Subgroups — C₁₃₉×#24063 #48018659

Order 35584.

1144 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#533×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#483×C₁₃₉	C₂	1	2	yes	maximal
3	C₂×#389×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	#2058×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2043×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#1872×C₁₃₉	C₂	1	2	yes	maximal
7	#1865×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	#1817×C₁₃₉	C₂	1	1	yes	maximal, characteristic
9	#533×C₁₃₉	—	2	8	no	—
10	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
12	C₂×#125×C₁₃₉	—	2	1	no	—
13	C₂×C₂²⋊Q₈×C₁₃₉	—	2	1	no	—
14	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
15	C₂×C₄×Q₈×C₁₃₉	—	2	1	no	—
16	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
17	C₂×#117×C₁₃₉	—	2	1	no	—
18	C₂²×C₄⋊C₄×C₁₃₉	—	2	1	no	—
19	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
22	#483×C₁₃₉	—	2	8	no	—
23	C₂×#106×C₁₃₉	C₂²	1	4	yes	—
24	C₂×#103×C₁₃₉	C₂²	1	4	yes	—
25	C₂×#103×C₁₃₉	C₂²	1	4	yes	—
26	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	2	yes	—
27	#389×C₁₃₉	—	2	1	no	—
28	#389×C₁₃₉	—	2	1	no	—
29	#389×C₁₃₉	C₂²	1	2	yes	—
30	#389×C₁₃₉	C₂²	1	2	yes	—
31	C₂×#95×C₁₃₉	—	2	1	no	—
32	#340×C₁₃₉	C₂²	1	4	yes	—
33	#336×C₁₃₉	C₂²	1	2	yes	—
34	#336×C₁₃₉	C₂²	1	2	yes	—
35	C₂²×Q₈×C₁₃₉	—	2	1	no	—
36	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
37	C₂³×C₄×C₁₃₉	—	2	1	no	—
38	C₂³×C₄×C₁₃₉	—	2	1	no	—
39	C₂³×C₄×C₁₃₉	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₃₉	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₁₃₉	C₂³	1	4	yes	—
43	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
44	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
45	#125×C₁₃₉	—	2	8	no	—
46	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
47	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
48	C₂²⋊Q₈×C₁₃₉	D₄	1	8	yes	—
49	C₄×Q₈×C₁₃₉	—	2	8	no	—
50	C₄×Q₈×C₁₃₉	—	2	4	no	—
51	C₄×Q₈×C₁₃₉	—	2	4	no	—
52	#117×C₁₃₉	—	2	8	no	—
53	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
54	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
55	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
56	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
57	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
58	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
59	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
60	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
61	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
62	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
63	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
64	C₂×C₄⋊C₄×C₁₃₉	—	4	4	no	—
65	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
68	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
