Subgroups — #464×D₁₃₉ #31815844

Order 17792.

500 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₁₆×D₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×SD₁₆×D₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#124×D₁₃₉	C₂	1	1	yes	maximal, characteristic
4	C₄×Q₈×D₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#22581178	C₂	1	1	yes	maximal, characteristic, complemented
6	#22581177	C₂	1	1	yes	maximal, characteristic, complemented
7	#22581176	C₂	1	1	yes	maximal, characteristic, complemented
8	#22581175	C₂	1	1	yes	maximal, characteristic, complemented
9	#22581174	C₂	1	1	yes	maximal, characteristic, complemented
10	#22581173	C₂	1	1	yes	maximal, characteristic, complemented
11	#22581172	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄⋊C₈×D₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#103×D₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#102×D₁₃₉	C₂	1	1	yes	maximal, characteristic
15	#464×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×Q₈×D₁₃₉	C₂²	1	1	yes	characteristic
17	C₂×Q₈×D₁₃₉	C₂²	1	1	yes	characteristic
18	C₂×D₄×D₁₃₉	C₂²	1	1	yes	characteristic
19	C₂×Dic₅₅₆	C₂²	1	1	yes	characteristic, complemented
20	C₂×#14555775	C₂²	1	1	yes	characteristic, complemented
21	C₂×#14555775	C₂²	1	1	yes	characteristic, complemented
22	Q₁₆×D₁₃₉	—	2	4	no	—
23	C₂×#14555774	C₂²	1	1	yes	characteristic
24	C₂×#14555773	C₂²	1	1	yes	characteristic
25	C₂×#14555772	C₂²	1	1	yes	characteristic
26	SD₁₆×D₁₃₉	—	2	4	no	—
27	C₂×C₈×D₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×C₈×D₁₃₉	C₂²	1	1	yes	characteristic
29	#17984831	C₂²	1	1	yes	characteristic
30	#17984830	C₂²	1	1	yes	characteristic
31	#17984829	C₂²	1	1	yes	characteristic
32	#17984828	—	2	1	no	—
33	#17984828	—	2	1	no	—
34	Q₈×Dic₁₃₉	C₂²	1	1	yes	characteristic, complemented
35	C₄×Dic₂₇₈	—	2	1	no	—
36	C₄×Dic₂₇₈	C₂²	1	1	yes	characteristic, complemented
37	#17984807	—	2	1	no	—
38	#17984807	C₂²	1	1	yes	characteristic, complemented
39	C₄⋊C₄×D₁₃₉	—	2	1	no	—
40	C₄⋊C₄×D₁₃₉	C₂²	1	1	yes	characteristic
41	C₂²⋊C₄×D₁₃₉	—	2	1	no	—
42	C₂²⋊C₄×D₁₃₉	—	2	1	no	—
43	C₄²×D₁₃₉	—	2	1	no	—
44	C₄²×D₁₃₉	C₂²	1	1	yes	characteristic
45	C₄⋊(C₁₃₉⋊C₈)	C₂²	1	1	yes	characteristic, complemented
46	Dic₁₃₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
47	Dic₁₃₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
