Subgroups — #14577335

Order 2432.

1124 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927254	C₂	1	1	yes	maximal, characteristic, complemented
2	#11927252	C₂	1	1	yes	maximal, characteristic, complemented
3	#11927250	C₂	1	2	yes	maximal, complemented
4	#11927247	C₂	1	1	yes	maximal, characteristic, complemented
5	#11927245	C₂	1	2	yes	maximal, complemented
6	#11927238	C₂	1	1	yes	maximal, characteristic, complemented
7	#11927236	C₂	1	1	yes	maximal, characteristic, complemented
8	#11927227	C₂	1	2	yes	maximal, complemented
9	#11927198	C₂	1	1	yes	maximal, characteristic, complemented
10	#11927195	C₂	1	1	yes	maximal, characteristic, complemented
11	#11927192	C₂	1	2	yes	maximal, complemented
12	#11927174	C₂	1	1	yes	maximal, characteristic, complemented
13	#11927142	C₂	1	2	yes	maximal, complemented
14	#11927135	C₂	1	2	yes	maximal, complemented
15	#11927124	C₂	1	1	yes	maximal, characteristic, complemented
16	#11927057	C₂	1	1	yes	maximal, characteristic, complemented
17	#11927056	C₂	1	2	yes	maximal, complemented
18	#11927053	C₂	1	1	yes	maximal, characteristic, complemented
19	#11927052	C₂	1	2	yes	maximal, complemented
20	#11927026	C₂	1	1	yes	maximal, characteristic, complemented
21	#11927024	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₄⋊C₄×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₉×#552	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#64545	C₂²	1	1	yes	characteristic
25	C₂×#64543	C₂²	1	2	yes	—
26	C₂×#64541	C₂²	1	1	yes	characteristic
27	C₂×#64541	C₂²	1	2	yes	—
28	C₂²×C₄×D₁₉	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₁₉	C₂²	1	2	yes	—
30	C₁₉×#126	C₂²	1	2	yes	complemented
31	C₁₉×#125	C₂²	1	2	yes	complemented
32	C₁₉×#125	C₂²	1	1	yes	characteristic, complemented
33	C₁₉×#123	C₂²	1	2	yes	—
34	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
35	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
36	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
37	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
38	C₁₉×#117	C₂²	1	2	yes	—
39	C₁₉×#117	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
41	#10597392	C₂²	1	1	yes	characteristic
42	#10597392	C₂²	1	1	yes	characteristic, complemented
43	Q₈×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
44	#10597385	C₂²	1	1	yes	characteristic
45	#10597383	C₂²	1	1	yes	characteristic
46	#10597376	C₂²	1	1	yes	characteristic
47	#10597376	C₂²	1	1	yes	characteristic, complemented
48	#10597375	C₂²	1	2	yes	—
49	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
50	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
51	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
52	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic, complemented
53	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	—
54	#10597344	C₂²	1	2	yes	complemented
55	#10597344	C₂²	1	2	yes	complemented
56	#10597343	C₂²	1	2	yes	—
57	#10597343	C₂²	1	2	yes	—
58	#10597343	C₂²	1	2	yes	complemented