69	C₂×C₄²×C₁₃₉	—	2	4	no	—
70	C₂×C₄²×C₁₃₉	—	2	2	no	—
71	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
73	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
75	#106×C₁₃₉	—	2	8	no	—
76	#103×C₁₃₉	—	2	8	no	—
77	#103×C₁₃₉	—	2	8	no	—
78	C₂²⋊C₈×C₁₃₉	—	2	4	no	—
79	#95×C₁₃₉	—	2	2	no	—
80	#95×C₁₃₉	—	2	2	no	—
81	C₂⁴×C₁₃₉	C₂×D₄	1	1	yes	characteristic
82	C₂×Q₈×C₁₃₉	—	2	4	no	—
83	C₂×Q₈×C₁₃₉	—	2	2	no	—
84	C₂×Q₈×C₁₃₉	—	2	4	no	—
85	C₂×Q₈×C₁₃₉	—	2	4	no	—
86	C₂×Q₈×C₁₃₉	—	4	2	no	—
87	C₂×Q₈×C₁₃₉	—	4	2	no	—
88	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	—
89	C₂²×C₄×C₁₃₉	—	2	2	no	—
90	C₂²×C₄×C₁₃₉	—	2	2	no	—
91	C₂²×C₄×C₁₃₉	—	2	2	no	—
92	C₂²×C₄×C₁₃₉	—	2	2	no	—
93	C₂²×C₄×C₁₃₉	—	2	4	no	—
94	C₂²×C₄×C₁₃₉	—	2	2	no	—
95	C₂²×C₄×C₁₃₉	—	2	2	no	—
96	C₂²×C₄×C₁₃₉	—	2	2	no	—
97	C₂²×C₄×C₁₃₉	—	2	2	no	—
98	C₂²×C₄×C₁₃₉	—	2	2	no	—
99	C₂²×C₄×C₁₃₉	—	2	2	no	—
100	C₂²×C₄×C₁₃₉	—	4	1	no	—
101	C₂²×C₄×C₁₃₉	—	4	2	no	—
102	C₂²×C₄×C₁₃₉	—	4	2	no	—
103	C₂²×C₄×C₁₃₉	—	4	2	no	—
104	C₂²×C₄×C₁₃₉	—	4	2	no	—
105	C₂²×C₄×C₁₃₉	—	4	2	no	—
106	C₂²×C₄×C₁₃₉	SD₁₆	1	4	yes	—
107	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
110	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
114	C₂×C₈×C₁₃₉	—	2	4	no	—
115	C₂×C₈×C₁₃₉	—	2	4	no	—
116	C₂×C₈×C₁₃₉	—	2	4	no	—
117	C₄⋊C₄×C₁₃₉	—	2	4	no	—
118	C₄⋊C₄×C₁₃₉	—	2	4	no	—
119	C₄⋊C₄×C₁₃₉	—	2	4	no	—
120	C₄⋊C₄×C₁₃₉	—	2	8	no	—
121	C₄⋊C₄×C₁₃₉	—	2	4	no	—
122	C₄⋊C₄×C₁₃₉	—	2	8	no	—
123	C₄⋊C₄×C₁₃₉	—	2	2	no	—
124	C₄⋊C₄×C₁₃₉	—	2	2	no	—
125	C₄⋊C₄×C₁₃₉	—	2	4	no	—
126	C₄⋊C₄×C₁₃₉	—	4	2	no	—
127	C₄⋊C₄×C₁₃₉	—	4	4	no	—
128	C₄⋊C₄×C₁₃₉	—	4	4	no	—
129	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
130	C₄⋊C₄×C₁₃₉	#41	1	4	yes	—
131	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
132	C₄²×C₁₃₉	—	2	8	no	—
133	C₄²×C₁₃₉	—	2	2	no	—
134	C₄²×C₁₃₉	—	2	2	no	—
135	C₄²×C₁₃₉	—	2	2	no	—
136	C₄²×C₁₃₉	—	2	2	no	—
137	C₂³×C₁₃₉	—	2	1	no	—
138	C₂³×C₁₃₉	—	2	1	no	—
139	C₂³×C₁₃₉	—	2	1	no	—
140	C₂³×C₁₃₉	—	2	1	no	—
141	C₂³×C₁₃₉	#120	1	2	yes	—
142	C₂³×C₁₃₉	C₂×SD₁₆	1	2	yes	—
143	C₂³×C₁₃₉	#137	1	2	yes	—
144	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
145	Q₈×C₁₃₉	—	2	8	no	—
146	Q₈×C₁₃₉	—	4	8	no	—
147	Q₈×C₁₃₉	—	4	4	no	—
148	C₂×C₄×C₁₃₉	—	2	1	no	—
149	C₂×C₄×C₁₃₉	—	2	1	no	—
150	C₂×C₄×C₁₃₉	—	2	1	no	—
151	C₂×C₄×C₁₃₉	—	2	1	no	—
152	C₂×C₄×C₁₃₉	—	2	1	no	—
153	C₂×C₄×C₁₃₉	—	2	1	no	—
154	C₂×C₄×C₁₃₉	—	2	1	no	—
155	C₂×C₄×C₁₃₉	—	2	1	no	—
156	C₂×C₄×C₁₃₉	—	2	8	no	—
157	C₂×C₄×C₁₃₉	—	2	8	no	—
158	C₂×C₄×C₁₃₉	—	2	1	no	—
159	C₂×C₄×C₁₃₉	—	2	4	no	—
160	C₂×C₄×C₁₃₉	—	2	4	no	—
161	C₂×C₄×C₁₃₉	—	2	4	no	—
162	C₂×C₄×C₁₃₉	—	2	1	no	—
163	C₂×C₄×C₁₃₉	—	2	1	no	—
164	C₂×C₄×C₁₃₉	—	4	4	no	—
165	C₂×C₄×C₁₃₉	—	4	8	no	—
166	C₂×C₄×C₁₃₉	—	4	2	no	—
167	C₂×C₄×C₁₃₉	—	4	2	no	—
168	C₂×C₄×C₁₃₉	—	4	2	no	—
