Subgroups — #14578206

Order 2432.

1032 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927296	C₂	1	2	yes	maximal, complemented
2	#11927291	C₂	1	2	yes	maximal, complemented
3	#11927266	C₂	1	1	yes	maximal, characteristic, complemented
4	#11927264	C₂	1	1	yes	maximal, characteristic, complemented
5	#11927219	C₂	1	2	yes	maximal, complemented
6	#11927217	C₂	1	2	yes	maximal, complemented
7	Q₈×D₇₆	C₂	1	1	yes	maximal, characteristic, complemented
8	#11927207	C₂	1	1	yes	maximal, characteristic, complemented
9	#11927204	C₂	1	1	yes	maximal, characteristic, complemented
10	#11927200	C₂	1	1	yes	maximal, characteristic, complemented
11	#11927191	C₂	1	1	yes	maximal, characteristic, complemented
12	#11927189	C₂	1	1	yes	maximal, characteristic, complemented
13	#11927169	C₂	1	2	yes	maximal, complemented
14	#11927168	C₂	1	1	yes	maximal, characteristic, complemented
15	#11927167	C₂	1	2	yes	maximal, complemented
16	#11927163	C₂	1	2	yes	maximal, complemented
17	#11927128	C₂	1	2	yes	maximal, complemented
18	#11927120	C₂	1	1	yes	maximal, characteristic, complemented
19	#11927114	C₂	1	1	yes	maximal, characteristic, complemented
20	#11927099	C₂	1	1	yes	maximal, characteristic, complemented
21	#11927072	C₂	1	1	yes	maximal, characteristic, complemented
22	#124×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₉×#542	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×Q₈×D₁₉	C₂²	1	1	yes	characteristic
25	C₂×Q₈×D₁₉	C₂²	1	1	yes	characteristic, complemented
26	C₂×#64543	C₂²	1	1	yes	characteristic
27	C₂×D₄×D₁₉	C₂²	1	1	yes	characteristic
28	C₂×#64541	C₂²	1	1	yes	characteristic
29	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
30	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₁₉×#126	C₂²	1	2	yes	complemented
32	C₁₉×#124	C₂²	1	1	yes	characteristic
33	C₁₉×#124	C₂²	1	2	yes	complemented
34	C₁₉×#123	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
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	#10597393	C₂²	1	1	yes	characteristic
42	#10597393	C₂²	1	2	yes	complemented
43	#10597392	C₂²	1	2	yes	—
44	#10597392	C₂²	1	2	yes	complemented
45	Q₈×Dic₁₉	C₂²	1	2	yes	complemented
46	#10597390	C₂²	1	1	yes	characteristic, complemented
47	#10597385	C₂²	1	2	yes	complemented
48	#10597384	C₂²	1	2	yes	—
49	#10597383	C₂²	1	2	yes	—
50	#10597382	C₂²	1	1	yes	characteristic
51	#10597382	C₂²	1	1	yes	characteristic
52	D₄×Dic₁₉	C₂²	1	2	yes	complemented
53	#10597376	C₂²	1	2	yes	—
54	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
55	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic, complemented
56	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	—
57	#10597372	C₂²	1	2	yes	complemented
58	#10597370	C₂²	1	2	yes	complemented
59	#10597344	C₂²	1	2	yes	complemented
60	#10597344	C₂²	1	1	yes	characteristic, complemented
61	#10597344	C₂²	1	2	yes	complemented
62	#10597343	C₂²	1	1	yes	characteristic
