Subgroups — #14577678

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	#11927265	C₂	1	1	yes	maximal, characteristic, complemented
2	#11927248	C₂	1	2	yes	maximal, complemented
3	#11927229	C₂	1	1	yes	maximal, characteristic, complemented
4	#11927228	C₂	1	1	yes	maximal, characteristic, complemented
5	#11927221	C₂	1	2	yes	maximal, complemented
6	#11927220	C₂	1	2	yes	maximal, complemented
7	Q₈×C₂²⋊D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#11927205	C₂	1	1	yes	maximal, characteristic, complemented
9	#11927204	C₂	1	1	yes	maximal, characteristic, complemented
10	#11927196	C₂	1	1	yes	maximal, characteristic, complemented
11	#11927195	C₂	1	1	yes	maximal, characteristic, complemented
12	#11927184	C₂	1	2	yes	maximal, complemented
13	#11927164	C₂	1	2	yes	maximal, complemented
14	#11927141	C₂	1	2	yes	maximal, complemented
15	#11927140	C₂	1	2	yes	maximal, complemented
16	#11927096	C₂	1	1	yes	maximal, characteristic, complemented
17	#11927080	C₂	1	1	yes	maximal, characteristic, complemented
18	#11927057	C₂	1	1	yes	maximal, characteristic, complemented
19	#11927055	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²⋊Q₈×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
21	#11927025	C₂	1	2	yes	maximal, complemented
22	C₂×C₄×C₂²⋊D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₁₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
25	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₂²×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
27	C₂×#64545	C₂²	1	1	yes	characteristic, complemented
28	C₂×Q₈×D₁₉	C₂²	1	1	yes	characteristic, complemented
29	C₂×#64541	C₂²	1	2	yes	—
30	C₂×#64541	C₂²	1	1	yes	characteristic, complemented
31	C₂²×C₄×D₁₉	C₂²	1	1	yes	characteristic
32	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
33	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
34	C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
35	C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	complemented
36	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	complemented
39	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
41	#10597399	C₂²	1	2	yes	—
42	C₂×C₂²⋊Dic₁₉	C₂²	1	1	yes	characteristic
43	#10597393	C₂²	1	1	yes	characteristic, complemented
44	#10597393	C₂²	1	2	yes	complemented
45	#10597392	C₂²	1	1	yes	characteristic, complemented
46	#10597392	C₂²	1	2	yes	complemented
47	#10597392	C₂²	1	2	yes	complemented
48	#10597392	C₂²	1	1	yes	characteristic, complemented
49	Q₈×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
50	Q₈×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
51	#10597390	C₂²	1	1	yes	characteristic, complemented
52	#10597390	C₂²	1	2	yes	complemented
53	#10597376	C₂²	1	1	yes	characteristic
54	#10597376	C₂²	1	2	yes	—
55	#10597376	C₂²	1	1	yes	characteristic, complemented
56	#10597375	C₂²	1	2	yes	—
57	#10597375	C₂²	1	2	yes	complemented
58	#10597375	C₂²	1	2	yes	complemented
59	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	—
60	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
61	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
62	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
63	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	—
64	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
65	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
66	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
67	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
68	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
69	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
