Subgroups — C₁₃₉×#25589 #48020185

Order 35584.

1068 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3509×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	#3139×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#3039×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	#2868×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2005×C₁₃₉	C₂	1	4	yes	maximal
6	#1994×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#1966×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#1886×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	C₄×#104×C₁₃₉	C₂	1	1	yes	maximal, characteristic
10	C₂×#137×C₁₃₉	C₂²	1	2	yes	—
11	#557×C₁₃₉	—	2	2	no	—
12	#556×C₁₃₉	—	2	2	no	—
13	#552×C₁₃₉	—	2	4	no	—
14	#541×C₁₃₉	—	2	2	no	—
15	#536×C₁₃₉	C₂²	1	2	yes	—
16	#533×C₁₃₉	—	2	2	no	—
17	#533×C₁₃₉	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
19	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
21	#519×C₁₃₉	C₂²	1	2	yes	—
22	C₄×#41×C₁₃₉	C₂²	1	1	yes	characteristic
23	#491×C₁₃₉	—	2	2	no	—
24	#487×C₁₃₉	—	2	2	no	—
25	#462×C₁₃₉	—	2	2	no	—
26	#461×C₁₃₉	—	2	2	no	—
27	#423×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×#104×C₁₃₉	C₂²	1	2	yes	—
29	#419×C₁₃₉	C₂²	1	4	yes	—
30	#419×C₁₃₉	C₂²	1	2	yes	—
31	C₂×#101×C₁₃₉	C₂²	1	4	yes	—
32	C₄×M₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
33	#384×C₁₃₉	—	2	4	no	—
34	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
35	#339×C₁₃₉	C₂²	1	4	yes	—
36	#339×C₁₃₉	C₂²	1	2	yes	—
37	C₂×#41×C₁₃₉	C₂³	1	1	yes	characteristic
38	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
39	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
40	#137×C₁₃₉	—	4	4	no	—
41	C₂×Q₁₆×C₁₃₉	—	2	2	no	—
42	C₂×SD₁₆×C₁₃₉	—	2	2	no	—
43	C₂×M₁₆×C₁₃₉	C₂³	1	2	yes	—
44	C₂×M₁₆×C₁₃₉	C₂³	1	2	yes	—
45	C₄⋊Q₈×C₁₃₉	—	2	2	no	—
46	C₄⋊Q₈×C₁₃₉	—	2	1	no	—
47	C₄⋊Q₈×C₁₃₉	—	2	1	no	—
48	C₄⋊Q₈×C₁₃₉	—	2	2	no	—
49	C₄⋊Q₈×C₁₃₉	—	2	2	no	—
50	C₄⋊Q₈×C₁₃₉	—	2	1	no	—
51	C₄⋊Q₈×C₁₃₉	—	2	1	no	—
52	C₄⋊Q₈×C₁₃₉	—	2	8	no	—
53	C₄⋊Q₈×C₁₃₉	—	4	4	no	—
54	C₄⋊Q₈×C₁₃₉	D₄	1	2	yes	—
55	#126×C₁₃₉	—	2	8	no	—
56	#125×C₁₃₉	—	2	4	no	—
57	#125×C₁₃₉	—	2	8	no	—
58	#125×C₁₃₉	D₄	1	2	yes	—
59	#124×C₁₃₉	—	2	2	no	—
60	#123×C₁₃₉	—	2	4	no	—
61	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
62	C₂²⋊Q₈×C₁₃₉	—	2	2	no	—
63	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
64	C₄×Q₈×C₁₃₉	—	2	4	no	—
65	C₄×Q₈×C₁₃₉	—	2	4	no	—
66	C₄×Q₈×C₁₃₉	—	2	4	no	—
67	C₄×Q₈×C₁₃₉	—	2	2	no	—
68	C₄×Q₈×C₁₃₉	D₄	1	2	yes	—
69	C₄×D₄×C₁₃₉	—	2	2	no	—
70	C₄×D₄×C₁₃₉	D₄	1	2	yes	—