48	#17984767	C₂²	1	1	yes	characteristic, complemented
49	#17984766	C₂²	1	1	yes	characteristic, complemented
50	#17984765	C₂²	1	1	yes	characteristic, complemented
51	#17984764	C₂²	1	1	yes	characteristic
52	#17984763	C₂²	1	1	yes	characteristic
53	#17984762	C₂²	1	1	yes	characteristic
54	C₂×Q₁₆×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
55	C₂×SD₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
56	#124×C₁₃₉	C₂²	1	1	yes	characteristic
57	C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
58	C₄⋊C₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
59	#103×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
60	#102×C₁₃₉	C₂²	1	1	yes	characteristic
61	C₂³×D₁₃₉	—	2	1	no	—
62	C₂×Dic₂₇₈	—	2	1	no	—
63	C₂×Dic₂₇₈	—	2	1	no	—
64	C₂×Dic₂₇₈	C₂³	1	1	yes	characteristic
65	C₂×Dic₂₇₈	C₂³	1	1	yes	characteristic
66	Q₈×D₁₃₉	—	2	2	no	—
67	Q₈×D₁₃₉	—	2	2	no	—
68	Q₈×D₁₃₉	—	2	2	no	—
69	Q₈×D₁₃₉	D₄	1	4	yes	—
70	C₂×D₅₅₆	C₂³	1	1	yes	characteristic
71	C₂×C₂²⋊D₁₃₉	—	2	1	no	—
72	D₄×D₁₃₉	—	2	2	no	—
73	D₄×D₁₃₉	—	2	2	no	—
74	C₂×C₄×D₁₃₉	—	2	1	no	—
75	C₂×C₄×D₁₃₉	—	2	1	no	—
76	C₂×C₄×D₁₃₉	—	2	1	no	—
77	C₂×C₄×D₁₃₉	D₄	1	1	yes	characteristic
78	C₂×C₄×D₁₃₉	D₄	1	1	yes	characteristic
79	C₂×C₄×D₁₃₉	C₂³	1	1	yes	characteristic
80	Dic₅₅₆	—	2	2	no	—
81	#14555775	—	2	2	no	—
82	#14555775	—	2	2	no	—
83	#14555774	—	2	2	no	—
84	#14555773	—	2	2	no	—
85	#14555772	—	2	2	no	—
86	C₂×C₁₃₉⋊C₈	C₂³	1	1	yes	characteristic
87	C₂×C₁₃₉⋊C₈	C₂³	1	1	yes	characteristic
88	C₈×D₁₃₉	—	2	2	no	—
89	C₈×D₁₃₉	—	2	2	no	—
90	C₄⋊Dic₁₃₉	—	2	1	no	—
91	C₄⋊Dic₁₃₉	C₂³	1	1	yes	characteristic
92	Dic₁₃₉⋊C₄	—	2	1	no	—
93	Dic₁₃₉⋊C₄	—	2	1	no	—
94	Dic₁₃₉⋊C₄	—	2	1	no	—
95	C₂²⋊Dic₁₃₉	—	2	1	no	—
96	C₂²⋊Dic₁₃₉	—	2	1	no	—
97	(C₂×D₁₃₉)⋊C₄	—	2	1	no	—
98	(C₂×D₁₃₉)⋊C₄	—	2	1	no	—
99	(C₂×D₁₃₉)⋊C₄	—	2	1	no	—
100	(C₂×D₁₃₉)⋊C₄	—	2	1	no	—
101	C₄×Dic₁₃₉	—	2	1	no	—
102	C₄×Dic₁₃₉	—	2	1	no	—
103	C₄×Dic₁₃₉	—	2	1	no	—
104	C₄×Dic₁₃₉	D₄	1	1	yes	characteristic
105	C₄×Dic₁₃₉	D₄	1	1	yes	characteristic
106	C₄×Dic₁₃₉	C₂³	1	1	yes	characteristic
107	C₂×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
108	C₂×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
109	C₂×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
110	Q₁₆×C₁₃₉	—	2	2	no	—
111	SD₁₆×C₁₃₉	—	2	2	no	—
