Subgroups — #14578136

Order 2432.

930 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927295	C₂	1	2	yes	maximal, complemented
2	#11927295	C₂	1	2	yes	maximal, complemented
3	#11927277	C₂	1	1	yes	maximal, characteristic, complemented
4	#11927277	C₂	1	1	yes	maximal, characteristic, complemented
5	#11927271	C₂	1	1	yes	maximal, characteristic, complemented
6	#11927269	C₂	1	1	yes	maximal, characteristic, complemented
7	#11927267	C₂	1	1	yes	maximal, characteristic, complemented
8	#11927264	C₂	1	1	yes	maximal, characteristic, complemented
9	#11927250	C₂	1	1	yes	maximal, characteristic, complemented
10	#11927229	C₂	1	2	yes	maximal, complemented
11	#11927228	C₂	1	2	yes	maximal, complemented
12	#11927168	C₂	1	1	yes	maximal, characteristic, complemented
13	#11927167	C₂	1	2	yes	maximal, complemented
14	#11927164	C₂	1	2	yes	maximal, complemented
15	#11927159	C₂	1	1	yes	maximal, characteristic, complemented
16	#11927157	C₂	1	1	yes	maximal, characteristic, complemented
17	#11927145	C₂	1	1	yes	maximal, characteristic
18	#11927141	C₂	1	2	yes	maximal, complemented
19	#11927140	C₂	1	2	yes	maximal, complemented
20	#11927098	C₂	1	1	yes	maximal, characteristic, complemented
21	#11927079	C₂	1	1	yes	maximal, characteristic, complemented
22	#11927076	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₉×#554	C₂	1	1	yes	maximal, characteristic, complemented
24	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₁₉×#125	C₂²	1	1	yes	characteristic
26	C₁₉×#125	C₂²	1	1	yes	characteristic
27	C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
28	C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
29	C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
30	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
31	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
32	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
33	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
35	#10597393	C₂²	1	2	yes	—
36	#10597392	C₂²	1	1	yes	characteristic
37	#10597392	C₂²	1	2	yes	—
38	#10597392	C₂²	1	2	yes	—
39	Q₈×Dic₁₉	C₂²	1	2	yes	—
40	#10597390	C₂²	1	1	yes	characteristic
41	#10597390	C₂²	1	2	yes	—
42	#10597386	C₂²	1	1	yes	characteristic
43	#10597384	C₂²	1	1	yes	characteristic
44	#10597382	C₂²	1	1	yes	characteristic
45	#10597382	C₂²	1	1	yes	characteristic
46	#10597376	C₂²	1	2	yes	—
47	#10597375	C₂²	1	2	yes	—
48	#10597375	C₂²	1	2	yes	—
49	#10597375	C₂²	1	2	yes	—
50	#10597375	C₂²	1	2	yes	—
51	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	—
52	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	—
53	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	—
54	#10597372	C₂²	1	2	yes	—
55	#10597372	C₂²	1	2	yes	—
56	#10597370	C₂²	1	2	yes	—
57	#10597370	C₂²	1	2	yes	—
58	#10597344	C₂²	1	2	yes	—
59	#10597344	C₂²	1	2	yes	—
60	#10597344	C₂²	1	2	yes	—
61	#10597344	C₂²	1	2	yes	—
62	#10597344	C₂²	1	2	yes	—
63	#10597344	C₂²	1	2	yes	—
64	#10597343	C₂²	1	1	yes	characteristic
65	#10597343	C₂²	1	1	yes	characteristic
66	#10597343	C₂²	1	1	yes	characteristic
67	#10597343	C₂²	1	2	yes	—
68	#10597342	C₂²	1	1	yes	characteristic
69	#10597342	C₂²	1	1	yes	characteristic
70	#10597342	C₂²	1	2	yes	—
71	#10597342	C₂²	1	2	yes	—
72	#10597341	C₂²	1	1	yes	characteristic
73	#10597340	C₂²	1	2	yes	—
74	#10597340	C₂²	1	2	yes	—
75	#10597339	C₂²	1	2	yes	—
76	#10597339	C₂²	1	1	yes	characteristic
77	#10597339	C₂²	1	1	yes	characteristic
78	#10597338	C₂²	1	2	yes	—
79	#10597338	C₂²	1	2	yes	—
