Subgroups — C₁₃₉×#20014 #48014610

Order 35584.

568 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3395×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#3364×C₁₃₉	C₂	1	2	yes	maximal
3	#3342×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	#1707×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#1680×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#1674×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#1669×C₁₃₉	C₂	1	1	yes	maximal, characteristic
8	#1653×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#1652×C₁₃₉	C₂	1	2	yes	maximal
10	C₈×Q₁₆×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×SD₁₆×C₁₃₉	C₂	1	1	yes	maximal, characteristic
12	#557×C₁₃₉	C₂²	1	2	yes	—
13	#556×C₁₃₉	C₂²	1	2	yes	—
14	#500×C₁₃₉	C₂²	1	1	yes	characteristic
15	#498×C₁₃₉	C₂²	1	2	yes	—
16	#494×C₁₃₉	—	2	1	no	—
17	#494×C₁₃₉	C₂²	1	1	yes	characteristic
18	#488×C₁₃₉	—	2	2	no	—
19	#487×C₁₃₉	C₂²	1	2	yes	—
20	#485×C₁₃₉	—	2	2	no	—
21	#479×C₁₃₉	—	2	2	no	—
22	#475×C₁₃₉	C₂²	1	2	yes	—
23	#474×C₁₃₉	C₂²	1	2	yes	—
24	#467×C₁₃₉	—	2	1	no	—
25	#464×C₁₃₉	—	2	2	no	—
26	#462×C₁₃₉	—	2	2	no	—
27	#462×C₁₃₉	C₂²	1	2	yes	—
28	#462×C₁₃₉	C₂²	1	2	yes	—
29	C₈×Q₈×C₁₃₉	C₂²	1	2	yes	—
30	C₈×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₄×Q₁₆×C₁₃₉	—	2	1	no	—
32	C₄×Q₁₆×C₁₃₉	—	2	2	no	—
33	C₄×Q₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
34	C₄×SD₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
35	C₈×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
36	#427×C₁₃₉	—	2	1	no	—
37	#335×C₁₃₉	C₂²	1	1	yes	characteristic
38	#334×C₁₃₉	C₂²	1	1	yes	characteristic
39	#332×C₁₃₉	C₂²	1	2	yes	—
40	#332×C₁₃₉	C₂²	1	2	yes	—
41	Q₈⋊C₈×C₁₃₉	C₂²	1	1	yes	characteristic
42	Q₈⋊C₈×C₁₃₉	C₂²	1	2	yes	—
43	D₄⋊C₈×C₁₃₉	C₂²	1	1	yes	characteristic
44	C₈²×C₁₃₉	C₂²	1	1	yes	characteristic
45	C₂×Q₁₆×C₁₃₉	—	2	2	no	—
46	C₂×Q₁₆×C₁₃₉	—	2	2	no	—
47	C₂×Q₁₆×C₁₃₉	—	2	1	no	—
48	C₂×Q₁₆×C₁₃₉	—	2	1	no	—
49	C₂×Q₁₆×C₁₃₉	D₄	1	1	yes	characteristic
50	C₂×SD₁₆×C₁₃₉	D₄	1	1	yes	characteristic
51	C₂²×C₈×C₁₃₉	—	2	1	no	—
52	C₄⋊Q₈×C₁₃₉	—	2	2	no	—
53	C₄⋊Q₈×C₁₃₉	C₂³	1	2	yes	—
54	C₄⋊Q₈×C₁₃₉	C₂³	1	2	yes	—
55	#126×C₁₃₉	—	4	2	no	—
56	#125×C₁₃₉	—	2	2	no	—
57	#125×C₁₃₉	—	4	2	no	—
58	#124×C₁₃₉	—	2	2	no	—
59	C₂²⋊Q₈×C₁₃₉	—	2	2	no	—
60	C₄×Q₈×C₁₃₉	—	2	2	no	—
61	C₄×Q₈×C₁₃₉	—	2	2	no	—
62	C₄×Q₈×C₁₃₉	—	2	2	no	—
63	C₄×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
64	C₄×Q₈×C₁₃₉	C₂³	1	2	yes	—
65	C₄×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
66	#117×C₁₃₉	—	2	2	no	—
