Subgroups — C₁₃₉×#12740 #48007336

Order 35584.

914 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#575×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	#2148×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	#2143×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	C₂×#349×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#1811×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#41×C₁₃₉	—	2	1	no	—
7	#575×C₁₃₉	—	2	4	no	—
8	#575×C₁₃₉	—	2	2	no	—
9	#575×C₁₃₉	C₄	1	4	yes	—
10	C₂×#137×C₁₃₉	—	2	2	no	—
11	C₂×AGL(1,ℤ/8)×C₁₃₉	—	2	2	no	—
12	C₂×#135×C₁₃₉	—	2	1	no	—
13	C₂×#135×C₁₃₉	C₂²	1	2	yes	—
14	C₂²×M₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
15	C₂×M₃₂×C₁₃₉	C₂²	1	2	yes	complemented
16	C₂×#108×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
17	C₂×#108×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
18	#407×C₁₃₉	—	2	1	no	—
19	#362×C₁₃₉	—	2	2	no	—
20	#361×C₁₃₉	—	2	2	no	—
21	#359×C₁₃₉	—	2	4	no	—
22	#349×C₁₃₉	—	2	2	no	—
23	#341×C₁₃₉	—	2	1	no	—
24	C₂×#41×C₁₃₉	—	2	2	no	—
25	C₂×#41×C₁₃₉	—	2	4	no	—
26	C₂×#41×C₁₃₉	—	2	4	no	—
27	C₂×#41×C₁₃₉	—	2	2	no	—
28	C₂×#41×C₁₃₉	—	4	1	no	—
29	C₂×#41×C₁₃₉	—	4	2	no	—
30	C₂×#41×C₁₃₉	—	4	2	no	—
31	C₂×#41×C₁₃₉	—	4	1	no	—
32	C₂²×Q₈×C₁₃₉	—	2	1	no	—
33	C₂²×D₄×C₁₃₉	—	2	1	no	—
34	C₂²×D₄×C₁₃₉	—	4	1	no	—
35	C₂³×C₄×C₁₃₉	—	4	1	no	—
36	C₂³×C₄×C₁₃₉	D₄	1	1	yes	characteristic
37	#137×C₁₃₉	—	2	8	no	—
38	#137×C₁₃₉	—	2	8	no	—
39	AGL(1,ℤ/8)×C₁₃₉	—	2	8	no	—
40	AGL(1,ℤ/8)×C₁₃₉	—	2	8	no	—
41	#135×C₁₃₉	—	2	4	no	—
42	#135×C₁₃₉	—	2	4	no	—
43	#135×C₁₃₉	—	2	2	no	—
44	#135×C₁₃₉	—	2	2	no	—
45	#135×C₁₃₉	C₂×C₄	1	4	yes	—
46	#135×C₁₃₉	D₄	1	4	yes	—
47	C₂×Q₁₆×C₁₃₉	—	2	1	no	—
48	C₂×Q₁₆×C₁₃₉	D₄	1	2	yes	—
49	C₂×SD₁₆×C₁₃₉	—	2	2	no	—
50	C₂×SD₁₆×C₁₃₉	—	2	2	no	—
51	C₂×D₈×C₁₃₉	—	2	1	no	—
52	C₂×D₈×C₁₃₉	D₄	1	2	yes	—
53	C₂×M₁₆×C₁₃₉	—	2	2	no	—
54	C₂×M₁₆×C₁₃₉	—	2	2	no	—
55	C₂×M₁₆×C₁₃₉	—	2	1	no	—
56	C₂×M₁₆×C₁₃₉	—	2	1	no	—
57	C₂×M₁₆×C₁₃₉	C₂×C₄	1	2	yes	—
58	C₂×M₁₆×C₁₃₉	D₄	1	2	yes	—
59	C₂²×C₈×C₁₃₉	D₄	1	1	yes	characteristic