59	#10597342	C₂²	1	2	yes	—
60	#10597342	C₂²	1	2	yes	—
61	#10597342	C₂²	1	1	yes	characteristic
62	#10597342	C₂²	1	2	yes	complemented
63	#10597342	C₂²	1	2	yes	complemented
64	#10597342	C₂²	1	2	yes	complemented
65	#10597341	C₂²	1	2	yes	—
66	#10597341	C₂²	1	2	yes	—
67	#10597341	C₂²	1	1	yes	characteristic
68	#10597341	C₂²	1	1	yes	characteristic, complemented
69	#10597340	C₂²	1	1	yes	characteristic
70	#10597340	C₂²	1	2	yes	—
71	#10597340	C₂²	1	2	yes	complemented
72	#10597340	C₂²	1	2	yes	complemented
73	#10597339	C₂²	1	2	yes	—
74	#10597339	C₂²	1	2	yes	—
75	#10597339	C₂²	1	2	yes	—
76	#10597339	C₂²	1	1	yes	characteristic, complemented
77	#10597338	C₂²	1	1	yes	characteristic
78	#10597338	C₂²	1	1	yes	characteristic, complemented
79	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic
80	C₄⋊C₄×D₁₉	C₂²	1	2	yes	—
81	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic
82	C₄⋊C₄×D₁₉	C₂²	1	2	yes	—
83	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic
84	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic
85	C₄⋊C₄×D₁₉	C₂²	1	2	yes	complemented
86	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic, complemented
87	#10597336	C₂²	1	2	yes	complemented
88	#10597336	C₂²	1	1	yes	characteristic, complemented
89	#10597335	C₂²	1	2	yes	complemented
90	#10597335	C₂²	1	2	yes	complemented
91	#10597334	C₂²	1	2	yes	complemented
92	#10597334	C₂²	1	1	yes	characteristic, complemented
93	#10597332	C₂²	1	2	yes	—
94	#10597332	C₂²	1	2	yes	—
95	#10597332	C₂²	1	2	yes	complemented
96	#10597330	C₂²	1	2	yes	—
97	#10597330	C₂²	1	2	yes	—
98	#10597330	C₂²	1	1	yes	characteristic
99	#10597330	C₂²	1	2	yes	complemented
100	#10597329	C₂²	1	1	yes	characteristic
101	#10597329	C₂²	1	2	yes	complemented
102	#10597328	C₂²	1	2	yes	—
103	#10597328	C₂²	1	1	yes	characteristic
104	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	—
105	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	—
106	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	—
107	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	complemented
108	#10597324	C₂²	1	1	yes	characteristic
109	#10597324	C₂²	1	2	yes	complemented
110	#10597323	C₂²	1	2	yes	—
111	#10597322	C₂²	1	2	yes	complemented
112	C₄×D₇₆	C₂²	1	1	yes	characteristic
113	C₄×D₇₆	C₂²	1	2	yes	—
114	C₄×D₇₆	C₂²	1	2	yes	—
115	C₄×D₇₆	C₂²	1	2	yes	—
116	C₄×D₇₆	C₂²	1	2	yes	—
117	C₄×D₇₆	C₂²	1	1	yes	characteristic, complemented
118	#10597318	C₂²	1	1	yes	characteristic
119	#10597318	C₂²	1	2	yes	complemented
120	#10597316	C₂²	1	2	yes	complemented
121	#10597315	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₃₈	C₂²	1	2	yes	complemented
123	C₂³×D₁₉	C₂³	1	1	yes	characteristic
124	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
125	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
126	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
127	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
129	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
