Subgroups — #18083637

Order 4864.

738 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926892	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#11926739	C₂	1	1	yes	maximal, characteristic
3	#14564562	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11926290	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₄⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561476	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2542	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#64525	—	2	1	no	—
9	C₂×#10597320	C₂²	1	1	yes	characteristic
10	#11926892	—	2	2	no	—
11	#11926892	—	2	2	no	—
12	#11926739	—	2	2	no	—
13	#11926739	—	2	2	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	2	no	—
17	C₂×#10597266	—	2	1	no	—
18	C₂×#10597266	—	2	2	no	—
19	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
20	#11926290	—	2	2	no	—
21	D₄⋊(C₁₉⋊C₈)	—	2	2	no	—
22	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×C₂²⋊Q₈	—	2	2	no	—
24	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
25	C₁₉×#399	—	2	2	no	—
26	C₁₉×#390	—	2	1	no	—
27	C₁₉×#384	—	2	1	no	—
28	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
29	C₂²×Q₈×C₁₉	—	2	1	no	—
30	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
31	C₂³×C₄×C₁₉	—	2	1	no	—
32	C₂²×D₇₆	—	2	1	no	—
33	C₂²×D₇₆	—	2	1	no	—
34	C₂²×D₇₆	—	2	1	no	—
35	C₁₉×C₄⋊Q₈	—	2	1	no	—
36	C₁₉×C₄⋊Q₈	—	2	1	no	—
37	C₁₉×C₄⋊Q₈	—	2	1	no	—
38	C₁₉×C₄⋊Q₈	—	2	1	no	—
39	C₁₉×C₂²⋊Q₈	—	4	4	no	—
40	C₁₉×C₂²⋊Q₈	—	4	4	no	—
41	C₄×D₄×C₁₉	—	2	1	no	—
42	C₄×D₄×C₁₉	—	2	1	no	—
43	C₄×D₄×C₁₉	—	2	1	no	—
44	C₄×D₄×C₁₉	—	2	1	no	—
45	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
46	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
47	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
48	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
49	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
50	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
51	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
52	C₂×C₄²×C₁₉	—	2	1	no	—
53	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
54	C₂×#64525	—	2	4	no	—
55	C₂×#64525	—	4	2	no	—
56	C₂×#64525	—	4	2	no	—
57	C₂²×C₁₉⋊C₈	—	2	1	no	—
58	C₂²×C₁₉⋊C₈	—	2	1	no	—
59	C₂²×C₁₉⋊C₈	—	2	1	no	—
60	#10597320	—	2	1	no	—
61	#10597320	—	2	1	no	—
62	#10597320	—	2	1	no	—
63	#10597320	D₄	1	2	yes	—
64	C₁₉×#95	—	2	1	no	—
65	#10597266	—	2	8	no	—
66	#10597266	—	2	4	no	—
67	#10597266	—	4	4	no	—
68	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
69	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
70	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
71	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
72	C₄×C₁₉⋊C₈	—	2	1	no	—
73	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
