Subgroups — #14577681

Order 2432.

1124 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927262	C₂	1	1	yes	maximal, characteristic, complemented
2	#11927250	C₂	1	2	yes	maximal, complemented
3	#11927232	C₂	1	1	yes	maximal, characteristic, complemented
4	#11927219	C₂	1	2	yes	maximal, complemented
5	#11927218	C₂	1	2	yes	maximal, complemented
6	#11927207	C₂	1	1	yes	maximal, characteristic, complemented
7	#11927206	C₂	1	1	yes	maximal, characteristic, complemented
8	#11927203	C₂	1	1	yes	maximal, characteristic, complemented
9	#11927196	C₂	1	1	yes	maximal, characteristic, complemented
10	#11927195	C₂	1	1	yes	maximal, characteristic, complemented
11	#11927186	C₂	1	2	yes	maximal, complemented
12	#11927160	C₂	1	2	yes	maximal, complemented
13	#11927142	C₂	1	2	yes	maximal, complemented
14	#11927138	C₂	1	2	yes	maximal, complemented
15	#11927098	C₂	1	1	yes	maximal, characteristic, complemented
16	#11927079	C₂	1	1	yes	maximal, characteristic, complemented
17	#11927057	C₂	1	1	yes	maximal, characteristic, complemented
18	#11927056	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#10597343	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²⋊Q₈×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
21	#11927024	C₂	1	2	yes	maximal, complemented
22	C₄×D₄×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, complemented
25	C₂×Q₈×D₁₉	C₂²	1	1	yes	characteristic, complemented
26	C₂×D₄×D₁₉	C₂²	1	1	yes	characteristic
27	C₂×#64541	C₂²	1	2	yes	—
28	C₂×#64541	C₂²	1	1	yes	characteristic, complemented
29	C₂²×C₄×D₁₉	C₂²	1	1	yes	characteristic
30	C₂²×C₄×D₁₉	C₂²	1	1	yes	characteristic
31	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
32	C₁₉×#126	C₂²	1	2	yes	complemented
33	C₁₉×#125	C₂²	1	1	yes	characteristic, complemented
34	C₁₉×#125	C₂²	1	2	yes	complemented
35	C₁₉×#123	C₂²	1	2	yes	—
36	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
38	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
39	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
40	C₁₉×#117	C₂²	1	1	yes	characteristic, complemented
41	C₁₉×#117	C₂²	1	2	yes	complemented
42	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
43	#10597392	C₂²	1	1	yes	characteristic
44	#10597390	C₂²	1	1	yes	characteristic, complemented
45	#10597385	C₂²	1	2	yes	—
46	D₄×Dic₁₉	C₂²	1	1	yes	characteristic
47	#10597376	C₂²	1	1	yes	characteristic, complemented
48	#10597375	C₂²	1	2	yes	complemented
49	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
50	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
51	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	—
52	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	complemented
53	#10597370	C₂²	1	1	yes	characteristic, complemented
54	#10597344	C₂²	1	2	yes	complemented
55	#10597344	C₂²	1	2	yes	complemented
56	#10597343	C₂²	1	1	yes	characteristic
57	#10597343	C₂²	1	1	yes	characteristic
58	#10597343	C₂²	1	2	yes	—
59	#10597343	C₂²	1	2	yes	complemented
