Subgroups — #18085934

Order 4864.

516 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14568804	C₂	1	1	yes	maximal, characteristic
2	#14564436	C₂	1	1	yes	maximal, characteristic, complemented
3	#14563632	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926292	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11926271	C₂	1	1	yes	maximal, characteristic
6	#14561476	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1947	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10597315	C₂²	1	1	yes	characteristic
9	C₂×C₄×D₇₆	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×#10597267	—	2	2	no	—
12	C₂×#10597266	—	2	1	no	—
13	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
14	#11926457	—	2	2	no	—
15	#11926446	—	2	1	no	—
16	#11926410	—	2	1	no	—
17	#11926401	—	2	1	no	—
18	#11926401	—	2	1	no	—
19	#11926306	—	2	1	no	—
20	#11926292	—	2	2	no	—
21	#11926271	—	2	2	no	—
22	C₂×C₁₉×#107	—	2	1	no	—
23	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₁₉×#384	C₂²	1	1	yes	characteristic
25	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×#340	—	2	1	no	—
27	C₂²×D₇₆	D₄	1	1	yes	characteristic
28	C₂²×C₄×D₁₉	—	2	1	no	—
29	C₂²×Dic₃₈	D₄	1	2	yes	—
30	C₂²×C₈×C₁₉	—	2	1	no	—
31	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
32	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
33	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
34	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
35	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₉	—	2	1	no	—
37	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
38	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
39	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
40	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
41	C₂×C₄⋊Dic₁₉	—	2	1	no	—
42	C₂×C₄⋊Dic₁₉	—	2	1	no	—
43	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
44	C₂²×C₁₉⋊C₈	—	2	1	no	—
45	C₂²×C₁₉⋊C₈	—	2	1	no	—
46	C₄×D₇₆	—	2	1	no	—
47	C₄×D₇₆	—	2	1	no	—
48	C₄×D₇₆	—	2	1	no	—
49	C₄×D₇₆	—	2	1	no	—
50	#10597315	—	2	1	no	—
51	#10597315	—	2	1	no	—
52	#10597315	—	2	1	no	—
53	#10597315	—	2	1	no	—
54	C₁₉×#107	—	4	2	no	—
55	C₁₉×C₄⋊C₈	—	2	1	no	—
56	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
57	C₁₉×#95	—	2	1	no	—
58	C₁₉⋊#95	—	2	2	no	—
59	C₁₉⋊#95	—	2	2	no	—
60	#10597267	—	4	4	no	—
61	#10597266	—	4	2	no	—
62	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
63	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
64	C₄×C₁₉⋊C₈	—	2	1	no	—
65	C₄×C₁₉⋊C₈	—	2	1	no	—
66	C₂³×D₁₉	—	2	1	no	—
67	C₂²×C₄×C₁₉	—	2	1	no	—
68	C₂²×C₄×C₁₉	—	2	1	no	—
69	C₂²×C₄×C₁₉	—	4	1	no	—
70	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
73	C₂²×Dic₁₉	—	2	2	no	—
74	C₂²×Dic₁₉	—	2	1	no	—
