Subgroups — C₁₃₉×#33870 #48028466

Order 35584.

558 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3341×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#3283×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2241×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2237×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2226×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2217×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2208×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2186×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	C₄×D₁₆×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	D₄×C₁₆×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#2138×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	C₂×#135×C₁₃₉	C₂²	1	2	yes	—
13	#555×C₁₃₉	—	2	1	no	—
14	#547×C₁₃₉	—	2	1	no	—
15	C₂×SD₃₂×C₁₃₉	C₂²	1	2	yes	—
16	C₂×D₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
17	C₂²×C₁₆×C₁₃₉	C₂²	1	2	yes	—
18	#500×C₁₃₉	C₂²	1	1	yes	characteristic
19	#494×C₁₃₉	C₂²	1	1	yes	characteristic
20	#482×C₁₃₉	—	2	2	no	—
21	#476×C₁₃₉	—	2	1	no	—
22	#467×C₁₃₉	C₂²	1	2	yes	—
23	#466×C₁₃₉	C₂²	1	2	yes	—
24	#461×C₁₃₉	—	2	1	no	—
25	#452×C₁₃₉	—	2	2	no	—
26	C₄×D₈×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₄×D₈×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₈×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
29	#427×C₁₃₉	C₂²	1	2	yes	—
30	#367×C₁₃₉	C₂²	1	2	yes	—
31	#366×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₄⋊C₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
33	#358×C₁₃₉	C₂²	1	2	yes	—
34	#358×C₁₃₉	C₂²	1	2	yes	—
35	#358×C₁₃₉	C₂²	1	2	yes	—
36	#357×C₁₃₉	C₂²	1	1	yes	characteristic
37	#357×C₁₃₉	C₂²	1	2	yes	—
38	#357×C₁₃₉	C₂²	1	1	yes	characteristic
39	C₂²⋊C₁₆×C₁₃₉	C₂²	1	2	yes	—
40	C₄×C₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
41	C₂×#41×C₁₃₉	—	2	2	no	—
42	#135×C₁₃₉	—	2	4	no	—
43	#135×C₁₃₉	—	4	2	no	—
44	C₂×Q₁₆×C₁₃₉	—	2	1	no	—
45	C₂×Q₁₆×C₁₃₉	C₂³	1	2	yes	—
46	C₂×SD₁₆×C₁₃₉	—	2	2	no	—
47	C₂×D₈×C₁₃₉	C₂³	1	1	yes	characteristic
48	C₂×D₈×C₁₃₉	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₁₃₉	C₂³	1	2	yes	—
