Subgroups — #14577385

Order 2432.

1022 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927263	C₂	1	2	yes	maximal, complemented
2	#11927248	C₂	1	2	yes	maximal, complemented
3	#11927231	C₂	1	2	yes	maximal, complemented
4	#11927230	C₂	1	2	yes	maximal, complemented
5	#11927230	C₂	1	2	yes	maximal, complemented
6	#11927228	C₂	1	2	yes	maximal, complemented
7	#11927224	C₂	1	2	yes	maximal, complemented
8	#11927222	C₂	1	2	yes	maximal, complemented
9	#11927171	C₂	1	1	yes	maximal, characteristic, complemented
10	#11927161	C₂	1	1	yes	maximal, characteristic, complemented
11	#11927156	C₂	1	1	yes	maximal, characteristic, complemented
12	#11927154	C₂	1	1	yes	maximal, characteristic, complemented
13	#11927114	C₂	1	1	yes	maximal, characteristic, complemented
14	#11927099	C₂	1	1	yes	maximal, characteristic, complemented
15	#11927098	C₂	1	1	yes	maximal, characteristic, complemented
16	#11927076	C₂	1	1	yes	maximal, characteristic, complemented
17	#11927073	C₂	1	1	yes	maximal, characteristic, complemented
18	#11927054	C₂	1	1	yes	maximal, characteristic
19	C₂²⋊Q₈×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
20	#11927023	C₂	1	1	yes	maximal, characteristic, complemented
21	#11927020	C₂	1	1	yes	maximal, characteristic, complemented
22	#117×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×#64543	C₂²	1	1	yes	characteristic
26	C₂²×C₄×D₁₉	C₂²	1	1	yes	characteristic
27	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
28	C₁₉×#126	C₂²	1	2	yes	complemented
29	C₁₉×#124	C₂²	1	2	yes	—
30	C₁₉×#124	C₂²	1	1	yes	characteristic, complemented
31	C₁₉×#123	C₂²	1	2	yes	—
32	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
33	C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	complemented
34	C₁₉×#121	C₂²	1	1	yes	characteristic
35	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
36	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
37	C₁₉×#117	C₂²	1	1	yes	characteristic
38	#10597392	C₂²	1	1	yes	characteristic
39	#10597392	C₂²	1	2	yes	—
40	#10597392	C₂²	1	2	yes	—
41	Q₈×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
42	Q₈×Dic₁₉	C₂²	1	2	yes	complemented
43	#10597390	C₂²	1	1	yes	characteristic, complemented
44	#10597390	C₂²	1	2	yes	complemented
45	#10597384	C₂²	1	1	yes	characteristic
46	#10597383	C₂²	1	2	yes	—
47	#10597382	C₂²	1	2	yes	—
48	#10597382	C₂²	1	1	yes	characteristic, complemented
49	#10597381	C₂²	1	2	yes	—
50	D₄×Dic₁₉	C₂²	1	2	yes	—
51	D₄×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
52	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	—
53	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	—
54	#10597372	C₂²	1	1	yes	characteristic
55	#10597372	C₂²	1	2	yes	complemented
56	#10597370	C₂²	1	1	yes	characteristic
57	#10597370	C₂²	1	1	yes	characteristic
58	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	complemented
