Subgroups — C₁₃₉×#17673 #48012269

Order 35584.

972 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3444×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	#2920×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	#1537×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#1536×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#1529×C₁₃₉	C₂	1	8	yes	maximal, complemented
6	#533×C₁₃₉	C₄	1	2	yes	—
7	#533×C₁₃₉	C₂²	1	1	yes	characteristic
8	#532×C₁₃₉	C₄	1	2	yes	—
9	#532×C₁₃₉	C₂²	1	1	yes	characteristic
10	#529×C₁₃₉	—	2	2	no	—
11	#529×C₁₃₉	—	2	2	no	—
12	#529×C₁₃₉	C₂²	1	4	yes	—
13	#525×C₁₃₉	—	2	2	no	—
14	#525×C₁₃₉	C₄	1	2	yes	—
15	C₄×#41×C₁₃₉	—	2	2	no	—
16	C₄×#41×C₁₃₉	C₄	1	2	yes	—
17	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
18	#432×C₁₃₉	C₂²	1	4	yes	—
19	#432×C₁₃₉	C₂²	1	4	yes	—
20	#431×C₁₃₉	—	2	2	no	—
21	#431×C₁₃₉	—	2	2	no	—
22	#423×C₁₃₉	—	2	2	no	—
23	#407×C₁₃₉	—	2	2	no	—
24	C₄×M₁₆×C₁₃₉	C₂²	1	4	yes	—
25	#330×C₁₃₉	C₂²	1	8	yes	complemented
26	#329×C₁₃₉	C₂²	1	8	yes	complemented
27	C₂×#41×C₁₃₉	—	2	2	no	—
28	C₂×#41×C₁₃₉	C₂×C₄	1	2	yes	—
29	C₂³×C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₃₉	D₄	1	2	yes	—
31	C₂×M₁₆×C₁₃₉	—	2	4	no	—
32	C₄⋊Q₈×C₁₃₉	C₂×C₄	1	1	yes	characteristic
33	C₄⋊Q₈×C₁₃₉	C₂×C₄	1	2	yes	—
34	#127×C₁₃₉	C₂×C₄	1	1	yes	characteristic
35	#126×C₁₃₉	—	2	4	no	—
36	#125×C₁₃₉	—	2	2	no	—
37	#125×C₁₃₉	C₂³	1	2	yes	—
38	#124×C₁₃₉	—	2	2	no	—
39	#124×C₁₃₉	C₂³	1	2	yes	—
40	#123×C₁₃₉	—	2	2	no	—
41	#123×C₁₃₉	—	2	4	no	—
42	C₂²⋊Q₈×C₁₃₉	—	2	2	no	—
43	C₂²⋊Q₈×C₁₃₉	—	2	2	no	—
44	C₂²⋊Q₈×C₁₃₉	C₂×C₄	1	4	yes	—
45	#121×C₁₃₉	—	2	2	no	—
46	#121×C₁₃₉	—	2	2	no	—
47	#121×C₁₃₉	C₂×C₄	1	4	yes	—
48	#120×C₁₃₉	—	2	2	no	—
49	C₄×Q₈×C₁₃₉	—	2	2	no	—
50	C₄×Q₈×C₁₃₉	—	2	2	no	—
51	C₄×Q₈×C₁₃₉	C₂×C₄	1	4	yes	—
52	C₄×D₄×C₁₃₉	—	2	4	no	—
53	C₄×D₄×C₁₃₉	—	2	4	no	—
54	C₄×D₄×C₁₃₉	—	2	4	no	—
55	C₄×D₄×C₁₃₉	—	2	2	no	—
56	C₄×D₄×C₁₃₉	—	2	2	no	—
57	C₄×D₄×C₁₃₉	C₂×C₄	1	4	yes	—
58	#117×C₁₃₉	—	2	2	no	—
59	#117×C₁₃₉	—	2	2	no	—
60	#117×C₁₃₉	—	2	4	no	—
61	#117×C₁₃₉	C₂×C₄	1	2	yes	—
62	C₂×C₄²×C₁₃₉	—	2	2	no	—
63	C₂×C₄²×C₁₃₉	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₁₃₉	C₂×C₄	1	2	yes	—
65	C₂×C₄²×C₁₃₉	D₄	1	2	yes	—
66	C₂×C₄²×C₁₃₉	D₄	1	2	yes	—
67	C₂×C₄²×C₁₃₉	D₄	1	2	yes	—
68	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
69	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
70	C₄⋊C₈×C₁₃₉	—	2	4	no	—
71	C₄⋊C₈×C₁₃₉	—	2	4	no	—
72	C₂²⋊C₈×C₁₃₉	—	2	4	no	—
73	C₂²⋊C₈×C₁₃₉	—	2	4	no	—
74	#97×C₁₃₉	C₂³	1	8	yes	—
75	C₄×C₈×C₁₃₉	—	2	4	no	—
