Subgroups — C₂×#11927261 #14577178

Order 2432.

1112 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927261	C₂	1	16	yes	maximal, direct product factor
2	C₂×#10597334	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#10597344	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#10597344	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#10597325	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10597331	C₂	1	1	yes	maximal, characteristic
7	C₂×#10597331	C₂	1	1	yes	maximal, characteristic
8	C₂×#10597342	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#10597324	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄×Dic₃₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#10597333	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#10597333	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×(C₂²⋊D₁₉)⋊C₄	C₂	1	1	yes	maximal, characteristic
14	C₂×#10597318	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#10597323	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×#126	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
18	C₂³×Dic₁₉	C₂²	1	1	yes	characteristic
19	C₂²×C₄×D₁₉	C₂²	1	1	yes	characteristic
20	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
21	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
22	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
23	C₁₉×#126	C₂²	1	8	yes	complemented
24	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
30	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊Dic₁₉	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊Dic₁₉	C₂²	1	1	yes	characteristic
33	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	1	yes	characteristic
35	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	1	yes	characteristic
36	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	1	yes	characteristic
37	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	1	yes	characteristic
38	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
40	C₂×Dic₁₉⋊C₄	C₂²	1	1	yes	characteristic
41	C₂×Dic₁₉⋊C₄	C₂²	1	1	yes	characteristic
42	C₂×Dic₁₉⋊C₄	C₂²	1	1	yes	characteristic
43	C₂×Dic₁₉⋊C₄	C₂²	1	1	yes	characteristic
44	C₂×Dic₁₉⋊C₄	C₂²	1	1	yes	characteristic
45	C₂×Dic₁₉⋊C₄	C₂²	1	1	yes	characteristic
46	C₂×Dic₁₉⋊C₄	C₂²	1	1	yes	characteristic
47	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
48	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
49	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
50	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
51	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
52	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
53	#10597344	C₂²	1	8	yes	complemented
54	#10597344	C₂²	1	8	yes	complemented
55	#10597342	C₂²	1	8	yes	complemented
56	#10597334	C₂²	1	8	yes	complemented
57	#10597333	C₂²	1	8	yes	complemented
58	#10597333	C₂²	1	8	yes	complemented
59	#10597331	C₂²	1	8	yes	—
60	#10597331	C₂²	1	8	yes	—
61	(C₂²⋊D₁₉)⋊C₄	C₂²	1	8	yes	—
62	#10597325	C₂²	1	8	yes	complemented
63	#10597324	C₂²	1	8	yes	complemented
64	#10597323	C₂²	1	8	yes	complemented
65	#10597318	C₂²	1	8	yes	complemented
66	C₄×Dic₃₈	C₂²	1	8	yes	complemented
67	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
68	C₂³×D₁₉	C₂³	1	1	yes	characteristic
