Subgroups — #18083621

Order 4864.

702 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926890	C₂	1	1	yes	maximal, characteristic, complemented
2	#14568627	C₂	1	1	yes	maximal, characteristic, complemented
3	#14564563	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11926291	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₄⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561474	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#459	C₂	1	1	yes	maximal, characteristic
8	C₂×#10597315	C₂²	1	1	yes	characteristic
9	C₂×#10597382	—	2	1	no	—
10	#11926890	—	2	2	no	—
11	#11926890	—	2	2	no	—
12	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
13	C₂×#10597289	—	2	2	no	—
14	C₂×#10597289	—	2	2	no	—
15	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
16	#11926469	—	2	2	no	—
17	#11926449	—	2	1	no	—
18	#11926404	—	2	2	no	—
19	C₄×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
20	#11926291	—	2	2	no	—
21	D₄⋊(C₁₉⋊C₈)	—	2	2	no	—
22	C₂²×D₈×C₁₉	—	2	1	no	—
23	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
25	C₁₉×#459	—	2	2	no	—
26	C₁₉×#459	—	2	2	no	—
27	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#102	—	2	1	no	—
29	C₂²×D₄×C₁₉	—	2	1	no	—
30	C₂²×D₄×C₁₉	—	2	1	no	—
31	C₂²×D₄×C₁₉	—	2	1	no	—
32	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₉	—	2	1	no	—
34	C₂²×Dic₃₈	—	2	1	no	—
35	C₂×D₈×C₁₉	—	2	4	no	—
36	C₂×D₈×C₁₉	—	4	2	no	—
37	C₂×D₈×C₁₉	—	4	2	no	—
38	C₂²×C₈×C₁₉	—	2	1	no	—
39	C₁₉×#127	—	2	1	no	—
40	C₁₉×#127	—	2	1	no	—
41	C₁₉×#127	—	2	1	no	—
42	C₁₉×#127	D₄	1	2	yes	—
43	C₄×D₄×C₁₉	—	2	1	no	—
44	C₄×D₄×C₁₉	—	2	1	no	—
45	C₄×D₄×C₁₉	—	2	1	no	—
46	C₄×D₄×C₁₉	—	2	1	no	—
47	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
48	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
49	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
50	C₂×C₂²⋊Dic₁₉	—	2	4	no	—
51	#10597382	—	4	2	no	—
52	#10597382	—	4	2	no	—
53	C₂×C₄⋊Dic₁₉	—	2	1	no	—
54	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
55	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
56	C₂×C₄×Dic₁₉	—	2	1	no	—
57	C₂²×C₁₉⋊C₈	—	2	1	no	—
58	C₂²×C₁₉⋊C₈	—	2	1	no	—
59	#10597315	—	2	1	no	—
60	#10597315	—	2	1	no	—
61	#10597315	—	2	1	no	—
62	#10597315	—	2	1	no	—
63	C₁₉×C₄⋊C₈	—	2	1	no	—
64	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
65	C₁₉×#102	—	2	4	no	—
66	#10597289	—	2	8	no	—
67	#10597289	—	4	4	no	—
68	C₁₉⋊#95	—	2	4	no	—
69	C₁₉⋊#95	—	2	1	no	—
70	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
71	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
72	C₄×C₁₉⋊C₈	—	2	1	no	—
73	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
74	C₂⁴×C₁₉	—	2	1	no	—
75	C₂⁴×C₁₉	—	4	1	no	—
76	C₂×D₄×C₁₉	—	2	1	no	—
77	C₂×D₄×C₁₉	—	2	2	no	—