67	#107×C₁₃₉	—	2	1	no	—
68	#107×C₁₃₉	—	2	1	no	—
69	#107×C₁₃₉	—	2	2	no	—
70	#107×C₁₃₉	D₄	1	1	yes	characteristic
71	#106×C₁₃₉	—	2	2	no	—
72	#106×C₁₃₉	—	4	2	no	—
73	#106×C₁₃₉	D₄	1	1	yes	characteristic
74	C₄⋊C₈×C₁₃₉	—	2	1	no	—
75	C₄⋊C₈×C₁₃₉	—	2	2	no	—
76	C₄⋊C₈×C₁₃₉	C₂³	1	1	yes	characteristic
77	C₄⋊C₈×C₁₃₉	C₂³	1	1	yes	characteristic
78	C₄⋊C₈×C₁₃₉	C₂³	1	2	yes	—
79	#103×C₁₃₉	—	2	2	no	—
80	#103×C₁₃₉	—	2	2	no	—
81	#103×C₁₃₉	—	2	2	no	—
82	#103×C₁₃₉	—	2	2	no	—
83	#103×C₁₃₉	—	2	2	no	—
84	#103×C₁₃₉	D₄	1	1	yes	characteristic
85	#103×C₁₃₉	D₄	1	2	yes	—
86	#102×C₁₃₉	—	2	2	no	—
87	#102×C₁₃₉	D₄	1	1	yes	characteristic
88	C₂²⋊C₈×C₁₃₉	—	2	1	no	—
89	C₄×C₈×C₁₃₉	—	2	2	no	—
90	C₄×C₈×C₁₃₉	—	2	1	no	—
91	C₄×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
94	C₂×Q₈×C₁₃₉	—	2	2	no	—
95	C₂×Q₈×C₁₃₉	—	2	2	no	—
96	C₂×Q₈×C₁₃₉	C₂×D₄	1	2	yes	—
97	C₂×Q₈×C₁₃₉	C₂×D₄	1	1	yes	characteristic
98	C₂×D₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₃₉	—	2	1	no	—
100	Q₁₆×C₁₃₉	—	2	2	no	—
101	Q₁₆×C₁₃₉	—	4	4	no	—
102	Q₁₆×C₁₃₉	—	4	2	no	—
103	Q₁₆×C₁₃₉	—	8	1	no	—
104	Q₁₆×C₁₃₉	—	8	2	no	—
105	SD₁₆×C₁₃₉	—	2	2	no	—
106	C₂×C₈×C₁₃₉	—	2	1	no	—
107	C₂×C₈×C₁₃₉	—	2	2	no	—
108	C₂×C₈×C₁₃₉	—	2	1	no	—
109	C₂×C₈×C₁₃₉	—	2	1	no	—
110	C₂×C₈×C₁₃₉	—	4	2	no	—
111	C₂×C₈×C₁₃₉	C₂×D₄	1	1	yes	characteristic
112	C₂×C₈×C₁₃₉	C₂×D₄	1	1	yes	characteristic
113	C₂×C₈×C₁₃₉	C₂×D₄	1	1	yes	characteristic
114	C₂×C₈×C₁₃₉	C₂×D₄	1	1	yes	characteristic
115	C₄⋊C₄×C₁₃₉	—	2	1	no	—
116	C₄⋊C₄×C₁₃₉	—	2	2	no	—
117	C₄⋊C₄×C₁₃₉	—	2	2	no	—
118	C₄⋊C₄×C₁₃₉	—	2	2	no	—
119	C₄⋊C₄×C₁₃₉	—	2	2	no	—
120	C₄⋊C₄×C₁₃₉	—	2	2	no	—
121	C₄⋊C₄×C₁₃₉	—	4	2	no	—
122	C₄⋊C₄×C₁₃₉	—	4	2	no	—
123	C₄⋊C₄×C₁₃₉	—	4	2	no	—
124	C₄⋊C₄×C₁₃₉	—	4	2	no	—
125	C₄⋊C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
126	C₄⋊C₄×C₁₃₉	C₂×D₄	1	2	yes	—
127	C₄⋊C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
128	C₂²⋊C₄×C₁₃₉	—	2	1	no	—
129	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
130	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
131	C₄²×C₁₃₉	—	2	2	no	—
132	C₄²×C₁₃₉	—	2	1	no	—
133	C₄²×C₁₃₉	—	4	2	no	—
134	C₄²×C₁₃₉	—	4	2	no	—
135	C₄²×C₁₃₉	C₂⁴	1	1	yes	characteristic
136	C₂³×C₁₃₉	—	2	1	no	—
137	Q₈×C₁₃₉	—	2	1	no	—
138	Q₈×C₁₃₉	—	2	2	no	—
139	Q₈×C₁₃₉	—	2	2	no	—
140	Q₈×C₁₃₉	—	4	2	no	—
141	Q₈×C₁₃₉	—	4	2	no	—
142	Q₈×C₁₃₉	—	4	2	no	—
143	Q₈×C₁₃₉	—	4	2	no	—
144	Q₈×C₁₃₉	#135	1	2	yes	—
145	D₄×C₁₃₉	—	2	1	no	—
146	D₄×C₁₃₉	—	2	1	no	—
147	C₂×C₄×C₁₃₉	—	2	1	no	—
148	C₂×C₄×C₁₃₉	—	2	2	no	—
149	C₂×C₄×C₁₃₉	—	2	2	no	—