50	C₄⋊Q₈×C₁₃₉	—	2	1	no	—
51	C₄⋊Q₈×C₁₃₉	—	2	1	no	—
52	#124×C₁₃₉	—	4	2	no	—
53	#123×C₁₃₉	—	4	2	no	—
54	C₂²⋊Q₈×C₁₃₉	—	2	2	no	—
55	#121×C₁₃₉	—	2	2	no	—
56	#121×C₁₃₉	—	4	1	no	—
57	#121×C₁₃₉	—	4	1	no	—
58	C₄×D₄×C₁₃₉	—	2	1	no	—
59	C₄×D₄×C₁₃₉	—	2	1	no	—
60	C₄×D₄×C₁₃₉	D₄	1	1	yes	characteristic
61	#117×C₁₃₉	—	2	2	no	—
62	#117×C₁₃₉	—	4	1	no	—
63	C₂×C₄⋊C₄×C₁₃₉	—	4	1	no	—
64	SD₃₂×C₁₃₉	—	4	2	no	—
65	D₁₆×C₁₃₉	—	2	2	no	—
66	C₂×C₁₆×C₁₃₉	—	4	2	no	—
67	C₂×C₁₆×C₁₃₉	C₂³	1	1	yes	characteristic
68	C₂×C₁₆×C₁₃₉	C₂³	1	2	yes	—
69	C₂×C₁₆×C₁₃₉	C₂³	1	1	yes	characteristic
70	#107×C₁₃₉	—	2	1	no	—
71	#107×C₁₃₉	C₂³	1	1	yes	characteristic
72	#107×C₁₃₉	C₂³	1	2	yes	—
73	#107×C₁₃₉	C₂³	1	1	yes	characteristic
74	#106×C₁₃₉	—	2	2	no	—
75	C₄⋊C₈×C₁₃₉	D₄	1	1	yes	characteristic
76	#103×C₁₃₉	—	2	2	no	—
77	#102×C₁₃₉	—	2	1	no	—
78	#102×C₁₃₉	—	2	1	no	—
79	#102×C₁₃₉	—	2	2	no	—
80	C₂²⋊C₈×C₁₃₉	D₄	1	2	yes	—
81	C₄×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
82	#41×C₁₃₉	—	4	4	no	—
83	#41×C₁₃₉	—	8	2	no	—
84	C₂×Q₈×C₁₃₉	—	2	2	no	—
85	C₂×Q₈×C₁₃₉	—	4	1	no	—
86	C₂×D₄×C₁₃₉	—	2	1	no	—
87	C₂×D₄×C₁₃₉	—	2	1	no	—
88	C₂×D₄×C₁₃₉	—	4	2	no	—
89	C₂×D₄×C₁₃₉	—	4	2	no	—
90	C₂×D₄×C₁₃₉	D₈	1	1	yes	characteristic
91	C₂²×C₄×C₁₃₉	—	4	1	no	—
92	C₂²×C₄×C₁₃₉	—	4	2	no	—
93	C₂²×C₄×C₁₃₉	—	4	1	no	—
94	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
95	Q₁₆×C₁₃₉	—	2	2	no	—
96	Q₁₆×C₁₃₉	—	2	2	no	—
97	Q₁₆×C₁₃₉	—	8	1	no	—
98	SD₁₆×C₁₃₉	—	4	4	no	—
99	D₈×C₁₃₉	—	2	1	no	—
100	D₈×C₁₃₉	—	2	1	no	—
101	D₈×C₁₃₉	—	2	1	no	—
102	D₈×C₁₃₉	#41	1	2	yes	—
103	C₂×C₈×C₁₃₉	—	2	2	no	—
104	C₂×C₈×C₁₃₉	—	2	2	no	—
105	C₂×C₈×C₁₃₉	C₂×D₄	1	1	yes	characteristic
106	C₂×C₈×C₁₃₉	C₂×D₄	1	2	yes	—
107	C₂×C₈×C₁₃₉	C₂⁴	1	1	yes	characteristic
108	C₄⋊C₄×C₁₃₉	—	2	1	no	—
109	C₄⋊C₄×C₁₃₉	—	2	1	no	—
110	C₄⋊C₄×C₁₃₉	—	2	2	no	—
111	C₄⋊C₄×C₁₃₉	—	4	1	no	—
112	C₄⋊C₄×C₁₃₉	—	4	2	no	—
113	C₄⋊C₄×C₁₃₉	—	4	1	no	—
114	C₄⋊C₄×C₁₃₉	—	4	1	no	—
115	C₄⋊C₄×C₁₃₉	D₈	1	1	yes	characteristic
116	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
117	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
118	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
