Subgroups — #14578152

Order 2432.

1160 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927290	C₂	1	2	yes	maximal, complemented
2	#11927286	C₂	1	2	yes	maximal, complemented
3	#11927279	C₂	1	1	yes	maximal, characteristic, complemented
4	#11927276	C₂	1	1	yes	maximal, characteristic, complemented
5	#11927205	C₂	1	1	yes	maximal, characteristic, complemented
6	#11927189	C₂	1	2	yes	maximal, complemented
7	#11927185	C₂	1	1	yes	maximal, characteristic, complemented
8	#11927183	C₂	1	2	yes	maximal, complemented
9	#11927182	C₂	1	1	yes	maximal, characteristic, complemented
10	D₄×D₇₆	C₂	1	1	yes	maximal, characteristic, complemented
11	#11927178	C₂	1	1	yes	maximal, characteristic, complemented
12	#11927167	C₂	1	1	yes	maximal, characteristic, complemented
13	#11927166	C₂	1	1	yes	maximal, characteristic, complemented
14	#11927134	C₂	1	2	yes	maximal, complemented
15	#11927128	C₂	1	2	yes	maximal, complemented
16	#11927127	C₂	1	2	yes	maximal, complemented
17	#11927112	C₂	1	1	yes	maximal, characteristic, complemented
18	#11927108	C₂	1	1	yes	maximal, characteristic, complemented
19	#11927102	C₂	1	2	yes	maximal, complemented
20	#11927089	C₂	1	1	yes	maximal, characteristic, complemented
21	#11927074	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#10597393	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×#64545	C₂²	1	1	yes	characteristic, complemented
27	C₂×#64543	C₂²	1	2	yes	complemented
28	C₂×D₄×D₁₉	C₂²	1	2	yes	complemented
29	C₂×D₄×D₁₉	C₂²	1	2	yes	complemented
30	C₂×D₄×D₁₉	C₂²	1	1	yes	characteristic, complemented
31	C₂²×D₇₆	C₂²	1	1	yes	characteristic
32	C₂²×D₇₆	C₂²	1	1	yes	characteristic, complemented
33	C₁₉×#124	C₂²	1	1	yes	characteristic, complemented
34	C₁₉×#124	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, complemented
38	C₁₉×#121	C₂²	1	2	yes	complemented
39	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
40	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
41	C₄×D₄×C₁₉	C₂²	1	2	yes	complemented
42	#10597393	C₂²	1	1	yes	characteristic, complemented
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	1	yes	characteristic, complemented
47	#10597393	C₂²	1	2	yes	complemented
48	#10597393	C₂²	1	1	yes	characteristic, complemented
49	#10597393	C₂²	1	2	yes	complemented
50	#10597392	C₂²	1	2	yes	complemented
51	#10597392	C₂²	1	1	yes	characteristic, complemented
52	Q₈×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
53	#10597386	C₂²	1	1	yes	characteristic
54	#10597386	C₂²	1	1	yes	characteristic, complemented
55	#10597385	C₂²	1	1	yes	characteristic
56	#10597385	C₂²	1	2	yes	complemented
57	#10597385	C₂²	1	2	yes	complemented
58	#10597383	C₂²	1	2	yes	complemented
59	#10597383	C₂²	1	2	yes	complemented
60	#10597383	C₂²	1	2	yes	complemented
61	#10597383	C₂²	1	2	yes	complemented
62	#10597381	C₂²	1	1	yes	characteristic, complemented
63	D₄×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
64	#10597376	C₂²	1	1	yes	characteristic
65	#10597376	C₂²	1	1	yes	characteristic, complemented
66	#10597376	C₂²	1	2	yes	complemented
67	#10597376	C₂²	1	2	yes	complemented
68	#10597376	C₂²	1	2	yes	complemented
69	#10597375	C₂²	1	2	yes	complemented
70	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic, complemented
71	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic, complemented
72	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