169	C₂×C₄×C₁₃₉	—	4	2	no	—
170	C₂×C₄×C₁₃₉	—	4	2	no	—
171	C₂×C₄×C₁₃₉	—	4	2	no	—
172	C₂×C₄×C₁₃₉	—	4	2	no	—
173	C₂×C₄×C₁₃₉	—	4	2	no	—
174	C₂×C₄×C₁₃₉	—	4	2	no	—
175	C₂×C₄×C₁₃₉	—	8	4	no	—
176	C₂×C₄×C₁₃₉	#120	1	2	yes	—
177	C₂×C₄×C₁₃₉	C₂×SD₁₆	1	2	yes	—
178	C₂×C₄×C₁₃₉	C₂×SD₁₆	1	2	yes	—
179	C₂×C₄×C₁₃₉	#137	1	2	yes	—
180	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
181	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
182	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
183	C₈×C₁₃₉	—	4	4	no	—
184	C₂²×C₁₃₉	—	2	2	no	—
185	C₂²×C₁₃₉	—	2	2	no	—
186	C₂²×C₁₃₉	—	2	2	no	—
187	C₂²×C₁₃₉	—	2	2	no	—
188	C₂²×C₁₃₉	—	2	2	no	—
189	C₂²×C₁₃₉	—	2	2	no	—
190	C₂²×C₁₃₉	#448	1	4	yes	—
191	C₂²×C₁₃₉	C₂×#120	1	1	yes	characteristic
192	C₂²×C₁₃₉	#525	1	1	yes	characteristic
193	C₂²×C₁₃₉	#536	1	1	yes	characteristic
194	C₂²×C₁₃₉	C₂²×SD₁₆	1	1	yes	characteristic
195	C₂²×C₁₃₉	C₂×#137	1	1	yes	characteristic
196	C₂²×C₁₃₉	C₂×#137	1	1	yes	characteristic
197	C₂²×C₁₃₉	#575	1	1	yes	characteristic
198	C₄×C₁₃₉	—	2	2	no	—
199	C₄×C₁₃₉	—	2	2	no	—
200	C₄×C₁₃₉	—	2	2	no	—
201	C₄×C₁₃₉	—	2	2	no	—
202	C₄×C₁₃₉	—	4	4	no	—
203	C₄×C₁₃₉	—	4	4	no	—
204	C₄×C₁₃₉	—	4	1	no	—
205	C₄×C₁₃₉	—	4	4	no	—
206	C₄×C₁₃₉	—	8	2	no	—
207	C₄×C₁₃₉	#547	1	4	yes	—
208	C₂×C₁₃₉	—	2	4	no	—
209	C₂×C₁₃₉	#2406	1	1	yes	characteristic
210	C₂×C₁₃₉	C₂×#448	1	1	yes	characteristic
211	C₂×C₁₃₉	#3007	1	1	yes	characteristic
212	C₂×C₁₃₉	#3101	1	1	yes	characteristic
213	C₂×C₁₃₉	#3113	1	1	yes	characteristic
214	C₂×C₁₃₉	#3229	1	1	yes	characteristic
215	C₂×C₁₃₉	#3236	1	1	yes	characteristic
216	#24063	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
217	C₁₃₉	#24063	1	1	yes	characteristic, direct product factor, Sylow
218	C₂×#533	C₂×C₁₃₉	1	1	yes	characteristic
219	C₂×#483	C₂×C₁₃₉	1	2	yes	—
220	C₂×#389	C₂×C₁₃₉	1	1	yes	characteristic
221	#2058	C₂×C₁₃₉	1	2	yes	complemented
222	#2043	C₂×C₁₃₉	1	2	yes	complemented
223	#1872	C₂×C₁₃₉	1	2	yes	—
224	#1865	C₂×C₁₃₉	1	4	yes	complemented
225	#1817	C₂×C₁₃₉	1	1	yes	characteristic
226	#533	—	2	8	no	—
227	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
228	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
229	C₂×#125	—	2	1	no	—
230	C₂×C₂²⋊Q₈	—	2	1	no	—
231	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
232	C₂×C₄×Q₈	—	2	1	no	—
233	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
234	C₂×#117	—	2	1	no	—
235	C₂²×C₄⋊C₄	—	2	1	no	—
236	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
237	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
238	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
239	#483	—	2	8	no	—
240	C₂×#106	C₂²×C₁₃₉	1	4	yes	—
241	C₂×#103	C₂²×C₁₃₉	1	4	yes	—
242	C₂×#103	C₂²×C₁₃₉	1	4	yes	—
243	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	2	yes	—
244	#389	—	2	1	no	—