70	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
71	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	1	yes	characteristic
72	#10597372	C₂²	1	1	yes	characteristic, complemented
73	#10597372	C₂²	1	2	yes	complemented
74	#10597370	C₂²	1	1	yes	characteristic
75	#10597370	C₂²	1	1	yes	characteristic, complemented
76	#10597370	C₂²	1	2	yes	complemented
77	C₂×Dic₁₉⋊C₄	C₂²	1	1	yes	characteristic
78	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
79	#10597344	C₂²	1	2	yes	complemented
80	#10597344	C₂²	1	2	yes	complemented
81	#10597344	C₂²	1	2	yes	complemented
82	#10597343	C₂²	1	1	yes	characteristic, complemented
83	#10597342	C₂²	1	2	yes	complemented
84	#10597342	C₂²	1	2	yes	complemented
85	#10597342	C₂²	1	2	yes	complemented
86	#10597341	C₂²	1	1	yes	characteristic, complemented
87	#10597340	C₂²	1	2	yes	complemented
88	#10597340	C₂²	1	2	yes	complemented
89	#10597340	C₂²	1	2	yes	complemented
90	#10597339	C₂²	1	2	yes	complemented
91	#10597339	C₂²	1	1	yes	characteristic, complemented
92	#10597339	C₂²	1	2	yes	complemented
93	#10597338	C₂²	1	1	yes	characteristic, complemented
94	#10597338	C₂²	1	2	yes	complemented
95	#10597338	C₂²	1	2	yes	complemented
96	C₄⋊C₄×D₁₉	C₂²	1	2	yes	complemented
97	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic, complemented
98	C₄⋊C₄×D₁₉	C₂²	1	2	yes	complemented
99	#10597336	C₂²	1	1	yes	characteristic, complemented
100	#10597335	C₂²	1	2	yes	complemented
101	#10597335	C₂²	1	2	yes	complemented
102	#10597335	C₂²	1	2	yes	complemented
103	#10597334	C₂²	1	1	yes	characteristic, complemented
104	#10597333	C₂²	1	2	yes	complemented
105	#10597333	C₂²	1	1	yes	characteristic, complemented
106	#10597333	C₂²	1	2	yes	complemented
107	#10597332	C₂²	1	2	yes	—
108	#10597331	C₂²	1	2	yes	—
109	#10597331	C₂²	1	2	yes	complemented
110	#10597330	C₂²	1	2	yes	—
111	#10597330	C₂²	1	2	yes	—
112	#10597329	C₂²	1	2	yes	—
113	#10597329	C₂²	1	2	yes	complemented
114	#10597328	C₂²	1	2	yes	—
115	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	—
116	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	—
117	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	—
118	#10597325	C₂²	1	2	yes	complemented
119	#10597325	C₂²	1	2	yes	complemented
120	#10597324	C₂²	1	2	yes	—
121	#10597324	C₂²	1	2	yes	—
122	#10597323	C₂²	1	2	yes	—
123	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
124	C₂³×D₁₉	C₂³	1	1	yes	characteristic
125	C₂×Q₈×C₁₉	—	4	2	no	—
126	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
127	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
128	C₂×Q₈×C₁₉	C₂³	1	2	yes	—
129	C₂²×C₄×C₁₉	—	4	2	no	—
130	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
132	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
133	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
134	C₂²×C₄×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	1	yes	characteristic
138	C₂×C₂²⋊D₁₉	—	2	4	no	—
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	1	yes	characteristic
143	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
144	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
145	C₂×C₂²⋊D₁₉	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	1	yes	characteristic
149	#64545	—	4	2	no	—
150	Q₈×D₁₉	—	4	2	no	—
151	#64541	—	2	8	no	—
152	#64541	—	4	2	no	—
153	C₂×D₇₆	C₂³	1	1	yes	characteristic
154	C₂×D₇₆	C₂³	1	2	yes	—
155	C₂×D₇₆	C₂³	1	2	yes	—
156	C₂×C₄×D₁₉	—	4	2	no	—
157	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
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	2	yes	—
163	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
