	C₂×D₄	—	76	2	no	—
493	C₂×D₄	—	76	2	no	—
494	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
495	C₂×D₄	C₂²×D₁₉	1	2	yes	—
496	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
497	C₂×D₄	C₂²×D₁₉	1	2	yes	—
498	C₂²×C₄	—	19	1	no	—
499	C₂²×C₄	—	19	1	no	—
500	C₂²×C₄	—	19	1	no	—
501	C₂²×C₄	—	19	1	no	—
502	C₂²×C₄	—	19	2	no	—
503	C₂²×C₄	—	19	1	no	—
504	C₂²×C₄	—	19	1	no	—
505	C₂²×C₄	—	19	2	no	—
506	C₂²×C₄	—	19	1	no	—
507	C₂²×C₄	—	19	2	no	—
508	C₂²×C₄	—	19	2	no	—
509	C₂²×C₄	—	19	2	no	—
510	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
511	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
512	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
513	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
514	C₄⋊C₄	—	19	1	no	—
515	C₄⋊C₄	—	19	2	no	—
516	C₄⋊C₄	—	19	2	no	—
517	C₄⋊C₄	—	19	1	no	—
518	C₄⋊C₄	—	19	1	no	—
519	C₄⋊C₄	—	19	1	no	—
520	C₄⋊C₄	—	19	2	no	—
521	C₄⋊C₄	—	19	2	no	—
522	C₄⋊C₄	—	19	2	no	—
523	C₄⋊C₄	—	19	2	no	—
524	C₄⋊C₄	—	19	2	no	—
525	C₄⋊C₄	—	19	1	no	—
526	C₄⋊C₄	—	19	1	no	—
527	C₄⋊C₄	—	19	2	no	—
528	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
529	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
530	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
531	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
532	C₂²⋊C₄	—	19	2	no	—
533	C₂²⋊C₄	—	19	2	no	—
534	C₂²⋊C₄	—	19	2	no	—
535	C₂²⋊C₄	—	19	1	no	—
536	C₂²⋊C₄	—	19	1	no	—
537	C₂²⋊C₄	—	19	2	no	—
538	C₂²⋊C₄	—	19	1	no	—
539	C₂²⋊C₄	—	19	2	no	—
540	C₂²⋊C₄	—	19	2	no	—
541	C₂²⋊C₄	—	19	2	no	—
542	C₂²⋊C₄	—	19	2	no	—
543	C₂²⋊C₄	—	19	2	no	—
544	C₂²⋊C₄	—	19	2	no	—
545	C₂²⋊C₄	—	19	2	no	—
546	C₂²⋊C₄	—	19	2	no	—
547	C₂²⋊C₄	—	19	2	no	—
548	C₂²⋊C₄	—	19	2	no	—
549	C₂²⋊C₄	—	19	2	no	—
550	C₂²⋊C₄	—	19	2	no	—
551	C₂²⋊C₄	—	19	1	no	—
552	C₂²⋊C₄	—	19	2	no	—
553	C₂²⋊C₄	—	19	2	no	—
554	C₂²⋊C₄	—	19	2	no	—
555	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
556	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
557	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
558	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
559	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
560	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
561	C₄²	—	19	1	no	—
562	C₄²	—	19	1	no	—
563	C₄²	—	19	1	no	—
564	C₄²	—	19	1	no	—
565	C₄²	—	19	1	no	—
566	C₄²	—	19	1	no	—
567	C₄²	—	19	1	no	—
568	C₄²	—	19	1	no	—
569	C₄²	—	19	1	no	—
570	C₄²	—	19	2	no	—
571	C₄²	—	19	2	no	—
572	C₄²	C₂²×D₁₉	1	1	yes	characteristic
573	C₄²	C₂²×D₁₉	1	2	yes	—
574	C₂³	—	19	1	no	—
575	C₂³	—	19	2	no	—
576	C₂³	—	19	2	no	—
577	C₂³	—	38	4	no	—
578	C₂³	—	38	4	no	—
579	C₂³	—	76	2	no	—
580	C₂³	—	76	2	no	—
581	C₂³	—	76	2	no	—
582	C₂³	—	76	2	no	—