59	#10597343	C₂²	1	1	yes	characteristic
60	#10597343	C₂²	1	1	yes	characteristic
61	#10597342	C₂²	1	2	yes	—
62	#10597342	C₂²	1	2	yes	—
63	#10597342	C₂²	1	2	yes	—
64	#10597338	C₂²	1	1	yes	characteristic
65	#10597338	C₂²	1	2	yes	—
66	#10597338	C₂²	1	2	yes	—
67	#10597338	C₂²	1	1	yes	characteristic
68	#10597338	C₂²	1	1	yes	characteristic
69	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic
70	C₄⋊C₄×D₁₉	C₂²	1	2	yes	—
71	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic
72	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic
73	#10597336	C₂²	1	1	yes	characteristic, complemented
74	#10597336	C₂²	1	2	yes	complemented
75	#10597336	C₂²	1	2	yes	complemented
76	#10597335	C₂²	1	2	yes	complemented
77	#10597335	C₂²	1	2	yes	complemented
78	#10597335	C₂²	1	2	yes	complemented
79	#10597335	C₂²	1	2	yes	complemented
80	#10597335	C₂²	1	2	yes	complemented
81	#10597334	C₂²	1	1	yes	characteristic, complemented
82	#10597333	C₂²	1	1	yes	characteristic, complemented
83	#10597333	C₂²	1	1	yes	characteristic, complemented
84	#10597333	C₂²	1	2	yes	complemented
85	#10597329	C₂²	1	2	yes	—
86	#10597329	C₂²	1	2	yes	—
87	#10597329	C₂²	1	2	yes	—
88	#10597329	C₂²	1	2	yes	—
89	#10597329	C₂²	1	2	yes	—
90	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	—
91	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	—
92	(C₂²⋊D₁₉)⋊C₄	C₂²	1	2	yes	—
93	C₂²⋊C₄×D₁₉	C₂²	1	1	yes	characteristic
94	C₂²⋊C₄×D₁₉	C₂²	1	2	yes	—
95	C₂²⋊C₄×D₁₉	C₂²	1	1	yes	characteristic
96	#10597325	C₂²	1	2	yes	—
97	#10597325	C₂²	1	2	yes	—
98	#10597325	C₂²	1	2	yes	—
99	#10597325	C₂²	1	2	yes	—
100	#10597325	C₂²	1	2	yes	complemented
101	#10597325	C₂²	1	2	yes	complemented
102	#10597325	C₂²	1	2	yes	complemented
103	#10597324	C₂²	1	2	yes	—
104	#10597324	C₂²	1	2	yes	complemented
105	#10597324	C₂²	1	2	yes	complemented
106	#10597324	C₂²	1	2	yes	complemented
107	#10597323	C₂²	1	1	yes	characteristic
108	#10597323	C₂²	1	1	yes	characteristic
109	#10597323	C₂²	1	2	yes	complemented
110	#10597323	C₂²	1	2	yes	complemented
111	#10597318	C₂²	1	2	yes	—
112	#10597318	C₂²	1	1	yes	characteristic
113	#10597318	C₂²	1	2	yes	—
114	#10597318	C₂²	1	1	yes	characteristic
115	C₄²×D₁₉	C₂²	1	1	yes	characteristic
116	C₄²×D₁₉	C₂²	1	1	yes	characteristic
117	#10597316	C₂²	1	1	yes	characteristic, complemented
118	#10597315	C₂²	1	1	yes	characteristic, complemented
119	C₄×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
120	C₄×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₃₈	C₂²	1	2	yes	complemented
122	C₄×Dic₃₈	C₂²	1	2	yes	complemented
123	C₂³×D₁₉	C₂³	1	1	yes	characteristic
124	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
125	C₂×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	2	yes	—
131	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
132	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
