Subgroups — C₁₃₉×#10959 #48005555

Order 35584.

990 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	C₂×#421×C₁₃₉	C₂	1	2	yes	maximal
2	#2873×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2297×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	#1740×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#339×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
7	C₂²×M₁₆×C₁₃₉	C₂²	1	2	yes	—
8	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
9	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
10	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
11	#421×C₁₃₉	—	2	4	no	—
12	#421×C₁₃₉	C₄	1	8	yes	complemented
13	C₂×#104×C₁₃₉	—	2	4	no	—
14	#405×C₁₃₉	—	2	4	no	—
15	C₄×M₁₆×C₁₃₉	—	2	2	no	—
16	#391×C₁₃₉	C₄	1	2	yes	complemented
17	#390×C₁₃₉	C₄	1	2	yes	complemented
18	#386×C₁₃₉	—	2	2	no	—
19	C₄×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
20	#342×C₁₃₉	—	2	2	no	—
21	#339×C₁₃₉	—	2	4	no	—
22	C₂×#41×C₁₃₉	—	2	2	no	—
23	C₂×#41×C₁₃₉	—	2	2	no	—
24	C₂×#41×C₁₃₉	—	2	2	no	—
25	C₂×#41×C₁₃₉	—	2	2	no	—
26	C₂×#41×C₁₃₉	—	2	2	no	—
27	C₂×#41×C₁₃₉	C₂×C₄	1	4	yes	—
28	C₂²×Q₈×C₁₃₉	C₂×C₄	1	1	yes	characteristic
29	C₂²×D₄×C₁₃₉	—	2	1	no	—
30	C₂²×D₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
31	C₂³×C₄×C₁₃₉	—	2	1	no	—
32	C₂³×C₄×C₁₃₉	—	2	1	no	—
33	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
34	C₂×M₁₆×C₁₃₉	—	2	2	no	—
35	C₂×M₁₆×C₁₃₉	—	2	2	no	—
36	C₂×M₁₆×C₁₃₉	—	2	2	no	—
37	C₂×M₁₆×C₁₃₉	C₂×C₄	1	4	yes	—
38	C₂×M₁₆×C₁₃₉	D₄	1	4	yes	—
39	C₂×M₁₆×C₁₃₉	D₄	1	4	yes	—
40	C₂²×C₈×C₁₃₉	—	2	2	no	—
41	#117×C₁₃₉	—	2	2	no	—
42	#117×C₁₃₉	—	2	2	no	—
43	#117×C₁₃₉	—	2	2	no	—
44	#117×C₁₃₉	—	2	2	no	—
45	#117×C₁₃₉	—	2	2	no	—
46	#117×C₁₃₉	C₂×C₄	1	4	yes	—
47	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
48	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	2	yes	—
49	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
50	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
51	C₂×C₂²⋊C₄×C₁₃₉	D₄	1	2	yes	—
52	C₂×C₄²×C₁₃₉	—	2	2	no	—
53	C₂×C₄²×C₁₃₉	—	2	2	no	—
54	C₂×C₄²×C₁₃₉	—	2	2	no	—
55	C₂×C₄²×C₁₃₉	—	2	1	no	—
56	C₂×C₄²×C₁₃₉	C₂×C₄	1	2	yes	—
57	C₂×C₄²×C₁₃₉	D₄	1	2	yes	—