71	#117×C₁₃₉	—	2	4	no	—
72	#117×C₁₃₉	—	2	4	no	—
73	#117×C₁₃₉	—	2	1	no	—
74	#117×C₁₃₉	C₂³	1	1	yes	characteristic
75	#117×C₁₃₉	C₂³	1	2	yes	—
76	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
77	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
78	C₂×C₄⋊C₄×C₁₃₉	D₄	1	4	yes	—
79	C₂×C₄²×C₁₃₉	—	2	2	no	—
80	C₂×C₄²×C₁₃₉	—	2	1	no	—
81	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
82	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
83	C₄⋊C₈×C₁₃₉	—	2	2	no	—
84	#104×C₁₃₉	—	2	4	no	—
85	#103×C₁₃₉	—	2	4	no	—
86	#103×C₁₃₉	—	2	8	no	—
87	#101×C₁₃₉	—	4	4	no	—
88	#97×C₁₃₉	—	2	1	no	—
89	C₄×C₈×C₁₃₉	—	2	1	no	—
90	#41×C₁₃₉	—	2	2	no	—
91	#41×C₁₃₉	—	2	2	no	—
92	C₂×Q₈×C₁₃₉	—	2	2	no	—
93	C₂×Q₈×C₁₃₉	—	2	2	no	—
94	C₂×Q₈×C₁₃₉	—	2	2	no	—
95	C₂×Q₈×C₁₃₉	—	2	4	no	—
96	C₂×Q₈×C₁₃₉	—	2	4	no	—
97	C₂×Q₈×C₁₃₉	—	2	2	no	—
98	C₂×Q₈×C₁₃₉	—	2	2	no	—
99	C₂×Q₈×C₁₃₉	—	2	4	no	—
100	C₂×Q₈×C₁₃₉	—	2	4	no	—
101	C₂×Q₈×C₁₃₉	C₂×D₄	1	1	yes	characteristic
102	C₂×D₄×C₁₃₉	—	2	1	no	—
103	C₂×D₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃₉	—	2	2	no	—
105	C₂²×C₄×C₁₃₉	—	2	2	no	—
106	C₂²×C₄×C₁₃₉	—	2	1	no	—
107	C₂²×C₄×C₁₃₉	—	2	2	no	—
108	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
109	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
111	Q₁₆×C₁₃₉	—	4	4	no	—
112	SD₁₆×C₁₃₉	—	4	4	no	—
113	M₁₆×C₁₃₉	—	2	2	no	—
114	M₁₆×C₁₃₉	—	2	2	no	—
115	M₁₆×C₁₃₉	—	2	4	no	—
116	C₂×C₈×C₁₃₉	—	2	2	no	—
117	C₂×C₈×C₁₃₉	—	2	2	no	—
118	C₄⋊C₄×C₁₃₉	—	2	8	no	—
119	C₄⋊C₄×C₁₃₉	—	2	8	no	—
120	C₄⋊C₄×C₁₃₉	—	2	4	no	—
121	C₄⋊C₄×C₁₃₉	—	2	4	no	—
122	C₄⋊C₄×C₁₃₉	—	2	2	no	—
123	C₄⋊C₄×C₁₃₉	—	2	2	no	—
124	C₄⋊C₄×C₁₃₉	—	2	4	no	—
125	C₄⋊C₄×C₁₃₉	—	4	16	no	—
126	C₄⋊C₄×C₁₃₉	—	4	2	no	—
127	C₄⋊C₄×C₁₃₉	—	4	2	no	—
128	C₄⋊C₄×C₁₃₉	C₂×D₄	1	2	yes	—
129	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
130	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
131	C₂²⋊C₄×C₁₃₉	—	2	1	no	—
132	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
133	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
134	C₄²×C₁₃₉	—	2	8	no	—
135	C₄²×C₁₃₉	—	2	8	no	—
136	C₄²×C₁₃₉	—	2	2	no	—
137	C₄²×C₁₃₉	—	2	1	no	—
138	C₄²×C₁₃₉	—	2	2	no	—
139	C₄²×C₁₃₉	—	2	2	no	—
140	C₄²×C₁₃₉	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₁₃₉	C₂×D₄	1	1	yes	characteristic
142	C₄²×C₁₃₉	C₂×D₄	1	2	yes	—
143	C₄²×C₁₃₉	#41	1	4	yes	—
144	C₂³×C₁₃₉	—	2	1	no	—
145	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
146	Q₈×C₁₃₉	—	2	1	no	—
147	Q₈×C₁₃₉	—	2	1	no	—
148	Q₈×C₁₃₉	—	4	2	no	—
149	Q₈×C₁₃₉	—	4	2	no	—
150	Q₈×C₁₃₉	—	4	4	no	—