76	C₂⁴×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
77	#41×C₁₃₉	—	4	8	no	—
78	#41×C₁₃₉	—	4	4	no	—
79	C₂×Q₈×C₁₃₉	—	2	2	no	—
80	C₂×Q₈×C₁₃₉	C₂²×C₄	1	2	yes	—
81	C₂×D₄×C₁₃₉	—	2	2	no	—
82	C₂×D₄×C₁₃₉	—	2	4	no	—
83	C₂×D₄×C₁₃₉	—	2	2	no	—
84	C₂×D₄×C₁₃₉	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₁₃₉	—	2	2	no	—
86	C₂²×C₄×C₁₃₉	—	2	4	no	—
87	C₂²×C₄×C₁₃₉	—	4	2	no	—
88	C₂²×C₄×C₁₃₉	—	4	4	no	—
89	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	2	yes	—
90	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	2	yes	—
91	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	2	yes	—
92	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	2	yes	—
93	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
99	M₁₆×C₁₃₉	—	4	8	no	—
100	C₂×C₈×C₁₃₉	—	2	8	no	—
101	C₄⋊C₄×C₁₃₉	—	2	2	no	—
102	C₄⋊C₄×C₁₃₉	—	2	2	no	—
103	C₄⋊C₄×C₁₃₉	—	2	4	no	—
104	C₄⋊C₄×C₁₃₉	—	2	4	no	—
105	C₄⋊C₄×C₁₃₉	—	2	4	no	—
106	C₄⋊C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
107	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
108	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
109	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
110	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
111	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
112	C₄²×C₁₃₉	—	2	4	no	—
113	C₄²×C₁₃₉	—	2	2	no	—
114	C₄²×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
115	C₄²×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
116	C₄²×C₁₃₉	C₂²⋊C₄	1	2	yes	—
117	C₄²×C₁₃₉	C₂²⋊C₄	1	2	yes	—
118	C₄²×C₁₃₉	C₂²×C₄	1	2	yes	—
119	C₄²×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
120	C₄²×C₁₃₉	C₂×D₄	1	2	yes	—
121	C₄²×C₁₃₉	C₂×D₄	1	2	yes	—
122	C₄²×C₁₃₉	C₂×D₄	1	2	yes	—
123	C₄²×C₁₃₉	C₂⁴	1	1	yes	characteristic
124	C₂³×C₁₃₉	—	2	2	no	—
125	C₂³×C₁₃₉	—	4	1	no	—
126	C₂³×C₁₃₉	—	4	2	no	—
127	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
128	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
129	Q₈×C₁₃₉	—	4	2	no	—
130	Q₈×C₁₃₉	—	4	4	no	—
131	D₄×C₁₃₉	—	4	2	no	—
132	D₄×C₁₃₉	—	4	4	no	—
133	D₄×C₁₃₉	—	4	4	no	—
134	D₄×C₁₃₉	—	4	8	no	—
135	C₂×C₄×C₁₃₉	—	2	4	no	—
136	C₂×C₄×C₁₃₉	—	2	2	no	—
137	C₂×C₄×C₁₃₉	—	2	4	no	—
138	C₂×C₄×C₁₃₉	—	2	4	no	—
139	C₂×C₄×C₁₃₉	—	2	4	no	—
140	C₂×C₄×C₁₃₉	—	2	2	no	—
141	C₂×C₄×C₁₃₉	—	2	4	no	—
142	C₂×C₄×C₁₃₉	—	4	1	no	—
143	C₂×C₄×C₁₃₉	—	4	2	no	—
144	C₂×C₄×C₁₃₉	—	4	2	no	—
145	C₂×C₄×C₁₃₉	—	4	2	no	—
146	C₂×C₄×C₁₃₉	—	4	2	no	—
147	C₂×C₄×C₁₃₉	—	4	4	no	—
148	C₂×C₄×C₁₃₉	—	4	8	no	—
149	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