133	C₂²×Dic₁₉	C₂³	1	2	yes	—
134	C₂²×Dic₁₉	C₂³	1	2	yes	—
135	Q₈×D₁₉	—	2	4	no	—
136	#64543	—	2	4	no	—
137	C₂×C₄×D₁₉	—	2	4	no	—
138	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
139	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
140	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
141	C₂×C₄×D₁₉	C₂³	1	2	yes	—
142	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
143	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
145	C₂×C₄×D₁₉	C₂³	1	2	yes	—
146	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
147	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
148	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
149	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
150	C₂×Dic₃₈	C₂³	1	2	yes	—
151	C₂×Dic₃₈	C₂³	1	2	yes	—
152	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
153	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
154	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
155	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
156	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
157	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
158	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
159	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
160	C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
161	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
162	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
163	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
164	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
165	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
166	C₄²×C₁₉	C₂³	1	1	yes	characteristic
167	C₄²×C₁₉	C₂³	1	1	yes	characteristic
168	C₄²×C₁₉	C₂³	1	2	yes	—
169	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
170	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
171	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
172	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
173	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
174	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
175	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
177	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
178	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
183	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
184	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
185	C₄⋊Dic₁₉	C₂³	1	2	yes	—
186	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
187	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
188	C₄⋊Dic₁₉	C₂³	1	2	yes	—
189	C₄⋊Dic₁₉	C₂³	1	2	yes	—
190	C₄⋊Dic₁₉	C₂³	1	2	yes	—
191	C₄⋊Dic₁₉	C₂³	1	2	yes	—
192	C₄⋊Dic₁₉	C₂³	1	2	yes	—
193	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
194	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
195	Dic₁₉⋊C₄	C₂³	1	2	yes	—
196	Dic₁₉⋊C₄	C₂³	1	2	yes	—
197	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
