Subgroups — #14566743

Order 2432.

560 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10597331	C₂	1	1	yes	maximal, characteristic
2	#11926450	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926448	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926437	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926436	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926435	C₂	1	1	yes	maximal, characteristic, complemented
7	#11926432	C₂	1	1	yes	maximal, characteristic, complemented
8	#11926423	C₂	1	1	yes	maximal, characteristic
9	#11926420	C₂	1	1	yes	maximal, characteristic
10	C₄×(C₂×D₁₉)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₂²⋊Dic₁₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#11926391	C₂	1	1	yes	maximal, characteristic, complemented
13	#11926390	C₂	1	1	yes	maximal, characteristic, complemented
14	#11926389	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₂²⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₁₉	C₂²	1	1	yes	characteristic
19	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
20	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
23	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊Dic₁₉	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊Dic₁₉	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊Dic₁₉	C₂²	1	1	yes	characteristic
27	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
33	C₂×Dic₁₉⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
35	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
36	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
38	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
39	#10597331	C₄	1	8	yes	complemented
40	C₁₉×#95	C₂²	1	1	yes	characteristic
41	C₁₉×#95	C₂²	1	1	yes	characteristic
42	C₁₉⋊#95	C₂²	1	1	yes	characteristic
43	C₁₉⋊#95	C₂²	1	1	yes	characteristic
44	C₁₉⋊#95	C₂²	1	1	yes	characteristic
45	C₁₉⋊#95	C₂²	1	1	yes	characteristic
46	C₁₉⋊#95	C₂²	1	1	yes	characteristic
47	C₁₉⋊#95	C₂²	1	1	yes	characteristic
48	C₁₉⋊#95	C₂²	1	1	yes	characteristic
49	C₁₉⋊#95	C₂²	1	1	yes	characteristic
50	C₁₉⋊#95	C₂²	1	1	yes	characteristic
51	C₁₉⋊#95	C₂²	1	1	yes	characteristic
52	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
53	C₂³×D₁₉	C₂³	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	—	2	2	no	—
55	C₂²×C₄×C₁₉	—	2	2	no	—
56	C₂²×C₄×C₁₉	—	4	1	no	—
57	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
58	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
59	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
60	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
61	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