131	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
132	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
133	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
135	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
136	C₂²×Dic₁₉	C₂³	1	2	yes	—
137	C₂²×Dic₁₉	C₂³	1	2	yes	—
138	#64545	—	2	4	no	—
139	#64543	—	4	4	no	—
140	#64541	—	2	4	no	—
141	#64541	—	4	4	no	—
142	C₂×D₇₆	C₂³	1	1	yes	characteristic
143	C₂×D₇₆	C₂³	1	1	yes	characteristic
144	C₂×D₇₆	C₂³	1	2	yes	—
145	C₂×D₇₆	C₂³	1	1	yes	characteristic
146	C₂×D₇₆	C₂³	1	2	yes	—
147	C₂×D₇₆	C₂³	1	2	yes	—
148	C₂×C₄×D₁₉	—	2	4	no	—
149	C₂×C₄×D₁₉	—	4	4	no	—
150	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
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	2	yes	—
157	C₂×C₄×D₁₉	C₂³	1	2	yes	—
158	C₂×C₄×D₁₉	C₂³	1	2	yes	—
159	C₂×C₄×D₁₉	C₂³	1	2	yes	—
160	C₂×C₄×D₁₉	C₂³	1	2	yes	—
161	C₂×C₄×D₁₉	C₂³	1	2	yes	—
162	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
163	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
164	C₂×Dic₃₈	C₂³	1	2	yes	—
165	C₂×Dic₃₈	C₂³	1	2	yes	—
166	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
167	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
168	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
169	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
170	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
171	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
172	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
173	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
174	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
175	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
176	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
177	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
178	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
179	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
180	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
181	C₄²×C₁₉	C₂³	1	2	yes	—
182	C₄²×C₁₉	C₂³	1	2	yes	—
183	C₄²×C₁₉	C₂³	1	1	yes	characteristic
184	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
185	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
186	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
187	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
189	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
194	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
195	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
196	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
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	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
203	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
204	C₄⋊Dic₁₉	C₂³	1	2	yes	—
205	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
206	C₄⋊Dic₁₉	C₂³	1	2	yes	—
207	C₄⋊Dic₁₉	C₂³	1	2	yes	—
208	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
209	C₄⋊Dic₁₉	C₂³	1	2	yes	—
210	C₄⋊Dic₁₉	C₂³	1	2	yes	—