75	C₂×D₇₆	—	2	1	no	—
76	C₂×D₇₆	—	2	1	no	—
77	C₂×D₇₆	—	2	1	no	—
78	C₂×D₇₆	—	2	1	no	—
79	C₂×D₇₆	—	2	1	no	—
80	C₂×D₇₆	Q₁₆	1	2	yes	—
81	C₂×C₄×D₁₉	—	4	1	no	—
82	C₂×C₄×D₁₉	—	4	1	no	—
83	C₂×C₄×D₁₉	—	4	1	no	—
84	C₂×C₄×D₁₉	—	4	1	no	—
85	C₂×C₄×D₁₉	—	4	1	no	—
86	C₂×C₄×D₁₉	—	4	1	no	—
87	C₂×Dic₃₈	—	2	2	no	—
88	C₂×Dic₃₈	—	2	2	no	—
89	C₂×Dic₃₈	—	4	2	no	—
90	C₂×Dic₃₈	—	4	2	no	—
91	C₂×C₈×C₁₉	—	2	2	no	—
92	C₂×C₈×C₁₉	—	4	1	no	—
93	C₂×C₈×C₁₉	—	4	1	no	—
94	C₄⋊C₄×C₁₉	—	2	1	no	—
95	C₄⋊C₄×C₁₉	—	2	1	no	—
96	C₄⋊C₄×C₁₉	—	2	1	no	—
97	C₄⋊C₄×C₁₉	—	2	1	no	—
98	C₄⋊C₄×C₁₉	—	4	2	no	—
99	C₄⋊C₄×C₁₉	—	4	1	no	—
100	C₄⋊C₄×C₁₉	—	4	1	no	—
101	C₄⋊C₄×C₁₉	—	4	1	no	—
102	C₄⋊C₄×C₁₉	—	4	1	no	—
103	C₄²×C₁₉	—	4	1	no	—
104	C₄²×C₁₉	—	4	1	no	—
105	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
106	C₄²×C₁₉	#41	1	1	yes	characteristic
107	C₄²×C₁₉	#41	1	1	yes	characteristic
108	C₄²×C₁₉	#41	1	1	yes	characteristic
109	(C₂×D₁₉)⋊C₄	—	4	1	no	—
110	(C₂×D₁₉)⋊C₄	—	4	1	no	—
111	(C₂×D₁₉)⋊C₄	—	8	2	no	—
112	(C₂×D₁₉)⋊C₄	—	8	2	no	—
113	C₄⋊Dic₁₉	—	2	1	no	—
114	C₄⋊Dic₁₉	—	2	1	no	—
115	C₄⋊Dic₁₉	—	4	1	no	—
116	C₄⋊Dic₁₉	—	4	1	no	—
117	C₄⋊Dic₁₉	—	4	1	no	—
118	C₄⋊Dic₁₉	—	4	1	no	—
119	C₂×C₁₉⋊C₈	—	2	2	no	—
120	C₂×C₁₉⋊C₈	—	4	1	no	—
121	C₂×C₁₉⋊C₈	—	4	1	no	—
122	C₂×C₁₉⋊C₈	—	4	1	no	—
123	C₂×C₁₉⋊C₈	—	4	1	no	—
124	C₂×C₁₉⋊C₈	—	4	1	no	—
125	#10413	—	19	1	no	maximal, Sylow
126	C₂³×C₁₉	#120	1	1	yes	characteristic
127	C₂²×D₁₉	—	2	2	no	—
128	C₂²×D₁₉	—	4	1	no	—
129	C₂²×D₁₉	—	4	1	no	—
130	C₂²×D₁₉	—	4	1	no	—
131	C₂²×D₁₉	—	4	1	no	—
132	C₂²×D₁₉	—	4	1	no	—
133	C₂²×D₁₉	—	4	1	no	—
134	C₂×C₄×C₁₉	—	2	1	no	—
135	C₂×C₄×C₁₉	—	2	1	no	—
136	C₂×C₄×C₁₉	—	4	1	no	—
137	C₂×C₄×C₁₉	—	4	1	no	—
138	C₂×C₄×C₁₉	—	4	1	no	—
139	C₂×C₄×C₁₉	—	4	1	no	—
140	C₂×C₄×C₁₉	—	4	1	no	—
141	C₂×C₄×C₁₉	—	4	1	no	—
142	C₂×C₄×C₁₉	—	8	1	no	—
143	C₂×C₄×C₁₉	—	8	1	no	—
144	C₂×C₄×C₁₉	—	8	1	no	—
145	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
146	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
147	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
148	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
149	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
150	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
151	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
152	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
153	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
154	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
155	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
156	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
157	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
158	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
159	C₂×Dic₁₉	—	4	1	no	—
