Subgroups — #14577434

Order 2432.

1100 conjugacy classes of subgroups.

The subgroup lattice has 638 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	#11927253	C₂	1	1	yes	maximal, characteristic, complemented
3	#11927253	C₂	1	1	yes	maximal, characteristic, complemented
4	#11927250	C₂	1	1	yes	maximal, characteristic, complemented
5	#11927250	C₂	1	1	yes	maximal, characteristic, complemented
6	#11927249	C₂	1	2	yes	maximal, complemented
7	#11927248	C₂	1	2	yes	maximal, complemented
8	#11927248	C₂	1	2	yes	maximal, complemented
9	D₄×Dic₃₈	C₂	1	1	yes	maximal, characteristic, complemented
10	#11927209	C₂	1	1	yes	maximal, characteristic, complemented
11	#11927207	C₂	1	2	yes	maximal, complemented
12	#11927174	C₂	1	1	yes	maximal, characteristic, complemented
13	#11927171	C₂	1	1	yes	maximal, characteristic, complemented
14	#11927169	C₂	1	2	yes	maximal, complemented
15	#11927169	C₂	1	2	yes	maximal, complemented
16	#11927100	C₂	1	1	yes	maximal, characteristic, complemented
17	#11927098	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#10597342	C₂	1	2	yes	maximal, complemented
19	C₂²⋊Q₈×D₁₉	C₂	1	2	yes	maximal, complemented
20	#11927016	C₂	1	1	yes	maximal, characteristic
21	#11927016	C₂	1	1	yes	maximal, characteristic
22	C₄×D₄×D₁₉	C₂	1	1	yes	maximal, characteristic
23	C₁₉×#554	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×Q₈×D₁₉	C₂²	1	2	yes	complemented
25	C₂×D₄×D₁₉	C₂²	1	1	yes	characteristic
26	C₂²×C₄×D₁₉	C₂²	1	2	yes	—
27	C₂²×Dic₃₈	C₂²	1	2	yes	complemented
28	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₁₉×#125	C₂²	1	1	yes	characteristic, complemented
30	C₁₉×#125	C₂²	1	1	yes	characteristic, complemented
31	C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	complemented
32	C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	complemented
33	C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	complemented
34	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
35	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
36	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
37	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
38	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	complemented
39	#10597392	C₂²	1	1	yes	characteristic
40	#10597392	C₂²	1	2	yes	—
41	#10597392	C₂²	1	2	yes	complemented
42	#10597392	C₂²	1	2	yes	complemented
43	#10597390	C₂²	1	1	yes	characteristic, complemented
44	#10597390	C₂²	1	2	yes	complemented
45	D₄×Dic₁₉	C₂²	1	1	yes	characteristic
46	D₄×Dic₁₉	C₂²	1	1	yes	characteristic
47	D₄×Dic₁₉	C₂²	1	1	yes	characteristic
48	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	—
49	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	—
50	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	—
51	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	—
52	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	—
53	#10597370	C₂²	1	2	yes	complemented
54	#10597370	C₂²	1	2	yes	complemented
55	#10597370	C₂²	1	2	yes	complemented
56	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	complemented
