Subgroups — C₁₃₉×#18186 #48012782

Order 35584.

1198 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3497×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#3109×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	#2398×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#1616×C₁₃₉	C₂	1	4	yes	maximal, complemented
5	#1598×C₁₃₉	C₂	1	4	yes	maximal, complemented
6	#1505×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#1467×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×2₋¹⁺⁴×C₁₃₉	—	2	1	no	—
9	#550×C₁₃₉	—	2	2	no	—
10	D₄×Q₈×C₁₃₉	—	2	2	no	—
11	#548×C₁₃₉	—	2	4	no	—
12	#537×C₁₃₉	—	2	1	no	—
13	#537×C₁₃₉	C₂²	1	4	yes	—
14	#532×C₁₃₉	—	2	2	no	—
15	#532×C₁₃₉	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
18	#481×C₁₃₉	C₂²	1	4	yes	—
19	#476×C₁₃₉	—	2	2	no	—
20	#459×C₁₃₉	—	2	2	no	—
21	#447×C₁₃₉	C₂²	1	4	yes	—
22	#442×C₁₃₉	—	2	4	no	—
23	#432×C₁₃₉	C₂²	1	2	yes	—
24	#400×C₁₃₉	C₂²	1	2	yes	—
25	#397×C₁₃₉	—	2	1	no	—
26	#394×C₁₃₉	C₂²	1	2	yes	—
27	#393×C₁₃₉	—	2	1	no	—
28	C₄×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
29	#376×C₁₃₉	C₂²	1	1	yes	characteristic
30	#327×C₁₃₉	C₂²	1	8	yes	—
31	#324×C₁₃₉	C₂²	1	4	yes	—
32	2₋¹⁺⁴×C₁₃₉	—	4	8	no	—
33	C₂×#41×C₁₃₉	—	2	4	no	—
34	C₂×#41×C₁₃₉	—	2	4	no	—
35	C₂×#41×C₁₃₉	—	2	2	no	—
36	C₂²×Q₈×C₁₃₉	—	2	4	no	—
37	C₂²×Q₈×C₁₃₉	D₄	1	1	yes	characteristic
38	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
39	C₂³×C₄×C₁₃₉	—	2	1	no	—
40	C₂×D₈×C₁₃₉	—	2	4	no	—
41	C₄⋊Q₈×C₁₃₉	—	2	2	no	—
42	C₄⋊Q₈×C₁₃₉	D₄	1	2	yes	—
43	#127×C₁₃₉	—	2	2	no	—
44	#127×C₁₃₉	D₄	1	2	yes	—
45	#124×C₁₃₉	—	2	4	no	—
46	#124×C₁₃₉	—	2	2	no	—
47	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
48	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
49	#121×C₁₃₉	—	2	4	no	—
50	#121×C₁₃₉	—	2	8	no	—
51	#121×C₁₃₉	—	2	2	no	—
52	#121×C₁₃₉	—	2	4	no	—
53	#121×C₁₃₉	C₂³	1	4	yes	—
54	C₄×Q₈×C₁₃₉	—	2	2	no	—
55	C₄×Q₈×C₁₃₉	—	2	2	no	—
56	C₄×D₄×C₁₃₉	—	2	4	no	—
57	C₄×D₄×C₁₃₉	—	2	4	no	—
58	C₄×D₄×C₁₃₉	—	2	2	no	—
59	C₄×D₄×C₁₃₉	—	2	2	no	—
60	C₄×D₄×C₁₃₉	—	2	2	no	—
61	C₄×D₄×C₁₃₉	D₄	1	4	yes	—
62	C₂×C₄⋊C₄×C₁₃₉	D₄	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
65	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
66	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
68	C₂×C₄²×C₁₃₉	—	2	1	no	—
69	C₂×C₄²×C₁₃₉	D₄	1	2	yes	—
70	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
71	#106×C₁₃₉	—	2	4	no	—
72	C₄⋊C₈×C₁₃₉	—	2	2	no	—
