Subgroups — #18086749

Order 4864.

554 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926918	C₂	1	1	yes	maximal, characteristic
2	#14564562	C₂	1	1	yes	maximal, characteristic
3	#14564354	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11926290	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11926287	C₂	1	1	yes	maximal, characteristic
6	#14561469	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1988	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#64527	—	2	1	no	—
9	C₂²×#64527	—	2	1	no	—
10	C₂×#10597320	C₂²	1	1	yes	characteristic
11	#11926918	—	2	2	no	—
12	#11926918	—	2	2	no	—
13	C₂×C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
14	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×#10597266	—	2	1	no	—
17	C₂×#10597266	—	2	1	no	—
18	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
19	#11926299	—	2	1	no	—
20	#11926290	—	2	2	no	—
21	#11926287	—	2	2	no	—
22	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
25	C₁₉×#340	—	2	1	no	—
26	C₁₉×#340	—	2	1	no	—
27	C₂²×Q₈×C₁₉	—	2	1	no	—
28	C₂²×D₇₆	—	2	1	no	—
29	C₂²×D₇₆	—	2	1	no	—
30	C₂²×D₇₆	—	2	1	no	—
31	C₂²×C₈×C₁₉	—	2	1	no	—
32	C₁₉×C₄⋊Q₈	—	2	1	no	—
33	C₁₉×C₄⋊Q₈	—	2	1	no	—
34	C₁₉×C₄⋊Q₈	—	2	1	no	—
35	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
36	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
37	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
38	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
39	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₉	—	2	1	no	—
41	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
42	C₂×#64527	—	2	4	no	—
43	C₂×#64527	—	2	4	no	—
44	C₂×#64527	—	4	2	no	—
45	C₂×#64527	—	4	2	no	—
46	C₂×#64527	—	4	2	no	—
47	C₂×#64527	—	4	2	no	—
48	C₂²×C₁₉⋊C₈	—	2	1	no	—
49	C₂²×C₁₉⋊C₈	—	2	1	no	—
50	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
51	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
52	#10597320	—	2	1	no	—
53	#10597320	—	2	1	no	—
54	#10597320	—	2	1	no	—
55	#10597320	D₄	1	2	yes	—
56	C₁₉×C₄⋊C₈	—	2	1	no	—
57	C₁₉×C₄⋊C₈	—	2	1	no	—
58	C₁₉×#95	—	2	1	no	—
59	#10597266	—	4	2	no	—
60	#10597266	—	4	2	no	—
61	C₄⋊(C₁₉⋊C₈)	—	2	1	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)	—	4	2	no	—
66	C₄×C₁₉⋊C₈	—	2	1	no	—
67	C₄×C₁₉⋊C₈	—	2	1	no	—
68	C₂³×D₁₉	—	4	1	no	—
69	C₂×Q₈×C₁₉	—	2	2	no	—
70	C₂×Q₈×C₁₉	—	4	1	no	—
71	C₂×Q₈×C₁₉	—	4	1	no	—
72	C₂×Q₈×C₁₉	—	4	1	no	—
73	C₂×Q₈×C₁₉	—	4	1	no	—
74	C₂×Q₈×C₁₉	—	4	1	no	—
75	C₂²×C₄×C₁₉	—	2	1	no	—
76	C₂²×C₄×C₁₉	—	2	1	no	—
77	C₂²×C₄×C₁₉	—	4	1	no	—
78	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
81	C₂×D₇₆	—	2	2	no	—
82	C₂×D₇₆	—	2	2	no	—
83	C₂×D₇₆	—	2	2	no	—