73	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	complemented
74	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	complemented
75	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	complemented
76	#10597372	C₂²	1	1	yes	characteristic, complemented
77	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
78	#10597344	C₂²	1	1	yes	characteristic, complemented
79	#10597344	C₂²	1	2	yes	complemented
80	#10597343	C₂²	1	2	yes	complemented
81	#10597342	C₂²	1	2	yes	complemented
82	#10597341	C₂²	1	1	yes	characteristic
83	#10597341	C₂²	1	2	yes	complemented
84	#10597341	C₂²	1	2	yes	complemented
85	#10597340	C₂²	1	2	yes	complemented
86	#10597340	C₂²	1	2	yes	complemented
87	#10597340	C₂²	1	2	yes	complemented
88	#10597340	C₂²	1	2	yes	complemented
89	#10597339	C₂²	1	1	yes	characteristic, complemented
90	#10597339	C₂²	1	1	yes	characteristic, complemented
91	#10597335	C₂²	1	1	yes	characteristic, complemented
92	#10597334	C₂²	1	1	yes	characteristic, complemented
93	#10597332	C₂²	1	1	yes	characteristic, complemented
94	#10597332	C₂²	1	2	yes	complemented
95	#10597331	C₂²	1	1	yes	characteristic, 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	complemented
100	#10597330	C₂²	1	2	yes	complemented
101	#10597330	C₂²	1	2	yes	complemented
102	#10597329	C₂²	1	2	yes	complemented
103	#10597329	C₂²	1	2	yes	complemented
104	#10597328	C₂²	1	2	yes	complemented
105	#10597328	C₂²	1	2	yes	complemented
106	#10597328	C₂²	1	2	yes	complemented
107	#10597328	C₂²	1	2	yes	complemented
108	#10597328	C₂²	1	2	yes	complemented
109	#10597328	C₂²	1	2	yes	complemented
110	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	complemented
111	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	complemented
112	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	complemented
113	#10597325	C₂²	1	1	yes	characteristic, complemented
114	#10597324	C₂²	1	1	yes	characteristic, complemented
115	#10597322	C₂²	1	2	yes	complemented
116	#10597321	C₂²	1	2	yes	complemented
117	#10597321	C₂²	1	2	yes	complemented
118	#10597320	C₂²	1	1	yes	characteristic
119	C₄×D₇₆	C₂²	1	2	yes	complemented
120	C₄×D₇₆	C₂²	1	1	yes	characteristic, complemented
121	#10597318	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	C₂³×D₁₉	C₂³	1	2	yes	—
126	#41×C₁₉	—	4	2	no	—
127	C₂×Q₈×C₁₉	—	4	2	no	—
128	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
129	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
130	C₂×Q₈×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	C₂×D₄×C₁₉	C₂³	1	2	yes	—
135	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
136	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
137	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
138	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
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	2	yes	—
145	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
146	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
147	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
148	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
149	C₂²×Dic₁₉	C₂³	1	2	yes	—
150	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
151	#64545	—	4	2	no	—
152	#64543	—	4	4	no	—
153	D₄×D₁₉	—	4	2	no	—
154	D₄×D₁₉	—	4	4	no	—
155	D₄×D₁₉	—	4	4	no	—
156	C₂×D₇₆	—	4	2	no	—
157	C₂×D₇₆	—	4	2	no	—