62	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
63	C₂×C₂²⋊D₁₉	—	4	1	no	—
64	C₂×C₂²⋊D₁₉	—	4	1	no	—
65	C₂×C₂²⋊D₁₉	C₂×C₄	1	4	yes	—
66	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
67	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
68	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
69	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
70	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
71	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
72	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
73	C₂×C₄×D₁₉	—	2	2	no	—
74	C₂×C₄×D₁₉	—	2	2	no	—
75	C₂×C₄×D₁₉	—	4	1	no	—
76	C₂×Dic₃₈	—	4	1	no	—
77	C₂×Dic₃₈	—	4	1	no	—
78	C₂×Dic₃₈	C₂×C₄	1	4	yes	complemented
79	C₂²⋊C₄×C₁₉	—	2	2	no	—
80	C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	complemented
81	C₄²×C₁₉	—	2	2	no	—
82	C₄²×C₁₉	—	4	1	no	—
83	C₂²⋊Dic₁₉	—	2	2	no	—
84	C₂²⋊Dic₁₉	—	4	1	no	—
85	C₂²⋊Dic₁₉	C₂×C₄	1	4	yes	complemented
86	(C₂×D₁₉)⋊C₄	—	2	2	no	—
87	(C₂×D₁₉)⋊C₄	—	2	2	no	—
88	(C₂×D₁₉)⋊C₄	—	4	1	no	—
89	(C₂×D₁₉)⋊C₄	C₂×C₄	1	4	yes	complemented
90	(C₂×D₁₉)⋊C₄	C₂×C₄	1	4	yes	complemented
91	C₄⋊Dic₁₉	—	4	1	no	—
92	Dic₁₉⋊C₄	—	4	1	no	—
93	C₄×Dic₁₉	—	2	2	no	—
94	C₄×Dic₁₉	—	2	2	no	—
95	C₄×Dic₁₉	—	2	2	no	—
96	C₄×Dic₁₉	—	4	1	no	—
97	C₄×Dic₁₉	C₂×C₄	1	4	yes	complemented
98	C₂³×C₁₉	—	2	1	no	—
99	C₂³×C₁₉	—	2	1	no	—
100	C₂³×C₁₉	—	2	1	no	—
101	C₂³×C₁₉	—	2	1	no	—
102	C₂³×C₁₉	—	2	1	no	—
103	C₂³×C₁₉	—	2	1	no	—
104	C₂³×C₁₉	C₂²×C₄	1	2	yes	—
105	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
106	C₂²×D₁₉	—	2	1	no	—
107	C₂²×D₁₉	—	2	1	no	—
108	C₂²×D₁₉	—	2	1	no	—
109	C₂²×D₁₉	—	2	1	no	—
110	C₂²×D₁₉	—	2	1	no	—
111	C₂²×D₁₉	—	2	1	no	—
112	C₂²×D₁₉	C₂²×C₄	1	2	yes	—
113	C₂×C₄×C₁₉	—	2	1	no	—
114	C₂×C₄×C₁₉	—	2	1	no	—
115	C₂×C₄×C₁₉	—	2	1	no	—
116	C₂×C₄×C₁₉	—	2	1	no	—
117	C₂×C₄×C₁₉	—	2	1	no	—
118	C₂×C₄×C₁₉	—	2	1	no	—
119	C₂×C₄×C₁₉	—	2	1	no	—
120	C₂×C₄×C₁₉	—	2	1	no	—
121	C₂×C₄×C₁₉	—	2	1	no	—
122	C₂×C₄×C₁₉	—	2	1	no	—
123	C₂×C₄×C₁₉	—	2	1	no	—
124	C₂×C₄×C₁₉	—	2	1	no	—
125	C₂×C₄×C₁₉	—	2	1	no	—
126	C₂×C₄×C₁₉	—	4	4	no	—
127	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
128	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
129	C₂×C₄×C₁₉	#41	1	2	yes	—
130	C₂×C₄×C₁₉	#41	1	2	yes	—
131	C₂×C₄×C₁₉	#41	1	2	yes	—
132	C₂²⋊D₁₉	—	4	4	no	—
133	C₂×Dic₁₉	—	2	1	no	—
134	C₂×Dic₁₉	—	2	1	no	—
135	C₂×Dic₁₉	—	2	1	no	—
136	C₂×Dic₁₉	—	2	1	no	—
137	C₂×Dic₁₉	—	2	1	no	—
138	C₂×Dic₁₉	—	2	1	no	—
139	C₂×Dic₁₉	—	2	1	no	—
140	C₂×Dic₁₉	—	2	1	no	—
141	C₂×Dic₁₉	—	2	1	no	—
142	C₂×Dic₁₉	—	2	1	no	—
143	C₂×Dic₁₉	—	2	1	no	—
144	C₂×Dic₁₉	—	2	1	no	—
145	C₂×Dic₁₉	—	2	1	no	—