73	#102×C₁₃₉	—	2	4	no	—
74	#102×C₁₃₉	—	2	4	no	—
75	C₂²⋊C₈×C₁₃₉	C₂³	1	4	yes	—
76	#97×C₁₃₉	—	2	2	no	—
77	#95×C₁₃₉	—	2	2	no	—
78	#95×C₁₃₉	—	2	1	no	—
79	#95×C₁₃₉	—	2	2	no	—
80	#95×C₁₃₉	C₂³	1	2	yes	—
81	C₂⁴×C₁₃₉	—	2	1	no	—
82	#41×C₁₃₉	—	4	8	no	—
83	#41×C₁₃₉	—	4	8	no	—
84	#41×C₁₃₉	—	4	16	no	—
85	#41×C₁₃₉	—	4	8	no	—
86	C₂×Q₈×C₁₃₉	—	2	4	no	—
87	C₂×Q₈×C₁₃₉	—	2	2	no	—
88	C₂×Q₈×C₁₃₉	—	2	2	no	—
89	C₂×Q₈×C₁₃₉	—	2	4	no	—
90	C₂×Q₈×C₁₃₉	—	4	16	no	—
91	C₂×D₄×C₁₃₉	—	2	4	no	—
92	C₂×D₄×C₁₃₉	—	2	4	no	—
93	C₂×D₄×C₁₃₉	—	2	4	no	—
94	C₂×D₄×C₁₃₉	—	2	2	no	—
95	C₂×D₄×C₁₃₉	—	2	2	no	—
96	C₂×D₄×C₁₃₉	—	2	2	no	—
97	C₂×D₄×C₁₃₉	—	4	2	no	—
98	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
99	C₂²×C₄×C₁₃₉	—	2	8	no	—
100	C₂²×C₄×C₁₃₉	—	2	4	no	—
101	C₂²×C₄×C₁₃₉	—	2	1	no	—
102	C₂²×C₄×C₁₃₉	—	2	2	no	—
103	C₂²×C₄×C₁₃₉	—	4	4	no	—
104	C₂²×C₄×C₁₃₉	—	4	1	no	—
105	C₂²×C₄×C₁₃₉	—	4	1	no	—
106	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
111	D₈×C₁₃₉	—	4	8	no	—
112	C₂×C₈×C₁₃₉	—	2	4	no	—
113	C₄⋊C₄×C₁₃₉	—	2	4	no	—
114	C₄⋊C₄×C₁₃₉	—	2	2	no	—
115	C₄⋊C₄×C₁₃₉	—	2	2	no	—
116	C₄⋊C₄×C₁₃₉	—	2	4	no	—
117	C₄⋊C₄×C₁₃₉	—	2	2	no	—
118	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
119	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
120	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
121	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
122	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
123	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
124	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
125	C₄²×C₁₃₉	—	2	2	no	—
126	C₄²×C₁₃₉	—	2	2	no	—
127	C₄²×C₁₃₉	—	4	2	no	—
128	C₄²×C₁₃₉	C₂×D₄	1	2	yes	—
129	C₄²×C₁₃₉	C₂×D₄	1	2	yes	—
130	C₂³×C₁₃₉	—	2	2	no	—
131	C₂³×C₁₃₉	—	2	4	no	—
132	C₂³×C₁₃₉	—	4	2	no	—
133	C₂³×C₁₃₉	—	4	1	no	—
134	C₂³×C₁₃₉	—	4	1	no	—
135	C₂³×C₁₃₉	—	4	2	no	—
136	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
137	Q₈×C₁₃₉	—	2	8	no	—
138	Q₈×C₁₃₉	—	4	4	no	—
139	Q₈×C₁₃₉	—	4	8	no	—
140	D₄×C₁₃₉	—	2	4	no	—
141	D₄×C₁₃₉	—	4	4	no	—
142	D₄×C₁₃₉	—	4	2	no	—
143	D₄×C₁₃₉	—	4	4	no	—
144	D₄×C₁₃₉	—	4	8	no	—
145	D₄×C₁₃₉	—	4	8	no	—
146	D₄×C₁₃₉	—	4	4	no	—
147	D₄×C₁₃₉	—	8	4	no	—
148	C₂×C₄×C₁₃₉	—	2	2	no	—
149	C₂×C₄×C₁₃₉	—	2	2	no	—
150	C₂×C₄×C₁₃₉	—	2	2	no	—
151	C₂×C₄×C₁₃₉	—	2	2	no	—
152	C₂×C₄×C₁₃₉	—	2	2	no	—
153	C₂×C₄×C₁₃₉	—	2	4	no	—
154	C₂×C₄×C₁₃₉	—	4	1	no	—
155	C₂×C₄×C₁₃₉	—	4	8	no	—
156	C₂×C₄×C₁₃₉	—	4	16	no	—
