Subgroups — C₁₃₉×#20855 #48015451

Order 35584.

1422 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3428×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	#2911×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	C₂×#413×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	#2297×C₁₃₉	C₂	1	1	yes	maximal, characteristic
5	#1857×C₁₃₉	C₂	1	4	yes	maximal, complemented
6	#1856×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	C₂×#339×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₁₃₉	C₂²	1	2	yes	—
10	#520×C₁₃₉	—	2	4	no	—
11	#519×C₁₃₉	C₂²	1	2	yes	—
12	#518×C₁₃₉	—	2	2	no	—
13	#518×C₁₃₉	C₂²	1	2	yes	—
14	C₄×#41×C₁₃₉	—	2	4	no	—
15	C₂×#117×C₁₃₉	—	2	2	no	—
16	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
17	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
19	#428×C₁₃₉	—	2	4	no	—
20	#428×C₁₃₉	C₂²	1	8	yes	—
21	#427×C₁₃₉	—	2	4	no	—
22	#413×C₁₃₉	C₄	1	8	yes	complemented
23	C₂×#101×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#100×C₁₃₉	C₂²	1	2	yes	—
25	#391×C₁₃₉	C₂²	1	2	yes	—
26	#390×C₁₃₉	C₂²	1	2	yes	—
27	#386×C₁₃₉	—	2	2	no	—
28	C₄×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
29	#339×C₁₃₉	C₂²	1	8	yes	—
30	C₂×#41×C₁₃₉	—	2	2	no	—
31	C₂×#41×C₁₃₉	—	2	2	no	—
32	C₂×#41×C₁₃₉	—	2	4	no	—
33	C₂×#41×C₁₃₉	C₂×C₄	1	4	yes	—
34	C₂×#41×C₁₃₉	Q₈	1	4	yes	—
35	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
36	C₂²×D₄×C₁₃₉	D₄	1	2	yes	—
37	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
38	C₂³×C₄×C₁₃₉	—	2	1	no	—
39	C₂³×C₄×C₁₃₉	D₄	1	2	yes	—
40	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
41	C₂×M₁₆×C₁₃₉	—	2	2	no	—
42	C₂×M₁₆×C₁₃₉	—	2	4	no	—
43	C₂×M₁₆×C₁₃₉	C₂×C₄	1	8	yes	complemented
44	C₂×M₁₆×C₁₃₉	C₂³	1	4	yes	—
45	C₂²×C₈×C₁₃₉	—	2	2	no	—
46	C₄×Q₈×C₁₃₉	—	2	8	no	—
47	C₄×D₄×C₁₃₉	—	2	16	no	—
48	C₄×D₄×C₁₃₉	—	2	8	no	—
49	#117×C₁₃₉	—	2	4	no	—
50	#117×C₁₃₉	—	2	4	no	—
51	#117×C₁₃₉	—	2	2	no	—
52	#117×C₁₃₉	—	2	4	no	—
53	#117×C₁₃₉	—	2	2	no	—
54	#117×C₁₃₉	—	2	2	no	—
55	#117×C₁₃₉	—	2	2	no	—
56	#117×C₁₃₉	D₄	1	4	yes	—
57	#117×C₁₃₉	C₂³	1	4	yes	—
58	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
59	C₂×C₄⋊C₄×C₁₃₉	D₄	1	4	yes	—
60	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
61	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