63	#10597343	C₂²	1	1	yes	characteristic
64	#10597343	C₂²	1	2	yes	—
65	#10597343	C₂²	1	2	yes	complemented
66	#10597343	C₂²	1	2	yes	complemented
67	#10597343	C₂²	1	2	yes	complemented
68	#10597343	C₂²	1	1	yes	characteristic, complemented
69	#10597342	C₂²	1	1	yes	characteristic
70	#10597342	C₂²	1	2	yes	—
71	#10597342	C₂²	1	2	yes	complemented
72	#10597342	C₂²	1	2	yes	complemented
73	#10597341	C₂²	1	1	yes	characteristic
74	#10597340	C₂²	1	1	yes	characteristic
75	#10597340	C₂²	1	2	yes	complemented
76	#10597339	C₂²	1	1	yes	characteristic
77	#10597339	C₂²	1	2	yes	complemented
78	#10597338	C₂²	1	2	yes	—
79	#10597336	C₂²	1	2	yes	complemented
80	#10597335	C₂²	1	1	yes	characteristic, complemented
81	#10597334	C₂²	1	2	yes	complemented
82	#10597333	C₂²	1	1	yes	characteristic, complemented
83	#10597333	C₂²	1	1	yes	characteristic, complemented
84	#10597333	C₂²	1	1	yes	characteristic, complemented
85	#10597332	C₂²	1	2	yes	—
86	#10597332	C₂²	1	2	yes	complemented
87	#10597332	C₂²	1	2	yes	complemented
88	#10597331	C₂²	1	2	yes	—
89	#10597331	C₂²	1	2	yes	—
90	#10597331	C₂²	1	1	yes	characteristic, complemented
91	#10597331	C₂²	1	2	yes	complemented
92	#10597331	C₂²	1	2	yes	complemented
93	#10597330	C₂²	1	1	yes	characteristic
94	#10597330	C₂²	1	2	yes	complemented
95	#10597329	C₂²	1	2	yes	—
96	#10597329	C₂²	1	1	yes	characteristic
97	#10597329	C₂²	1	2	yes	complemented
98	#10597329	C₂²	1	2	yes	complemented
99	#10597328	C₂²	1	2	yes	—
100	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	—
101	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	—
102	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	—
103	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	—
104	#10597325	C₂²	1	2	yes	complemented
105	#10597325	C₂²	1	1	yes	characteristic, complemented
106	#10597325	C₂²	1	2	yes	complemented
107	#10597324	C₂²	1	2	yes	complemented
108	#10597324	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
113	#10597321	C₂²	1	1	yes	characteristic
114	C₄×D₇₆	C₂²	1	1	yes	characteristic
115	C₄×D₇₆	C₂²	1	2	yes	—
116	#10597318	C₂²	1	1	yes	characteristic, complemented
117	#10597318	C₂²	1	2	yes	complemented
118	C₄²×D₁₉	C₂²	1	1	yes	characteristic
119	#10597315	C₂²	1	2	yes	complemented
120	#10597315	C₂²	1	1	yes	characteristic, complemented
121	#10597315	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₉	C₂³	1	2	yes	—
124	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
125	C₂×Q₈×C₁₉	C₂³	1	2	yes	—
126	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
127	C₂×D₄×C₁₉	C₂³	1	2	yes	—
128	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
131	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
135	C₂²×Dic₁₉	C₂³	1	2	yes	—
136	C₂²×Dic₁₉	C₂³	1	2	yes	—
137	Q₈×D₁₉	—	4	2	no	—
138	Q₈×D₁₉	—	4	2	no	—
139	#64543	—	4	2	no	—
140	D₄×D₁₉	—	4	2	no	—
141	#64541	—	4	2	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×C₄×D₁₉	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