211	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
212	Dic₁₉⋊C₄	C₂³	1	2	yes	—
213	Dic₁₉⋊C₄	C₂³	1	2	yes	—
214	Dic₁₉⋊C₄	C₂³	1	2	yes	—
215	Dic₁₉⋊C₄	C₂³	1	2	yes	—
216	Dic₁₉⋊C₄	C₂³	1	2	yes	—
217	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
218	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
219	Dic₁₉⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
224	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
225	C₄×Dic₁₉	C₂³	1	2	yes	—
226	C₄×Dic₁₉	C₂³	1	2	yes	—
227	C₄×Dic₁₉	C₂³	1	2	yes	—
228	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
229	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
230	C₂²×D₁₉	—	2	2	no	—
231	C₂²×D₁₉	—	2	2	no	—
232	C₂²×D₁₉	—	2	2	no	—
233	C₂²×D₁₉	C₂⁴	1	2	yes	—
234	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
235	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
236	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
237	Q₈×C₁₉	—	2	2	no	—
238	D₄×C₁₉	—	2	2	no	—
239	C₂×C₄×C₁₉	—	2	4	no	—
240	C₂×C₄×C₁₉	—	2	2	no	—
241	C₂×C₄×C₁₉	—	2	2	no	—
242	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
243	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
244	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
245	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
246	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
247	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
251	C₂²⋊D₁₉	—	2	2	no	—
252	C₂²⋊D₁₉	—	2	4	no	—
253	C₂²⋊D₁₉	—	2	2	no	—
254	C₂²⋊D₁₉	—	2	2	no	—
255	C₂²⋊D₁₉	—	2	2	no	—
256	C₂²⋊D₁₉	—	4	2	no	—
257	C₂×Dic₁₉	—	2	4	no	—
258	C₂×Dic₁₉	—	2	2	no	—
259	C₂×Dic₁₉	—	4	2	no	—
260	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
261	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
262	C₂×Dic₁₉	C₂⁴	1	2	yes	—
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	—	2	4	no	—
270	D₇₆	—	2	2	no	—
271	D₇₆	—	2	4	no	—
272	D₇₆	—	2	2	no	—
273	D₇₆	—	4	2	no	—
274	C₄×D₁₉	—	2	2	no	—
275	C₄×D₁₉	—	2	2	no	—
276	C₄×D₁₉	—	2	2	no	—
277	C₄×D₁₉	—	2	2	no	—
278	C₄×D₁₉	—	2	4	no	—
279	C₄×D₁₉	—	4	2	no	—
280	C₄×D₁₉	—	4	2	no	—
281	C₄×D₁₉	—	4	2	no	—
282	C₄×D₁₉	—	4	2	no	—
283	C₄×D₁₉	—	4	2	no	—
284	C₄×D₁₉	—	4	2	no	—
285	C₄×D₁₉	—	4	2	no	—
286	C₄×D₁₉	#41	1	4	yes	complemented
287	Dic₃₈	—	2	2	no	—
288	Dic₃₈	—	4	2	no	—
289	Dic₃₈	—	4	2	no	—
290	#3492	—	19	1	no	maximal, Sylow
291	C₂²×C₁₉	—	2	1	no	—
292	C₂²×C₁₉	—	2	1	no	—
293	C₂²×C₁₉	—	2	1	no	—
294	C₂²×C₁₉	—	2	1	no	—
295	C₂²×C₁₉	—	2	1	no	—
296	C₂²×C₁₉	H(5,𝔽₂)	1	2	yes	—
297	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
298	C₂×D₁₉	—	2	8	no	—
299	C₂×D₁₉	—	2	1	no	—
300	C₂×D₁₉	—	2	1	no	—
301	C₂×D₁₉	—	2	1	no	—
302	C₂×D₁₉	—	2	1	no	—
303	C₂×D₁₉	—	2	2	no	—
304	C₂×D₁₉	—	2	1	no	—
305	C₂×D₁₉	—	2	1	no	—
306	C₂×D₁₉	—	2	2	no	—
307	C₂×D₁₉	—	2	2	no	—
308	C₂×D₁₉	—	2	1	no	—
309	C₂×D₁₉	C₂×#41	1	2	yes	—
310	C₂×D₁₉	2₋¹⁺⁴	1	2	yes	—
311	C₄×C₁₉	—	2	1	no	—
312	C₄×C₁₉	—	2	1	no	—
313	C₄×C₁₉	—	2	2	no	—
314	C₄×C₁₉	—	2	1	no	—
315	C₄×C₁₉	—	2	2	no	—
316	C₄×C₁₉	—	2	2	no	—
317	C₄×C₁₉	—	2	2	no	—