74	C₂⁴×C₁₉	—	2	1	no	—
75	C₂³×D₁₉	—	4	1	no	—
76	C₂×Q₈×C₁₉	—	4	1	no	—
77	C₂×Q₈×C₁₉	—	4	1	no	—
78	C₂×Q₈×C₁₉	—	4	2	no	—
79	C₂×Q₈×C₁₉	—	4	2	no	—
80	C₂×D₄×C₁₉	—	2	1	no	—
81	C₂×D₄×C₁₉	—	2	1	no	—
82	C₂×D₄×C₁₉	—	2	1	no	—
83	C₂×D₄×C₁₉	—	2	1	no	—
84	C₂×D₄×C₁₉	—	2	1	no	—
85	C₂×D₄×C₁₉	SD₁₆	1	2	yes	—
86	C₂²×C₄×C₁₉	—	2	2	no	—
87	C₂²×C₄×C₁₉	—	2	2	no	—
88	C₂²×C₄×C₁₉	—	2	1	no	—
89	C₂²×C₄×C₁₉	—	4	1	no	—
90	C₂²×C₄×C₁₉	—	4	1	no	—
91	C₂²×C₄×C₁₉	—	4	2	no	—
92	C₂²×C₄×C₁₉	—	4	2	no	—
93	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
96	C₂×D₇₆	—	2	2	no	—
97	C₂×D₇₆	—	2	2	no	—
98	C₂×D₇₆	—	2	2	no	—
99	C₂×D₇₆	—	4	4	no	—
100	C₂×D₇₆	—	4	2	no	—
101	C₂×D₇₆	—	4	1	no	—
102	C₂×D₇₆	—	4	1	no	—
103	C₂×D₇₆	—	4	1	no	—
104	C₂×D₇₆	—	4	2	no	—
105	C₂×D₇₆	—	4	1	no	—
106	C₂×D₇₆	—	4	1	no	—
107	C₂×D₇₆	—	4	1	no	—
108	C₂×D₇₆	—	4	1	no	—
109	C₄⋊C₄×C₁₉	—	2	2	no	—
110	C₄⋊C₄×C₁₉	—	2	1	no	—
111	C₄⋊C₄×C₁₉	—	2	2	no	—
112	C₄⋊C₄×C₁₉	—	2	1	no	—
113	C₄⋊C₄×C₁₉	—	2	2	no	—
114	C₄⋊C₄×C₁₉	—	4	8	no	—
115	C₄⋊C₄×C₁₉	—	4	1	no	—
116	C₄⋊C₄×C₁₉	—	4	1	no	—
117	C₄⋊C₄×C₁₉	D₈	1	4	yes	complemented
118	C₂²⋊C₄×C₁₉	—	4	8	no	—
119	C₂²⋊C₄×C₁₉	—	4	1	no	—
120	C₂²⋊C₄×C₁₉	—	4	1	no	—
121	C₄²×C₁₉	—	4	1	no	—
122	C₄²×C₁₉	—	4	1	no	—
123	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
124	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
125	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₁₉	#41	1	1	yes	characteristic
127	#64525	—	4	8	no	—
128	C₂×C₁₉⋊C₈	—	2	2	no	—
129	C₂×C₁₉⋊C₈	—	2	2	no	—
130	C₂×C₁₉⋊C₈	—	4	2	no	—
131	C₂×C₁₉⋊C₈	—	4	1	no	—
132	C₂×C₁₉⋊C₈	—	4	1	no	—
133	C₂×C₁₉⋊C₈	—	4	1	no	—
134	C₂×C₁₉⋊C₈	—	4	2	no	—
135	#10052	—	19	1	no	maximal, Sylow
136	C₂³×C₁₉	—	2	2	no	—
137	C₂³×C₁₉	—	4	1	no	—
138	C₂³×C₁₉	—	4	2	no	—
139	C₂³×C₁₉	—	4	1	no	—
140	C₂³×C₁₉	—	4	2	no	—
141	C₂³×C₁₉	#120	1	1	yes	characteristic
142	C₂²×D₁₉	—	4	2	no	—
143	C₂²×D₁₉	—	8	2	no	—
144	C₂²×D₁₉	—	8	1	no	—
145	C₂²×D₁₉	—	8	1	no	—
146	C₂²×D₁₉	—	8	2	no	—
147	Q₈×C₁₉	—	8	2	no	—
148	Q₈×C₁₉	—	8	1	no	—
149	Q₈×C₁₉	—	8	1	no	—
150	D₄×C₁₉	—	2	2	no	—
151	D₄×C₁₉	—	2	2	no	—
152	D₄×C₁₉	—	4	1	no	—
153	D₄×C₁₉	—	4	1	no	—
154	C₂×C₄×C₁₉	—	2	2	no	—
155	C₂×C₄×C₁₉	—	2	4	no	—
156	C₂×C₄×C₁₉	—	4	2	no	—
157	C₂×C₄×C₁₉	—	4	2	no	—
158	C₂×C₄×C₁₉	—	4	1	no	—
159	C₂×C₄×C₁₉	—	4	2	no	—
160	C₂×C₄×C₁₉	—	4	4	no	—
161	C₂×C₄×C₁₉	—	4	2	no	—
162	C₂×C₄×C₁₉	—	8	2	no	—
163	C₂×C₄×C₁₉	—	8	1	no	—
164	C₂×C₄×C₁₉	—	8	1	no	—
165	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
166	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
167	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
168	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
169	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
170	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