150	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
151	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
152	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
154	C₂×C₄×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
155	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
156	C₈×C₁₃₉	—	4	8	no	—
157	C₂²×C₁₃₉	—	2	1	no	—
158	C₂²×C₁₃₉	—	2	2	no	—
159	C₂²×C₁₃₉	—	2	2	no	—
160	C₂²×C₁₃₉	—	2	2	no	—
161	C₂²×C₁₃₉	—	2	2	no	—
162	C₂²×C₁₃₉	—	4	4	no	—
163	C₂²×C₁₃₉	—	4	2	no	—
164	C₂²×C₁₃₉	—	4	4	no	—
165	C₂²×C₁₃₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
166	C₄×C₁₃₉	—	2	2	no	—
167	C₄×C₁₃₉	—	2	1	no	—
168	C₄×C₁₃₉	—	2	2	no	—
169	C₄×C₁₃₉	—	2	2	no	—
170	C₄×C₁₃₉	—	2	2	no	—
171	C₄×C₁₃₉	—	4	2	no	—
172	C₄×C₁₃₉	—	4	4	no	—
173	C₄×C₁₃₉	#413	1	2	yes	—
174	C₄×C₁₃₉	#421	1	4	yes	—
175	C₂×C₁₃₉	—	4	1	no	—
176	C₂×C₁₃₉	—	4	2	no	—
177	C₂×C₁₃₉	—	8	2	no	—
178	C₂×C₁₃₉	C₂×#413	1	1	yes	characteristic
179	C₂×C₁₃₉	C₂×#421	1	2	yes	—
180	#17673	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
181	C₁₃₉	#17673	1	1	yes	characteristic, direct product factor, Sylow
182	#3444	C₂×C₁₃₉	1	1	yes	characteristic
183	#2920	C₂×C₁₃₉	1	2	yes	complemented
184	#1537	C₂×C₁₃₉	1	2	yes	complemented
185	#1536	C₂×C₁₃₉	1	2	yes	complemented
186	#1529	C₂×C₁₃₉	1	8	yes	complemented
187	#533	C₄×C₁₃₉	1	2	yes	—
188	#533	C₂²×C₁₃₉	1	1	yes	characteristic
189	#532	C₄×C₁₃₉	1	2	yes	—
190	#532	C₂²×C₁₃₉	1	1	yes	characteristic
191	#529	—	2	2	no	—
192	#529	—	2	2	no	—
193	#529	C₂²×C₁₃₉	1	4	yes	—
194	#525	—	2	2	no	—
195	#525	C₄×C₁₃₉	1	2	yes	—
196	C₄×#41	—	2	2	no	—
197	C₄×#41	C₄×C₁₃₉	1	2	yes	—
198	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
199	#432	C₂²×C₁₃₉	1	4	yes	—
200	#432	C₂²×C₁₃₉	1	4	yes	—
201	#431	—	2	2	no	—
202	#431	—	2	2	no	—
203	#423	—	2	2	no	—
204	#407	—	2	2	no	—
205	C₄×M₁₆	C₂²×C₁₃₉	1	4	yes	—
206	#330	C₂²×C₁₃₉	1	8	yes	complemented
207	#329	C₂²×C₁₃₉	1	8	yes	complemented
208	C₂×#41	—	2	2	no	—
209	C₂×#41	C₂×C₄×C₁₃₉	1	2	yes	—
210	C₂³×C₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
211	C₂³×C₄	D₄×C₁₃₉	1	2	yes	—
212	C₂×M₁₆	—	2	4	no	—
213	C₄⋊Q₈	C₂×C₄×C₁₃₉	1	1	yes	characteristic
214	C₄⋊Q₈	C₂×C₄×C₁₃₉	1	2	yes	—
215	#127	C₂×C₄×C₁₃₉	1	1	yes	characteristic
216	#126	—	2	4	no	—
217	#125	—	2	2	no	—
218	#125	C₂³×C₁₃₉	1	2	yes	—
219	#124	—	2	2	no	—
220	#124	C₂³×C₁₃₉	1	2	yes	—
221	#123	—	2	2	no	—
222	#123	—	2	4	no	—
223	C₂²⋊Q₈	—	2	2	no	—
224	C₂²⋊Q₈	—	2	2	no	—
225	C₂²⋊Q₈	C₂×C₄×C₁₃₉	1	4	yes	—
226	#121	—	2	2	no	—
227	#121	—	2	2	no	—