80	C₄⋊C₄×D₁₉	C₂²	1	2	yes	—
81	#10597336	C₂²	1	1	yes	characteristic
82	#10597336	C₂²	1	1	yes	characteristic
83	#10597336	C₂²	1	2	yes	—
84	#10597336	C₂²	1	2	yes	—
85	#10597335	C₂²	1	1	yes	characteristic
86	#10597335	C₂²	1	1	yes	characteristic
87	#10597335	C₂²	1	2	yes	—
88	#10597335	C₂²	1	2	yes	—
89	#10597335	C₂²	1	2	yes	—
90	#10597335	C₂²	1	2	yes	—
91	#10597334	C₂²	1	1	yes	characteristic
92	#10597334	C₂²	1	1	yes	characteristic
93	#10597334	C₂²	1	2	yes	—
94	#10597333	C₂²	1	1	yes	characteristic
95	#10597333	C₂²	1	1	yes	characteristic
96	#10597333	C₂²	1	1	yes	characteristic
97	#10597333	C₂²	1	2	yes	—
98	#10597333	C₂²	1	1	yes	characteristic
99	#10597331	C₂²	1	2	yes	—
100	#10597331	C₂²	1	2	yes	—
101	#10597331	C₂²	1	2	yes	—
102	#10597330	C₂²	1	2	yes	—
103	#10597329	C₂²	1	2	yes	—
104	#10597329	C₂²	1	2	yes	—
105	#10597329	C₂²	1	2	yes	—
106	#10597329	C₂²	1	2	yes	—
107	#10597325	C₂²	1	2	yes	—
108	#10597325	C₂²	1	2	yes	—
109	#10597325	C₂²	1	2	yes	—
110	#10597325	C₂²	1	2	yes	—
111	#10597321	C₂²	1	1	yes	characteristic
112	#10597321	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	#10597315	C₂²	1	1	yes	characteristic
118	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
119	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
120	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
121	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
122	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
123	C₂×Q₈×C₁₉	C₂³	1	2	yes	—
124	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
125	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
126	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
127	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
128	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
129	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
132	C₂×D₇₆	C₂³	1	1	yes	characteristic
133	C₂×D₇₆	C₂³	1	2	yes	—
134	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
135	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
136	C₂×C₄×D₁₉	C₂³	1	2	yes	—
137	C₂×C₄×D₁₉	C₂³	1	2	yes	—
138	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
139	C₂×C₄×D₁₉	C₂³	1	2	yes	—
140	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
141	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
142	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
143	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
144	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
145	C₂×Dic₃₈	C₂³	1	2	yes	—
146	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
147	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
148	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
149	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
150	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
151	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
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	2	yes	—
156	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
157	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
158	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
159	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
160	C₄²×C₁₉	C₂³	1	1	yes	characteristic
161	C₄²×C₁₉	C₂³	1	1	yes	characteristic
162	C₄²×C₁₉	C₂³	1	1	yes	characteristic
163	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
164	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
165	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