58	#104×C₁₃₉	—	2	16	no	—
59	#97×C₁₃₉	—	2	4	no	—
60	C₄×C₈×C₁₃₉	—	2	4	no	—
61	#95×C₁₃₉	—	2	4	no	—
62	C₂⁴×C₁₃₉	—	2	1	no	—
63	C₂⁴×C₁₃₉	C₂×D₄	1	1	yes	characteristic
64	#41×C₁₃₉	—	2	4	no	—
65	#41×C₁₃₉	—	2	4	no	—
66	#41×C₁₃₉	—	2	4	no	—
67	#41×C₁₃₉	—	2	4	no	—
68	#41×C₁₃₉	—	4	2	no	—
69	#41×C₁₃₉	—	4	2	no	—
70	#41×C₁₃₉	—	4	2	no	—
71	#41×C₁₃₉	—	4	2	no	—
72	C₂×Q₈×C₁₃₉	—	2	1	no	—
73	C₂×Q₈×C₁₃₉	—	2	2	no	—
74	C₂×Q₈×C₁₃₉	—	2	2	no	—
75	C₂×Q₈×C₁₃₉	C₄²	1	2	yes	—
76	C₂×D₄×C₁₃₉	—	2	4	no	—
77	C₂×D₄×C₁₃₉	—	2	1	no	—
78	C₂×D₄×C₁₃₉	—	2	2	no	—
79	C₂×D₄×C₁₃₉	—	2	2	no	—
80	C₂×D₄×C₁₃₉	—	4	2	no	—
81	C₂×D₄×C₁₃₉	—	4	1	no	—
82	C₂×D₄×C₁₃₉	—	4	1	no	—
83	C₂×D₄×C₁₃₉	C₄²	1	2	yes	—
84	C₂²×C₄×C₁₃₉	—	2	1	no	—
85	C₂²×C₄×C₁₃₉	—	2	2	no	—
86	C₂²×C₄×C₁₃₉	—	2	4	no	—
87	C₂²×C₄×C₁₃₉	—	4	4	no	—
88	C₂²×C₄×C₁₃₉	—	4	1	no	—
89	C₂²×C₄×C₁₃₉	—	4	1	no	—
90	C₂²×C₄×C₁₃₉	—	4	1	no	—
91	C₂²×C₄×C₁₃₉	—	4	2	no	—
92	C₂²×C₄×C₁₃₉	—	4	1	no	—
93	C₂²×C₄×C₁₃₉	—	4	2	no	—
94	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	4	yes	—
95	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
101	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
102	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
103	M₁₆×C₁₃₉	—	2	4	no	—
104	M₁₆×C₁₃₉	—	2	4	no	—
105	M₁₆×C₁₃₉	—	2	4	no	—
106	M₁₆×C₁₃₉	C₂²⋊C₄	1	8	yes	complemented
107	C₂×C₈×C₁₃₉	—	2	4	no	—
108	C₂×C₈×C₁₃₉	—	2	4	no	—
109	C₂×C₈×C₁₃₉	—	2	4	no	—
110	C₄⋊C₄×C₁₃₉	—	2	4	no	—
111	C₄⋊C₄×C₁₃₉	—	2	4	no	—
112	C₄⋊C₄×C₁₃₉	—	4	2	no	—
113	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
114	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
115	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
116	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
117	C₄²×C₁₃₉	—	2	2	no	—
118	C₄²×C₁₃₉	—	2	2	no	—
119	C₄²×C₁₃₉	—	2	4	no	—
120	C₄²×C₁₃₉	—	2	4	no	—
121	C₄²×C₁₃₉	—	4	2	no	—
122	C₄²×C₁₃₉	—	4	2	no	—
123	C₂³×C₁₃₉	—	2	2	no	—
124	C₂³×C₁₃₉	—	4	2	no	—
125	C₂³×C₁₃₉	—	4	4	no	—
126	C₂³×C₁₃₉	—	4	1	no	—
127	C₂³×C₁₃₉	—	4	1	no	—
128	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
129	C₂³×C₁₃₉	C₄×D₄	1	2	yes	—
130	C₂³×C₁₃₉	#121	1	2	yes	—
131	C₂³×C₁₃₉	#124	1	1	yes	characteristic
132	C₂³×C₁₃₉	#127	1	1	yes	characteristic