57	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	complemented
58	#10597343	C₂²	1	1	yes	characteristic
59	#10597343	C₂²	1	2	yes	—
60	#10597343	C₂²	1	2	yes	complemented
61	#10597343	C₂²	1	2	yes	complemented
62	#10597342	C₂²	1	1	yes	characteristic
63	#10597342	C₂²	1	2	yes	—
64	#10597342	C₂²	1	2	yes	—
65	#10597342	C₂²	1	2	yes	—
66	#10597342	C₂²	1	1	yes	characteristic
67	#10597342	C₂²	1	2	yes	—
68	#10597342	C₂²	1	2	yes	complemented
69	#10597342	C₂²	1	2	yes	complemented
70	#10597342	C₂²	1	2	yes	complemented
71	#10597342	C₂²	1	2	yes	complemented
72	#10597342	C₂²	1	2	yes	complemented
73	#10597342	C₂²	1	2	yes	complemented
74	#10597342	C₂²	1	2	yes	complemented
75	#10597342	C₂²	1	2	yes	complemented
76	#10597339	C₂²	1	1	yes	characteristic
77	#10597339	C₂²	1	1	yes	characteristic
78	#10597339	C₂²	1	1	yes	characteristic
79	#10597338	C₂²	1	1	yes	characteristic
80	#10597338	C₂²	1	1	yes	characteristic
81	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic
82	C₄⋊C₄×D₁₉	C₂²	1	2	yes	complemented
83	C₄⋊C₄×D₁₉	C₂²	1	2	yes	complemented
84	C₄⋊C₄×D₁₉	C₂²	1	2	yes	complemented
85	#10597336	C₂²	1	1	yes	characteristic, complemented
86	#10597336	C₂²	1	1	yes	characteristic, complemented
87	#10597335	C₂²	1	1	yes	characteristic, complemented
88	#10597335	C₂²	1	1	yes	characteristic, complemented
89	#10597335	C₂²	1	2	yes	complemented
90	#10597335	C₂²	1	2	yes	complemented
91	#10597334	C₂²	1	1	yes	characteristic, complemented
92	#10597334	C₂²	1	1	yes	characteristic, complemented
93	#10597334	C₂²	1	1	yes	characteristic, complemented
94	#10597334	C₂²	1	1	yes	characteristic, complemented
95	#10597334	C₂²	1	2	yes	complemented
96	#10597334	C₂²	1	1	yes	characteristic, complemented
97	#10597333	C₂²	1	2	yes	complemented
98	#10597333	C₂²	1	2	yes	complemented
99	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	—
100	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	—
101	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	—
102	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	—
103	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	—
104	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	—
105	#10597324	C₂²	1	2	yes	complemented
106	#10597324	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	C₄×D₇₆	C₂²	1	1	yes	characteristic
112	C₄×D₇₆	C₂²	1	1	yes	characteristic
113	C₄×D₇₆	C₂²	1	1	yes	characteristic
114	#10597318	C₂²	1	1	yes	characteristic
115	#10597318	C₂²	1	1	yes	characteristic
116	C₄²×D₁₉	C₂²	1	1	yes	characteristic
117	#10597316	C₂²	1	1	yes	characteristic, complemented
118	#10597316	C₂²	1	1	yes	characteristic, complemented
119	#10597315	C₂²	1	1	yes	characteristic, complemented
120	C₄×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₃₈	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	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
128	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
129	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
131	C₂²×Dic₁₉	C₂³	1	2	yes	—
132	C₂²×Dic₁₉	C₂³	1	2	yes	—