84	C₂×D₇₆	—	4	1	no	—
85	C₂×D₇₆	—	4	1	no	—
86	C₂×D₇₆	—	4	1	no	—
87	C₂×D₇₆	—	4	1	no	—
88	C₂×D₇₆	—	4	1	no	—
89	C₂×D₇₆	—	4	1	no	—
90	C₂×D₇₆	—	4	1	no	—
91	C₂×D₇₆	—	4	1	no	—
92	C₂×D₇₆	—	4	1	no	—
93	C₂×D₇₆	—	4	1	no	—
94	C₂×D₇₆	—	4	1	no	—
95	C₂×D₇₆	—	8	1	no	—
96	C₂×D₇₆	—	8	1	no	—
97	C₂×C₈×C₁₉	—	4	1	no	—
98	C₂×C₈×C₁₉	—	4	1	no	—
99	C₂×C₈×C₁₉	—	4	1	no	—
100	C₄⋊C₄×C₁₉	—	2	1	no	—
101	C₄⋊C₄×C₁₉	—	2	2	no	—
102	C₄⋊C₄×C₁₉	—	2	2	no	—
103	C₄⋊C₄×C₁₉	—	2	1	no	—
104	C₄⋊C₄×C₁₉	—	2	1	no	—
105	C₄⋊C₄×C₁₉	—	4	1	no	—
106	C₄⋊C₄×C₁₉	—	4	1	no	—
107	C₄⋊C₄×C₁₉	SD₁₆	1	2	yes	complemented
108	C₄²×C₁₉	—	4	1	no	—
109	C₄²×C₁₉	—	4	1	no	—
110	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
111	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
112	C₄²×C₁₉	#41	1	1	yes	characteristic
113	C₄²×C₁₉	#41	1	1	yes	characteristic
114	#64527	—	4	8	no	—
115	#64527	—	4	8	no	—
116	C₂×C₁₉⋊C₈	—	2	1	no	—
117	C₂×C₁₉⋊C₈	—	2	1	no	—
118	C₂×C₁₉⋊C₈	—	2	1	no	—
119	C₂×C₁₉⋊C₈	—	2	1	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	C₂×C₁₉⋊C₈	—	4	1	no	—
126	C₂×C₁₉⋊C₈	D₈	1	2	yes	—
127	C₂×C₁₉⋊C₈	SD₁₆	1	2	yes	—
128	#10537	—	19	1	no	maximal, Sylow
129	C₂³×C₁₉	#121	1	1	yes	characteristic
130	C₂²×D₁₉	—	4	2	no	—
131	C₂²×D₁₉	—	8	1	no	—
132	C₂²×D₁₉	—	8	1	no	—
133	C₂²×D₁₉	—	8	1	no	—
134	C₂²×D₁₉	—	8	1	no	—
135	C₂²×D₁₉	—	8	1	no	—
136	C₂²×D₁₉	—	8	1	no	—
137	Q₈×C₁₉	—	4	2	no	—
138	Q₈×C₁₉	—	4	2	no	—
139	Q₈×C₁₉	—	8	1	no	—
140	Q₈×C₁₉	—	8	1	no	—
141	C₂×C₄×C₁₉	—	2	1	no	—
142	C₂×C₄×C₁₉	—	2	1	no	—
143	C₂×C₄×C₁₉	—	2	2	no	—
144	C₂×C₄×C₁₉	—	4	1	no	—
145	C₂×C₄×C₁₉	—	4	1	no	—
146	C₂×C₄×C₁₉	—	4	2	no	—
147	C₂×C₄×C₁₉	—	4	1	no	—
148	C₂×C₄×C₁₉	—	4	1	no	—
149	C₂×C₄×C₁₉	—	4	1	no	—
150	C₂×C₄×C₁₉	—	8	1	no	—
151	C₂×C₄×C₁₉	—	8	1	no	—
152	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
153	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
154	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
155	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
156	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
157	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
158	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
159	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
160	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
161	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
162	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
163	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
164	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
165	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
166	D₇₆	—	4	2	no	—
167	D₇₆	—	4	2	no	—
168	D₇₆	—	4	2	no	—
169	D₇₆	—	4	2	no	—
170	D₇₆	—	8	2	no	—