60	#10597343	C₂²	1	1	yes	characteristic, complemented
61	#10597343	C₂²	1	1	yes	characteristic, complemented
62	#10597343	C₂²	1	1	yes	characteristic, complemented
63	#10597343	C₂²	1	2	yes	complemented
64	#10597342	C₂²	1	2	yes	—
65	#10597342	C₂²	1	2	yes	—
66	#10597342	C₂²	1	2	yes	complemented
67	#10597342	C₂²	1	2	yes	complemented
68	#10597342	C₂²	1	2	yes	complemented
69	#10597341	C₂²	1	1	yes	characteristic
70	#10597341	C₂²	1	2	yes	—
71	#10597341	C₂²	1	1	yes	characteristic, complemented
72	#10597340	C₂²	1	2	yes	—
73	#10597340	C₂²	1	2	yes	—
74	#10597340	C₂²	1	2	yes	complemented
75	#10597340	C₂²	1	2	yes	complemented
76	#10597340	C₂²	1	2	yes	complemented
77	#10597339	C₂²	1	2	yes	—
78	#10597339	C₂²	1	2	yes	—
79	#10597339	C₂²	1	1	yes	characteristic
80	#10597339	C₂²	1	1	yes	characteristic, complemented
81	#10597338	C₂²	1	1	yes	characteristic, complemented
82	#10597338	C₂²	1	2	yes	complemented
83	#10597338	C₂²	1	2	yes	complemented
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	C₄⋊C₄×D₁₉	C₂²	1	2	yes	complemented
88	#10597336	C₂²	1	2	yes	complemented
89	#10597335	C₂²	1	2	yes	complemented
90	#10597334	C₂²	1	1	yes	characteristic, complemented
91	#10597334	C₂²	1	2	yes	complemented
92	#10597333	C₂²	1	1	yes	characteristic, complemented
93	#10597332	C₂²	1	2	yes	complemented
94	#10597331	C₂²	1	2	yes	—
95	#10597331	C₂²	1	2	yes	complemented
96	#10597330	C₂²	1	2	yes	—
97	#10597329	C₂²	1	2	yes	complemented
98	#10597328	C₂²	1	2	yes	—
99	#10597328	C₂²	1	2	yes	—
100	(C₂²⋊D₁₉)⋊C₄	C₂²	1	1	yes	characteristic
101	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	—
102	(C₂²⋊D₁₉)⋊C₄	C₂²	1	1	yes	characteristic
103	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	complemented
104	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	complemented
105	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	—
106	C₂²⋊C₄×D₁₉	C₂²	1	1	yes	characteristic
107	C₂²⋊C₄×D₁₉	C₂²	1	1	yes	characteristic
108	#10597325	C₂²	1	2	yes	complemented
109	#10597324	C₂²	1	2	yes	complemented
110	#10597324	C₂²	1	2	yes	complemented
111	#10597322	C₂²	1	2	yes	complemented
112	#10597321	C₂²	1	1	yes	characteristic, complemented
113	#10597321	C₂²	1	2	yes	complemented
114	C₄×D₇₆	C₂²	1	2	yes	—
115	C₄×D₇₆	C₂²	1	1	yes	characteristic
116	C₄×D₇₆	C₂²	1	2	yes	complemented
117	C₄×D₇₆	C₂²	1	2	yes	complemented
118	#10597318	C₂²	1	2	yes	—
119	C₄²×D₁₉	C₂²	1	1	yes	characteristic
120	C₄×Dic₃₈	C₂²	1	2	yes	complemented
121	C₄×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₃₈	C₂²	1	2	yes	complemented
123	C₂³×D₁₉	C₂³	1	1	yes	characteristic
124	C₂³×D₁₉	C₂³	1	1	yes	characteristic
125	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
126	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
127	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
129	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
130	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