228	#121	C₂×C₄×C₁₃₉	1	4	yes	—
229	#120	—	2	2	no	—
230	C₄×Q₈	—	2	2	no	—
231	C₄×Q₈	—	2	2	no	—
232	C₄×Q₈	C₂×C₄×C₁₃₉	1	4	yes	—
233	C₄×D₄	—	2	4	no	—
234	C₄×D₄	—	2	4	no	—
235	C₄×D₄	—	2	4	no	—
236	C₄×D₄	—	2	2	no	—
237	C₄×D₄	—	2	2	no	—
238	C₄×D₄	C₂×C₄×C₁₃₉	1	4	yes	—
239	#117	—	2	2	no	—
240	#117	—	2	2	no	—
241	#117	—	2	4	no	—
242	#117	C₂×C₄×C₁₃₉	1	2	yes	—
243	C₂×C₄²	—	2	2	no	—
244	C₂×C₄²	C₂×C₄×C₁₃₉	1	1	yes	characteristic
245	C₂×C₄²	C₂×C₄×C₁₃₉	1	2	yes	—
246	C₂×C₄²	D₄×C₁₃₉	1	2	yes	—
247	C₂×C₄²	D₄×C₁₃₉	1	2	yes	—
248	C₂×C₄²	D₄×C₁₃₉	1	2	yes	—
249	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
250	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
251	C₄⋊C₈	—	2	4	no	—
252	C₄⋊C₈	—	2	4	no	—
253	C₂²⋊C₈	—	2	4	no	—
254	C₂²⋊C₈	—	2	4	no	—
255	#97	C₂³×C₁₃₉	1	8	yes	—
256	C₄×C₈	—	2	4	no	—
257	C₂⁴	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
258	#41	—	4	8	no	—
259	#41	—	4	4	no	—
260	C₂×Q₈	—	2	2	no	—
261	C₂×Q₈	C₂²×C₄×C₁₃₉	1	2	yes	—
262	C₂×D₄	—	2	2	no	—
263	C₂×D₄	—	2	4	no	—
264	C₂×D₄	—	2	2	no	—
265	C₂×D₄	C₂²×C₄×C₁₃₉	1	2	yes	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	4	no	—
268	C₂²×C₄	—	4	2	no	—
269	C₂²×C₄	—	4	4	no	—
270	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	2	yes	—
271	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	2	yes	—
272	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	2	yes	—
273	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	2	yes	—
274	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
275	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
276	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
277	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
278	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
279	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
280	M₁₆	—	4	8	no	—
281	C₂×C₈	—	2	8	no	—
282	C₄⋊C₄	—	2	2	no	—
283	C₄⋊C₄	—	2	2	no	—
284	C₄⋊C₄	—	2	4	no	—
285	C₄⋊C₄	—	2	4	no	—
286	C₄⋊C₄	—	2	4	no	—
287	C₄⋊C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
288	C₂²⋊C₄	—	2	4	no	—
289	C₂²⋊C₄	—	2	2	no	—
290	C₂²⋊C₄	—	2	4	no	—
291	C₂²⋊C₄	—	2	4	no	—
292	C₂²⋊C₄	—	2	4	no	—
293	C₄²	—	2	4	no	—
294	C₄²	—	2	2	no	—
295	C₄²	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
296	C₄²	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
297	C₄²	C₂²⋊C₄×C₁₃₉	1	2	yes	—
298	C₄²	C₂²⋊C₄×C₁₃₉	1	2	yes	—
299	C₄²	C₂²×C₄×C₁₃₉	1	2	yes	—
300	C₄²	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
301	C₄²	C₂×D₄×C₁₃₉	1	2	yes	—
302	C₄²	C₂×D₄×C₁₃₉	1	2	yes	—