160	C₂×Dic₁₉	—	4	2	no	—
161	C₂×Dic₁₉	—	4	1	no	—
162	C₂×Dic₁₉	—	4	1	no	—
163	C₂×Dic₁₉	—	4	2	no	—
164	C₂×Dic₁₉	—	4	2	no	—
165	D₇₆	—	2	2	no	—
166	D₇₆	—	2	2	no	—
167	D₇₆	—	4	1	no	—
168	D₇₆	—	4	1	no	—
169	C₄×D₁₉	—	8	1	no	—
170	C₄×D₁₉	—	8	1	no	—
171	C₄×D₁₉	—	8	1	no	—
172	C₄×D₁₉	—	8	1	no	—
173	Dic₃₈	—	4	4	no	—
174	Dic₃₈	—	8	2	no	—
175	C₈×C₁₉	—	4	2	no	—
176	C₁₉⋊C₈	—	4	2	no	—
177	C₁₉⋊C₈	—	8	1	no	—
178	#2563	—	19	1	no	—
179	#1956	—	19	1	no	—
180	#1947	D₁₉	1	1	yes	characteristic, complemented
181	#1802	—	19	1	no	—
182	C₂×#333	—	19	1	no	—
183	C₂×D₄⋊C₈	—	19	1	no	—
184	#1279	—	19	1	no	—
185	C₂²×C₁₉	#394	1	1	yes	characteristic
186	C₂²×C₁₉	#449	1	1	yes	characteristic
187	C₂²×C₁₉	#449	1	1	yes	characteristic
188	C₂²×C₁₉	#451	1	1	yes	characteristic
189	C₂²×C₁₉	#452	1	1	yes	characteristic
190	C₂²×C₁₉	#453	1	1	yes	characteristic
191	C₂²×C₁₉	#455	1	1	yes	characteristic
192	C₂×D₁₉	—	4	2	no	—
193	C₂×D₁₉	—	4	2	no	—
194	C₂×D₁₉	—	4	2	no	—
195	C₂×D₁₉	—	8	1	no	—
196	C₂×D₁₉	—	8	1	no	—
197	C₂×D₁₉	—	8	1	no	—
198	C₂×D₁₉	—	8	1	no	—
199	C₄×C₁₉	—	2	1	no	—
200	C₄×C₁₉	—	2	1	no	—
201	C₄×C₁₉	—	8	1	no	—
202	C₄×C₁₉	—	8	1	no	—
203	C₄×C₁₉	—	16	1	no	—
204	C₄×C₁₉	#463	1	1	yes	characteristic
205	C₄×C₁₉	#464	1	1	yes	characteristic
206	C₄×C₁₉	#467	1	1	yes	characteristic
207	C₄×C₁₉	#468	1	1	yes	characteristic
208	C₄×C₁₉	#484	1	1	yes	characteristic
209	C₄×C₁₉	#485	1	1	yes	characteristic
210	C₄×C₁₉	#488	1	1	yes	characteristic
211	C₄×C₁₉	#489	1	1	yes	characteristic
212	Dic₁₉	—	8	2	no	—
213	Dic₁₉	—	8	1	no	—
214	C₂×C₄⋊Q₈	—	19	1	no	—
215	C₂×C₄×D₄	—	19	1	no	—
216	C₂×#107	—	2	1	no	—
217	C₂×C₄⋊C₈	—	19	1	no	—
218	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
219	C₂×#103	—	38	2	no	—
220	C₂×#102	—	38	1	no	—
221	C₂×C₄×C₈	—	19	1	no	—
222	#393	—	38	2	no	—
223	#390	—	38	1	no	—
224	#384	C₂×D₁₉	1	1	yes	characteristic
225	#382	—	38	1	no	—
226	#380	—	38	1	no	—
227	#380	—	38	1	no	—
228	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
229	#340	—	2	1	no	—
230	#340	—	38	1	no	—
231	#333	—	38	2	no	—
232	D₄⋊C₈	—	38	2	no	—
233	C₂×C₁₉	#1624	1	1	yes	characteristic
234	C₂×C₁₉	#1632	1	1	yes	characteristic
235	C₂×C₁₉	#1644	1	1	yes	characteristic
236	C₂×C₁₉	#1646	1	1	yes	characteristic
237	C₂×C₁₉	#2036	1	1	yes	characteristic
238	C₂×C₁₉	#2037	1	1	yes	characteristic
239	C₂×C₁₉	#2042	1	1	yes	characteristic
240	D₁₉	—	8	2	no	—
241	C₂²×Q₈	—	19	2	no	—
242	C₂²×D₄	—	19	1	no	—
243	C₂³×C₄	—	38	1	no	—
244	C₂²×C₈	—	2	1	no	—
245	C₂²×C₈	—	38	1	no	—
246	C₂²×C₈	—	38	1	no	—
247	C₄⋊Q₈	—	38	1	no	—
248	C₄⋊Q₈	—	38	1	no	—
249	C₄⋊Q₈	—	38	1	no	—
250	C₄⋊Q₈	—	38	1	no	—
251	C₄×D₄	—	38	1	no	—
252	C₄×D₄	—	38	1	no	—
253	C₄×D₄	—	38	1	no	—
254	C₄×D₄	—	38	1	no	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	19	1	no	—