158	C₂×D₇₆	C₂³	1	1	yes	characteristic
159	C₂×D₇₆	C₂³	1	1	yes	characteristic
160	C₂×D₇₆	C₂³	1	1	yes	characteristic
161	C₂×D₇₆	C₂³	1	2	yes	—
162	C₂×D₇₆	C₂³	1	2	yes	—
163	C₂×D₇₆	C₂³	1	2	yes	—
164	C₂×D₇₆	C₂³	1	2	yes	—
165	C₂×D₇₆	C₂³	1	2	yes	—
166	C₂×D₇₆	C₂³	1	2	yes	—
167	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
168	C₂×C₄×D₁₉	C₂³	1	2	yes	—
169	C₂×C₄×D₁₉	C₂³	1	2	yes	—
170	C₂×C₄×D₁₉	C₂³	1	2	yes	—
171	C₂×C₄×D₁₉	C₂³	1	2	yes	—
172	C₂×Dic₃₈	C₂³	1	2	yes	—
173	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
174	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
175	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
176	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
177	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
178	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
179	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
180	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
181	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
182	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
183	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
184	C₄²×C₁₉	C₂³	1	1	yes	characteristic
185	C₄²×C₁₉	C₂³	1	2	yes	—
186	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
187	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
188	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
189	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
190	C₂²⋊Dic₁₉	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	2	yes	—
196	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
197	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
198	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
199	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
200	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
201	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
202	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
203	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
204	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
205	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
206	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
207	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
208	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
209	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
210	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
211	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
212	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
213	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
214	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
215	C₄⋊Dic₁₉	C₂³	1	2	yes	—
216	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
217	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
218	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
219	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
220	Dic₁₉⋊C₄	C₂³	1	2	yes	—
221	Dic₁₉⋊C₄	C₂³	1	2	yes	—
222	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
223	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
224	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
229	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
230	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
231	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
232	C₂³×C₁₉	C₂⁴	1	2	yes	—