78	C₂×D₄×C₁₉	—	2	2	no	—
79	C₂×D₄×C₁₉	—	2	1	no	—
80	C₂×D₄×C₁₉	—	2	2	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	—	4	4	no	—
85	C₂×D₄×C₁₉	—	4	1	no	—
86	C₂×D₄×C₁₉	—	4	1	no	—
87	C₂×D₄×C₁₉	—	4	1	no	—
88	C₂×D₄×C₁₉	—	4	1	no	—
89	C₂×D₄×C₁₉	—	4	1	no	—
90	C₂×D₄×C₁₉	—	4	2	no	—
91	C₂×D₄×C₁₉	—	4	1	no	—
92	C₂×D₄×C₁₉	—	4	1	no	—
93	C₂×D₄×C₁₉	—	4	2	no	—
94	C₂×D₄×C₁₉	D₈	1	2	yes	—
95	C₂²×C₄×C₁₉	—	2	1	no	—
96	C₂²×C₄×C₁₉	—	4	1	no	—
97	C₂²×C₄×C₁₉	—	4	1	no	—
98	C₂²×C₄×C₁₉	—	4	2	no	—
99	C₂²×C₄×C₁₉	—	4	2	no	—
100	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×Dic₁₉	—	2	2	no	—
104	C₂²×Dic₁₉	—	2	2	no	—
105	C₂×Dic₃₈	—	4	1	no	—
106	C₂×Dic₃₈	—	4	1	no	—
107	C₂×Dic₃₈	—	4	1	no	—
108	C₂×Dic₃₈	—	4	1	no	—
109	C₂×Dic₃₈	—	4	1	no	—
110	C₂×Dic₃₈	—	4	1	no	—
111	D₈×C₁₉	—	4	8	no	—
112	C₂×C₈×C₁₉	—	2	2	no	—
113	C₂×C₈×C₁₉	—	4	1	no	—
114	C₂×C₈×C₁₉	—	4	1	no	—
115	C₄⋊C₄×C₁₉	—	2	1	no	—
116	C₄⋊C₄×C₁₉	—	2	1	no	—
117	C₂²⋊C₄×C₁₉	—	4	1	no	—
118	C₂²⋊C₄×C₁₉	—	4	1	no	—
119	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
120	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
121	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₁₉	#41	1	1	yes	characteristic
123	C₂²⋊Dic₁₉	—	4	8	no	—
124	C₄⋊Dic₁₉	—	2	2	no	—
125	C₄⋊Dic₁₉	—	2	2	no	—
126	C₄⋊Dic₁₉	—	2	2	no	—
127	C₄⋊Dic₁₉	—	2	2	no	—
128	C₄⋊Dic₁₉	—	4	1	no	—
129	C₄⋊Dic₁₉	—	4	1	no	—
130	C₄×Dic₁₉	—	4	1	no	—
131	C₄×Dic₁₉	—	4	1	no	—
132	C₂×C₁₉⋊C₈	—	2	2	no	—
133	C₂×C₁₉⋊C₈	—	4	2	no	—
134	C₂×C₁₉⋊C₈	—	4	1	no	—
135	C₂×C₁₉⋊C₈	—	4	2	no	—
136	#10050	—	19	1	no	maximal, Sylow
137	C₂³×C₁₉	—	2	2	no	—
138	C₂³×C₁₉	—	4	1	no	—
139	C₂³×C₁₉	—	4	2	no	—
140	C₂³×C₁₉	—	4	1	no	—
141	C₂³×C₁₉	—	4	2	no	—
142	C₂³×C₁₉	—	4	2	no	—
143	C₂³×C₁₉	—	8	1	no	—
144	C₂³×C₁₉	—	8	2	no	—
145	C₂³×C₁₉	—	8	1	no	—
146	C₂³×C₁₉	—	8	2	no	—
147	C₂³×C₁₉	#120	1	1	yes	characteristic
148	D₄×C₁₉	—	2	2	no	—
149	D₄×C₁₉	—	2	2	no	—
150	D₄×C₁₉	—	4	4	no	—
151	D₄×C₁₉	—	4	2	no	—
152	D₄×C₁₉	—	4	1	no	—
153	D₄×C₁₉	—	4	2	no	—
154	D₄×C₁₉	—	4	4	no	—
155	D₄×C₁₉	—	4	1	no	—
156	D₄×C₁₉	—	8	2	no	—
157	D₄×C₁₉	—	8	1	no	—
158	D₄×C₁₉	—	8	1	no	—
159	D₄×C₁₉	—	8	1	no	—
160	D₄×C₁₉	—	8	1	no	—
161	C₂×C₄×C₁₉	—	2	2	no	—
162	C₂×C₄×C₁₉	—	4	1	no	—
163	C₂×C₄×C₁₉	—	4	2	no	—
164	C₂×C₄×C₁₉	—	8	2	no	—
165	C₂×C₄×C₁₉	—	8	1	no	—
166	C₂×C₄×C₁₉	—	8	1	no	—
167	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
168	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
169	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
170	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
171	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
172	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
173	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
174	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