119	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
120	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
121	C₂²⋊C₄×C₁₃₉	D₈	1	2	yes	—
122	C₄²×C₁₃₉	—	4	2	no	—
123	C₄²×C₁₃₉	C₂×D₄	1	1	yes	characteristic
124	C₁₆×C₁₃₉	—	2	1	no	—
125	C₁₆×C₁₃₉	—	2	1	no	—
126	C₁₆×C₁₃₉	—	2	2	no	—
127	C₂³×C₁₃₉	—	4	1	no	—
128	C₂³×C₁₃₉	—	4	1	no	—
129	C₂³×C₁₃₉	C₂×D₈	1	2	yes	—
130	Q₈×C₁₃₉	—	4	2	no	—
131	Q₈×C₁₃₉	—	4	2	no	—
132	Q₈×C₁₃₉	—	16	1	no	—
133	D₄×C₁₃₉	—	2	2	no	—
134	D₄×C₁₃₉	—	2	2	no	—
135	D₄×C₁₃₉	—	4	1	no	—
136	D₄×C₁₃₉	—	4	1	no	—
137	D₄×C₁₃₉	—	4	1	no	—
138	D₄×C₁₃₉	—	8	4	no	—
139	D₄×C₁₃₉	—	16	2	no	—
140	C₂×C₄×C₁₃₉	—	2	2	no	—
141	C₂×C₄×C₁₃₉	—	2	2	no	—
142	C₂×C₄×C₁₃₉	—	4	1	no	—
143	C₂×C₄×C₁₃₉	—	4	2	no	—
144	C₂×C₄×C₁₃₉	—	4	1	no	—
145	C₂×C₄×C₁₃₉	—	4	2	no	—
146	C₂×C₄×C₁₃₉	—	8	4	no	—
147	C₂×C₄×C₁₃₉	—	8	2	no	—
148	C₂×C₄×C₁₃₉	—	8	2	no	—
149	C₂×C₄×C₁₃₉	C₂×D₈	1	2	yes	—
150	C₂×C₄×C₁₃₉	C₂×D₈	1	1	yes	characteristic
151	C₂×C₄×C₁₃₉	C₂×D₈	1	1	yes	characteristic
152	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
153	C₈×C₁₃₉	—	2	2	no	—
154	C₈×C₁₃₉	—	2	1	no	—
155	C₈×C₁₃₉	C₂×#41	1	1	yes	characteristic
156	C₈×C₁₃₉	H(5,𝔽₂)	1	1	yes	characteristic
157	C₂²×C₁₃₉	—	2	2	no	—
158	C₂²×C₁₃₉	—	2	2	no	—
159	C₂²×C₁₃₉	—	2	2	no	—
160	C₂²×C₁₃₉	—	4	2	no	—
161	C₂²×C₁₃₉	—	8	1	no	—
162	C₂²×C₁₃₉	—	8	1	no	—
163	C₂²×C₁₃₉	—	8	1	no	—
164	C₂²×C₁₃₉	—	8	1	no	—
165	C₂²×C₁₃₉	—	8	1	no	—
166	C₂²×C₁₃₉	C₂²×D₈	1	1	yes	characteristic
167	C₄×C₁₃₉	—	2	1	no	—
168	C₄×C₁₃₉	—	2	2	no	—
169	C₄×C₁₃₉	—	8	1	no	—
170	C₄×C₁₃₉	—	8	1	no	—
171	C₄×C₁₃₉	—	8	2	no	—
172	C₄×C₁₃₉	—	8	2	no	—
173	C₄×C₁₃₉	#508	1	2	yes	—
174	C₄×C₁₃₉	#546	1	1	yes	characteristic
175	C₄×C₁₃₉	#577	1	1	yes	characteristic
176	C₂×C₁₃₉	—	4	2	no	—
177	C₂×C₁₃₉	—	8	2	no	—
178	C₂×C₁₃₉	—	16	1	no	—
179	C₂×C₁₃₉	#3294	1	1	yes	characteristic
180	C₂×C₁₃₉	C₂×#508	1	1	yes	characteristic
181	C₂×C₁₃₉	#3416	1	1	yes	characteristic
182	#33870	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
183	C₁₃₉	#33870	1	1	yes	characteristic, direct product factor, Sylow
184	#3341	C₂×C₁₃₉	1	1	yes	characteristic, complemented
185	#3283	C₂×C₁₃₉	1	1	yes	characteristic, complemented