60	C₂²×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
61	M₃₂×C₁₃₉	—	2	2	no	—
62	M₃₂×C₁₃₉	—	2	2	no	—
63	C₂×C₁₆×C₁₃₉	—	2	2	no	—
64	#108×C₁₃₉	—	2	2	no	—
65	#108×C₁₃₉	—	2	2	no	—
66	C₂²⋊C₈×C₁₃₉	—	4	2	no	—
67	C₂⁴×C₁₃₉	—	4	1	no	—
68	C₂⁴×C₁₃₉	SD₁₆	1	1	yes	characteristic
69	#41×C₁₃₉	—	2	8	no	—
70	#41×C₁₃₉	—	2	4	no	—
71	#41×C₁₃₉	—	2	4	no	—
72	#41×C₁₃₉	—	4	4	no	—
73	#41×C₁₃₉	—	4	4	no	—
74	#41×C₁₃₉	—	4	4	no	—
75	#41×C₁₃₉	—	4	4	no	—
76	#41×C₁₃₉	—	4	4	no	—
77	#41×C₁₃₉	—	4	2	no	—
78	#41×C₁₃₉	—	4	2	no	—
79	C₂×Q₈×C₁₃₉	—	2	4	no	—
80	C₂×Q₈×C₁₃₉	—	2	2	no	—
81	C₂×Q₈×C₁₃₉	—	4	1	no	—
82	C₂×Q₈×C₁₃₉	—	4	2	no	—
83	C₂×D₄×C₁₃₉	—	2	4	no	—
84	C₂×D₄×C₁₃₉	—	2	2	no	—
85	C₂×D₄×C₁₃₉	—	4	1	no	—
86	C₂×D₄×C₁₃₉	—	4	2	no	—
87	C₂×D₄×C₁₃₉	—	4	4	no	—
88	C₂×D₄×C₁₃₉	—	4	2	no	—
89	C₂×D₄×C₁₃₉	—	4	4	no	—
90	C₂×D₄×C₁₃₉	—	4	2	no	—
91	C₂²×C₄×C₁₃₉	—	2	1	no	—
92	C₂²×C₄×C₁₃₉	—	2	1	no	—
93	C₂²×C₄×C₁₃₉	—	2	1	no	—
94	C₂²×C₄×C₁₃₉	—	2	1	no	—
95	C₂²×C₄×C₁₃₉	—	4	2	no	—
96	C₂²×C₄×C₁₃₉	—	4	4	no	—
97	C₂²×C₄×C₁₃₉	—	4	4	no	—
98	C₂²×C₄×C₁₃₉	—	4	1	no	—
99	C₂²×C₄×C₁₃₉	—	4	2	no	—
100	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	2	yes	—
101	C₂²×C₄×C₁₃₉	D₈	1	2	yes	—
102	C₂²×C₄×C₁₃₉	SD₁₆	1	1	yes	characteristic
103	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
104	Q₁₆×C₁₃₉	—	2	4	no	—
105	Q₁₆×C₁₃₉	—	2	2	no	—
106	Q₁₆×C₁₃₉	C₂²⋊C₄	1	4	yes	—
107	SD₁₆×C₁₃₉	—	2	8	no	—
108	SD₁₆×C₁₃₉	—	2	4	no	—
109	SD₁₆×C₁₃₉	—	2	4	no	—
110	D₈×C₁₃₉	—	2	4	no	—
111	D₈×C₁₃₉	—	2	2	no	—
112	D₈×C₁₃₉	C₂²⋊C₄	1	4	yes	—
113	M₁₆×C₁₃₉	—	2	4	no	—
114	M₁₆×C₁₃₉	—	2	4	no	—
115	M₁₆×C₁₃₉	—	4	1	no	—
116	M₁₆×C₁₃₉	—	4	1	no	—
117	M₁₆×C₁₃₉	—	4	1	no	—
118	M₁₆×C₁₃₉	—	4	1	no	—
119	C₂×C₈×C₁₃₉	—	2	1	no	—
120	C₂×C₈×C₁₃₉	—	2	1	no	—
121	C₂×C₈×C₁₃₉	—	4	1	no	—
122	C₂×C₈×C₁₃₉	—	4	1	no	—
123	C₂×C₈×C₁₃₉	C₂²⋊C₄	1	2	yes	—
124	C₂×C₈×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₈×C₁₃₉	C₂×D₄	1	2	yes	—
126	C₂×C₈×C₁₃₉	C₂×D₄	1	2	yes	—
127	C₂×C₈×C₁₃₉	C₂×D₄	1	1	yes	characteristic
128	C₁₆×C₁₃₉	—	4	2	no	—
129	C₂³×C₁₃₉	—	2	1	no	—
130	C₂³×C₁₃₉	—	2	1	no	—