259	C₂×C₄⋊C₄	—	38	1	no	—
260	C₂×C₄⋊C₄	—	38	1	no	—
261	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
262	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
263	C₂×C₂²⋊C₄	—	38	1	no	—
264	C₂×C₂²⋊C₄	—	38	2	no	—
265	C₂×C₂²⋊C₄	—	38	2	no	—
266	C₂×C₄²	—	2	1	no	—
267	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
268	#107	—	4	2	no	—
269	C₄⋊C₈	—	2	1	no	—
270	C₄⋊C₈	—	38	1	no	—
271	C₄⋊C₈	—	38	1	no	—
272	C₄⋊C₈	D₇₆	1	2	yes	—
273	#103	—	76	4	no	—
274	#102	—	76	2	no	—
275	C₄×C₈	—	38	1	no	—
276	C₄×C₈	—	38	1	no	—
277	#95	—	2	1	no	—
278	#95	—	38	2	no	—
279	#95	—	38	2	no	—
280	C₁₉	#10413	1	1	yes	characteristic, complemented, Sylow
281	C₂⁴	—	38	1	no	—
282	C₂×Q₈	—	38	2	no	—
283	C₂×Q₈	—	38	2	no	—
284	C₂×Q₈	—	76	2	no	—
285	C₂×Q₈	—	76	2	no	—
286	C₂×D₄	—	19	2	no	—
287	C₂×D₄	—	38	1	no	—
288	C₂×D₄	—	38	1	no	—
289	C₂×D₄	—	38	1	no	—
290	C₂×D₄	—	38	1	no	—
291	C₂×D₄	—	38	1	no	—
292	C₂²×C₄	—	2	1	no	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	4	1	no	—
295	C₂²×C₄	—	38	1	no	—
296	C₂²×C₄	—	38	2	no	—
297	C₂²×C₄	—	76	1	no	—
298	C₂²×C₄	—	76	1	no	—
299	C₂²×C₄	—	76	1	no	—
300	C₂²×C₄	—	76	1	no	—
301	C₂²×C₄	—	76	1	no	—
302	C₂²×C₄	—	76	1	no	—
303	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
304	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
305	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	4	1	no	—
308	C₂×C₈	—	4	1	no	—
309	C₂×C₈	—	38	2	no	—
310	C₂×C₈	—	76	1	no	—
311	C₂×C₈	—	76	1	no	—
312	C₂×C₈	—	76	1	no	—
313	C₂×C₈	—	76	1	no	—
314	C₂×C₈	—	76	1	no	—
315	C₄⋊C₄	—	2	1	no	—
316	C₄⋊C₄	—	2	1	no	—
317	C₄⋊C₄	—	2	1	no	—
318	C₄⋊C₄	—	2	1	no	—
319	C₄⋊C₄	—	4	2	no	—
320	C₄⋊C₄	—	4	1	no	—
321	C₄⋊C₄	—	4	1	no	—
322	C₄⋊C₄	—	4	1	no	—
323	C₄⋊C₄	—	4	1	no	—
324	C₄⋊C₄	—	38	1	no	—
325	C₄⋊C₄	—	38	1	no	—
326	C₄⋊C₄	—	76	1	no	—
327	C₄⋊C₄	—	76	1	no	—
328	C₄⋊C₄	—	76	1	no	—
329	C₄⋊C₄	—	76	1	no	—
330	C₂²⋊C₄	—	76	1	no	—
331	C₂²⋊C₄	—	76	1	no	—
332	C₂²⋊C₄	—	152	2	no	—
333	C₂²⋊C₄	—	152	2	no	—
334	C₄²	—	4	1	no	—
335	C₄²	—	4	1	no	—
336	C₄²	C₂×D₇₆	1	1	yes	characteristic
337	C₄²	#64541	1	1	yes	characteristic
338	C₄²	#64545	1	1	yes	characteristic
339	C₄²	#64545	1	1	yes	characteristic
340	C₂³	—	38	2	no	—
341	C₂³	—	76	1	no	—
342	C₂³	—	76	1	no	—
343	C₂³	—	76	1	no	—
344	C₂³	—	76	1	no	—
345	C₂³	—	76	1	no	—
346	C₂³	—	76	1	no	—
347	C₂³	#10597383	1	1	yes	characteristic
348	Q₈	—	76	4	no	—
349	Q₈	—	152	2	no	—
350	D₄	—	38	2	no	—
351	D₄	—	38	2	no	—
352	D₄	—	76	1	no	—
353	D₄	—	76	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	8	1	no	—
363	C₂×C₄	—	8	1	no	—
364	C₂×C₄	—	8	1	no	—
365	C₂×C₄	—	76	1	no	—
366	C₂×C₄	—	76	1	no	—
367	C₂×C₄	—	76	2	no	—
368	C₂×C₄	—	76	1	no	—
369	C₂×C₄	—	76	2	no	—