147	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₁₉	C₂³	1	2	yes	—
149	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₁₉	C₂³	1	2	yes	—
151	C₂×C₄×D₁₉	C₂³	1	2	yes	—
152	C₂×C₄×D₁₉	C₂³	1	2	yes	—
153	C₂×Dic₃₈	—	4	2	no	—
154	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
155	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
156	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
157	C₂×Dic₃₈	C₂³	1	2	yes	—
158	C₂×Dic₃₈	C₂³	1	2	yes	—
159	C₂×Dic₃₈	C₂³	1	2	yes	—
160	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
161	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
162	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
163	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
164	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
165	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
166	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
167	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
168	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
169	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
170	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
171	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
172	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
173	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
174	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
175	C₄²×C₁₉	C₂³	1	1	yes	characteristic
176	C₄²×C₁₉	C₂³	1	1	yes	characteristic
177	C₄²×C₁₉	C₂³	1	2	yes	—
178	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
179	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
180	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
181	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
182	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
183	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
184	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
185	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
186	(C₂×D₁₉)⋊C₄	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	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	2	yes	—
196	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
197	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
203	C₄⋊Dic₁₉	C₂³	1	2	yes	—
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	1	yes	characteristic
208	C₄⋊Dic₁₉	C₂³	1	2	yes	—
209	C₄⋊Dic₁₉	C₂³	1	2	yes	—
210	Dic₁₉⋊C₄	C₂³	1	2	yes	—
211	Dic₁₉⋊C₄	C₂³	1	2	yes	—
212	Dic₁₉⋊C₄	C₂³	1	2	yes	—
213	Dic₁₉⋊C₄	C₂³	1	2	yes	—
214	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
215	Dic₁₉⋊C₄	C₂³	1	2	yes	—
216	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
217	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
218	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
219	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	C₂³×C₁₉	C₂⁴	1	2	yes	—
