Subgroups — C₁₃₉×#36446 #48031042

Order 35584.

2314 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#557×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄×Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2862×C₁₃₉	C₂	1	3	yes	maximal, complemented
4	#2568×C₁₃₉	C₂	1	3	yes	maximal, complemented
5	#2547×C₁₃₉	C₂	1	3	yes	maximal
6	#2489×C₁₃₉	C₂	1	12	yes	maximal, complemented
7	Q₈×C₂²⋊C₄×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	C₄×#124×C₁₃₉	C₂	1	3	yes	maximal
9	C₄²×Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×Q₈×C₁₃₉	C₂²	1	2	yes	—
11	#557×C₁₃₉	—	2	8	no	—
12	D₄×Q₈×C₁₃₉	—	2	8	no	—
13	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	3	yes	—
14	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	3	yes	—
15	C₂×#125×C₁₃₉	C₂²	1	6	yes	—
16	C₂×#124×C₁₃₉	C₂²	1	3	yes	—
17	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	6	yes	—
18	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
19	C₂×C₄×Q₈×C₁₃₉	C₂²	1	3	yes	—
20	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
21	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₁₃₉	C₂²	1	3	yes	—
23	#400×C₁₃₉	C₂²	1	12	yes	—
24	#397×C₁₃₉	C₂²	1	12	yes	—
25	#391×C₁₃₉	C₂²	1	6	yes	—
26	#391×C₁₃₉	C₂²	1	3	yes	—
27	#391×C₁₃₉	C₂²	1	12	yes	—
28	#391×C₁₃₉	C₂²	1	12	yes	—
29	#390×C₁₃₉	C₂²	1	1	yes	characteristic
30	#388×C₁₃₉	C₂²	1	12	yes	—
31	#382×C₁₃₉	C₂²	1	3	yes	—
32	#382×C₁₃₉	C₂²	1	12	yes	—
33	#380×C₁₃₉	C₂²	1	12	yes	—
34	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	3	yes	—
35	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	6	yes	—
36	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	12	yes	—
37	C₄³×C₁₃₉	C₂²	1	3	yes	—
38	C₂²×Q₈×C₁₃₉	—	2	8	no	—
39	C₂²×Q₈×C₁₃₉	—	2	16	no	—
40	C₂²×Q₈×C₁₃₉	C₂³	1	3	yes	—
41	C₂²×Q₈×C₁₃₉	C₂³	1	6	yes	—
42	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
43	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₁₃₉	C₂³	1	6	yes	—
45	C₄⋊Q₈×C₁₃₉	—	2	12	no	—
46	C₄⋊Q₈×C₁₃₉	—	2	12	no	—
47	#125×C₁₃₉	—	2	24	no	—
48	#124×C₁₃₉	—	2	12	no	—
49	C₂²⋊Q₈×C₁₃₉	—	2	24	no	—
50	C₄×Q₈×C₁₃₉	—	2	8	no	—
51	C₄×Q₈×C₁₃₉	—	2	8	no	—
52	C₄×Q₈×C₁₃₉	—	2	12	no	—
53	C₄×Q₈×C₁₃₉	D₄	1	8	yes	—
54	C₄×D₄×C₁₃₉	—	2	12	no	—
55	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
56	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
57	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
58	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
59	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
61	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
62	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
63	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