133	C₂²×Dic₁₉	C₂³	1	2	yes	—
134	Q₈×D₁₉	—	4	4	no	—
135	D₄×D₁₉	Q₈	1	8	yes	complemented
136	C₂×D₇₆	C₂³	1	1	yes	characteristic
137	C₂×C₄×D₁₉	—	4	4	no	—
138	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
139	C₂×C₄×D₁₉	C₂³	1	2	yes	—
140	C₂×C₄×D₁₉	C₂³	1	2	yes	—
141	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
142	C₂×C₄×D₁₉	C₂³	1	2	yes	—
143	C₂×C₄×D₁₉	C₂³	1	2	yes	—
144	C₂×C₄×D₁₉	C₂³	1	2	yes	—
145	C₂×C₄×D₁₉	C₂³	1	2	yes	—
146	C₂×C₄×D₁₉	C₂³	1	2	yes	—
147	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
148	C₂×Dic₃₈	—	4	4	no	—
149	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
150	C₂×Dic₃₈	C₂³	1	2	yes	—
151	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
152	C₂×Dic₃₈	C₂³	1	2	yes	—
153	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
154	C₂×Dic₃₈	C₂³	1	2	yes	—
155	C₂×Dic₃₈	C₂³	1	2	yes	—
156	C₂×Dic₃₈	C₂³	1	2	yes	—
157	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
158	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
159	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
160	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
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	1	yes	characteristic
166	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
167	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
168	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
169	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
170	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
171	C₄²×C₁₉	C₂³	1	1	yes	characteristic
172	C₄²×C₁₉	C₂³	1	1	yes	characteristic
173	C₄²×C₁₉	C₂³	1	1	yes	characteristic
174	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
175	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
176	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
177	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
178	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
179	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
180	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
181	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
182	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
183	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
184	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
185	(C₂×D₁₉)⋊C₄	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	2	yes	—
189	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
190	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
191	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
192	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
193	C₄⋊Dic₁₉	C₂³	1	2	yes	—
194	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
195	C₄⋊Dic₁₉	C₂³	1	2	yes	—
196	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
197	C₄⋊Dic₁₉	C₂³	1	2	yes	—
198	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
199	Dic₁₉⋊C₄	C₂³	1	2	yes	—
200	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
201	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
202	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