112	C₂×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
113	C₂×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
114	C₄⋊C₄×C₁₃₉	—	2	1	no	—
115	C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
116	C₂²⋊C₄×C₁₃₉	—	2	1	no	—
117	C₂²⋊C₄×C₁₃₉	—	2	1	no	—
118	C₄²×C₁₃₉	—	2	1	no	—
119	C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
120	C₂²×D₁₃₉	—	2	1	no	—
121	C₂²×D₁₃₉	—	4	2	no	—
122	C₂²×D₁₃₉	—	4	2	no	—
123	C₂²×D₁₃₉	—	4	2	no	—
124	C₂²×D₁₃₉	C₂×D₄	1	1	yes	characteristic
125	Dic₂₇₈	—	2	1	no	—
126	Dic₂₇₈	—	2	4	no	—
127	Dic₂₇₈	—	2	1	no	—
128	Dic₂₇₈	—	2	1	no	—
129	Dic₂₇₈	—	4	2	no	—
130	Dic₂₇₈	C₂×D₄	1	2	yes	—
131	D₅₅₆	—	2	1	no	—
132	D₅₅₆	—	2	1	no	—
133	C₂²⋊D₁₃₉	—	4	2	no	—
134	C₂×Dic₁₃₉	—	2	1	no	—
135	C₂×Dic₁₃₉	—	2	1	no	—
136	C₂×Dic₁₃₉	—	2	1	no	—
137	C₂×Dic₁₃₉	C₂×D₄	1	1	yes	characteristic
138	C₂×Dic₁₃₉	C₂×D₄	1	1	yes	characteristic
139	C₂×Dic₁₃₉	C₂×D₄	1	1	yes	characteristic
140	C₄×D₁₃₉	—	2	4	no	—
141	C₄×D₁₃₉	—	2	2	no	—
142	C₄×D₁₃₉	—	2	2	no	—
143	C₄×D₁₃₉	—	4	2	no	—
144	C₄×D₁₃₉	—	4	2	no	—
145	C₄×D₁₃₉	C₂×D₄	1	2	yes	—
146	C₄×D₁₃₉	#41	1	2	yes	—
147	C₁₃₉⋊C₈	—	2	1	no	—
148	C₁₃₉⋊C₈	—	2	1	no	—
149	C₂³×C₁₃₉	—	2	1	no	—
150	Q₈×C₁₃₉	—	2	1	no	—
151	Q₈×C₁₃₉	—	2	1	no	—
152	Q₈×C₁₃₉	—	2	1	no	—
153	Q₈×C₁₃₉	C₂×D₄	1	2	yes	—
154	D₄×C₁₃₉	—	2	1	no	—
155	D₄×C₁₃₉	—	2	1	no	—
156	C₂×C₄×C₁₃₉	—	2	1	no	—
157	C₂×C₄×C₁₃₉	—	2	1	no	—
158	C₂×C₄×C₁₃₉	—	2	1	no	—
159	C₂×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
160	C₂×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
161	C₂×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
162	C₈×C₁₃₉	—	2	1	no	—
163	C₈×C₁₃₉	—	2	1	no	—
164	C₂²×C₁₃₉	—	4	1	no	—
165	C₂²×C₁₃₉	—	4	1	no	—
166	C₂²×C₁₃₉	—	4	1	no	—
167	C₂²×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
168	C₂×D₁₃₉	—	4	1	no	—
169	C₂×D₁₃₉	—	4	1	no	—
170	C₂×D₁₃₉	—	4	1	no	—
171	C₂×D₁₃₉	—	8	4	no	—
172	C₂×D₁₃₉	#121	1	2	yes	—
173	C₂×D₁₃₉	#135	1	2	yes	—
174	C₂×D₁₃₉	#137	1	2	yes	—
175	C₄×C₁₃₉	—	2	2	no	—
176	C₄×C₁₃₉	—	2	1	no	—
177	C₄×C₁₃₉	—	2	1	no	—
178	C₄×C₁₃₉	—	4	1	no	—
179	C₄×C₁₃₉	—	4	1	no	—
180	C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
181	C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
182	Dic₁₃₉	—	2	2	no	—
183	Dic₁₃₉	—	2	1	no	—
184	Dic₁₃₉	—	2	1	no	—
185	Dic₁₃₉	—	4	1	no	—
186	Dic₁₃₉	—	4	1	no	—
187	Dic₁₃₉	#121	1	2	yes	—
188	C₂×C₁₃₉	—	8	1	no	—
