Subgroups — #18083614

Order 4864.

714 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926916	C₂	1	1	yes	maximal, characteristic
2	#14568840	C₂	1	1	yes	maximal, characteristic, complemented
3	#14564563	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926292	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Q₈⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561474	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#460	C₂	1	1	yes	maximal, characteristic
8	C₂²×#64526	—	2	2	no	—
9	C₂×#10597315	C₂²	1	1	yes	characteristic
10	#11926916	—	2	2	no	—
11	#11926916	—	2	2	no	—
12	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
13	C₂×#10597289	—	2	2	no	—
14	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
15	#11926464	—	2	2	no	—
16	#11926451	—	2	1	no	—
17	#11926442	—	2	2	no	—
18	#11926413	—	2	1	no	—
19	C₄×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
20	#11926292	—	2	2	no	—
21	Q₈⋊(C₁₉⋊C₈)	—	2	2	no	—
22	C₂²×SD₁₆×C₁₉	—	2	1	no	—
23	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
25	C₁₉×#460	—	2	2	no	—
26	C₁₉×#460	—	2	2	no	—
27	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#102	—	2	1	no	—
29	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
30	C₂²×D₄×C₁₉	—	2	1	no	—
31	C₂²×D₄×C₁₉	—	2	1	no	—
32	C₂²×D₄×C₁₉	—	2	1	no	—
33	C₂²×Dic₃₈	D₄	1	2	yes	—
34	C₂×SD₁₆×C₁₉	—	2	4	no	—
35	C₂×SD₁₆×C₁₉	—	4	2	no	—
36	C₂×SD₁₆×C₁₉	—	4	2	no	—
37	C₂²×C₈×C₁₉	—	2	1	no	—
38	C₁₉×#127	—	2	1	no	—
39	C₁₉×#127	—	2	1	no	—
40	C₁₉×#127	—	2	1	no	—
41	C₁₉×#127	D₄	1	2	yes	—
42	C₄×Q₈×C₁₉	—	2	1	no	—
43	C₄×Q₈×C₁₉	—	2	1	no	—
44	C₄×Q₈×C₁₉	—	2	1	no	—
45	C₄×Q₈×C₁₉	—	2	1	no	—
46	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
47	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
48	C₂×C₄²×C₁₉	—	2	1	no	—
49	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
50	C₂×#64526	—	2	8	no	—
51	C₂×#64526	—	4	8	no	—
52	C₂×C₄⋊Dic₁₉	—	2	1	no	—
53	C₂×C₄⋊Dic₁₉	—	2	1	no	—
54	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
55	C₂×Dic₁₉⋊C₄	—	2	4	no	—
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	—	4	4	no	—
67	C₁₉⋊#95	—	2	4	no	—
68	C₁₉⋊#95	—	2	1	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	D₄	1	2	yes	—
73	C₂⁴×C₁₉	—	4	1	no	—
74	C₂×Q₈×C₁₉	—	2	1	no	—
75	C₂×Q₈×C₁₉	—	2	1	no	—
76	C₂×Q₈×C₁₉	—	2	1	no	—
77	C₂×Q₈×C₁₉	—	2	1	no	—
78	C₂×Q₈×C₁₉	—	2	1	no	—
79	C₂×Q₈×C₁₉	SD₁₆	1	2	yes	complemented
80	C₂×D₄×C₁₉	—	2	2	no	—
81	C₂×D₄×C₁₉	—	2	2	no	—
82	C₂×D₄×C₁₉	—	2	2	no	—
83	C₂×D₄×C₁₉	—	4	4	no	—