203	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
204	Dic₁₉⋊C₄	C₂³	1	2	yes	—
205	Dic₁₉⋊C₄	C₂³	1	2	yes	—
206	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
207	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
208	Dic₁₉⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
215	Dic₁₉⋊C₄	C₂³	1	2	yes	—
216	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
217	Dic₁₉⋊C₄	C₂³	1	2	yes	—
218	Dic₁₉⋊C₄	C₂³	1	2	yes	—
219	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
220	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
221	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
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	C₂³×C₁₉	C₂⁴	1	2	yes	—
227	C₂²×D₁₉	—	4	2	no	—
228	C₂²×D₁₉	—	4	2	no	—
229	C₂²×D₁₉	C₂×Q₈	1	8	yes	complemented
230	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
231	C₂²×D₁₉	C₂⁴	1	2	yes	—
232	Q₈×C₁₉	—	4	2	no	—
233	Q₈×C₁₉	—	4	1	no	—
234	D₄×C₁₉	C₂×Q₈	1	4	yes	complemented
235	C₂×C₄×C₁₉	—	4	2	no	—
236	C₂×C₄×C₁₉	—	4	2	no	—
237	C₂×C₄×C₁₉	—	4	2	no	—
238	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
239	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
240	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
241	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
242	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
248	C₂²⋊D₁₉	C₂×Q₈	1	8	yes	complemented
249	C₂×Dic₁₉	—	2	4	no	—
250	C₂×Dic₁₉	—	4	2	no	—
251	C₂×Dic₁₉	—	4	2	no	—
252	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
253	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
254	C₂×Dic₁₉	C₂⁴	1	2	yes	—
255	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
256	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
257	C₂×Dic₁₉	C₂⁴	1	2	yes	—
258	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₁₉	C₂⁴	1	2	yes	—
260	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
261	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
262	D₇₆	C₂×Q₈	1	4	yes	complemented
263	C₄×D₁₉	—	2	2	no	—
264	C₄×D₁₉	—	2	4	no	—
265	C₄×D₁₉	—	4	2	no	—
266	C₄×D₁₉	—	4	2	no	—
267	C₄×D₁₉	—	4	1	no	—
268	C₄×D₁₉	—	4	2	no	—
269	C₄×D₁₉	—	4	2	no	—
270	C₄×D₁₉	—	4	2	no	—
271	C₄×D₁₉	—	4	2	no	—
272	C₄×D₁₉	C₂×Q₈	1	4	yes	complemented
273	Dic₃₈	—	2	2	no	—
274	Dic₃₈	—	2	4	no	—
275	Dic₃₈	—	2	2	no	—
276	Dic₃₈	—	4	2	no	—
277	Dic₃₈	—	4	2	no	—
278	Dic₃₈	—	4	2	no	—
279	Dic₃₈	—	4	1	no	—
280	Dic₃₈	—	4	2	no	—
281	#3501	—	19	1	no	maximal, Sylow
282	C₂²×C₁₉	—	2	2	no	—
283	C₂²×C₁₉	—	2	2	no	—
284	C₂²×C₁₉	C₂²×Q₈	1	4	yes	—
285	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
286	C₂×D₁₉	—	2	2	no	—
287	C₂×D₁₉	—	2	1	no	—
288	C₂×D₁₉	—	2	2	no	—
289	C₂×D₁₉	—	2	1	no	—
290	C₂×D₁₉	—	4	8	no	—
291	C₂×D₁₉	C₂²×Q₈	1	2	yes	—
292	C₂×D₁₉	C₂²×Q₈	1	4	yes	—
293	C₄×C₁₉	—	2	1	no	—
294	C₄×C₁₉	—	2	2	no	—
295	C₄×C₁₉	—	2	1	no	—
296	C₄×C₁₉	—	2	2	no	—
297	C₄×C₁₉	—	2	1	no	—
298	C₄×C₁₉	—	2	2	no	—
299	C₄×C₁₉	—	2	1	no	—
300	C₄×C₁₉	—	2	1	no	—
301	C₄×C₁₉	—	2	1	no	—
302	C₄×C₁₉	C₂²×Q₈	1	2	yes	—
303	Dic₁₉	—	2	1	no	—
304	Dic₁₉	—	2	2	no	—
305	Dic₁₉	—	2	1	no	—
306	Dic₁₉	—	2	2	no	—