164	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
165	C₂×C₄×D₁₉	C₂³	1	2	yes	—
166	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
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	2	yes	—
171	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
172	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
173	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
174	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
175	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
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	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
181	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
183	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
184	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
185	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
186	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
187	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
189	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
190	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
191	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
192	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
193	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
194	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
200	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
201	C₄⋊Dic₁₉	C₂³	1	2	yes	—
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	2	yes	—
206	C₄⋊Dic₁₉	C₂³	1	2	yes	—
207	Dic₁₉⋊C₄	C₂³	1	2	yes	—
208	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
221	C₄×Dic₁₉	C₂³	1	2	yes	—
222	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
223	C₄×Dic₁₉	C₂³	1	2	yes	—
224	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
225	C₄×Dic₁₉	C₂³	1	2	yes	—
226	C₄×Dic₁₉	C₂³	1	2	yes	—
227	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
228	C₄×Dic₁₉	C₂³	1	2	yes	—
229	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
230	C₂³×C₁₉	—	2	2	no	—
231	C₂³×C₁₉	—	2	2	no	—
232	C₂³×C₁₉	—	4	1	no	—
233	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
234	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
235	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
236	C₂²×D₁₉	—	2	2	no	—
237	C₂²×D₁₉	—	2	2	no	—
238	C₂²×D₁₉	—	4	1	no	—
239	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
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	C₂×C₄×C₁₉	—	2	4	no	—
246	C₂×C₄×C₁₉	—	2	2	no	—
247	C₂×C₄×C₁₉	—	2	2	no	—
248	C₂×C₄×C₁₉	—	2	2	no	—
249	C₂×C₄×C₁₉	—	4	1	no	—
250	C₂×C₄×C₁₉	—	4	1	no	—
251	C₂×C₄×C₁₉	—	4	1	no	—
252	C₂×C₄×C₁₉	—	4	2	no	—
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	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
257	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
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	C₂²⋊D₁₉	—	2	4	no	—
262	C₂²⋊D₁₉	—	2	2	no	—
263	C₂²⋊D₁₉	—	2	4	no	—
264	C₂²⋊D₁₉	—	2	2	no	—
265	C₂²⋊D₁₉	—	2	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	C₂⁴	1	1	yes	characteristic
272	C₂×Dic₁₉	C₂⁴	1	2	yes	—
273	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
274	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
275	C₂×Dic₁₉	C₂⁴	1	2	yes	—
276	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
277	C₂×Dic₁₉	C₂⁴	1	2	yes	—
278	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
279	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
280	D₇₆	—	2	4	no	—
281	D₇₆	—	2	2	no	—
282	D₇₆	—	4	2	no	—
283	C₄×D₁₉	—	2	4	no	—
284	C₄×D₁₉	—	2	2	no	—
285	C₄×D₁₉	—	2	2	no	—
286	C₄×D₁₉	—	2	4	no	—
287	C₄×D₁₉	—	4	1	no	—
288	C₄×D₁₉	—	4	1	no	—