318	C₄×C₁₉	—	2	1	no	—
319	C₄×C₁₉	C₂×#41	1	2	yes	—
320	Dic₁₉	—	2	1	no	—
321	Dic₁₉	—	2	1	no	—
322	Dic₁₉	—	2	1	no	—
323	Dic₁₉	—	2	2	no	—
324	Dic₁₉	—	2	2	no	—
325	Dic₁₉	—	2	2	no	—
326	Dic₁₉	—	2	1	no	—
327	Dic₁₉	C₂×#41	1	2	yes	—
328	#554	—	19	2	no	—
329	#554	—	19	1	no	—
330	#554	—	19	1	no	—
331	#553	—	19	2	no	—
332	#553	—	19	1	no	—
333	#553	—	19	1	no	—
334	#552	—	19	1	no	—
335	#552	—	19	2	no	—
336	#552	D₁₉	1	1	yes	characteristic, complemented
337	#547	—	19	2	no	—
338	#547	—	19	1	no	—
339	#547	—	19	1	no	—
340	#544	—	19	1	no	—
341	#539	—	19	2	no	—
342	#539	—	19	2	no	—
343	#537	—	19	1	no	—
344	#525	—	19	2	no	—
345	#525	—	19	1	no	—
346	#525	—	19	1	no	—
347	#525	—	19	2	no	—
348	#520	—	19	1	no	—
349	#520	—	19	1	no	—
350	C₂²×C₄⋊C₄	—	19	1	no	—
351	C₂×C₁₉	—	2	2	no	—
352	C₂×C₁₉	—	4	1	no	—
353	C₂×C₁₉	C₂²×#41	1	1	yes	characteristic
354	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
355	C₂×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
356	D₁₉	—	2	2	no	—
357	D₁₉	—	2	2	no	—
358	D₁₉	—	4	2	no	—
359	D₁₉	—	4	1	no	—
360	C₂×#41	—	19	1	no	—
361	C₂×#41	—	19	2	no	—
362	C₂×#41	—	19	1	no	—
363	C₂×#41	—	19	2	no	—
364	C₂³×C₄	—	19	1	no	—
365	C₂³×C₄	—	19	2	no	—
366	C₄⋊Q₈	—	19	2	no	—
367	C₄⋊Q₈	—	19	1	no	—
368	C₄⋊Q₈	—	19	1	no	—
369	#126	—	19	2	no	—
370	#126	—	19	2	no	—
371	#126	—	19	2	no	—
372	#126	C₂×D₁₉	1	2	yes	complemented
373	#125	—	19	2	no	—
374	#125	—	19	2	no	—
375	#125	—	19	2	no	—
376	#125	—	19	1	no	—
377	#125	—	19	2	no	—
378	#125	C₂×D₁₉	1	2	yes	complemented
379	#125	C₂×D₁₉	1	1	yes	characteristic, complemented
380	#123	—	19	2	no	—
381	#123	—	19	2	no	—
382	#123	—	19	1	no	—
383	#123	—	19	2	no	—
384	#123	—	19	2	no	—
385	#123	—	19	1	no	—
386	#123	—	19	2	no	—
387	#123	—	19	2	no	—
388	#123	—	19	2	no	—
389	#123	—	19	2	no	—
390	#123	C₂×D₁₉	1	2	yes	—
391	C₂²⋊Q₈	—	19	1	no	—
392	C₂²⋊Q₈	—	19	1	no	—
393	C₂²⋊Q₈	—	19	2	no	—
394	C₂²⋊Q₈	—	19	2	no	—
395	C₂²⋊Q₈	—	19	1	no	—
396	C₂²⋊Q₈	—	19	2	no	—
397	C₂²⋊Q₈	—	19	2	no	—
398	C₂²⋊Q₈	—	19	2	no	—
399	C₂²⋊Q₈	—	19	2	no	—
400	C₂²⋊Q₈	—	19	2	no	—
401	C₂²⋊Q₈	—	19	2	no	—
402	C₂²⋊Q₈	—	19	1	no	—
403	C₂²⋊Q₈	—	19	2	no	—
404	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
405	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
406	#121	—	19	1	no	—
407	#121	—	19	1	no	—
408	#121	—	19	1	no	—
409	#121	—	19	2	no	—
410	#121	—	19	2	no	—
411	#121	—	19	1	no	—
412	#121	—	19	1	no	—
413	#121	—	19	2	no	—
414	#121	—	19	2	no	—
415	#121	—	19	1	no	—
416	#121	—	19	2	no	—
417	#120	—	19	1	no	—
418	#120	—	19	2	no	—
419	#120	—	19	1	no	—
420	C₄×Q₈	—	19	1	no	—
421	C₄×Q₈	—	19	2	no	—
422	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
423	C₄×D₄	—	19	1	no	—
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	2	no	—
429	C₄×D₄	—	19	2	no	—
430	C₄×D₄	—	19	2	no	—
431	C₄×D₄	—	19	2	no	—
432	C₄×D₄	—	19	2	no	—
433	C₄×D₄	—	19	2	no	—
434	C₄×D₄	—	19	2	no	—
435	C₄×D₄	—	19	1	no	—
436	C₄×D₄	—	19	2	no	—
437	C₄×D₄	—	19	1	no	—
438	C₄×D₄	—	19	2	no	—