62	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
64	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
65	C₂×C₄²×C₁₃₉	—	2	4	no	—
66	C₂×C₄²×C₁₃₉	—	2	2	no	—
67	C₂×C₄²×C₁₃₉	—	2	4	no	—
68	C₂×C₄²×C₁₃₉	—	2	1	no	—
69	C₂×C₄²×C₁₃₉	—	2	1	no	—
70	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
71	#107×C₁₃₉	—	2	8	no	—
72	#106×C₁₃₉	—	2	8	no	—
73	#101×C₁₃₉	C₂×C₄	1	8	yes	complemented
74	#100×C₁₃₉	C₂×C₄	1	8	yes	complemented
75	#95×C₁₃₉	—	2	4	no	—
76	C₂⁴×C₁₃₉	C₂×D₄	1	2	yes	—
77	C₂⁴×C₁₃₉	C₂×D₄	1	1	yes	characteristic
78	#41×C₁₃₉	—	2	8	no	—
79	#41×C₁₃₉	—	2	8	no	—
80	#41×C₁₃₉	—	2	8	no	—
81	#41×C₁₃₉	—	2	8	no	—
82	C₂×Q₈×C₁₃₉	—	2	2	no	—
83	C₂×Q₈×C₁₃₉	—	2	2	no	—
84	C₂×Q₈×C₁₃₉	C₂²×C₄	1	2	yes	—
85	C₂×Q₈×C₁₃₉	C₂×Q₈	1	2	yes	—
86	C₂×D₄×C₁₃₉	—	2	4	no	—
87	C₂×D₄×C₁₃₉	—	2	4	no	—
88	C₂×D₄×C₁₃₉	—	2	2	no	—
89	C₂×D₄×C₁₃₉	—	2	2	no	—
90	C₂×D₄×C₁₃₉	C₄⋊C₄	1	8	yes	—
91	C₂×D₄×C₁₃₉	C₂²×C₄	1	2	yes	—
92	C₂×D₄×C₁₃₉	C₂×Q₈	1	2	yes	—
93	C₂²×C₄×C₁₃₉	—	2	2	no	—
94	C₂²×C₄×C₁₃₉	—	2	2	no	—
95	C₂²×C₄×C₁₃₉	—	2	4	no	—
96	C₂²×C₄×C₁₃₉	—	2	2	no	—
97	C₂²×C₄×C₁₃₉	—	2	8	no	—
98	C₂²×C₄×C₁₃₉	—	2	4	no	—
99	C₂²×C₄×C₁₃₉	—	2	2	no	—
100	C₂²×C₄×C₁₃₉	—	4	4	no	—
101	C₂²×C₄×C₁₃₉	—	4	2	no	—
102	C₂²×C₄×C₁₃₉	C₄⋊C₄	1	8	yes	—
103	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₁₃₉	C₂×Q₈	1	2	yes	—
109	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
110	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
111	M₁₆×C₁₃₉	—	2	8	no	—
112	M₁₆×C₁₃₉	—	2	4	no	—
113	M₁₆×C₁₃₉	C₂²×C₄	1	8	yes	—
114	C₂×C₈×C₁₃₉	—	2	8	no	—
115	C₂×C₈×C₁₃₉	—	2	4	no	—
116	C₄⋊C₄×C₁₃₉	—	2	8	no	—
117	C₄⋊C₄×C₁₃₉	—	2	4	no	—
118	C₄⋊C₄×C₁₃₉	—	2	4	no	—
119	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
120	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
121	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
122	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
123	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
124	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
125	C₄²×C₁₃₉	—	2	8	no	—
126	C₄²×C₁₃₉	—	2	4	no	—
127	C₄²×C₁₃₉	—	2	4	no	—
128	C₄²×C₁₃₉	—	2	4	no	—
129	C₄²×C₁₃₉	—	4	1	no	—
130	C₄²×C₁₃₉	—	4	1	no	—
131	C₄²×C₁₃₉	—	4	2	no	—
132	C₂³×C₁₃₉	—	2	2	no	—
133	C₂³×C₁₃₉	—	2	2	no	—
134	C₂³×C₁₃₉	—	4	2	no	—
135	C₂³×C₁₃₉	—	4	4	no	—
136	C₂³×C₁₃₉	C₂×C₄⋊C₄	1	4	yes	—