69	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
70	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
71	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
72	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
73	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
74	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
75	C₂×C₂²⋊D₁₉	—	2	4	no	—
76	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
77	C₂²×Dic₁₉	—	2	4	no	—
78	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
79	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
80	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
81	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
82	C₂²×Dic₁₉	C₂³	1	4	yes	—
83	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
84	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
85	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
86	C₂×C₄×D₁₉	—	2	4	no	—
87	C₂×C₄×D₁₉	C₂³	1	4	yes	—
88	C₂×Dic₃₈	—	2	4	no	—
89	C₂×Dic₃₈	—	2	4	no	—
90	C₂×Dic₃₈	—	2	4	no	—
91	C₂×Dic₃₈	C₂³	1	4	yes	—
92	C₂×Dic₃₈	C₂³	1	4	yes	—
93	C₂×Dic₃₈	C₂³	1	4	yes	—
94	C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
95	C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
96	C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
97	C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
98	C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
99	C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
100	C₄²×C₁₉	C₂³	1	4	yes	—
101	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
102	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
103	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
104	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
105	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
106	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
107	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
108	C₄⋊Dic₁₉	C₂³	1	4	yes	—
109	C₄⋊Dic₁₉	C₂³	1	4	yes	—
110	Dic₁₉⋊C₄	C₂³	1	4	yes	—
111	Dic₁₉⋊C₄	C₂³	1	4	yes	—
112	Dic₁₉⋊C₄	C₂³	1	4	yes	—
113	Dic₁₉⋊C₄	C₂³	1	4	yes	—
114	Dic₁₉⋊C₄	C₂³	1	4	yes	—
115	Dic₁₉⋊C₄	C₂³	1	4	yes	—
116	Dic₁₉⋊C₄	C₂³	1	4	yes	—
117	C₄×Dic₁₉	C₂³	1	4	yes	—
118	C₄×Dic₁₉	C₂³	1	4	yes	—
119	C₄×Dic₁₉	C₂³	1	4	yes	—
120	C₄×Dic₁₉	C₂³	1	4	yes	—
121	C₄×Dic₁₉	C₂³	1	4	yes	—
122	C₄×Dic₁₉	C₂³	1	4	yes	—
123	C₂³×C₁₉	—	2	2	no	—
124	C₂³×C₁₉	—	2	2	no	—
125	C₂³×C₁₉	—	2	2	no	—
126	C₂³×C₁₉	C₂⁴	1	2	yes	—
127	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
128	C₂²×D₁₉	—	2	2	no	—
129	C₂²×D₁₉	—	2	2	no	—
130	C₂²×D₁₉	—	2	2	no	—
131	C₂²×D₁₉	C₂⁴	1	2	yes	—
132	C₂×C₄×C₁₉	—	2	2	no	—
133	C₂×C₄×C₁₉	—	2	2	no	—
134	C₂×C₄×C₁₉	—	2	2	no	—
135	C₂×C₄×C₁₉	—	2	2	no	—
136	C₂×C₄×C₁₉	—	2	2	no	—
137	C₂×C₄×C₁₉	—	2	2	no	—
138	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
139	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
140	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
141	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
142	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
143	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
144	C₂²⋊D₁₉	—	2	8	no	—
145	C₂×Dic₁₉	—	2	2	no	—
146	C₂×Dic₁₉	—	2	2	no	—
147	C₂×Dic₁₉	—	2	2	no	—
148	C₂×Dic₁₉	—	2	2	no	—
149	C₂×Dic₁₉	—	2	2	no	—
150	C₂×Dic₁₉	—	2	8	no	—
151	C₂×Dic₁₉	#41	1	4	yes	—