439	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
440	#117	—	19	1	no	—
441	#117	—	19	1	no	—
442	#117	—	19	2	no	—
443	#117	—	19	1	no	—
444	#117	—	19	2	no	—
445	#117	C₂×D₁₉	1	2	yes	—
446	#117	C₂×D₁₉	1	1	yes	characteristic, complemented
447	C₂×C₄⋊C₄	—	19	2	no	—
448	C₂×C₄⋊C₄	—	19	1	no	—
449	C₂×C₄⋊C₄	—	19	1	no	—
450	C₂×C₄⋊C₄	—	19	1	no	—
451	C₂×C₄⋊C₄	—	19	1	no	—
452	C₂×C₄⋊C₄	—	19	2	no	—
453	C₂×C₄⋊C₄	—	19	2	no	—
454	C₂×C₄⋊C₄	—	19	1	no	—
455	C₂×C₄⋊C₄	—	19	1	no	—
456	C₂×C₄⋊C₄	—	19	2	no	—
457	C₂×C₄⋊C₄	—	19	1	no	—
458	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
459	C₁₉	#3492	1	1	yes	characteristic, complemented, Sylow
460	C₂⁴	—	19	1	no	—
461	#41	—	38	4	no	—
462	#41	—	38	4	no	—
463	#41	—	76	4	no	—
464	#41	—	76	4	no	—
465	C₂×Q₈	—	19	1	no	—
466	C₂×Q₈	—	19	2	no	—
467	C₂×Q₈	—	19	2	no	—
468	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
469	C₂×D₄	—	19	1	no	—
470	C₂×D₄	—	19	1	no	—
471	C₂×D₄	—	19	1	no	—
472	C₂×D₄	—	19	2	no	—
473	C₂×D₄	—	19	1	no	—
474	C₂×D₄	—	19	2	no	—
475	C₂×D₄	—	19	2	no	—
476	C₂×D₄	—	19	1	no	—
477	C₂×D₄	—	19	2	no	—
478	C₂×D₄	—	19	1	no	—
479	C₂×D₄	—	19	1	no	—
480	C₂×D₄	—	19	2	no	—
481	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
482	C₂²×C₄	—	19	1	no	—
483	C₂²×C₄	—	19	2	no	—
484	C₂²×C₄	—	19	1	no	—
485	C₂²×C₄	—	19	2	no	—
486	C₂²×C₄	—	19	1	no	—
487	C₂²×C₄	—	19	1	no	—
488	C₂²×C₄	—	19	1	no	—
489	C₂²×C₄	—	19	2	no	—
490	C₂²×C₄	—	19	1	no	—
491	C₂²×C₄	—	19	2	no	—
492	C₂²×C₄	—	19	2	no	—
493	C₂²×C₄	—	19	2	no	—
494	C₂²×C₄	—	19	2	no	—
495	C₂²×C₄	—	19	2	no	—
496	C₂²×C₄	—	19	2	no	—
497	C₂²×C₄	—	19	2	no	—
498	C₂²×C₄	—	38	4	no	—
499	C₂²×C₄	—	76	4	no	—
500	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
501	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
502	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
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	2	no	—
509	C₄⋊C₄	—	19	1	no	—
510	C₄⋊C₄	—	19	2	no	—
511	C₄⋊C₄	—	19	2	no	—
512	C₄⋊C₄	—	19	1	no	—
513	C₄⋊C₄	—	19	2	no	—
514	C₄⋊C₄	—	19	2	no	—
515	C₄⋊C₄	—	19	1	no	—
516	C₄⋊C₄	—	19	1	no	—
517	C₄⋊C₄	—	19	1	no	—
518	C₄⋊C₄	—	19	2	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	1	no	—
525	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
526	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
527	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
528	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
529	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
530	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
531	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
532	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
533	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
534	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
535	C₂²⋊C₄	—	19	1	no	—
536	C₂²⋊C₄	—	19	1	no	—
537	C₂²⋊C₄	—	19	1	no	—
538	C₂²⋊C₄	—	19	2	no	—
539	C₂²⋊C₄	—	19	1	no	—
540	C₂²⋊C₄	—	19	2	no	—
541	C₂²⋊C₄	—	19	2	no	—
542	C₂²⋊C₄	—	19	2	no	—
543	C₂²⋊C₄	—	19	1	no	—
544	C₂²⋊C₄	—	19	2	no	—
