Subgroups — C₁₃₉×#26578 #48021174

Order 35584.

752 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3098×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	#2946×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	#2093×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2051×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2006×C₁₃₉	C₂	1	1	yes	maximal, characteristic
6	#1952×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#1929×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#1859×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#1856×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×AGL(1,ℤ/8)×C₁₃₉	C₂²	1	2	yes	—
11	#537×C₁₃₉	C₂²	1	1	yes	characteristic
12	#520×C₁₃₉	C₂²	1	2	yes	—
13	#518×C₁₃₉	C₂²	1	1	yes	characteristic
14	#485×C₁₃₉	—	2	2	no	—
15	#484×C₁₃₉	—	2	2	no	—
16	#482×C₁₃₉	—	2	2	no	—
17	#480×C₁₃₉	—	2	2	no	—
18	#442×C₁₃₉	—	2	2	no	—
19	#440×C₁₃₉	—	2	2	no	—
20	C₄×SD₁₆×C₁₃₉	—	2	2	no	—
21	C₄×D₈×C₁₃₉	—	2	2	no	—
22	C₂×#108×C₁₃₉	C₂²	1	2	yes	—
23	#428×C₁₃₉	C₂²	1	2	yes	—
24	#428×C₁₃₉	C₂²	1	2	yes	—
25	C₂×#107×C₁₃₉	C₂²	1	2	yes	—
26	C₂×#104×C₁₃₉	C₂²	1	2	yes	—
27	#417×C₁₃₉	C₂²	1	2	yes	—
28	#416×C₁₃₉	C₂²	1	2	yes	—
29	C₂×#102×C₁₃₉	C₂²	1	2	yes	—
30	C₂×#100×C₁₃₉	C₂²	1	1	yes	characteristic
31	#408×C₁₃₉	C₂²	1	2	yes	—
32	#405×C₁₃₉	C₂²	1	2	yes	—
33	#390×C₁₃₉	C₂²	1	1	yes	characteristic
34	#384×C₁₃₉	C₂²	1	1	yes	characteristic
35	#343×C₁₃₉	C₂²	1	1	yes	characteristic
36	#343×C₁₃₉	C₂²	1	2	yes	—
37	#339×C₁₃₉	C₂²	1	2	yes	—
38	#336×C₁₃₉	C₂²	1	1	yes	characteristic
39	C₂×#41×C₁₃₉	C₂³	1	2	yes	—
40	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
41	AGL(1,ℤ/8)×C₁₃₉	—	2	4	no	—
42	AGL(1,ℤ/8)×C₁₃₉	—	2	4	no	—
43	C₂×SD₁₆×C₁₃₉	—	2	2	no	—
44	C₂×D₈×C₁₃₉	—	2	2	no	—
45	C₂×M₁₆×C₁₃₉	C₂³	1	2	yes	—
46	C₂×M₁₆×C₁₃₉	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₃₉	C₂³	1	2	yes	—
48	C₂²⋊Q₈×C₁₃₉	—	2	2	no	—
49	#121×C₁₃₉	—	2	2	no	—
50	#121×C₁₃₉	—	4	1	no	—
51	C₄×Q₈×C₁₃₉	—	2	2	no	—
52	C₄×D₄×C₁₃₉	—	2	2	no	—
53	C₄×D₄×C₁₃₉	—	2	2	no	—
54	C₄×D₄×C₁₃₉	—	2	2	no	—
55	C₄×D₄×C₁₃₉	—	4	2	no	—
56	#117×C₁₃₉	—	2	2	no	—