186	#2241	C₂×C₁₃₉	1	1	yes	characteristic, complemented
187	#2237	C₂×C₁₃₉	1	2	yes	complemented
188	#2226	C₂×C₁₃₉	1	1	yes	characteristic, complemented
189	#2217	C₂×C₁₃₉	1	2	yes	complemented
190	#2208	C₂×C₁₃₉	1	1	yes	characteristic, complemented
191	#2186	C₂×C₁₃₉	1	2	yes	complemented
192	C₄×D₁₆	C₂×C₁₃₉	1	1	yes	characteristic, complemented
193	D₄×C₁₆	C₂×C₁₃₉	1	1	yes	characteristic, complemented
194	#2138	C₂×C₁₃₉	1	2	yes	complemented
195	C₂×#135	C₂²×C₁₃₉	1	2	yes	—
196	#555	—	2	1	no	—
197	#547	—	2	1	no	—
198	C₂×SD₃₂	C₂²×C₁₃₉	1	2	yes	—
199	C₂×D₁₆	C₂²×C₁₃₉	1	1	yes	characteristic
200	C₂²×C₁₆	C₂²×C₁₃₉	1	2	yes	—
201	#500	C₂²×C₁₃₉	1	1	yes	characteristic
202	#494	C₂²×C₁₃₉	1	1	yes	characteristic
203	#482	—	2	2	no	—
204	#476	—	2	1	no	—
205	#467	C₂²×C₁₃₉	1	2	yes	—
206	#466	C₂²×C₁₃₉	1	2	yes	—
207	#461	—	2	1	no	—
208	#452	—	2	2	no	—
209	C₄×D₈	C₂²×C₁₃₉	1	1	yes	characteristic
210	C₄×D₈	C₂²×C₁₃₉	1	1	yes	characteristic
211	C₈×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
212	#427	C₂²×C₁₃₉	1	2	yes	—
213	#367	C₂²×C₁₃₉	1	2	yes	—
214	#366	C₂²×C₁₃₉	1	1	yes	characteristic
215	C₄⋊C₁₆	C₂²×C₁₃₉	1	1	yes	characteristic
216	#358	C₂²×C₁₃₉	1	2	yes	—
217	#358	C₂²×C₁₃₉	1	2	yes	—
218	#358	C₂²×C₁₃₉	1	2	yes	—
219	#357	C₂²×C₁₃₉	1	1	yes	characteristic
220	#357	C₂²×C₁₃₉	1	2	yes	—
221	#357	C₂²×C₁₃₉	1	1	yes	characteristic
222	C₂²⋊C₁₆	C₂²×C₁₃₉	1	2	yes	—
223	C₄×C₁₆	C₂²×C₁₃₉	1	1	yes	characteristic
224	C₂×#41	—	2	2	no	—
225	#135	—	2	4	no	—
226	#135	—	4	2	no	—
227	C₂×Q₁₆	—	2	1	no	—
228	C₂×Q₁₆	C₂³×C₁₃₉	1	2	yes	—
229	C₂×SD₁₆	—	2	2	no	—
230	C₂×D₈	C₂³×C₁₃₉	1	1	yes	characteristic
231	C₂×D₈	C₂³×C₁₃₉	1	1	yes	characteristic
232	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
233	C₄⋊Q₈	—	2	1	no	—
234	C₄⋊Q₈	—	2	1	no	—
235	#124	—	4	2	no	—
236	#123	—	4	2	no	—
237	C₂²⋊Q₈	—	2	2	no	—
238	#121	—	2	2	no	—
239	#121	—	4	1	no	—
240	#121	—	4	1	no	—
241	C₄×D₄	—	2	1	no	—
242	C₄×D₄	—	2	1	no	—
243	C₄×D₄	D₄×C₁₃₉	1	1	yes	characteristic
244	#117	—	2	2	no	—
245	#117	—	4	1	no	—
246	C₂×C₄⋊C₄	—	4	1	no	—
247	SD₃₂	—	4	2	no	—
248	D₁₆	—	2	2	no	—
249	C₂×C₁₆	—	4	2	no	—
250	C₂×C₁₆	C₂³×C₁₃₉	1	1	yes	characteristic