171	D₇₆	—	8	2	no	—
172	D₇₆	—	8	1	no	—
173	D₇₆	—	8	1	no	—
174	D₇₆	—	8	1	no	—
175	D₇₆	—	8	1	no	—
176	C₈×C₁₉	—	8	1	no	—
177	C₁₉⋊C₈	—	2	2	no	—
178	C₁₉⋊C₈	—	2	2	no	—
179	C₁₉⋊C₈	—	8	1	no	—
180	C₁₉⋊C₈	—	8	1	no	—
181	C₂×#492	—	19	1	no	—
182	#1988	D₁₉	1	1	yes	characteristic, complemented
183	#1982	—	19	1	no	—
184	#1939	—	19	1	no	—
185	C₂×#332	—	19	1	no	—
186	C₂×#331	—	19	1	no	—
187	#1277	—	19	1	no	—
188	C₂²×C₁₉	#394	1	1	yes	characteristic
189	C₂²×C₁₉	#459	1	1	yes	characteristic
190	C₂²×C₁₉	#460	1	1	yes	characteristic
191	C₂²×C₁₉	#465	1	1	yes	characteristic
192	C₂²×C₁₉	#468	1	1	yes	characteristic
193	C₂²×C₁₉	#471	1	1	yes	characteristic
194	C₂²×C₁₉	#471	1	1	yes	characteristic
195	C₂×D₁₉	—	8	2	no	—
196	C₂×D₁₉	—	8	2	no	—
197	C₂×D₁₉	—	8	2	no	—
198	C₂×D₁₉	—	16	1	no	—
199	C₂×D₁₉	—	16	1	no	—
200	C₂×D₁₉	—	16	1	no	—
201	C₂×D₁₉	—	16	1	no	—
202	C₄×C₁₉	—	2	1	no	—
203	C₄×C₁₉	—	2	1	no	—
204	C₄×C₁₉	—	4	2	no	—
205	C₄×C₁₉	—	8	1	no	—
206	C₄×C₁₉	—	8	2	no	—
207	C₄×C₁₉	#447	1	1	yes	characteristic
208	C₄×C₁₉	#450	1	1	yes	characteristic
209	C₄×C₁₉	#460	1	1	yes	characteristic
210	C₄×C₁₉	#461	1	1	yes	characteristic
211	C₄×C₁₉	#463	1	1	yes	characteristic
212	C₄×C₁₉	#464	1	1	yes	characteristic
213	C₄×C₁₉	#486	1	1	yes	characteristic
214	C₄×C₁₉	#490	1	1	yes	characteristic
215	C₂²×SD₁₆	—	38	1	no	—
216	C₂²×SD₁₆	—	38	1	no	—
217	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
218	C₂×#127	—	19	1	no	—
219	#492	—	38	2	no	—
220	#492	—	38	2	no	—
221	C₂×C₄⋊C₈	—	19	1	no	—
222	C₂×C₄⋊C₈	—	19	1	no	—
223	C₂×C₄⋊C₈	—	38	1	no	—
224	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
225	C₂×#102	—	38	1	no	—
226	C₂×#102	—	38	1	no	—
227	C₂×C₄×C₈	—	19	1	no	—
228	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
229	#340	—	2	1	no	—
230	#340	—	2	1	no	—
231	#336	—	38	1	no	—
232	#332	—	38	2	no	—
233	#331	—	38	2	no	—
234	C₂×C₁₉	#1665	1	1	yes	characteristic
235	C₂×C₁₉	#1666	1	1	yes	characteristic
236	C₂×C₁₉	#1685	1	1	yes	characteristic
237	C₂×C₁₉	#1686	1	1	yes	characteristic
238	C₂×C₁₉	#2041	1	1	yes	characteristic
239	C₂×C₁₉	#2046	1	1	yes	characteristic
240	C₂×C₁₉	#2055	1	1	yes	characteristic
241	D₁₉	—	16	2	no	—
242	C₂²×Q₈	—	2	1	no	—
243	C₂²×D₄	—	38	1	no	—
244	C₂²×D₄	—	38	1	no	—
245	C₂²×D₄	—	38	1	no	—
246	C₂×SD₁₆	—	38	4	no	—
247	C₂×SD₁₆	—	38	4	no	—
248	C₂×SD₁₆	—	76	2	no	—
249	C₂×SD₁₆	—	76	2	no	—
250	C₂×SD₁₆	—	76	2	no	—
251	C₂×SD₁₆	—	76	2	no	—
252	C₂²×C₈	—	2	1	no	—
253	C₂²×C₈	—	19	1	no	—
254	C₂²×C₈	—	19	1	no	—
255	C₂²×C₈	—	38	1	no	—
256	C₂²×C₈	—	38	1	no	—
257	C₄⋊Q₈	—	2	1	no	—
258	C₄⋊Q₈	—	2	1	no	—
259	C₄⋊Q₈	—	2	1	no	—
260	C₄⋊Q₈	D₇₆	1	2	yes	—
261	#127	—	19	2	no	—
262	#127	—	38	1	no	—