57	#117×C₁₃₉	C₂³	1	2	yes	—
58	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
59	C₂×C₄⋊C₄×C₁₃₉	—	4	1	no	—
60	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
62	C₂×C₂²⋊C₄×C₁₃₉	—	4	1	no	—
63	C₂×C₂²⋊C₄×C₁₃₉	—	4	1	no	—
64	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
65	#108×C₁₃₉	—	2	4	no	—
66	#107×C₁₃₉	—	2	2	no	—
67	#107×C₁₃₉	—	2	2	no	—
68	#107×C₁₃₉	—	2	2	no	—
69	#107×C₁₃₉	—	2	2	no	—
70	#106×C₁₃₉	—	2	2	no	—
71	#106×C₁₃₉	—	2	2	no	—
72	#104×C₁₃₉	—	2	4	no	—
73	#103×C₁₃₉	—	2	2	no	—
74	#103×C₁₃₉	D₄	1	2	yes	—
75	#103×C₁₃₉	D₄	1	2	yes	—
76	#102×C₁₃₉	—	2	2	no	—
77	#102×C₁₃₉	—	2	2	no	—
78	#102×C₁₃₉	—	2	2	no	—
79	#102×C₁₃₉	D₄	1	2	yes	—
80	#102×C₁₃₉	D₄	1	2	yes	—
81	#100×C₁₃₉	—	2	2	no	—
82	C₂²⋊C₈×C₁₃₉	—	2	2	no	—
83	C₂²⋊C₈×C₁₃₉	—	2	2	no	—
84	#97×C₁₃₉	—	2	2	no	—
85	C₄×C₈×C₁₃₉	—	2	2	no	—
86	C₂⁴×C₁₃₉	—	2	1	no	—
87	#41×C₁₃₉	—	2	2	no	—
88	#41×C₁₃₉	—	2	2	no	—
89	#41×C₁₃₉	—	2	2	no	—
90	#41×C₁₃₉	—	2	2	no	—
91	C₂×Q₈×C₁₃₉	C₂×D₄	1	2	yes	—
92	C₂×D₄×C₁₃₉	—	2	2	no	—
93	C₂×D₄×C₁₃₉	—	2	2	no	—
94	C₂×D₄×C₁₃₉	—	2	2	no	—
95	C₂×D₄×C₁₃₉	—	2	1	no	—
96	C₂×D₄×C₁₃₉	—	4	1	no	—
97	C₂×D₄×C₁₃₉	C₂×D₄	1	2	yes	—
98	C₂×D₄×C₁₃₉	#41	1	2	yes	—
99	C₂²×C₄×C₁₃₉	—	2	1	no	—
100	C₂²×C₄×C₁₃₉	—	2	2	no	—
101	C₂²×C₄×C₁₃₉	—	2	1	no	—
102	C₂²×C₄×C₁₃₉	—	2	2	no	—
103	C₂²×C₄×C₁₃₉	—	4	1	no	—
104	C₂²×C₄×C₁₃₉	—	4	1	no	—
105	C₂²×C₄×C₁₃₉	—	4	2	no	—
106	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
107	SD₁₆×C₁₃₉	—	2	8	no	—
108	D₈×C₁₃₉	—	2	8	no	—
109	M₁₆×C₁₃₉	—	2	2	no	—
110	M₁₆×C₁₃₉	—	2	2	no	—
111	M₁₆×C₁₃₉	—	2	2	no	—
112	M₁₆×C₁₃₉	#41	1	4	yes	—
113	C₂×C₈×C₁₃₉	—	2	2	no	—
114	C₂×C₈×C₁₃₉	—	2	2	no	—
115	C₂×C₈×C₁₃₉	—	2	2	no	—
116	C₂×C₈×C₁₃₉	—	2	2	no	—
117	C₂×C₈×C₁₃₉	C₂×D₄	1	2	yes	—
118	C₂×C₈×C₁₃₉	C₂×D₄	1	2	yes	—
119	C₄⋊C₄×C₁₃₉	—	2	2	no	—
120	C₄⋊C₄×C₁₃₉	—	2	2	no	—
121	C₄⋊C₄×C₁₃₉	—	2	2	no	—
122	C₄⋊C₄×C₁₃₉	—	4	2	no	—
123	C₄⋊C₄×C₁₃₉	—	4	1	no	—
124	C₄⋊C₄×C₁₃₉	—	8	2	no	—
125	C₄⋊C₄×C₁₃₉	C₂×D₄	1	2	yes	—
126	C₄⋊C₄×C₁₃₉	C₂×D₄	1	2	yes	—
127	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
128	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
129	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