229	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
230	C₂²×D₁₉	—	2	4	no	—
231	C₂²×D₁₉	—	4	2	no	—
232	C₂²×D₁₉	—	4	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	Q₈×C₁₉	—	2	2	no	—
237	Q₈×C₁₉	—	4	2	no	—
238	D₄×C₁₉	—	2	2	no	—
239	D₄×C₁₉	—	4	2	no	—
240	C₂×C₄×C₁₉	—	2	2	no	—
241	C₂×C₄×C₁₉	—	4	2	no	—
242	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
243	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
245	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
246	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
247	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
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	—	4	2	no	—
253	C₂²⋊D₁₉	—	4	2	no	—
254	C₂²⋊D₁₉	—	4	2	no	—
255	C₂²⋊D₁₉	—	4	1	no	—
256	C₂×Dic₁₉	—	4	2	no	—
257	C₂×Dic₁₉	—	4	2	no	—
258	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
260	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
261	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
262	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
263	C₂×Dic₁₉	C₂⁴	1	2	yes	—
264	C₂×Dic₁₉	C₂⁴	1	2	yes	—
265	C₂×Dic₁₉	C₂⁴	1	2	yes	—
266	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
267	D₇₆	—	2	2	no	—
268	D₇₆	—	2	2	no	—
269	D₇₆	—	4	2	no	—
270	C₄×D₁₉	—	2	2	no	—
271	C₄×D₁₉	—	2	2	no	—
272	C₄×D₁₉	—	2	2	no	—
273	C₄×D₁₉	—	4	2	no	—
274	C₄×D₁₉	—	4	1	no	—
275	C₄×D₁₉	—	4	2	no	—
276	C₄×D₁₉	—	4	2	no	—
277	C₄×D₁₉	—	4	2	no	—
278	Dic₃₈	—	2	2	no	—
279	Dic₃₈	—	2	2	no	—
280	Dic₃₈	—	2	2	no	—
281	Dic₃₈	—	4	2	no	—
282	Dic₃₈	—	4	1	no	—
283	Dic₃₈	—	4	2	no	—
284	Dic₃₈	—	4	2	no	—
285	#3561	—	19	1	no	maximal, Sylow
286	C₂²×C₁₉	—	2	1	no	—
287	C₂²×C₁₉	—	2	2	no	—
288	C₂²×C₁₉	—	2	1	no	—
289	C₂²×C₁₉	—	2	2	no	—
290	C₂²×C₁₉	—	2	1	no	—
291	C₂²×C₁₉	—	2	2	no	—
292	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
293	C₂×D₁₉	—	2	1	no	—
294	C₂×D₁₉	—	2	1	no	—
295	C₂×D₁₉	—	2	1	no	—
296	C₂×D₁₉	—	2	2	no	—
297	C₂×D₁₉	—	2	1	no	—
298	C₂×D₁₉	—	2	2	no	—
299	C₂×D₁₉	—	2	2	no	—
300	C₂×D₁₉	—	2	1	no	—
301	C₂×D₁₉	—	8	4	no	—
302	C₂×D₁₉	2₋¹⁺⁴	1	2	yes	—
303	C₄×C₁₉	—	2	1	no	—
304	C₄×C₁₉	—	2	2	no	—
305	C₄×C₁₉	—	2	1	no	—
306	C₄×C₁₉	—	2	1	no	—
307	C₄×C₁₉	—	2	1	no	—
308	C₄×C₁₉	—	2	2	no	—
309	C₄×C₁₉	—	2	1	no	—
310	C₄×C₁₉	—	2	2	no	—
311	C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
312	Dic₁₉	—	2	2	no	—
313	Dic₁₉	—	2	2	no	—
314	Dic₁₉	—	2	2	no	—
315	Dic₁₉	—	2	1	no	—
316	Dic₁₉	—	2	1	no	—
317	Dic₁₉	—	2	1	no	—
318	Dic₁₉	—	2	1	no	—
319	Dic₁₉	—	2	1	no	—
320	Dic₁₉	—	2	1	no	—
321	#563	—	19	2	no	—
322	#562	—	19	2	no	—
323	#556	—	19	1	no	—
324	#556	—	19	1	no	—
325	#551	—	19	2	no	—
326	#551	—	19	2	no	—
327	D₄×Q₈	—	19	1	no	—
328	D₄×Q₈	—	19	1	no	—
329	#548	—	19	1	no	—
330	#548	—	19	1	no	—
331	#546	—	19	1	no	—
332	#546	—	19	1	no	—
333	#543	—	19	2	no	—
334	#542	—	19	1	no	—
335	#542	—	19	2	no	—
336	#542	—	19	2	no	—
337	#542	D₁₉	1	1	yes	characteristic, complemented
338	#538	—	19	2	no	—