84	C₂×D₄×C₁₉	—	4	1	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	2	no	—
89	C₂×D₄×C₁₉	—	4	1	no	—
90	C₂×D₄×C₁₉	—	4	1	no	—
91	C₂×D₄×C₁₉	—	4	1	no	—
92	C₂×D₄×C₁₉	—	4	2	no	—
93	C₂²×C₄×C₁₉	—	2	1	no	—
94	C₂²×C₄×C₁₉	—	2	1	no	—
95	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
98	C₂²×Dic₁₉	—	2	2	no	—
99	C₂²×Dic₁₉	—	2	2	no	—
100	C₂×Dic₃₈	—	2	2	no	—
101	C₂×Dic₃₈	—	2	2	no	—
102	C₂×Dic₃₈	—	4	4	no	—
103	SD₁₆×C₁₉	—	4	8	no	—
104	C₂×C₈×C₁₉	—	2	2	no	—
105	C₂×C₈×C₁₉	—	4	1	no	—
106	C₂×C₈×C₁₉	—	4	1	no	—
107	C₄⋊C₄×C₁₉	—	2	1	no	—
108	C₄⋊C₄×C₁₉	—	2	1	no	—
109	C₄⋊C₄×C₁₉	—	4	1	no	—
110	C₄⋊C₄×C₁₉	—	4	1	no	—
111	C₄²×C₁₉	—	4	1	no	—
112	C₄²×C₁₉	—	4	1	no	—
113	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
114	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
115	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
116	C₄²×C₁₉	#41	1	1	yes	characteristic
117	#64526	—	4	16	no	—
118	C₄⋊Dic₁₉	—	2	2	no	—
119	C₄⋊Dic₁₉	—	4	1	no	—
120	C₄⋊Dic₁₉	—	4	1	no	—
121	C₄⋊Dic₁₉	—	4	1	no	—
122	C₄⋊Dic₁₉	—	4	1	no	—
123	C₄⋊Dic₁₉	SD₁₆	1	4	yes	complemented
124	Dic₁₉⋊C₄	—	8	4	no	—
125	C₄×Dic₁₉	—	4	1	no	—
126	C₄×Dic₁₉	—	4	1	no	—
127	C₂×C₁₉⋊C₈	—	2	4	no	—
128	C₂×C₁₉⋊C₈	—	2	2	no	—
129	C₂×C₁₉⋊C₈	—	4	1	no	—
130	C₂×C₁₉⋊C₈	—	4	2	no	—
131	#10049	—	19	1	no	maximal, Sylow
132	C₂³×C₁₉	—	4	2	no	—
133	C₂³×C₁₉	—	8	2	no	—
134	C₂³×C₁₉	—	8	1	no	—
135	C₂³×C₁₉	—	8	1	no	—
136	C₂³×C₁₉	—	8	2	no	—
137	C₂³×C₁₉	#120	1	1	yes	characteristic
138	Q₈×C₁₉	—	2	2	no	—
139	Q₈×C₁₉	—	2	2	no	—
140	Q₈×C₁₉	—	4	1	no	—
141	Q₈×C₁₉	—	4	1	no	—
142	D₄×C₁₉	—	4	4	no	—
143	D₄×C₁₉	—	4	2	no	—
144	D₄×C₁₉	—	4	2	no	—
145	D₄×C₁₉	—	4	4	no	—
146	D₄×C₁₉	—	8	2	no	—
147	D₄×C₁₉	—	8	1	no	—
148	D₄×C₁₉	—	8	1	no	—
149	D₄×C₁₉	—	8	1	no	—
150	D₄×C₁₉	—	8	1	no	—
151	C₂×C₄×C₁₉	—	2	2	no	—
152	C₂×C₄×C₁₉	—	2	2	no	—
153	C₂×C₄×C₁₉	—	4	1	no	—
154	C₂×C₄×C₁₉	—	4	1	no	—
155	C₂×C₄×C₁₉	—	4	1	no	—
156	C₂×C₄×C₁₉	—	4	2	no	—
157	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
158	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
159	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
160	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
161	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
162	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
163	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
164	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
165	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
166	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