151	Q₈×C₁₃₉	—	4	4	no	—
152	Q₈×C₁₃₉	—	4	2	no	—
153	Q₈×C₁₃₉	—	4	2	no	—
154	Q₈×C₁₃₉	—	4	4	no	—
155	D₄×C₁₃₉	—	2	1	no	—
156	D₄×C₁₃₉	—	2	1	no	—
157	D₄×C₁₃₉	—	4	2	no	—
158	C₂×C₄×C₁₃₉	—	2	8	no	—
159	C₂×C₄×C₁₃₉	—	2	4	no	—
160	C₂×C₄×C₁₃₉	—	2	4	no	—
161	C₂×C₄×C₁₃₉	—	2	2	no	—
162	C₂×C₄×C₁₃₉	—	2	4	no	—
163	C₂×C₄×C₁₃₉	—	2	4	no	—
164	C₂×C₄×C₁₃₉	—	2	1	no	—
165	C₂×C₄×C₁₃₉	—	2	8	no	—
166	C₂×C₄×C₁₃₉	—	4	2	no	—
167	C₂×C₄×C₁₃₉	—	4	4	no	—
168	C₂×C₄×C₁₃₉	—	4	2	no	—
169	C₂×C₄×C₁₃₉	—	4	4	no	—
170	C₂×C₄×C₁₃₉	#120	1	2	yes	—
171	C₂×C₄×C₁₃₉	#120	1	2	yes	—
172	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
175	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
176	C₈×C₁₃₉	—	4	2	no	—
177	C₈×C₁₃₉	—	4	2	no	—
178	C₂²×C₁₃₉	—	2	2	no	—
179	C₂²×C₁₃₉	—	4	1	no	—
180	C₂²×C₁₃₉	—	4	2	no	—
181	C₂²×C₁₃₉	C₂×#120	1	1	yes	characteristic
182	C₂²×C₁₃₉	#546	1	2	yes	—
183	C₄×C₁₃₉	—	2	8	no	—
184	C₄×C₁₃₉	—	2	2	no	—
185	C₄×C₁₃₉	—	4	4	no	—
186	C₄×C₁₃₉	—	4	1	no	—
187	C₄×C₁₃₉	—	4	2	no	—
188	C₄×C₁₃₉	—	4	4	no	—
189	C₄×C₁₃₉	—	8	2	no	—
190	C₄×C₁₃₉	#456	1	4	yes	—
191	C₄×C₁₃₉	#532	1	1	yes	characteristic
192	C₄×C₁₃₉	#535	1	1	yes	characteristic
193	C₄×C₁₃₉	#550	1	2	yes	—
194	C₂×C₁₃₉	—	2	2	no	—
195	C₂×C₁₃₉	—	8	1	no	—
196	C₂×C₁₃₉	#2431	1	1	yes	characteristic
197	C₂×C₁₃₉	C₂×#456	1	2	yes	—
198	#25589	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
199	C₁₃₉	#25589	1	1	yes	characteristic, direct product factor, Sylow
200	#3509	C₂×C₁₃₉	1	1	yes	characteristic
201	#3139	C₂×C₁₃₉	1	1	yes	characteristic, complemented
202	#3039	C₂×C₁₃₉	1	1	yes	characteristic
203	#2868	C₂×C₁₃₉	1	1	yes	characteristic, complemented
204	#2005	C₂×C₁₃₉	1	4	yes	—
205	#1994	C₂×C₁₃₉	1	1	yes	characteristic, complemented
206	#1966	C₂×C₁₃₉	1	1	yes	characteristic, complemented
207	#1886	C₂×C₁₃₉	1	4	yes	complemented
208	C₄×#104	C₂×C₁₃₉	1	1	yes	characteristic
209	C₂×#137	C₂²×C₁₃₉	1	2	yes	—
210	#557	—	2	2	no	—
211	#556	—	2	2	no	—
212	#552	—	2	4	no	—
213	#541	—	2	2	no	—
214	#536	C₂²×C₁₃₉	1	2	yes	—
215	#533	—	2	2	no	—
216	#533	C₂²×C₁₃₉	1	1	yes	characteristic
217	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
218	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
219	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
220	#519	C₂²×C₁₃₉	1	2	yes	—
221	C₄×#41	C₂²×C₁₃₉	1	1	yes	characteristic
222	#491	—	2	2	no	—
223	#487	—	2	2	no	—
224	#462	—	2	2	no	—
225	#461	—	2	2	no	—
226	#423	C₂²×C₁₃₉	1	1	yes	characteristic
227	C₂×#104	C₂²×C₁₃₉	1	2	yes	—
228	#419	C₂²×C₁₃₉	1	4	yes	—
229	#419	C₂²×C₁₃₉	1	2	yes	—