198	Dic₁₉⋊C₄	C₂³	1	2	yes	—
199	Dic₁₉⋊C₄	C₂³	1	2	yes	—
200	Dic₁₉⋊C₄	C₂³	1	2	yes	—
201	Dic₁₉⋊C₄	C₂³	1	2	yes	—
202	Dic₁₉⋊C₄	C₂³	1	2	yes	—
203	Dic₁₉⋊C₄	C₂³	1	2	yes	—
204	Dic₁₉⋊C₄	C₂³	1	2	yes	—
205	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
206	Dic₁₉⋊C₄	C₂³	1	2	yes	—
207	Dic₁₉⋊C₄	C₂³	1	2	yes	—
208	Dic₁₉⋊C₄	C₂³	1	2	yes	—
209	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
210	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
211	Dic₁₉⋊C₄	C₂³	1	2	yes	—
212	Dic₁₉⋊C₄	C₂³	1	2	yes	—
213	C₄×Dic₁₉	C₂³	1	2	yes	—
214	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
215	C₄×Dic₁₉	C₂³	1	2	yes	—
216	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
217	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
218	C₄×Dic₁₉	C₂³	1	2	yes	—
219	C₄×Dic₁₉	C₂³	1	2	yes	—
220	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
221	C₄×Dic₁₉	C₂³	1	2	yes	—
222	C₄×Dic₁₉	C₂³	1	2	yes	—
223	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
224	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
225	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
226	C₂³×C₁₉	C₂⁴	1	2	yes	—
227	C₂²×D₁₉	—	2	2	no	—
228	C₂²×D₁₉	—	2	2	no	—
229	C₂²×D₁₉	—	4	1	no	—
230	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
231	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
232	Q₈×C₁₉	—	2	2	no	—
233	Q₈×C₁₉	—	4	2	no	—
234	D₄×C₁₉	—	2	2	no	—
235	D₄×C₁₉	—	4	2	no	—
236	C₂×C₄×C₁₉	—	2	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	1	yes	characteristic
242	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
243	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
244	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
245	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
246	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
247	C₂²⋊D₁₉	—	2	4	no	—
248	C₂²⋊D₁₉	—	2	4	no	—
249	C₂×Dic₁₉	—	2	2	no	—
250	C₂×Dic₁₉	—	2	4	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	1	yes	characteristic
255	C₂×Dic₁₉	C₂⁴	1	2	yes	—
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	2	yes	—
261	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
262	C₄×D₁₉	—	2	2	no	—
263	C₄×D₁₉	—	2	4	no	—
264	C₄×D₁₉	—	2	2	no	—
265	C₄×D₁₉	—	2	2	no	—
266	C₄×D₁₉	—	2	2	no	—
267	C₄×D₁₉	—	2	2	no	—
268	C₄×D₁₉	—	4	1	no	—
269	C₄×D₁₉	—	4	2	no	—
270	C₄×D₁₉	—	4	1	no	—
271	C₄×D₁₉	#41	1	4	yes	—
272	Dic₃₈	—	2	2	no	—
273	Dic₃₈	—	2	2	no	—
274	Dic₃₈	—	2	4	no	—
275	Dic₃₈	—	4	2	no	—
276	#3495	—	19	1	no	maximal, Sylow
277	C₂²×C₁₉	—	2	2	no	—
278	C₂²×C₁₉	—	2	1	no	—
279	C₂²×C₁₉	—	2	2	no	—
280	C₂²×C₁₉	—	2	1	no	—
281	C₂²×C₁₉	—	2	2	no	—
282	C₂²×C₁₉	—	2	1	no	—
283	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
284	C₂×D₁₉	—	2	1	no	—
285	C₂×D₁₉	—	2	1	no	—
286	C₂×D₁₉	—	2	1	no	—
287	C₂×D₁₉	—	2	1	no	—
288	C₂×D₁₉	—	4	4	no	—
289	C₂×D₁₉	C₂×#41	1	2	yes	—
290	C₂×D₁₉	2₋¹⁺⁴	1	2	yes	—