167	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
168	C₂×C₄×C₁₉	#137	1	2	yes	—
169	C₂×Dic₁₉	—	2	4	no	—
170	C₂×Dic₁₉	—	4	2	no	—
171	C₂×Dic₁₉	—	4	2	no	—
172	C₂×Dic₁₉	—	4	2	no	—
173	C₂×Dic₁₉	—	4	4	no	—
174	Dic₃₈	—	4	4	no	—
175	Dic₃₈	—	8	2	no	—
176	C₈×C₁₉	—	4	2	no	—
177	C₁₉⋊C₈	—	2	4	no	—
178	C₁₉⋊C₈	—	8	1	no	—
179	C₂×#492	—	19	1	no	—
180	C₂×#460	D₁₉	1	1	yes	characteristic
181	#2567	—	19	1	no	—
182	#1982	—	19	1	no	—
183	C₂×#333	—	19	1	no	—
184	C₂×Q₈⋊C₈	—	19	1	no	—
185	#1279	—	19	1	no	—
186	C₂²×C₁₉	—	8	2	no	—
187	C₂²×C₁₉	—	8	2	no	—
188	C₂²×C₁₉	—	8	2	no	—
189	C₂²×C₁₉	—	16	2	no	—
190	C₂²×C₁₉	—	16	2	no	—
191	C₂²×C₁₉	#392	1	1	yes	characteristic
192	C₂²×C₁₉	#448	1	2	yes	—
193	C₂²×C₁₉	#448	1	1	yes	characteristic
194	C₂²×C₁₉	#449	1	1	yes	characteristic
195	C₂²×C₁₉	#453	1	2	yes	—
196	C₄×C₁₉	—	2	1	no	—
197	C₄×C₁₉	—	2	1	no	—
198	C₄×C₁₉	—	4	2	no	—
199	C₄×C₁₉	—	8	1	no	—
200	C₄×C₁₉	#450	1	1	yes	characteristic
201	C₄×C₁₉	#452	1	1	yes	characteristic
202	C₄×C₁₉	#461	1	2	yes	—
203	C₄×C₁₉	#465	1	1	yes	characteristic
204	C₄×C₁₉	#468	1	1	yes	characteristic
205	C₄×C₁₉	#492	1	1	yes	characteristic
206	C₄×C₁₉	#497	1	1	yes	characteristic
207	Dic₁₉	—	4	4	no	—
208	Dic₁₉	—	8	2	no	—
209	C₂²×SD₁₆	—	2	1	no	—
210	C₂²×SD₁₆	—	38	2	no	—
211	C₂×C₄⋊Q₈	—	19	1	no	—
212	C₂×#127	C₂×D₁₉	1	1	yes	characteristic
213	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
214	#492	—	38	2	no	—
215	#492	—	38	2	no	—
216	#460	—	2	2	no	—
217	#460	—	2	2	no	—
218	C₂×C₄⋊C₈	—	19	1	no	—
219	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
220	C₂×#102	—	2	1	no	—
221	C₂×#102	—	38	2	no	—
222	C₂×C₄×C₈	—	19	1	no	—
223	#395	—	38	2	no	—
224	#391	—	38	1	no	—
225	#389	—	38	2	no	—
226	#384	—	38	1	no	—
227	C₄×C₄⋊C₄	—	19	1	no	—
228	#333	—	38	2	no	—
229	Q₈⋊C₈	—	38	2	no	—
230	C₂×C₁₉	—	16	2	no	—
231	C₂×C₁₉	#1622	1	2	yes	—
232	C₂×C₁₉	#1623	1	2	yes	—
233	C₂×C₁₉	#2000	1	1	yes	characteristic
234	C₂×C₁₉	#2002	1	1	yes	characteristic
235	C₂×C₁₉	#2013	1	1	yes	characteristic
236	C₂²×Q₈	—	19	2	no	—
237	C₂²×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
238	C₂²×D₄	—	2	1	no	—
239	C₂²×D₄	—	2	1	no	—
240	C₂²×D₄	—	2	1	no	—
241	C₂×SD₁₆	—	2	4	no	—
242	C₂×SD₁₆	—	4	2	no	—
243	C₂×SD₁₆	—	4	2	no	—
244	C₂×SD₁₆	—	38	8	no	—
245	C₂×SD₁₆	—	76	8	no	—
246	C₂²×C₈	—	2	1	no	—
247	C₂²×C₈	—	38	1	no	—
248	C₂²×C₈	—	38	1	no	—
249	C₄⋊Q₈	—	38	1	no	—
250	C₄⋊Q₈	—	38	1	no	—
251	C₄⋊Q₈	—	38	1	no	—
252	C₄⋊Q₈	—	38	1	no	—
253	#127	—	2	1	no	—