175	C₂×C₄×C₁₉	#135	1	2	yes	—
176	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
177	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
178	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
179	C₂×Dic₁₉	—	4	2	no	—
180	C₂×Dic₁₉	—	4	2	no	—
181	C₂×Dic₁₉	—	4	2	no	—
182	C₂×Dic₁₉	—	4	2	no	—
183	C₂×Dic₁₉	—	4	2	no	—
184	C₂×Dic₁₉	—	4	2	no	—
185	Dic₃₈	—	8	1	no	—
186	Dic₃₈	—	8	1	no	—
187	Dic₃₈	—	8	1	no	—
188	Dic₃₈	—	8	1	no	—
189	C₈×C₁₉	—	4	2	no	—
190	C₁₉⋊C₈	—	4	2	no	—
191	C₁₉⋊C₈	—	8	1	no	—
192	C₂×#486	—	19	1	no	—
193	C₂×#459	D₁₉	1	1	yes	characteristic
194	#2547	—	19	1	no	—
195	#1982	—	19	1	no	—
196	C₂×#332	—	19	1	no	—
197	C₂×D₄⋊C₈	—	19	1	no	—
198	#1279	—	19	1	no	—
199	C₂²×C₁₉	—	4	4	no	—
200	C₂²×C₁₉	—	4	2	no	—
201	C₂²×C₁₉	—	8	2	no	—
202	C₂²×C₁₉	—	8	1	no	—
203	C₂²×C₁₉	—	8	1	no	—
204	C₂²×C₁₉	—	8	2	no	—
205	C₂²×C₁₉	—	8	2	no	—
206	C₂²×C₁₉	—	8	2	no	—
207	C₂²×C₁₉	—	16	2	no	—
208	C₂²×C₁₉	—	16	2	no	—
209	C₂²×C₁₉	#392	1	1	yes	characteristic
210	C₂²×C₁₉	#447	1	1	yes	characteristic
211	C₂²×C₁₉	#449	1	2	yes	—
212	C₂²×C₁₉	#449	1	1	yes	characteristic
213	C₂²×C₁₉	#454	1	2	yes	—
214	C₄×C₁₉	—	2	1	no	—
215	C₄×C₁₉	—	2	1	no	—
216	C₄×C₁₉	—	8	1	no	—
217	C₄×C₁₉	#447	1	1	yes	characteristic
218	C₄×C₁₉	#449	1	1	yes	characteristic
219	C₄×C₁₉	#463	1	2	yes	—
220	C₄×C₁₉	#466	1	1	yes	characteristic
221	C₄×C₁₉	#469	1	1	yes	characteristic
222	C₄×C₁₉	#495	1	1	yes	characteristic
223	C₄×C₁₉	#496	1	1	yes	characteristic
224	Dic₁₉	—	8	2	no	—
225	Dic₁₉	—	8	2	no	—
226	C₂²×D₈	—	2	1	no	—
227	C₂×C₄⋊Q₈	—	19	1	no	—
228	C₂×#127	C₂×D₁₉	1	1	yes	characteristic
229	C₂×#124	—	38	1	no	—
230	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
231	#486	—	38	2	no	—
232	#486	—	38	2	no	—
233	#459	—	2	2	no	—
234	#459	—	2	2	no	—
235	C₂×C₄⋊C₈	—	19	1	no	—
236	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
237	C₂×#102	—	2	1	no	—
238	C₂×#102	—	38	2	no	—
239	C₂×#102	—	38	2	no	—
240	C₂×C₄×C₈	—	19	1	no	—
241	#397	—	38	2	no	—
242	#391	—	38	1	no	—
243	#380	—	38	2	no	—
244	C₄×C₄⋊C₄	—	19	1	no	—
245	#332	—	38	2	no	—
246	D₄⋊C₈	—	38	2	no	—
247	C₂×C₁₉	—	8	2	no	—
248	C₂×C₁₉	—	16	2	no	—
249	C₂×C₁₉	#1625	1	2	yes	—
250	C₂×C₁₉	#1628	1	2	yes	—
251	C₂×C₁₉	#1999	1	1	yes	characteristic
252	C₂×C₁₉	#2003	1	1	yes	characteristic
253	C₂×C₁₉	#2012	1	1	yes	characteristic
254	C₂²×Q₈	—	38	1	no	—
255	C₂²×D₄	—	2	1	no	—
256	C₂²×D₄	—	2	1	no	—
257	C₂²×D₄	—	2	1	no	—
258	C₂²×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
259	C₂³×C₄	—	2	1	no	—
260	C₂×D₈	—	2	4	no	—
261	C₂×D₈	—	4	2	no	—
262	C₂×D₈	—	4	2	no	—
263	C₂²×C₈	—	2	1	no	—
264	C₂²×C₈	—	38	1	no	—
265	C₂²×C₈	—	38	1	no	—
266	C₄⋊Q₈	—	38	1	no	—
267	C₄⋊Q₈	—	38	1	no	—
268	C₄⋊Q₈	—	38	1	no	—
269	C₄⋊Q₈	—	38	1	no	—
270	#127	—	2	1	no	—
271	#127	—	2	1	no	—