307	Dic₁₉	—	2	1	no	—
308	Dic₁₉	—	2	1	no	—
309	Dic₁₉	—	2	2	no	—
310	Dic₁₉	—	2	1	no	—
311	Dic₁₉	C₂²×Q₈	1	2	yes	—
312	Dic₁₉	H(5,𝔽₂)	1	2	yes	—
313	#554	—	19	1	no	—
314	#554	—	19	1	no	—
315	#554	—	19	2	no	—
316	#554	—	19	2	no	—
317	#554	—	19	1	no	—
318	#554	—	19	1	no	—
319	#554	—	19	1	no	—
320	#554	—	19	2	no	—
321	#554	D₁₉	1	1	yes	characteristic, complemented
322	D₄×Q₈	—	19	1	no	—
323	D₄×Q₈	—	19	2	no	—
324	D₄×Q₈	—	19	1	no	—
325	#544	—	19	1	no	—
326	#544	—	19	1	no	—
327	#543	—	19	2	no	—
328	#543	—	19	2	no	—
329	#533	—	19	1	no	—
330	#533	—	19	1	no	—
331	C₂×C₂²⋊Q₈	—	19	2	no	—
332	C₂×C₂²⋊Q₈	—	19	2	no	—
333	#518	—	19	1	no	—
334	#518	—	19	1	no	—
335	C₂×C₄×D₄	—	19	1	no	—
336	C₂×C₁₉	—	2	4	no	—
337	C₂×C₁₉	C₂³×Q₈	1	1	yes	characteristic
338	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
339	C₂×C₁₉	#585	1	1	yes	characteristic
340	D₁₉	—	2	2	no	—
341	D₁₉	—	2	4	no	—
342	C₂²×Q₈	—	19	2	no	—
343	C₂²×Q₈	—	19	2	no	—
344	C₂²×D₄	—	19	1	no	—
345	C₂³×C₄	—	19	2	no	—
346	C₄⋊Q₈	—	19	1	no	—
347	C₄⋊Q₈	—	19	2	no	—
348	C₄⋊Q₈	—	19	1	no	—
349	C₄⋊Q₈	—	19	1	no	—
350	C₄⋊Q₈	—	19	1	no	—
351	C₄⋊Q₈	—	19	2	no	—
352	C₄⋊Q₈	—	19	1	no	—
353	C₄⋊Q₈	—	19	1	no	—
354	C₄⋊Q₈	—	19	1	no	—
355	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
356	#125	—	19	1	no	—
357	#125	—	19	1	no	—
358	#125	—	19	2	no	—
359	#125	—	19	2	no	—
360	#125	—	19	1	no	—
361	#125	—	19	1	no	—
362	#125	—	19	1	no	—
363	#125	—	19	1	no	—
364	#125	C₂×D₁₉	1	1	yes	characteristic, complemented
365	#125	C₂×D₁₉	1	1	yes	characteristic, complemented
366	C₂²⋊Q₈	—	19	2	no	—
367	C₂²⋊Q₈	—	19	1	no	—
368	C₂²⋊Q₈	—	19	2	no	—
369	C₂²⋊Q₈	—	19	2	no	—
370	C₂²⋊Q₈	—	19	2	no	—
371	C₂²⋊Q₈	—	19	2	no	—
372	C₂²⋊Q₈	—	19	2	no	—
373	C₂²⋊Q₈	—	19	1	no	—
374	C₂²⋊Q₈	—	19	2	no	—
375	C₂²⋊Q₈	—	19	1	no	—
376	C₂²⋊Q₈	—	19	2	no	—
377	C₂²⋊Q₈	—	19	2	no	—
378	C₂²⋊Q₈	—	19	2	no	—
379	C₂²⋊Q₈	—	19	2	no	—
380	C₂²⋊Q₈	—	19	2	no	—
381	C₂²⋊Q₈	—	19	2	no	—
382	C₂²⋊Q₈	—	19	2	no	—
383	C₂²⋊Q₈	—	19	2	no	—
384	C₂²⋊Q₈	—	19	1	no	—
385	C₂²⋊Q₈	—	19	2	no	—
386	C₂²⋊Q₈	—	19	2	no	—
387	C₂²⋊Q₈	—	19	2	no	—
388	C₂²⋊Q₈	—	19	2	no	—
389	C₂²⋊Q₈	—	19	2	no	—
390	C₂²⋊Q₈	—	19	2	no	—
391	C₂²⋊Q₈	—	19	2	no	—
392	C₂²⋊Q₈	—	19	2	no	—
393	C₂²⋊Q₈	—	19	2	no	—
394	C₂²⋊Q₈	—	19	2	no	—
395	C₂²⋊Q₈	—	19	2	no	—
396	C₂²⋊Q₈	—	19	2	no	—
397	C₂²⋊Q₈	C₂×D₁₉	1	2	yes	complemented
398	C₂²⋊Q₈	C₂×D₁₉	1	2	yes	complemented
399	C₂²⋊Q₈	C₂×D₁₉	1	2	yes	complemented
400	C₄×Q₈	—	19	2	no	—
401	C₄×Q₈	—	19	2	no	—
402	C₄×Q₈	—	19	1	no	—
403	C₄×Q₈	—	19	1	no	—
404	C₄×Q₈	—	19	1	no	—
405	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
406	C₄×D₄	—	19	1	no	—
407	C₄×D₄	—	19	1	no	—
408	C₄×D₄	—	19	1	no	—
409	C₄×D₄	—	19	2	no	—
410	C₄×D₄	—	19	2	no	—
411	C₄×D₄	—	19	2	no	—
412	C₄×D₄	—	19	1	no	—
413	C₄×D₄	—	19	1	no	—
414	C₄×D₄	—	19	1	no	—
415	C₄×D₄	—	19	2	no	—
416	C₄×D₄	—	19	2	no	—
417	C₄×D₄	—	19	2	no	—
418	C₄×D₄	—	19	1	no	—
419	C₄×D₄	—	19	1	no	—
420	C₄×D₄	—	19	1	no	—
421	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
422	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
423	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