583	C₂³	C₂³×D₁₉	1	2	yes	—
584	C₂³	C₂³×D₁₉	1	1	yes	characteristic
585	C₂³	C₂³×D₁₉	1	1	yes	characteristic
586	Q₈	—	2	2	no	—
587	Q₈	—	2	2	no	—
588	Q₈	—	4	2	no	—
589	Q₈	—	38	2	no	—
590	Q₈	—	38	2	no	—
591	Q₈	—	76	2	no	—
592	D₄	—	2	4	no	—
593	D₄	—	2	2	no	—
594	D₄	—	2	2	no	—
595	D₄	—	4	2	no	—
596	D₄	—	19	4	no	—
597	D₄	—	38	4	no	—
598	D₄	—	38	4	no	—
599	D₄	—	38	2	no	—
600	D₄	—	38	2	no	—
601	D₄	—	38	2	no	—
602	D₄	—	76	2	no	—
603	D₄	—	76	2	no	—
604	D₄	—	76	2	no	—
605	D₄	—	76	2	no	—
606	D₄	—	76	2	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	4	2	no	—
610	C₂×C₄	—	4	2	no	—
611	C₂×C₄	—	19	1	no	—
612	C₂×C₄	—	19	1	no	—
613	C₂×C₄	—	19	1	no	—
614	C₂×C₄	—	19	1	no	—
615	C₂×C₄	—	19	1	no	—
616	C₂×C₄	—	19	1	no	—
617	C₂×C₄	—	19	1	no	—
618	C₂×C₄	—	19	2	no	—
619	C₂×C₄	—	19	2	no	—
620	C₂×C₄	—	38	4	no	—
621	C₂×C₄	—	38	2	no	—
622	C₂×C₄	—	38	2	no	—
623	C₂×C₄	—	38	2	no	—
624	C₂×C₄	—	38	2	no	—
625	C₂×C₄	—	76	2	no	—
626	C₂×C₄	—	76	2	no	—
627	C₂×C₄	—	76	1	no	—
628	C₂×C₄	—	76	2	no	—
629	C₂×C₄	—	76	1	no	—
630	C₂×C₄	—	76	2	no	—
631	C₂×C₄	—	76	1	no	—
632	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
633	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
634	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
635	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
636	C₂×C₄	C₂³×D₁₉	1	2	yes	—
637	C₂×C₄	C₂³×D₁₉	1	2	yes	—
638	C₂×C₄	C₂³×D₁₉	1	2	yes	—
639	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
640	C₂²	—	2	1	no	—
641	C₂²	—	2	1	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	1	no	—
645	C₂²	—	2	2	no	—
646	C₂²	—	2	1	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	19	2	no	—
649	C₂²	—	38	1	no	—
650	C₂²	—	38	1	no	—
651	C₂²	—	38	2	no	—
652	C₂²	—	38	2	no	—
653	C₂²	—	38	2	no	—
654	C₂²	—	38	2	no	—
655	C₂²	—	38	2	no	—
656	C₂²	—	38	2	no	—
657	C₂²	—	152	4	no	—
658	C₂²	—	152	4	no	—
659	C₂²	#41×D₁₉	1	2	yes	—
660	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
661	C₄	—	2	2	no	—
662	C₄	—	2	1	no	—
663	C₄	—	2	1	no	—
664	C₄	—	2	1	no	—
665	C₄	—	2	2	no	—
666	C₄	—	2	2	no	—
667	C₄	—	2	1	no	—
668	C₄	—	19	2	no	—
669	C₄	—	38	1	no	—
670	C₄	—	38	1	no	—
671	C₄	—	38	1	no	—
672	C₄	—	38	2	no	—
673	C₄	—	38	1	no	—
674	C₄	—	38	1	no	—
675	C₄	—	38	2	no	—
676	C₄	—	38	1	no	—
677	C₄	#10597430	1	2	yes	—
678	C₂	—	2	2	no	—
679	C₂	—	4	2	no	—
680	C₂	—	4	1	no	—
681	C₂	—	38	2	no	—
682	C₂	—	76	2	no	—
683	C₂	—	76	2	no	—
684	C₂	C₂×#41×D₁₉	1	1	yes	characteristic
685	C₂	C₂×#10597430	1	1	yes	characteristic
686	C₂	#11927381	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₁₉×#548	C₂
hypercenter	#548	D₁₉
hypocenter	C₁₉	#3514
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ #548

