Subgroups — #14577044

Order 2432.

1160 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927170	C₂	1	1	yes	maximal, characteristic, complemented
2	#11927141	C₂	1	2	yes	maximal, complemented
3	#11927136	C₂	1	4	yes	maximal, complemented
4	#11927132	C₂	1	2	yes	maximal, complemented
5	#11927127	C₂	1	4	yes	maximal, complemented
6	#11927106	C₂	1	1	yes	maximal, characteristic, complemented
7	#11927103	C₂	1	2	yes	maximal, complemented
8	#11927078	C₂	1	2	yes	maximal, complemented
9	#11927074	C₂	1	4	yes	maximal, complemented
10	#11927055	C₂	1	2	yes	maximal, complemented
11	#11927053	C₂	1	4	yes	maximal, complemented
12	C₂×C₄×C₂²⋊D₁₉	C₂	1	2	yes	maximal, complemented
13	C₂×C₄×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
17	C₂²×C₂²⋊D₁₉	C₂²	1	2	yes	—
18	C₂×#64541	C₂²	1	2	yes	complemented
19	C₂²×C₄×D₁₉	C₂²	1	2	yes	complemented
20	C₄×D₄×C₁₉	C₂²	1	4	yes	complemented
21	C₄×D₄×C₁₉	C₂²	1	4	yes	complemented
22	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic, complemented
26	#10597399	C₂²	1	4	yes	complemented
27	C₂×C₂²⋊Dic₁₉	C₂²	1	2	yes	—
28	#10597385	C₂²	1	4	yes	—
29	#10597385	C₂²	1	4	yes	—
30	#10597383	C₂²	1	4	yes	complemented
31	#10597381	C₂²	1	4	yes	complemented
32	#10597376	C₂²	1	2	yes	—
33	#10597376	C₂²	1	2	yes	—
34	#10597376	C₂²	1	2	yes	complemented
35	#10597375	C₂²	1	4	yes	complemented
36	#10597375	C₂²	1	4	yes	complemented
37	C₄×C₂²⋊D₁₉	C₂²	1	4	yes	complemented
38	C₄×C₂²⋊D₁₉	C₂²	1	4	yes	complemented
39	C₄×C₂²⋊D₁₉	C₂²	1	4	yes	complemented
40	C₄×C₂²⋊D₁₉	C₂²	1	4	yes	complemented
41	C₄×C₂²⋊D₁₉	C₂²	1	4	yes	complemented
42	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	complemented
43	#10597372	C₂²	1	2	yes	complemented
44	#10597370	C₂²	1	2	yes	complemented
45	#10597370	C₂²	1	2	yes	complemented
46	#10597370	C₂²	1	2	yes	complemented
47	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	complemented
48	C₂×C₄×Dic₁₉	C₂²	1	2	yes	complemented
49	#10597344	C₂²	1	4	yes	complemented
50	#10597342	C₂²	1	4	yes	complemented
51	#10597340	C₂²	1	4	yes	complemented
52	#10597335	C₂²	1	4	yes	complemented
53	#10597332	C₂²	1	4	yes	complemented
54	#10597331	C₂²	1	4	yes	complemented
55	#10597330	C₂²	1	4	yes	complemented
56	#10597329	C₂²	1	4	yes	complemented
57	#10597328	C₂²	1	4	yes	complemented
58	#10597325	C₂²	1	4	yes	complemented
59	#10597324	C₂²	1	4	yes	complemented
60	#10597324	C₂²	1	4	yes	complemented
61	#10597322	C₂²	1	4	yes	complemented
62	#10597321	C₂²	1	2	yes	complemented
63	C₄×D₇₆	C₂²	1	2	yes	complemented
64	#10597318	C₂²	1	4	yes	complemented