291	C₄×C₁₉	—	2	2	no	—
292	C₄×C₁₉	—	2	1	no	—
293	C₄×C₁₉	—	2	1	no	—
294	C₄×C₁₉	—	2	1	no	—
295	C₄×C₁₉	—	2	2	no	—
296	C₄×C₁₉	—	2	1	no	—
297	C₄×C₁₉	—	2	2	no	—
298	C₄×C₁₉	—	2	1	no	—
299	C₄×C₁₉	C₂×#41	1	2	yes	—
300	Dic₁₉	—	2	2	no	—
301	Dic₁₉	—	2	2	no	—
302	Dic₁₉	—	2	1	no	—
303	Dic₁₉	—	2	1	no	—
304	Dic₁₉	—	2	1	no	—
305	Dic₁₉	—	2	2	no	—
306	Dic₁₉	—	2	1	no	—
307	Dic₁₉	—	2	2	no	—
308	Dic₁₉	—	2	1	no	—
309	Dic₁₉	C₂×#41	1	2	yes	—
310	#556	—	19	2	no	—
311	#554	—	19	2	no	—
312	#552	—	19	2	no	—
313	#552	—	19	2	no	—
314	#552	—	19	2	no	—
315	#552	—	19	2	no	—
316	#551	—	19	2	no	—
317	#551	—	19	2	no	—
318	#544	—	19	1	no	—
319	#542	—	19	1	no	—
320	#542	D₁₉	1	1	yes	characteristic, complemented
321	#541	—	19	1	no	—
322	#541	—	19	1	no	—
323	#536	—	19	1	no	—
324	#533	—	19	1	no	—
325	#533	—	19	1	no	—
326	#529	—	19	1	no	—
327	#529	—	19	1	no	—
328	#525	—	19	1	no	—
329	C₂×C₂²⋊Q₈	—	19	1	no	—
330	#520	—	19	1	no	—
331	#519	—	19	1	no	—
332	C₂×#117	—	19	1	no	—
333	C₂×C₁₉	—	4	1	no	—
334	C₂×C₁₉	—	4	2	no	—
335	C₂×C₁₉	C₂²×#41	1	1	yes	characteristic
336	C₂×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
337	C₂×C₁₉	#585	1	1	yes	characteristic
338	D₁₉	—	2	2	no	—
339	D₁₉	—	2	2	no	—
340	C₂×#41	—	19	1	no	—
341	C₂²×Q₈	—	19	1	no	—
342	C₂³×C₄	—	19	1	no	—
343	C₄⋊Q₈	—	19	1	no	—
344	C₄⋊Q₈	—	19	2	no	—
345	C₄⋊Q₈	—	19	1	no	—
346	C₄⋊Q₈	—	19	1	no	—
347	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
348	#126	—	19	2	no	—
349	#126	—	19	2	no	—
350	#126	—	19	2	no	—
351	#126	—	19	2	no	—
352	#126	—	19	2	no	—
353	#126	—	19	2	no	—
354	#126	—	19	2	no	—
355	#126	C₂×D₁₉	1	2	yes	complemented
356	#125	—	19	1	no	—
357	#125	—	19	2	no	—
358	#125	—	19	2	no	—
359	#125	—	19	2	no	—
360	#125	—	19	2	no	—
361	#125	—	19	2	no	—
362	#125	—	19	2	no	—
363	#125	—	19	2	no	—
364	#125	—	19	1	no	—
365	#124	—	19	2	no	—
366	#124	—	19	1	no	—
367	#124	C₂×D₁₉	1	2	yes	—
368	#124	C₂×D₁₉	1	1	yes	characteristic, complemented
369	#123	—	19	2	no	—
370	#123	—	19	2	no	—
371	#123	—	19	2	no	—
372	#123	—	19	2	no	—
373	#123	—	19	2	no	—
374	#123	—	19	2	no	—
375	#123	C₂×D₁₉	1	2	yes	—
376	C₂²⋊Q₈	—	19	1	no	—
377	C₂²⋊Q₈	—	19	2	no	—
378	C₂²⋊Q₈	—	19	2	no	—
379	C₂²⋊Q₈	—	19	1	no	—
380	C₂²⋊Q₈	—	19	1	no	—
381	C₂²⋊Q₈	—	19	1	no	—
382	C₂²⋊Q₈	—	19	2	no	—
383	C₂²⋊Q₈	—	19	1	no	—
384	C₂²⋊Q₈	—	19	2	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	C₂×D₁₉	1	1	yes	characteristic
391	C₂²⋊Q₈	C₂×D₁₉	1	2	yes	complemented
392	#121	—	19	1	no	—
393	#121	C₂×D₁₉	1	1	yes	characteristic
394	#120	—	19	2	no	—
395	C₄×Q₈	—	19	1	no	—
396	C₄×Q₈	—	19	2	no	—
397	C₄×Q₈	—	19	1	no	—
398	C₄×Q₈	—	19	2	no	—
399	C₄×Q₈	—	19	1	no	—
400	C₄×Q₈	—	19	1	no	—
401	C₄×Q₈	—	19	2	no	—
402	C₄×Q₈	—	19	1	no	—
403	C₄×Q₈	—	19	2	no	—
404	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
405	C₄×D₄	—	19	2	no	—
406	C₄×D₄	—	19	1	no	—
407	C₄×D₄	—	19	2	no	—
408	C₄×D₄	—	19	2	no	—
409	C₄×D₄	—	19	2	no	—