Complements

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

N	H ≅ G/N	type
1. #11927276	C₂	semidirect
2. #11927266	C₂	semidirect
3. #11927256	C₂	semidirect
4. #11927223	C₂	semidirect
5. #11927221	C₂	semidirect
6. Q₈×C₂²⋊D₁₉	C₂	semidirect
7. #11927204	C₂	semidirect
8. #11927190	C₂	semidirect
9. #11927183	C₂	semidirect
10. #11927182	C₂	semidirect
11. #11927178	C₂	semidirect
12. #11927164	C₂	semidirect
13. #11927131	C₂	semidirect
14. #11927128	C₂	semidirect
15. #11927090	C₂	semidirect
16. #11927081	C₂	semidirect
17. #11927080	C₂	semidirect
18. #11927075	C₂	semidirect
19. C₂×#10597393	C₂	semidirect
20. #124×D₁₉	C₂	semidirect
21. #11927016	C₂	semidirect
22. C₄×#64543	C₂	semidirect
23. C₁₉×#548	C₂	semidirect
24. C₂×#41×C₁₉	C₂²	semidirect
25. C₂²×Q₈×C₁₉	C₂²	semidirect
26. C₂×Q₈×D₁₉	C₂²	semidirect
30. C₂×#64541	C₂²	semidirect
32. C₁₉×#124	C₂²	semidirect
33. C₁₉×#124	C₂²	semidirect
34. C₁₉×C₂²⋊Q₈	C₂²	semidirect
35. C₁₉×C₂²⋊Q₈	C₂²	semidirect
37. C₁₉×#121	C₂²	semidirect
38. C₄×Q₈×C₁₉	C₂²	semidirect
39. C₄×D₄×C₁₉	C₂²	semidirect
40. C₄×D₄×C₁₉	C₂²	semidirect
43. #10597393	C₂²	semidirect
44. #10597393	C₂²	semidirect
45. #10597393	C₂²	semidirect
46. #10597393	C₂²	semidirect
47. #10597392	C₂²	semidirect
48. #10597392	C₂²	semidirect
49. Q₈×Dic₁₉	C₂²	semidirect
50. #10597390	C₂²	semidirect
51. #10597390	C₂²	semidirect
53. #10597385	C₂²	semidirect
54. #10597385	C₂²	semidirect
55. #10597385	C₂²	semidirect
57. #10597383	C₂²	semidirect
58. #10597383	C₂²	semidirect
59. #10597382	C₂²	semidirect
60. #10597381	C₂²	semidirect
61. D₄×Dic₁₉	C₂²	semidirect
62. D₄×Dic₁₉	C₂²	semidirect
63. D₄×Dic₁₉	C₂²	semidirect
65. #10597375	C₂²	semidirect
68. C₄×C₂²⋊D₁₉	C₂²	semidirect
69. C₄×C₂²⋊D₁₉	C₂²	semidirect
70. C₄×C₂²⋊D₁₉	C₂²	semidirect
71. C₂×(C₂×D₁₉)⋊C₄	C₂²	semidirect
72. C₂×(C₂×D₁₉)⋊C₄	C₂²	semidirect
73. C₂×(C₂×D₁₉)⋊C₄	C₂²	semidirect
74. #10597370	C₂²	semidirect
75. #10597370	C₂²	semidirect
76. C₂×C₄×Dic₁₉	C₂²	semidirect
77. C₂×C₄×Dic₁₉	C₂²	semidirect
78. #10597344	C₂²	semidirect
79. #10597344	C₂²	semidirect
80. #10597344	C₂²	semidirect
81. #10597342	C₂²	semidirect
82. #10597342	C₂²	semidirect
84. #10597340	C₂²	semidirect
85. #10597340	C₂²	semidirect
87. #10597339	C₂²	semidirect
88. #10597338	C₂²	semidirect
89. #10597338	C₂²	semidirect
90. #10597336	C₂²	semidirect
91. #10597333	C₂²	semidirect
92. #10597333	C₂²	semidirect
93. #10597332	C₂²	semidirect
94. #10597332	C₂²	semidirect
95. #10597331	C₂²	semidirect
96. #10597331	C₂²	semidirect
97. #10597331	C₂²	semidirect
98. #10597331	C₂²	semidirect
100. #10597330	C₂²	semidirect
101. #10597330	C₂²	semidirect
102. #10597329	C₂²	semidirect
105. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
106. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
107. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
108. C₂²⋊C₄×D₁₉	C₂²	semidirect
109. C₂²⋊C₄×D₁₉	C₂²	semidirect
110. C₂²⋊C₄×D₁₉	C₂²	semidirect
111. #10597325	C₂²	semidirect
112. #10597323	C₂²	semidirect
113. #10597323	C₂²	semidirect
114. #10597323	C₂²	semidirect
115. #10597322	C₂²	semidirect
117. C₄×D₇₆	C₂²	semidirect
118. C₄×D₇₆	C₂²	semidirect
119. #10597318	C₂²	semidirect
120. #10597318	C₂²	semidirect
121. C₄²×D₁₉	C₂²	semidirect
122. C₄×Dic₃₈	C₂²	semidirect
267. C₂²⋊D₁₉	#41	semidirect
342. #548	D₁₉	semidirect
369. C₂×#41	C₂×D₁₉	semidirect
371. C₂²×Q₈	C₂×D₁₉	semidirect
396. #124	C₂×D₁₉	semidirect
397. #124	C₂×D₁₉	semidirect
411. C₂²⋊Q₈	C₂×D₁₉	semidirect
412. C₂²⋊Q₈	C₂×D₁₉	semidirect
422. #121	C₂×D₁₉	semidirect
431. C₄×Q₈	C₂×D₁₉	semidirect
448. C₄×D₄	C₂×D₁₉	semidirect
449. C₄×D₄	C₂×D₁₉	semidirect
466. C₁₉	#3514	semidirect

Maximal subgroups

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

subgroup	index
#11927276	2
#11927266	2
#11927256	2
#11927223	2
#11927221	2
Q₈×C₂²⋊D₁₉	2
#11927204	2
#11927190	2
#11927183	2
#11927182	2
#11927178	2
#11927164	2
#11927131	2
#11927128	2
#11927090	2
#11927081	2
#11927080	2
#11927075	2
C₂×#10597393	2
#124×D₁₉	2
#11927016	2
C₄×#64543	2
C₁₉×#548	2
#3514	19