157	C₂×C₄×C₁₃₉	—	4	2	no	—
158	C₂×C₄×C₁₃₉	—	4	2	no	—
159	C₂×C₄×C₁₃₉	—	4	2	no	—
160	C₂×C₄×C₁₃₉	—	4	2	no	—
161	C₂×C₄×C₁₃₉	—	4	1	no	—
162	C₂×C₄×C₁₃₉	—	4	2	no	—
163	C₂×C₄×C₁₃₉	—	8	2	no	—
164	C₂×C₄×C₁₃₉	—	8	2	no	—
165	C₂×C₄×C₁₃₉	#120	1	1	yes	characteristic
166	C₂×C₄×C₁₃₉	#120	1	2	yes	—
167	C₂×C₄×C₁₃₉	#120	1	1	yes	characteristic
168	C₂×C₄×C₁₃₉	AGL(1,ℤ/8)	1	4	yes	—
169	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
170	C₈×C₁₃₉	—	4	4	no	—
171	C₂²×C₁₃₉	—	2	1	no	—
172	C₂²×C₁₃₉	—	2	1	no	—
173	C₂²×C₁₃₉	—	4	4	no	—
174	C₂²×C₁₃₉	—	4	4	no	—
175	C₂²×C₁₃₉	—	4	4	no	—
176	C₂²×C₁₃₉	—	4	2	no	—
177	C₂²×C₁₃₉	—	4	4	no	—
178	C₂²×C₁₃₉	—	8	2	no	—
179	C₂²×C₁₃₉	—	8	1	no	—
180	C₂²×C₁₃₉	—	8	1	no	—
181	C₂²×C₁₃₉	C₂×#120	1	1	yes	characteristic
182	C₂²×C₁₃₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
183	C₄×C₁₃₉	—	2	2	no	—
184	C₄×C₁₃₉	—	2	4	no	—
185	C₄×C₁₃₉	—	2	1	no	—
186	C₄×C₁₃₉	—	2	2	no	—
187	C₄×C₁₃₉	—	4	4	no	—
188	C₄×C₁₃₉	—	4	2	no	—
189	C₄×C₁₃₉	—	8	2	no	—
190	C₄×C₁₃₉	—	8	1	no	—
191	C₄×C₁₃₉	#454	1	2	yes	—
192	C₂×C₁₃₉	—	2	2	no	—
193	C₂×C₁₃₉	—	8	4	no	—
194	C₂×C₁₃₉	—	8	2	no	—
195	C₂×C₁₃₉	#3003	1	1	yes	characteristic
196	C₂×C₁₃₉	C₂×#454	1	1	yes	characteristic
197	C₂×C₁₃₉	#3025	1	1	yes	characteristic
198	#18186	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
199	C₁₃₉	#18186	1	1	yes	characteristic, direct product factor, Sylow
200	#3497	C₂×C₁₃₉	1	1	yes	characteristic, complemented
201	#3109	C₂×C₁₃₉	1	2	yes	complemented
202	#2398	C₂×C₁₃₉	1	1	yes	characteristic, complemented
203	#1616	C₂×C₁₃₉	1	4	yes	complemented
204	#1598	C₂×C₁₃₉	1	4	yes	complemented
205	#1505	C₂×C₁₃₉	1	2	yes	complemented
206	#1467	C₂×C₁₃₉	1	1	yes	characteristic, complemented
207	C₂×2₋¹⁺⁴	—	2	1	no	—
208	#550	—	2	2	no	—
209	D₄×Q₈	—	2	2	no	—
210	#548	—	2	4	no	—
211	#537	—	2	1	no	—
212	#537	C₂²×C₁₃₉	1	4	yes	—
213	#532	—	2	2	no	—
214	#532	C₂²×C₁₃₉	1	2	yes	—
215	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
216	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
217	#481	C₂²×C₁₃₉	1	4	yes	—
218	#476	—	2	2	no	—
219	#459	—	2	2	no	—
220	#447	C₂²×C₁₃₉	1	4	yes	—
221	#442	—	2	4	no	—
222	#432	C₂²×C₁₃₉	1	2	yes	—
223	#400	C₂²×C₁₃₉	1	2	yes	—
224	#397	—	2	1	no	—
225	#394	C₂²×C₁₃₉	1	2	yes	—
226	#393	—	2	1	no	—
227	C₄×C₂²⋊C₄	—	2	2	no	—
228	#376	C₂²×C₁₃₉	1	1	yes	characteristic
229	#327	C₂²×C₁₃₉	1	8	yes	—
230	#324	C₂²×C₁₃₉	1	4	yes	—
231	2₋¹⁺⁴	—	4	8	no	—
232	C₂×#41	—	2	4	no	—