137	C₂³×C₁₃₉	C₂×C₄⋊C₄	1	2	yes	—
138	C₂³×C₁₃₉	#120	1	2	yes	—
139	C₂³×C₁₃₉	#123	1	2	yes	—
140	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
141	Q₈×C₁₃₉	—	2	4	no	—
142	Q₈×C₁₃₉	—	2	4	no	—
143	D₄×C₁₃₉	—	2	16	no	—
144	D₄×C₁₃₉	—	2	4	no	—
145	D₄×C₁₃₉	—	2	4	no	—
146	C₂×C₄×C₁₃₉	—	2	2	no	—
147	C₂×C₄×C₁₃₉	—	2	2	no	—
148	C₂×C₄×C₁₃₉	—	2	8	no	—
149	C₂×C₄×C₁₃₉	—	2	8	no	—
150	C₂×C₄×C₁₃₉	—	2	4	no	—
151	C₂×C₄×C₁₃₉	—	2	8	no	—
152	C₂×C₄×C₁₃₉	—	4	2	no	—
153	C₂×C₄×C₁₃₉	—	4	8	no	—
154	C₂×C₄×C₁₃₉	—	4	2	no	—
155	C₂×C₄×C₁₃₉	—	4	4	no	—
156	C₂×C₄×C₁₃₉	—	4	2	no	—
157	C₂×C₄×C₁₃₉	—	8	4	no	—
158	C₂×C₄×C₁₃₉	—	8	8	no	—
159	C₂×C₄×C₁₃₉	C₂×C₄⋊C₄	1	4	yes	—
160	C₂×C₄×C₁₃₉	C₂×C₄⋊C₄	1	2	yes	—
161	C₂×C₄×C₁₃₉	C₄×D₄	1	4	yes	—
162	C₂×C₄×C₁₃₉	C₄×D₄	1	4	yes	—
163	C₂×C₄×C₁₃₉	#120	1	1	yes	characteristic
164	C₂×C₄×C₁₃₉	#120	1	1	yes	characteristic
165	C₂×C₄×C₁₃₉	C₂²⋊Q₈	1	4	yes	—
166	C₂×C₄×C₁₃₉	C₂²⋊Q₈	1	4	yes	—
167	C₂×C₄×C₁₃₉	#123	1	2	yes	—
168	C₂×C₄×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
169	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
170	C₂×C₄×C₁₃₉	C₂²×Q₈	1	1	yes	characteristic
171	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
172	C₈×C₁₃₉	—	2	8	no	—
173	C₂²×C₁₃₉	—	2	2	no	—
174	C₂²×C₁₃₉	—	2	4	no	—
175	C₂²×C₁₃₉	—	2	4	no	—
176	C₂²×C₁₃₉	—	4	2	no	—
177	C₂²×C₁₃₉	—	4	2	no	—
178	C₂²×C₁₃₉	—	4	4	no	—
179	C₂²×C₁₃₉	—	4	4	no	—
180	C₂²×C₁₃₉	—	8	2	no	—
181	C₂²×C₁₃₉	#385	1	4	yes	—
182	C₂²×C₁₃₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
183	C₂²×C₁₃₉	C₂×#120	1	1	yes	characteristic
184	C₂²×C₁₃₉	C₂×#123	1	1	yes	characteristic
185	C₄×C₁₃₉	—	2	4	no	—
186	C₄×C₁₃₉	—	4	4	no	—
187	C₄×C₁₃₉	—	4	8	no	—
188	C₄×C₁₃₉	—	8	2	no	—
189	C₄×C₁₃₉	#385	1	2	yes	—
190	C₄×C₁₃₉	#385	1	2	yes	—
191	C₄×C₁₃₉	C₂×C₄×D₄	1	2	yes	—
192	C₄×C₁₃₉	C₂×C₂²⋊Q₈	1	2	yes	—
193	C₂×C₁₃₉	—	2	1	no	—
194	C₂×C₁₃₉	—	2	1	no	—
195	C₂×C₁₃₉	—	2	4	no	—
196	C₂×C₁₃₉	—	4	4	no	—
197	C₂×C₁₃₉	C₂×#385	1	1	yes	characteristic
198	C₂×C₁₃₉	#3018	1	2	yes	—
199	#20855	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
200	C₁₃₉	#20855	1	1	yes	characteristic, direct product factor, Sylow
201	#3428	C₂×C₁₃₉	1	1	yes	characteristic
202	#2911	C₂×C₁₃₉	1	2	yes	complemented
203	C₂×#413	C₂×C₁₃₉	1	1	yes	characteristic
204	#2297	C₂×C₁₃₉	1	1	yes	characteristic