171	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
172	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
173	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
174	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
175	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
176	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
177	D₇₆	—	4	4	no	—
178	D₇₆	—	4	2	no	—
179	D₇₆	—	4	2	no	—
180	D₇₆	—	4	4	no	—
181	D₇₆	—	8	2	no	—
182	D₇₆	—	8	1	no	—
183	D₇₆	—	8	1	no	—
184	D₇₆	—	8	1	no	—
185	D₇₆	—	8	1	no	—
186	C₁₉⋊C₈	—	4	2	no	—
187	C₁₉⋊C₈	—	4	2	no	—
188	C₁₉⋊C₈	—	8	1	no	—
189	C₂×#486	—	19	1	no	—
190	C₂×#459	—	19	1	no	—
191	#2542	D₁₉	1	1	yes	characteristic, complemented
192	#1982	—	19	1	no	—
193	C₂×#332	—	19	1	no	—
194	C₂×D₄⋊C₈	—	19	1	no	—
195	#1279	—	19	1	no	—
196	C₂²×C₁₉	—	4	4	no	—
197	C₂²×C₁₉	—	4	2	no	—
198	C₂²×C₁₉	—	8	2	no	—
199	C₂²×C₁₉	—	8	1	no	—
200	C₂²×C₁₉	—	8	1	no	—
201	C₂²×C₁₉	#392	1	1	yes	characteristic
202	C₂²×C₁₉	#447	1	2	yes	—
203	C₂²×C₁₉	#448	1	1	yes	characteristic
204	C₂²×C₁₉	#449	1	1	yes	characteristic
205	C₂²×C₁₉	#454	1	2	yes	—
206	C₂×D₁₉	—	8	2	no	—
207	C₂×D₁₉	—	8	2	no	—
208	C₂×D₁₉	—	8	2	no	—
209	C₂×D₁₉	—	16	2	no	—
210	C₂×D₁₉	—	16	2	no	—
211	C₄×C₁₉	—	2	1	no	—
212	C₄×C₁₉	—	2	1	no	—
213	C₄×C₁₉	—	4	4	no	—
214	C₄×C₁₉	—	8	1	no	—
215	C₄×C₁₉	—	8	2	no	—
216	C₄×C₁₉	#450	1	1	yes	characteristic
217	C₄×C₁₉	#452	1	1	yes	characteristic
218	C₄×C₁₉	#459	1	2	yes	—
219	C₄×C₁₉	#465	1	1	yes	characteristic
220	C₄×C₁₉	#468	1	1	yes	characteristic
221	C₄×C₁₉	#493	1	1	yes	characteristic
222	C₄×C₁₉	#496	1	1	yes	characteristic
223	C₂²×D₈	—	38	1	no	—
224	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
225	C₂×#127	—	19	1	no	—
226	C₂×C₂²⋊Q₈	—	2	2	no	—
227	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
228	#486	—	38	2	no	—
229	#486	—	38	2	no	—
230	#459	—	38	2	no	—
231	#459	—	38	2	no	—
232	C₂×C₄⋊C₈	—	19	1	no	—
233	C₂×C₄⋊C₈	—	19	1	no	—
234	C₂×#102	—	38	2	no	—
235	C₂×#102	—	38	1	no	—
236	C₂×#102	—	38	2	no	—
237	C₂×C₄×C₈	—	19	1	no	—
238	#399	—	2	2	no	—
239	#390	—	2	1	no	—
240	#384	—	2	1	no	—
241	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
242	#332	—	38	2	no	—
243	D₄⋊C₈	—	38	2	no	—
244	C₂×C₁₉	—	8	2	no	—
245	C₂×C₁₉	#1625	1	2	yes	—
246	C₂×C₁₉	#1627	1	2	yes	—
247	C₂×C₁₉	#2000	1	1	yes	characteristic
248	C₂×C₁₉	#2003	1	1	yes	characteristic
249	C₂×C₁₉	#2011	1	1	yes	characteristic
250	D₁₉	—	16	2	no	—
251	C₂²×Q₈	—	2	1	no	—
252	C₂²×D₄	—	38	1	no	—
253	C₂²×D₄	—	38	1	no	—
254	C₂²×D₄	—	38	1	no	—
255	C₂²×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
256	C₂³×C₄	—	2	1	no	—
257	C₂×D₈	—	38	4	no	—
258	C₂×D₈	—	76	2	no	—
259	C₂×D₈	—	76	2	no	—
260	C₂²×C₈	—	38	1	no	—
261	C₂²×C₈	—	38	1	no	—
262	C₂²×C₈	—	38	1	no	—
263	C₄⋊Q₈	—	2	1	no	—