132	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
134	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
135	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
136	C₂²×Dic₁₉	C₂³	1	2	yes	—
137	#64545	—	4	2	no	—
138	Q₈×D₁₉	—	4	2	no	—
139	D₄×D₁₉	—	2	4	no	—
140	#64541	—	2	8	no	—
141	#64541	—	4	2	no	—
142	C₂×D₇₆	C₂³	1	1	yes	characteristic
143	C₂×D₇₆	C₂³	1	2	yes	—
144	C₂×D₇₆	C₂³	1	1	yes	characteristic
145	C₂×D₇₆	C₂³	1	2	yes	—
146	C₂×D₇₆	C₂³	1	2	yes	—
147	C₂×C₄×D₁₉	—	4	2	no	—
148	C₂×C₄×D₁₉	—	4	2	no	—
149	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₁₉	C₂³	1	2	yes	—
153	C₂×C₄×D₁₉	C₂³	1	2	yes	—
154	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
160	C₂×C₄×D₁₉	C₂³	1	2	yes	—
161	C₂×C₄×D₁₉	C₂³	1	2	yes	—
162	C₂×C₄×D₁₉	C₂³	1	2	yes	—
163	C₂×Dic₃₈	—	4	2	no	—
164	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
165	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
166	C₂×Dic₃₈	C₂³	1	2	yes	—
167	C₂×Dic₃₈	C₂³	1	2	yes	—
168	C₂×Dic₃₈	C₂³	1	2	yes	—
169	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
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	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
175	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
176	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
177	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
178	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
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	1	yes	characteristic
183	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
184	C₄²×C₁₉	C₂³	1	2	yes	—
185	C₄²×C₁₉	C₂³	1	2	yes	—
186	C₄²×C₁₉	C₂³	1	1	yes	characteristic
187	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
188	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
189	C₂²⋊Dic₁₉	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	1	yes	characteristic
195	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
205	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
206	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
207	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
208	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
209	C₄⋊Dic₁₉	C₂³	1	2	yes	—
210	C₄⋊Dic₁₉	C₂³	1	2	yes	—
211	C₄⋊Dic₁₉	C₂³	1	2	yes	—
212	C₄⋊Dic₁₉	C₂³	1	2	yes	—
213	C₄⋊Dic₁₉	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	2	yes	—
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	2	yes	—
223	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
224	C₄×Dic₁₉	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	2	yes	—
228	C₄×Dic₁₉	C₂³	1	2	yes	—
229	C₄×Dic₁₉	C₂³	1	2	yes	—
230	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
231	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
232	C₂²×D₁₉	—	2	2	no	—
233	C₂²×D₁₉	—	2	2	no	—
234	C₂²×D₁₉	—	2	2	no	—
235	C₂²×D₁₉	—	2	2	no	—
236	C₂²×D₁₉	—	4	1	no	—
237	C₂²×D₁₉	—	4	1	no	—
238	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
239	C₂²×D₁₉	C₂⁴	1	2	yes	—