251	C₂×C₁₆	C₂³×C₁₃₉	1	1	yes	characteristic
252	C₂×C₁₆	C₂³×C₁₃₉	1	2	yes	—
253	#107	—	2	1	no	—
254	#107	C₂³×C₁₃₉	1	1	yes	characteristic
255	#107	C₂³×C₁₃₉	1	2	yes	—
256	#107	C₂³×C₁₃₉	1	1	yes	characteristic
257	#106	—	2	2	no	—
258	C₄⋊C₈	D₄×C₁₃₉	1	1	yes	characteristic
259	#103	—	2	2	no	—
260	#102	—	2	1	no	—
261	#102	—	2	1	no	—
262	#102	—	2	2	no	—
263	C₂²⋊C₈	D₄×C₁₃₉	1	2	yes	—
264	C₄×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
265	#41	—	4	4	no	—
266	#41	—	8	2	no	—
267	C₂×Q₈	—	2	2	no	—
268	C₂×Q₈	—	4	1	no	—
269	C₂×D₄	—	2	1	no	—
270	C₂×D₄	—	2	1	no	—
271	C₂×D₄	—	4	2	no	—
272	C₂×D₄	—	4	2	no	—
273	C₂×D₄	D₈×C₁₃₉	1	1	yes	characteristic
274	C₂²×C₄	—	4	1	no	—
275	C₂²×C₄	—	4	2	no	—
276	C₂²×C₄	—	4	1	no	—
277	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
278	Q₁₆	—	2	2	no	—
279	Q₁₆	—	2	2	no	—
280	Q₁₆	—	8	1	no	—
281	SD₁₆	—	4	4	no	—
282	D₈	—	2	1	no	—
283	D₈	—	2	1	no	—
284	D₈	—	2	1	no	—
285	D₈	#41×C₁₃₉	1	2	yes	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	C₂×D₄×C₁₃₉	1	1	yes	characteristic
289	C₂×C₈	C₂×D₄×C₁₃₉	1	2	yes	—
290	C₂×C₈	C₂⁴×C₁₃₉	1	1	yes	characteristic
291	C₄⋊C₄	—	2	1	no	—
292	C₄⋊C₄	—	2	1	no	—
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	—	4	1	no	—
295	C₄⋊C₄	—	4	2	no	—
296	C₄⋊C₄	—	4	1	no	—
297	C₄⋊C₄	—	4	1	no	—
298	C₄⋊C₄	D₈×C₁₃₉	1	1	yes	characteristic
299	C₂²⋊C₄	—	4	2	no	—
300	C₂²⋊C₄	—	4	2	no	—
301	C₂²⋊C₄	—	4	2	no	—
302	C₂²⋊C₄	—	4	1	no	—
303	C₂²⋊C₄	—	4	1	no	—
304	C₂²⋊C₄	D₈×C₁₃₉	1	2	yes	—
305	C₄²	—	4	2	no	—
306	C₄²	C₂×D₄×C₁₃₉	1	1	yes	characteristic
307	C₁₆	—	2	1	no	—
308	C₁₆	—	2	1	no	—
309	C₁₆	—	2	2	no	—
310	C₂³	—	4	1	no	—
311	C₂³	—	4	1	no	—
312	C₂³	C₂×D₈×C₁₃₉	1	2	yes	—
313	Q₈	—	4	2	no	—
314	Q₈	—	4	2	no	—
315	Q₈	—	16	1	no	—
316	D₄	—	2	2	no	—
317	D₄	—	2	2	no	—
318	D₄	—	4	1	no	—
319	D₄	—	4	1	no	—
320	D₄	—	4	1	no	—
321	D₄	—	8	4	no	—
322	D₄	—	16	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	4	1	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	4	1	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	8	4	no	—
330	C₂×C₄	—	8	2	no	—
331	C₂×C₄	—	8	2	no	—
332	C₂×C₄	C₂×D₈×C₁₃₉	1	2	yes	—
333	C₂×C₄	C₂×D₈×C₁₃₉	1	1	yes	characteristic