146	C₂×Dic₁₉	—	2	1	no	—
147	C₂×Dic₁₉	—	2	1	no	—
148	C₂×Dic₁₉	—	2	1	no	—
149	C₂×Dic₁₉	—	2	1	no	—
150	C₂×Dic₁₉	C₂²×C₄	1	2	yes	—
151	C₂×Dic₁₉	C₂²×C₄	1	2	yes	—
152	C₂×Dic₁₉	C₂²×C₄	1	2	yes	—
153	C₂×Dic₁₉	#41	1	2	yes	—
154	C₄×D₁₉	—	4	4	no	—
155	Dic₃₈	—	4	4	no	—
156	#2372	—	19	1	no	maximal, Sylow
157	C₂²×C₁₉	—	2	2	no	—
158	C₂²×C₁₉	—	2	2	no	—
159	C₂²×C₁₉	—	2	2	no	—
160	C₂²×C₁₉	—	4	1	no	—
161	C₂²×C₁₉	—	4	1	no	—
162	C₂²×C₁₉	—	4	1	no	—
163	C₂²×C₁₉	—	4	1	no	—
164	C₂²×C₁₉	C₂³×C₄	1	1	yes	characteristic
165	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
166	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
167	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
168	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
169	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
170	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
171	C₂×D₁₉	—	2	2	no	—
172	C₂×D₁₉	—	2	2	no	—
173	C₂×D₁₉	—	2	2	no	—
174	C₂×D₁₉	—	4	1	no	—
175	C₂×D₁₉	—	4	1	no	—
176	C₂×D₁₉	—	4	1	no	—
177	C₂×D₁₉	—	4	1	no	—
178	C₄×C₁₉	—	2	2	no	—
179	C₄×C₁₉	—	2	2	no	—
180	C₄×C₁₉	—	2	2	no	—
181	C₄×C₁₉	—	2	2	no	—
182	C₄×C₁₉	—	2	2	no	—
183	C₄×C₁₉	—	4	1	no	—
184	Dic₁₉	—	2	2	no	—
185	Dic₁₉	—	2	2	no	—
186	Dic₁₉	—	2	2	no	—
187	Dic₁₉	—	2	2	no	—
188	Dic₁₉	—	4	1	no	—
189	Dic₁₉	—	4	1	no	—
190	Dic₁₉	—	4	1	no	—
191	C₂×#124	—	19	1	no	—
192	#391	—	19	1	no	—
193	#391	—	19	1	no	—
194	#388	—	19	1	no	—
195	#388	—	19	1	no	—
196	#388	—	19	1	no	—
197	#388	—	19	1	no	—
198	#386	—	19	1	no	—
199	#386	—	19	1	no	—
200	C₄×C₂²⋊C₄	—	19	1	no	—
201	C₄×C₂²⋊C₄	—	19	1	no	—
202	C₄×C₂²⋊C₄	—	19	1	no	—
203	C₄×C₂²⋊C₄	D₁₉	1	1	yes	characteristic, complemented
204	#376	—	19	1	no	—
205	#376	—	19	1	no	—
206	C₂×C₁₉	—	4	2	no	—
207	C₂×C₁₉	C₄×#41	1	1	yes	characteristic
208	C₂×C₁₉	C₄×#41	1	1	yes	characteristic
209	C₂×C₁₉	#518	1	1	yes	characteristic
210	C₂×C₁₉	#551	1	1	yes	characteristic
211	C₂×C₁₉	#551	1	1	yes	characteristic
212	C₂×C₁₉	#555	1	1	yes	characteristic
213	C₂×C₁₉	#555	1	1	yes	characteristic
214	D₁₉	—	4	2	no	—
215	C₂²×Q₈	—	19	1	no	—
216	C₂²×D₄	—	19	1	no	—
217	C₂³×C₄	—	19	1	no	—
218	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
219	#124	—	19	8	no	—
220	C₂×C₄⋊C₄	—	19	1	no	—
221	C₂×C₄⋊C₄	—	19	1	no	—
222	C₂×C₂²⋊C₄	—	19	1	no	—
223	C₂×C₂²⋊C₄	—	19	1	no	—
224	C₂×C₂²⋊C₄	—	19	1	no	—
225	C₂×C₂²⋊C₄	—	19	1	no	—
226	C₂×C₂²⋊C₄	—	19	1	no	—
227	C₂×C₂²⋊C₄	—	19	1	no	—
228	C₂×C₂²⋊C₄	—	19	1	no	—
229	C₂×C₂²⋊C₄	—	19	1	no	—
230	C₂×C₂²⋊C₄	C₂×D₁₉	1	1	yes	characteristic
231	C₂×C₂²⋊C₄	C₂×D₁₉	1	1	yes	characteristic
232	C₂×C₄²	—	19	1	no	—
233	C₂×C₄²	—	19	1	no	—
234	C₂×C₄²	—	19	1	no	—
235	C₂×C₄²	—	19	1	no	—