233	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
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	—	4	2	no	—
240	C₂²×D₁₉	—	4	2	no	—
241	C₂²×D₁₉	—	4	2	no	—
242	C₂²×D₁₉	—	4	2	no	—
243	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
244	C₂²×D₁₉	C₂⁴	1	2	yes	—
245	C₂²×D₁₉	C₂⁴	1	2	yes	—
246	C₂²×D₁₉	C₂⁴	1	2	yes	—
247	Q₈×C₁₉	—	2	2	no	—
248	Q₈×C₁₉	—	2	2	no	—
249	Q₈×C₁₉	—	4	2	no	—
250	D₄×C₁₉	—	2	2	no	—
251	D₄×C₁₉	—	2	4	no	—
252	D₄×C₁₉	—	2	2	no	—
253	D₄×C₁₉	—	4	2	no	—
254	C₂×C₄×C₁₉	—	2	2	no	—
255	C₂×C₄×C₁₉	—	2	2	no	—
256	C₂×C₄×C₁₉	—	4	2	no	—
257	C₂×C₄×C₁₉	—	4	2	no	—
258	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
259	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
260	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
261	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
262	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
263	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
264	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
265	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
266	C₂²⋊D₁₉	—	2	2	no	—
267	C₂²⋊D₁₉	—	2	4	no	—
268	C₂²⋊D₁₉	—	4	2	no	—
269	C₂²⋊D₁₉	—	4	2	no	—
270	C₂²⋊D₁₉	—	4	2	no	—
271	C₂²⋊D₁₉	—	4	2	no	—
272	C₂²⋊D₁₉	—	4	1	no	—
273	C₂²⋊D₁₉	—	4	2	no	—
274	C₂²⋊D₁₉	—	4	2	no	—
275	C₂×Dic₁₉	—	2	2	no	—
276	C₂×Dic₁₉	—	4	2	no	—
277	C₂×Dic₁₉	—	4	1	no	—
278	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
279	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
280	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
281	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
282	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
283	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
284	C₂×Dic₁₉	C₂⁴	1	2	yes	—
285	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
286	D₇₆	—	2	2	no	—
287	D₇₆	—	2	2	no	—
288	D₇₆	—	2	2	no	—
289	D₇₆	—	4	2	no	—
290	D₇₆	—	4	2	no	—
291	D₇₆	—	4	2	no	—
292	D₇₆	—	4	2	no	—
293	D₇₆	—	4	2	no	—
294	D₇₆	—	4	2	no	—
295	C₄×D₁₉	—	2	2	no	—
296	C₄×D₁₉	—	4	2	no	—
297	C₄×D₁₉	—	4	2	no	—
298	C₄×D₁₉	—	4	2	no	—
299	C₄×D₁₉	—	4	2	no	—
300	Dic₃₈	—	4	1	no	—
301	Dic₃₈	—	4	2	no	—
302	#3558	—	19	1	no	maximal, Sylow
303	C₂²×C₁₉	—	2	1	no	—
304	C₂²×C₁₉	—	2	1	no	—
305	C₂²×C₁₉	—	2	2	no	—
306	C₂²×C₁₉	—	2	1	no	—
307	C₂²×C₁₉	—	2	2	no	—
308	C₂²×C₁₉	—	2	1	no	—
309	C₂²×C₁₉	—	2	2	no	—
310	C₂²×C₁₉	—	2	1	no	—
311	C₂²×C₁₉	H(5,𝔽₂)	1	2	yes	—
312	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
313	C₂×D₁₉	—	2	1	no	—
314	C₂×D₁₉	—	2	2	no	—
315	C₂×D₁₉	—	2	2	no	—
316	C₂×D₁₉	—	2	2	no	—
317	C₂×D₁₉	—	2	2	no	—
318	C₂×D₁₉	—	2	2	no	—
319	C₂×D₁₉	—	2	2	no	—
320	C₂×D₁₉	—	2	1	no	—
321	C₂×D₁₉	—	2	2	no	—
322	C₂×D₁₉	—	2	2	no	—
323	C₂×D₁₉	—	2	1	no	—
324	C₂×D₁₉	—	2	2	no	—
325	C₂×D₁₉	—	8	4	no	—
326	C₂×D₁₉	—	8	4	no	—
327	C₂×D₁₉	—	8	4	no	—
328	C₄×C₁₉	—	2	2	no	—
329	C₄×C₁₉	—	2	1	no	—
330	C₄×C₁₉	—	2	2	no	—
331	C₄×C₁₉	—	2	1	no	—
332	C₄×C₁₉	—	2	1	no	—
333	C₄×C₁₉	—	2	2	no	—
334	C₄×C₁₉	—	2	1	no	—
335	C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
336	Dic₁₉	—	2	1	no	—
337	Dic₁₉	—	2	2	no	—
338	Dic₁₉	—	2	1	no	—
339	Dic₁₉	—	2	1	no	—
340	Dic₁₉	—	2	1	no	—
341	Dic₁₉	—	2	1	no	—
342	Dic₁₉	—	2	1	no	—
343	Dic₁₉	—	2	1	no	—
344	#562	—	19	2	no	—
345	H(3,𝔽₄)	—	19	2	no	—
346	#559	—	19	1	no	—
347	#559	—	19	1	no	—
348	#548	—	19	1	no	—
349	#548	D₁₉	1	1	yes	characteristic, complemented
350	#546	—	19	1	no	—
351	#546	—	19	1	no	—