131	C₂³×C₁₃₉	—	4	4	no	—
132	C₂³×C₁₃₉	—	4	2	no	—
133	C₂³×C₁₃₉	—	8	1	no	—
134	C₂³×C₁₃₉	—	8	4	no	—
135	C₂³×C₁₃₉	#102	1	2	yes	—
136	C₂³×C₁₃₉	C₂×SD₁₆	1	1	yes	characteristic
137	Q₈×C₁₃₉	—	2	4	no	—
138	Q₈×C₁₃₉	—	4	4	no	—
139	Q₈×C₁₃₉	—	4	2	no	—
140	D₄×C₁₃₉	—	2	4	no	—
141	D₄×C₁₃₉	—	4	4	no	—
142	D₄×C₁₃₉	—	4	8	no	—
143	D₄×C₁₃₉	—	4	4	no	—
144	D₄×C₁₃₉	—	4	4	no	—
145	D₄×C₁₃₉	—	4	2	no	—
146	C₂×C₄×C₁₃₉	—	2	1	no	—
147	C₂×C₄×C₁₃₉	—	2	1	no	—
148	C₂×C₄×C₁₃₉	—	2	2	no	—
149	C₂×C₄×C₁₃₉	—	2	2	no	—
150	C₂×C₄×C₁₃₉	—	2	2	no	—
151	C₂×C₄×C₁₃₉	—	2	2	no	—
152	C₂×C₄×C₁₃₉	—	4	8	no	—
153	C₂×C₄×C₁₃₉	—	4	4	no	—
154	C₂×C₄×C₁₃₉	—	4	2	no	—
155	C₂×C₄×C₁₃₉	—	4	4	no	—
156	C₂×C₄×C₁₃₉	—	4	4	no	—
157	C₂×C₄×C₁₃₉	#102	1	2	yes	—
158	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₁₃₉	#120	1	1	yes	characteristic
160	C₂×C₄×C₁₃₉	#120	1	1	yes	characteristic
161	C₂×C₄×C₁₃₉	C₂×D₈	1	1	yes	characteristic
162	C₂×C₄×C₁₃₉	AGL(1,ℤ/8)	1	1	yes	characteristic
163	C₂×C₄×C₁₃₉	AGL(1,ℤ/8)	1	1	yes	characteristic
164	C₈×C₁₃₉	—	2	2	no	—
165	C₈×C₁₃₉	—	8	1	no	—
166	C₈×C₁₃₉	—	8	1	no	—
167	C₈×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
168	C₈×C₁₃₉	#120	1	2	yes	—
169	C₂²×C₁₃₉	—	2	2	no	—
170	C₂²×C₁₃₉	—	4	1	no	—
171	C₂²×C₁₃₉	—	4	2	no	—
172	C₂²×C₁₃₉	—	4	2	no	—
173	C₂²×C₁₃₉	—	4	4	no	—
174	C₂²×C₁₃₉	—	8	1	no	—
175	C₂²×C₁₃₉	—	8	4	no	—
176	C₂²×C₁₃₉	—	8	8	no	—
177	C₂²×C₁₃₉	C₂×#102	1	1	yes	characteristic
178	C₂²×C₁₃₉	#450	1	1	yes	characteristic
179	C₂²×C₁₃₉	#450	1	1	yes	characteristic
180	C₄×C₁₃₉	—	2	2	no	—
181	C₄×C₁₃₉	—	4	4	no	—
182	C₄×C₁₃₉	#379	1	1	yes	characteristic
183	C₄×C₁₃₉	#418	1	1	yes	characteristic
184	C₄×C₁₃₉	#447	1	1	yes	characteristic
185	C₄×C₁₃₉	#447	1	1	yes	characteristic
186	C₂×C₁₃₉	—	2	1	no	—
187	C₂×C₁₃₉	—	2	1	no	—
188	C₂×C₁₃₉	—	2	1	no	—
189	C₂×C₁₃₉	—	4	2	no	—
190	C₂×C₁₃₉	—	8	4	no	—
191	C₂×C₁₃₉	#1786	1	1	yes	characteristic
192	#12740	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
193	C₁₃₉	#12740	1	1	yes	characteristic, direct product factor, Sylow
194	C₂×#575	C₂×C₁₃₉	1	1	yes	characteristic
