Subgroups — #18078804

Order 4864.

724 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14573635	C₂	1	1	yes	maximal, characteristic
2	#14564463	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562129	C₂	1	1	yes	maximal, characteristic, complemented
4	#14562060	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561538	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561468	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄²×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#11927094	C₂²	1	1	yes	characteristic
9	#11926857	—	2	1	no	—
10	#11926824	C₄	1	2	yes	complemented
11	#11926739	C₄	1	2	yes	complemented
12	#11926678	—	2	1	no	—
13	C₄×#64525	—	2	2	no	—
14	#11926597	C₂²	1	1	yes	characteristic
15	#11926597	C₂²	1	1	yes	characteristic
16	#11926568	C₂²	1	1	yes	characteristic
17	C₂×#10597262	—	2	1	no	—
18	C₂×#10597262	—	2	1	no	—
19	#11926277	—	2	2	no	—
20	D₄⋊(C₁₉⋊C₈)	—	2	2	no	—
21	C₂×C₄×D₄×C₁₉	—	2	1	no	—
22	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₂²×C₄²×C₁₉	—	2	1	no	—
24	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
25	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₄×C₂²⋊C₄×C₁₉	—	2	2	no	—
27	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
28	C₄³×C₁₉	C₂²	1	1	yes	characteristic
29	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₉	—	2	2	no	—
31	C₂³×C₄×C₁₉	—	2	1	no	—
32	C₂×#64541	—	2	1	no	—
33	C₄×D₄×C₁₉	—	2	8	no	—
34	C₄×D₄×C₁₉	—	2	1	no	—
35	C₄×D₄×C₁₉	—	2	1	no	—
36	C₄×D₄×C₁₉	C₂×C₄	1	2	yes	—
37	C₄×D₄×C₁₉	D₄	1	2	yes	—
38	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
39	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
40	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
41	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
42	C₂×C₄²×C₁₉	—	2	1	no	—
43	C₂×C₄²×C₁₉	—	2	2	no	—
44	C₂×C₄²×C₁₉	—	2	1	no	—
45	C₂×C₄²×C₁₉	—	2	1	no	—
46	C₂×C₄²×C₁₉	—	4	2	no	—
47	C₂×C₄²×C₁₉	—	4	2	no	—
48	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
49	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
50	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
51	C₂×#64525	—	2	2	no	—
52	#10597376	—	2	1	no	—
53	#10597376	—	2	1	no	—
54	C₂×#64520	—	2	1	no	—
55	#10597321	—	2	1	no	—
56	#10597320	C₂×C₄	1	1	yes	characteristic, complemented
57	C₄×D₇₆	—	2	1	no	—
58	C₄×D₇₆	—	2	1	no	—
59	#10597315	C₂×C₄	1	1	yes	characteristic, complemented
60	C₁₉×#95	—	2	2	no	—
61	C₁₉×#95	D₄	1	2	yes	—
62	#10597289	—	2	2	no	—
63	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
64	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
65	#10597266	—	2	2	no	—
66	#10597264	—	2	2	no	—
67	#10597262	—	4	2	no	—
68	#10597262	—	4	2	no	—
69	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