65	#10597316	C₂²	1	2	yes	complemented
66	C₄×Dic₃₈	C₂²	1	2	yes	complemented
67	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
68	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
69	C₂³×D₁₉	C₂³	1	2	yes	—
70	C₂×D₄×C₁₉	—	2	4	no	—
71	C₂×D₄×C₁₉	C₂³	1	4	yes	—
72	C₂²×C₄×C₁₉	—	4	2	no	—
73	C₂²×C₄×C₁₉	—	4	2	no	—
74	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
75	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
76	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
77	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
78	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
79	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
80	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
81	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
82	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
83	C₂×C₂²⋊D₁₉	—	2	8	no	—
84	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
85	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
86	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
87	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
88	C₂²×Dic₁₉	C₂³	1	2	yes	—
89	C₂²×Dic₁₉	C₂³	1	2	yes	—
90	C₂²×Dic₁₉	C₂³	1	2	yes	—
91	#64541	—	4	4	no	—
92	C₂×D₇₆	C₂³	1	2	yes	—
93	C₂×D₇₆	C₂³	1	2	yes	—
94	C₂×C₄×D₁₉	—	4	4	no	—
95	C₂×C₄×D₁₉	C₂³	1	4	yes	—
96	C₂×C₄×D₁₉	C₂³	1	4	yes	—
97	C₂×Dic₃₈	C₂³	1	2	yes	—
98	C₂×Dic₃₈	C₂³	1	2	yes	—
99	C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
100	C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
101	C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
102	C₄²×C₁₉	C₂³	1	2	yes	—
103	C₄²×C₁₉	C₂³	1	2	yes	—
104	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
105	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
106	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
107	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
108	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
109	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
110	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
111	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
112	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
113	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
114	C₄⋊Dic₁₉	C₂³	1	2	yes	—
115	C₄⋊Dic₁₉	C₂³	1	2	yes	—
116	C₄⋊Dic₁₉	C₂³	1	2	yes	—
117	C₄⋊Dic₁₉	C₂³	1	2	yes	—
118	Dic₁₉⋊C₄	C₂³	1	4	yes	—
119	Dic₁₉⋊C₄	C₂³	1	4	yes	—
120	Dic₁₉⋊C₄	C₂³	1	4	yes	—
121	Dic₁₉⋊C₄	C₂³	1	4	yes	—
122	Dic₁₉⋊C₄	C₂³	1	4	yes	—
123	Dic₁₉⋊C₄	C₂³	1	4	yes	—
124	C₄×Dic₁₉	C₂³	1	4	yes	—