264	C₄⋊Q₈	—	2	1	no	—
265	C₄⋊Q₈	—	2	1	no	—
266	C₄⋊Q₈	—	2	1	no	—
267	#127	—	19	2	no	—
268	#127	—	38	1	no	—
269	#127	—	38	1	no	—
270	#127	—	38	1	no	—
271	C₂²⋊Q₈	—	4	4	no	—
272	C₂²⋊Q₈	—	4	4	no	—
273	C₄×D₄	—	2	1	no	—
274	C₄×D₄	—	2	1	no	—
275	C₄×D₄	—	2	1	no	—
276	C₄×D₄	—	2	1	no	—
277	C₂×C₄⋊C₄	—	2	4	no	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
280	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
281	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
282	C₂×C₂²⋊C₄	—	2	4	no	—
283	C₂×C₂²⋊C₄	—	2	1	no	—
284	C₂×C₄²	—	2	1	no	—
285	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
286	C₄⋊C₈	—	19	2	no	—
287	C₄⋊C₈	—	38	1	no	—
288	C₄⋊C₈	—	38	1	no	—
289	C₄⋊C₈	—	38	1	no	—
290	#102	—	38	4	no	—
291	#102	—	38	8	no	—
292	#102	—	76	4	no	—
293	C₄×C₈	—	19	2	no	—
294	C₄×C₈	—	38	1	no	—
295	#95	—	2	1	no	—
296	C₁₉	#10052	1	1	yes	characteristic, complemented, Sylow
297	C₂⁴	—	2	1	no	—
298	C₂⁴	—	76	1	no	—
299	C₂×Q₈	—	4	2	no	—
300	C₂×Q₈	—	4	2	no	—
301	C₂×Q₈	—	4	1	no	—
302	C₂×Q₈	—	4	1	no	—
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	—	2	1	no	—
305	C₂×D₄	—	2	1	no	—
306	C₂×D₄	—	2	1	no	—
307	C₂×D₄	—	2	1	no	—
308	C₂×D₄	—	38	2	no	—
309	C₂×D₄	—	38	2	no	—
310	C₂×D₄	—	38	2	no	—
311	C₂×D₄	—	76	4	no	—
312	C₂×D₄	—	76	2	no	—
313	C₂×D₄	—	76	2	no	—
314	C₂×D₄	—	76	1	no	—
315	C₂×D₄	—	76	1	no	—
316	C₂×D₄	—	76	1	no	—
317	C₂×D₄	—	76	1	no	—
318	C₂×D₄	—	76	1	no	—
319	C₂×D₄	—	76	1	no	—
320	C₂×D₄	—	76	1	no	—
321	C₂×D₄	#64527	1	2	yes	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	4	2	no	—
326	C₂²×C₄	—	4	2	no	—
327	C₂²×C₄	—	4	1	no	—
328	C₂²×C₄	—	4	1	no	—
329	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
330	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
331	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
332	D₈	—	76	8	no	—
333	C₂×C₈	—	38	2	no	—
334	C₂×C₈	—	38	2	no	—
335	C₂×C₈	—	76	2	no	—
336	C₂×C₈	—	76	1	no	—
337	C₂×C₈	—	76	1	no	—
338	C₂×C₈	—	76	2	no	—
339	C₂×C₈	—	76	1	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	1	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	4	8	no	—
346	C₄⋊C₄	—	4	1	no	—
347	C₄⋊C₄	—	4	1	no	—
348	C₄⋊C₄	#64525	1	4	yes	complemented
349	C₂²⋊C₄	—	4	8	no	—
350	C₂²⋊C₄	—	4	1	no	—
351	C₂²⋊C₄	—	4	1	no	—
352	C₄²	—	4	1	no	—
353	C₄²	—	4	1	no	—
354	C₄²	D₄×D₁₉	1	1	yes	characteristic
355	C₄²	D₄×D₁₉	1	1	yes	characteristic
356	C₄²	D₄×D₁₉	1	1	yes	characteristic
357	C₄²	#64543	1	1	yes	characteristic
358	C₂³	—	2	2	no	—
359	C₂³	—	4	2	no	—
360	C₂³	—	4	1	no	—
361	C₂³	—	4	1	no	—
362	C₂³	—	4	2	no	—
363	C₂³	—	76	2	no	—
364	C₂³	—	152	2	no	—
365	C₂³	—	152	1	no	—
366	C₂³	—	152	1	no	—
367	C₂³	—	152	2	no	—
368	C₂³	#10597399	1	1	yes	characteristic
369	Q₈	—	8	1	no	—
370	Q₈	—	8	1	no	—
371	Q₈	—	8	2	no	—