352	#546	—	19	2	no	—
353	#546	—	19	2	no	—
354	D₄²	—	19	1	no	—
355	D₄²	—	19	1	no	—
356	#542	—	19	1	no	—
357	#542	—	19	1	no	—
358	#538	—	19	2	no	—
359	#538	—	19	2	no	—
360	#538	—	19	2	no	—
361	#535	—	19	1	no	—
362	#535	—	19	1	no	—
363	#534	—	19	2	no	—
364	#532	—	19	1	no	—
365	#529	—	19	1	no	—
366	C₂×#124	—	19	1	no	—
367	C₂×C₁₉	—	2	2	no	—
368	C₂×C₁₉	—	4	1	no	—
369	C₂×C₁₉	—	4	2	no	—
370	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
371	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
372	C₂×C₁₉	#585	1	1	yes	characteristic
373	D₁₉	—	4	2	no	—
374	D₁₉	—	4	1	no	—
375	D₁₉	—	4	2	no	—
376	D₁₉	—	4	2	no	—
377	C₂×#41	—	19	1	no	—
378	C₂×#41	—	19	2	no	—
379	C₂×#41	C₂×D₁₉	1	1	yes	characteristic, complemented
380	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
381	C₂²×D₄	—	19	2	no	—
382	C₂²×D₄	—	19	2	no	—
383	C₂²×D₄	—	19	1	no	—
384	C₂²×D₄	—	19	1	no	—
385	C₂²×D₄	—	19	1	no	—
386	C₄⋊Q₈	—	19	1	no	—
387	#127	—	19	1	no	—
388	#127	—	19	1	no	—
389	#127	—	19	1	no	—
390	#126	—	19	1	no	—
391	#126	—	19	2	no	—
392	#126	—	19	1	no	—
393	#126	—	19	2	no	—
394	#125	—	19	1	no	—
395	#124	—	19	1	no	—
396	#124	—	19	1	no	—
397	#124	—	19	2	no	—
398	#124	—	19	1	no	—
399	#124	—	19	1	no	—
400	#124	—	19	2	no	—
401	#124	—	19	1	no	—
402	#124	—	19	2	no	—
403	#124	—	19	1	no	—
404	#124	—	19	2	no	—
405	#124	—	19	2	no	—
406	#124	—	19	2	no	—
407	#124	—	19	2	no	—
408	#124	—	19	2	no	—
409	#124	C₂×D₁₉	1	1	yes	characteristic, complemented
410	#124	C₂×D₁₉	1	2	yes	complemented
411	#123	—	19	1	no	—
412	#123	—	19	2	no	—
413	#123	—	19	2	no	—
414	#123	—	19	2	no	—
415	#123	—	19	2	no	—
416	#123	—	19	2	no	—
417	#123	—	19	1	no	—
418	#123	—	19	2	no	—
419	#123	—	19	2	no	—
420	#123	—	19	2	no	—
421	C₂²⋊Q₈	—	19	2	no	—
422	C₂²⋊Q₈	—	19	1	no	—
423	C₂²⋊Q₈	—	19	2	no	—
424	C₂²⋊Q₈	—	19	2	no	—
425	C₂²⋊Q₈	—	19	1	no	—
426	C₂²⋊Q₈	C₂×D₁₉	1	2	yes	complemented
427	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
428	#121	—	19	1	no	—
429	#121	—	19	2	no	—
430	#121	—	19	2	no	—
431	#121	—	19	1	no	—
432	#121	—	19	1	no	—
433	#121	—	19	2	no	—
434	#121	—	19	2	no	—
435	#121	—	19	2	no	—
436	#121	—	19	2	no	—
437	#121	—	19	2	no	—
438	#121	—	19	1	no	—
439	#121	—	19	2	no	—
440	#121	—	19	2	no	—
441	#121	—	19	2	no	—
442	#121	C₂×D₁₉	1	1	yes	characteristic, complemented
443	#121	C₂×D₁₉	1	2	yes	complemented
444	#120	—	19	2	no	—
445	#120	—	19	2	no	—
446	#120	—	19	2	no	—
447	#120	—	19	2	no	—
448	#120	—	19	2	no	—
449	#120	—	19	2	no	—
450	#120	—	19	2	no	—
451	#120	—	19	2	no	—
452	#120	—	19	2	no	—
453	#120	—	19	2	no	—
454	C₄×Q₈	—	19	1	no	—
455	C₄×Q₈	—	19	1	no	—
456	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
457	C₄×D₄	—	19	1	no	—
458	C₄×D₄	—	19	1	no	—
459	C₄×D₄	—	19	1	no	—
460	C₄×D₄	—	19	2	no	—
461	C₄×D₄	—	19	1	no	—
462	C₄×D₄	—	19	1	no	—
463	C₄×D₄	—	19	2	no	—
464	C₄×D₄	—	19	2	no	—
465	C₄×D₄	—	19	2	no	—
466	C₄×D₄	—	19	1	no	—
467	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic, complemented
468	C₄×D₄	C₂×D₁₉	1	2	yes	complemented
469	#117	—	19	1	no	—
470	#117	—	19	1	no	—
471	C₂×C₂²⋊C₄	—	19	2	no	—
472	C₂×C₂²⋊C₄	—	19	2	no	—
473	C₂×C₂²⋊C₄	—	19	2	no	—
474	C₂×C₂²⋊C₄	—	19	2	no	—
475	C₂×C₄²	—	19	1	no	—
476	C₁₉	#3558	1	1	yes	characteristic, complemented, Sylow
477	C₂⁴	—	19	2	no	—
478	C₂⁴	—	19	2	no	—
479	C₂⁴	—	19	2	no	—
480	#41	—	4	2	no	—
481	#41	—	76	4	no	—
482	#41	—	76	2	no	—
483	C₂×Q₈	—	4	2	no	—