205	#1857	C₂×C₁₃₉	1	4	yes	complemented
206	#1856	C₂×C₁₃₉	1	4	yes	complemented
207	C₂×#339	C₂×C₁₃₉	1	2	yes	complemented
208	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
209	C₂²×M₁₆	C₂²×C₁₃₉	1	2	yes	—
210	#520	—	2	4	no	—
211	#519	C₂²×C₁₃₉	1	2	yes	—
212	#518	—	2	2	no	—
213	#518	C₂²×C₁₃₉	1	2	yes	—
214	C₄×#41	—	2	4	no	—
215	C₂×#117	—	2	2	no	—
216	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
217	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
218	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
219	#428	—	2	4	no	—
220	#428	C₂²×C₁₃₉	1	8	yes	—
221	#427	—	2	4	no	—
222	#413	C₄×C₁₃₉	1	8	yes	complemented
223	C₂×#101	C₂²×C₁₃₉	1	2	yes	—
224	C₂×#100	C₂²×C₁₃₉	1	2	yes	—
225	#391	C₂²×C₁₃₉	1	2	yes	—
226	#390	C₂²×C₁₃₉	1	2	yes	—
227	#386	—	2	2	no	—
228	C₄×C₂²⋊C₄	—	2	2	no	—
229	#339	C₂²×C₁₃₉	1	8	yes	—
230	C₂×#41	—	2	2	no	—
231	C₂×#41	—	2	2	no	—
232	C₂×#41	—	2	4	no	—
233	C₂×#41	C₂×C₄×C₁₃₉	1	4	yes	—
234	C₂×#41	Q₈×C₁₃₉	1	4	yes	—
235	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
236	C₂²×D₄	D₄×C₁₃₉	1	2	yes	—
237	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
238	C₂³×C₄	—	2	1	no	—
239	C₂³×C₄	D₄×C₁₃₉	1	2	yes	—
240	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
241	C₂×M₁₆	—	2	2	no	—
242	C₂×M₁₆	—	2	4	no	—
243	C₂×M₁₆	C₂×C₄×C₁₃₉	1	8	yes	complemented
244	C₂×M₁₆	C₂³×C₁₃₉	1	4	yes	—
245	C₂²×C₈	—	2	2	no	—
246	C₄×Q₈	—	2	8	no	—
247	C₄×D₄	—	2	16	no	—
248	C₄×D₄	—	2	8	no	—
249	#117	—	2	4	no	—
250	#117	—	2	4	no	—
251	#117	—	2	2	no	—
252	#117	—	2	4	no	—
253	#117	—	2	2	no	—
254	#117	—	2	2	no	—
255	#117	—	2	2	no	—
256	#117	D₄×C₁₃₉	1	4	yes	—
257	#117	C₂³×C₁₃₉	1	4	yes	—
258	C₂×C₄⋊C₄	—	2	4	no	—
259	C₂×C₄⋊C₄	D₄×C₁₃₉	1	4	yes	—
260	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
261	C₂×C₂²⋊C₄	—	2	4	no	—
262	C₂×C₂²⋊C₄	—	2	2	no	—
263	C₂×C₂²⋊C₄	—	2	1	no	—
264	C₂×C₂²⋊C₄	—	2	4	no	—
265	C₂×C₄²	—	2	4	no	—
266	C₂×C₄²	—	2	2	no	—
267	C₂×C₄²	—	2	4	no	—
268	C₂×C₄²	—	2	1	no	—
269	C₂×C₄²	—	2	1	no	—
270	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
271	#107	—	2	8	no	—
272	#106	—	2	8	no	—
273	#101	C₂×C₄×C₁₃₉	1	8	yes	complemented
274	#100	C₂×C₄×C₁₃₉	1	8	yes	complemented
275	#95	—	2	4	no	—
276	C₂⁴	C₂×D₄×C₁₃₉	1	2	yes	—
277	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