339	#536	—	19	1	no	—
340	#536	—	19	1	no	—
341	#533	—	19	1	no	—
342	#529	—	19	1	no	—
343	C₂×#124	—	19	1	no	—
344	C₂×C₁₉	—	4	2	no	—
345	C₂×C₁₉	—	4	1	no	—
346	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
347	C₂×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
348	C₂×C₁₉	#585	1	1	yes	characteristic
349	D₁₉	—	2	2	no	—
350	D₁₉	—	4	1	no	—
351	D₁₉	—	4	2	no	—
352	C₂×#41	—	19	1	no	—
353	C₂×#41	—	19	1	no	—
354	C₂²×Q₈	—	19	1	no	—
355	C₂²×Q₈	—	19	1	no	—
356	C₂²×Q₈	—	19	1	no	—
357	C₂²×D₄	—	19	1	no	—
358	C₄⋊Q₈	—	19	1	no	—
359	C₄⋊Q₈	—	19	2	no	—
360	C₄⋊Q₈	—	19	1	no	—
361	C₄⋊Q₈	—	19	1	no	—
362	C₄⋊Q₈	—	19	2	no	—
363	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
364	#126	—	19	1	no	—
365	#126	—	19	2	no	—
366	#126	—	19	2	no	—
367	#126	—	19	1	no	—
368	#126	—	19	2	no	—
369	#126	—	19	2	no	—
370	#126	—	19	2	no	—
371	#126	C₂×D₁₉	1	2	yes	complemented
372	#125	—	19	1	no	—
373	#125	—	19	2	no	—
374	#124	—	19	1	no	—
375	#124	—	19	2	no	—
376	#124	—	19	1	no	—
377	#124	—	19	1	no	—
378	#124	—	19	2	no	—
379	#124	—	19	2	no	—
380	#124	—	19	1	no	—
381	#124	—	19	2	no	—
382	#124	—	19	2	no	—
383	#124	—	19	1	no	—
384	#124	—	19	1	no	—
385	#124	C₂×D₁₉	1	1	yes	characteristic
386	#124	C₂×D₁₉	1	2	yes	complemented
387	#123	—	19	1	no	—
388	#123	—	19	2	no	—
389	#123	—	19	1	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	C₂×D₁₉	1	2	yes	complemented
397	C₂²⋊Q₈	—	19	2	no	—
398	C₂²⋊Q₈	—	19	2	no	—
399	C₂²⋊Q₈	—	19	2	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	2	no	—
405	C₂²⋊Q₈	—	19	1	no	—
406	C₂²⋊Q₈	—	19	2	no	—
407	C₂²⋊Q₈	—	19	2	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	—	19	2	no	—
413	C₂²⋊Q₈	—	19	2	no	—
414	C₂²⋊Q₈	—	19	2	no	—
415	C₂²⋊Q₈	C₂×D₁₉	1	2	yes	complemented
416	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
417	#121	—	19	2	no	—
418	#121	—	19	2	no	—
419	#121	—	19	2	no	—
420	#121	—	19	1	no	—
421	#121	—	19	1	no	—
422	#121	—	19	2	no	—
423	#121	C₂×D₁₉	1	1	yes	characteristic
424	#120	—	19	2	no	—
425	#120	—	19	2	no	—
426	C₄×Q₈	—	19	2	no	—
427	C₄×Q₈	—	19	1	no	—
428	C₄×Q₈	—	19	1	no	—
429	C₄×Q₈	—	19	1	no	—
430	C₄×Q₈	—	19	1	no	—
431	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
432	C₄×D₄	—	19	2	no	—
433	C₄×D₄	—	19	1	no	—
434	C₄×D₄	—	19	1	no	—
435	C₄×D₄	—	19	1	no	—
436	C₄×D₄	—	19	2	no	—
437	C₄×D₄	—	19	2	no	—
438	C₄×D₄	—	19	1	no	—
439	C₄×D₄	—	19	2	no	—
440	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
441	#117	—	19	2	no	—
442	#117	—	19	2	no	—
443	#117	—	19	1	no	—
444	#117	—	19	2	no	—
445	#117	C₂×D₁₉	1	1	yes	characteristic, complemented
446	C₂×C₂²⋊C₄	—	19	2	no	—
447	C₂×C₂²⋊C₄	—	19	2	no	—
448	C₂×C₂²⋊C₄	—	19	2	no	—
449	C₂×C₂²⋊C₄	—	19	2	no	—
450	C₂×C₄²	—	19	1	no	—
451	C₁₉	#3561	1	1	yes	characteristic, complemented, Sylow
452	C₂⁴	—	19	2	no	—
453	#41	—	76	2	no	—
454	#41	—	76	2	no	—
455	C₂×Q₈	—	19	1	no	—
456	C₂×Q₈	—	19	1	no	—
457	C₂×Q₈	—	19	1	no	—
458	C₂×Q₈	—	19	1	no	—