125	C₄×Dic₁₉	C₂³	1	4	yes	—
126	C₂³×C₁₉	—	2	2	no	—
127	C₂³×C₁₉	—	4	1	no	—
128	C₂³×C₁₉	—	4	1	no	—
129	C₂³×C₁₉	—	4	1	no	—
130	C₂³×C₁₉	—	4	1	no	—
131	C₂³×C₁₉	#41	1	4	yes	complemented
132	C₂³×C₁₉	C₂⁴	1	2	yes	—
133	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
134	C₂³×C₁₉	C₂⁴	1	2	yes	—
135	C₂²×D₁₉	—	2	4	no	—
136	C₂²×D₁₉	—	4	2	no	—
137	C₂²×D₁₉	—	4	2	no	—
138	C₂²×D₁₉	C₂⁴	1	4	yes	—
139	D₄×C₁₉	—	2	8	no	—
140	C₂×C₄×C₁₉	—	2	2	no	—
141	C₂×C₄×C₁₉	—	2	4	no	—
142	C₂×C₄×C₁₉	—	2	4	no	—
143	C₂×C₄×C₁₉	—	2	2	no	—
144	C₂×C₄×C₁₉	—	4	1	no	—
145	C₂×C₄×C₁₉	—	4	2	no	—
146	C₂×C₄×C₁₉	—	4	1	no	—
147	C₂×C₄×C₁₉	—	4	2	no	—
148	C₂×C₄×C₁₉	—	4	1	no	—
149	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
150	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
151	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
152	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
153	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
154	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
155	C₂²⋊D₁₉	—	2	8	no	—
156	C₂²⋊D₁₉	—	2	8	no	—
157	C₂²⋊D₁₉	—	4	4	no	—
158	C₂²⋊D₁₉	—	4	4	no	—
159	C₂×Dic₁₉	—	2	4	no	—
160	C₂×Dic₁₉	—	4	2	no	—
161	C₂×Dic₁₉	—	4	2	no	—
162	C₂×Dic₁₉	C₂⁴	1	4	yes	—
163	C₂×Dic₁₉	C₂⁴	1	4	yes	—
164	C₂×Dic₁₉	C₂⁴	1	4	yes	—
165	D₇₆	—	4	2	no	—
166	D₇₆	—	4	2	no	—
167	C₄×D₁₉	—	2	8	no	—
168	C₄×D₁₉	—	4	4	no	—
169	Dic₃₈	—	4	2	no	—
170	Dic₃₈	—	4	2	no	—
171	#3459	—	19	1	no	maximal, Sylow
172	C₂²×C₁₉	—	2	2	no	—
173	C₂²×C₁₉	—	2	1	no	—
174	C₂²×C₁₉	—	2	2	no	—
175	C₂²×C₁₉	—	2	1	no	—
176	C₂²×C₁₉	—	2	2	no	—
177	C₂²×C₁₉	—	2	2	no	—
178	C₂²×C₁₉	—	2	2	no	—
179	C₂²×C₁₉	—	4	4	no	—
180	C₂²×C₁₉	—	4	4	no	—
181	C₂²×C₁₉	C₂×#41	1	4	yes	—
182	C₂²×C₁₉	C₂×#41	1	2	yes	—
183	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
184	C₂×D₁₉	—	2	4	no	—
185	C₂×D₁₉	—	2	4	no	—
186	C₂×D₁₉	—	2	4	no	—
187	C₂×D₁₉	—	4	8	no	—
188	C₄×C₁₉	—	2	2	no	—
189	C₄×C₁₉	—	2	2	no	—
190	C₄×C₁₉	—	2	2	no	—
191	C₄×C₁₉	—	2	1	no	—
192	C₄×C₁₉	—	2	2	no	—
193	C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
194	Dic₁₉	—	2	4	no	—
195	Dic₁₉	—	2	4	no	—
196	Dic₁₉	—	2	4	no	—
197	#543	—	19	1	no	—
198	#539	—	19	4	no	—
199	#539	—	19	2	no	—
200	#538	—	19	4	no	—
201	#538	—	19	2	no	—
202	#534	—	19	2	no	—
203	#534	—	19	1	no	—
204	#529	—	19	4	no	—
205	#529	—	19	2	no	—
206	#525	—	19	2	no	—
207	#525	—	19	4	no	—
208	C₂×C₄×D₄	—	19	2	no	—
209	C₂×C₄×D₄	D₁₉	1	1	yes	characteristic, complemented
210	C₂×C₁₉	—	2	4	no	—
211	C₂×C₁₉	—	2	2	no	—
212	C₂×C₁₉	—	4	2	no	—
213	C₂×C₁₉	C₂²×#41	1	1	yes	characteristic