410	C₄×D₄	—	19	2	no	—
411	C₄×D₄	—	19	2	no	—
412	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic, complemented
413	#117	—	19	1	no	—
414	#117	—	19	2	no	—
415	#117	—	19	1	no	—
416	#117	—	19	1	no	—
417	#117	—	19	1	no	—
418	#117	—	19	2	no	—
419	#117	—	19	2	no	—
420	#117	—	19	1	no	—
421	#117	—	19	1	no	—
422	#117	—	19	2	no	—
423	#117	—	19	2	no	—
424	#117	—	19	1	no	—
425	#117	—	19	1	no	—
426	#117	—	19	2	no	—
427	#117	—	19	2	no	—
428	#117	C₂×D₁₉	1	1	yes	characteristic
429	C₂×C₄⋊C₄	—	19	2	no	—
430	C₂×C₄⋊C₄	—	19	1	no	—
431	C₂×C₄⋊C₄	—	19	1	no	—
432	C₂×C₄⋊C₄	—	19	1	no	—
433	C₂×C₄⋊C₄	—	19	2	no	—
434	C₂×C₂²⋊C₄	—	19	1	no	—
435	C₂×C₂²⋊C₄	—	19	1	no	—
436	C₂×C₂²⋊C₄	—	19	2	no	—
437	C₂×C₄²	—	19	1	no	—
438	C₂×C₄²	—	19	1	no	—
439	C₁₉	#3495	1	1	yes	characteristic, complemented, Sylow
440	C₂⁴	—	19	1	no	—
441	#41	—	38	4	no	—
442	C₂×Q₈	—	19	2	no	—
443	C₂×Q₈	—	19	1	no	—
444	C₂×Q₈	—	19	1	no	—
445	C₂×Q₈	—	19	2	no	—
446	C₂×Q₈	—	38	4	no	—
447	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
448	C₂×Q₈	C₂²×D₁₉	1	2	yes	—
449	C₂×D₄	—	19	2	no	—
450	C₂×D₄	—	19	2	no	—
451	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
452	C₂×D₄	C₂²×D₁₉	1	2	yes	—
453	C₂²×C₄	—	19	1	no	—
454	C₂²×C₄	—	19	2	no	—
455	C₂²×C₄	—	19	1	no	—
456	C₂²×C₄	—	19	2	no	—
457	C₂²×C₄	—	19	1	no	—
458	C₂²×C₄	—	19	1	no	—
459	C₂²×C₄	—	19	1	no	—
460	C₂²×C₄	—	19	2	no	—
461	C₂²×C₄	—	19	1	no	—
462	C₂²×C₄	—	19	1	no	—
463	C₂²×C₄	—	19	1	no	—
464	C₂²×C₄	—	19	1	no	—
465	C₂²×C₄	—	19	2	no	—
466	C₂²×C₄	—	38	4	no	—
467	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
468	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
469	C₄⋊C₄	—	19	1	no	—
470	C₄⋊C₄	—	19	2	no	—
471	C₄⋊C₄	—	19	1	no	—
472	C₄⋊C₄	—	19	1	no	—
473	C₄⋊C₄	—	19	1	no	—
474	C₄⋊C₄	—	19	2	no	—
475	C₄⋊C₄	—	19	2	no	—
476	C₄⋊C₄	—	19	2	no	—
477	C₄⋊C₄	—	19	2	no	—
478	C₄⋊C₄	—	19	2	no	—
479	C₄⋊C₄	—	19	2	no	—
480	C₄⋊C₄	—	19	2	no	—
481	C₄⋊C₄	—	19	2	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	1	no	—
488	C₄⋊C₄	—	19	1	no	—
489	C₄⋊C₄	—	19	2	no	—
490	C₄⋊C₄	—	19	1	no	—
491	C₄⋊C₄	—	19	1	no	—
492	C₄⋊C₄	—	19	2	no	—
493	C₄⋊C₄	—	19	2	no	—
494	C₄⋊C₄	—	19	2	no	—
495	C₄⋊C₄	—	19	2	no	—
496	C₄⋊C₄	—	19	2	no	—
497	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
498	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
499	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
500	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
501	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
502	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
503	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
504	C₂²⋊C₄	—	19	1	no	—
505	C₂²⋊C₄	—	19	1	no	—
506	C₂²⋊C₄	—	19	2	no	—
507	C₂²⋊C₄	—	19	2	no	—
508	C₂²⋊C₄	—	19	2	no	—
509	C₂²⋊C₄	—	19	2	no	—
510	C₂²⋊C₄	—	19	2	no	—
511	C₂²⋊C₄	—	19	2	no	—
512	C₂²⋊C₄	—	19	1	no	—
513	C₂²⋊C₄	—	19	1	no	—
514	C₂²⋊C₄	—	19	1	no	—