166	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
167	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
168	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
169	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
170	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
171	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
172	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
173	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
174	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
175	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
176	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
177	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
178	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
179	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
180	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
181	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
182	C₄⋊Dic₁₉	C₂³	1	2	yes	—
183	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
184	C₄⋊Dic₁₉	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	2	yes	—
188	C₄⋊Dic₁₉	C₂³	1	2	yes	—
189	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
190	C₄⋊Dic₁₉	C₂³	1	2	yes	—
191	C₄⋊Dic₁₉	C₂³	1	2	yes	—
192	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
193	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
194	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
195	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
196	Dic₁₉⋊C₄	C₂³	1	2	yes	—
197	Dic₁₉⋊C₄	C₂³	1	2	yes	—
198	Dic₁₉⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
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	1	yes	characteristic
209	Dic₁₉⋊C₄	C₂³	1	2	yes	—
210	Dic₁₉⋊C₄	C₂³	1	2	yes	—
211	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
212	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
213	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
214	C₄×Dic₁₉	C₂³	1	2	yes	—
215	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
216	C₄×Dic₁₉	C₂³	1	2	yes	—
217	C₄×Dic₁₉	C₂³	1	2	yes	—
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	C₂³×C₁₉	C₂⁴	1	2	yes	—
223	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
224	C₂²×D₁₉	C₂⁴	1	2	yes	—
225	Q₈×C₁₉	—	4	1	no	—
226	Q₈×C₁₉	—	4	2	no	—
227	D₄×C₁₉	—	2	2	no	—
228	C₂×C₄×C₁₉	—	4	2	no	—
229	C₂×C₄×C₁₉	—	4	2	no	—
230	C₂×C₄×C₁₉	—	4	2	no	—
231	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
232	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
233	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
234	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
235	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
236	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
237	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
238	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
239	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
240	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
241	C₂²⋊D₁₉	—	4	2	no	—
242	C₂²⋊D₁₉	—	4	2	no	—
243	C₂²⋊D₁₉	—	4	2	no	—
244	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
245	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
246	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
247	C₂×Dic₁₉	C₂⁴	1	2	yes	—
248	C₂×Dic₁₉	C₂⁴	1	2	yes	—
249	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
250	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
251	C₂×Dic₁₉	C₂⁴	1	2	yes	—
252	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