545	C₂²⋊C₄	—	19	1	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	1	no	—
551	C₂²⋊C₄	—	19	1	no	—
552	C₂²⋊C₄	—	19	2	no	—
553	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
554	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
555	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
556	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
557	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
558	C₄²	—	19	2	no	—
559	C₄²	—	19	2	no	—
560	C₄²	—	19	2	no	—
561	C₄²	—	19	1	no	—
562	C₄²	C₂²×D₁₉	1	2	yes	—
563	C₄²	C₂²×D₁₉	1	1	yes	characteristic
564	C₄²	C₂²×D₁₉	1	2	yes	—
565	C₂³	—	19	1	no	—
566	C₂³	—	19	1	no	—
567	C₂³	—	19	1	no	—
568	C₂³	—	19	2	no	—
569	C₂³	—	38	2	no	—
570	C₂³	—	38	2	no	—
571	C₂³	—	38	2	no	—
572	C₂³	C₂³×D₁₉	1	1	yes	characteristic
573	C₂³	C₂³×D₁₉	1	1	yes	characteristic
574	Q₈	—	2	2	no	—
575	Q₈	—	38	2	no	—
576	Q₈	—	76	2	no	—
577	Q₈	—	76	2	no	—
578	D₄	—	2	2	no	—
579	D₄	—	38	2	no	—
580	D₄	—	38	4	no	—
581	D₄	—	38	4	no	—
582	D₄	—	38	2	no	—
583	D₄	—	38	2	no	—
584	D₄	—	38	2	no	—
585	D₄	—	38	2	no	—
586	D₄	—	38	2	no	—
587	D₄	—	38	4	no	—
588	D₄	—	38	2	no	—
589	D₄	—	76	2	no	—
590	D₄	—	76	2	no	—
591	C₂×C₄	—	2	4	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	19	1	no	—
595	C₂×C₄	—	19	4	no	—
596	C₂×C₄	—	19	1	no	—
597	C₂×C₄	—	19	1	no	—
598	C₂×C₄	—	19	2	no	—
599	C₂×C₄	—	19	1	no	—
600	C₂×C₄	—	19	2	no	—
601	C₂×C₄	—	19	1	no	—
602	C₂×C₄	—	19	2	no	—
603	C₂×C₄	—	38	2	no	—
604	C₂×C₄	—	38	4	no	—
605	C₂×C₄	—	38	2	no	—
606	C₂×C₄	—	38	2	no	—
607	C₂×C₄	—	38	4	no	—
608	C₂×C₄	—	38	2	no	—
609	C₂×C₄	—	38	2	no	—
610	C₂×C₄	—	76	2	no	—
611	C₂×C₄	—	76	2	no	—
612	C₂×C₄	—	76	2	no	—
613	C₂×C₄	—	76	2	no	—
614	C₂×C₄	—	76	2	no	—
615	C₂×C₄	—	76	2	no	—
616	C₂×C₄	—	76	2	no	—
617	C₂×C₄	—	76	2	no	—
618	C₂×C₄	C₂³×D₁₉	1	2	yes	—
619	C₂×C₄	C₂³×D₁₉	1	2	yes	—
620	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
621	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
622	C₂×C₄	C₂³×D₁₉	1	2	yes	—
623	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
624	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
625	C₂×C₄	C₂³×D₁₉	1	2	yes	—
626	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
627	C₂²	—	2	1	no	—
628	C₂²	—	2	1	no	—
629	C₂²	—	2	1	no	—
630	C₂²	—	2	1	no	—
631	C₂²	—	2	1	no	—
632	C₂²	—	19	2	no	—
633	C₂²	—	19	2	no	—
634	C₂²	—	38	8	no	—
635	C₂²	—	38	1	no	—
636	C₂²	—	38	1	no	—
637	C₂²	—	38	1	no	—
638	C₂²	—	38	1	no	—
639	C₂²	—	38	2	no	—
640	C₂²	—	38	1	no	—
641	C₂²	—	38	1	no	—
642	C₂²	—	38	2	no	—
643	C₂²	—	38	1	no	—
644	C₂²	—	38	2	no	—
645	C₂²	#10597435	1	2	yes	—
646	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
647	C₄	—	2	1	no	—
648	C₄	—	2	1	no	—
649	C₄	—	2	2	no	—
650	C₄	—	2	2	no	—
651	C₄	—	2	2	no	—
652	C₄	—	2	1	no	—
653	C₄	—	2	2	no	—
654	C₄	—	2	1	no	—
655	C₄	—	19	2	no	—
656	C₄	—	38	1	no	—
657	C₄	—	38	1	no	—
658	C₄	—	38	2	no	—
659	C₄	—	38	2	no	—
660	C₄	—	38	1	no	—
661	C₄	—	38	2	no	—
662	C₄	—	38	1	no	—
663	C₄	#41×D₁₉	1	2	yes	—