484	C₂×Q₈	—	19	1	no	—
485	C₂×Q₈	—	19	2	no	—
486	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
487	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
488	C₂×Q₈	C₂²×D₁₉	1	2	yes	—
489	C₂×D₄	—	19	2	no	—
490	C₂×D₄	—	19	1	no	—
491	C₂×D₄	—	19	1	no	—
492	C₂×D₄	—	19	2	no	—
493	C₂×D₄	—	19	2	no	—
494	C₂×D₄	—	19	2	no	—
495	C₂×D₄	—	19	2	no	—
496	C₂×D₄	—	19	2	no	—
497	C₂×D₄	—	19	2	no	—
498	C₂×D₄	—	19	1	no	—
499	C₂×D₄	—	19	1	no	—
500	C₂×D₄	—	19	1	no	—
501	C₂×D₄	—	19	2	no	—
502	C₂×D₄	—	19	2	no	—
503	C₂×D₄	—	19	2	no	—
504	C₂×D₄	—	19	2	no	—
505	C₂×D₄	—	19	2	no	—
506	C₂×D₄	—	19	2	no	—
507	C₂×D₄	—	76	2	no	—
508	C₂×D₄	—	76	2	no	—
509	C₂×D₄	—	76	2	no	—
510	C₂×D₄	—	76	4	no	—
511	C₂×D₄	—	76	4	no	—
512	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
513	C₂×D₄	C₂²×D₁₉	1	2	yes	—
514	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
515	C₂×D₄	C₂²×D₁₉	1	2	yes	—
516	C₂²×C₄	—	19	1	no	—
517	C₂²×C₄	—	19	1	no	—
518	C₂²×C₄	—	19	2	no	—
519	C₂²×C₄	—	19	1	no	—
520	C₂²×C₄	—	19	2	no	—
521	C₂²×C₄	—	19	2	no	—
522	C₂²×C₄	—	19	2	no	—
523	C₂²×C₄	—	19	2	no	—
524	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
525	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
526	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
527	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
528	C₄⋊C₄	—	19	1	no	—
529	C₄⋊C₄	—	19	1	no	—
530	C₄⋊C₄	—	19	1	no	—
531	C₄⋊C₄	—	19	1	no	—
532	C₄⋊C₄	—	19	2	no	—
533	C₄⋊C₄	—	19	2	no	—
534	C₄⋊C₄	—	19	1	no	—
535	C₄⋊C₄	—	19	1	no	—
536	C₄⋊C₄	—	19	1	no	—
537	C₄⋊C₄	—	19	1	no	—
538	C₄⋊C₄	—	19	1	no	—
539	C₄⋊C₄	—	19	1	no	—
540	C₄⋊C₄	—	19	2	no	—
541	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
542	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
543	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
544	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
545	C₂²⋊C₄	—	19	1	no	—
546	C₂²⋊C₄	—	19	1	no	—
547	C₂²⋊C₄	—	19	1	no	—
548	C₂²⋊C₄	—	19	1	no	—
549	C₂²⋊C₄	—	19	2	no	—
550	C₂²⋊C₄	—	19	1	no	—
551	C₂²⋊C₄	—	19	2	no	—
552	C₂²⋊C₄	—	19	2	no	—
553	C₂²⋊C₄	—	19	2	no	—
554	C₂²⋊C₄	—	19	2	no	—
555	C₂²⋊C₄	—	19	2	no	—
556	C₂²⋊C₄	—	19	2	no	—
557	C₂²⋊C₄	—	19	2	no	—
558	C₂²⋊C₄	—	19	2	no	—
559	C₂²⋊C₄	—	19	2	no	—
560	C₂²⋊C₄	—	19	2	no	—
561	C₂²⋊C₄	—	19	2	no	—
562	C₂²⋊C₄	—	19	1	no	—
563	C₂²⋊C₄	—	19	1	no	—
564	C₂²⋊C₄	—	19	2	no	—
565	C₂²⋊C₄	—	19	2	no	—
566	C₂²⋊C₄	—	19	1	no	—
567	C₂²⋊C₄	—	19	2	no	—
568	C₂²⋊C₄	—	19	2	no	—
569	C₂²⋊C₄	—	19	2	no	—
570	C₂²⋊C₄	—	19	2	no	—
571	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
572	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
573	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
574	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
575	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
576	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
577	C₄²	—	19	1	no	—
578	C₄²	—	19	1	no	—
579	C₄²	—	19	1	no	—
580	C₄²	—	19	1	no	—
581	C₄²	—	19	1	no	—
582	C₄²	—	19	2	no	—
583	C₄²	C₂²×D₁₉	1	1	yes	characteristic
584	C₄²	C₂²×D₁₉	1	2	yes	—
585	C₂³	—	19	1	no	—
586	C₂³	—	19	2	no	—
587	C₂³	—	19	2	no	—
588	C₂³	—	19	2	no	—
589	C₂³	—	38	4	no	—
590	C₂³	—	76	2	no	—
591	C₂³	—	76	2	no	—
592	C₂³	—	76	2	no	—
593	C₂³	—	76	2	no	—
594	C₂³	—	76	2	no	—
595	C₂³	—	76	2	no	—
596	C₂³	—	76	2	no	—
597	C₂³	—	76	2	no	—
598	C₂³	C₂³×D₁₉	1	1	yes	characteristic
599	C₂³	C₂³×D₁₉	1	2	yes	—