195	#2148	C₂×C₁₃₉	1	2	yes	complemented
196	#2143	C₂×C₁₃₉	1	2	yes	complemented
197	C₂×#349	C₂×C₁₃₉	1	1	yes	characteristic, complemented
198	#1811	C₂×C₁₃₉	1	1	yes	characteristic, complemented
199	C₂²×#41	—	2	1	no	—
200	#575	—	2	4	no	—
201	#575	—	2	2	no	—
202	#575	C₄×C₁₃₉	1	4	yes	—
203	C₂×#137	—	2	2	no	—
204	C₂×AGL(1,ℤ/8)	—	2	2	no	—
205	C₂×#135	—	2	1	no	—
206	C₂×#135	C₂²×C₁₃₉	1	2	yes	—
207	C₂²×M₁₆	C₂²×C₁₃₉	1	1	yes	characteristic
208	C₂×M₃₂	C₂²×C₁₃₉	1	2	yes	complemented
209	C₂×#108	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
210	C₂×#108	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
211	#407	—	2	1	no	—
212	#362	—	2	2	no	—
213	#361	—	2	2	no	—
214	#359	—	2	4	no	—
215	#349	—	2	2	no	—
216	#341	—	2	1	no	—
217	C₂×#41	—	2	2	no	—
218	C₂×#41	—	2	4	no	—
219	C₂×#41	—	2	4	no	—
220	C₂×#41	—	2	2	no	—
221	C₂×#41	—	4	1	no	—
222	C₂×#41	—	4	2	no	—
223	C₂×#41	—	4	2	no	—
224	C₂×#41	—	4	1	no	—
225	C₂²×Q₈	—	2	1	no	—
226	C₂²×D₄	—	2	1	no	—
227	C₂²×D₄	—	4	1	no	—
228	C₂³×C₄	—	4	1	no	—
229	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
230	#137	—	2	8	no	—
231	#137	—	2	8	no	—
232	AGL(1,ℤ/8)	—	2	8	no	—
233	AGL(1,ℤ/8)	—	2	8	no	—
234	#135	—	2	4	no	—
235	#135	—	2	4	no	—
236	#135	—	2	2	no	—
237	#135	—	2	2	no	—
238	#135	C₂×C₄×C₁₃₉	1	4	yes	—
239	#135	D₄×C₁₃₉	1	4	yes	—
240	C₂×Q₁₆	—	2	1	no	—
241	C₂×Q₁₆	D₄×C₁₃₉	1	2	yes	—
242	C₂×SD₁₆	—	2	2	no	—
243	C₂×SD₁₆	—	2	2	no	—
244	C₂×D₈	—	2	1	no	—
245	C₂×D₈	D₄×C₁₃₉	1	2	yes	—
246	C₂×M₁₆	—	2	2	no	—
247	C₂×M₁₆	—	2	2	no	—
248	C₂×M₁₆	—	2	1	no	—
249	C₂×M₁₆	—	2	1	no	—
250	C₂×M₁₆	C₂×C₄×C₁₃₉	1	2	yes	—
251	C₂×M₁₆	D₄×C₁₃₉	1	2	yes	—
252	C₂²×C₈	D₄×C₁₃₉	1	1	yes	characteristic
253	C₂²×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
254	M₃₂	—	2	2	no	—
255	M₃₂	—	2	2	no	—
256	C₂×C₁₆	—	2	2	no	—
257	#108	—	2	2	no	—
258	#108	—	2	2	no	—
259	C₂²⋊C₈	—	4	2	no	—
260	C₂⁴	—	4	1	no	—
261	C₂⁴	SD₁₆×C₁₃₉	1	1	yes	characteristic
262	#41	—	2	8	no	—
263	#41	—	2	4	no	—
264	#41	—	2	4	no	—
265	#41	—	4	4	no	—
266	#41	—	4	4	no	—