236	C₂×C₄²	—	19	1	no	—
237	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
238	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
239	#95	—	19	1	no	—
240	#95	—	19	1	no	—
241	#95	—	19	1	no	—
242	#95	—	19	1	no	—
243	#95	—	19	1	no	—
244	#95	—	19	1	no	—
245	#95	—	19	1	no	—
246	#95	—	19	1	no	—
247	#95	—	19	1	no	—
248	#95	—	19	1	no	—
249	#95	C₂×D₁₉	1	1	yes	characteristic
250	#95	C₂×D₁₉	1	1	yes	characteristic
251	C₁₉	#2372	1	1	yes	characteristic, complemented, Sylow
252	C₂⁴	—	19	1	no	—
253	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
254	C₂×Q₈	—	19	4	no	—
255	C₂×Q₈	—	76	1	no	—
256	C₂×Q₈	—	76	1	no	—
257	C₂×D₄	—	19	4	no	—
258	C₂×D₄	—	76	1	no	—
259	C₂×D₄	—	76	1	no	—
260	C₂²×C₄	—	2	2	no	—
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	—	4	1	no	—
263	C₂²×C₄	—	19	1	no	—
264	C₂²×C₄	—	19	1	no	—
265	C₂²×C₄	—	19	1	no	—
266	C₂²×C₄	—	19	1	no	—
267	C₂²×C₄	—	19	1	no	—
268	C₂²×C₄	—	19	1	no	—
269	C₂²×C₄	—	19	1	no	—
270	C₂²×C₄	—	38	2	no	—
271	C₂²×C₄	—	38	2	no	—
272	C₂²×C₄	—	76	1	no	—
273	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
274	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
275	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
276	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
277	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
278	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
279	C₄⋊C₄	—	76	1	no	—
280	C₄⋊C₄	—	76	1	no	—
281	C₂²⋊C₄	—	2	2	no	—
282	C₂²⋊C₄	—	19	4	no	—
283	C₂²⋊C₄	—	19	4	no	—
284	C₂²⋊C₄	—	19	4	no	—
285	C₂²⋊C₄	—	38	2	no	—
286	C₂²⋊C₄	—	38	2	no	—
287	C₂²⋊C₄	—	38	2	no	—
288	C₂²⋊C₄	—	76	1	no	—
289	C₂²⋊C₄	—	76	1	no	—
290	C₂²⋊C₄	C₄×D₁₉	1	4	yes	complemented
291	C₄²	—	2	2	no	—
292	C₄²	—	4	1	no	—
293	C₄²	—	19	4	no	—
294	C₄²	—	38	2	no	—
295	C₄²	—	38	2	no	—
296	C₄²	—	38	2	no	—
297	C₄²	—	76	1	no	—
298	C₂³	—	2	1	no	—
299	C₂³	—	2	1	no	—
300	C₂³	—	2	1	no	—
301	C₂³	—	2	1	no	—
302	C₂³	—	2	1	no	—
303	C₂³	—	2	1	no	—
304	C₂³	—	19	2	no	—
305	C₂³	—	38	1	no	—
306	C₂³	—	38	1	no	—
307	C₂³	—	38	1	no	—
308	C₂³	—	38	1	no	—
309	C₂³	—	38	1	no	—
310	C₂³	—	38	1	no	—
311	C₂³	C₂×C₄×D₁₉	1	2	yes	—
312	C₂³	C₂³×D₁₉	1	1	yes	characteristic
313	Q₈	—	76	4	no	—
314	D₄	—	76	4	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	4	4	no	—
329	C₂×C₄	—	19	2	no	—
330	C₂×C₄	—	19	2	no	—
331	C₂×C₄	—	19	2	no	—
332	C₂×C₄	—	19	2	no	—
333	C₂×C₄	—	38	1	no	—
334	C₂×C₄	—	38	1	no	—
335	C₂×C₄	—	38	1	no	—
336	C₂×C₄	—	38	1	no	—
337	C₂×C₄	—	38	1	no	—
338	C₂×C₄	—	38	1	no	—
339	C₂×C₄	—	38	1	no	—
340	C₂×C₄	—	38	1	no	—
341	C₂×C₄	—	38	1	no	—
342	C₂×C₄	—	38	1	no	—
343	C₂×C₄	—	38	1	no	—
344	C₂×C₄	—	38	1	no	—