600	C₂³	C₂³×D₁₉	1	1	yes	characteristic
601	Q₈	—	2	2	no	—
602	Q₈	—	2	2	no	—
603	Q₈	—	4	2	no	—
604	Q₈	—	76	2	no	—
605	Q₈	—	76	1	no	—
606	D₄	—	2	2	no	—
607	D₄	—	2	4	no	—
608	D₄	—	2	2	no	—
609	D₄	—	4	2	no	—
610	D₄	—	38	2	no	—
611	D₄	—	38	4	no	—
612	D₄	—	38	2	no	—
613	D₄	—	38	2	no	—
614	D₄	—	38	2	no	—
615	D₄	—	76	2	no	—
616	D₄	—	76	2	no	—
617	D₄	—	76	2	no	—
618	D₄	—	76	2	no	—
619	D₄	—	76	2	no	—
620	D₄	—	76	2	no	—
621	D₄	—	76	2	no	—
622	D₄	—	76	2	no	—
623	D₄	—	76	2	no	—
624	D₄	—	76	2	no	—
625	D₄	—	76	2	no	—
626	D₄	—	76	1	no	—
627	D₄	—	76	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	4	2	no	—
631	C₂×C₄	—	4	2	no	—
632	C₂×C₄	—	19	1	no	—
633	C₂×C₄	—	19	1	no	—
634	C₂×C₄	—	19	1	no	—
635	C₂×C₄	—	19	1	no	—
636	C₂×C₄	—	19	1	no	—
637	C₂×C₄	—	19	2	no	—
638	C₂×C₄	—	19	1	no	—
639	C₂×C₄	—	19	1	no	—
640	C₂×C₄	—	38	2	no	—
641	C₂×C₄	—	38	2	no	—
642	C₂×C₄	—	76	2	no	—
643	C₂×C₄	—	76	2	no	—
644	C₂×C₄	—	76	2	no	—
645	C₂×C₄	—	76	2	no	—
646	C₂×C₄	—	76	2	no	—
647	C₂×C₄	—	76	1	no	—
648	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
649	C₂×C₄	C₂³×D₁₉	1	2	yes	—
650	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
651	C₂×C₄	C₂³×D₁₉	1	2	yes	—
652	C₂×C₄	C₂³×D₁₉	1	2	yes	—
653	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
654	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
655	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
656	C₂²	—	2	1	no	—
657	C₂²	—	2	1	no	—
658	C₂²	—	2	1	no	—
659	C₂²	—	2	2	no	—
660	C₂²	—	2	2	no	—
661	C₂²	—	2	1	no	—
662	C₂²	—	2	2	no	—
663	C₂²	—	2	1	no	—
664	C₂²	—	38	1	no	—
665	C₂²	—	38	2	no	—
666	C₂²	—	38	2	no	—
667	C₂²	—	38	2	no	—
668	C₂²	—	38	2	no	—
669	C₂²	—	38	2	no	—
670	C₂²	—	38	2	no	—
671	C₂²	—	38	1	no	—
672	C₂²	—	38	2	no	—
673	C₂²	—	38	2	no	—
674	C₂²	—	38	1	no	—
675	C₂²	—	38	2	no	—
676	C₂²	—	152	4	no	—
677	C₂²	—	152	4	no	—
678	C₂²	—	152	4	no	—
679	C₂²	#10597435	1	2	yes	—
680	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
681	C₄	—	2	1	no	—
682	C₄	—	2	1	no	—
683	C₄	—	2	2	no	—
684	C₄	—	2	2	no	—
685	C₄	—	2	1	no	—
686	C₄	—	2	2	no	—
687	C₄	—	2	1	no	—
688	C₄	—	38	1	no	—
689	C₄	—	38	1	no	—
690	C₄	—	38	1	no	—
691	C₄	—	38	1	no	—
692	C₄	—	38	2	no	—
693	C₄	—	38	1	no	—
694	C₄	—	38	1	no	—
695	C₄	—	38	1	no	—
696	C₄	#10597430	1	2	yes	—
697	C₂	—	2	2	no	—
698	C₂	—	4	1	no	—
699	C₂	—	4	2	no	—
700	C₂	—	76	1	no	—
701	C₂	—	76	2	no	—
702	C₂	—	76	2	no	—
703	C₂	—	76	2	no	—
704	C₂	C₂×#10597430	1	1	yes	characteristic
705	C₂	C₂×#10597435	1	1	yes	characteristic
706	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	#3558
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. #11927290	C₂	semidirect
2. #11927286	C₂	semidirect
3. #11927279	C₂	semidirect
4. #11927276	C₂	semidirect
5. #11927205	C₂	semidirect
6. #11927189	C₂	semidirect
7. #11927185	C₂	semidirect
8. #11927183	C₂	semidirect
9. #11927182	C₂	semidirect
10. D₄×D₇₆	C₂	semidirect
11. #11927178	C₂	semidirect
12. #11927167	C₂	semidirect
13. #11927166	C₂	semidirect
14. #11927134	C₂	semidirect
15. #11927128	C₂	semidirect
16. #11927127	C₂	semidirect
17. #11927112	C₂	semidirect
18. #11927108	C₂	semidirect
19. #11927102	C₂	semidirect
20. #11927089	C₂	semidirect
21. #11927074	C₂	semidirect
22. C₂×#10597393	C₂	semidirect
23. C₁₉×#548	C₂	semidirect
24. C₂×#41×C₁₉	C₂²	semidirect
25. C₂²×Q₈×C₁₉	C₂²	semidirect
26. C₂×#64545	C₂²	semidirect
27. C₂×#64543	C₂²	semidirect