515	C₂²⋊C₄	—	19	1	no	—
516	C₂²⋊C₄	—	19	2	no	—
517	C₂²⋊C₄	—	19	2	no	—
518	C₂²⋊C₄	—	19	2	no	—
519	C₂²⋊C₄	—	19	2	no	—
520	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
521	C₂²⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
522	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
523	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
524	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
525	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
526	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
527	C₄²	—	19	1	no	—
528	C₄²	—	19	1	no	—
529	C₄²	—	19	1	no	—
530	C₄²	—	19	1	no	—
531	C₄²	—	19	1	no	—
532	C₄²	—	19	1	no	—
533	C₄²	—	19	2	no	—
534	C₄²	—	19	2	no	—
535	C₄²	—	19	2	no	—
536	C₄²	—	19	2	no	—
537	C₄²	—	19	2	no	—
538	C₄²	—	19	2	no	—
539	C₄²	C₂²×D₁₉	1	1	yes	characteristic
540	C₄²	C₂²×D₁₉	1	1	yes	characteristic
541	C₄²	C₂²×D₁₉	1	2	yes	—
542	C₂³	—	19	1	no	—
543	C₂³	—	19	1	no	—
544	C₂³	—	38	2	no	—
545	C₂³	—	38	2	no	—
546	C₂³	—	76	1	no	—
547	C₂³	C₂³×D₁₉	1	1	yes	characteristic
548	C₂³	C₂³×D₁₉	1	2	yes	—
549	Q₈	—	2	2	no	—
550	Q₈	—	4	2	no	—
551	Q₈	—	38	4	no	—
552	Q₈	—	38	2	no	—
553	Q₈	—	38	2	no	—
554	Q₈	—	76	2	no	—
555	D₄	—	2	2	no	—
556	D₄	—	4	2	no	—
557	D₄	—	38	4	no	—
558	D₄	—	38	4	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	19	1	no	—
562	C₂×C₄	—	19	4	no	—
563	C₂×C₄	—	19	1	no	—
564	C₂×C₄	—	19	1	no	—
565	C₂×C₄	—	19	1	no	—
566	C₂×C₄	—	19	2	no	—
567	C₂×C₄	—	19	1	no	—
568	C₂×C₄	—	19	2	no	—
569	C₂×C₄	—	19	1	no	—
570	C₂×C₄	—	19	2	no	—
571	C₂×C₄	—	19	2	no	—
572	C₂×C₄	—	38	2	no	—
573	C₂×C₄	—	38	2	no	—
574	C₂×C₄	—	38	4	no	—
575	C₂×C₄	—	38	2	no	—
576	C₂×C₄	—	38	2	no	—
577	C₂×C₄	—	38	2	no	—
578	C₂×C₄	—	38	4	no	—
579	C₂×C₄	—	38	2	no	—
580	C₂×C₄	—	76	1	no	—
581	C₂×C₄	—	76	2	no	—
582	C₂×C₄	—	76	1	no	—
583	C₂×C₄	—	76	2	no	—
584	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
585	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
586	C₂×C₄	C₂³×D₁₉	1	2	yes	—
587	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
588	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
589	C₂×C₄	C₂³×D₁₉	1	2	yes	—
590	C₂×C₄	C₂³×D₁₉	1	2	yes	—
591	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
592	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
593	C₂²	—	2	1	no	—
594	C₂²	—	2	2	no	—
595	C₂²	—	2	2	no	—
596	C₂²	—	2	1	no	—
597	C₂²	—	2	2	no	—
598	C₂²	—	2	1	no	—
599	C₂²	—	19	2	no	—
600	C₂²	—	19	2	no	—
601	C₂²	—	38	1	no	—
602	C₂²	—	38	1	no	—
603	C₂²	—	38	1	no	—
604	C₂²	—	38	1	no	—
605	C₂²	—	76	4	no	—
606	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
607	C₄	—	2	1	no	—
608	C₄	—	2	2	no	—
609	C₄	—	2	1	no	—
610	C₄	—	2	1	no	—
611	C₄	—	2	1	no	—
612	C₄	—	2	2	no	—
613	C₄	—	2	1	no	—
614	C₄	—	2	2	no	—
615	C₄	—	19	2	no	—
616	C₄	—	38	1	no	—
617	C₄	—	38	2	no	—
618	C₄	—	38	2	no	—
619	C₄	—	38	1	no	—
620	C₄	—	38	1	no	—
621	C₄	—	38	2	no	—
622	C₄	—	38	1	no	—