70	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
71	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
72	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	complemented
73	C₄×C₁₉⋊C₈	—	2	1	no	—
74	C₄×C₁₉⋊C₈	—	2	1	no	—
75	C₂⁴×C₁₉	—	2	1	no	—
76	C₂×D₄×C₁₉	—	2	4	no	—
77	C₂×D₄×C₁₉	—	2	1	no	—
78	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
79	C₂²×C₄×C₁₉	—	2	1	no	—
80	C₂²×C₄×C₁₉	—	2	8	no	—
81	C₂²×C₄×C₁₉	—	2	1	no	—
82	C₂²×C₄×C₁₉	—	2	2	no	—
83	C₂²×C₄×C₁₉	—	2	1	no	—
84	C₂²×C₄×C₁₉	—	2	2	no	—
85	C₂²×C₄×C₁₉	—	2	2	no	—
86	C₂²×C₄×C₁₉	—	4	4	no	—
87	C₂²×C₄×C₁₉	—	4	4	no	—
88	C₂²×C₄×C₁₉	—	4	1	no	—
89	C₂²×C₄×C₁₉	—	4	1	no	—
90	C₂²×C₄×C₁₉	—	4	1	no	—
91	C₂²×C₄×C₁₉	—	4	1	no	—
92	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
95	C₂×C₂²⋊D₁₉	—	4	1	no	—
96	#64541	—	4	1	no	—
97	#64541	—	4	1	no	—
98	#64541	—	4	1	no	—
99	#64541	—	4	1	no	—
100	C₂×D₇₆	—	2	1	no	—
101	C₂×D₇₆	—	2	1	no	—
102	C₂×D₇₆	—	2	1	no	—
103	C₂×C₄×D₁₉	—	4	1	no	—
104	C₂×Dic₃₈	—	2	1	no	—
105	C₄⋊C₄×C₁₉	—	2	4	no	—
106	C₄⋊C₄×C₁₉	—	2	1	no	—
107	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
108	C₂²⋊C₄×C₁₉	—	2	8	no	—
109	C₂²⋊C₄×C₁₉	—	2	2	no	—
110	C₂²⋊C₄×C₁₉	—	2	2	no	—
111	C₄²×C₁₉	—	2	4	no	—
112	C₄²×C₁₉	—	2	1	no	—
113	C₄²×C₁₉	—	2	1	no	—
114	C₄²×C₁₉	—	2	1	no	—
115	C₄²×C₁₉	—	4	2	no	—
116	C₄²×C₁₉	—	4	4	no	—
117	C₄²×C₁₉	—	4	1	no	—
118	C₄²×C₁₉	—	4	1	no	—
119	C₄²×C₁₉	D₈	1	2	yes	complemented
120	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
121	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₁₉	#41	1	1	yes	characteristic
123	C₄²×C₁₉	#41	1	1	yes	characteristic
124	#64525	—	4	4	no	—
125	(C₂×D₁₉)⋊C₄	—	4	1	no	—
126	(C₂×D₁₉)⋊C₄	—	4	1	no	—
127	C₄⋊Dic₁₉	—	2	1	no	—
128	C₄⋊Dic₁₉	—	2	1	no	—
129	#64520	—	4	1	no	—
130	#64520	—	4	1	no	—
131	C₂×C₁₉⋊C₈	—	2	2	no	—
132	C₂×C₁₉⋊C₈	—	4	1	no	—
133	C₂×C₁₉⋊C₈	—	4	1	no	—
134	#9233	—	19	1	no	maximal, Sylow
135	C₂³×C₁₉	—	2	4	no	—
136	C₂³×C₁₉	—	2	2	no	—
137	C₂³×C₁₉	—	4	2	no	—
138	C₂³×C₁₉	—	4	1	no	—
139	C₂³×C₁₉	—	4	1	no	—
140	C₂³×C₁₉	#120	1	1	yes	characteristic
141	C₂²×D₁₉	—	4	1	no	—
142	D₄×C₁₉	—	2	4	no	—
143	D₄×C₁₉	—	2	2	no	—
144	D₄×C₁₉	#104	1	4	yes	complemented
145	C₂×C₄×C₁₉	—	2	2	no	—
146	C₂×C₄×C₁₉	—	2	2	no	—
147	C₂×C₄×C₁₉	—	2	2	no	—
148	C₂×C₄×C₁₉	—	2	2	no	—
149	C₂×C₄×C₁₉	—	2	2	no	—
150	C₂×C₄×C₁₉	—	2	4	no	—
151	C₂×C₄×C₁₉	—	2	2	no	—
152	C₂×C₄×C₁₉	—	4	1	no	—
153	C₂×C₄×C₁₉	—	4	16	no	—
154	C₂×C₄×C₁₉	—	4	1	no	—
155	C₂×C₄×C₁₉	—	4	2	no	—
156	C₂×C₄×C₁₉	—	4	2	no	—
157	C₂×C₄×C₁₉	—	4	1	no	—
158	C₂×C₄×C₁₉	—	4	1	no	—
159	C₂×C₄×C₁₉	—	4	1	no	—
160	C₂×C₄×C₁₉	—	4	2	no	—
161	C₂×C₄×C₁₉	—	4	2	no	—
162	C₂×C₄×C₁₉	—	4	2	no	—
163	C₂×C₄×C₁₉	—	4	2	no	—
164	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
165	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