245	#389	—	2	1	no	—
246	#389	C₂²×C₁₃₉	1	2	yes	—
247	#389	C₂²×C₁₃₉	1	2	yes	—
248	C₂×#95	—	2	1	no	—
249	#340	C₂²×C₁₃₉	1	4	yes	—
250	#336	C₂²×C₁₃₉	1	2	yes	—
251	#336	C₂²×C₁₃₉	1	2	yes	—
252	C₂²×Q₈	—	2	1	no	—
253	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
254	C₂³×C₄	—	2	1	no	—
255	C₂³×C₄	—	2	1	no	—
256	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
257	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
258	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
259	C₂²×C₈	C₂³×C₁₃₉	1	4	yes	—
260	C₄⋊Q₈	—	2	4	no	—
261	C₄⋊Q₈	—	2	4	no	—
262	#125	—	2	8	no	—
263	C₂²⋊Q₈	—	2	8	no	—
264	C₂²⋊Q₈	—	2	4	no	—
265	C₂²⋊Q₈	D₄×C₁₃₉	1	8	yes	—
266	C₄×Q₈	—	2	8	no	—
267	C₄×Q₈	—	2	4	no	—
268	C₄×Q₈	—	2	4	no	—
269	#117	—	2	8	no	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄⋊C₄	—	2	1	no	—
274	C₂×C₄⋊C₄	—	2	2	no	—
275	C₂×C₄⋊C₄	—	2	2	no	—
276	C₂×C₄⋊C₄	—	2	4	no	—
277	C₂×C₄⋊C₄	—	2	4	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	—	2	2	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	4	4	no	—
282	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
283	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
284	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
285	C₂×C₂²⋊C₄	—	2	2	no	—
286	C₂×C₄²	—	2	2	no	—
287	C₂×C₄²	—	2	4	no	—
288	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
289	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
290	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
291	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
292	#106	—	2	8	no	—
293	#103	—	2	8	no	—
294	#103	—	2	8	no	—
295	C₂²⋊C₈	—	2	4	no	—
296	#95	—	2	2	no	—
297	#95	—	2	2	no	—
298	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
299	C₂×Q₈	—	2	4	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	2	4	no	—
302	C₂×Q₈	—	2	4	no	—
303	C₂×Q₈	—	4	2	no	—
304	C₂×Q₈	—	4	2	no	—
305	C₂×Q₈	C₂×D₄×C₁₃₉	1	4	yes	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	4	1	no	—
318	C₂²×C₄	—	4	2	no	—
319	C₂²×C₄	—	4	2	no	—
320	C₂²×C₄	—	4	2	no	—
321	C₂²×C₄	—	4	2	no	—
322	C₂²×C₄	—	4	2	no	—
323	C₂²×C₄	SD₁₆×C₁₃₉	1	4	yes	—
324	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
325	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
326	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
327	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
328	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
329	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
330	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
331	C₂×C₈	—	2	4	no	—
332	C₂×C₈	—	2	4	no	—
333	C₂×C₈	—	2	4	no	—
334	C₄⋊C₄	—	2	4	no	—
335	C₄⋊C₄	—	2	4	no	—
336	C₄⋊C₄	—	2	4	no	—
337	C₄⋊C₄	—	2	8	no	—
338	C₄⋊C₄	—	2	4	no	—
339	C₄⋊C₄	—	2	8	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	4	no	—