267	#41	—	4	4	no	—
268	#41	—	4	4	no	—
269	#41	—	4	4	no	—
270	#41	—	4	2	no	—
271	#41	—	4	2	no	—
272	C₂×Q₈	—	2	4	no	—
273	C₂×Q₈	—	2	2	no	—
274	C₂×Q₈	—	4	1	no	—
275	C₂×Q₈	—	4	2	no	—
276	C₂×D₄	—	2	4	no	—
277	C₂×D₄	—	2	2	no	—
278	C₂×D₄	—	4	1	no	—
279	C₂×D₄	—	4	2	no	—
280	C₂×D₄	—	4	4	no	—
281	C₂×D₄	—	4	2	no	—
282	C₂×D₄	—	4	4	no	—
283	C₂×D₄	—	4	2	no	—
284	C₂²×C₄	—	2	1	no	—
285	C₂²×C₄	—	2	1	no	—
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	2	1	no	—
288	C₂²×C₄	—	4	2	no	—
289	C₂²×C₄	—	4	4	no	—
290	C₂²×C₄	—	4	4	no	—
291	C₂²×C₄	—	4	1	no	—
292	C₂²×C₄	—	4	2	no	—
293	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	2	yes	—
294	C₂²×C₄	D₈×C₁₃₉	1	2	yes	—
295	C₂²×C₄	SD₁₆×C₁₃₉	1	1	yes	characteristic
296	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
297	Q₁₆	—	2	4	no	—
298	Q₁₆	—	2	2	no	—
299	Q₁₆	C₂²⋊C₄×C₁₃₉	1	4	yes	—
300	SD₁₆	—	2	8	no	—
301	SD₁₆	—	2	4	no	—
302	SD₁₆	—	2	4	no	—
303	D₈	—	2	4	no	—
304	D₈	—	2	2	no	—
305	D₈	C₂²⋊C₄×C₁₃₉	1	4	yes	—
306	M₁₆	—	2	4	no	—
307	M₁₆	—	2	4	no	—
308	M₁₆	—	4	1	no	—
309	M₁₆	—	4	1	no	—
310	M₁₆	—	4	1	no	—
311	M₁₆	—	4	1	no	—
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	4	1	no	—
315	C₂×C₈	—	4	1	no	—
316	C₂×C₈	C₂²⋊C₄×C₁₃₉	1	2	yes	—
317	C₂×C₈	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
318	C₂×C₈	C₂×D₄×C₁₃₉	1	2	yes	—
319	C₂×C₈	C₂×D₄×C₁₃₉	1	2	yes	—
320	C₂×C₈	C₂×D₄×C₁₃₉	1	1	yes	characteristic
321	C₁₆	—	4	2	no	—
322	C₂³	—	2	1	no	—
323	C₂³	—	2	1	no	—
324	C₂³	—	4	4	no	—
325	C₂³	—	4	2	no	—
326	C₂³	—	8	1	no	—
327	C₂³	—	8	4	no	—
328	C₂³	#102×C₁₃₉	1	2	yes	—
329	C₂³	C₂×SD₁₆×C₁₃₉	1	1	yes	characteristic
330	Q₈	—	2	4	no	—
331	Q₈	—	4	4	no	—
332	Q₈	—	4	2	no	—
333	D₄	—	2	4	no	—
334	D₄	—	4	4	no	—
335	D₄	—	4	8	no	—
336	D₄	—	4	4	no	—
337	D₄	—	4	4	no	—
338	D₄	—	4	2	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	4	8	no	—
346	C₂×C₄	—	4	4	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	4	no	—
349	C₂×C₄	—	4	4	no	—
350	C₂×C₄	#102×C₁₃₉	1	2	yes	—
351	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