150	C₂×C₄×C₁₃₉	—	2	1	no	—
151	C₂×C₄×C₁₃₉	—	2	1	no	—
152	C₂×C₄×C₁₃₉	—	4	1	no	—
153	C₂×C₄×C₁₃₉	—	4	1	no	—
154	C₂×C₄×C₁₃₉	—	4	2	no	—
155	C₂×C₄×C₁₃₉	—	4	2	no	—
156	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
157	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	1	yes	characteristic
159	C₈×C₁₃₉	—	2	2	no	—
160	C₈×C₁₃₉	—	2	1	no	—
161	C₈×C₁₃₉	—	2	1	no	—
162	C₈×C₁₃₉	—	2	1	no	—
163	C₈×C₁₃₉	—	4	1	no	—
164	C₈×C₁₃₉	—	4	2	no	—
165	C₈×C₁₃₉	—	4	1	no	—
166	C₈×C₁₃₉	#135	1	2	yes	—
167	C₂²×C₁₃₉	—	4	1	no	—
168	C₂²×C₁₃₉	—	4	1	no	—
169	C₂²×C₁₃₉	—	4	1	no	—
170	C₂²×C₁₃₉	D₄²	1	1	yes	characteristic
171	C₄×C₁₃₉	—	2	2	no	—
172	C₄×C₁₃₉	—	2	1	no	—
173	C₄×C₁₃₉	—	4	1	no	—
174	C₄×C₁₃₉	—	4	2	no	—
175	C₄×C₁₃₉	—	4	2	no	—
176	C₄×C₁₃₉	—	4	1	no	—
177	C₄×C₁₃₉	—	8	2	no	—
178	C₄×C₁₃₉	—	8	2	no	—
179	C₄×C₁₃₉	C₂×#135	1	1	yes	characteristic
180	C₄×C₁₃₉	C₂×#135	1	1	yes	characteristic
181	C₄×C₁₃₉	#577	1	1	yes	characteristic
182	C₄×C₁₃₉	#578	1	1	yes	characteristic
183	C₂×C₁₃₉	—	8	1	no	—
184	C₂×C₁₃₉	#3284	1	1	yes	characteristic
185	C₂×C₁₃₉	#3285	1	1	yes	characteristic
186	C₂×C₁₃₉	#3293	1	1	yes	characteristic
187	#20014	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
188	C₁₃₉	#20014	1	1	yes	characteristic, direct product factor, Sylow
189	#3395	C₂×C₁₃₉	1	1	yes	characteristic, complemented
190	#3364	C₂×C₁₃₉	1	2	yes	—
191	#3342	C₂×C₁₃₉	1	1	yes	characteristic
192	#1707	C₂×C₁₃₉	1	1	yes	characteristic, complemented
193	#1680	C₂×C₁₃₉	1	2	yes	complemented
194	#1674	C₂×C₁₃₉	1	1	yes	characteristic, complemented
195	#1669	C₂×C₁₃₉	1	1	yes	characteristic
196	#1653	C₂×C₁₃₉	1	2	yes	complemented
197	#1652	C₂×C₁₃₉	1	2	yes	—
198	C₈×Q₁₆	C₂×C₁₃₉	1	1	yes	characteristic, complemented
199	C₈×SD₁₆	C₂×C₁₃₉	1	1	yes	characteristic
200	#557	C₂²×C₁₃₉	1	2	yes	—
201	#556	C₂²×C₁₃₉	1	2	yes	—
202	#500	C₂²×C₁₃₉	1	1	yes	characteristic
203	#498	C₂²×C₁₃₉	1	2	yes	—
204	#494	—	2	1	no	—
205	#494	C₂²×C₁₃₉	1	1	yes	characteristic
206	#488	—	2	2	no	—
207	#487	C₂²×C₁₃₉	1	2	yes	—
208	#485	—	2	2	no	—
209	#479	—	2	2	no	—
210	#475	C₂²×C₁₃₉	1	2	yes	—
211	#474	C₂²×C₁₃₉	1	2	yes	—
212	#467	—	2	1	no	—
213	#464	—	2	2	no	—
214	#462	—	2	2	no	—
215	#462	C₂²×C₁₃₉	1	2	yes	—
216	#462	C₂²×C₁₃₉	1	2	yes	—
217	C₈×Q₈	C₂²×C₁₃₉	1	2	yes	—
218	C₈×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
219	C₄×Q₁₆	—	2	1	no	—
220	C₄×Q₁₆	—	2	2	no	—
221	C₄×Q₁₆	C₂²×C₁₃₉	1	1	yes	characteristic
222	C₄×SD₁₆	C₂²×C₁₃₉	1	1	yes	characteristic
223	C₈×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