370	C₂×C₄	—	76	2	no	—
371	C₂×C₄	—	152	1	no	—
372	C₂×C₄	—	152	1	no	—
373	C₂×C₄	—	152	1	no	—
374	C₂×C₄	—	152	1	no	—
375	C₂×C₄	#10597340	1	1	yes	characteristic
376	C₂×C₄	#10597340	1	1	yes	characteristic
377	C₂×C₄	#10597341	1	1	yes	characteristic
378	C₂×C₄	#10597341	1	1	yes	characteristic
379	C₂×C₄	#10597357	1	1	yes	characteristic
380	C₂×C₄	#10597358	1	1	yes	characteristic
381	C₂×C₄	Q₁₆×D₁₉	1	1	yes	characteristic
382	C₂×C₄	#10597364	1	1	yes	characteristic
383	C₂×C₄	#10597376	1	1	yes	characteristic
384	C₂×C₄	#10597378	1	1	yes	characteristic
385	C₂×C₄	#10597388	1	1	yes	characteristic
386	C₂×C₄	#10597393	1	1	yes	characteristic
387	C₂×C₄	#10597396	1	1	yes	characteristic
388	C₂×C₄	#10597396	1	1	yes	characteristic
389	C₈	—	4	2	no	—
390	C₈	—	76	2	no	—
391	C₈	—	152	1	no	—
392	C₂²	—	76	2	no	—
393	C₂²	—	76	2	no	—
394	C₂²	—	76	2	no	—
395	C₂²	—	152	1	no	—
396	C₂²	—	152	1	no	—
397	C₂²	—	152	1	no	—
398	C₂²	—	152	1	no	—
399	C₂²	#11926461	1	1	yes	characteristic
400	C₂²	#11926686	1	1	yes	characteristic
401	C₂²	#11926687	1	1	yes	characteristic
402	C₂²	#11926698	1	1	yes	characteristic
403	C₂²	#11926704	1	1	yes	characteristic
404	C₂²	#11926710	1	1	yes	characteristic
405	C₂²	#11926720	1	1	yes	characteristic
406	C₄	—	2	1	no	—
407	C₄	—	2	1	no	—
408	C₄	—	8	1	no	—
409	C₄	—	8	1	no	—
410	C₄	—	16	1	no	—
411	C₄	—	152	1	no	—
412	C₄	—	152	2	no	—
413	C₄	#11926759	1	1	yes	characteristic
414	C₄	#11926766	1	1	yes	characteristic
415	C₄	#11926786	1	1	yes	characteristic
416	C₄	#11926791	1	1	yes	characteristic
417	C₄	#11926881	1	1	yes	characteristic
418	C₄	#11926887	1	1	yes	characteristic
419	C₄	#11926901	1	1	yes	characteristic
420	C₄	#11926906	1	1	yes	characteristic
421	C₂	—	152	2	no	—
422	C₂	#14562717	1	1	yes	characteristic
423	C₂	#14562768	1	1	yes	characteristic
424	C₂	#14562847	1	1	yes	characteristic
425	C₂	#14562862	1	1	yes	characteristic
426	C₂	#14564840	1	1	yes	characteristic
427	C₂	#14564847	1	1	yes	characteristic
428	C₂	#14564876	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597383
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1947	C₂
socle	C₂³×C₁₉	#120
prime radical	C₂²×D₇₆	D₄
hypercenter	#1947	D₁₉
hypocenter	C₁₉	#10413
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1947

Complements

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

N	H ≅ G/N	type
2. #14564436	C₂	semidirect
4. C₂×#11926292	C₂	semidirect
6. #14561476	C₂	semidirect
7. C₁₉×#1947	C₂	semidirect
180. #1947	D₁₉	semidirect
280. C₁₉	#10413	semidirect

Maximal subgroups

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

subgroup	index
#14568804	2
#14564436	2
#14563632	2
C₂×#11926292	2
C₂×#11926271	2
#14561476	2
C₁₉×#1947	2
#10413	19