230	C₂×#101	C₂²×C₁₃₉	1	4	yes	—
231	C₄×M₁₆	C₂²×C₁₃₉	1	1	yes	characteristic
232	#384	—	2	4	no	—
233	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
234	#339	C₂²×C₁₃₉	1	2	yes	—
235	#339	C₂²×C₁₃₉	1	4	yes	—
236	C₂×#41	C₂³×C₁₃₉	1	1	yes	characteristic
237	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
238	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
239	#137	—	4	4	no	—
240	C₂×Q₁₆	—	2	2	no	—
241	C₂×SD₁₆	—	2	2	no	—
242	C₂×M₁₆	C₂³×C₁₃₉	1	2	yes	—
243	C₂×M₁₆	C₂³×C₁₃₉	1	2	yes	—
244	C₄⋊Q₈	—	2	2	no	—
245	C₄⋊Q₈	—	2	1	no	—
246	C₄⋊Q₈	—	2	1	no	—
247	C₄⋊Q₈	—	2	2	no	—
248	C₄⋊Q₈	—	2	2	no	—
249	C₄⋊Q₈	—	2	1	no	—
250	C₄⋊Q₈	—	2	1	no	—
251	C₄⋊Q₈	—	2	8	no	—
252	C₄⋊Q₈	—	4	4	no	—
253	C₄⋊Q₈	D₄×C₁₃₉	1	2	yes	—
254	#126	—	2	8	no	—
255	#125	—	2	4	no	—
256	#125	—	2	8	no	—
257	#125	D₄×C₁₃₉	1	2	yes	—
258	#124	—	2	2	no	—
259	#123	—	2	4	no	—
260	C₂²⋊Q₈	—	2	4	no	—
261	C₂²⋊Q₈	—	2	2	no	—
262	C₂²⋊Q₈	—	2	4	no	—
263	C₄×Q₈	—	2	4	no	—
264	C₄×Q₈	—	2	4	no	—
265	C₄×Q₈	—	2	4	no	—
266	C₄×Q₈	—	2	2	no	—
267	C₄×Q₈	D₄×C₁₃₉	1	2	yes	—
268	C₄×D₄	—	2	2	no	—
269	C₄×D₄	D₄×C₁₃₉	1	2	yes	—
270	#117	—	2	4	no	—
271	#117	—	2	4	no	—
272	#117	—	2	1	no	—
273	#117	C₂³×C₁₃₉	1	1	yes	characteristic
274	#117	C₂³×C₁₃₉	1	2	yes	—
275	C₂×C₄⋊C₄	—	2	8	no	—
276	C₂×C₄⋊C₄	—	2	2	no	—
277	C₂×C₄⋊C₄	D₄×C₁₃₉	1	4	yes	—
278	C₂×C₄²	—	2	2	no	—
279	C₂×C₄²	—	2	1	no	—
280	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
281	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
282	C₄⋊C₈	—	2	2	no	—
283	#104	—	2	4	no	—
284	#103	—	2	4	no	—
285	#103	—	2	8	no	—
286	#101	—	4	4	no	—
287	#97	—	2	1	no	—
288	C₄×C₈	—	2	1	no	—
289	#41	—	2	2	no	—
290	#41	—	2	2	no	—
291	C₂×Q₈	—	2	2	no	—
292	C₂×Q₈	—	2	2	no	—
293	C₂×Q₈	—	2	2	no	—
294	C₂×Q₈	—	2	4	no	—
295	C₂×Q₈	—	2	4	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	—	2	2	no	—
298	C₂×Q₈	—	2	4	no	—
299	C₂×Q₈	—	2	4	no	—
300	C₂×Q₈	C₂×D₄×C₁₃₉	1	1	yes	characteristic
301	C₂×D₄	—	2	1	no	—
302	C₂×D₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
308	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
309	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
310	Q₁₆	—	4	4	no	—
311	SD₁₆	—	4	4	no	—
312	M₁₆	—	2	2	no	—
313	M₁₆	—	2	2	no	—
314	M₁₆	—	2	4	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₄⋊C₄	—	2	8	no	—
318	C₄⋊C₄	—	2	8	no	—
319	C₄⋊C₄	—	2	4	no	—
320	C₄⋊C₄	—	2	4	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	4	no	—
324	C₄⋊C₄	—	4	16	no	—
325	C₄⋊C₄	—	4	2	no	—
326	C₄⋊C₄	—	4	2	no	—
327	C₄⋊C₄	C₂×D₄×C₁₃₉	1	2	yes	—