28. C₂×D₄×D₁₉	C₂²	semidirect
29. C₂×D₄×D₁₉	C₂²	semidirect
30. C₂×D₄×D₁₉	C₂²	semidirect
32. C₂²×D₇₆	C₂²	semidirect
33. C₁₉×#124	C₂²	semidirect
34. C₁₉×#124	C₂²	semidirect
35. C₁₉×C₂²⋊Q₈	C₂²	semidirect
36. C₁₉×C₂²⋊Q₈	C₂²	semidirect
37. C₁₉×#121	C₂²	semidirect
38. C₁₉×#121	C₂²	semidirect
39. C₄×Q₈×C₁₉	C₂²	semidirect
40. C₄×D₄×C₁₉	C₂²	semidirect
41. C₄×D₄×C₁₉	C₂²	semidirect
42. #10597393	C₂²	semidirect
43. #10597393	C₂²	semidirect
44. #10597393	C₂²	semidirect
45. #10597393	C₂²	semidirect
46. #10597393	C₂²	semidirect
47. #10597393	C₂²	semidirect
48. #10597393	C₂²	semidirect
49. #10597393	C₂²	semidirect
50. #10597392	C₂²	semidirect
51. #10597392	C₂²	semidirect
52. Q₈×Dic₁₉	C₂²	semidirect
54. #10597386	C₂²	semidirect
56. #10597385	C₂²	semidirect
57. #10597385	C₂²	semidirect
58. #10597383	C₂²	semidirect
59. #10597383	C₂²	semidirect
60. #10597383	C₂²	semidirect
61. #10597383	C₂²	semidirect
62. #10597381	C₂²	semidirect
63. D₄×Dic₁₉	C₂²	semidirect
65. #10597376	C₂²	semidirect
66. #10597376	C₂²	semidirect
67. #10597376	C₂²	semidirect
68. #10597376	C₂²	semidirect
69. #10597375	C₂²	semidirect
70. C₄×C₂²⋊D₁₉	C₂²	semidirect
71. C₄×C₂²⋊D₁₉	C₂²	semidirect
72. C₄×C₂²⋊D₁₉	C₂²	semidirect
73. C₂×(C₂×D₁₉)⋊C₄	C₂²	semidirect
74. C₂×(C₂×D₁₉)⋊C₄	C₂²	semidirect
75. C₂×(C₂×D₁₉)⋊C₄	C₂²	semidirect
76. #10597372	C₂²	semidirect
77. C₂×C₄×Dic₁₉	C₂²	semidirect
78. #10597344	C₂²	semidirect
79. #10597344	C₂²	semidirect
80. #10597343	C₂²	semidirect
81. #10597342	C₂²	semidirect
83. #10597341	C₂²	semidirect
84. #10597341	C₂²	semidirect
85. #10597340	C₂²	semidirect
86. #10597340	C₂²	semidirect
87. #10597340	C₂²	semidirect
88. #10597340	C₂²	semidirect
89. #10597339	C₂²	semidirect
90. #10597339	C₂²	semidirect
91. #10597335	C₂²	semidirect
92. #10597334	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
99. #10597330	C₂²	semidirect
100. #10597330	C₂²	semidirect
101. #10597330	C₂²	semidirect
102. #10597329	C₂²	semidirect
103. #10597329	C₂²	semidirect
104. #10597328	C₂²	semidirect
105. #10597328	C₂²	semidirect
106. #10597328	C₂²	semidirect
107. #10597328	C₂²	semidirect
108. #10597328	C₂²	semidirect
109. #10597328	C₂²	semidirect
110. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
111. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
112. C₂²⋊C₄×D₁₉	C₂²	semidirect
113. #10597325	C₂²	semidirect
114. #10597324	C₂²	semidirect
115. #10597322	C₂²	semidirect
116. #10597321	C₂²	semidirect
117. #10597321	C₂²	semidirect
119. C₄×D₇₆	C₂²	semidirect
120. C₄×D₇₆	C₂²	semidirect
121. #10597318	C₂²	semidirect
122. C₄×Dic₃₈	C₂²	semidirect
349. #548	D₁₉	semidirect
379. C₂×#41	C₂×D₁₉	semidirect
380. C₂²×Q₈	C₂×D₁₉	semidirect
409. #124	C₂×D₁₉	semidirect
410. #124	C₂×D₁₉	semidirect
426. C₂²⋊Q₈	C₂×D₁₉	semidirect
427. C₂²⋊Q₈	C₂×D₁₉	semidirect
442. #121	C₂×D₁₉	semidirect
443. #121	C₂×D₁₉	semidirect
456. C₄×Q₈	C₂×D₁₉	semidirect
467. C₄×D₄	C₂×D₁₉	semidirect
468. C₄×D₄	C₂×D₁₉	semidirect
476. C₁₉	#3558	semidirect

Maximal subgroups

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

subgroup	index
#11927290	2
#11927286	2
#11927279	2
#11927276	2
#11927205	2
#11927189	2
#11927185	2
#11927183	2
#11927182	2
D₄×D₇₆	2
#11927178	2
#11927167	2
#11927166	2
#11927134	2
#11927128	2
#11927127	2
#11927112	2
#11927108	2
#11927102	2
#11927089	2
#11927074	2
C₂×#10597393	2
C₁₉×#548	2
#3558	19