130	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
131	C₂²⋊C₄×C₁₃₉	—	8	2	no	—
132	C₄²×C₁₃₉	—	2	2	no	—
133	C₄²×C₁₃₉	—	2	2	no	—
134	C₄²×C₁₃₉	—	4	2	no	—
135	C₂³×C₁₃₉	—	2	2	no	—
136	C₂³×C₁₃₉	—	2	2	no	—
137	C₂³×C₁₃₉	—	4	1	no	—
138	C₂³×C₁₃₉	—	4	1	no	—
139	C₂³×C₁₃₉	—	8	1	no	—
140	C₂³×C₁₃₉	—	8	1	no	—
141	C₂³×C₁₃₉	H(5,𝔽₂)	1	1	yes	characteristic
142	Q₈×C₁₃₉	—	2	2	no	—
143	Q₈×C₁₃₉	—	2	2	no	—
144	D₄×C₁₃₉	—	2	2	no	—
145	D₄×C₁₃₉	—	2	4	no	—
146	D₄×C₁₃₉	—	2	2	no	—
147	D₄×C₁₃₉	—	4	2	no	—
148	D₄×C₁₃₉	—	4	2	no	—
149	D₄×C₁₃₉	—	4	2	no	—
150	D₄×C₁₃₉	—	16	1	no	—
151	C₂×C₄×C₁₃₉	—	2	2	no	—
152	C₂×C₄×C₁₃₉	—	2	2	no	—
153	C₂×C₄×C₁₃₉	—	2	2	no	—
154	C₂×C₄×C₁₃₉	—	2	2	no	—
155	C₂×C₄×C₁₃₉	—	4	1	no	—
156	C₂×C₄×C₁₃₉	—	4	1	no	—
157	C₂×C₄×C₁₃₉	—	4	2	no	—
158	C₂×C₄×C₁₃₉	—	4	2	no	—
159	C₂×C₄×C₁₃₉	—	4	2	no	—
160	C₂×C₄×C₁₃₉	—	4	1	no	—
161	C₂×C₄×C₁₃₉	—	8	1	no	—
162	C₂×C₄×C₁₃₉	—	8	2	no	—
163	C₂×C₄×C₁₃₉	—	16	1	no	—
164	C₂×C₄×C₁₃₉	—	16	1	no	—
165	C₂×C₄×C₁₃₉	—	16	2	no	—
166	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
167	C₂×C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
168	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
169	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	1	yes	characteristic
170	C₈×C₁₃₉	—	2	4	no	—
171	C₈×C₁₃₉	—	2	2	no	—
172	C₈×C₁₃₉	—	2	2	no	—
173	C₈×C₁₃₉	—	4	2	no	—
174	C₂²×C₁₃₉	—	2	1	no	—
175	C₂²×C₁₃₉	—	2	1	no	—
176	C₂²×C₁₃₉	—	4	2	no	—
177	C₂²×C₁₃₉	—	4	2	no	—
178	C₂²×C₁₃₉	—	4	2	no	—
179	C₂²×C₁₃₉	—	4	2	no	—
180	C₂²×C₁₃₉	—	8	2	no	—
181	C₂²×C₁₃₉	—	8	1	no	—
182	C₂²×C₁₃₉	—	8	1	no	—
183	C₂²×C₁₃₉	—	16	1	no	—
184	C₂²×C₁₃₉	#539	1	1	yes	characteristic
185	C₂²×C₁₃₉	D₄²	1	1	yes	characteristic
186	C₂²×C₁₃₉	#559	1	1	yes	characteristic
187	C₄×C₁₃₉	—	4	2	no	—
188	C₄×C₁₃₉	—	4	2	no	—
189	C₄×C₁₃₉	—	4	2	no	—
190	C₄×C₁₃₉	—	4	2	no	—
191	C₄×C₁₃₉	—	8	2	no	—
192	C₄×C₁₃₉	—	8	1	no	—
193	C₄×C₁₃₉	#525	1	2	yes	—
194	C₄×C₁₃₉	#547	1	2	yes	—
195	C₂×C₁₃₉	—	2	1	no	—
196	C₂×C₁₃₉	—	2	1	no	—
197	C₂×C₁₃₉	—	8	2	no	—
198	C₂×C₁₃₉	—	8	2	no	—
199	C₂×C₁₃₉	#2455	1	1	yes	characteristic
200	C₂×C₁₃₉	#3289	1	1	yes	characteristic