64	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	12	yes	—
65	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
66	C₂×C₄²×C₁₃₉	C₂³	1	6	yes	—
67	C₂×C₄²×C₁₃₉	C₂³	1	6	yes	—
68	C₂×C₄²×C₁₃₉	C₂³	1	3	yes	—
69	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₁₃₉	C₂³	1	6	yes	—
71	C₂×C₄²×C₁₃₉	C₂³	1	3	yes	—
72	#95×C₁₃₉	C₂³	1	6	yes	—
73	#95×C₁₃₉	C₂³	1	24	yes	—
74	#95×C₁₃₉	C₂³	1	12	yes	—
75	#95×C₁₃₉	C₂³	1	12	yes	—
76	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
77	C₂×Q₈×C₁₃₉	—	2	6	no	—
78	C₂×Q₈×C₁₃₉	—	2	12	no	—
79	C₂×Q₈×C₁₃₉	—	2	6	no	—
80	C₂×Q₈×C₁₃₉	—	2	24	no	—
81	C₂×Q₈×C₁₃₉	—	2	6	no	—
82	C₂×Q₈×C₁₃₉	—	4	32	no	—
83	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	—
84	C₂×Q₈×C₁₃₉	#41	1	8	yes	—
85	C₂×D₄×C₁₃₉	—	2	2	no	—
86	C₂×D₄×C₁₃₉	—	2	2	no	—
87	C₂×D₄×C₁₃₉	#41	1	4	yes	—
88	C₂²×C₄×C₁₃₉	—	2	12	no	—
89	C₂²×C₄×C₁₃₉	—	2	24	no	—
90	C₂²×C₄×C₁₃₉	C₂⁴	1	6	yes	—
91	C₂²×C₄×C₁₃₉	C₂⁴	1	6	yes	—
92	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
93	C₂²×C₄×C₁₃₉	C₂⁴	1	6	yes	—
94	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
95	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
96	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
97	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
98	C₄⋊C₄×C₁₃₉	—	2	6	no	—
99	C₄⋊C₄×C₁₃₉	—	2	2	no	—
100	C₄⋊C₄×C₁₃₉	—	2	12	no	—
101	C₄⋊C₄×C₁₃₉	—	2	12	no	—
102	C₄⋊C₄×C₁₃₉	—	2	12	no	—
103	C₄⋊C₄×C₁₃₉	—	2	12	no	—
104	C₄⋊C₄×C₁₃₉	—	2	12	no	—
105	C₄⋊C₄×C₁₃₉	C₂×D₄	1	12	yes	—
106	C₂²⋊C₄×C₁₃₉	—	2	24	no	—
107	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
108	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
109	C₄²×C₁₃₉	—	2	12	no	—
110	C₄²×C₁₃₉	—	2	12	no	—
111	C₄²×C₁₃₉	—	2	6	no	—
112	C₄²×C₁₃₉	—	2	2	no	—
113	C₄²×C₁₃₉	—	2	12	no	—
114	C₄²×C₁₃₉	C₂×D₄	1	12	yes	—
115	C₂³×C₁₃₉	—	2	2	no	—
116	C₂³×C₁₃₉	—	2	4	no	—
117	C₂³×C₁₃₉	—	2	4	no	—
118	C₂³×C₁₃₉	—	2	2	no	—
119	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
120	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
121	Q₈×C₁₃₉	—	4	24	no	—
122	Q₈×C₁₃₉	—	4	12	no	—
123	Q₈×C₁₃₉	#124	1	16	yes	complemented
124	D₄×C₁₃₉	—	2	8	no	—
125	C₂×C₄×C₁₃₉	—	2	2	no	—
126	C₂×C₄×C₁₃₉	—	2	6	no	—
127	C₂×C₄×C₁₃₉	—	2	2	no	—
128	C₂×C₄×C₁₃₉	—	2	2	no	—
129	C₂×C₄×C₁₃₉	—	2	6	no	—
130	C₂×C₄×C₁₃₉	—	2	6	no	—
131	C₂×C₄×C₁₃₉	—	2	6	no	—
132	C₂×C₄×C₁₃₉	—	2	6	no	—
133	C₂×C₄×C₁₃₉	—	2	6	no	—
134	C₂×C₄×C₁₃₉	—	2	12	no	—
135	C₂×C₄×C₁₃₉	—	2	6	no	—
136	C₂×C₄×C₁₃₉	—	2	4	no	—
137	C₂×C₄×C₁₃₉	—	2	6	no	—
138	C₂×C₄×C₁₃₉	—	4	24	no	—
139	C₂×C₄×C₁₃₉	C₂²×D₄	1	6	yes	—
140	C₂×C₄×C₁₃₉	C₂²×D₄	1	6	yes	—
141	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
142	C₂×C₄×C₁₃₉	C₂×#41	1	12	yes	—