289	C₄×D₁₉	—	4	2	no	—
290	C₄×D₁₉	—	4	2	no	—
291	C₄×D₁₉	—	4	2	no	—
292	Dic₃₈	—	2	2	no	—
293	Dic₃₈	—	2	4	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	—	2	1	no	—
302	C₂²×C₁₉	—	2	1	no	—
303	C₂²×C₁₉	—	4	4	no	—
304	C₂²×C₁₉	C₂×#41	1	2	yes	—
305	C₂²×C₁₉	2₋¹⁺⁴	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	1	no	—
311	C₂×D₁₉	—	2	1	no	—
312	C₂×D₁₉	—	2	2	no	—
313	C₂×D₁₉	—	2	2	no	—
314	C₂×D₁₉	—	2	1	no	—
315	C₂×D₁₉	—	4	4	no	—
316	C₂×D₁₉	C₂×#41	1	2	yes	—
317	C₄×C₁₉	—	2	2	no	—
318	C₄×C₁₉	—	2	2	no	—
319	C₄×C₁₉	—	2	2	no	—
320	C₄×C₁₉	—	2	1	no	—
321	C₄×C₁₉	—	2	1	no	—
322	C₄×C₁₉	—	2	2	no	—
323	C₄×C₁₉	—	2	1	no	—
324	C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
325	Dic₁₉	—	2	2	no	—
326	Dic₁₉	—	2	1	no	—
327	Dic₁₉	—	2	2	no	—
328	Dic₁₉	—	2	1	no	—
329	Dic₁₉	—	2	1	no	—
330	Dic₁₉	—	2	1	no	—
331	Dic₁₉	—	2	1	no	—
332	Dic₁₉	—	2	2	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	—	19	1	no	—
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	D₁₉	1	1	yes	characteristic, complemented
355	#520	—	19	2	no	—
356	C₂×C₄×D₄	—	19	1	no	—
357	C₂×C₁₉	—	2	2	no	—
358	C₂×C₁₉	—	2	2	no	—
359	C₂×C₁₉	—	4	1	no	—
360	C₂×C₁₉	C₂²×#41	1	1	yes	characteristic
361	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
362	C₂×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
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	C₂×D₁₉	1	1	yes	characteristic, complemented
371	C₂²×D₄	—	19	1	no	—
372	C₂³×C₄	—	19	1	no	—
373	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
374	C₄⋊Q₈	—	19	1	no	—
375	C₄⋊Q₈	—	19	2	no	—
376	C₄⋊Q₈	—	19	1	no	—
377	#126	—	19	2	no	—
378	#126	—	19	2	no	—
379	#126	—	19	2	no	—
380	#126	—	19	2	no	—
381	#126	—	19	2	no	—
382	#125	—	19	1	no	—
383	#125	—	19	2	no	—
384	#125	—	19	2	no	—
385	#125	—	19	2	no	—
386	#124	—	19	1	no	—
387	#124	—	19	2	no	—
388	#124	—	19	2	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	—	19	2	no	—
399	C₂²⋊Q₈	—	19	1	no	—
400	C₂²⋊Q₈	—	19	1	no	—
401	C₂²⋊Q₈	—	19	2	no	—
402	C₂²⋊Q₈	—	19	2	no	—
403	C₂²⋊Q₈	—	19	1	no	—
404	C₂²⋊Q₈	—	19	1	no	—
405	C₂²⋊Q₈	—	19	2	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	—	19	2	no	—
412	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
413	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
414	C₂²⋊Q₈	C₂×D₁₉	1	2	yes	—
415	C₂²⋊Q₈	C₂×D₁₉	1	2	yes	complemented
416	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
417	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
418	#121	—	19	1	no	—
419	#121	—	19	2	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	1	no	—
428	C₄×Q₈	—	19	2	no	—
429	C₄×Q₈	—	19	2	no	—
430	C₄×Q₈	—	19	1	no	—
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	1	no	—
436	C₄×D₄	—	19	1	no	—
437	C₄×D₄	—	19	1	no	—
438	C₄×D₄	—	19	1	no	—
439	C₄×D₄	—	19	2	no	—
440	C₄×D₄	—	19	2	no	—
441	C₄×D₄	—	19	2	no	—
442	C₄×D₄	—	19	2	no	—
443	C₄×D₄	—	19	2	no	—
444	C₄×D₄	—	19	2	no	—
445	C₄×D₄	—	19	1	no	—
446	C₄×D₄	—	19	2	no	—
447	C₄×D₄	—	19	2	no	—
448	#117	—	19	2	no	—
449	#117	—	19	1	no	—
450	#117	—	19	2	no	—
451	#117	—	19	2	no	—
452	#117	—	19	1	no	—
453	#117	—	19	2	no	—
454	C₂×C₄⋊C₄	—	19	1	no	—
455	C₂×C₄⋊C₄	—	19	2	no	—
456	C₂×C₄⋊C₄	—	19	2	no	—
457	C₂×C₄⋊C₄	—	19	1	no	—
458	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	complemented
459	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic, complemented
460	C₂×C₂²⋊C₄	—	19	1	no	—
461	C₂×C₂²⋊C₄	—	19	1	no	—
462	C₂×C₂²⋊C₄	—	19	2	no	—
463	C₂×C₂²⋊C₄	C₂×D₁₉	1	2	yes	—
464	C₂×C₄²	—	19	1	no	—
465	C₁₉	#3520	1	1	yes	characteristic, complemented, Sylow
466	C₂⁴	—	19	1	no	—
467	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
468	#41	—	38	8	no	—