459	C₂×Q₈	—	19	2	no	—
460	C₂×Q₈	—	19	2	no	—
461	C₂×Q₈	—	19	2	no	—
462	C₂×Q₈	—	76	2	no	—
463	C₂×Q₈	—	76	2	no	—
464	C₂×Q₈	—	76	2	no	—
465	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
466	C₂×Q₈	C₂²×D₁₉	1	2	yes	—
467	C₂×D₄	—	19	1	no	—
468	C₂×D₄	—	19	1	no	—
469	C₂×D₄	—	19	2	no	—
470	C₂×D₄	—	19	2	no	—
471	C₂×D₄	—	19	2	no	—
472	C₂×D₄	—	19	1	no	—
473	C₂×D₄	—	19	1	no	—
474	C₂×D₄	—	19	2	no	—
475	C₂×D₄	—	76	2	no	—
476	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
477	C₂×D₄	C₂²×D₁₉	1	2	yes	—
478	C₂²×C₄	—	19	2	no	—
479	C₂²×C₄	—	19	2	no	—
480	C₂²×C₄	—	19	1	no	—
481	C₂²×C₄	—	19	1	no	—
482	C₂²×C₄	—	19	1	no	—
483	C₂²×C₄	—	19	1	no	—
484	C₂²×C₄	—	19	2	no	—
485	C₂²×C₄	—	19	2	no	—
486	C₂²×C₄	—	19	2	no	—
487	C₂²×C₄	—	19	2	no	—
488	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
489	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
490	C₄⋊C₄	—	19	1	no	—
491	C₄⋊C₄	—	19	1	no	—
492	C₄⋊C₄	—	19	2	no	—
493	C₄⋊C₄	—	19	1	no	—
494	C₄⋊C₄	—	19	1	no	—
495	C₄⋊C₄	—	19	2	no	—
496	C₄⋊C₄	—	19	1	no	—
497	C₄⋊C₄	—	19	2	no	—
498	C₄⋊C₄	—	19	2	no	—
499	C₄⋊C₄	—	19	1	no	—
500	C₄⋊C₄	—	19	2	no	—
501	C₄⋊C₄	—	19	1	no	—
502	C₄⋊C₄	—	19	2	no	—
503	C₄⋊C₄	—	19	2	no	—
504	C₄⋊C₄	—	19	2	no	—
505	C₄⋊C₄	—	19	2	no	—
506	C₄⋊C₄	—	19	1	no	—
507	C₄⋊C₄	—	19	2	no	—
508	C₄⋊C₄	—	19	2	no	—
509	C₄⋊C₄	—	19	2	no	—
510	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
511	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
512	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
513	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
514	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
515	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
516	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
517	C₂²⋊C₄	—	19	2	no	—
518	C₂²⋊C₄	—	19	2	no	—
519	C₂²⋊C₄	—	19	2	no	—
520	C₂²⋊C₄	—	19	2	no	—
521	C₂²⋊C₄	—	19	1	no	—
522	C₂²⋊C₄	—	19	1	no	—
523	C₂²⋊C₄	—	19	1	no	—
524	C₂²⋊C₄	—	19	1	no	—
525	C₂²⋊C₄	—	19	2	no	—
526	C₂²⋊C₄	—	19	2	no	—
527	C₂²⋊C₄	—	19	2	no	—
528	C₂²⋊C₄	—	19	2	no	—
529	C₂²⋊C₄	—	19	2	no	—
530	C₂²⋊C₄	—	19	2	no	—
531	C₂²⋊C₄	—	19	2	no	—
532	C₂²⋊C₄	—	19	2	no	—
533	C₂²⋊C₄	—	19	2	no	—
534	C₂²⋊C₄	—	19	1	no	—
535	C₂²⋊C₄	—	19	1	no	—
536	C₂²⋊C₄	—	19	1	no	—
537	C₂²⋊C₄	—	19	2	no	—
538	C₂²⋊C₄	—	19	1	no	—
539	C₂²⋊C₄	—	19	2	no	—
540	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
541	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
542	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
543	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
544	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
545	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
546	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
547	C₄²	—	19	1	no	—
548	C₄²	—	19	1	no	—
549	C₄²	—	19	1	no	—
550	C₄²	—	19	2	no	—
551	C₄²	—	19	2	no	—
552	C₄²	—	19	1	no	—
553	C₄²	—	19	2	no	—
554	C₄²	C₂²×D₁₉	1	1	yes	characteristic
555	C₄²	C₂²×D₁₉	1	2	yes	—