254	#127	—	2	1	no	—
255	#127	—	2	1	no	—
256	#127	C₂²⋊D₁₉	1	2	yes	—
257	C₄×Q₈	—	2	1	no	—
258	C₄×Q₈	—	2	1	no	—
259	C₄×Q₈	—	2	1	no	—
260	C₄×Q₈	—	2	1	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	19	2	no	—
263	C₂×C₄⋊C₄	—	38	1	no	—
264	C₂×C₄⋊C₄	—	38	1	no	—
265	C₂×C₄⋊C₄	—	38	4	no	—
266	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
267	C₂×C₄²	—	2	1	no	—
268	C₂×C₄²	—	38	1	no	—
269	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
270	C₄⋊C₈	—	2	1	no	—
271	C₄⋊C₈	—	38	1	no	—
272	C₄⋊C₈	—	38	1	no	—
273	C₄⋊C₈	C₂²⋊D₁₉	1	2	yes	—
274	#102	—	2	4	no	—
275	#102	—	76	4	no	—
276	C₄×C₈	—	19	2	no	—
277	C₄×C₈	—	38	1	no	—
278	#95	—	38	4	no	—
279	#95	—	38	1	no	—
280	C₁₉	#10049	1	1	yes	characteristic, complemented, Sylow
281	C₂⁴	—	4	1	no	—
282	C₂×Q₈	—	2	1	no	—
283	C₂×Q₈	—	2	1	no	—
284	C₂×Q₈	—	2	1	no	—
285	C₂×Q₈	—	2	1	no	—
286	C₂×Q₈	—	2	1	no	—
287	C₂×Q₈	—	38	2	no	—
288	C₂×Q₈	—	38	2	no	—
289	C₂×Q₈	—	76	4	no	—
290	C₂×Q₈	#64526	1	2	yes	complemented
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	4	4	no	—
295	C₂×D₄	—	4	1	no	—
296	C₂×D₄	—	4	1	no	—
297	C₂×D₄	—	4	1	no	—
298	C₂×D₄	—	4	1	no	—
299	C₂×D₄	—	4	1	no	—
300	C₂×D₄	—	4	1	no	—
301	C₂×D₄	—	4	1	no	—
302	C₂×D₄	—	4	2	no	—
303	C₂×D₄	—	4	2	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	38	2	no	—
307	C₂²×C₄	—	38	2	no	—
308	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
309	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
310	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
311	SD₁₆	—	4	8	no	—
312	SD₁₆	—	76	16	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	4	1	no	—
315	C₂×C₈	—	4	1	no	—
316	C₂×C₈	—	38	4	no	—
317	C₂×C₈	—	38	2	no	—
318	C₂×C₈	—	76	1	no	—
319	C₂×C₈	—	76	2	no	—
320	C₄⋊C₄	—	2	1	no	—
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	4	1	no	—
323	C₄⋊C₄	—	4	1	no	—
324	C₄⋊C₄	—	19	4	no	—
325	C₄⋊C₄	—	38	2	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	C₄⋊C₄	—	152	4	no	—
331	C₄²	—	4	1	no	—
332	C₄²	—	4	1	no	—
333	C₄²	—	76	1	no	—
334	C₄²	—	76	1	no	—
335	C₄²	D₄×D₁₉	1	1	yes	characteristic
336	C₄²	#64543	1	1	yes	characteristic
337	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
338	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
339	C₂³	—	4	2	no	—
340	C₂³	—	8	2	no	—
341	C₂³	—	8	1	no	—
342	C₂³	—	8	1	no	—
343	C₂³	—	8	2	no	—
344	C₂³	#10597383	1	1	yes	characteristic
345	Q₈	—	2	2	no	—
346	Q₈	—	2	2	no	—
347	Q₈	—	4	1	no	—
348	Q₈	—	4	1	no	—
349	Q₈	—	76	4	no	—
350	Q₈	—	152	2	no	—
351	D₄	—	4	4	no	—