143	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
144	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	4	yes	—
145	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
146	C₂²×C₁₃₉	—	2	4	no	—
147	C₂²×C₁₃₉	—	2	8	no	—
148	C₂²×C₁₃₉	—	4	2	no	—
149	C₂²×C₁₃₉	—	4	2	no	—
150	C₂²×C₁₃₉	—	4	4	no	—
151	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
152	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
153	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
154	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
155	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	2	yes	—
156	C₄×C₁₃₉	—	2	6	no	—
157	C₄×C₁₃₉	—	2	4	no	—
158	C₄×C₁₃₉	—	4	6	no	—
159	C₄×C₁₃₉	—	4	6	no	—
160	C₄×C₁₃₉	—	4	6	no	—
161	C₄×C₁₃₉	—	4	2	no	—
162	C₄×C₁₃₉	C₂×#124	1	12	yes	—
163	C₄×C₁₃₉	#548	1	4	yes	—
164	C₂×C₁₃₉	—	4	4	no	—
165	C₂×C₁₃₉	C₂²×#124	1	1	yes	characteristic
166	C₂×C₁₃₉	C₂×#548	1	1	yes	characteristic
167	C₂×C₁₃₉	#3482	1	2	yes	—
168	C₂×C₁₃₉	#3499	1	1	yes	characteristic
169	C₂×C₁₃₉	#3523	1	2	yes	—
170	#36446	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
171	C₁₃₉	#36446	1	1	yes	characteristic, direct product factor, Sylow
172	C₂×#557	C₂×C₁₃₉	1	1	yes	characteristic, complemented
173	C₂×D₄×Q₈	C₂×C₁₃₉	1	1	yes	characteristic
174	#2862	C₂×C₁₃₉	1	3	yes	complemented
175	#2568	C₂×C₁₃₉	1	3	yes	complemented
176	#2547	C₂×C₁₃₉	1	3	yes	—
177	#2489	C₂×C₁₃₉	1	12	yes	complemented
178	Q₈×C₂²⋊C₄	C₂×C₁₃₉	1	4	yes	complemented
179	C₄×#124	C₂×C₁₃₉	1	3	yes	—
180	C₄²×Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
181	C₂³×Q₈	C₂²×C₁₃₉	1	2	yes	—
182	#557	—	2	8	no	—
183	D₄×Q₈	—	2	8	no	—
184	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	3	yes	—
185	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	3	yes	—
186	C₂×#125	C₂²×C₁₃₉	1	6	yes	—
187	C₂×#124	C₂²×C₁₃₉	1	3	yes	—
188	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	6	yes	—
189	C₂×C₄×Q₈	C₂²×C₁₃₉	1	3	yes	—
190	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
191	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
192	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
193	C₂×C₄×D₄	C₂²×C₁₃₉	1	3	yes	—
194	#400	C₂²×C₁₃₉	1	12	yes	—
195	#397	C₂²×C₁₃₉	1	12	yes	—
196	#391	C₂²×C₁₃₉	1	12	yes	—
197	#391	C₂²×C₁₃₉	1	6	yes	—
198	#391	C₂²×C₁₃₉	1	12	yes	—
199	#391	C₂²×C₁₃₉	1	3	yes	—
200	#390	C₂²×C₁₃₉	1	1	yes	characteristic
201	#388	C₂²×C₁₃₉	1	12	yes	—
202	#382	C₂²×C₁₃₉	1	3	yes	—
203	#382	C₂²×C₁₃₉	1	12	yes	—
204	#380	C₂²×C₁₃₉	1	12	yes	—
205	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	3	yes	—
206	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	6	yes	—
207	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	12	yes	—