424	#117	—	19	1	no	—
425	#117	—	19	1	no	—
426	#117	—	19	1	no	—
427	#117	—	19	1	no	—
428	C₂×C₄⋊C₄	—	19	2	no	—
429	C₂×C₄⋊C₄	—	19	2	no	—
430	C₂×C₄⋊C₄	—	19	1	no	—
431	C₂×C₄⋊C₄	—	19	2	no	—
432	C₂×C₄⋊C₄	—	19	2	no	—
433	C₂×C₄⋊C₄	—	19	2	no	—
434	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	complemented
435	C₂×C₂²⋊C₄	—	19	2	no	—
436	C₂×C₂²⋊C₄	—	19	2	no	—
437	C₂×C₂²⋊C₄	—	19	2	no	—
438	C₂×C₂²⋊C₄	—	19	2	no	—
439	C₂×C₂²⋊C₄	—	19	2	no	—
440	C₂×C₄²	—	19	1	no	—
441	C₁₉	#3501	1	1	yes	characteristic, complemented, Sylow
442	C₂⁴	—	19	2	no	—
443	C₂×Q₈	—	19	2	no	—
444	C₂×Q₈	—	19	1	no	—
445	C₂×Q₈	—	19	1	no	—
446	C₂×Q₈	—	19	2	no	—
447	C₂×Q₈	—	19	1	no	—
448	C₂×Q₈	—	19	2	no	—
449	C₂×Q₈	—	19	2	no	—
450	C₂×Q₈	—	19	2	no	—
451	C₂×Q₈	—	76	4	no	—
452	C₂×Q₈	—	76	4	no	—
453	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
454	C₂×Q₈	C₂²×D₁₉	1	2	yes	—
455	C₂×D₄	—	19	2	no	—
456	C₂×D₄	—	19	8	no	—
457	C₂×D₄	—	19	1	no	—
458	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
459	C₂²×C₄	—	19	1	no	—
460	C₂²×C₄	—	19	2	no	—
461	C₂²×C₄	—	19	2	no	—
462	C₂²×C₄	—	19	2	no	—
463	C₂²×C₄	—	19	1	no	—
464	C₂²×C₄	—	19	2	no	—
465	C₂²×C₄	—	19	1	no	—
466	C₂²×C₄	—	19	2	no	—
467	C₂²×C₄	—	19	2	no	—
468	C₂²×C₄	—	19	2	no	—
469	C₂²×C₄	—	19	2	no	—
470	C₂²×C₄	—	19	2	no	—
471	C₂²×C₄	—	19	2	no	—
472	C₂²×C₄	—	76	4	no	—
473	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
474	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
475	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
476	C₄⋊C₄	—	19	1	no	—
477	C₄⋊C₄	—	19	1	no	—
478	C₄⋊C₄	—	19	2	no	—
479	C₄⋊C₄	—	19	2	no	—
480	C₄⋊C₄	—	19	1	no	—
481	C₄⋊C₄	—	19	1	no	—
482	C₄⋊C₄	—	19	2	no	—
483	C₄⋊C₄	—	19	2	no	—
484	C₄⋊C₄	—	19	2	no	—
485	C₄⋊C₄	—	19	2	no	—
486	C₄⋊C₄	—	19	2	no	—
487	C₄⋊C₄	—	19	2	no	—
488	C₄⋊C₄	—	19	2	no	—
489	C₄⋊C₄	—	19	1	no	—
490	C₄⋊C₄	—	19	1	no	—
491	C₄⋊C₄	—	19	1	no	—
492	C₄⋊C₄	—	19	1	no	—
493	C₄⋊C₄	—	19	1	no	—
494	C₄⋊C₄	—	19	1	no	—
495	C₄⋊C₄	—	19	2	no	—
496	C₄⋊C₄	—	19	2	no	—
497	C₄⋊C₄	—	19	1	no	—
498	C₄⋊C₄	—	19	2	no	—
499	C₄⋊C₄	—	19	2	no	—
500	C₄⋊C₄	—	19	2	no	—
501	C₄⋊C₄	—	19	1	no	—
502	C₄⋊C₄	—	19	1	no	—
503	C₄⋊C₄	—	19	1	no	—
504	C₄⋊C₄	—	19	1	no	—
505	C₄⋊C₄	—	19	1	no	—
506	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
507	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
508	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
509	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
510	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
511	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
512	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
513	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
514	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
515	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
516	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
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	2	no	—
524	C₂²⋊C₄	—	19	1	no	—
525	C₂²⋊C₄	—	19	1	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	C₂²×D₁₉	1	2	yes	—