214	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
215	C₂×C₁₉	#585	1	1	yes	characteristic
216	D₁₉	—	4	4	no	—
217	C₂×#41	—	19	2	no	—
218	C₂²×D₄	—	19	2	no	—
219	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
220	C₂³×C₄	—	19	2	no	—
221	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
222	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic, complemented
223	#126	—	19	4	no	—
224	#126	—	19	4	no	—
225	#126	—	19	4	no	—
226	#125	—	19	4	no	—
227	#125	—	19	2	no	—
228	#124	—	19	4	no	—
229	#124	—	19	2	no	—
230	#123	—	19	4	no	—
231	#123	—	19	4	no	—
232	#123	—	19	4	no	—
233	#123	—	19	4	no	—
234	#123	—	19	4	no	—
235	#123	—	19	4	no	—
236	C₂²⋊Q₈	—	19	2	no	—
237	C₂²⋊Q₈	—	19	2	no	—
238	C₂²⋊Q₈	—	19	2	no	—
239	C₂²⋊Q₈	—	19	4	no	—
240	C₂²⋊Q₈	—	19	4	no	—
241	C₂²⋊Q₈	—	19	4	no	—
242	#121	—	19	4	no	—
243	#121	—	19	4	no	—
244	#121	—	19	2	no	—
245	#121	—	19	2	no	—
246	#121	—	19	2	no	—
247	#121	—	19	4	no	—
248	#120	—	19	4	no	—
249	#120	—	19	4	no	—
250	#120	—	19	4	no	—
251	C₄×Q₈	—	19	2	no	—
252	C₄×D₄	—	19	4	no	—
253	C₄×D₄	—	19	4	no	—
254	C₄×D₄	—	19	4	no	—
255	C₄×D₄	—	19	4	no	—
256	C₄×D₄	—	19	4	no	—
257	C₄×D₄	—	19	2	no	—
258	C₄×D₄	C₂×D₁₉	1	4	yes	complemented
259	C₄×D₄	C₂×D₁₉	1	4	yes	complemented
260	#117	—	19	2	no	—
261	#117	—	19	4	no	—
262	C₂×C₄⋊C₄	—	19	2	no	—
263	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic, complemented
264	C₂×C₂²⋊C₄	—	19	2	no	—
265	C₂×C₂²⋊C₄	—	19	2	no	—
266	C₂×C₂²⋊C₄	C₂×D₁₉	1	1	yes	characteristic
267	C₂×C₂²⋊C₄	C₂×D₁₉	1	1	yes	characteristic, complemented
268	C₂×C₄²	—	19	2	no	—
269	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic, complemented
270	C₁₉	#3459	1	1	yes	characteristic, complemented, Sylow
271	C₂⁴	—	19	2	no	—
272	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
273	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
274	#41	—	76	4	no	—
275	C₂×Q₈	—	19	2	no	—
276	C₂×Q₈	—	19	2	no	—
277	C₂×D₄	—	2	4	no	—
278	C₂×D₄	—	19	4	no	—
279	C₂×D₄	—	19	4	no	—
280	C₂×D₄	—	19	4	no	—
281	C₂×D₄	—	19	4	no	—
282	C₂×D₄	—	19	2	no	—
283	C₂×D₄	—	19	2	no	—
284	C₂×D₄	—	38	8	no	—
285	C₂×D₄	C₂²×D₁₉	1	4	yes	—
286	C₂²×C₄	—	4	2	no	—
287	C₂²×C₄	—	4	2	no	—
288	C₂²×C₄	—	19	2	no	—
289	C₂²×C₄	—	19	2	no	—
290	C₂²×C₄	—	19	2	no	—
291	C₂²×C₄	—	19	4	no	—
292	C₂²×C₄	—	19	4	no	—
293	C₂²×C₄	—	76	4	no	—
294	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
295	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
296	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
297	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