240	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
241	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
242	Q₈×C₁₉	—	2	2	no	—
243	D₄×C₁₉	—	2	2	no	—
244	C₂×C₄×C₁₉	—	2	4	no	—
245	C₂×C₄×C₁₉	—	2	2	no	—
246	C₂×C₄×C₁₉	—	2	2	no	—
247	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
249	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
251	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
252	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
253	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
254	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
255	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
256	C₂²⋊D₁₉	—	2	4	no	—
257	C₂²⋊D₁₉	—	2	2	no	—
258	C₂²⋊D₁₉	—	4	2	no	—
259	C₂²⋊D₁₉	#41	1	4	yes	complemented
260	C₂×Dic₁₉	—	4	2	no	—
261	C₂×Dic₁₉	—	4	1	no	—
262	C₂×Dic₁₉	—	4	1	no	—
263	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
264	C₂×Dic₁₉	C₂⁴	1	2	yes	—
265	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
266	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
267	C₂×Dic₁₉	C₂⁴	1	2	yes	—
268	C₂×Dic₁₉	C₂⁴	1	2	yes	—
269	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
270	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
271	D₇₆	—	2	4	no	—
272	D₇₆	—	2	2	no	—
273	D₇₆	—	2	4	no	—
274	D₇₆	—	2	2	no	—
275	D₇₆	—	4	2	no	—
276	C₄×D₁₉	—	2	4	no	—
277	C₄×D₁₉	—	2	2	no	—
278	C₄×D₁₉	—	2	2	no	—
279	C₄×D₁₉	—	2	2	no	—
280	C₄×D₁₉	—	2	2	no	—
281	C₄×D₁₉	—	2	4	no	—
282	C₄×D₁₉	—	2	2	no	—
283	C₄×D₁₉	—	4	1	no	—
284	C₄×D₁₉	—	4	1	no	—
285	C₄×D₁₉	—	4	1	no	—
286	C₄×D₁₉	—	4	1	no	—
287	C₄×D₁₉	—	4	2	no	—
288	C₄×D₁₉	—	4	2	no	—
289	C₄×D₁₉	—	4	2	no	—
290	Dic₃₈	—	2	2	no	—
291	Dic₃₈	—	2	2	no	—
292	Dic₃₈	—	2	4	no	—
293	Dic₃₈	—	4	2	no	—
294	Dic₃₈	—	4	2	no	—
295	#3520	—	19	1	no	maximal, Sylow
296	C₂²×C₁₉	—	2	1	no	—
297	C₂²×C₁₉	—	2	1	no	—
298	C₂²×C₁₉	—	2	1	no	—
299	C₂²×C₁₉	—	2	1	no	—
300	C₂²×C₁₉	—	2	1	no	—
301	C₂²×C₁₉	C₂×#41	1	2	yes	—
302	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
303	C₂×D₁₉	—	2	1	no	—
304	C₂×D₁₉	—	2	1	no	—
305	C₂×D₁₉	—	2	1	no	—
306	C₂×D₁₉	—	2	1	no	—
307	C₂×D₁₉	—	2	2	no	—
308	C₂×D₁₉	—	2	1	no	—
309	C₂×D₁₉	—	2	1	no	—
310	C₂×D₁₉	—	2	2	no	—
311	C₂×D₁₉	—	2	2	no	—
312	C₂×D₁₉	—	2	1	no	—
313	C₂×D₁₉	—	4	4	no	—
314	C₂×D₁₉	—	4	4	no	—
315	C₂×D₁₉	C₂×#41	1	2	yes	—
316	C₂×D₁₉	2₋¹⁺⁴	1	2	yes	—
317	C₄×C₁₉	—	2	2	no	—
318	C₄×C₁₉	—	2	2	no	—
319	C₄×C₁₉	—	2	1	no	—
320	C₄×C₁₉	—	2	1	no	—
321	C₄×C₁₉	—	2	2	no	—
322	C₄×C₁₉	—	2	1	no	—
323	C₄×C₁₉	—	2	1	no	—
324	C₄×C₁₉	—	2	2	no	—
325	C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
326	Dic₁₉	—	2	2	no	—
327	Dic₁₉	—	2	2	no	—
328	Dic₁₉	—	2	2	no	—
329	Dic₁₉	—	2	1	no	—
330	Dic₁₉	—	2	1	no	—
331	Dic₁₉	—	2	1	no	—
332	Dic₁₉	—	2	1	no	—
333	Dic₁₉	C₂×#41	1	2	yes	—
334	#556	—	19	1	no	—
335	#554	—	19	2	no	—
336	#552	—	19	1	no	—
337	#552	D₁₉	1	1	yes	characteristic, complemented
338	#551	—	19	2	no	—
339	#551	—	19	2	no	—
340	D₄×Q₈	—	19	1	no	—
341	#548	—	19	1	no	—
342	#548	—	19	1	no	—
343	#547	—	19	1	no	—