272	#127	—	2	1	no	—
273	#127	C₂²⋊D₁₉	1	2	yes	—
274	#124	—	76	2	no	—
275	#124	—	76	2	no	—
276	C₄×D₄	—	2	1	no	—
277	C₄×D₄	—	2	1	no	—
278	C₄×D₄	—	2	1	no	—
279	C₄×D₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	19	2	no	—
281	C₂×C₄⋊C₄	—	19	2	no	—
282	C₂×C₄⋊C₄	—	38	1	no	—
283	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
284	C₂×C₂²⋊C₄	—	2	1	no	—
285	C₂×C₂²⋊C₄	—	38	4	no	—
286	C₂×C₄²	—	38	1	no	—
287	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
288	C₄⋊C₈	—	2	1	no	—
289	C₄⋊C₈	—	38	1	no	—
290	C₄⋊C₈	—	38	1	no	—
291	C₄⋊C₈	C₂²⋊D₁₉	1	2	yes	—
292	#102	—	2	4	no	—
293	#102	—	38	8	no	—
294	#102	—	76	4	no	—
295	C₄×C₈	—	19	2	no	—
296	C₄×C₈	—	38	1	no	—
297	#95	—	38	4	no	—
298	#95	—	38	1	no	—
299	C₁₉	#10050	1	1	yes	characteristic, complemented, Sylow
300	C₂⁴	—	2	1	no	—
301	C₂⁴	—	4	1	no	—
302	C₂×Q₈	—	76	1	no	—
303	C₂×Q₈	—	76	1	no	—
304	C₂×Q₈	—	76	1	no	—
305	C₂×Q₈	—	76	1	no	—
306	C₂×Q₈	—	76	1	no	—
307	C₂×Q₈	—	76	1	no	—
308	C₂×D₄	—	2	1	no	—
309	C₂×D₄	—	2	2	no	—
310	C₂×D₄	—	2	1	no	—
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	—	2	1	no	—
313	C₂×D₄	—	2	1	no	—
314	C₂×D₄	—	2	1	no	—
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	—	4	4	no	—
317	C₂×D₄	—	4	1	no	—
318	C₂×D₄	—	4	1	no	—
319	C₂×D₄	—	4	1	no	—
320	C₂×D₄	—	4	1	no	—
321	C₂×D₄	—	4	1	no	—
322	C₂×D₄	—	4	1	no	—
323	C₂×D₄	—	4	1	no	—
324	C₂×D₄	—	4	2	no	—
325	C₂×D₄	—	4	2	no	—
326	C₂×D₄	#64525	1	2	yes	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	4	1	no	—
329	C₂²×C₄	—	4	1	no	—
330	C₂²×C₄	—	4	2	no	—
331	C₂²×C₄	—	4	2	no	—
332	C₂²×C₄	—	38	2	no	—
333	C₂²×C₄	—	38	2	no	—
334	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
335	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
336	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
337	D₈	—	4	8	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	4	1	no	—
340	C₂×C₈	—	4	1	no	—
341	C₂×C₈	—	38	2	no	—
342	C₂×C₈	—	76	2	no	—
343	C₂×C₈	—	76	1	no	—
344	C₂×C₈	—	76	2	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	38	2	no	—
348	C₄⋊C₄	—	38	2	no	—
349	C₄⋊C₄	—	38	2	no	—
350	C₄⋊C₄	—	38	2	no	—
351	C₄⋊C₄	—	76	1	no	—
352	C₄⋊C₄	—	76	1	no	—
353	C₂²⋊C₄	—	4	1	no	—
354	C₂²⋊C₄	—	4	1	no	—
355	C₂²⋊C₄	—	76	8	no	—
356	C₄²	—	76	1	no	—
357	C₄²	—	76	1	no	—
358	C₄²	D₄×D₁₉	1	1	yes	characteristic
359	C₄²	#64543	1	1	yes	characteristic
360	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
361	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
362	C₂³	—	2	2	no	—
363	C₂³	—	4	2	no	—
364	C₂³	—	4	1	no	—
365	C₂³	—	4	1	no	—
366	C₂³	—	4	2	no	—
367	C₂³	—	4	2	no	—
368	C₂³	—	8	1	no	—
369	C₂³	—	8	2	no	—
370	C₂³	—	8	1	no	—
371	C₂³	—	8	2	no	—
372	C₂³	#10597383	1	1	yes	characteristic
373	Q₈	—	152	1	no	—
374	Q₈	—	152	1	no	—
375	Q₈	—	152	1	no	—