253	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
254	D₇₆	—	2	2	no	—
255	D₇₆	—	4	2	no	—
256	C₄×D₁₉	—	2	2	no	—
257	C₄×D₁₉	—	4	1	no	—
258	C₄×D₁₉	—	4	2	no	—
259	C₄×D₁₉	—	4	2	no	—
260	C₄×D₁₉	—	4	2	no	—
261	C₄×D₁₉	—	4	1	no	—
262	Dic₃₈	—	2	2	no	—
263	Dic₃₈	—	2	2	no	—
264	Dic₃₈	—	4	2	no	—
265	Dic₃₈	—	4	1	no	—
266	Dic₃₈	—	4	1	no	—
267	Dic₃₈	—	4	1	no	—
268	#3557	—	19	1	no	maximal, Sylow
269	C₂²×C₁₉	—	2	2	no	—
270	C₂²×C₁₉	—	2	2	no	—
271	C₂²×C₁₉	—	2	2	no	—
272	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
273	C₂×D₁₉	—	2	1	no	—
274	C₂×D₁₉	—	2	2	no	—
275	C₂×D₁₉	—	2	2	no	—
276	C₂×D₁₉	—	2	1	no	—
277	C₂×D₁₉	—	2	2	no	—
278	C₂×D₁₉	—	2	1	no	—
279	C₄×C₁₉	—	2	2	no	—
280	C₄×C₁₉	—	2	1	no	—
281	C₄×C₁₉	—	2	1	no	—
282	C₄×C₁₉	—	2	1	no	—
283	C₄×C₁₉	—	2	1	no	—
284	C₄×C₁₉	—	2	1	no	—
285	C₄×C₁₉	—	2	2	no	—
286	C₄×C₁₉	—	2	2	no	—
287	C₄×C₁₉	—	2	1	no	—
288	C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
289	Dic₁₉	—	2	2	no	—
290	Dic₁₉	—	2	2	no	—
291	Dic₁₉	—	2	1	no	—
292	Dic₁₉	—	2	1	no	—
293	Dic₁₉	—	2	1	no	—
294	Dic₁₉	—	2	1	no	—
295	Dic₁₉	—	2	2	no	—
296	Dic₁₉	—	2	1	no	—
297	Dic₁₉	—	2	1	no	—
298	Dic₁₉	—	2	1	no	—
299	#563	—	19	2	no	—
300	#563	—	19	2	no	—
301	#559	—	19	1	no	—
302	#559	—	19	1	no	—
303	#557	—	19	1	no	—
304	#557	—	19	1	no	—
305	#556	—	19	1	no	—
306	#556	—	19	1	no	—
307	#554	—	19	1	no	—
308	#554	D₁₉	1	1	yes	characteristic, complemented
309	#552	—	19	2	no	—
310	#552	—	19	2	no	—
311	#542	—	19	1	no	—
312	#542	—	19	2	no	—
313	#542	—	19	2	no	—
314	#542	—	19	1	no	—
315	#541	—	19	1	no	—
316	#540	—	19	1	no	—
317	#539	—	19	2	no	—
318	#539	—	19	2	no	—
319	#533	—	19	1	no	—
320	#529	—	19	1	no	—
321	#529	—	19	1	no	—
322	C₂×C₁₉	—	4	2	no	—
323	C₂×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
324	C₂×C₁₉	#585	1	1	yes	characteristic
325	C₂×C₁₉	#585	1	1	yes	characteristic
326	D₁₉	—	4	1	no	—
327	D₁₉	—	4	2	no	—
328	C₄⋊Q₈	—	19	1	no	—
329	C₄⋊Q₈	—	19	2	no	—
330	C₄⋊Q₈	—	19	1	no	—
331	C₄⋊Q₈	—	19	1	no	—
332	C₄⋊Q₈	—	19	2	no	—
333	C₄⋊Q₈	—	19	1	no	—
334	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
335	#127	—	19	1	no	—
336	#126	—	19	2	no	—
337	#126	—	19	2	no	—
338	#126	—	19	2	no	—
339	#126	—	19	2	no	—
340	#126	—	19	2	no	—
341	#126	—	19	2	no	—
342	#126	—	19	2	no	—
343	#126	—	19	2	no	—
344	#126	—	19	2	no	—
345	#126	—	19	2	no	—
346	#125	—	19	1	no	—
347	#125	—	19	1	no	—
348	#125	—	19	1	no	—
349	#125	—	19	2	no	—
350	#125	—	19	2	no	—
351	#125	—	19	2	no	—
352	#125	—	19	2	no	—
353	#125	—	19	1	no	—
354	#125	—	19	2	no	—
355	#125	—	19	2	no	—
356	#125	C₂×D₁₉	1	1	yes	characteristic
357	#125	C₂×D₁₉	1	1	yes	characteristic
358	#124	—	19	2	no	—
359	#124	—	19	1	no	—
360	#124	—	19	1	no	—
361	#124	—	19	2	no	—
362	#124	—	19	2	no	—
363	#124	—	19	2	no	—
364	#124	—	19	1	no	—
365	#124	—	19	1	no	—
366	#123	—	19	2	no	—
367	#123	—	19	2	no	—
368	#123	—	19	2	no	—
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	—	19	2	no	—
376	C₂²⋊Q₈	—	19	1	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	1	no	—
382	C₂²⋊Q₈	—	19	1	no	—
383	C₂²⋊Q₈	—	19	1	no	—
384	C₂²⋊Q₈	—	19	1	no	—
385	C₂²⋊Q₈	—	19	1	no	—
386	C₂²⋊Q₈	—	19	2	no	—
387	C₂²⋊Q₈	—	19	2	no	—
388	C₂²⋊Q₈	—	19	2	no	—
389	C₂²⋊Q₈	C₂×D₁₉	1	2	yes	—
390	C₂²⋊Q₈	C₂×D₁₉	1	2	yes	—
391	C₂²⋊Q₈	C₂×D₁₉	1	2	yes	—
392	#121	—	19	1	no	—
393	#121	—	19	2	no	—
394	#121	—	19	1	no	—
395	#121	—	19	2	no	—
396	C₄×Q₈	—	19	2	no	—
397	C₄×Q₈	—	19	1	no	—
398	C₄×Q₈	—	19	1	no	—
399	C₄×Q₈	—	19	1	no	—
400	C₄×Q₈	—	19	2	no	—