344	#547	—	19	1	no	—
345	#546	—	19	2	no	—
346	#542	—	19	2	no	—
347	#539	—	19	2	no	—
348	#539	—	19	2	no	—
349	#533	—	19	1	no	—
350	#529	—	19	1	no	—
351	#525	—	19	1	no	—
352	#525	—	19	1	no	—
353	C₂×C₂²⋊Q₈	—	19	1	no	—
354	C₂×C₂²⋊Q₈	—	19	1	no	—
355	#520	—	19	2	no	—
356	C₂×C₄×D₄	—	19	1	no	—
357	C₂×C₁₉	—	2	2	no	—
358	C₂×C₁₉	—	4	1	no	—
359	C₂×C₁₉	C₂²×#41	1	1	yes	characteristic
360	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
361	C₂×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
362	D₁₉	—	2	2	no	—
363	D₁₉	—	2	2	no	—
364	D₁₉	—	4	2	no	—
365	D₁₉	—	4	1	no	—
366	C₂×#41	—	19	1	no	—
367	C₂×#41	—	19	2	no	—
368	C₂×#41	—	19	1	no	—
369	C₂²×Q₈	—	19	1	no	—
370	C₂²×Q₈	—	19	1	no	—
371	C₂²×D₄	—	19	1	no	—
372	C₂³×C₄	—	19	1	no	—
373	C₂³×C₄	—	19	1	no	—
374	C₄⋊Q₈	—	19	1	no	—
375	C₄⋊Q₈	—	19	1	no	—
376	C₄⋊Q₈	—	19	2	no	—
377	#126	—	19	2	no	—
378	#126	—	19	2	no	—
379	#126	—	19	2	no	—
380	#126	—	19	2	no	—
381	#126	C₂×D₁₉	1	2	yes	complemented
382	#125	—	19	2	no	—
383	#125	—	19	2	no	—
384	#125	C₂×D₁₉	1	1	yes	characteristic, complemented
385	#125	C₂×D₁₉	1	2	yes	complemented
386	#124	—	19	2	no	—
387	#124	—	19	2	no	—
388	#124	—	19	1	no	—
389	#124	—	19	2	no	—
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	—	19	2	no	—
398	#123	C₂×D₁₉	1	2	yes	—
399	C₂²⋊Q₈	—	19	1	no	—
400	C₂²⋊Q₈	—	19	1	no	—
401	C₂²⋊Q₈	—	19	1	no	—
402	C₂²⋊Q₈	—	19	1	no	—
403	C₂²⋊Q₈	—	19	2	no	—
404	C₂²⋊Q₈	—	19	1	no	—
405	C₂²⋊Q₈	—	19	1	no	—
406	C₂²⋊Q₈	—	19	2	no	—
407	C₂²⋊Q₈	—	19	2	no	—
408	C₂²⋊Q₈	—	19	1	no	—
409	C₂²⋊Q₈	—	19	2	no	—
410	C₂²⋊Q₈	—	19	2	no	—
411	C₂²⋊Q₈	—	19	2	no	—
412	C₂²⋊Q₈	—	19	2	no	—
413	C₂²⋊Q₈	—	19	2	no	—
414	C₂²⋊Q₈	—	19	2	no	—
415	C₂²⋊Q₈	—	19	2	no	—
416	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
417	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
418	#121	—	19	2	no	—
419	#121	—	19	1	no	—
420	#121	—	19	1	no	—
421	#121	—	19	1	no	—
422	#121	—	19	2	no	—
423	#121	—	19	2	no	—
424	#120	—	19	2	no	—
425	#120	—	19	2	no	—
426	C₄×Q₈	—	19	1	no	—
427	C₄×Q₈	—	19	2	no	—
428	C₄×Q₈	—	19	2	no	—
429	C₄×Q₈	—	19	1	no	—
430	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
431	C₄×D₄	—	19	1	no	—
432	C₄×D₄	—	19	1	no	—
433	C₄×D₄	—	19	1	no	—
434	C₄×D₄	—	19	1	no	—
435	C₄×D₄	—	19	2	no	—
436	C₄×D₄	—	19	2	no	—
437	C₄×D₄	—	19	1	no	—
438	C₄×D₄	—	19	1	no	—
439	C₄×D₄	—	19	1	no	—
440	C₄×D₄	—	19	2	no	—
441	C₄×D₄	—	19	2	no	—
442	C₄×D₄	—	19	2	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	C₂×D₁₉	1	1	yes	characteristic
448	#117	—	19	2	no	—
449	#117	—	19	2	no	—
450	#117	—	19	1	no	—
451	#117	—	19	2	no	—
452	#117	C₂×D₁₉	1	2	yes	complemented
453	#117	C₂×D₁₉	1	1	yes	characteristic, complemented
454	C₂×C₄⋊C₄	—	19	2	no	—
455	C₂×C₄⋊C₄	—	19	1	no	—
456	C₂×C₄⋊C₄	—	19	2	no	—
457	C₂×C₄⋊C₄	—	19	2	no	—
458	C₂×C₄⋊C₄	—	19	1	no	—
459	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic, complemented
460	C₂×C₂²⋊C₄	—	19	2	no	—
461	C₂×C₂²⋊C₄	—	19	1	no	—
462	C₂×C₂²⋊C₄	—	19	1	no	—