201	C₂×C₁₃₉	#3292	1	1	yes	characteristic
202	#26578	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
203	C₁₃₉	#26578	1	1	yes	characteristic, direct product factor, Sylow
204	#3098	C₂×C₁₃₉	1	2	yes	complemented
205	#2946	C₂×C₁₃₉	1	2	yes	complemented
206	#2093	C₂×C₁₃₉	1	1	yes	characteristic, complemented
207	#2051	C₂×C₁₃₉	1	2	yes	complemented
208	#2006	C₂×C₁₃₉	1	1	yes	characteristic
209	#1952	C₂×C₁₃₉	1	2	yes	complemented
210	#1929	C₂×C₁₃₉	1	2	yes	complemented
211	#1859	C₂×C₁₃₉	1	2	yes	complemented
212	#1856	C₂×C₁₃₉	1	1	yes	characteristic, complemented
213	C₂×AGL(1,ℤ/8)	C₂²×C₁₃₉	1	2	yes	—
214	#537	C₂²×C₁₃₉	1	1	yes	characteristic
215	#520	C₂²×C₁₃₉	1	2	yes	—
216	#518	C₂²×C₁₃₉	1	1	yes	characteristic
217	#485	—	2	2	no	—
218	#484	—	2	2	no	—
219	#482	—	2	2	no	—
220	#480	—	2	2	no	—
221	#442	—	2	2	no	—
222	#440	—	2	2	no	—
223	C₄×SD₁₆	—	2	2	no	—
224	C₄×D₈	—	2	2	no	—
225	C₂×#108	C₂²×C₁₃₉	1	2	yes	—
226	#428	C₂²×C₁₃₉	1	2	yes	—
227	#428	C₂²×C₁₃₉	1	2	yes	—
228	C₂×#107	C₂²×C₁₃₉	1	2	yes	—
229	C₂×#104	C₂²×C₁₃₉	1	2	yes	—
230	#417	C₂²×C₁₃₉	1	2	yes	—
231	#416	C₂²×C₁₃₉	1	2	yes	—
232	C₂×#102	C₂²×C₁₃₉	1	2	yes	—
233	C₂×#100	C₂²×C₁₃₉	1	1	yes	characteristic
234	#408	C₂²×C₁₃₉	1	2	yes	—
235	#405	C₂²×C₁₃₉	1	2	yes	—
236	#390	C₂²×C₁₃₉	1	1	yes	characteristic
237	#384	C₂²×C₁₃₉	1	1	yes	characteristic
238	#343	C₂²×C₁₃₉	1	2	yes	—
239	#343	C₂²×C₁₃₉	1	1	yes	characteristic
240	#339	C₂²×C₁₃₉	1	2	yes	—
241	#336	C₂²×C₁₃₉	1	1	yes	characteristic
242	C₂×#41	C₂³×C₁₃₉	1	2	yes	—
243	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
244	AGL(1,ℤ/8)	—	2	4	no	—
245	AGL(1,ℤ/8)	—	2	4	no	—
246	C₂×SD₁₆	—	2	2	no	—
247	C₂×D₈	—	2	2	no	—
248	C₂×M₁₆	C₂³×C₁₃₉	1	2	yes	—
249	C₂×M₁₆	C₂³×C₁₃₉	1	2	yes	—
250	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
251	C₂²⋊Q₈	—	2	2	no	—
252	#121	—	2	2	no	—
253	#121	—	4	1	no	—
254	C₄×Q₈	—	2	2	no	—
255	C₄×D₄	—	2	2	no	—
256	C₄×D₄	—	2	2	no	—
257	C₄×D₄	—	2	2	no	—
258	C₄×D₄	—	4	2	no	—
259	#117	—	2	2	no	—
260	#117	C₂³×C₁₃₉	1	2	yes	—
261	C₂×C₄⋊C₄	—	2	2	no	—
262	C₂×C₄⋊C₄	—	4	1	no	—
263	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