278	#41	—	2	8	no	—
279	#41	—	2	8	no	—
280	#41	—	2	8	no	—
281	#41	—	2	8	no	—
282	C₂×Q₈	—	2	2	no	—
283	C₂×Q₈	—	2	2	no	—
284	C₂×Q₈	C₂²×C₄×C₁₃₉	1	2	yes	—
285	C₂×Q₈	C₂×Q₈×C₁₃₉	1	2	yes	—
286	C₂×D₄	—	2	4	no	—
287	C₂×D₄	—	2	4	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	C₄⋊C₄×C₁₃₉	1	8	yes	—
291	C₂×D₄	C₂²×C₄×C₁₃₉	1	2	yes	—
292	C₂×D₄	C₂×Q₈×C₁₃₉	1	2	yes	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	8	no	—
298	C₂²×C₄	—	2	4	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	4	4	no	—
301	C₂²×C₄	—	4	2	no	—
302	C₂²×C₄	C₄⋊C₄×C₁₃₉	1	8	yes	—
303	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
304	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
305	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
306	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
307	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
308	C₂²×C₄	C₂×Q₈×C₁₃₉	1	2	yes	—
309	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
310	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
311	M₁₆	—	2	8	no	—
312	M₁₆	—	2	4	no	—
313	M₁₆	C₂²×C₄×C₁₃₉	1	8	yes	—
314	C₂×C₈	—	2	8	no	—
315	C₂×C₈	—	2	4	no	—
316	C₄⋊C₄	—	2	8	no	—
317	C₄⋊C₄	—	2	4	no	—
318	C₄⋊C₄	—	2	4	no	—
319	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
320	C₂²⋊C₄	—	2	8	no	—
321	C₂²⋊C₄	—	2	4	no	—
322	C₂²⋊C₄	—	2	4	no	—
323	C₂²⋊C₄	—	4	8	no	—
324	C₂²⋊C₄	—	4	2	no	—
325	C₄²	—	2	8	no	—
326	C₄²	—	2	4	no	—
327	C₄²	—	2	4	no	—
328	C₄²	—	2	4	no	—
329	C₄²	—	4	1	no	—
330	C₄²	—	4	1	no	—
331	C₄²	—	4	2	no	—
332	C₂³	—	2	2	no	—
333	C₂³	—	2	2	no	—
334	C₂³	—	4	2	no	—
335	C₂³	—	4	4	no	—
336	C₂³	C₂×C₄⋊C₄×C₁₃₉	1	4	yes	—
337	C₂³	C₂×C₄⋊C₄×C₁₃₉	1	2	yes	—
338	C₂³	#120×C₁₃₉	1	2	yes	—
339	C₂³	#123×C₁₃₉	1	2	yes	—
340	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
341	Q₈	—	2	4	no	—
342	Q₈	—	2	4	no	—
343	D₄	—	2	16	no	—
344	D₄	—	2	4	no	—
345	D₄	—	2	4	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	8	no	—
349	C₂×C₄	—	2	8	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	8	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	8	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	4	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	8	4	no	—
358	C₂×C₄	—	8	8	no	—
359	C₂×C₄	C₂×C₄⋊C₄×C₁₃₉	1	4	yes	—
360	C₂×C₄	C₂×C₄⋊C₄×C₁₃₉	1	2	yes	—
361	C₂×C₄	C₄×D₄×C₁₃₉	1	4	yes	—