152	C₂×Dic₁₉	#41	1	4	yes	—
153	C₂×Dic₁₉	C₂⁴	1	2	yes	—
154	C₂×Dic₁₉	C₂⁴	1	2	yes	—
155	C₂×Dic₁₉	C₂⁴	1	2	yes	—
156	C₂×Dic₁₉	C₂⁴	1	2	yes	—
157	C₂×Dic₁₉	C₂⁴	1	2	yes	—
158	C₂×Dic₁₉	C₂⁴	1	2	yes	—
159	C₂×Dic₁₉	C₂⁴	1	2	yes	—
160	C₄×D₁₉	—	2	8	no	—
161	Dic₃₈	—	2	8	no	—
162	Dic₃₈	—	2	8	no	—
163	Dic₃₈	—	2	8	no	—
164	C₂×#556	—	19	1	no	maximal, Sylow
165	C₂²×C₁₉	—	2	2	no	—
166	C₂²×C₁₉	—	2	2	no	—
167	C₂²×C₁₉	—	2	2	no	—
168	C₂²×C₁₉	—	4	4	no	—
169	C₂²×C₁₉	C₂×#41	1	2	yes	—
170	C₂²×C₁₉	C₂×#41	1	2	yes	—
171	C₂²×C₁₉	2₋¹⁺⁴	1	2	yes	—
172	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
173	C₂×D₁₉	—	2	2	no	—
174	C₂×D₁₉	—	2	2	no	—
175	C₂×D₁₉	—	2	2	no	—
176	C₂×D₁₉	—	4	4	no	—
177	C₄×C₁₉	—	2	2	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	Dic₁₉	—	2	2	no	—
184	Dic₁₉	—	2	2	no	—
185	Dic₁₉	—	2	2	no	—
186	Dic₁₉	—	2	2	no	—
187	Dic₁₉	—	2	2	no	—
188	Dic₁₉	C₂×#41	1	4	yes	—
189	Dic₁₉	C₂×#41	1	4	yes	—
190	#556	—	19	16	no	—
191	C₂×C₄⋊Q₈	—	19	1	no	—
192	C₂×#126	—	19	1	no	—
193	C₂×#126	—	19	1	no	—
194	C₂×#126	—	19	1	no	—
195	C₂×#126	D₁₉	1	1	yes	characteristic, complemented
196	C₂×#124	—	19	1	no	—
197	C₂×#124	—	19	1	no	—
198	C₂×C₂²⋊Q₈	—	19	1	no	—
199	C₂×C₂²⋊Q₈	—	19	1	no	—
200	C₂×C₄×Q₈	—	19	1	no	—
201	C₂×C₄×Q₈	—	19	1	no	—
202	C₂×C₄×Q₈	—	19	1	no	—
203	C₂×C₄×D₄	—	19	1	no	—
204	C₂×#117	—	19	1	no	—
205	C₂×#117	—	19	1	no	—
206	C₂×C₁₉	—	4	2	no	—
207	C₂×C₁₉	#556	1	4	yes	complemented
208	C₂×C₁₉	C₂²×#41	1	1	yes	characteristic
209	C₂×C₁₉	C₂²×#41	1	1	yes	characteristic
210	C₂×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
211	D₁₉	—	4	2	no	—
212	C₂²×Q₈	—	19	1	no	—
213	C₂²×Q₈	—	19	1	no	—
214	C₂²×Q₈	—	19	1	no	—
215	C₂²×D₄	—	19	1	no	—
216	C₂³×C₄	—	19	1	no	—
217	C₂³×C₄	—	19	1	no	—
218	C₄⋊Q₈	—	19	8	no	—
219	#126	—	19	8	no	—
220	#126	—	19	8	no	—
221	#126	—	19	8	no	—
222	#126	C₂×D₁₉	1	8	yes	complemented
223	#124	—	19	8	no	—
224	#124	—	19	8	no	—
225	C₂²⋊Q₈	—	19	8	no	—
226	C₂²⋊Q₈	—	19	8	no	—
227	C₄×Q₈	—	19	8	no	—
228	C₄×Q₈	—	19	8	no	—
229	C₄×Q₈	—	19	8	no	—
230	C₄×D₄	—	19	8	no	—
231	#117	—	19	8	no	—
232	#117	—	19	8	no	—
233	C₂×C₄⋊C₄	—	19	1	no	—
234	C₂×C₄⋊C₄	—	19	1	no	—
235	C₂×C₄⋊C₄	—	19	1	no	—
236	C₂×C₄⋊C₄	—	19	1	no	—
237	C₂×C₄⋊C₄	—	19	1	no	—
238	C₂×C₄⋊C₄	—	19	1	no	—
239	C₂×C₄⋊C₄	—	19	1	no	—
240	C₂×C₄⋊C₄	—	19	1	no	—
241	C₂×C₄⋊C₄	—	19	1	no	—
242	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
243	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
244	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
245	C₂×C₂²⋊C₄	—	19	1	no	—
246	C₂×C₂²⋊C₄	—	19	1	no	—
247	C₂×C₂²⋊C₄	—	19	1	no	—
248	C₂×C₂²⋊C₄	—	19	1	no	—
249	C₂×C₂²⋊C₄	—	19	1	no	—
250	C₂×C₂²⋊C₄	—	19	1	no	—
251	C₂×C₂²⋊C₄	—	19	1	no	—
252	C₂×C₂²⋊C₄	C₂×D₁₉	1	1	yes	characteristic
253	C₂×C₂²⋊C₄	C₂×D₁₉	1	1	yes	characteristic
254	C₂×C₂²⋊C₄	C₂×D₁₉	1	1	yes	characteristic
255	C₂×C₄²	—	19	1	no	—
256	C₂×C₄²	—	19	1	no	—
257	C₂×C₄²	—	19	1	no	—
258	C₂×C₄²	—	19	1	no	—
259	C₂×C₄²	—	19	1	no	—
260	C₂×C₄²	—	19	1	no	—
261	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
262	C₁₉	C₂×#556	1	1	yes	characteristic, complemented, Sylow
263	C₂⁴	—	19	1	no	—
264	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
265	C₂×Q₈	—	19	4	no	—
266	C₂×Q₈	—	19	4	no	—
267	C₂×Q₈	—	19	4	no	—
268	C₂×Q₈	—	38	4	no	—
269	C₂×Q₈	—	38	4	no	—