463	C₂×C₂²⋊C₄	—	19	2	no	—
464	C₂×C₄²	—	19	1	no	—
465	C₁₉	#3520	1	1	yes	characteristic, complemented, Sylow
466	C₂⁴	—	19	1	no	—
467	C₂⁴	—	19	1	no	—
468	#41	—	38	8	no	—
469	#41	—	76	2	no	—
470	#41	—	76	2	no	—
471	C₂×Q₈	—	19	2	no	—
472	C₂×Q₈	—	19	1	no	—
473	C₂×Q₈	—	19	1	no	—
474	C₂×Q₈	—	19	2	no	—
475	C₂×Q₈	—	19	2	no	—
476	C₂×Q₈	—	76	2	no	—
477	C₂×Q₈	—	76	2	no	—
478	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
479	C₂×D₄	—	19	1	no	—
480	C₂×D₄	—	19	2	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	1	no	—
486	C₂×D₄	—	19	1	no	—
487	C₂×D₄	—	19	2	no	—
488	C₂×D₄	—	38	4	no	—
489	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
490	C₂²×C₄	—	19	2	no	—
491	C₂²×C₄	—	19	1	no	—
492	C₂²×C₄	—	19	1	no	—
493	C₂²×C₄	—	19	1	no	—
494	C₂²×C₄	—	19	1	no	—
495	C₂²×C₄	—	19	1	no	—
496	C₂²×C₄	—	19	2	no	—
497	C₂²×C₄	—	19	2	no	—
498	C₂²×C₄	—	19	1	no	—
499	C₂²×C₄	—	19	1	no	—
500	C₂²×C₄	—	19	2	no	—
501	C₂²×C₄	—	19	1	no	—
502	C₂²×C₄	—	19	1	no	—
503	C₂²×C₄	—	19	1	no	—
504	C₂²×C₄	—	19	2	no	—
505	C₂²×C₄	—	19	2	no	—
506	C₂²×C₄	—	19	1	no	—
507	C₂²×C₄	—	76	2	no	—
508	C₂²×C₄	—	76	2	no	—
509	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
510	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
511	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
512	C₄⋊C₄	—	19	1	no	—
513	C₄⋊C₄	—	19	1	no	—
514	C₄⋊C₄	—	19	2	no	—
515	C₄⋊C₄	—	19	2	no	—
516	C₄⋊C₄	—	19	2	no	—
517	C₄⋊C₄	—	19	2	no	—
518	C₄⋊C₄	—	19	2	no	—
519	C₄⋊C₄	—	19	2	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	—	19	1	no	—
526	C₄⋊C₄	—	19	2	no	—
527	C₄⋊C₄	—	19	2	no	—
528	C₄⋊C₄	—	19	2	no	—
529	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
530	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
531	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
532	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
533	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
534	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
535	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
536	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
537	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
538	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
539	C₂²⋊C₄	—	19	1	no	—
540	C₂²⋊C₄	—	19	1	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	2	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	2	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	C₂²×D₁₉	1	1	yes	characteristic
560	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
561	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
562	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
563	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
564	C₄²	—	19	1	no	—
565	C₄²	—	19	1	no	—
566	C₄²	—	19	1	no	—
567	C₄²	—	19	2	no	—
568	C₄²	—	19	2	no	—
569	C₄²	—	19	2	no	—
570	C₄²	C₂²×D₁₉	1	1	yes	characteristic
571	C₄²	C₂²×D₁₉	1	2	yes	—
572	C₄²	C₂²×D₁₉	1	2	yes	—
573	C₂³	—	19	1	no	—
574	C₂³	—	19	1	no	—
575	C₂³	—	19	1	no	—