166	C₂×C₄×C₁₉	C₄×D₄	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	#123	1	1	yes	characteristic
170	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
171	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
172	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
173	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
174	C₂²⋊D₁₉	—	8	1	no	—
175	C₂²⋊D₁₉	—	8	1	no	—
176	C₂×Dic₁₉	—	4	1	no	—
177	D₇₆	—	4	2	no	—
178	D₇₆	—	4	1	no	—
179	D₇₆	—	4	1	no	—
180	D₇₆	—	8	1	no	—
181	C₄×D₁₉	—	8	1	no	—
182	C₄×D₁₉	—	8	1	no	—
183	Dic₃₈	—	4	1	no	—
184	Dic₃₈	—	4	1	no	—
185	C₁₉⋊C₈	—	4	2	no	—
186	C₁₉⋊C₈	—	8	1	no	—
187	C₁₉⋊C₈	—	8	1	no	—
188	#3100	—	19	1	no	—
189	C₄²×D₄	D₁₉	1	1	yes	characteristic, complemented
190	#1962	—	19	1	no	—
191	#1502	—	19	1	no	—
192	#1486	—	19	1	no	—
193	#1303	—	19	1	no	—
194	#1276	—	19	1	no	—
195	C₂²×C₁₉	—	2	1	no	—
196	C₂²×C₁₉	—	2	1	no	—
197	C₂²×C₁₉	—	2	4	no	—
198	C₂²×C₁₉	—	4	4	no	—
199	C₂²×C₁₉	—	4	4	no	—
200	C₂²×C₁₉	—	4	2	no	—
201	C₂²×C₁₉	—	4	2	no	—
202	C₂²×C₁₉	#386	1	1	yes	characteristic
203	C₂²×C₁₉	#447	1	1	yes	characteristic
204	C₂²×C₁₉	#449	1	1	yes	characteristic
205	C₂×D₁₉	—	8	1	no	—
206	C₂×D₁₉	—	8	1	no	—
207	C₂×D₁₉	—	8	1	no	—
208	C₄×C₁₉	—	2	4	no	—
209	C₄×C₁₉	—	2	1	no	—
210	C₄×C₁₉	—	2	1	no	—
211	C₄×C₁₉	—	2	1	no	—
212	C₄×C₁₉	—	4	2	no	—
213	C₄×C₁₉	—	4	4	no	—
214	C₄×C₁₉	—	4	2	no	—
215	C₄×C₁₉	C₂×#104	1	2	yes	—
216	C₄×C₁₉	C₄×D₈	1	1	yes	characteristic
217	C₄×C₁₉	#442	1	1	yes	characteristic
218	C₄×C₁₉	#459	1	1	yes	characteristic
219	C₄×C₁₉	#463	1	1	yes	characteristic
220	Dic₁₉	—	8	1	no	—
221	#532	—	19	1	no	—
222	C₂×C₄×D₄	—	2	1	no	—
223	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
224	C₂²×C₄²	—	2	1	no	—
225	#480	—	38	1	no	—
226	#474	—	19	2	no	—
227	#459	—	19	2	no	—
228	#447	—	38	1	no	—
229	C₄×D₈	—	38	2	no	—
230	#431	—	19	1	no	—
231	#431	—	19	1	no	—
232	#423	—	19	1	no	—
233	C₂×#104	—	38	1	no	—
234	C₂×#104	—	38	1	no	—
235	C₄×C₄⋊C₄	—	2	1	no	—
236	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
237	C₄×C₂²⋊C₄	—	2	1	no	—
238	C₄×C₂²⋊C₄	—	2	2	no	—
239	C₄³	C₂×D₁₉	1	1	yes	characteristic
240	#327	—	38	2	no	—
241	D₄⋊C₈	—	38	2	no	—
242	C₂×C₁₉	—	2	1	no	—
243	C₂×C₁₉	—	2	1	no	—
244	C₂×C₁₉	—	4	4	no	—
245	C₂×C₁₉	#1879	1	1	yes	characteristic
246	C₂×C₁₉	#1896	1	1	yes	characteristic
247	C₂×C₁₉	#1906	1	1	yes	characteristic
248	D₁₉	—	16	1	no	—
249	C₂×#41	—	38	1	no	—
250	C₂²×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
251	C₂³×C₄	—	2	2	no	—
252	C₂³×C₄	—	2	1	no	—
253	C₂×D₈	—	38	2	no	—
254	C₂×M₁₆	—	38	1	no	—
255	C₄⋊Q₈	—	19	1	no	—
256	#127	—	19	1	no	—
257	#124	—	38	1	no	—
258	#121	—	38	1	no	—
259	#121	—	38	1	no	—
260	C₄×D₄	—	2	8	no	—
261	C₄×D₄	—	2	1	no	—
262	C₄×D₄	—	2	1	no	—