263	#127	—	38	1	no	—
264	#127	—	38	1	no	—
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
268	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
269	C₂×C₄²	—	2	1	no	—
270	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
271	C₄⋊C₈	—	2	1	no	—
272	C₄⋊C₈	—	2	1	no	—
273	C₄⋊C₈	—	38	1	no	—
274	C₄⋊C₈	—	38	1	no	—
275	C₄⋊C₈	—	38	1	no	—
276	C₄⋊C₈	—	38	1	no	—
277	C₄⋊C₈	—	76	2	no	—
278	#102	—	76	2	no	—
279	#102	—	76	2	no	—
280	C₄×C₈	—	38	1	no	—
281	C₄×C₈	—	38	1	no	—
282	#95	—	2	1	no	—
283	C₁₉	#10537	1	1	yes	characteristic, complemented, Sylow
284	C₂⁴	—	76	1	no	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	4	1	no	—
287	C₂×Q₈	—	4	1	no	—
288	C₂×Q₈	—	4	1	no	—
289	C₂×Q₈	—	4	1	no	—
290	C₂×Q₈	—	4	1	no	—
291	C₂×D₄	—	38	2	no	—
292	C₂×D₄	—	38	2	no	—
293	C₂×D₄	—	38	2	no	—
294	C₂×D₄	—	76	1	no	—
295	C₂×D₄	—	76	1	no	—
296	C₂×D₄	—	76	1	no	—
297	C₂×D₄	—	76	1	no	—
298	C₂×D₄	—	76	1	no	—
299	C₂×D₄	—	76	1	no	—
300	C₂×D₄	—	76	1	no	—
301	C₂×D₄	—	76	1	no	—
302	C₂×D₄	—	76	1	no	—
303	C₂×D₄	—	76	1	no	—
304	C₂×D₄	—	76	1	no	—
305	C₂×D₄	—	152	1	no	—
306	C₂×D₄	—	152	1	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	4	1	no	—
310	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
311	C₂²×C₄	#64543	1	1	yes	characteristic
312	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
313	SD₁₆	—	76	8	no	—
314	SD₁₆	—	76	8	no	—
315	C₂×C₈	—	4	1	no	—
316	C₂×C₈	—	4	1	no	—
317	C₂×C₈	—	4	1	no	—
318	C₂×C₈	—	19	2	no	—
319	C₂×C₈	—	19	2	no	—
320	C₂×C₈	—	38	1	no	—
321	C₂×C₈	—	38	1	no	—
322	C₂×C₈	—	38	1	no	—
323	C₂×C₈	—	38	1	no	—
324	C₂×C₈	—	76	1	no	—
325	C₂×C₈	—	76	1	no	—
326	C₂×C₈	—	76	1	no	—
327	C₂×C₈	—	76	1	no	—
328	C₂×C₈	—	76	1	no	—
329	C₂×C₈	—	76	1	no	—
330	C₄⋊C₄	—	2	1	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	1	no	—
333	C₄⋊C₄	—	2	1	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	4	1	no	—
336	C₄⋊C₄	—	4	1	no	—
337	C₄⋊C₄	#64527	1	2	yes	complemented
338	C₄²	—	4	1	no	—
339	C₄²	—	4	1	no	—
340	C₄²	C₂×D₇₆	1	1	yes	characteristic
341	C₄²	#64541	1	1	yes	characteristic
342	C₄²	D₄×D₁₉	1	1	yes	characteristic
343	C₄²	#64543	1	1	yes	characteristic
344	C₂³	—	76	2	no	—
345	C₂³	—	152	1	no	—
346	C₂³	—	152	1	no	—
347	C₂³	—	152	1	no	—
348	C₂³	—	152	1	no	—
349	C₂³	—	152	1	no	—
350	C₂³	—	152	1	no	—
351	C₂³	#10597385	1	1	yes	characteristic
352	Q₈	—	4	2	no	—
353	Q₈	—	4	2	no	—
354	Q₈	—	8	1	no	—
355	Q₈	—	8	1	no	—
356	D₄	—	76	2	no	—
357	D₄	—	76	2	no	—
358	D₄	—	76	2	no	—
359	D₄	—	76	2	no	—
360	D₄	—	152	2	no	—
361	D₄	—	152	2	no	—
362	D₄	—	152	1	no	—
363	D₄	—	152	1	no	—
364	D₄	—	152	1	no	—
365	D₄	—	152	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	8	1	no	—