133	Q₈×C₁₃₉	—	2	4	no	—
134	Q₈×C₁₃₉	—	4	2	no	—
135	D₄×C₁₃₉	—	2	4	no	—
136	D₄×C₁₃₉	—	4	4	no	—
137	D₄×C₁₃₉	—	4	4	no	—
138	D₄×C₁₃₉	—	4	2	no	—
139	C₂×C₄×C₁₃₉	—	2	4	no	—
140	C₂×C₄×C₁₃₉	—	2	2	no	—
141	C₂×C₄×C₁₃₉	—	2	4	no	—
142	C₂×C₄×C₁₃₉	—	4	2	no	—
143	C₂×C₄×C₁₃₉	—	4	4	no	—
144	C₂×C₄×C₁₃₉	—	4	4	no	—
145	C₂×C₄×C₁₃₉	—	4	1	no	—
146	C₂×C₄×C₁₃₉	—	4	2	no	—
147	C₂×C₄×C₁₃₉	—	4	1	no	—
148	C₂×C₄×C₁₃₉	—	4	4	no	—
149	C₂×C₄×C₁₃₉	—	4	4	no	—
150	C₂×C₄×C₁₃₉	—	4	4	no	—
151	C₂×C₄×C₁₃₉	—	4	4	no	—
152	C₂×C₄×C₁₃₉	—	8	4	no	—
153	C₂×C₄×C₁₃₉	C₂×C₄²	1	1	yes	characteristic
154	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
155	C₂×C₄×C₁₃₉	#117	1	2	yes	—
156	C₂×C₄×C₁₃₉	#117	1	1	yes	characteristic
157	C₂×C₄×C₁₃₉	C₄×D₄	1	2	yes	—
158	C₂×C₄×C₁₃₉	C₄×D₄	1	2	yes	—
159	C₂×C₄×C₁₃₉	C₄×D₄	1	2	yes	—
160	C₂×C₄×C₁₃₉	C₄×D₄	1	2	yes	—
161	C₂×C₄×C₁₃₉	C₄×D₄	1	2	yes	—
162	C₂×C₄×C₁₃₉	#120	1	1	yes	characteristic
163	C₂×C₄×C₁₃₉	#121	1	2	yes	—
164	C₂×C₄×C₁₃₉	#121	1	2	yes	—
165	C₂×C₄×C₁₃₉	#123	1	2	yes	—
166	C₂×C₄×C₁₃₉	#123	1	1	yes	characteristic
167	C₂×C₄×C₁₃₉	#124	1	2	yes	—
168	C₂×C₄×C₁₃₉	#126	1	2	yes	—
169	C₈×C₁₃₉	—	2	8	no	—
170	C₂²×C₁₃₉	—	2	2	no	—
171	C₂²×C₁₃₉	—	2	4	no	—
172	C₂²×C₁₃₉	—	4	1	no	—
173	C₂²×C₁₃₉	—	4	1	no	—
174	C₂²×C₁₃₉	—	4	2	no	—
175	C₂²×C₁₃₉	—	4	4	no	—
176	C₂²×C₁₃₉	—	4	2	no	—
177	C₂²×C₁₃₉	—	8	2	no	—
178	C₂²×C₁₃₉	—	8	2	no	—
179	C₂²×C₁₃₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
180	C₂²×C₁₃₉	#386	1	1	yes	characteristic
181	C₂²×C₁₃₉	#388	1	2	yes	—
182	C₂²×C₁₃₉	#390	1	1	yes	characteristic
183	C₂²×C₁₃₉	#390	1	2	yes	—
184	C₄×C₁₃₉	—	4	4	no	—
185	C₄×C₁₃₉	—	4	4	no	—
186	C₄×C₁₃₉	—	4	2	no	—
187	C₄×C₁₃₉	—	8	4	no	—
188	C₄×C₁₃₉	C₄×C₂²⋊C₄	1	2	yes	—
189	C₄×C₁₃₉	#386	1	2	yes	—
190	C₄×C₁₃₉	#388	1	2	yes	—
191	C₄×C₁₃₉	#388	1	2	yes	—
192	C₂×C₁₃₉	—	2	1	no	—
193	C₂×C₁₃₉	—	2	2	no	—
194	C₂×C₁₃₉	—	2	1	no	—
195	C₂×C₁₃₉	—	2	2	no	—
196	C₂×C₁₃₉	—	8	2	no	—
197	C₂×C₁₃₉	#1437	1	1	yes	characteristic
198	C₂×C₁₃₉	#1884	1	2	yes	—
199	#10959	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
200	C₁₃₉	#10959	1	1	yes	characteristic, direct product factor, Sylow
201	C₂×#421	C₂×C₁₃₉	1	2	yes	—