664	C₂	—	2	2	no	—
665	C₂	—	4	1	no	—
666	C₂	—	38	2	no	—
667	C₂	—	38	2	no	—
668	C₂	—	76	2	no	—
669	C₂	—	76	1	no	—
670	C₂	C₂×#41×D₁₉	1	1	yes	characteristic
671	C₂	C₂×#10597435	1	1	yes	characteristic
672	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×#552	C₂
hypercenter	#552	D₁₉
hypocenter	C₁₉	#3492
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ #552

Complements

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

N	H ≅ G/N	type
1. #11927254	C₂	semidirect
2. #11927252	C₂	semidirect
3. #11927250	C₂	semidirect
4. #11927247	C₂	semidirect
5. #11927245	C₂	semidirect
6. #11927238	C₂	semidirect
7. #11927236	C₂	semidirect
8. #11927227	C₂	semidirect
9. #11927198	C₂	semidirect
10. #11927195	C₂	semidirect
11. #11927192	C₂	semidirect
12. #11927174	C₂	semidirect
13. #11927142	C₂	semidirect
14. #11927135	C₂	semidirect
15. #11927124	C₂	semidirect
16. #11927057	C₂	semidirect
17. #11927056	C₂	semidirect
18. #11927053	C₂	semidirect
19. #11927052	C₂	semidirect
20. #11927026	C₂	semidirect
21. #11927024	C₂	semidirect
22. C₂×C₄⋊C₄×D₁₉	C₂	semidirect
23. C₁₉×#552	C₂	semidirect
30. C₁₉×#126	C₂²	semidirect
31. C₁₉×#125	C₂²	semidirect
32. C₁₉×#125	C₂²	semidirect
35. C₁₉×C₂²⋊Q₈	C₂²	semidirect
36. C₄×Q₈×C₁₉	C₂²	semidirect
39. C₁₉×#117	C₂²	semidirect
42. #10597392	C₂²	semidirect
43. Q₈×Dic₁₉	C₂²	semidirect
47. #10597376	C₂²	semidirect
52. C₂×C₄⋊Dic₁₉	C₂²	semidirect
54. #10597344	C₂²	semidirect
55. #10597344	C₂²	semidirect
58. #10597343	C₂²	semidirect
62. #10597342	C₂²	semidirect
63. #10597342	C₂²	semidirect
64. #10597342	C₂²	semidirect
68. #10597341	C₂²	semidirect
71. #10597340	C₂²	semidirect
72. #10597340	C₂²	semidirect
76. #10597339	C₂²	semidirect
78. #10597338	C₂²	semidirect
85. C₄⋊C₄×D₁₉	C₂²	semidirect
86. C₄⋊C₄×D₁₉	C₂²	semidirect
87. #10597336	C₂²	semidirect
88. #10597336	C₂²	semidirect
89. #10597335	C₂²	semidirect
90. #10597335	C₂²	semidirect
91. #10597334	C₂²	semidirect
92. #10597334	C₂²	semidirect
95. #10597332	C₂²	semidirect
99. #10597330	C₂²	semidirect
101. #10597329	C₂²	semidirect
107. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
109. #10597324	C₂²	semidirect
111. #10597322	C₂²	semidirect
117. C₄×D₇₆	C₂²	semidirect
119. #10597318	C₂²	semidirect
120. #10597316	C₂²	semidirect
121. #10597315	C₂²	semidirect
122. C₄×Dic₃₈	C₂²	semidirect
286. C₄×D₁₉	#41	semidirect
336. #552	D₁₉	semidirect
372. #126	C₂×D₁₉	semidirect
378. #125	C₂×D₁₉	semidirect
379. #125	C₂×D₁₉	semidirect
405. C₂²⋊Q₈	C₂×D₁₉	semidirect
422. C₄×Q₈	C₂×D₁₉	semidirect
446. #117	C₂×D₁₉	semidirect
459. C₁₉	#3492	semidirect

Maximal subgroups

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

subgroup	index
#11927254	2
#11927252	2
#11927250	2
#11927247	2
#11927245	2
#11927238	2
#11927236	2
#11927227	2
#11927198	2
#11927195	2
#11927192	2
#11927174	2
#11927142	2
#11927135	2
#11927124	2
#11927057	2
#11927056	2
#11927053	2
#11927052	2
#11927026	2
#11927024	2
C₂×C₄⋊C₄×D₁₉	2
C₁₉×#552	2
#3492	19