376	Q₈	—	152	1	no	—
377	D₄	—	2	2	no	—
378	D₄	—	2	2	no	—
379	D₄	—	4	4	no	—
380	D₄	—	4	1	no	—
381	D₄	—	4	2	no	—
382	D₄	—	4	1	no	—
383	D₄	—	4	2	no	—
384	D₄	—	4	4	no	—
385	D₄	—	8	2	no	—
386	D₄	—	8	1	no	—
387	D₄	—	8	1	no	—
388	D₄	—	8	1	no	—
389	D₄	—	8	1	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	8	1	no	—
394	C₂×C₄	—	8	1	no	—
395	C₂×C₄	—	8	2	no	—
396	C₂×C₄	—	76	2	no	—
397	C₂×C₄	—	76	2	no	—
398	C₂×C₄	—	76	2	no	—
399	C₂×C₄	—	76	2	no	—
400	C₂×C₄	—	76	2	no	—
401	C₂×C₄	—	76	2	no	—
402	C₂×C₄	#10597357	1	2	yes	—
403	C₂×C₄	#10597358	1	2	yes	—
404	C₂×C₄	C₂×#64525	1	1	yes	characteristic
405	C₂×C₄	#10597378	1	1	yes	characteristic
406	C₂×C₄	#10597383	1	1	yes	characteristic
407	C₂×C₄	#10597384	1	1	yes	characteristic
408	C₂×C₄	#10597385	1	1	yes	characteristic
409	C₂×C₄	#10597385	1	1	yes	characteristic
410	C₂×C₄	#10597386	1	1	yes	characteristic
411	C₂×C₄	#10597395	1	1	yes	characteristic
412	C₂×C₄	#10597396	1	1	yes	characteristic
413	C₂×C₄	#10597399	1	1	yes	characteristic
414	C₈	—	4	2	no	—
415	C₈	—	76	2	no	—
416	C₈	—	152	1	no	—
417	C₂²	—	4	2	no	—
418	C₂²	—	4	4	no	—
419	C₂²	—	8	1	no	—
420	C₂²	—	8	1	no	—
421	C₂²	—	8	2	no	—
422	C₂²	—	8	2	no	—
423	C₂²	—	8	2	no	—
424	C₂²	—	8	2	no	—
425	C₂²	—	16	2	no	—
426	C₂²	—	16	2	no	—
427	C₂²	#11926452	1	1	yes	characteristic
428	C₂²	#11926677	1	1	yes	characteristic
429	C₂²	#11926686	1	2	yes	—
430	C₂²	#11926687	1	1	yes	characteristic
431	C₂²	#11926715	1	2	yes	—
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	8	1	no	—
435	C₄	—	152	2	no	—
436	C₄	—	152	2	no	—
437	C₄	#11926678	1	1	yes	characteristic
438	C₄	#11926689	1	1	yes	characteristic
439	C₄	#11926757	1	2	yes	—
440	C₄	#11926778	1	1	yes	characteristic
441	C₄	#11926795	1	1	yes	characteristic
442	C₄	#11926927	1	1	yes	characteristic
443	C₄	#11926932	1	1	yes	characteristic
444	C₂	—	8	2	no	—
445	C₂	—	16	2	no	—
446	C₂	#14562722	1	2	yes	—
447	C₂	#14562743	1	2	yes	—
448	C₂	#14564631	1	1	yes	characteristic
449	C₂	#14564654	1	1	yes	characteristic
450	C₂	#14564710	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597383
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting, prime radical	C₂×C₁₉×#459	C₂
socle	C₂³×C₁₉	#120
hypercenter	C₂×#459	D₁₉
hypocenter	C₁₉	#10050
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#459

Complements

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

N	H ≅ G/N	type
1. C₂×#11926890	C₂	semidirect
2. #14568627	C₂	semidirect
3. #14564563	C₂	semidirect
4. C₂×#11926291	C₂	semidirect
5. C₂×D₄⋊(C₁₉⋊C₈)	C₂	semidirect
6. #14561474	C₂	semidirect
299. C₁₉	#10050	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926890	2
#14568627	2
#14564563	2
C₂×#11926291	2
C₂×D₄⋊(C₁₉⋊C₈)	2
#14561474	2
C₂×C₁₉×#459	2
#10050	19