202	#2873	C₂×C₁₃₉	1	1	yes	characteristic, complemented
203	#2297	C₂×C₁₃₉	1	1	yes	characteristic
204	#1740	C₂×C₁₃₉	1	1	yes	characteristic, complemented
205	C₂×#339	C₂×C₁₃₉	1	2	yes	complemented
206	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
207	C₂²×M₁₆	C₂²×C₁₃₉	1	2	yes	—
208	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
209	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
210	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
211	#421	—	2	4	no	—
212	#421	C₄×C₁₃₉	1	8	yes	complemented
213	C₂×#104	—	2	4	no	—
214	#405	—	2	4	no	—
215	C₄×M₁₆	—	2	2	no	—
216	#391	C₄×C₁₃₉	1	2	yes	complemented
217	#390	C₄×C₁₃₉	1	2	yes	complemented
218	#386	—	2	2	no	—
219	C₄×C₂²⋊C₄	—	2	2	no	—
220	#342	—	2	2	no	—
221	#339	—	2	4	no	—
222	C₂×#41	—	2	2	no	—
223	C₂×#41	—	2	2	no	—
224	C₂×#41	—	2	2	no	—
225	C₂×#41	—	2	2	no	—
226	C₂×#41	—	2	2	no	—
227	C₂×#41	C₂×C₄×C₁₃₉	1	4	yes	—
228	C₂²×Q₈	C₂×C₄×C₁₃₉	1	1	yes	characteristic
229	C₂²×D₄	—	2	1	no	—
230	C₂²×D₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
231	C₂³×C₄	—	2	1	no	—
232	C₂³×C₄	—	2	1	no	—
233	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
234	C₂×M₁₆	—	2	2	no	—
235	C₂×M₁₆	—	2	2	no	—
236	C₂×M₁₆	—	2	2	no	—
237	C₂×M₁₆	C₂×C₄×C₁₃₉	1	4	yes	—
238	C₂×M₁₆	D₄×C₁₃₉	1	4	yes	—
239	C₂×M₁₆	D₄×C₁₃₉	1	4	yes	—
240	C₂²×C₈	—	2	2	no	—
241	#117	—	2	2	no	—
242	#117	—	2	2	no	—
243	#117	—	2	2	no	—
244	#117	—	2	2	no	—
245	#117	—	2	2	no	—
246	#117	C₂×C₄×C₁₃₉	1	4	yes	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	2	yes	—
249	C₂×C₂²⋊C₄	—	2	2	no	—
250	C₂×C₂²⋊C₄	—	2	4	no	—
251	C₂×C₂²⋊C₄	D₄×C₁₃₉	1	2	yes	—
252	C₂×C₄²	—	2	2	no	—
253	C₂×C₄²	—	2	2	no	—
254	C₂×C₄²	—	2	2	no	—
255	C₂×C₄²	—	2	1	no	—
256	C₂×C₄²	C₂×C₄×C₁₃₉	1	2	yes	—
257	C₂×C₄²	D₄×C₁₃₉	1	2	yes	—
258	#104	—	2	16	no	—
259	#97	—	2	4	no	—
260	C₄×C₈	—	2	4	no	—
261	#95	—	2	4	no	—
262	C₂⁴	—	2	1	no	—
263	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
264	#41	—	2	4	no	—
265	#41	—	2	4	no	—
266	#41	—	2	4	no	—
267	#41	—	2	4	no	—
268	#41	—	4	2	no	—
269	#41	—	4	2	no	—
270	#41	—	4	2	no	—
271	#41	—	4	2	no	—
272	C₂×Q₈	—	2	1	no	—
273	C₂×Q₈	—	2	2	no	—
274	C₂×Q₈	—	2	2	no	—