352	D₄	—	4	2	no	—
353	D₄	—	4	2	no	—
354	D₄	—	4	4	no	—
355	D₄	—	8	2	no	—
356	D₄	—	8	1	no	—
357	D₄	—	8	1	no	—
358	D₄	—	8	1	no	—
359	D₄	—	8	1	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	38	4	no	—
367	C₂×C₄	—	76	2	no	—
368	C₂×C₄	—	76	2	no	—
369	C₂×C₄	—	76	2	no	—
370	C₂×C₄	—	76	4	no	—
371	C₂×C₄	SD₁₆×D₁₉	1	2	yes	—
372	C₂×C₄	#10597361	1	2	yes	—
373	C₂×C₄	#10597378	1	1	yes	characteristic
374	C₂×C₄	C₂×#64526	1	1	yes	characteristic
375	C₂×C₄	#10597383	1	1	yes	characteristic
376	C₂×C₄	#10597384	1	1	yes	characteristic
377	C₂×C₄	#10597385	1	1	yes	characteristic
378	C₂×C₄	#10597385	1	1	yes	characteristic
379	C₂×C₄	#10597386	1	1	yes	characteristic
380	C₂×C₄	#10597396	1	1	yes	characteristic
381	C₂×C₄	#10597397	1	1	yes	characteristic
382	C₂×C₄	#10597399	1	1	yes	characteristic
383	C₈	—	4	2	no	—
384	C₈	—	38	4	no	—
385	C₈	—	152	1	no	—
386	C₂²	—	8	2	no	—
387	C₂²	—	8	2	no	—
388	C₂²	—	8	2	no	—
389	C₂²	—	16	2	no	—
390	C₂²	—	16	2	no	—
391	C₂²	#11926452	1	1	yes	characteristic
392	C₂²	#11926681	1	2	yes	—
393	C₂²	#11926682	1	1	yes	characteristic
394	C₂²	#11926687	1	1	yes	characteristic
395	C₂²	#11926710	1	2	yes	—
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	4	2	no	—
399	C₄	—	8	1	no	—
400	C₄	—	76	4	no	—
401	C₄	—	152	2	no	—
402	C₄	#11926695	1	1	yes	characteristic
403	C₄	#11926706	1	1	yes	characteristic
404	C₄	#11926747	1	2	yes	—
405	C₄	#11926771	1	1	yes	characteristic
406	C₄	#11926788	1	1	yes	characteristic
407	C₄	#11926915	1	1	yes	characteristic
408	C₄	#11926935	1	1	yes	characteristic
409	C₂	—	16	2	no	—
410	C₂	#14562706	1	2	yes	—
411	C₂	#14562712	1	2	yes	—
412	C₂	#14564638	1	1	yes	characteristic
413	C₂	#14564647	1	1	yes	characteristic
414	C₂	#14564716	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597383
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#460	C₂
socle	C₂³×C₁₉	#120
prime radical	C₂×C₁₉×#127	C₂²
hypercenter	C₂×#460	D₁₉
hypocenter	C₁₉	#10049
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#460

Complements

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

N	H ≅ G/N	type
2. #14568840	C₂	semidirect
4. C₂×#11926292	C₂	semidirect
5. C₂×Q₈⋊(C₁₉⋊C₈)	C₂	semidirect
6. #14561474	C₂	semidirect
79. C₂×Q₈×C₁₉	SD₁₆	semidirect
123. C₄⋊Dic₁₉	SD₁₆	semidirect
280. C₁₉	#10049	semidirect
290. C₂×Q₈	#64526	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926916	2
#14568840	2
#14564563	2
C₂×#11926292	2
C₂×Q₈⋊(C₁₉⋊C₈)	2
#14561474	2
C₂×C₁₉×#460	2
#10049	19