556	C₄²	C₂²×D₁₉	1	1	yes	characteristic
557	C₂³	—	19	1	no	—
558	C₂³	—	19	2	no	—
559	C₂³	—	19	1	no	—
560	C₂³	—	38	4	no	—
561	C₂³	—	76	2	no	—
562	C₂³	—	76	2	no	—
563	C₂³	C₂³×D₁₉	1	2	yes	—
564	C₂³	C₂³×D₁₉	1	1	yes	characteristic
565	Q₈	—	2	2	no	—
566	Q₈	—	4	2	no	—
567	Q₈	—	38	2	no	—
568	Q₈	—	38	2	no	—
569	Q₈	—	38	2	no	—
570	Q₈	—	76	2	no	—
571	Q₈	—	76	2	no	—
572	Q₈	—	76	2	no	—
573	Q₈	—	76	1	no	—
574	D₄	—	2	2	no	—
575	D₄	—	4	2	no	—
576	D₄	—	38	2	no	—
577	D₄	—	38	2	no	—
578	D₄	—	38	2	no	—
579	D₄	—	76	2	no	—
580	D₄	—	76	2	no	—
581	D₄	—	76	2	no	—
582	D₄	—	76	2	no	—
583	D₄	—	76	1	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	4	2	no	—
586	C₂×C₄	—	19	1	no	—
587	C₂×C₄	—	19	1	no	—
588	C₂×C₄	—	19	1	no	—
589	C₂×C₄	—	19	1	no	—
590	C₂×C₄	—	19	1	no	—
591	C₂×C₄	—	19	2	no	—
592	C₂×C₄	—	19	2	no	—
593	C₂×C₄	—	19	2	no	—
594	C₂×C₄	—	19	1	no	—
595	C₂×C₄	—	38	2	no	—
596	C₂×C₄	—	38	2	no	—
597	C₂×C₄	—	38	2	no	—
598	C₂×C₄	—	76	2	no	—
599	C₂×C₄	—	76	2	no	—
600	C₂×C₄	—	76	2	no	—
601	C₂×C₄	—	76	2	no	—
602	C₂×C₄	—	76	1	no	—
603	C₂×C₄	—	76	2	no	—
604	C₂×C₄	—	76	2	no	—
605	C₂×C₄	C₂³×D₁₉	1	2	yes	—
606	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
607	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
608	C₂×C₄	C₂³×D₁₉	1	2	yes	—
609	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
610	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
611	C₂×C₄	C₂³×D₁₉	1	2	yes	—
612	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
613	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
614	C₂²	—	2	1	no	—
615	C₂²	—	2	2	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	2	2	no	—
618	C₂²	—	2	2	no	—
619	C₂²	—	2	1	no	—
620	C₂²	—	19	2	no	—
621	C₂²	—	38	1	no	—
622	C₂²	—	38	1	no	—
623	C₂²	—	38	1	no	—
624	C₂²	—	38	2	no	—
625	C₂²	—	38	1	no	—
626	C₂²	—	38	2	no	—
627	C₂²	—	38	2	no	—
628	C₂²	—	38	1	no	—
629	C₂²	—	152	4	no	—
630	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
631	C₄	—	2	1	no	—
632	C₄	—	2	2	no	—
633	C₄	—	2	1	no	—
634	C₄	—	2	1	no	—
635	C₄	—	2	1	no	—
636	C₄	—	2	2	no	—
637	C₄	—	2	2	no	—
638	C₄	—	2	1	no	—
639	C₄	—	38	1	no	—
640	C₄	—	38	1	no	—
641	C₄	—	38	2	no	—
642	C₄	—	38	2	no	—
643	C₄	—	38	2	no	—
644	C₄	—	38	1	no	—
645	C₄	—	38	1	no	—
646	C₄	—	38	1	no	—
647	C₄	—	38	1	no	—
648	C₄	#10597435	1	2	yes	—
649	C₂	—	4	2	no	—
650	C₂	—	4	1	no	—
651	C₂	—	38	2	no	—
652	C₂	—	76	2	no	—
653	C₂	—	76	1	no	—
654	C₂	C₂×#10597435	1	1	yes	characteristic
655	C₂	2₋¹⁺⁴×D₁₉	1	1	yes	characteristic
656	C₂	#11927379	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₁₉×#542	C₂
hypercenter	#542	D₁₉
hypocenter	C₁₉	#3561
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ #542

Complements

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

N	H ≅ G/N	type
1. #11927296	C₂	semidirect
2. #11927291	C₂	semidirect
3. #11927266	C₂	semidirect
4. #11927264	C₂	semidirect
5. #11927219	C₂	semidirect