189	C₂×C₁₃₉	C₂×#121	1	1	yes	characteristic
190	C₂×C₁₃₉	C₂×#135	1	1	yes	characteristic
191	C₂×C₁₃₉	C₂×#137	1	1	yes	characteristic
192	D₁₃₉	—	8	1	no	—
193	D₁₃₉	#464	1	4	yes	direct product factor
194	C₁₃₉	C₂×#464	1	1	yes	characteristic, complemented, Sylow
195	C₂×#464	—	139	1	no	maximal, Sylow
196	C₂²×Q₁₆	—	139	1	no	—
197	C₂²×SD₁₆	—	139	1	no	—
198	C₂×#124	—	139	1	no	—
199	C₂×C₄×Q₈	—	139	1	no	—
200	#464	—	139	1	no	—
201	#464	—	139	1	no	—
202	#464	—	139	1	no	—
203	#464	—	139	1	no	—
204	#464	—	139	1	no	—
205	#464	—	139	1	no	—
206	#464	—	139	1	no	—
207	#464	D₁₃₉	1	1	yes	characteristic, direct product factor
208	C₂×C₄⋊C₈	—	139	1	no	—
209	C₂×#103	—	139	1	no	—
210	C₂×#102	—	139	1	no	—
211	C₂²×Q₈	—	139	1	no	—
212	C₂²×Q₈	—	139	1	no	—
213	C₂²×D₄	—	139	1	no	—
214	C₂×Q₁₆	—	278	4	no	—
215	C₂×Q₁₆	—	139	1	no	—
216	C₂×Q₁₆	—	139	1	no	—
217	C₂×Q₁₆	—	139	1	no	—
218	C₂×Q₁₆	C₂×D₁₃₉	1	1	yes	characteristic, complemented
219	C₂×SD₁₆	—	278	4	no	—
220	C₂×SD₁₆	—	139	1	no	—
221	C₂×SD₁₆	—	139	1	no	—
222	C₂×SD₁₆	—	139	1	no	—
223	C₂×SD₁₆	C₂×D₁₃₉	1	1	yes	characteristic
224	C₂²×C₈	—	139	1	no	—
225	C₂²×C₈	—	139	1	no	—
226	#124	—	278	1	no	—
227	#124	—	278	1	no	—
228	#124	—	139	1	no	—
229	#124	—	139	1	no	—
230	#124	—	139	1	no	—
231	#124	C₂×D₁₃₉	1	1	yes	characteristic
232	C₄×Q₈	—	278	1	no	—
233	C₄×Q₈	—	278	1	no	—
234	C₄×Q₈	—	139	1	no	—
235	C₄×Q₈	—	139	1	no	—
236	C₄×Q₈	—	139	1	no	—
237	C₄×Q₈	C₂×D₁₃₉	1	1	yes	characteristic, complemented
238	C₂×C₄⋊C₄	—	278	1	no	—
239	C₂×C₄⋊C₄	—	139	1	no	—
240	C₂×C₂²⋊C₄	—	278	1	no	—
241	C₂×C₂²⋊C₄	—	278	1	no	—
242	C₂×C₄²	—	278	1	no	—
243	C₂×C₄²	—	139	1	no	—
244	C₄⋊C₈	—	139	1	no	—
245	C₄⋊C₈	—	139	1	no	—
246	C₄⋊C₈	—	139	1	no	—
247	C₄⋊C₈	C₂×D₁₃₉	1	1	yes	characteristic, complemented
248	#103	—	139	1	no	—
249	#103	—	139	1	no	—
250	#103	—	139	1	no	—
251	#103	C₂×D₁₃₉	1	1	yes	characteristic, complemented
252	#102	—	139	1	no	—
253	#102	—	139	1	no	—
254	#102	—	139	1	no	—
255	#102	C₂×D₁₃₉	1	1	yes	characteristic
256	C₂⁴	—	278	1	no	—
257	C₂×Q₈	—	278	1	no	—
258	C₂×Q₈	—	278	1	no	—
259	C₂×Q₈	—	278	2	no	—
260	C₂×Q₈	—	278	2	no	—
261	C₂×Q₈	—	278	2	no	—
262	C₂×Q₈	—	139	4	no	—
263	C₂×Q₈	—	139	1	no	—
264	C₂×Q₈	—	139	1	no	—
265	C₂×Q₈	C₂²×D₁₃₉	1	1	yes	characteristic
266	C₂×Q₈	C₂²×D₁₃₉	1	1	yes	characteristic
267	C₂×D₄	—	278	2	no	—
268	C₂×D₄	—	278	2	no	—
269	C₂×D₄	—	278	1	no	—