298	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
299	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
300	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
301	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
302	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
303	C₄⋊C₄	—	19	4	no	—
304	C₄⋊C₄	—	19	4	no	—
305	C₄⋊C₄	—	19	4	no	—
306	C₄⋊C₄	—	19	4	no	—
307	C₄⋊C₄	—	19	4	no	—
308	C₄⋊C₄	—	19	4	no	—
309	C₄⋊C₄	—	19	2	no	—
310	C₄⋊C₄	—	19	2	no	—
311	C₄⋊C₄	—	19	2	no	—
312	C₄⋊C₄	—	19	2	no	—
313	C₄⋊C₄	C₂²×D₁₉	1	4	yes	—
314	C₂²⋊C₄	—	19	4	no	—
315	C₂²⋊C₄	—	19	4	no	—
316	C₂²⋊C₄	—	19	4	no	—
317	C₂²⋊C₄	—	19	4	no	—
318	C₂²⋊C₄	—	19	4	no	—
319	C₂²⋊C₄	—	19	4	no	—
320	C₂²⋊C₄	—	19	4	no	—
321	C₂²⋊C₄	—	19	4	no	—
322	C₂²⋊C₄	—	19	4	no	—
323	C₂²⋊C₄	—	19	4	no	—
324	C₂²⋊C₄	C₂²×D₁₉	1	4	yes	—
325	C₂²⋊C₄	C₂²×D₁₉	1	4	yes	—
326	C₄²	—	19	4	no	—
327	C₄²	—	19	4	no	—
328	C₄²	C₂²×D₁₉	1	2	yes	—
329	C₄²	C₂²×D₁₉	1	2	yes	—
330	C₂³	—	2	2	no	—
331	C₂³	—	4	1	no	—
332	C₂³	—	4	1	no	—
333	C₂³	—	4	1	no	—
334	C₂³	—	4	1	no	—
335	C₂³	—	19	4	no	—
336	C₂³	—	38	4	no	—
337	C₂³	—	76	2	no	—
338	C₂³	—	76	2	no	—
339	C₂³	#64541	1	4	yes	complemented
340	C₂³	C₂³×D₁₉	1	2	yes	—
341	C₂³	C₂³×D₁₉	1	1	yes	characteristic
342	C₂³	C₂³×D₁₉	1	2	yes	—
343	Q₈	—	76	2	no	—
344	Q₈	—	76	2	no	—
345	D₄	—	2	8	no	—
346	D₄	—	38	8	no	—
347	D₄	—	38	8	no	—
348	D₄	—	76	2	no	—
349	D₄	—	76	2	no	—
350	D₄	—	76	4	no	—
351	D₄	—	76	4	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	19	4	no	—
362	C₂×C₄	—	19	4	no	—
363	C₂×C₄	—	19	4	no	—
364	C₂×C₄	—	38	4	no	—
365	C₂×C₄	—	38	8	no	—
366	C₂×C₄	—	76	4	no	—
367	C₂×C₄	—	76	2	no	—
368	C₂×C₄	—	76	2	no	—
369	C₂×C₄	C₂³×D₁₉	1	2	yes	—
370	C₂×C₄	C₂³×D₁₉	1	2	yes	—
371	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
372	C₂×C₄	C₂³×D₁₉	1	2	yes	—
373	C₂×C₄	C₂³×D₁₉	1	2	yes	—
374	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
375	C₂²	—	2	1	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	2	2	no	—
379	C₂²	—	2	2	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	4	4	no	—
383	C₂²	—	4	4	no	—
384	C₂²	—	38	4	no	—
385	C₂²	—	38	4	no	—
386	C₂²	—	38	4	no	—
387	C₂²	—	76	8	no	—
388	C₂²	C₂×#64541	1	2	yes	—
389	C₂²	C₂×#64541	1	4	yes	—
390	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
391	C₄	—	2	2	no	—
392	C₄	—	2	1	no	—
393	C₄	—	2	2	no	—
394	C₄	—	2	2	no	—
395	C₄	—	2	2	no	—
396	C₄	—	38	4	no	—
397	C₄	—	38	4	no	—
398	C₄	—	38	4	no	—
399	C₄	#10597430	1	2	yes	—
400	C₂	—	2	2	no	—
401	C₂	—	2	4	no	—
402	C₂	—	4	2	no	—
403	C₂	—	76	4	no	—
404	C₂	C₂²×#64541	1	1	yes	characteristic