263	C₄×D₄	—	38	1	no	—
264	C₄×D₄	—	38	1	no	—
265	C₄×D₄	C₄×D₁₉	1	2	yes	—
266	C₄×D₄	D₇₆	1	2	yes	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
269	C₂×C₂²⋊C₄	—	2	2	no	—
270	C₂×C₂²⋊C₄	—	2	1	no	—
271	C₂×C₄²	—	2	1	no	—
272	C₂×C₄²	—	2	2	no	—
273	C₂×C₄²	—	2	1	no	—
274	C₂×C₄²	—	2	1	no	—
275	C₂×C₄²	—	4	2	no	—
276	C₂×C₄²	—	4	2	no	—
277	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
278	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
279	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
280	#107	—	38	2	no	—
281	C₄⋊C₈	—	19	2	no	—
282	C₄⋊C₈	—	38	1	no	—
283	C₄⋊C₈	—	38	1	no	—
284	C₄⋊C₈	—	38	1	no	—
285	#104	—	76	2	no	—
286	#104	—	76	2	no	—
287	#102	—	38	2	no	—
288	#102	—	38	2	no	—
289	C₂²⋊C₈	—	38	1	no	—
290	C₂²⋊C₈	—	38	1	no	—
291	C₄×C₈	—	38	1	no	—
292	C₄×C₈	—	38	1	no	—
293	#95	—	2	2	no	—
294	#95	C₂²⋊D₁₉	1	2	yes	—
295	C₁₉	#9233	1	1	yes	characteristic, complemented, Sylow
296	C₂⁴	—	2	1	no	—
297	#41	—	76	1	no	—
298	#41	—	76	1	no	—
299	#41	—	76	1	no	—
300	#41	—	76	1	no	—
301	C₂×Q₈	—	38	1	no	—
302	C₂×D₄	—	2	4	no	—
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	—	38	1	no	—
305	C₂×D₄	—	38	1	no	—
306	C₂×D₄	—	38	1	no	—
307	C₂×D₄	—	76	1	no	—
308	C₂×D₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	8	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	4	4	no	—
317	C₂²×C₄	—	4	4	no	—
318	C₂²×C₄	—	4	1	no	—
319	C₂²×C₄	—	4	1	no	—
320	C₂²×C₄	—	4	1	no	—
321	C₂²×C₄	—	4	1	no	—
322	C₂²×C₄	—	76	1	no	—
323	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
324	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
325	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
326	D₈	—	76	4	no	—
327	M₁₆	—	76	1	no	—
328	M₁₆	—	76	1	no	—
329	C₂×C₈	—	38	2	no	—
330	C₂×C₈	—	76	1	no	—
331	C₂×C₈	—	76	1	no	—
332	C₄⋊C₄	—	2	4	no	—
333	C₄⋊C₄	—	2	1	no	—
334	C₄⋊C₄	—	38	1	no	—
335	C₄⋊C₄	—	38	1	no	—
336	C₄⋊C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
337	C₂²⋊C₄	—	2	8	no	—
338	C₂²⋊C₄	—	2	2	no	—
339	C₂²⋊C₄	—	2	2	no	—
340	C₂²⋊C₄	—	76	1	no	—
341	C₂²⋊C₄	—	76	1	no	—
342	C₄²	—	2	4	no	—
343	C₄²	—	2	1	no	—
344	C₄²	—	2	1	no	—
345	C₄²	—	2	1	no	—
346	C₄²	—	4	2	no	—
347	C₄²	—	4	4	no	—
348	C₄²	—	4	1	no	—
349	C₄²	—	4	1	no	—
350	C₄²	#64525	1	2	yes	complemented
351	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
352	C₄²	C₂×D₇₆	1	1	yes	characteristic
353	C₄²	#64541	1	1	yes	characteristic
354	C₄²	#64541	1	1	yes	characteristic
355	C₂³	—	2	4	no	—
356	C₂³	—	2	2	no	—
357	C₂³	—	4	2	no	—
358	C₂³	—	4	1	no	—
359	C₂³	—	4	1	no	—
360	C₂³	—	76	1	no	—
361	C₂³	#10597399	1	1	yes	characteristic
362	Q₈	—	76	1	no	—
363	Q₈	—	76	1	no	—
364	D₄	—	2	4	no	—
365	D₄	—	2	2	no	—
366	D₄	—	76	2	no	—
367	D₄	—	76	1	no	—
368	D₄	—	76	1	no	—
369	D₄	—	152	1	no	—
370	D₄	—	152	1	no	—