469	#41	—	76	2	no	—
470	#41	—	76	2	no	—
471	C₂×Q₈	—	4	2	no	—
472	C₂×Q₈	—	19	2	no	—
473	C₂×Q₈	—	19	1	no	—
474	C₂×Q₈	—	19	2	no	—
475	C₂×Q₈	—	76	2	no	—
476	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
477	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
478	C₂×Q₈	C₂²×D₁₉	1	2	yes	—
479	C₂×D₄	—	19	1	no	—
480	C₂×D₄	—	19	2	no	—
481	C₂×D₄	—	19	2	no	—
482	C₂×D₄	—	19	1	no	—
483	C₂×D₄	—	19	1	no	—
484	C₂×D₄	—	19	1	no	—
485	C₂×D₄	—	19	2	no	—
486	C₂×D₄	—	19	2	no	—
487	C₂×D₄	—	19	1	no	—
488	C₂×D₄	—	19	2	no	—
489	C₂×D₄	—	38	4	no	—
490	C₂²×C₄	—	4	2	no	—
491	C₂²×C₄	—	19	1	no	—
492	C₂²×C₄	—	19	1	no	—
493	C₂²×C₄	—	19	1	no	—
494	C₂²×C₄	—	19	2	no	—
495	C₂²×C₄	—	19	2	no	—
496	C₂²×C₄	—	19	1	no	—
497	C₂²×C₄	—	19	1	no	—
498	C₂²×C₄	—	19	2	no	—
499	C₂²×C₄	—	19	1	no	—
500	C₂²×C₄	—	19	2	no	—
501	C₂²×C₄	—	19	2	no	—
502	C₂²×C₄	—	19	1	no	—
503	C₂²×C₄	—	76	2	no	—
504	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
505	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
506	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
507	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
508	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
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	1	no	—
515	C₄⋊C₄	—	19	1	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	2	no	—
525	C₄⋊C₄	—	19	2	no	—
526	C₄⋊C₄	—	19	2	no	—
527	C₄⋊C₄	—	19	1	no	—
528	C₄⋊C₄	—	19	2	no	—
529	C₄⋊C₄	—	19	1	no	—
530	C₄⋊C₄	—	19	2	no	—
531	C₄⋊C₄	—	19	2	no	—
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	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	2	no	—
541	C₂²⋊C₄	—	19	1	no	—
542	C₂²⋊C₄	—	19	1	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	1	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	—	19	2	no	—
560	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
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	1	no	—
568	C₄²	—	19	2	no	—
569	C₄²	—	19	2	no	—
570	C₄²	—	19	2	no	—
571	C₄²	—	19	2	no	—
572	C₄²	—	19	2	no	—
573	C₂³	—	2	2	no	—
574	C₂³	—	2	2	no	—
575	C₂³	—	4	1	no	—
576	C₂³	—	19	1	no	—
577	C₂³	—	19	1	no	—
578	C₂³	—	19	2	no	—
579	C₂³	—	38	2	no	—
580	C₂³	—	38	2	no	—
581	C₂³	—	76	1	no	—
582	C₂³	C₂³×D₁₉	1	1	yes	characteristic
583	C₂³	C₂³×D₁₉	1	1	yes	characteristic
584	C₂³	C₂³×D₁₉	1	1	yes	characteristic
585	Q₈	—	2	2	no	—
586	Q₈	—	2	2	no	—
587	Q₈	—	4	2	no	—
588	Q₈	—	38	4	no	—
589	Q₈	—	38	2	no	—
590	Q₈	—	76	2	no	—
591	D₄	—	19	4	no	—
592	D₄	—	38	4	no	—
593	D₄	—	38	2	no	—
594	D₄	—	38	2	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	—	2	2	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	2	no	—
609	C₂×C₄	—	19	1	no	—
610	C₂×C₄	—	19	1	no	—
611	C₂×C₄	—	19	2	no	—
612	C₂×C₄	—	19	1	no	—
613	C₂×C₄	—	19	2	no	—
614	C₂×C₄	—	19	1	no	—
615	C₂×C₄	—	19	1	no	—
616	C₂×C₄	—	19	2	no	—
617	C₂×C₄	—	19	1	no	—
618	C₂×C₄	—	38	4	no	—
619	C₂×C₄	—	38	4	no	—
620	C₂×C₄	—	38	2	no	—
621	C₂×C₄	—	38	2	no	—
622	C₂×C₄	—	38	2	no	—
623	C₂×C₄	—	38	2	no	—
624	C₂×C₄	—	76	1	no	—
625	C₂×C₄	—	76	1	no	—
626	C₂×C₄	—	76	2	no	—
627	C₂×C₄	—	76	2	no	—
628	C₂×C₄	—	76	2	no	—
629	C₂×C₄	—	76	1	no	—
630	C₂×C₄	C₂³×D₁₉	1	2	yes	—
631	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
632	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
633	C₂×C₄	C₂³×D₁₉	1	2	yes	—
634	C₂×C₄	C₂³×D₁₉	1	2	yes	—
635	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
636	C₂×C₄	C₂³×D₁₉	1	2	yes	—
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	—	2	1	no	—
644	C₂²	—	2	1	no	—
645	C₂²	—	4	4	no	—
646	C₂²	—	19	2	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	#10597433	1	2	yes	—