208	C₄³	C₂²×C₁₃₉	1	3	yes	—
209	C₂²×Q₈	—	2	8	no	—
210	C₂²×Q₈	—	2	16	no	—
211	C₂²×Q₈	C₂³×C₁₃₉	1	3	yes	—
212	C₂²×Q₈	C₂³×C₁₃₉	1	6	yes	—
213	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
214	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
215	C₂³×C₄	C₂³×C₁₃₉	1	6	yes	—
216	C₄⋊Q₈	—	2	12	no	—
217	C₄⋊Q₈	—	2	12	no	—
218	#125	—	2	24	no	—
219	#124	—	2	12	no	—
220	C₂²⋊Q₈	—	2	24	no	—
221	C₄×Q₈	—	2	8	no	—
222	C₄×Q₈	—	2	8	no	—
223	C₄×Q₈	—	2	12	no	—
224	C₄×Q₈	D₄×C₁₃₉	1	8	yes	—
225	C₄×D₄	—	2	12	no	—
226	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
227	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
228	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
229	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
230	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
231	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
232	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
233	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
234	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
235	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	12	yes	—
236	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
237	C₂×C₄²	C₂³×C₁₃₉	1	6	yes	—
238	C₂×C₄²	C₂³×C₁₃₉	1	6	yes	—
239	C₂×C₄²	C₂³×C₁₃₉	1	3	yes	—
240	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
241	C₂×C₄²	C₂³×C₁₃₉	1	6	yes	—
242	C₂×C₄²	C₂³×C₁₃₉	1	3	yes	—
243	#95	C₂³×C₁₃₉	1	12	yes	—
244	#95	C₂³×C₁₃₉	1	12	yes	—
245	#95	C₂³×C₁₃₉	1	6	yes	—
246	#95	C₂³×C₁₃₉	1	24	yes	—
247	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
248	C₂×Q₈	—	2	6	no	—
249	C₂×Q₈	—	2	12	no	—
250	C₂×Q₈	—	2	6	no	—
251	C₂×Q₈	—	2	24	no	—
252	C₂×Q₈	—	2	6	no	—
253	C₂×Q₈	—	4	32	no	—
254	C₂×Q₈	C₂×D₄×C₁₃₉	1	4	yes	—
255	C₂×Q₈	#41×C₁₃₉	1	8	yes	—
256	C₂×D₄	—	2	2	no	—
257	C₂×D₄	—	2	2	no	—
258	C₂×D₄	#41×C₁₃₉	1	4	yes	—
259	C₂²×C₄	—	2	12	no	—
260	C₂²×C₄	—	2	24	no	—
261	C₂²×C₄	C₂⁴×C₁₃₉	1	6	yes	—
262	C₂²×C₄	C₂⁴×C₁₃₉	1	6	yes	—
263	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
264	C₂²×C₄	C₂⁴×C₁₃₉	1	6	yes	—
265	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
266	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
267	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
268	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
269	C₄⋊C₄	—	2	6	no	—
270	C₄⋊C₄	—	2	2	no	—
271	C₄⋊C₄	—	2	12	no	—
272	C₄⋊C₄	—	2	12	no	—
273	C₄⋊C₄	—	2	12	no	—
274	C₄⋊C₄	—	2	12	no	—
275	C₄⋊C₄	—	2	12	no	—
276	C₄⋊C₄	C₂×D₄×C₁₃₉	1	12	yes	—
277	C₂²⋊C₄	—	2	24	no	—
278	C₂²⋊C₄	—	2	12	no	—
279	C₂²⋊C₄	—	2	8	no	—
280	C₄²	—	2	12	no	—
281	C₄²	—	2	12	no	—
282	C₄²	—	2	6	no	—
283	C₄²	—	2	2	no	—
284	C₄²	—	2	12	no	—