352	C₂×C₄	#120×C₁₃₉	1	1	yes	characteristic
353	C₂×C₄	#120×C₁₃₉	1	1	yes	characteristic
354	C₂×C₄	C₂×D₈×C₁₃₉	1	1	yes	characteristic
355	C₂×C₄	AGL(1,ℤ/8)×C₁₃₉	1	1	yes	characteristic
356	C₂×C₄	AGL(1,ℤ/8)×C₁₃₉	1	1	yes	characteristic
357	C₈	—	2	2	no	—
358	C₈	—	8	1	no	—
359	C₈	—	8	1	no	—
360	C₈	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
361	C₈	#120×C₁₃₉	1	2	yes	—
362	C₂²	—	2	2	no	—
363	C₂²	—	4	1	no	—
364	C₂²	—	4	2	no	—
365	C₂²	—	4	2	no	—
366	C₂²	—	4	4	no	—
367	C₂²	—	8	1	no	—
368	C₂²	—	8	4	no	—
369	C₂²	—	8	8	no	—
370	C₂²	C₂×#102×C₁₃₉	1	1	yes	characteristic
371	C₂²	#450×C₁₃₉	1	1	yes	characteristic
372	C₂²	#450×C₁₃₉	1	1	yes	characteristic
373	C₄	—	2	2	no	—
374	C₄	—	4	4	no	—
375	C₄	#379×C₁₃₉	1	1	yes	characteristic
376	C₄	#418×C₁₃₉	1	1	yes	characteristic
377	C₄	#447×C₁₃₉	1	1	yes	characteristic
378	C₄	#447×C₁₃₉	1	1	yes	characteristic
379	C₂	—	2	1	no	—
380	C₂	—	2	1	no	—
381	C₂	—	2	1	no	—
382	C₂	—	4	2	no	—
383	C₂	—	8	4	no	—
384	C₂	#1786×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₃₉	#447
commutator	C₂×C₈	C₂²×C₄×C₁₃₉
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃₉
socle	C₂×C₁₃₉	#1786
prime radical	C₂×#575×C₁₃₉	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃₉ ◁ C₂²×C₄×C₁₃₉ ◁ C₂²×M₁₆×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2148×C₁₃₉	C₂	semidirect
3. #2143×C₁₃₉	C₂	semidirect
4. C₂×#349×C₁₃₉	C₂	semidirect
5. #1811×C₁₃₉	C₂	semidirect
15. C₂×M₃₂×C₁₃₉	C₂²	semidirect
16. C₂×#108×C₁₃₉	C₂²	semidirect
17. C₂×#108×C₁₃₉	C₂²	semidirect
192. #12740	C₁₃₉	direct (N × H)
193. C₁₃₉	#12740	direct (N × H)
195. #2148	C₂×C₁₃₉	semidirect
196. #2143	C₂×C₁₃₉	semidirect
197. C₂×#349	C₂×C₁₃₉	semidirect
198. #1811	C₂×C₁₃₉	semidirect
208. C₂×M₃₂	C₂²×C₁₃₉	semidirect
209. C₂×#108	C₂²×C₁₃₉	semidirect
210. C₂×#108	C₂²×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#575×C₁₃₉	2
#2148×C₁₃₉	2
#2143×C₁₃₉	2
C₂×#349×C₁₃₉	2
#1811×C₁₃₉	2
#12740	139

Subgroups — C139×#12740 #48007336

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#12740 #48007336