405	C₂	C₂×#10597430	1	1	yes	characteristic
406	C₂	#11927380	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Frattini	C₂²	C₂⁴×D₁₉
Fitting	C₂×C₄×D₄×C₁₉	C₂
hypercenter	C₂×C₄×D₄	D₁₉
hypocenter	C₁₉	#3459
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. #11927170	C₂	semidirect
2. #11927141	C₂	semidirect
3. #11927136	C₂	semidirect
4. #11927132	C₂	semidirect
5. #11927127	C₂	semidirect
6. #11927106	C₂	semidirect
7. #11927103	C₂	semidirect
8. #11927078	C₂	semidirect
9. #11927074	C₂	semidirect
10. #11927055	C₂	semidirect
11. #11927053	C₂	semidirect
12. C₂×C₄×C₂²⋊D₁₉	C₂	semidirect
13. C₂×C₄×D₄×C₁₉	C₂	semidirect
16. C₂³×C₄×C₁₉	C₂²	semidirect
18. C₂×#64541	C₂²	semidirect
19. C₂²×C₄×D₁₉	C₂²	semidirect
20. C₄×D₄×C₁₉	C₂²	semidirect
21. C₄×D₄×C₁₉	C₂²	semidirect
22. C₂×C₄⋊C₄×C₁₉	C₂²	semidirect
24. C₂×C₂²⋊C₄×C₁₉	C₂²	semidirect
25. C₂×C₄²×C₁₉	C₂²	semidirect
26. #10597399	C₂²	semidirect
30. #10597383	C₂²	semidirect
31. #10597381	C₂²	semidirect
34. #10597376	C₂²	semidirect
35. #10597375	C₂²	semidirect
36. #10597375	C₂²	semidirect
37. C₄×C₂²⋊D₁₉	C₂²	semidirect
38. C₄×C₂²⋊D₁₉	C₂²	semidirect
39. C₄×C₂²⋊D₁₉	C₂²	semidirect
40. C₄×C₂²⋊D₁₉	C₂²	semidirect
41. C₄×C₂²⋊D₁₉	C₂²	semidirect
42. C₂×(C₂×D₁₉)⋊C₄	C₂²	semidirect
43. #10597372	C₂²	semidirect
44. #10597370	C₂²	semidirect
45. #10597370	C₂²	semidirect
46. #10597370	C₂²	semidirect
47. C₂×Dic₁₉⋊C₄	C₂²	semidirect
48. C₂×C₄×Dic₁₉	C₂²	semidirect
49. #10597344	C₂²	semidirect
50. #10597342	C₂²	semidirect
51. #10597340	C₂²	semidirect
52. #10597335	C₂²	semidirect
53. #10597332	C₂²	semidirect
54. #10597331	C₂²	semidirect
55. #10597330	C₂²	semidirect
56. #10597329	C₂²	semidirect
57. #10597328	C₂²	semidirect
58. #10597325	C₂²	semidirect
59. #10597324	C₂²	semidirect
60. #10597324	C₂²	semidirect
61. #10597322	C₂²	semidirect
62. #10597321	C₂²	semidirect
63. C₄×D₇₆	C₂²	semidirect
64. #10597318	C₂²	semidirect
65. #10597316	C₂²	semidirect
66. C₄×Dic₃₈	C₂²	semidirect
131. C₂³×C₁₉	#41	semidirect
209. C₂×C₄×D₄	D₁₉	semidirect
222. C₂³×C₄	C₂×D₁₉	semidirect
258. C₄×D₄	C₂×D₁₉	semidirect
259. C₄×D₄	C₂×D₁₉	semidirect
263. C₂×C₄⋊C₄	C₂×D₁₉	semidirect
267. C₂×C₂²⋊C₄	C₂×D₁₉	semidirect
269. C₂×C₄²	C₂×D₁₉	semidirect
270. C₁₉	#3459	semidirect
339. C₂³	#64541	semidirect

Maximal subgroups

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

subgroup	index
#11927170	2
#11927141	2
#11927136	2
#11927132	2
#11927127	2
#11927106	2
#11927103	2
#11927078	2
#11927074	2
#11927055	2
#11927053	2
C₂×C₄×C₂²⋊D₁₉	2
C₂×C₄×D₄×C₁₉	2
#3459	19