6. #11927217	C₂	semidirect
7. Q₈×D₇₆	C₂	semidirect
8. #11927207	C₂	semidirect
9. #11927204	C₂	semidirect
10. #11927200	C₂	semidirect
11. #11927191	C₂	semidirect
12. #11927189	C₂	semidirect
13. #11927169	C₂	semidirect
14. #11927168	C₂	semidirect
15. #11927167	C₂	semidirect
16. #11927163	C₂	semidirect
17. #11927128	C₂	semidirect
18. #11927120	C₂	semidirect
19. #11927114	C₂	semidirect
20. #11927099	C₂	semidirect
21. #11927072	C₂	semidirect
22. #124×D₁₉	C₂	semidirect
23. C₁₉×#542	C₂	semidirect
25. C₂×Q₈×D₁₉	C₂²	semidirect
29. C₂²×Dic₃₈	C₂²	semidirect
30. C₁₉×C₄⋊Q₈	C₂²	semidirect
31. C₁₉×#126	C₂²	semidirect
33. C₁₉×#124	C₂²	semidirect
34. C₁₉×#123	C₂²	semidirect
35. C₁₉×C₂²⋊Q₈	C₂²	semidirect
36. C₁₉×C₂²⋊Q₈	C₂²	semidirect
38. C₄×Q₈×C₁₉	C₂²	semidirect
40. C₁₉×#117	C₂²	semidirect
42. #10597393	C₂²	semidirect
44. #10597392	C₂²	semidirect
45. Q₈×Dic₁₉	C₂²	semidirect
46. #10597390	C₂²	semidirect
47. #10597385	C₂²	semidirect
52. D₄×Dic₁₉	C₂²	semidirect
55. C₄×C₂²⋊D₁₉	C₂²	semidirect
57. #10597372	C₂²	semidirect
58. #10597370	C₂²	semidirect
59. #10597344	C₂²	semidirect
60. #10597344	C₂²	semidirect
61. #10597344	C₂²	semidirect
65. #10597343	C₂²	semidirect
66. #10597343	C₂²	semidirect
67. #10597343	C₂²	semidirect
68. #10597343	C₂²	semidirect
71. #10597342	C₂²	semidirect
72. #10597342	C₂²	semidirect
75. #10597340	C₂²	semidirect
77. #10597339	C₂²	semidirect
79. #10597336	C₂²	semidirect
80. #10597335	C₂²	semidirect
81. #10597334	C₂²	semidirect
82. #10597333	C₂²	semidirect
83. #10597333	C₂²	semidirect
84. #10597333	C₂²	semidirect
86. #10597332	C₂²	semidirect
87. #10597332	C₂²	semidirect
90. #10597331	C₂²	semidirect
91. #10597331	C₂²	semidirect
92. #10597331	C₂²	semidirect
94. #10597330	C₂²	semidirect
97. #10597329	C₂²	semidirect
98. #10597329	C₂²	semidirect
104. #10597325	C₂²	semidirect
105. #10597325	C₂²	semidirect
106. #10597325	C₂²	semidirect
107. #10597324	C₂²	semidirect
108. #10597324	C₂²	semidirect
109. #10597324	C₂²	semidirect
110. #10597324	C₂²	semidirect
111. #10597322	C₂²	semidirect
116. #10597318	C₂²	semidirect
117. #10597318	C₂²	semidirect
119. #10597315	C₂²	semidirect
120. #10597315	C₂²	semidirect
121. #10597315	C₂²	semidirect
122. C₄×Dic₃₈	C₂²	semidirect
337. #542	D₁₉	semidirect
363. C₄⋊Q₈	C₂×D₁₉	semidirect
371. #126	C₂×D₁₉	semidirect
386. #124	C₂×D₁₉	semidirect
396. #123	C₂×D₁₉	semidirect
415. C₂²⋊Q₈	C₂×D₁₉	semidirect
416. C₂²⋊Q₈	C₂×D₁₉	semidirect
431. C₄×Q₈	C₂×D₁₉	semidirect
445. #117	C₂×D₁₉	semidirect
451. C₁₉	#3561	semidirect

Maximal subgroups

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

subgroup	index
#11927296	2
#11927291	2
#11927266	2
#11927264	2
#11927219	2
#11927217	2
Q₈×D₇₆	2
#11927207	2
#11927204	2
#11927200	2
#11927191	2
#11927189	2
#11927169	2
#11927168	2
#11927167	2
#11927163	2
#11927128	2
#11927120	2
#11927114	2
#11927099	2
#11927072	2
#124×D₁₉	2
C₁₉×#542	2
#3561	19