270	C₂×D₄	—	139	1	no	—
271	C₂×D₄	C₂²×D₁₃₉	1	1	yes	characteristic
272	C₂²×C₄	—	278	1	no	—
273	C₂²×C₄	—	278	1	no	—
274	C₂²×C₄	—	278	1	no	—
275	C₂²×C₄	—	139	1	no	—
276	C₂²×C₄	—	139	1	no	—
277	C₂²×C₄	—	139	1	no	—
278	Q₁₆	—	2	2	no	—
279	Q₁₆	—	278	2	no	—
280	Q₁₆	—	278	2	no	—
281	Q₁₆	—	278	2	no	—
282	SD₁₆	—	2	2	no	—
283	SD₁₆	—	278	2	no	—
284	SD₁₆	—	278	2	no	—
285	SD₁₆	—	278	2	no	—
286	C₂×C₈	—	278	2	no	—
287	C₂×C₈	—	278	2	no	—
288	C₂×C₈	—	139	1	no	—
289	C₂×C₈	—	139	1	no	—
290	C₂×C₈	C₂²×D₁₃₉	1	1	yes	characteristic
291	C₂×C₈	C₂²×D₁₃₉	1	1	yes	characteristic
292	C₄⋊C₄	—	2	1	no	—
293	C₄⋊C₄	—	278	1	no	—
294	C₄⋊C₄	—	278	1	no	—
295	C₄⋊C₄	—	278	1	no	—
296	C₄⋊C₄	—	278	1	no	—
297	C₄⋊C₄	—	139	1	no	—
298	C₄⋊C₄	C₂²×D₁₃₉	1	1	yes	characteristic
299	C₂²⋊C₄	—	2	1	no	—
300	C₂²⋊C₄	—	2	1	no	—
301	C₂²⋊C₄	—	278	1	no	—
302	C₂²⋊C₄	—	278	1	no	—
303	C₂²⋊C₄	—	278	1	no	—
304	C₂²⋊C₄	—	278	1	no	—
305	C₂²⋊C₄	—	278	1	no	—
306	C₂²⋊C₄	—	278	1	no	—
307	C₄²	—	2	1	no	—
308	C₄²	—	278	1	no	—
309	C₄²	—	278	1	no	—
310	C₄²	—	278	1	no	—
311	C₄²	—	139	1	no	—
312	C₄²	—	139	1	no	—
313	C₄²	—	139	1	no	—
314	C₄²	C₂²×D₁₃₉	1	1	yes	characteristic
315	C₂³	—	2	1	no	—
316	C₂³	—	278	1	no	—
317	C₂³	—	556	2	no	—
318	C₂³	—	556	2	no	—
319	C₂³	—	556	2	no	—
320	C₂³	—	139	1	no	—
321	Q₈	—	2	1	no	—
322	Q₈	—	2	1	no	—
323	Q₈	—	2	1	no	—
324	Q₈	—	278	4	no	—
325	Q₈	—	278	1	no	—
326	Q₈	—	278	1	no	—
327	Q₈	—	278	1	no	—
328	Q₈	—	556	2	no	—
329	Q₈	—	139	2	no	—
330	Q₈	D₄×D₁₃₉	1	2	yes	—
331	D₄	—	2	1	no	—
332	D₄	—	2	1	no	—
333	D₄	—	278	1	no	—
334	D₄	—	278	1	no	—
335	D₄	—	556	2	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	278	4	no	—
340	C₂×C₄	—	278	2	no	—
341	C₂×C₄	—	278	2	no	—
342	C₂×C₄	—	278	1	no	—
343	C₂×C₄	—	278	1	no	—
344	C₂×C₄	—	278	1	no	—
345	C₂×C₄	—	556	2	no	—
346	C₂×C₄	—	556	2	no	—
347	C₂×C₄	—	139	1	no	—
348	C₂×C₄	—	139	1	no	—
349	C₂×C₄	—	139	1	no	—
350	C₂×C₄	—	139	2	no	—
351	C₂×C₄	—	139	2	no	—
352	C₂×C₄	D₄×D₁₃₉	1	1	yes	characteristic
353	C₂×C₄	D₄×D₁₃₉	1	1	yes	characteristic
354	C₂×C₄	C₂³×D₁₃₉	1	1	yes	characteristic
355	C₈	—	2	1	no	—
356	C₈	—	2	1	no	—
357	C₈	—	278	1	no	—
358	C₈	—	278	1	no	—
359	C₂²	—	4	1	no	—
360	C₂²	—	4	1	no	—
361	C₂²	—	4	1	no	—
362	C₂²	—	556	1	no	—
363	C₂²	—	556	1	no	—
364	C₂²	—	556	1	no	—
365	C₂²	—	1112	4	no	—
366	C₂²	—	139	2	no	—
367	C₂²	—	139	2	no	—
368	C₂²	—	139	2	no	—