264	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
265	C₂×C₂²⋊C₄	—	4	1	no	—
266	C₂×C₂²⋊C₄	—	4	1	no	—
267	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
268	#108	—	2	4	no	—
269	#107	—	2	2	no	—
270	#107	—	2	2	no	—
271	#107	—	2	2	no	—
272	#107	—	2	2	no	—
273	#106	—	2	2	no	—
274	#106	—	2	2	no	—
275	#104	—	2	4	no	—
276	#103	—	2	2	no	—
277	#103	D₄×C₁₃₉	1	2	yes	—
278	#103	D₄×C₁₃₉	1	2	yes	—
279	#102	—	2	2	no	—
280	#102	—	2	2	no	—
281	#102	—	2	2	no	—
282	#102	D₄×C₁₃₉	1	2	yes	—
283	#102	D₄×C₁₃₉	1	2	yes	—
284	#100	—	2	2	no	—
285	C₂²⋊C₈	—	2	2	no	—
286	C₂²⋊C₈	—	2	2	no	—
287	#97	—	2	2	no	—
288	C₄×C₈	—	2	2	no	—
289	C₂⁴	—	2	1	no	—
290	#41	—	2	2	no	—
291	#41	—	2	2	no	—
292	#41	—	2	2	no	—
293	#41	—	2	2	no	—
294	C₂×Q₈	C₂×D₄×C₁₃₉	1	2	yes	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	2	1	no	—
299	C₂×D₄	—	4	1	no	—
300	C₂×D₄	C₂×D₄×C₁₃₉	1	2	yes	—
301	C₂×D₄	#41×C₁₃₉	1	2	yes	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	4	1	no	—
307	C₂²×C₄	—	4	1	no	—
308	C₂²×C₄	—	4	2	no	—
309	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
310	SD₁₆	—	2	8	no	—
311	D₈	—	2	8	no	—
312	M₁₆	—	2	2	no	—
313	M₁₆	—	2	2	no	—
314	M₁₆	—	2	2	no	—
315	M₁₆	#41×C₁₃₉	1	4	yes	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	C₂×D₄×C₁₃₉	1	2	yes	—
321	C₂×C₈	C₂×D₄×C₁₃₉	1	2	yes	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	4	2	no	—
326	C₄⋊C₄	—	4	1	no	—
327	C₄⋊C₄	—	8	2	no	—
328	C₄⋊C₄	C₂×D₄×C₁₃₉	1	2	yes	—
329	C₄⋊C₄	C₂×D₄×C₁₃₉	1	2	yes	—
330	C₂²⋊C₄	—	2	2	no	—
331	C₂²⋊C₄	—	4	2	no	—
332	C₂²⋊C₄	—	4	2	no	—
333	C₂²⋊C₄	—	4	2	no	—
334	C₂²⋊C₄	—	8	2	no	—
335	C₄²	—	2	2	no	—
336	C₄²	—	2	2	no	—
337	C₄²	—	4	2	no	—
338	C₂³	—	2	2	no	—
339	C₂³	—	2	2	no	—
340	C₂³	—	4	1	no	—
341	C₂³	—	4	1	no	—
342	C₂³	—	8	1	no	—
343	C₂³	—	8	1	no	—
344	C₂³	H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
345	Q₈	—	2	2	no	—
346	Q₈	—	2	2	no	—
347	D₄	—	2	2	no	—
348	D₄	—	2	4	no	—
349	D₄	—	2	2	no	—
350	D₄	—	4	2	no	—
351	D₄	—	4	2	no	—
352	D₄	—	4	2	no	—
353	D₄	—	16	1	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	8	1	no	—
365	C₂×C₄	—	8	2	no	—
366	C₂×C₄	—	16	1	no	—