233	C₂×#41	—	2	4	no	—
234	C₂×#41	—	2	2	no	—
235	C₂²×Q₈	—	2	4	no	—
236	C₂²×Q₈	D₄×C₁₃₉	1	1	yes	characteristic
237	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
238	C₂³×C₄	—	2	1	no	—
239	C₂×D₈	—	2	4	no	—
240	C₄⋊Q₈	—	2	2	no	—
241	C₄⋊Q₈	D₄×C₁₃₉	1	2	yes	—
242	#127	—	2	2	no	—
243	#127	D₄×C₁₃₉	1	2	yes	—
244	#124	—	2	4	no	—
245	#124	—	2	2	no	—
246	C₂²⋊Q₈	—	2	4	no	—
247	C₂²⋊Q₈	—	2	8	no	—
248	#121	—	2	4	no	—
249	#121	—	2	8	no	—
250	#121	—	2	2	no	—
251	#121	—	2	4	no	—
252	#121	C₂³×C₁₃₉	1	4	yes	—
253	C₄×Q₈	—	2	2	no	—
254	C₄×Q₈	—	2	2	no	—
255	C₄×D₄	—	2	4	no	—
256	C₄×D₄	—	2	4	no	—
257	C₄×D₄	—	2	2	no	—
258	C₄×D₄	—	2	2	no	—
259	C₄×D₄	—	2	2	no	—
260	C₄×D₄	D₄×C₁₃₉	1	4	yes	—
261	C₂×C₄⋊C₄	D₄×C₁₃₉	1	1	yes	characteristic
262	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
263	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
264	C₂×C₂²⋊C₄	—	2	1	no	—
265	C₂×C₂²⋊C₄	—	2	2	no	—
266	C₂×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₄²	—	2	1	no	—
268	C₂×C₄²	D₄×C₁₃₉	1	2	yes	—
269	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
270	#106	—	2	4	no	—
271	C₄⋊C₈	—	2	2	no	—
272	#102	—	2	4	no	—
273	#102	—	2	4	no	—
274	C₂²⋊C₈	C₂³×C₁₃₉	1	4	yes	—
275	#97	—	2	2	no	—
276	#95	—	2	1	no	—
277	#95	—	2	2	no	—
278	#95	—	2	2	no	—
279	#95	C₂³×C₁₃₉	1	2	yes	—
280	C₂⁴	—	2	1	no	—
281	#41	—	4	8	no	—
282	#41	—	4	8	no	—
283	#41	—	4	16	no	—
284	#41	—	4	8	no	—
285	C₂×Q₈	—	2	4	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	2	4	no	—
289	C₂×Q₈	—	4	16	no	—
290	C₂×D₄	—	2	4	no	—
291	C₂×D₄	—	2	4	no	—
292	C₂×D₄	—	2	4	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	4	2	no	—
297	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
298	C₂²×C₄	—	2	8	no	—
299	C₂²×C₄	—	2	4	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	4	4	no	—
303	C₂²×C₄	—	4	1	no	—
304	C₂²×C₄	—	4	1	no	—
305	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
306	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
307	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
308	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
309	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
310	D₈	—	4	8	no	—
311	C₂×C₈	—	2	4	no	—
312	C₄⋊C₄	—	2	4	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	4	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
318	C₂²⋊C₄	—	2	8	no	—
319	C₂²⋊C₄	—	2	4	no	—
320	C₂²⋊C₄	—	2	4	no	—
321	C₂²⋊C₄	—	4	4	no	—
322	C₂²⋊C₄	—	4	2	no	—