576	C₂³	—	19	2	no	—
577	C₂³	—	38	2	no	—
578	C₂³	—	38	2	no	—
579	C₂³	—	38	2	no	—
580	C₂³	—	38	2	no	—
581	C₂³	—	76	1	no	—
582	C₂³	—	76	1	no	—
583	C₂³	C₂³×D₁₉	1	1	yes	characteristic
584	C₂³	C₂³×D₁₉	1	1	yes	characteristic
585	Q₈	—	2	2	no	—
586	Q₈	—	38	4	no	—
587	Q₈	—	38	2	no	—
588	Q₈	—	38	2	no	—
589	Q₈	—	76	2	no	—
590	Q₈	—	76	2	no	—
591	D₄	—	2	2	no	—
592	D₄	—	19	4	no	—
593	D₄	—	38	2	no	—
594	D₄	—	38	4	no	—
595	D₄	—	38	4	no	—
596	D₄	—	38	2	no	—
597	D₄	—	38	4	no	—
598	D₄	—	38	2	no	—
599	D₄	—	76	2	no	—
600	D₄	—	76	2	no	—
601	C₂×C₄	—	2	4	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	19	1	no	—
605	C₂×C₄	—	19	1	no	—
606	C₂×C₄	—	19	2	no	—
607	C₂×C₄	—	19	1	no	—
608	C₂×C₄	—	19	1	no	—
609	C₂×C₄	—	19	2	no	—
610	C₂×C₄	—	19	2	no	—
611	C₂×C₄	—	19	1	no	—
612	C₂×C₄	—	38	2	no	—
613	C₂×C₄	—	38	4	no	—
614	C₂×C₄	—	38	4	no	—
615	C₂×C₄	—	38	2	no	—
616	C₂×C₄	—	38	2	no	—
617	C₂×C₄	—	38	2	no	—
618	C₂×C₄	—	38	2	no	—
619	C₂×C₄	—	76	1	no	—
620	C₂×C₄	—	76	1	no	—
621	C₂×C₄	—	76	1	no	—
622	C₂×C₄	—	76	1	no	—
623	C₂×C₄	—	76	2	no	—
624	C₂×C₄	—	76	2	no	—
625	C₂×C₄	—	76	2	no	—
626	C₂×C₄	—	76	1	no	—
627	C₂×C₄	—	76	1	no	—
628	C₂×C₄	—	76	2	no	—
629	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
630	C₂×C₄	C₂³×D₁₉	1	2	yes	—
631	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
632	C₂×C₄	C₂³×D₁₉	1	2	yes	—
633	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
634	C₂×C₄	C₂³×D₁₉	1	2	yes	—
635	C₂×C₄	C₂³×D₁₉	1	2	yes	—
636	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
637	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
638	C₂²	—	2	1	no	—
639	C₂²	—	2	1	no	—
640	C₂²	—	2	1	no	—
641	C₂²	—	2	1	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	19	2	no	—
644	C₂²	—	19	2	no	—
645	C₂²	—	38	1	no	—
646	C₂²	—	38	1	no	—
647	C₂²	—	38	1	no	—
648	C₂²	—	38	1	no	—
649	C₂²	—	38	2	no	—
650	C₂²	—	38	1	no	—
651	C₂²	—	38	1	no	—
652	C₂²	—	38	2	no	—
653	C₂²	—	38	2	no	—
654	C₂²	—	38	1	no	—
655	C₂²	—	76	4	no	—
656	C₂²	—	76	4	no	—
657	C₂²	#41×D₁₉	1	2	yes	—
658	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
659	C₄	—	2	2	no	—
660	C₄	—	2	2	no	—
661	C₄	—	2	1	no	—
662	C₄	—	2	1	no	—
663	C₄	—	2	1	no	—
664	C₄	—	2	2	no	—
665	C₄	—	2	1	no	—
666	C₄	—	2	2	no	—
667	C₄	—	19	2	no	—
668	C₄	—	38	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	2	no	—
674	C₄	—	38	1	no	—
675	C₄	#10597435	1	2	yes	—
676	C₂	—	2	2	no	—
677	C₂	—	4	1	no	—
678	C₂	—	38	2	no	—
679	C₂	—	38	2	no	—
680	C₂	—	76	1	no	—
681	C₂	—	76	2	no	—
682	C₂	C₂×#41×D₁₉	1	1	yes	characteristic
683	C₂	C₂×#10597435	1	1	yes	characteristic
684	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	#3520
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. #11927262	C₂	semidirect
2. #11927250	C₂	semidirect
3. #11927232	C₂	semidirect
4. #11927219	C₂	semidirect
5. #11927218	C₂	semidirect
6. #11927207	C₂	semidirect
7. #11927206	C₂	semidirect
8. #11927203	C₂	semidirect
9. #11927196	C₂	semidirect
10. #11927195	C₂	semidirect