224	#427	—	2	1	no	—
225	#335	C₂²×C₁₃₉	1	1	yes	characteristic
226	#334	C₂²×C₁₃₉	1	1	yes	characteristic
227	#332	C₂²×C₁₃₉	1	2	yes	—
228	#332	C₂²×C₁₃₉	1	2	yes	—
229	Q₈⋊C₈	C₂²×C₁₃₉	1	1	yes	characteristic
230	Q₈⋊C₈	C₂²×C₁₃₉	1	2	yes	—
231	D₄⋊C₈	C₂²×C₁₃₉	1	1	yes	characteristic
232	C₈²	C₂²×C₁₃₉	1	1	yes	characteristic
233	C₂×Q₁₆	—	2	2	no	—
234	C₂×Q₁₆	—	2	2	no	—
235	C₂×Q₁₆	—	2	1	no	—
236	C₂×Q₁₆	—	2	1	no	—
237	C₂×Q₁₆	D₄×C₁₃₉	1	1	yes	characteristic
238	C₂×SD₁₆	D₄×C₁₃₉	1	1	yes	characteristic
239	C₂²×C₈	—	2	1	no	—
240	C₄⋊Q₈	—	2	2	no	—
241	C₄⋊Q₈	C₂³×C₁₃₉	1	2	yes	—
242	C₄⋊Q₈	C₂³×C₁₃₉	1	2	yes	—
243	#126	—	4	2	no	—
244	#125	—	2	2	no	—
245	#125	—	4	2	no	—
246	#124	—	2	2	no	—
247	C₂²⋊Q₈	—	2	2	no	—
248	C₄×Q₈	—	2	2	no	—
249	C₄×Q₈	—	2	2	no	—
250	C₄×Q₈	—	2	2	no	—
251	C₄×Q₈	C₂³×C₁₃₉	1	2	yes	—
252	C₄×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
253	C₄×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
254	#117	—	2	2	no	—
255	#107	—	2	1	no	—
256	#107	—	2	1	no	—
257	#107	—	2	2	no	—
258	#107	D₄×C₁₃₉	1	1	yes	characteristic
259	#106	—	2	2	no	—
260	#106	—	4	2	no	—
261	#106	D₄×C₁₃₉	1	1	yes	characteristic
262	C₄⋊C₈	—	2	1	no	—
263	C₄⋊C₈	—	2	2	no	—
264	C₄⋊C₈	C₂³×C₁₃₉	1	1	yes	characteristic
265	C₄⋊C₈	C₂³×C₁₃₉	1	1	yes	characteristic
266	C₄⋊C₈	C₂³×C₁₃₉	1	2	yes	—
267	#103	—	2	2	no	—
268	#103	—	2	2	no	—
269	#103	—	2	2	no	—
270	#103	—	2	2	no	—
271	#103	—	2	2	no	—
272	#103	D₄×C₁₃₉	1	1	yes	characteristic
273	#103	D₄×C₁₃₉	1	2	yes	—
274	#102	—	2	2	no	—
275	#102	D₄×C₁₃₉	1	1	yes	characteristic
276	C₂²⋊C₈	—	2	1	no	—
277	C₄×C₈	—	2	2	no	—
278	C₄×C₈	—	2	1	no	—
279	C₄×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
280	C₄×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
281	C₄×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
282	C₂×Q₈	—	2	2	no	—
283	C₂×Q₈	—	2	2	no	—
284	C₂×Q₈	C₂×D₄×C₁₃₉	1	2	yes	—
285	C₂×Q₈	C₂×D₄×C₁₃₉	1	1	yes	characteristic
286	C₂×D₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
287	C₂²×C₄	—	2	1	no	—
288	Q₁₆	—	2	2	no	—
289	Q₁₆	—	4	4	no	—
290	Q₁₆	—	4	2	no	—
291	Q₁₆	—	8	1	no	—
292	Q₁₆	—	8	2	no	—
293	SD₁₆	—	2	2	no	—
294	C₂×C₈	—	2	1	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	1	no	—
297	C₂×C₈	—	2	1	no	—
298	C₂×C₈	—	4	2	no	—
299	C₂×C₈	C₂×D₄×C₁₃₉	1	1	yes	characteristic
300	C₂×C₈	C₂×D₄×C₁₃₉	1	1	yes	characteristic
301	C₂×C₈	C₂×D₄×C₁₃₉	1	1	yes	characteristic
302	C₂×C₈	C₂×D₄×C₁₃₉	1	1	yes	characteristic
303	C₄⋊C₄	—	2	1	no	—
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	4	2	no	—