285	C₄²	C₂×D₄×C₁₃₉	1	12	yes	—
286	C₂³	—	2	2	no	—
287	C₂³	—	2	4	no	—
288	C₂³	—	2	4	no	—
289	C₂³	—	2	2	no	—
290	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
291	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
292	Q₈	—	4	24	no	—
293	Q₈	—	4	12	no	—
294	Q₈	#124×C₁₃₉	1	16	yes	complemented
295	D₄	—	2	8	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	6	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	6	no	—
301	C₂×C₄	—	2	6	no	—
302	C₂×C₄	—	2	6	no	—
303	C₂×C₄	—	2	6	no	—
304	C₂×C₄	—	2	6	no	—
305	C₂×C₄	—	2	12	no	—
306	C₂×C₄	—	2	6	no	—
307	C₂×C₄	—	2	4	no	—
308	C₂×C₄	—	2	6	no	—
309	C₂×C₄	—	4	24	no	—
310	C₂×C₄	C₂²×D₄×C₁₃₉	1	6	yes	—
311	C₂×C₄	C₂²×D₄×C₁₃₉	1	6	yes	—
312	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
313	C₂×C₄	C₂×#41×C₁₃₉	1	12	yes	—
314	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
315	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	4	yes	—
316	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
317	C₂²	—	2	4	no	—
318	C₂²	—	2	8	no	—
319	C₂²	—	4	2	no	—
320	C₂²	—	4	2	no	—
321	C₂²	—	4	4	no	—
322	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
323	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
324	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
325	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
326	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	2	yes	—
327	C₄	—	2	6	no	—
328	C₄	—	2	4	no	—
329	C₄	—	4	6	no	—
330	C₄	—	4	6	no	—
331	C₄	—	4	6	no	—
332	C₄	—	4	2	no	—
333	C₄	C₂×#124×C₁₃₉	1	12	yes	—
334	C₄	#548×C₁₃₉	1	4	yes	—
335	C₂	—	4	4	no	—
336	C₂	C₂²×#124×C₁₃₉	1	1	yes	characteristic
337	C₂	C₂×#548×C₁₃₉	1	1	yes	characteristic
338	C₂	#3482×C₁₃₉	1	2	yes	—
339	C₂	#3499×C₁₃₉	1	1	yes	characteristic
340	C₂	#3523×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂²×D₄×C₁₃₉	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#557×C₁₃₉	C₂	semidirect
3. #2862×C₁₃₉	C₂	semidirect
4. #2568×C₁₃₉	C₂	semidirect
6. #2489×C₁₃₉	C₂	semidirect
7. Q₈×C₂²⋊C₄×C₁₃₉	C₂	semidirect
9. C₄²×Q₈×C₁₃₉	C₂	semidirect
123. Q₈×C₁₃₉	#124	semidirect
170. #36446	C₁₃₉	direct (N × H)
171. C₁₃₉	#36446	direct (N × H)
172. C₂×#557	C₂×C₁₃₉	semidirect
174. #2862	C₂×C₁₃₉	semidirect
175. #2568	C₂×C₁₃₉	semidirect
177. #2489	C₂×C₁₃₉	semidirect
178. Q₈×C₂²⋊C₄	C₂×C₁₃₉	semidirect
180. C₄²×Q₈	C₂×C₁₃₉	semidirect
294. Q₈	#124×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#557×C₁₃₉	2
C₂×D₄×Q₈×C₁₃₉	2
#2862×C₁₃₉	2
#2568×C₁₃₉	2
#2547×C₁₃₉	2
#2489×C₁₃₉	2
Q₈×C₂²⋊C₄×C₁₃₉	2
C₄×#124×C₁₃₉	2
C₄²×Q₈×C₁₃₉	2
#36446	139

Subgroups — C139×#36446 #48031042

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36446 #48031042