11. #11927186	C₂	semidirect
12. #11927160	C₂	semidirect
13. #11927142	C₂	semidirect
14. #11927138	C₂	semidirect
15. #11927098	C₂	semidirect
16. #11927079	C₂	semidirect
17. #11927057	C₂	semidirect
18. #11927056	C₂	semidirect
19. C₂×#10597343	C₂	semidirect
20. C₂²⋊Q₈×D₁₉	C₂	semidirect
21. #11927024	C₂	semidirect
22. C₄×D₄×D₁₉	C₂	semidirect
23. C₁₉×#552	C₂	semidirect
24. C₂×#64545	C₂²	semidirect
25. C₂×Q₈×D₁₉	C₂²	semidirect
28. C₂×#64541	C₂²	semidirect
31. C₂²×Dic₃₈	C₂²	semidirect
32. C₁₉×#126	C₂²	semidirect
33. C₁₉×#125	C₂²	semidirect
34. C₁₉×#125	C₂²	semidirect
36. C₁₉×C₂²⋊Q₈	C₂²	semidirect
37. C₁₉×C₂²⋊Q₈	C₂²	semidirect
38. C₄×Q₈×C₁₉	C₂²	semidirect
40. C₁₉×#117	C₂²	semidirect
41. C₁₉×#117	C₂²	semidirect
42. C₂×C₄⋊C₄×C₁₉	C₂²	semidirect
44. #10597390	C₂²	semidirect
47. #10597376	C₂²	semidirect
48. #10597375	C₂²	semidirect
52. C₂×C₄⋊Dic₁₉	C₂²	semidirect
53. #10597370	C₂²	semidirect
54. #10597344	C₂²	semidirect
55. #10597344	C₂²	semidirect
59. #10597343	C₂²	semidirect
60. #10597343	C₂²	semidirect
61. #10597343	C₂²	semidirect
62. #10597343	C₂²	semidirect
63. #10597343	C₂²	semidirect
66. #10597342	C₂²	semidirect
67. #10597342	C₂²	semidirect
68. #10597342	C₂²	semidirect
71. #10597341	C₂²	semidirect
74. #10597340	C₂²	semidirect
75. #10597340	C₂²	semidirect
76. #10597340	C₂²	semidirect
80. #10597339	C₂²	semidirect
81. #10597338	C₂²	semidirect
82. #10597338	C₂²	semidirect
83. #10597338	C₂²	semidirect
85. C₄⋊C₄×D₁₉	C₂²	semidirect
86. C₄⋊C₄×D₁₉	C₂²	semidirect
87. C₄⋊C₄×D₁₉	C₂²	semidirect
88. #10597336	C₂²	semidirect
89. #10597335	C₂²	semidirect
90. #10597334	C₂²	semidirect
91. #10597334	C₂²	semidirect
92. #10597333	C₂²	semidirect
93. #10597332	C₂²	semidirect
95. #10597331	C₂²	semidirect
97. #10597329	C₂²	semidirect
103. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
104. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
108. #10597325	C₂²	semidirect
109. #10597324	C₂²	semidirect
110. #10597324	C₂²	semidirect
111. #10597322	C₂²	semidirect
112. #10597321	C₂²	semidirect
113. #10597321	C₂²	semidirect
116. C₄×D₇₆	C₂²	semidirect
117. C₄×D₇₆	C₂²	semidirect
120. C₄×Dic₃₈	C₂²	semidirect
121. C₄×Dic₃₈	C₂²	semidirect
122. C₄×Dic₃₈	C₂²	semidirect
259. C₂²⋊D₁₉	#41	semidirect
337. #552	D₁₉	semidirect
381. #126	C₂×D₁₉	semidirect
384. #125	C₂×D₁₉	semidirect
385. #125	C₂×D₁₉	semidirect
416. C₂²⋊Q₈	C₂×D₁₉	semidirect
417. C₂²⋊Q₈	C₂×D₁₉	semidirect
430. C₄×Q₈	C₂×D₁₉	semidirect
452. #117	C₂×D₁₉	semidirect
453. #117	C₂×D₁₉	semidirect
459. C₂×C₄⋊C₄	C₂×D₁₉	semidirect
465. C₁₉	#3520	semidirect

Maximal subgroups

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

subgroup	index
#11927262	2
#11927250	2
#11927232	2
#11927219	2
#11927218	2
#11927207	2
#11927206	2
#11927203	2
#11927196	2
#11927195	2
#11927186	2
#11927160	2
#11927142	2
#11927138	2
#11927098	2
#11927079	2
#11927057	2
#11927056	2
C₂×#10597343	2
C₂²⋊Q₈×D₁₉	2
#11927024	2
C₄×D₄×D₁₉	2
C₁₉×#552	2
#3520	19