303	C₄²	C₂×D₄×C₁₃₉	1	2	yes	—
304	C₄²	C₂⁴×C₁₃₉	1	1	yes	characteristic
305	C₂³	—	2	2	no	—
306	C₂³	—	4	1	no	—
307	C₂³	—	4	2	no	—
308	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
309	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
310	Q₈	—	4	2	no	—
311	Q₈	—	4	4	no	—
312	D₄	—	4	2	no	—
313	D₄	—	4	4	no	—
314	D₄	—	4	4	no	—
315	D₄	—	4	8	no	—
316	C₂×C₄	—	2	4	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	4	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	4	no	—
323	C₂×C₄	—	4	1	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	4	4	no	—
329	C₂×C₄	—	4	8	no	—
330	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
331	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
332	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
333	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
334	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
335	C₂×C₄	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
336	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
337	C₈	—	4	8	no	—
338	C₂²	—	2	1	no	—
339	C₂²	—	2	2	no	—
340	C₂²	—	2	2	no	—
341	C₂²	—	2	2	no	—
342	C₂²	—	2	2	no	—
343	C₂²	—	4	4	no	—
344	C₂²	—	4	2	no	—
345	C₂²	—	4	4	no	—
346	C₂²	C₂²×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
347	C₄	—	2	2	no	—
348	C₄	—	2	1	no	—
349	C₄	—	2	2	no	—
350	C₄	—	2	2	no	—
351	C₄	—	2	2	no	—
352	C₄	—	4	2	no	—
353	C₄	—	4	4	no	—
354	C₄	#413×C₁₃₉	1	2	yes	—
355	C₄	#421×C₁₃₉	1	4	yes	—
356	C₂	—	4	1	no	—
357	C₂	—	4	2	no	—
358	C₂	—	8	2	no	—
359	C₂	C₂×#413×C₁₃₉	1	1	yes	characteristic
360	C₂	C₂×#421×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃₉	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₉
Frattini, cosocle	C₄²	C₂⁴×C₁₃₉
prime radical	#3444×C₁₃₉	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₉ ◁ C₂²×C₄²×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2920×C₁₃₉	C₂	semidirect
3. #1537×C₁₃₉	C₂	semidirect
4. #1536×C₁₃₉	C₂	semidirect
5. #1529×C₁₃₉	C₂	semidirect
25. #330×C₁₃₉	C₂²	semidirect
26. #329×C₁₃₉	C₂²	semidirect
180. #17673	C₁₃₉	direct (N × H)
181. C₁₃₉	#17673	direct (N × H)
183. #2920	C₂×C₁₃₉	semidirect
184. #1537	C₂×C₁₃₉	semidirect
185. #1536	C₂×C₁₃₉	semidirect
186. #1529	C₂×C₁₃₉	semidirect
206. #330	C₂²×C₁₃₉	semidirect
207. #329	C₂²×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#3444×C₁₃₉	2
#2920×C₁₃₉	2
#1537×C₁₃₉	2
#1536×C₁₃₉	2
#1529×C₁₃₉	2
#17673	139

Subgroups — C139×#17673 #48012269

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#17673 #48012269