323	C₂²⋊C₄	—	4	4	no	—
324	C₄²	—	2	2	no	—
325	C₄²	—	2	2	no	—
326	C₄²	—	4	2	no	—
327	C₄²	C₂×D₄×C₁₃₉	1	2	yes	—
328	C₄²	C₂×D₄×C₁₃₉	1	2	yes	—
329	C₂³	—	2	2	no	—
330	C₂³	—	2	4	no	—
331	C₂³	—	4	2	no	—
332	C₂³	—	4	1	no	—
333	C₂³	—	4	1	no	—
334	C₂³	—	4	2	no	—
335	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
336	Q₈	—	2	8	no	—
337	Q₈	—	4	4	no	—
338	Q₈	—	4	8	no	—
339	D₄	—	2	4	no	—
340	D₄	—	4	4	no	—
341	D₄	—	4	2	no	—
342	D₄	—	4	4	no	—
343	D₄	—	4	8	no	—
344	D₄	—	4	8	no	—
345	D₄	—	4	4	no	—
346	D₄	—	8	4	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	8	no	—
355	C₂×C₄	—	4	16	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	8	2	no	—
363	C₂×C₄	—	8	2	no	—
364	C₂×C₄	#120×C₁₃₉	1	1	yes	characteristic
365	C₂×C₄	#120×C₁₃₉	1	2	yes	—
366	C₂×C₄	#120×C₁₃₉	1	1	yes	characteristic
367	C₂×C₄	AGL(1,ℤ/8)×C₁₃₉	1	4	yes	—
368	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
369	C₈	—	4	4	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	4	4	no	—
373	C₂²	—	4	2	no	—
374	C₂²	—	4	4	no	—
375	C₂²	—	4	4	no	—
376	C₂²	—	4	4	no	—
377	C₂²	—	8	2	no	—
378	C₂²	—	8	1	no	—
379	C₂²	—	8	1	no	—
380	C₂²	C₂×#120×C₁₃₉	1	1	yes	characteristic
381	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₉	1	2	yes	—
382	C₄	—	2	2	no	—
383	C₄	—	2	2	no	—
384	C₄	—	2	4	no	—
385	C₄	—	2	1	no	—
386	C₄	—	4	2	no	—
387	C₄	—	4	4	no	—
388	C₄	—	8	2	no	—
389	C₄	—	8	1	no	—
390	C₄	#454×C₁₃₉	1	2	yes	—
391	C₂	—	2	2	no	—
392	C₂	—	8	2	no	—
393	C₂	—	8	4	no	—
394	C₂	#3003×C₁₃₉	1	1	yes	characteristic
395	C₂	C₂×#454×C₁₃₉	1	1	yes	characteristic
396	C₂	#3025×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₉ ◁ C₂×C₄²×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. #3497×C₁₃₉	C₂	semidirect
2. #3109×C₁₃₉	C₂	semidirect
3. #2398×C₁₃₉	C₂	semidirect
4. #1616×C₁₃₉	C₂	semidirect
5. #1598×C₁₃₉	C₂	semidirect
6. #1505×C₁₃₉	C₂	semidirect
7. #1467×C₁₃₉	C₂	semidirect
198. #18186	C₁₃₉	direct (N × H)
199. C₁₃₉	#18186	direct (N × H)
200. #3497	C₂×C₁₃₉	semidirect
201. #3109	C₂×C₁₃₉	semidirect
202. #2398	C₂×C₁₃₉	semidirect
203. #1616	C₂×C₁₃₉	semidirect
204. #1598	C₂×C₁₃₉	semidirect
205. #1505	C₂×C₁₃₉	semidirect
206. #1467	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#3497×C₁₃₉	2
#3109×C₁₃₉	2
#2398×C₁₃₉	2
#1616×C₁₃₉	2
#1598×C₁₃₉	2
#1505×C₁₃₉	2
#1467×C₁₃₉	2
#18186	139

Subgroups — C139×#18186 #48012782

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#18186 #48012782