533	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
534	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
535	C₄²	—	19	1	no	—
536	C₄²	—	19	1	no	—
537	C₄²	—	19	1	no	—
538	C₄²	—	19	2	no	—
539	C₄²	—	19	2	no	—
540	C₄²	—	19	1	no	—
541	C₄²	—	19	1	no	—
542	C₄²	C₂²×D₁₉	1	1	yes	characteristic
543	C₄²	C₂²×D₁₉	1	1	yes	characteristic
544	C₄²	C₂²×D₁₉	1	1	yes	characteristic
545	C₂³	—	19	1	no	—
546	C₂³	—	19	2	no	—
547	C₂³	—	19	8	no	—
548	C₂³	—	76	2	no	—
549	C₂³	—	76	2	no	—
550	C₂³	C₂³×D₁₉	1	2	yes	—
551	Q₈	—	4	2	no	—
552	Q₈	—	4	1	no	—
553	Q₈	—	38	2	no	—
554	Q₈	—	38	4	no	—
555	Q₈	—	38	2	no	—
556	Q₈	—	76	2	no	—
557	Q₈	—	76	2	no	—
558	Q₈	—	76	2	no	—
559	Q₈	—	76	2	no	—
560	Q₈	—	76	1	no	—
561	D₄	—	19	8	no	—
562	D₄	—	19	4	no	—
563	D₄	Q₈×D₁₉	1	4	yes	complemented
564	C₂×C₄	—	4	2	no	—
565	C₂×C₄	—	4	2	no	—
566	C₂×C₄	—	4	2	no	—
567	C₂×C₄	—	19	1	no	—
568	C₂×C₄	—	19	1	no	—
569	C₂×C₄	—	19	4	no	—
570	C₂×C₄	—	19	1	no	—
571	C₂×C₄	—	19	1	no	—
572	C₂×C₄	—	19	2	no	—
573	C₂×C₄	—	19	1	no	—
574	C₂×C₄	—	19	1	no	—
575	C₂×C₄	—	19	2	no	—
576	C₂×C₄	—	19	1	no	—
577	C₂×C₄	—	19	2	no	—
578	C₂×C₄	—	38	2	no	—
579	C₂×C₄	—	38	4	no	—
580	C₂×C₄	—	38	4	no	—
581	C₂×C₄	—	76	2	no	—
582	C₂×C₄	—	76	2	no	—
583	C₂×C₄	—	76	2	no	—
584	C₂×C₄	—	76	2	no	—
585	C₂×C₄	—	76	2	no	—
586	C₂×C₄	—	76	2	no	—
587	C₂×C₄	—	76	1	no	—
588	C₂×C₄	—	76	2	no	—
589	C₂×C₄	—	76	2	no	—
590	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
591	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
592	C₂×C₄	C₂³×D₁₉	1	2	yes	—
593	C₂×C₄	C₂³×D₁₉	1	2	yes	—
594	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
595	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
596	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
597	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
598	C₂×C₄	C₂³×D₁₉	1	2	yes	—
599	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
600	C₂²	—	2	2	no	—
601	C₂²	—	2	2	no	—
602	C₂²	—	19	2	no	—
603	C₂²	—	19	4	no	—
604	C₂²	—	38	2	no	—
605	C₂²	—	38	1	no	—
606	C₂²	—	38	2	no	—
607	C₂²	—	38	1	no	—
608	C₂²	—	76	8	no	—
609	C₂²	C₂×Q₈×D₁₉	1	4	yes	—
610	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
611	C₄	—	2	1	no	—
612	C₄	—	2	1	no	—
613	C₄	—	2	2	no	—
614	C₄	—	2	2	no	—
615	C₄	—	2	1	no	—
616	C₄	—	2	1	no	—
617	C₄	—	2	2	no	—
618	C₄	—	2	1	no	—
619	C₄	—	2	1	no	—
620	C₄	—	19	2	no	—
621	C₄	—	19	2	no	—
622	C₄	—	38	2	no	—
623	C₄	—	38	1	no	—
624	C₄	—	38	2	no	—
625	C₄	—	38	1	no	—
626	C₄	—	38	1	no	—
627	C₄	—	38	2	no	—
628	C₄	—	38	1	no	—
629	C₄	—	38	1	no	—
630	C₄	C₂×Q₈×D₁₉	1	2	yes	—
631	C₂	—	2	4	no	—
632	C₂	—	38	2	no	—
633	C₂	—	38	4	no	—
634	C₂	C₂²×Q₈×D₁₉	1	1	yes	characteristic
635	C₂	H(5,𝔽₂)×D₁₉	1	1	yes	characteristic
636	C₂	#11927380	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₁₉×#554	C₂
prime radical	C₂×D₄×D₁₉	C₂²
hypercenter	#554	D₁₉
hypocenter	C₁₉	#3501
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ #554

Complements

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

N	H ≅ G/N	type
1. #11927254	C₂	semidirect
2. #11927253	C₂	semidirect
3. #11927253	C₂	semidirect