328	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
329	C₂²⋊C₄	—	2	8	no	—
330	C₂²⋊C₄	—	2	1	no	—
331	C₂²⋊C₄	—	2	2	no	—
332	C₂²⋊C₄	—	2	2	no	—
333	C₄²	—	2	8	no	—
334	C₄²	—	2	8	no	—
335	C₄²	—	2	2	no	—
336	C₄²	—	2	1	no	—
337	C₄²	—	2	2	no	—
338	C₄²	—	2	2	no	—
339	C₄²	C₂×D₄×C₁₃₉	1	1	yes	characteristic
340	C₄²	C₂×D₄×C₁₃₉	1	1	yes	characteristic
341	C₄²	C₂×D₄×C₁₃₉	1	2	yes	—
342	C₄²	#41×C₁₃₉	1	4	yes	—
343	C₂³	—	2	1	no	—
344	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
345	Q₈	—	2	1	no	—
346	Q₈	—	2	1	no	—
347	Q₈	—	4	4	no	—
348	Q₈	—	4	2	no	—
349	Q₈	—	4	2	no	—
350	Q₈	—	4	4	no	—
351	Q₈	—	4	2	no	—
352	Q₈	—	4	2	no	—
353	Q₈	—	4	4	no	—
354	D₄	—	2	1	no	—
355	D₄	—	2	1	no	—
356	D₄	—	4	2	no	—
357	C₂×C₄	—	2	8	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	8	no	—
365	C₂×C₄	—	4	4	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	4	no	—
369	C₂×C₄	#120×C₁₃₉	1	2	yes	—
370	C₂×C₄	#120×C₁₃₉	1	2	yes	—
371	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
372	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
373	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
374	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
375	C₈	—	4	2	no	—
376	C₈	—	4	2	no	—
377	C₂²	—	2	2	no	—
378	C₂²	—	4	1	no	—
379	C₂²	—	4	2	no	—
380	C₂²	C₂×#120×C₁₃₉	1	1	yes	characteristic
381	C₂²	#546×C₁₃₉	1	2	yes	—
382	C₄	—	2	8	no	—
383	C₄	—	2	2	no	—
384	C₄	—	4	4	no	—
385	C₄	—	4	1	no	—
386	C₄	—	4	2	no	—
387	C₄	—	4	4	no	—
388	C₄	—	8	2	no	—
389	C₄	#456×C₁₃₉	1	4	yes	—
390	C₄	#532×C₁₃₉	1	1	yes	characteristic
391	C₄	#535×C₁₃₉	1	1	yes	characteristic
392	C₄	#550×C₁₃₉	1	2	yes	—
393	C₂	—	2	2	no	—
394	C₂	—	8	1	no	—
395	C₂	#2431×C₁₃₉	1	1	yes	characteristic
396	C₂	C₂×#456×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
prime radical	C₂×#41×C₁₃₉	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₉ ◁ C₂×C₄²×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. #3139×C₁₃₉	C₂	semidirect
4. #2868×C₁₃₉	C₂	semidirect
6. #1994×C₁₃₉	C₂	semidirect
7. #1966×C₁₃₉	C₂	semidirect
8. #1886×C₁₃₉	C₂	semidirect
198. #25589	C₁₃₉	direct (N × H)
199. C₁₃₉	#25589	direct (N × H)
201. #3139	C₂×C₁₃₉	semidirect
203. #2868	C₂×C₁₃₉	semidirect
205. #1994	C₂×C₁₃₉	semidirect
206. #1966	C₂×C₁₃₉	semidirect
207. #1886	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#3509×C₁₃₉	2
#3139×C₁₃₉	2
#3039×C₁₃₉	2
#2868×C₁₃₉	2
#2005×C₁₃₉	2
#1994×C₁₃₉	2
#1966×C₁₃₉	2
#1886×C₁₃₉	2
C₄×#104×C₁₃₉	2
#25589	139

Subgroups — C139×#25589 #48020185

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#25589 #48020185