310	C₄⋊C₄	—	4	2	no	—
311	C₄⋊C₄	—	4	2	no	—
312	C₄⋊C₄	—	4	2	no	—
313	C₄⋊C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
314	C₄⋊C₄	C₂×D₄×C₁₃₉	1	2	yes	—
315	C₄⋊C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
316	C₂²⋊C₄	—	2	1	no	—
317	C₂²⋊C₄	—	4	2	no	—
318	C₂²⋊C₄	—	4	2	no	—
319	C₄²	—	2	2	no	—
320	C₄²	—	2	1	no	—
321	C₄²	—	4	2	no	—
322	C₄²	—	4	2	no	—
323	C₄²	C₂⁴×C₁₃₉	1	1	yes	characteristic
324	C₂³	—	2	1	no	—
325	Q₈	—	2	1	no	—
326	Q₈	—	2	2	no	—
327	Q₈	—	2	2	no	—
328	Q₈	—	4	2	no	—
329	Q₈	—	4	2	no	—
330	Q₈	—	4	2	no	—
331	Q₈	—	4	2	no	—
332	Q₈	#135×C₁₃₉	1	2	yes	—
333	D₄	—	2	1	no	—
334	D₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
345	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
346	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
347	C₈	—	2	2	no	—
348	C₈	—	2	1	no	—
349	C₈	—	2	1	no	—
350	C₈	—	2	1	no	—
351	C₈	—	4	1	no	—
352	C₈	—	4	2	no	—
353	C₈	—	4	1	no	—
354	C₈	#135×C₁₃₉	1	2	yes	—
355	C₂²	—	4	1	no	—
356	C₂²	—	4	1	no	—
357	C₂²	—	4	1	no	—
358	C₂²	D₄²×C₁₃₉	1	1	yes	characteristic
359	C₄	—	2	2	no	—
360	C₄	—	2	1	no	—
361	C₄	—	4	1	no	—
362	C₄	—	4	2	no	—
363	C₄	—	4	2	no	—
364	C₄	—	4	1	no	—
365	C₄	—	8	2	no	—
366	C₄	—	8	2	no	—
367	C₄	C₂×#135×C₁₃₉	1	1	yes	characteristic
368	C₄	C₂×#135×C₁₃₉	1	1	yes	characteristic
369	C₄	#577×C₁₃₉	1	1	yes	characteristic
370	C₄	#578×C₁₃₉	1	1	yes	characteristic
371	C₂	—	8	1	no	—
372	C₂	#3284×C₁₃₉	1	1	yes	characteristic
373	C₂	#3285×C₁₃₉	1	1	yes	characteristic
374	C₂	#3293×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₉	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃₉
prime radical	C₂×D₄×C₁₃₉	C₂×D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₉ ◁ C₄²×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. #3395×C₁₃₉	C₂	semidirect
4. #1707×C₁₃₉	C₂	semidirect
5. #1680×C₁₃₉	C₂	semidirect
6. #1674×C₁₃₉	C₂	semidirect
8. #1653×C₁₃₉	C₂	semidirect
10. C₈×Q₁₆×C₁₃₉	C₂	semidirect
187. #20014	C₁₃₉	direct (N × H)
188. C₁₃₉	#20014	direct (N × H)
189. #3395	C₂×C₁₃₉	semidirect
192. #1707	C₂×C₁₃₉	semidirect
193. #1680	C₂×C₁₃₉	semidirect
194. #1674	C₂×C₁₃₉	semidirect
196. #1653	C₂×C₁₃₉	semidirect
198. C₈×Q₁₆	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#3395×C₁₃₉	2
#3364×C₁₃₉	2
#3342×C₁₃₉	2
#1707×C₁₃₉	2
#1680×C₁₃₉	2
#1674×C₁₃₉	2
#1669×C₁₃₉	2
#1653×C₁₃₉	2
#1652×C₁₃₉	2
C₈×Q₁₆×C₁₃₉	2
C₈×SD₁₆×C₁₃₉	2
#20014	139

Subgroups — C139×#20014 #48014610

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#20014 #48014610