4. #11927250	C₂	semidirect
5. #11927250	C₂	semidirect
6. #11927249	C₂	semidirect
7. #11927248	C₂	semidirect
8. #11927248	C₂	semidirect
9. D₄×Dic₃₈	C₂	semidirect
10. #11927209	C₂	semidirect
11. #11927207	C₂	semidirect
12. #11927174	C₂	semidirect
13. #11927171	C₂	semidirect
14. #11927169	C₂	semidirect
15. #11927169	C₂	semidirect
16. #11927100	C₂	semidirect
17. #11927098	C₂	semidirect
18. C₂×#10597342	C₂	semidirect
19. C₂²⋊Q₈×D₁₉	C₂	semidirect
23. C₁₉×#554	C₂	semidirect
24. C₂×Q₈×D₁₉	C₂²	semidirect
27. C₂²×Dic₃₈	C₂²	semidirect
28. C₁₉×C₄⋊Q₈	C₂²	semidirect
29. C₁₉×#125	C₂²	semidirect
30. C₁₉×#125	C₂²	semidirect
31. C₁₉×C₂²⋊Q₈	C₂²	semidirect
32. C₁₉×C₂²⋊Q₈	C₂²	semidirect
33. C₁₉×C₂²⋊Q₈	C₂²	semidirect
34. C₄×Q₈×C₁₉	C₂²	semidirect
38. C₂×C₄⋊C₄×C₁₉	C₂²	semidirect
41. #10597392	C₂²	semidirect
42. #10597392	C₂²	semidirect
43. #10597390	C₂²	semidirect
44. #10597390	C₂²	semidirect
53. #10597370	C₂²	semidirect
54. #10597370	C₂²	semidirect
55. #10597370	C₂²	semidirect
56. C₂×Dic₁₉⋊C₄	C₂²	semidirect
57. C₂×Dic₁₉⋊C₄	C₂²	semidirect
60. #10597343	C₂²	semidirect
61. #10597343	C₂²	semidirect
68. #10597342	C₂²	semidirect
69. #10597342	C₂²	semidirect
70. #10597342	C₂²	semidirect
71. #10597342	C₂²	semidirect
72. #10597342	C₂²	semidirect
73. #10597342	C₂²	semidirect
74. #10597342	C₂²	semidirect
75. #10597342	C₂²	semidirect
82. C₄⋊C₄×D₁₉	C₂²	semidirect
83. C₄⋊C₄×D₁₉	C₂²	semidirect
84. C₄⋊C₄×D₁₉	C₂²	semidirect
85. #10597336	C₂²	semidirect
86. #10597336	C₂²	semidirect
87. #10597335	C₂²	semidirect
88. #10597335	C₂²	semidirect
89. #10597335	C₂²	semidirect
90. #10597335	C₂²	semidirect
91. #10597334	C₂²	semidirect
92. #10597334	C₂²	semidirect
93. #10597334	C₂²	semidirect
94. #10597334	C₂²	semidirect
95. #10597334	C₂²	semidirect
96. #10597334	C₂²	semidirect
97. #10597333	C₂²	semidirect
98. #10597333	C₂²	semidirect
105. #10597324	C₂²	semidirect
106. #10597324	C₂²	semidirect
107. #10597324	C₂²	semidirect
108. #10597324	C₂²	semidirect
109. #10597324	C₂²	semidirect
110. #10597324	C₂²	semidirect
117. #10597316	C₂²	semidirect
118. #10597316	C₂²	semidirect
119. #10597315	C₂²	semidirect
120. C₄×Dic₃₈	C₂²	semidirect
121. C₄×Dic₃₈	C₂²	semidirect
122. C₄×Dic₃₈	C₂²	semidirect
135. D₄×D₁₉	Q₈	semidirect
229. C₂²×D₁₉	C₂×Q₈	semidirect
234. D₄×C₁₉	C₂×Q₈	semidirect
248. C₂²⋊D₁₉	C₂×Q₈	semidirect
262. D₇₆	C₂×Q₈	semidirect
272. C₄×D₁₉	C₂×Q₈	semidirect
321. #554	D₁₉	semidirect
355. C₄⋊Q₈	C₂×D₁₉	semidirect
364. #125	C₂×D₁₉	semidirect
365. #125	C₂×D₁₉	semidirect
397. C₂²⋊Q₈	C₂×D₁₉	semidirect
398. C₂²⋊Q₈	C₂×D₁₉	semidirect
399. C₂²⋊Q₈	C₂×D₁₉	semidirect
405. C₄×Q₈	C₂×D₁₉	semidirect
434. C₂×C₄⋊C₄	C₂×D₁₉	semidirect
441. C₁₉	#3501	semidirect
563. D₄	Q₈×D₁₉	semidirect

Maximal subgroups

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

subgroup	index
#11927254	2
#11927253	2
#11927250	2
#11927249	2
#11927248	2
D₄×Dic₃₈	2
#11927209	2
#11927207	2
#11927174	2
#11927171	2
#11927169	2
#11927100	2
#11927098	2
C₂×#10597342	2
C₂²⋊Q₈×D₁₉	2
#11927016	2
C₄×D₄×D₁₉	2
C₁₉×#554	2
#3501	19