270	C₂×Q₈	—	38	4	no	—
271	C₂×D₄	—	19	4	no	—
272	C₂×D₄	—	38	4	no	—
273	C₂²×C₄	—	19	1	no	—
274	C₂²×C₄	—	19	1	no	—
275	C₂²×C₄	—	19	4	no	—
276	C₂²×C₄	—	19	1	no	—
277	C₂²×C₄	—	19	1	no	—
278	C₂²×C₄	—	19	1	no	—
279	C₂²×C₄	—	19	1	no	—
280	C₂²×C₄	—	19	1	no	—
281	C₂²×C₄	—	19	4	no	—
282	C₂²×C₄	—	38	4	no	—
283	C₂²×C₄	—	38	4	no	—
284	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
285	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
286	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
287	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
288	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
289	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
290	C₄⋊C₄	—	19	4	no	—
291	C₄⋊C₄	—	19	4	no	—
292	C₄⋊C₄	—	19	4	no	—
293	C₄⋊C₄	—	19	4	no	—
294	C₄⋊C₄	—	19	4	no	—
295	C₄⋊C₄	—	19	4	no	—
296	C₄⋊C₄	—	19	4	no	—
297	C₄⋊C₄	—	19	4	no	—
298	C₄⋊C₄	—	19	4	no	—
299	C₄⋊C₄	C₂²×D₁₉	1	4	yes	—
300	C₄⋊C₄	C₂²×D₁₉	1	4	yes	—
301	C₄⋊C₄	C₂²×D₁₉	1	4	yes	—
302	C₂²⋊C₄	—	19	4	no	—
303	C₂²⋊C₄	—	19	4	no	—
304	C₂²⋊C₄	—	19	4	no	—
305	C₂²⋊C₄	—	19	4	no	—
306	C₂²⋊C₄	—	19	4	no	—
307	C₂²⋊C₄	—	19	4	no	—
308	C₂²⋊C₄	—	19	4	no	—
309	C₂²⋊C₄	C₂²×D₁₉	1	4	yes	—
310	C₂²⋊C₄	C₂²×D₁₉	1	4	yes	—
311	C₂²⋊C₄	C₂²×D₁₉	1	4	yes	—
312	C₄²	—	19	4	no	—
313	C₄²	—	19	4	no	—
314	C₄²	—	19	4	no	—
315	C₄²	—	19	4	no	—
316	C₄²	—	19	4	no	—
317	C₄²	—	19	4	no	—
318	C₄²	C₂²×D₁₉	1	4	yes	—
319	C₂³	—	2	2	no	—
320	C₂³	—	2	2	no	—
321	C₂³	—	2	2	no	—
322	C₂³	—	19	2	no	—
323	C₂³	—	38	2	no	—
324	C₂³	—	38	2	no	—
325	C₂³	—	38	2	no	—
326	C₂³	C₂³×D₁₉	1	2	yes	—
327	C₂³	C₂³×D₁₉	1	1	yes	characteristic
328	Q₈	—	38	8	no	—
329	Q₈	—	38	8	no	—
330	Q₈	—	38	8	no	—
331	D₄	—	38	8	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	19	4	no	—
339	C₂×C₄	—	19	4	no	—
340	C₂×C₄	—	19	2	no	—
341	C₂×C₄	—	19	2	no	—
342	C₂×C₄	—	19	2	no	—
343	C₂×C₄	—	19	2	no	—
344	C₂×C₄	—	19	2	no	—
345	C₂×C₄	—	19	2	no	—
346	C₂×C₄	—	19	2	no	—
347	C₂×C₄	—	38	8	no	—
348	C₂×C₄	—	38	8	no	—
349	C₂×C₄	—	38	2	no	—
350	C₂×C₄	—	38	2	no	—
351	C₂×C₄	—	38	2	no	—
352	C₂×C₄	—	38	2	no	—
353	C₂×C₄	—	38	2	no	—
354	C₂×C₄	C₂³×D₁₉	1	2	yes	—
355	C₂×C₄	C₂³×D₁₉	1	2	yes	—
356	C₂×C₄	C₂³×D₁₉	1	2	yes	—
357	C₂×C₄	C₂³×D₁₉	1	2	yes	—
358	C₂×C₄	C₂³×D₁₉	1	2	yes	—
359	C₂×C₄	C₂³×D₁₉	1	2	yes	—
360	C₂²	—	2	2	no	—
361	C₂²	—	2	2	no	—
362	C₂²	—	2	2	no	—
363	C₂²	—	4	4	no	—
364	C₂²	—	38	2	no	—
365	C₂²	—	38	2	no	—
366	C₂²	—	38	2	no	—
367	C₂²	—	76	4	no	—
368	C₂²	#41×D₁₉	1	2	yes	—
369	C₂²	#41×D₁₉	1	2	yes	—
370	C₂²	#10597436	1	2	yes	—
371	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
372	C₄	—	2	2	no	—
373	C₄	—	2	2	no	—
374	C₄	—	2	2	no	—
375	C₄	—	2	2	no	—
376	C₄	—	2	2	no	—
377	C₄	—	2	2	no	—
378	C₄	—	19	4	no	—
379	C₄	—	19	4	no	—
380	C₄	—	38	2	no	—
381	C₄	—	38	2	no	—
382	C₄	—	38	2	no	—
383	C₄	—	38	2	no	—
384	C₄	—	38	2	no	—
385	C₂	—	4	2	no	—
386	C₂	—	76	2	no	—
387	C₂	#11927261	1	4	yes	direct product factor
388	C₂	C₂×#41×D₁₉	1	1	yes	characteristic
389	C₂	C₂×#41×D₁₉	1	1	yes	characteristic
390	C₂	C₂×#10597436	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₁₉
commutator, cosocle	C₂²×C₁₉	C₂⁵
Frattini	C₂²	C₂⁴×D₁₉
Fitting	C₂×C₁₉×#126	C₂
socle	C₂³×C₁₉	C₂⁴
prime radical	C₂²×C₂²⋊D₁₉	C₂²
hypercenter	C₂×#126	D₁₉
hypocenter	C₁₉	C₂×#556
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×#126