376	C₂×C₄	—	8	1	no	—
377	C₂×C₄	#10597328	1	1	yes	characteristic
378	C₂×C₄	#10597329	1	1	yes	characteristic
379	C₂×C₄	#10597331	1	1	yes	characteristic
380	C₂×C₄	#10597332	1	1	yes	characteristic
381	C₂×C₄	D₈×D₁₉	1	1	yes	characteristic
382	C₂×C₄	#10597357	1	1	yes	characteristic
383	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
384	C₂×C₄	#10597360	1	1	yes	characteristic
385	C₂×C₄	#10597376	1	1	yes	characteristic
386	C₂×C₄	#10597384	1	1	yes	characteristic
387	C₂×C₄	C₂×#64527	1	1	yes	characteristic
388	C₂×C₄	#10597388	1	1	yes	characteristic
389	C₂×C₄	#10597395	1	1	yes	characteristic
390	C₂×C₄	#10597396	1	1	yes	characteristic
391	C₈	—	8	1	no	—
392	C₈	—	38	2	no	—
393	C₈	—	38	2	no	—
394	C₈	—	152	1	no	—
395	C₈	—	152	1	no	—
396	C₂²	—	304	1	no	—
397	C₂²	—	304	1	no	—
398	C₂²	—	304	1	no	—
399	C₂²	—	304	1	no	—
400	C₂²	—	152	2	no	—
401	C₂²	—	152	2	no	—
402	C₂²	—	152	2	no	—
403	C₂²	#11926460	1	1	yes	characteristic
404	C₂²	#11926737	1	1	yes	characteristic
405	C₂²	#11926742	1	1	yes	characteristic
406	C₂²	#11926775	1	1	yes	characteristic
407	C₂²	#11926792	1	1	yes	characteristic
408	C₂²	#11926809	1	1	yes	characteristic
409	C₂²	#11926809	1	1	yes	characteristic
410	C₄	—	2	1	no	—
411	C₄	—	2	1	no	—
412	C₄	—	4	2	no	—
413	C₄	—	8	2	no	—
414	C₄	—	8	1	no	—
415	C₄	#11926679	1	1	yes	characteristic
416	C₄	#11926696	1	1	yes	characteristic
417	C₄	#11926744	1	1	yes	characteristic
418	C₄	#11926746	1	1	yes	characteristic
419	C₄	#11926756	1	1	yes	characteristic
420	C₄	#11926766	1	1	yes	characteristic
421	C₄	#11926889	1	1	yes	characteristic
422	C₄	#11926907	1	1	yes	characteristic
423	C₂	—	304	2	no	—
424	C₂	#14562978	1	1	yes	characteristic
425	C₂	#14562985	1	1	yes	characteristic
426	C₂	#14563102	1	1	yes	characteristic
427	C₂	#14563109	1	1	yes	characteristic
428	C₂	#14564868	1	1	yes	characteristic
429	C₂	#14564895	1	1	yes	characteristic
430	C₂	#14564950	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597385
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1988	C₂
socle	C₂³×C₁₉	#121
prime radical	C₂×#10597320	C₂²
hypercenter	#1988	D₁₉
hypocenter	C₁₉	#10537
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1988

Complements

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

N	H ≅ G/N	type
3. #14564354	C₂	semidirect
4. C₂×#11926290	C₂	semidirect
6. #14561469	C₂	semidirect
7. C₁₉×#1988	C₂	semidirect
107. C₄⋊C₄×C₁₉	SD₁₆	semidirect
182. #1988	D₁₉	semidirect
283. C₁₉	#10537	semidirect
337. C₄⋊C₄	#64527	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926918	2
#14564562	2
#14564354	2
C₂×#11926290	2
C₂×#11926287	2
#14561469	2
C₁₉×#1988	2
#10537	19