362	C₂×C₄	C₄×D₄×C₁₃₉	1	4	yes	—
363	C₂×C₄	#120×C₁₃₉	1	1	yes	characteristic
364	C₂×C₄	#120×C₁₃₉	1	1	yes	characteristic
365	C₂×C₄	C₂²⋊Q₈×C₁₃₉	1	4	yes	—
366	C₂×C₄	C₂²⋊Q₈×C₁₃₉	1	4	yes	—
367	C₂×C₄	#123×C₁₃₉	1	2	yes	—
368	C₂×C₄	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
369	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
370	C₂×C₄	C₂²×Q₈×C₁₃₉	1	1	yes	characteristic
371	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
372	C₈	—	2	8	no	—
373	C₂²	—	2	2	no	—
374	C₂²	—	2	4	no	—
375	C₂²	—	2	4	no	—
376	C₂²	—	4	2	no	—
377	C₂²	—	4	2	no	—
378	C₂²	—	4	4	no	—
379	C₂²	—	4	4	no	—
380	C₂²	—	8	2	no	—
381	C₂²	#385×C₁₃₉	1	4	yes	—
382	C₂²	C₂²×C₄⋊C₄×C₁₃₉	1	1	yes	characteristic
383	C₂²	C₂×#120×C₁₃₉	1	1	yes	characteristic
384	C₂²	C₂×#123×C₁₃₉	1	1	yes	characteristic
385	C₄	—	2	4	no	—
386	C₄	—	4	4	no	—
387	C₄	—	4	8	no	—
388	C₄	—	8	2	no	—
389	C₄	#385×C₁₃₉	1	2	yes	—
390	C₄	#385×C₁₃₉	1	2	yes	—
391	C₄	C₂×C₄×D₄×C₁₃₉	1	2	yes	—
392	C₄	C₂×C₂²⋊Q₈×C₁₃₉	1	2	yes	—
393	C₂	—	2	1	no	—
394	C₂	—	2	1	no	—
395	C₂	—	2	4	no	—
396	C₂	—	4	4	no	—
397	C₂	C₂×#385×C₁₃₉	1	1	yes	characteristic
398	C₂	#3018×C₁₃₉	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₃₉	#120
commutator	C₂×C₄	C₂³×C₄×C₁₃₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
socle	C₂²×C₁₃₉	C₂×#120
prime radical	C₂²×#41×C₁₃₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃₉ ◁ C₂³×C₄×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2911×C₁₃₉	C₂	semidirect
5. #1857×C₁₃₉	C₂	semidirect
6. #1856×C₁₃₉	C₂	semidirect
7. C₂×#339×C₁₃₉	C₂	semidirect
22. #413×C₁₃₉	C₄	semidirect
43. C₂×M₁₆×C₁₃₉	C₂×C₄	semidirect
73. #101×C₁₃₉	C₂×C₄	semidirect
74. #100×C₁₃₉	C₂×C₄	semidirect
199. #20855	C₁₃₉	direct (N × H)
200. C₁₃₉	#20855	direct (N × H)
202. #2911	C₂×C₁₃₉	semidirect
205. #1857	C₂×C₁₃₉	semidirect
206. #1856	C₂×C₁₃₉	semidirect
207. C₂×#339	C₂×C₁₃₉	semidirect
222. #413	C₄×C₁₃₉	semidirect
243. C₂×M₁₆	C₂×C₄×C₁₃₉	semidirect
273. #101	C₂×C₄×C₁₃₉	semidirect
274. #100	C₂×C₄×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#3428×C₁₃₉	2
#2911×C₁₃₉	2
C₂×#413×C₁₃₉	2
#2297×C₁₃₉	2
#1857×C₁₃₉	2
#1856×C₁₃₉	2
C₂×#339×C₁₃₉	2
#20855	139

Subgroups — C139×#20855 #48015451

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#20855 #48015451