343	C₄⋊C₄	—	4	2	no	—
344	C₄⋊C₄	—	4	4	no	—
345	C₄⋊C₄	—	4	4	no	—
346	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
347	C₄⋊C₄	#41×C₁₃₉	1	4	yes	—
348	C₂²⋊C₄	—	2	8	no	—
349	C₄²	—	2	8	no	—
350	C₄²	—	2	2	no	—
351	C₄²	—	2	2	no	—
352	C₄²	—	2	2	no	—
353	C₄²	—	2	2	no	—
354	C₂³	—	2	1	no	—
355	C₂³	—	2	1	no	—
356	C₂³	—	2	1	no	—
357	C₂³	—	2	1	no	—
358	C₂³	#120×C₁₃₉	1	2	yes	—
359	C₂³	C₂×SD₁₆×C₁₃₉	1	2	yes	—
360	C₂³	#137×C₁₃₉	1	2	yes	—
361	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
362	Q₈	—	2	8	no	—
363	Q₈	—	4	8	no	—
364	Q₈	—	4	4	no	—
365	C₂×C₄	—	2	8	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	8	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	4	4	no	—
382	C₂×C₄	—	4	8	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	8	4	no	—
393	C₂×C₄	#120×C₁₃₉	1	2	yes	—
394	C₂×C₄	C₂×SD₁₆×C₁₃₉	1	2	yes	—
395	C₂×C₄	C₂×SD₁₆×C₁₃₉	1	2	yes	—
396	C₂×C₄	#137×C₁₃₉	1	2	yes	—
397	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
398	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
399	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
400	C₈	—	4	4	no	—
401	C₂²	—	2	2	no	—
402	C₂²	—	2	2	no	—
403	C₂²	—	2	2	no	—
404	C₂²	—	2	2	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	2	2	no	—
407	C₂²	#448×C₁₃₉	1	4	yes	—
408	C₂²	C₂×#120×C₁₃₉	1	1	yes	characteristic
409	C₂²	#525×C₁₃₉	1	1	yes	characteristic
410	C₂²	#536×C₁₃₉	1	1	yes	characteristic
411	C₂²	C₂²×SD₁₆×C₁₃₉	1	1	yes	characteristic
412	C₂²	C₂×#137×C₁₃₉	1	1	yes	characteristic
413	C₂²	C₂×#137×C₁₃₉	1	1	yes	characteristic
414	C₂²	#575×C₁₃₉	1	1	yes	characteristic
415	C₄	—	2	2	no	—
416	C₄	—	2	2	no	—
417	C₄	—	2	2	no	—
418	C₄	—	2	2	no	—
419	C₄	—	4	4	no	—
420	C₄	—	4	4	no	—
421	C₄	—	4	1	no	—
422	C₄	—	4	4	no	—
423	C₄	—	8	2	no	—
424	C₄	#547×C₁₃₉	1	4	yes	—
425	C₂	—	2	4	no	—
426	C₂	#2406×C₁₃₉	1	1	yes	characteristic
427	C₂	C₂×#448×C₁₃₉	1	1	yes	characteristic
428	C₂	#3007×C₁₃₉	1	1	yes	characteristic
429	C₂	#3101×C₁₃₉	1	1	yes	characteristic
430	C₂	#3113×C₁₃₉	1	1	yes	characteristic
431	C₂	#3229×C₁₃₉	1	1	yes	characteristic
432	C₂	#3236×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
prime radical	C₂⁴×C₁₃₉	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ C₂²×C₄²×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. #2058×C₁₃₉	C₂	semidirect
5. #2043×C₁₃₉	C₂	semidirect
7. #1865×C₁₃₉	C₂	semidirect
216. #24063	C₁₃₉	direct (N × H)
217. C₁₃₉	#24063	direct (N × H)
221. #2058	C₂×C₁₃₉	semidirect
222. #2043	C₂×C₁₃₉	semidirect
224. #1865	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#533×C₁₃₉	2
C₂×#483×C₁₃₉	2
C₂×#389×C₁₃₉	2
#2058×C₁₃₉	2
#2043×C₁₃₉	2
#1872×C₁₃₉	2
#1865×C₁₃₉	2
#1817×C₁₃₉	2
#24063	139

Subgroups — C139×#24063 #48018659

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#24063 #48018659