372	D₄	—	2	2	no	—
373	D₄	—	2	2	no	—
374	D₄	—	4	1	no	—
375	D₄	—	4	1	no	—
376	D₄	—	76	4	no	—
377	D₄	—	76	2	no	—
378	D₄	—	76	2	no	—
379	D₄	—	76	4	no	—
380	D₄	—	152	2	no	—
381	D₄	—	152	1	no	—
382	D₄	—	152	1	no	—
383	D₄	—	152	1	no	—
384	D₄	—	152	1	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	4	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	8	1	no	—
394	C₂×C₄	—	8	1	no	—
395	C₂×C₄	—	8	2	no	—
396	C₂×C₄	C₂×#64525	1	2	yes	—
397	C₂×C₄	#10597378	1	2	yes	—
398	C₂×C₄	#10597383	1	1	yes	characteristic
399	C₂×C₄	#10597383	1	1	yes	characteristic
400	C₂×C₄	#10597384	1	1	yes	characteristic
401	C₂×C₄	#10597385	1	1	yes	characteristic
402	C₂×C₄	#10597385	1	1	yes	characteristic
403	C₂×C₄	#10597386	1	1	yes	characteristic
404	C₂×C₄	C₂×#64527	1	1	yes	characteristic
405	C₂×C₄	#10597388	1	1	yes	characteristic
406	C₂×C₄	#10597395	1	1	yes	characteristic
407	C₂×C₄	#10597396	1	1	yes	characteristic
408	C₈	—	76	2	no	—
409	C₈	—	76	2	no	—
410	C₈	—	152	1	no	—
411	C₂²	—	4	2	no	—
412	C₂²	—	4	4	no	—
413	C₂²	—	8	1	no	—
414	C₂²	—	8	1	no	—
415	C₂²	—	8	2	no	—
416	C₂²	—	304	2	no	—
417	C₂²	—	304	2	no	—
418	C₂²	—	152	2	no	—
419	C₂²	—	152	2	no	—
420	C₂²	—	152	2	no	—
421	C₂²	#11926452	1	1	yes	characteristic
422	C₂²	#11926678	1	2	yes	—
423	C₂²	#11926683	1	1	yes	characteristic
424	C₂²	#11926689	1	1	yes	characteristic
425	C₂²	#11926717	1	2	yes	—
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	4	4	no	—
429	C₄	—	8	1	no	—
430	C₄	—	8	2	no	—
431	C₄	#11926694	1	1	yes	characteristic
432	C₄	#11926704	1	1	yes	characteristic
433	C₄	#11926736	1	2	yes	—
434	C₄	#11926775	1	1	yes	characteristic
435	C₄	#11926792	1	1	yes	characteristic
436	C₄	#11926920	1	1	yes	characteristic
437	C₄	#11926931	1	1	yes	characteristic
438	C₂	—	8	2	no	—
439	C₂	—	304	2	no	—
440	C₂	#14562724	1	2	yes	—
441	C₂	#14562738	1	2	yes	—
442	C₂	#14564636	1	1	yes	characteristic
443	C₂	#14564655	1	1	yes	characteristic
444	C₂	#14564706	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597399
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2542	C₂
socle	C₂³×C₁₉	#120
prime radical	C₂×#11926739	C₂
hypercenter	#2542	D₁₉
hypocenter	C₁₉	#10052
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2542

Complements

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

N	H ≅ G/N	type
1. C₂×#11926892	C₂	semidirect
3. #14564562	C₂	semidirect
4. C₂×#11926290	C₂	semidirect
5. C₂×D₄⋊(C₁₉⋊C₈)	C₂	semidirect
6. #14561476	C₂	semidirect
7. C₁₉×#2542	C₂	semidirect
117. C₄⋊C₄×C₁₉	D₈	semidirect
191. #2542	D₁₉	semidirect
296. C₁₉	#10052	semidirect
348. C₄⋊C₄	#64525	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926892	2
C₂×#11926739	2
#14564562	2
C₂×#11926290	2
C₂×D₄⋊(C₁₉⋊C₈)	2
#14561476	2
C₁₉×#2542	2
#10052	19