275	C₂×Q₈	C₄²×C₁₃₉	1	2	yes	—
276	C₂×D₄	—	2	4	no	—
277	C₂×D₄	—	2	1	no	—
278	C₂×D₄	—	2	2	no	—
279	C₂×D₄	—	2	2	no	—
280	C₂×D₄	—	4	2	no	—
281	C₂×D₄	—	4	1	no	—
282	C₂×D₄	—	4	1	no	—
283	C₂×D₄	C₄²×C₁₃₉	1	2	yes	—
284	C₂²×C₄	—	2	1	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	4	4	no	—
288	C₂²×C₄	—	4	1	no	—
289	C₂²×C₄	—	4	1	no	—
290	C₂²×C₄	—	4	1	no	—
291	C₂²×C₄	—	4	2	no	—
292	C₂²×C₄	—	4	1	no	—
293	C₂²×C₄	—	4	2	no	—
294	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	4	yes	—
295	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
296	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
297	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
298	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
299	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
300	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
301	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
302	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
303	M₁₆	—	2	4	no	—
304	M₁₆	—	2	4	no	—
305	M₁₆	—	2	4	no	—
306	M₁₆	C₂²⋊C₄×C₁₃₉	1	8	yes	complemented
307	C₂×C₈	—	2	4	no	—
308	C₂×C₈	—	2	4	no	—
309	C₂×C₈	—	2	4	no	—
310	C₄⋊C₄	—	2	4	no	—
311	C₄⋊C₄	—	2	4	no	—
312	C₄⋊C₄	—	4	2	no	—
313	C₂²⋊C₄	—	2	4	no	—
314	C₂²⋊C₄	—	2	4	no	—
315	C₂²⋊C₄	—	4	8	no	—
316	C₂²⋊C₄	—	4	2	no	—
317	C₄²	—	2	2	no	—
318	C₄²	—	2	2	no	—
319	C₄²	—	2	4	no	—
320	C₄²	—	2	4	no	—
321	C₄²	—	4	2	no	—
322	C₄²	—	4	2	no	—
323	C₂³	—	2	2	no	—
324	C₂³	—	4	2	no	—
325	C₂³	—	4	4	no	—
326	C₂³	—	4	1	no	—
327	C₂³	—	4	1	no	—
328	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
329	C₂³	C₄×D₄×C₁₃₉	1	2	yes	—
330	C₂³	#121×C₁₃₉	1	2	yes	—
331	C₂³	#124×C₁₃₉	1	1	yes	characteristic
332	C₂³	#127×C₁₃₉	1	1	yes	characteristic
333	Q₈	—	2	4	no	—
334	Q₈	—	4	2	no	—
335	D₄	—	2	4	no	—
336	D₄	—	4	4	no	—
337	D₄	—	4	4	no	—
338	D₄	—	4	2	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	4	no	—
344	C₂×C₄	—	4	4	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	4	no	—
349	C₂×C₄	—	4	4	no	—
350	C₂×C₄	—	4	4	no	—
351	C₂×C₄	—	4	4	no	—
352	C₂×C₄	—	8	4	no	—
353	C₂×C₄	C₂×C₄²×C₁₃₉	1	1	yes	characteristic
354	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