623	C₄	—	38	2	no	—
624	C₄	—	38	1	no	—
625	C₄	#41×D₁₉	1	2	yes	—
626	C₂	—	4	1	no	—
627	C₂	—	4	2	no	—
628	C₂	—	38	2	no	—
629	C₂	—	38	2	no	—
630	C₂	C₂×#41×D₁₉	1	1	yes	characteristic
631	C₂	2₋¹⁺⁴×D₁₉	1	1	yes	characteristic
632	C₂	#11927379	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₁₉×#542	C₂
prime radical	#11927054	C₂
hypercenter	#542	D₁₉
hypocenter	C₁₉	#3495
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. #11927263	C₂	semidirect
2. #11927248	C₂	semidirect
3. #11927231	C₂	semidirect
4. #11927230	C₂	semidirect
5. #11927230	C₂	semidirect
6. #11927228	C₂	semidirect
7. #11927224	C₂	semidirect
8. #11927222	C₂	semidirect
9. #11927171	C₂	semidirect
10. #11927161	C₂	semidirect
11. #11927156	C₂	semidirect
12. #11927154	C₂	semidirect
13. #11927114	C₂	semidirect
14. #11927099	C₂	semidirect
15. #11927098	C₂	semidirect
16. #11927076	C₂	semidirect
17. #11927073	C₂	semidirect
19. C₂²⋊Q₈×D₁₉	C₂	semidirect
20. #11927023	C₂	semidirect
21. #11927020	C₂	semidirect
22. #117×D₁₉	C₂	semidirect
23. C₁₉×#542	C₂	semidirect
27. C₁₉×C₄⋊Q₈	C₂²	semidirect
28. C₁₉×#126	C₂²	semidirect
30. C₁₉×#124	C₂²	semidirect
33. C₁₉×C₂²⋊Q₈	C₂²	semidirect
35. C₄×Q₈×C₁₉	C₂²	semidirect
36. C₄×D₄×C₁₉	C₂²	semidirect
41. Q₈×Dic₁₉	C₂²	semidirect
42. Q₈×Dic₁₉	C₂²	semidirect
43. #10597390	C₂²	semidirect
44. #10597390	C₂²	semidirect
48. #10597382	C₂²	semidirect
51. D₄×Dic₁₉	C₂²	semidirect
55. #10597372	C₂²	semidirect
58. C₂×Dic₁₉⋊C₄	C₂²	semidirect
73. #10597336	C₂²	semidirect
74. #10597336	C₂²	semidirect
75. #10597336	C₂²	semidirect
76. #10597335	C₂²	semidirect
77. #10597335	C₂²	semidirect
78. #10597335	C₂²	semidirect
79. #10597335	C₂²	semidirect
80. #10597335	C₂²	semidirect
81. #10597334	C₂²	semidirect
82. #10597333	C₂²	semidirect
83. #10597333	C₂²	semidirect
84. #10597333	C₂²	semidirect
100. #10597325	C₂²	semidirect
101. #10597325	C₂²	semidirect
102. #10597325	C₂²	semidirect
104. #10597324	C₂²	semidirect
105. #10597324	C₂²	semidirect
106. #10597324	C₂²	semidirect
109. #10597323	C₂²	semidirect
110. #10597323	C₂²	semidirect
117. #10597316	C₂²	semidirect
118. #10597315	C₂²	semidirect
119. C₄×Dic₃₈	C₂²	semidirect
120. C₄×Dic₃₈	C₂²	semidirect
121. C₄×Dic₃₈	C₂²	semidirect
122. C₄×Dic₃₈	C₂²	semidirect
320. #542	D₁₉	semidirect
347. C₄⋊Q₈	C₂×D₁₉	semidirect
355. #126	C₂×D₁₉	semidirect
368. #124	C₂×D₁₉	semidirect
391. C₂²⋊Q₈	C₂×D₁₉	semidirect
404. C₄×Q₈	C₂×D₁₉	semidirect
412. C₄×D₄	C₂×D₁₉	semidirect
439. C₁₉	#3495	semidirect

Maximal subgroups

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

subgroup	index
#11927263	2
#11927248	2
#11927231	2
#11927230	2
#11927228	2
#11927224	2
#11927222	2
#11927171	2
#11927161	2
#11927156	2
#11927154	2
#11927114	2
#11927099	2
#11927098	2
#11927076	2
#11927073	2
#11927054	2
C₂²⋊Q₈×D₁₉	2
#11927023	2
#11927020	2
#117×D₁₉	2
C₁₉×#542	2
#3495	19