345	C₂×C₄	—	38	1	no	—
346	C₂×C₄	—	38	1	no	—
347	C₂×C₄	—	38	1	no	—
348	C₂×C₄	—	38	1	no	—
349	C₂×C₄	—	38	1	no	—
350	C₂×C₄	—	76	4	no	—
351	C₂×C₄	C₂×C₄×D₁₉	1	2	yes	—
352	C₂×C₄	C₂×C₄×D₁₉	1	2	yes	—
353	C₂×C₄	#64541	1	2	yes	—
354	C₂×C₄	#64541	1	2	yes	—
355	C₂×C₄	#64543	1	2	yes	—
356	C₂²	—	2	2	no	—
357	C₂²	—	2	2	no	—
358	C₂²	—	2	2	no	—
359	C₂²	—	4	1	no	—
360	C₂²	—	4	1	no	—
361	C₂²	—	4	1	no	—
362	C₂²	—	4	1	no	—
363	C₂²	—	38	2	no	—
364	C₂²	—	38	2	no	—
365	C₂²	—	38	2	no	—
366	C₂²	—	76	1	no	—
367	C₂²	—	76	1	no	—
368	C₂²	—	76	1	no	—
369	C₂²	—	76	1	no	—
370	C₂²	C₂²×C₄×D₁₉	1	1	yes	characteristic
371	C₂²	C₂×#64541	1	1	yes	characteristic
372	C₂²	C₂×#64541	1	1	yes	characteristic
373	C₂²	C₂×#64543	1	1	yes	characteristic
374	C₂²	#10597430	1	1	yes	characteristic
375	C₂²	#41×D₁₉	1	1	yes	characteristic
376	C₂²	#10597435	1	1	yes	characteristic
377	C₄	—	2	2	no	—
378	C₄	—	2	2	no	—
379	C₄	—	2	2	no	—
380	C₄	—	2	2	no	—
381	C₄	—	2	2	no	—
382	C₄	—	4	1	no	—
383	C₄	—	38	2	no	—
384	C₄	—	38	2	no	—
385	C₄	—	38	2	no	—
386	C₄	—	38	2	no	—
387	C₄	—	76	1	no	—
388	C₄	—	76	1	no	—
389	C₄	—	76	1	no	—
390	C₂	—	4	2	no	—
391	C₂	—	76	2	no	—
392	C₂	C₄×#64543	1	1	yes	characteristic
393	C₂	C₄×#64541	1	1	yes	characteristic
394	C₂	#11927016	1	1	yes	characteristic
395	C₂	#11927220	1	1	yes	characteristic
396	C₂	#11927223	1	1	yes	characteristic
397	C₂	#11927257	1	1	yes	characteristic
398	C₂	#11927259	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator	C₂²×C₁₉	C₂³×C₄
Fitting	C₄×C₂²⋊C₄×C₁₉	C₂
socle, cosocle	C₂³×C₁₉	C₂⁴
prime radical	C₂²×C₂²⋊D₁₉	C₂²
hypercenter	C₄×C₂²⋊C₄	D₁₉
hypocenter	C₁₉	#2372
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₄×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
2. #11926450	C₂	semidirect
3. #11926448	C₂	semidirect
4. #11926437	C₂	semidirect
5. #11926436	C₂	semidirect
6. #11926435	C₂	semidirect
7. #11926432	C₂	semidirect
10. C₄×(C₂×D₁₉)⋊C₄	C₂	semidirect
11. C₄×C₂²⋊Dic₁₉	C₂	semidirect
12. #11926391	C₂	semidirect
13. #11926390	C₂	semidirect
14. #11926389	C₂	semidirect
15. C₄×C₂²⋊C₄×C₁₉	C₂	semidirect
39. #10597331	C₄	semidirect
78. C₂×Dic₃₈	C₂×C₄	semidirect
80. C₂²⋊C₄×C₁₉	C₂×C₄	semidirect
85. C₂²⋊Dic₁₉	C₂×C₄	semidirect
89. (C₂×D₁₉)⋊C₄	C₂×C₄	semidirect
90. (C₂×D₁₉)⋊C₄	C₂×C₄	semidirect
97. C₄×Dic₁₉	C₂×C₄	semidirect
203. C₄×C₂²⋊C₄	D₁₉	semidirect
251. C₁₉	#2372	semidirect
290. C₂²⋊C₄	C₄×D₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10597331	2
#11926450	2
#11926448	2
#11926437	2
#11926436	2
#11926435	2
#11926432	2
#11926423	2
#11926420	2
C₄×(C₂×D₁₉)⋊C₄	2
C₄×C₂²⋊Dic₁₉	2
#11926391	2
#11926390	2
#11926389	2
C₄×C₂²⋊C₄×C₁₉	2
#2372	19