Complements

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

N	H ≅ G/N	type
1. #11927261	C₂	direct (N × H)
2. C₂×#10597334	C₂	semidirect
3. C₂×#10597344	C₂	semidirect
4. C₂×#10597344	C₂	semidirect
5. C₂×#10597325	C₂	semidirect
8. C₂×#10597342	C₂	semidirect
9. C₂×#10597324	C₂	semidirect
10. C₂×C₄×Dic₃₈	C₂	semidirect
11. C₂×#10597333	C₂	semidirect
12. C₂×#10597333	C₂	semidirect
14. C₂×#10597318	C₂	semidirect
15. C₂×#10597323	C₂	semidirect
16. C₂×C₁₉×#126	C₂	semidirect
23. C₁₉×#126	C₂²	semidirect
53. #10597344	C₂²	semidirect
54. #10597344	C₂²	semidirect
55. #10597342	C₂²	semidirect
56. #10597334	C₂²	semidirect
57. #10597333	C₂²	semidirect
58. #10597333	C₂²	semidirect
62. #10597325	C₂²	semidirect
63. #10597324	C₂²	semidirect
64. #10597323	C₂²	semidirect
65. #10597318	C₂²	semidirect
66. C₄×Dic₃₈	C₂²	semidirect
195. C₂×#126	D₁₉	semidirect
207. C₂×C₁₉	#556	semidirect
222. #126	C₂×D₁₉	semidirect
262. C₁₉	C₂×#556	semidirect
387. C₂	#11927261	direct (N × H)

Maximal subgroups

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

subgroup	index
#11927261	2
C₂×#10597334	2
C₂×#10597344	2
C₂×#10597325	2
C₂×#10597331	2
C₂×#10597342	2
C₂×#10597324	2
C₂×C₄×Dic₃₈	2
C₂×#10597333	2
C₂×(C₂²⋊D₁₉)⋊C₄	2
C₂×#10597318	2
C₂×#10597323	2
C₂×C₁₉×#126	2
C₂×#556	19

Subgroups — C2×#11927261 #14577178

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11927261 #14577178