334	C₂×C₄	C₂×D₈×C₁₃₉	1	1	yes	characteristic
335	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
336	C₈	—	2	2	no	—
337	C₈	—	2	1	no	—
338	C₈	C₂×#41×C₁₃₉	1	1	yes	characteristic
339	C₈	H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
340	C₂²	—	2	2	no	—
341	C₂²	—	2	2	no	—
342	C₂²	—	2	2	no	—
343	C₂²	—	4	2	no	—
344	C₂²	—	8	1	no	—
345	C₂²	—	8	1	no	—
346	C₂²	—	8	1	no	—
347	C₂²	—	8	1	no	—
348	C₂²	—	8	1	no	—
349	C₂²	C₂²×D₈×C₁₃₉	1	1	yes	characteristic
350	C₄	—	2	2	no	—
351	C₄	—	2	1	no	—
352	C₄	—	8	2	no	—
353	C₄	—	8	1	no	—
354	C₄	—	8	1	no	—
355	C₄	—	8	2	no	—
356	C₄	#508×C₁₃₉	1	2	yes	—
357	C₄	#546×C₁₃₉	1	1	yes	characteristic
358	C₄	#577×C₁₃₉	1	1	yes	characteristic
359	C₂	—	4	2	no	—
360	C₂	—	8	2	no	—
361	C₂	—	16	1	no	—
362	C₂	#3294×C₁₃₉	1	1	yes	characteristic
363	C₂	C₂×#508×C₁₃₉	1	1	yes	characteristic
364	C₂	#3416×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₉	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃₉
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₉ ◁ C₄×D₄×C₁₃₉ ◁ C₈×D₄×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. #3341×C₁₃₉	C₂	semidirect
2. #3283×C₁₃₉	C₂	semidirect
3. #2241×C₁₃₉	C₂	semidirect
4. #2237×C₁₃₉	C₂	semidirect
5. #2226×C₁₃₉	C₂	semidirect
6. #2217×C₁₃₉	C₂	semidirect
7. #2208×C₁₃₉	C₂	semidirect
8. #2186×C₁₃₉	C₂	semidirect
9. C₄×D₁₆×C₁₃₉	C₂	semidirect
10. D₄×C₁₆×C₁₃₉	C₂	semidirect
11. #2138×C₁₃₉	C₂	semidirect
182. #33870	C₁₃₉	direct (N × H)
183. C₁₃₉	#33870	direct (N × H)
184. #3341	C₂×C₁₃₉	semidirect
185. #3283	C₂×C₁₃₉	semidirect
186. #2241	C₂×C₁₃₉	semidirect
187. #2237	C₂×C₁₃₉	semidirect
188. #2226	C₂×C₁₃₉	semidirect
189. #2217	C₂×C₁₃₉	semidirect
190. #2208	C₂×C₁₃₉	semidirect
191. #2186	C₂×C₁₃₉	semidirect
192. C₄×D₁₆	C₂×C₁₃₉	semidirect
193. D₄×C₁₆	C₂×C₁₃₉	semidirect
194. #2138	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#3341×C₁₃₉	2
#3283×C₁₃₉	2
#2241×C₁₃₉	2
#2237×C₁₃₉	2
#2226×C₁₃₉	2
#2217×C₁₃₉	2
#2208×C₁₃₉	2
#2186×C₁₃₉	2
C₄×D₁₆×C₁₃₉	2
D₄×C₁₆×C₁₃₉	2
#2138×C₁₃₉	2
#33870	139

Subgroups — C139×#33870 #48028466

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#33870 #48028466