401	C₄×Q₈	—	19	1	no	—
402	C₄×Q₈	—	19	1	no	—
403	C₄×Q₈	—	19	1	no	—
404	C₄×Q₈	—	19	1	no	—
405	C₄×Q₈	—	19	1	no	—
406	C₄×Q₈	—	19	1	no	—
407	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
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	—	19	1	no	—
413	C₄×D₄	—	19	1	no	—
414	C₄×D₄	—	19	1	no	—
415	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
416	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
417	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
418	#117	—	19	2	no	—
419	#117	—	19	2	no	—
420	#117	—	19	2	no	—
421	#117	—	19	2	no	—
422	#117	—	19	1	no	—
423	#117	—	19	1	no	—
424	C₂×C₄⋊C₄	—	19	2	no	—
425	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
426	C₂×C₄²	—	19	1	no	—
427	C₁₉	#3557	1	1	yes	characteristic, complemented, Sylow
428	C₂×Q₈	—	19	1	no	—
429	C₂×Q₈	—	19	1	no	—
430	C₂×Q₈	—	19	1	no	—
431	C₂×Q₈	—	19	2	no	—
432	C₂×Q₈	—	19	1	no	—
433	C₂×Q₈	—	19	1	no	—
434	C₂×Q₈	C₂²×D₁₉	1	2	yes	—
435	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
436	C₂×D₄	—	19	2	no	—
437	C₂×D₄	—	19	2	no	—
438	C₂×D₄	—	19	2	no	—
439	C₂×D₄	—	19	1	no	—
440	C₂×D₄	—	19	2	no	—
441	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
442	C₂²×C₄	—	19	1	no	—
443	C₂²×C₄	—	19	1	no	—
444	C₂²×C₄	—	19	1	no	—
445	C₂²×C₄	—	19	2	no	—
446	C₂²×C₄	—	19	2	no	—
447	C₂²×C₄	—	19	2	no	—
448	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
449	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
450	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
451	C₄⋊C₄	—	19	1	no	—
452	C₄⋊C₄	—	19	2	no	—
453	C₄⋊C₄	—	19	1	no	—
454	C₄⋊C₄	—	19	1	no	—
455	C₄⋊C₄	—	19	1	no	—
456	C₄⋊C₄	—	19	1	no	—
457	C₄⋊C₄	—	19	1	no	—
458	C₄⋊C₄	—	19	1	no	—
459	C₄⋊C₄	—	19	2	no	—
460	C₄⋊C₄	—	19	1	no	—
461	C₄⋊C₄	—	19	2	no	—
462	C₄⋊C₄	—	19	1	no	—
463	C₄⋊C₄	—	19	2	no	—
464	C₄⋊C₄	—	19	2	no	—
465	C₄⋊C₄	—	19	1	no	—
466	C₄⋊C₄	—	19	2	no	—
467	C₄⋊C₄	—	19	2	no	—
468	C₄⋊C₄	—	19	2	no	—
469	C₄⋊C₄	—	19	2	no	—
470	C₄⋊C₄	—	19	2	no	—
471	C₄⋊C₄	—	19	1	no	—
472	C₄⋊C₄	—	19	2	no	—
473	C₄⋊C₄	—	19	2	no	—
474	C₄⋊C₄	—	19	2	no	—
475	C₄⋊C₄	—	19	2	no	—
476	C₄⋊C₄	—	19	1	no	—
477	C₄⋊C₄	—	19	1	no	—
478	C₄⋊C₄	—	19	2	no	—
479	C₄⋊C₄	—	19	1	no	—
480	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
481	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
482	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
483	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
484	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
485	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
486	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
487	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
488	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
489	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
490	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
491	C₂²⋊C₄	—	19	2	no	—
492	C₂²⋊C₄	—	19	2	no	—
493	C₂²⋊C₄	—	19	2	no	—
494	C₂²⋊C₄	—	19	2	no	—
495	C₂²⋊C₄	—	19	2	no	—
496	C₂²⋊C₄	—	19	2	no	—
497	C₂²⋊C₄	—	19	1	no	—
498	C₂²⋊C₄	—	19	1	no	—
499	C₂²⋊C₄	—	19	2	no	—
500	C₂²⋊C₄	—	19	1	no	—
501	C₂²⋊C₄	—	19	1	no	—
502	C₂²⋊C₄	—	19	2	no	—
503	C₂²⋊C₄	—	19	2	no	—
504	C₂²⋊C₄	—	19	2	no	—
505	C₂²⋊C₄	—	19	2	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	C₂²×D₁₉	1	2	yes	—
511	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
512	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
513	C₄²	—	19	1	no	—
514	C₄²	—	19	1	no	—
515	C₄²	—	19	1	no	—
516	C₄²	—	19	2	no	—
517	C₄²	—	19	2	no	—
518	C₄²	—	19	1	no	—