369	C₂²	C₂×D₄×D₁₃₉	1	1	yes	characteristic
370	C₄	—	2	2	no	—
371	C₄	—	2	1	no	—
372	C₄	—	2	1	no	—
373	C₄	—	4	1	no	—
374	C₄	—	4	1	no	—
375	C₄	—	278	2	no	—
376	C₄	—	278	1	no	—
377	C₄	—	278	1	no	—
378	C₄	—	556	1	no	—
379	C₄	—	556	1	no	—
380	C₄	—	139	2	no	—
381	C₄	C₂×D₄×D₁₃₉	1	1	yes	characteristic
382	C₄	#41×D₁₃₉	1	1	yes	characteristic
383	C₂	—	8	1	no	—
384	C₂	—	1112	1	no	—
385	C₂	—	139	4	no	—
386	C₂	#121×D₁₃₉	1	1	yes	characteristic
387	C₂	#135×D₁₃₉	1	1	yes	characteristic
388	C₂	#137×D₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₃₉
commutator, cosocle	C₂×C₄×C₁₃₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₃₉
Fitting	#464×C₁₃₉	C₂
socle	C₂²×C₁₃₉	C₂²×D₄
prime radical	C₂×D₄×D₁₃₉	C₂²
hypercenter	#464	D₁₃₉
hypocenter	C₁₃₉	C₂×#464
LCS	G ▷ C₂×C₄×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #464

Complements

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

N	H ≅ G/N	type
1. C₂×Q₁₆×D₁₃₉	C₂	semidirect
4. C₄×Q₈×D₁₃₉	C₂	semidirect
5. #22581178	C₂	semidirect
6. #22581177	C₂	semidirect
7. #22581176	C₂	semidirect
8. #22581175	C₂	semidirect
9. #22581174	C₂	semidirect
10. #22581173	C₂	semidirect
11. #22581172	C₂	semidirect
12. C₄⋊C₈×D₁₃₉	C₂	semidirect
13. #103×D₁₃₉	C₂	semidirect
15. #464×C₁₃₉	C₂	semidirect
19. C₂×Dic₅₅₆	C₂²	semidirect
20. C₂×#14555775	C₂²	semidirect
21. C₂×#14555775	C₂²	semidirect
34. Q₈×Dic₁₃₉	C₂²	semidirect
36. C₄×Dic₂₇₈	C₂²	semidirect
38. #17984807	C₂²	semidirect
45. C₄⋊(C₁₃₉⋊C₈)	C₂²	semidirect
46. Dic₁₃₉⋊C₈	C₂²	semidirect
47. Dic₁₃₉⋊C₈	C₂²	semidirect
48. #17984767	C₂²	semidirect
49. #17984766	C₂²	semidirect
50. #17984765	C₂²	semidirect
54. C₂×Q₁₆×C₁₃₉	C₂²	semidirect
57. C₄×Q₈×C₁₃₉	C₂²	semidirect
58. C₄⋊C₈×C₁₃₉	C₂²	semidirect
59. #103×C₁₃₉	C₂²	semidirect
193. D₁₃₉	#464	direct (N × H)
194. C₁₃₉	C₂×#464	semidirect
207. #464	D₁₃₉	direct (N × H)
218. C₂×Q₁₆	C₂×D₁₃₉	semidirect
237. C₄×Q₈	C₂×D₁₃₉	semidirect
247. C₄⋊C₈	C₂×D₁₃₉	semidirect
251. #103	C₂×D₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₁₆×D₁₃₉	2
C₂×SD₁₆×D₁₃₉	2
#124×D₁₃₉	2
C₄×Q₈×D₁₃₉	2
#22581178	2
#22581177	2
#22581176	2
#22581175	2
#22581174	2
#22581173	2
#22581172	2
C₄⋊C₈×D₁₃₉	2
#103×D₁₃₉	2
#102×D₁₃₉	2
#464×C₁₃₉	2
C₂×#464	139

Subgroups — #464×D139 #31815844

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #464×D₁₃₉ #31815844