367	C₂×C₄	—	16	1	no	—
368	C₂×C₄	—	16	2	no	—
369	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
370	C₂×C₄	C₂×#41×C₁₃₉	1	1	yes	characteristic
371	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
372	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
373	C₈	—	2	4	no	—
374	C₈	—	2	2	no	—
375	C₈	—	2	2	no	—
376	C₈	—	4	2	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	2	1	no	—
379	C₂²	—	4	2	no	—
380	C₂²	—	4	2	no	—
381	C₂²	—	4	2	no	—
382	C₂²	—	4	2	no	—
383	C₂²	—	8	2	no	—
384	C₂²	—	8	1	no	—
385	C₂²	—	8	1	no	—
386	C₂²	—	16	1	no	—
387	C₂²	#539×C₁₃₉	1	1	yes	characteristic
388	C₂²	D₄²×C₁₃₉	1	1	yes	characteristic
389	C₂²	#559×C₁₃₉	1	1	yes	characteristic
390	C₄	—	4	2	no	—
391	C₄	—	4	2	no	—
392	C₄	—	4	2	no	—
393	C₄	—	4	2	no	—
394	C₄	—	8	2	no	—
395	C₄	—	8	1	no	—
396	C₄	#525×C₁₃₉	1	2	yes	—
397	C₄	#547×C₁₃₉	1	2	yes	—
398	C₂	—	2	1	no	—
399	C₂	—	2	1	no	—
400	C₂	—	8	2	no	—
401	C₂	—	8	2	no	—
402	C₂	#2455×C₁₃₉	1	1	yes	characteristic
403	C₂	#3289×C₁₃₉	1	1	yes	characteristic
404	C₂	#3292×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₉	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
prime radical	#2006×C₁₃₉	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₉ ◁ C₂²×C₄×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. #3098×C₁₃₉	C₂	semidirect
2. #2946×C₁₃₉	C₂	semidirect
3. #2093×C₁₃₉	C₂	semidirect
4. #2051×C₁₃₉	C₂	semidirect
6. #1952×C₁₃₉	C₂	semidirect
7. #1929×C₁₃₉	C₂	semidirect
8. #1859×C₁₃₉	C₂	semidirect
9. #1856×C₁₃₉	C₂	semidirect
202. #26578	C₁₃₉	direct (N × H)
203. C₁₃₉	#26578	direct (N × H)
204. #3098	C₂×C₁₃₉	semidirect
205. #2946	C₂×C₁₃₉	semidirect
206. #2093	C₂×C₁₃₉	semidirect
207. #2051	C₂×C₁₃₉	semidirect
209. #1952	C₂×C₁₃₉	semidirect
210. #1929	C₂×C₁₃₉	semidirect
211. #1859	C₂×C₁₃₉	semidirect
212. #1856	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#3098×C₁₃₉	2
#2946×C₁₃₉	2
#2093×C₁₃₉	2
#2051×C₁₃₉	2
#2006×C₁₃₉	2
#1952×C₁₃₉	2
#1929×C₁₃₉	2
#1859×C₁₃₉	2
#1856×C₁₃₉	2
#26578	139

Subgroups — C139×#26578 #48021174

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#26578 #48021174