371	D₄	—	152	1	no	—
372	D₄	#10597262	1	4	yes	complemented
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	16	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	76	1	no	—
393	C₂×C₄	—	152	1	no	—
394	C₂×C₄	—	152	1	no	—
395	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
396	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
397	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
398	C₂×C₄	#10597375	1	1	yes	characteristic
399	C₂×C₄	#10597376	1	1	yes	characteristic
400	C₂×C₄	#10597376	1	1	yes	characteristic
401	C₂×C₄	C₂×#64525	1	1	yes	characteristic
402	C₂×C₄	#10597378	1	1	yes	characteristic
403	C₂×C₄	#10597395	1	1	yes	characteristic
404	C₂×C₄	#10597396	1	1	yes	characteristic
405	C₈	—	76	2	no	—
406	C₈	—	152	1	no	—
407	C₈	—	152	1	no	—
408	C₂²	—	2	1	no	—
409	C₂²	—	2	1	no	—
410	C₂²	—	2	4	no	—
411	C₂²	—	4	4	no	—
412	C₂²	—	4	4	no	—
413	C₂²	—	4	2	no	—
414	C₂²	—	4	2	no	—
415	C₂²	—	152	1	no	—
416	C₂²	—	152	1	no	—
417	C₂²	—	152	1	no	—
418	C₂²	#11926423	1	1	yes	characteristic
419	C₂²	#11926678	1	1	yes	characteristic
420	C₂²	#11926689	1	1	yes	characteristic
421	C₄	—	2	4	no	—
422	C₄	—	2	1	no	—
423	C₄	—	2	1	no	—
424	C₄	—	2	1	no	—
425	C₄	—	4	4	no	—
426	C₄	—	4	2	no	—
427	C₄	—	4	2	no	—
428	C₄	—	152	1	no	—
429	C₄	C₂×#10597262	1	2	yes	—
430	C₄	C₄×#64525	1	1	yes	characteristic
431	C₄	#11926654	1	1	yes	characteristic
432	C₄	#11926739	1	1	yes	characteristic
433	C₄	#11926759	1	1	yes	characteristic
434	C₂	—	2	1	no	—
435	C₂	—	2	1	no	—
436	C₂	—	4	4	no	—
437	C₂	—	304	1	no	—
438	C₂	#14563983	1	1	yes	characteristic
439	C₂	#14564078	1	1	yes	characteristic
440	C₂	#14564136	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#10597376
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₄²×D₄×C₁₉	C₂
socle	C₂²×C₁₉	#386
prime radical	#14573635	C₂
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₄²×D₄	D₁₉
hypocenter	C₁₉	#9233
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄²×D₄

Complements

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

N	H ≅ G/N	type
2. #14564463	C₂	semidirect
3. #14562129	C₂	semidirect
4. #14562060	C₂	semidirect
5. #14561538	C₂	semidirect
6. #14561468	C₂	semidirect
7. C₄²×D₄×C₁₉	C₂	semidirect
10. #11926824	C₄	semidirect
11. #11926739	C₄	semidirect
56. #10597320	C₂×C₄	semidirect
59. #10597315	C₂×C₄	semidirect
72. C₄⋊(C₁₉⋊C₈)	C₂×C₄	semidirect
119. C₄²×C₁₉	D₈	semidirect
144. D₄×C₁₉	#104	semidirect
189. C₄²×D₄	D₁₉	semidirect
295. C₁₉	#9233	semidirect
350. C₄²	#64525	semidirect
372. D₄	#10597262	semidirect

Maximal subgroups

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

subgroup	index
#14573635	2
#14564463	2
#14562129	2
#14562060	2
#14561538	2
#14561468	2
C₄²×D₄×C₁₉	2
#9233	19