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	2	no	—
666	C₄	—	19	2	no	—
667	C₄	—	38	1	no	—
668	C₄	—	38	2	no	—
669	C₄	—	38	1	no	—
670	C₄	—	38	1	no	—
671	C₄	—	38	2	no	—
672	C₄	—	38	1	no	—
673	C₄	—	38	1	no	—
674	C₄	—	38	2	no	—
675	C₄	#10597430	1	2	yes	—
676	C₂	—	2	2	no	—
677	C₂	—	2	2	no	—
678	C₂	—	4	1	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×#10597430	1	1	yes	characteristic
684	C₂	C₂×#10597433	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₂×C₁₉×C₂²⋊Q₈	C₂
hypercenter	C₂×C₂²⋊Q₈	D₁₉
hypocenter	C₁₉	#3520
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. #11927265	C₂	semidirect
2. #11927248	C₂	semidirect
3. #11927229	C₂	semidirect
4. #11927228	C₂	semidirect
5. #11927221	C₂	semidirect
6. #11927220	C₂	semidirect
7. Q₈×C₂²⋊D₁₉	C₂	semidirect
8. #11927205	C₂	semidirect
9. #11927204	C₂	semidirect
10. #11927196	C₂	semidirect
11. #11927195	C₂	semidirect
12. #11927184	C₂	semidirect
13. #11927164	C₂	semidirect
14. #11927141	C₂	semidirect
15. #11927140	C₂	semidirect
16. #11927096	C₂	semidirect
17. #11927080	C₂	semidirect
18. #11927057	C₂	semidirect
19. #11927055	C₂	semidirect
20. C₂²⋊Q₈×D₁₉	C₂	semidirect
21. #11927025	C₂	semidirect
22. C₂×C₄×C₂²⋊D₁₉	C₂	semidirect
23. C₂×C₁₉×C₂²⋊Q₈	C₂	semidirect
24. C₂²×Q₈×C₁₉	C₂²	semidirect
27. C₂×#64545	C₂²	semidirect
28. C₂×Q₈×D₁₉	C₂²	semidirect
30. C₂×#64541	C₂²	semidirect
35. C₁₉×C₂²⋊Q₈	C₂²	semidirect
36. C₁₉×C₂²⋊Q₈	C₂²	semidirect
37. C₁₉×C₂²⋊Q₈	C₂²	semidirect
38. C₂×C₄⋊C₄×C₁₉	C₂²	semidirect
39. C₂×C₄⋊C₄×C₁₉	C₂²	semidirect
43. #10597393	C₂²	semidirect
44. #10597393	C₂²	semidirect
45. #10597392	C₂²	semidirect
46. #10597392	C₂²	semidirect
47. #10597392	C₂²	semidirect
48. #10597392	C₂²	semidirect
49. Q₈×Dic₁₉	C₂²	semidirect
50. Q₈×Dic₁₉	C₂²	semidirect
51. #10597390	C₂²	semidirect
52. #10597390	C₂²	semidirect
55. #10597376	C₂²	semidirect
57. #10597375	C₂²	semidirect
58. #10597375	C₂²	semidirect
69. C₄×C₂²⋊D₁₉	C₂²	semidirect
70. C₄×C₂²⋊D₁₉	C₂²	semidirect
72. #10597372	C₂²	semidirect
73. #10597372	C₂²	semidirect
75. #10597370	C₂²	semidirect
76. #10597370	C₂²	semidirect
79. #10597344	C₂²	semidirect
80. #10597344	C₂²	semidirect
81. #10597344	C₂²	semidirect
82. #10597343	C₂²	semidirect
83. #10597342	C₂²	semidirect
84. #10597342	C₂²	semidirect
85. #10597342	C₂²	semidirect
86. #10597341	C₂²	semidirect
87. #10597340	C₂²	semidirect
88. #10597340	C₂²	semidirect
89. #10597340	C₂²	semidirect
90. #10597339	C₂²	semidirect
91. #10597339	C₂²	semidirect
92. #10597339	C₂²	semidirect
93. #10597338	C₂²	semidirect
94. #10597338	C₂²	semidirect
95. #10597338	C₂²	semidirect
96. C₄⋊C₄×D₁₉	C₂²	semidirect
97. C₄⋊C₄×D₁₉	C₂²	semidirect
98. C₄⋊C₄×D₁₉	C₂²	semidirect
99. #10597336	C₂²	semidirect
100. #10597335	C₂²	semidirect
101. #10597335	C₂²	semidirect
102. #10597335	C₂²	semidirect
103. #10597334	C₂²	semidirect
104. #10597333	C₂²	semidirect
105. #10597333	C₂²	semidirect
106. #10597333	C₂²	semidirect
109. #10597331	C₂²	semidirect
113. #10597329	C₂²	semidirect
118. #10597325	C₂²	semidirect
119. #10597325	C₂²	semidirect
267. C₂²⋊D₁₉	#41	semidirect
354. C₂×C₂²⋊Q₈	D₁₉	semidirect
370. C₂²×Q₈	C₂×D₁₉	semidirect
415. C₂²⋊Q₈	C₂×D₁₉	semidirect
416. C₂²⋊Q₈	C₂×D₁₉	semidirect
417. C₂²⋊Q₈	C₂×D₁₉	semidirect
458. C₂×C₄⋊C₄	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
#11927265	2
#11927248	2
#11927229	2
#11927228	2
#11927221	2
#11927220	2
Q₈×C₂²⋊D₁₉	2
#11927205	2
#11927204	2
#11927196	2
#11927195	2
#11927184	2
#11927164	2
#11927141	2
#11927140	2
#11927096	2
#11927080	2
#11927057	2
#11927055	2
C₂²⋊Q₈×D₁₉	2
#11927025	2
C₂×C₄×C₂²⋊D₁₉	2
C₂×C₁₉×C₂²⋊Q₈	2
#3520	19