519	C₄²	—	19	1	no	—
520	C₄²	—	19	2	no	—
521	C₄²	—	19	2	no	—
522	C₄²	—	19	2	no	—
523	C₄²	—	19	2	no	—
524	C₄²	C₂²×D₁₉	1	1	yes	characteristic
525	C₄²	C₂²×D₁₉	1	1	yes	characteristic
526	C₄²	C₂²×D₁₉	1	1	yes	characteristic
527	C₂³	—	19	1	no	—
528	C₂³	—	19	2	no	—
529	C₂³	C₂³×D₁₉	1	2	yes	—
530	Q₈	—	4	2	no	—
531	Q₈	—	4	1	no	—
532	Q₈	—	38	2	no	—
533	Q₈	—	38	2	no	—
534	Q₈	—	76	1	no	—
535	Q₈	—	76	1	no	—
536	Q₈	—	76	2	no	—
537	Q₈	—	76	1	no	—
538	D₄	—	2	2	no	—
539	D₄	—	38	2	no	—
540	D₄	—	76	2	no	—
541	D₄	—	76	2	no	—
542	D₄	—	76	2	no	—
543	D₄	—	76	2	no	—
544	C₂×C₄	—	4	2	no	—
545	C₂×C₄	—	4	2	no	—
546	C₂×C₄	—	4	2	no	—
547	C₂×C₄	—	19	1	no	—
548	C₂×C₄	—	19	2	no	—
549	C₂×C₄	—	19	2	no	—
550	C₂×C₄	—	19	1	no	—
551	C₂×C₄	—	19	1	no	—
552	C₂×C₄	—	19	1	no	—
553	C₂×C₄	—	19	1	no	—
554	C₂×C₄	—	19	1	no	—
555	C₂×C₄	—	19	2	no	—
556	C₂×C₄	—	19	1	no	—
557	C₂×C₄	—	38	2	no	—
558	C₂×C₄	—	76	1	no	—
559	C₂×C₄	—	76	2	no	—
560	C₂×C₄	—	76	2	no	—
561	C₂×C₄	—	76	2	no	—
562	C₂×C₄	—	76	1	no	—
563	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
564	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
565	C₂×C₄	C₂³×D₁₉	1	2	yes	—
566	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
567	C₂×C₄	C₂³×D₁₉	1	2	yes	—
568	C₂×C₄	C₂³×D₁₉	1	2	yes	—
569	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
570	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
571	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
572	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
573	C₂²	—	2	2	no	—
574	C₂²	—	2	2	no	—
575	C₂²	—	2	2	no	—
576	C₂²	—	38	1	no	—
577	C₂²	—	38	2	no	—
578	C₂²	—	38	1	no	—
579	C₂²	—	38	2	no	—
580	C₂²	—	38	2	no	—
581	C₂²	—	38	1	no	—
582	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
583	C₄	—	2	1	no	—
584	C₄	—	2	1	no	—
585	C₄	—	2	2	no	—
586	C₄	—	2	2	no	—
587	C₄	—	2	1	no	—
588	C₄	—	2	1	no	—
589	C₄	—	2	2	no	—
590	C₄	—	2	1	no	—
591	C₄	—	2	1	no	—
592	C₄	—	38	1	no	—
593	C₄	—	38	2	no	—
594	C₄	—	38	2	no	—
595	C₄	—	38	1	no	—
596	C₄	—	38	1	no	—
597	C₄	—	38	1	no	—
598	C₄	—	38	1	no	—
599	C₄	—	38	2	no	—
600	C₄	—	38	1	no	—
601	C₄	—	38	1	no	—
602	C₄	#10597433	1	2	yes	—
603	C₂	—	4	2	no	—
604	C₂	—	76	1	no	—
605	C₂	—	76	2	no	—
606	C₂	C₂×#10597433	1	1	yes	characteristic
607	C₂	#11927379	1	1	yes	characteristic
608	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	#11927145	C₂
hypercenter	#554	D₁₉
hypocenter	C₁₉	#3557
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. #11927295	C₂	semidirect
2. #11927295	C₂	semidirect
3. #11927277	C₂	semidirect
4. #11927277	C₂	semidirect
5. #11927271	C₂	semidirect
6. #11927269	C₂	semidirect
7. #11927267	C₂	semidirect
8. #11927264	C₂	semidirect
9. #11927250	C₂	semidirect
10. #11927229	C₂	semidirect
11. #11927228	C₂	semidirect
12. #11927168	C₂	semidirect
13. #11927167	C₂	semidirect
14. #11927164	C₂	semidirect
15. #11927159	C₂	semidirect
16. #11927157	C₂	semidirect
18. #11927141	C₂	semidirect
19. #11927140	C₂	semidirect
20. #11927098	C₂	semidirect
21. #11927079	C₂	semidirect
22. #11927076	C₂	semidirect
23. C₁₉×#554	C₂	semidirect
308. #554	D₁₉	semidirect
427. C₁₉	#3557	semidirect

Maximal subgroups

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

subgroup	index
#11927295	2
#11927277	2
#11927271	2
#11927269	2
#11927267	2
#11927264	2
#11927250	2
#11927229	2
#11927228	2
#11927168	2
#11927167	2
#11927164	2
#11927159	2
#11927157	2
#11927145	2
#11927141	2
#11927140	2
#11927098	2
#11927079	2
#11927076	2
C₁₉×#554	2
#3557	19