355	C₂×C₄	#117×C₁₃₉	1	2	yes	—
356	C₂×C₄	#117×C₁₃₉	1	1	yes	characteristic
357	C₂×C₄	C₄×D₄×C₁₃₉	1	2	yes	—
358	C₂×C₄	C₄×D₄×C₁₃₉	1	2	yes	—
359	C₂×C₄	C₄×D₄×C₁₃₉	1	2	yes	—
360	C₂×C₄	C₄×D₄×C₁₃₉	1	2	yes	—
361	C₂×C₄	C₄×D₄×C₁₃₉	1	2	yes	—
362	C₂×C₄	#120×C₁₃₉	1	1	yes	characteristic
363	C₂×C₄	#121×C₁₃₉	1	2	yes	—
364	C₂×C₄	#121×C₁₃₉	1	2	yes	—
365	C₂×C₄	#123×C₁₃₉	1	2	yes	—
366	C₂×C₄	#123×C₁₃₉	1	1	yes	characteristic
367	C₂×C₄	#124×C₁₃₉	1	2	yes	—
368	C₂×C₄	#126×C₁₃₉	1	2	yes	—
369	C₈	—	2	8	no	—
370	C₂²	—	2	2	no	—
371	C₂²	—	2	4	no	—
372	C₂²	—	4	1	no	—
373	C₂²	—	4	1	no	—
374	C₂²	—	4	2	no	—
375	C₂²	—	4	4	no	—
376	C₂²	—	4	2	no	—
377	C₂²	—	8	2	no	—
378	C₂²	—	8	2	no	—
379	C₂²	C₄×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
380	C₂²	#386×C₁₃₉	1	1	yes	characteristic
381	C₂²	#388×C₁₃₉	1	2	yes	—
382	C₂²	#390×C₁₃₉	1	1	yes	characteristic
383	C₂²	#390×C₁₃₉	1	2	yes	—
384	C₄	—	4	4	no	—
385	C₄	—	4	4	no	—
386	C₄	—	4	2	no	—
387	C₄	—	8	4	no	—
388	C₄	C₄×C₂²⋊C₄×C₁₃₉	1	2	yes	—
389	C₄	#386×C₁₃₉	1	2	yes	—
390	C₄	#388×C₁₃₉	1	2	yes	—
391	C₄	#388×C₁₃₉	1	2	yes	—
392	C₂	—	2	1	no	—
393	C₂	—	2	2	no	—
394	C₂	—	2	1	no	—
395	C₂	—	2	2	no	—
396	C₂	—	8	2	no	—
397	C₂	#1437×C₁₃₉	1	1	yes	characteristic
398	C₂	#1884×C₁₃₉	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₃₉	#120
commutator	C₂×C₄	C₂×C₄²×C₁₃₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₃₉
socle	C₂²×C₁₃₉	#386
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. #2873×C₁₃₉	C₂	semidirect
4. #1740×C₁₃₉	C₂	semidirect
5. C₂×#339×C₁₃₉	C₂	semidirect
12. #421×C₁₃₉	C₄	semidirect
16. #391×C₁₃₉	C₄	semidirect
17. #390×C₁₃₉	C₄	semidirect
106. M₁₆×C₁₃₉	C₂²⋊C₄	semidirect
199. #10959	C₁₃₉	direct (N × H)
200. C₁₃₉	#10959	direct (N × H)
202. #2873	C₂×C₁₃₉	semidirect
204. #1740	C₂×C₁₃₉	semidirect
205. C₂×#339	C₂×C₁₃₉	semidirect
212. #421	C₄×C₁₃₉	semidirect
216. #391	C₄×C₁₃₉	semidirect
217. #390	C₄×C₁₃₉	semidirect
306. M₁₆	C₂²⋊C₄×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#421×C₁₃₉	2
#2873×C₁₃₉	2
#2297×C₁₃₉	2
#1740×C₁₃₉	2
C₂×#339×C₁₃₉	2
#10959	139

Subgroups — C139×#10959 #48005555

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#10959 #48005555