Subgroups — C₁₃₉×#29270 #48023866

Order 35584.

612 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2960×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#2957×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2098×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2031×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#1976×C₁₃₉	C₂	1	1	yes	maximal, characteristic
6	#1974×C₁₃₉	C₂	1	1	yes	maximal, characteristic
7	#1953×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#1945×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#1868×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#1861×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#1833×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#135×C₁₃₉	C₂²	1	1	yes	characteristic
13	#568×C₁₃₉	C₂²	1	2	yes	—
14	#533×C₁₃₉	C₂²	1	1	yes	characteristic
15	#446×C₁₃₉	—	2	2	no	—
16	C₈×Q₈×C₁₃₉	—	2	2	no	—
17	#444×C₁₃₉	—	2	2	no	—
18	#443×C₁₃₉	—	2	2	no	—
19	#430×C₁₃₉	C₂²	1	2	yes	—
20	C₂×#108×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×#108×C₁₃₉	C₂²	1	1	yes	characteristic
22	#427×C₁₃₉	C₂²	1	1	yes	characteristic
23	#424×C₁₃₉	C₂²	1	1	yes	characteristic
24	#424×C₁₃₉	C₂²	1	1	yes	characteristic
25	#424×C₁₃₉	C₂²	1	2	yes	—
26	#423×C₁₃₉	C₂²	1	1	yes	characteristic
27	#421×C₁₃₉	C₂²	1	2	yes	—
28	#421×C₁₃₉	C₂²	1	2	yes	—
29	C₂×#104×C₁₃₉	C₂²	1	2	yes	—
30	#410×C₁₃₉	C₂²	1	2	yes	—
31	#408×C₁₃₉	C₂²	1	2	yes	—
32	#405×C₁₃₉	C₂²	1	1	yes	characteristic
33	#405×C₁₃₉	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₈×C₁₃₉	C₂²	1	1	yes	characteristic
35	#344×C₁₃₉	C₂²	1	2	yes	—
36	#344×C₁₃₉	C₂²	1	2	yes	—
37	#339×C₁₃₉	C₂²	1	2	yes	—
38	H(3,ℤ/4)×C₁₃₉	C₂²	1	2	yes	—
39	C₂×#41×C₁₃₉	C₂³	1	2	yes	—
40	#135×C₁₃₉	—	2	1	no	—
41	#135×C₁₃₉	—	2	1	no	—
42	#135×C₁₃₉	—	2	1	no	—
43	#135×C₁₃₉	—	2	1	no	—
44	C₂×Q₁₆×C₁₃₉	Q₈	1	1	yes	characteristic, complemented
45	C₂×SD₁₆×C₁₃₉	Q₈	1	2	yes	complemented
46	C₂×D₈×C₁₃₉	Q₈	1	1	yes	characteristic, complemented
47	#131×C₁₃₉	—	2	4	no	—
48	#131×C₁₃₉	—	4	2	no	—
49	C₂×M₁₆×C₁₃₉	—	4	2	no	—
50	C₂×M₁₆×C₁₃₉	C₂³	1	1	yes	characteristic
51	C₂×M₁₆×C₁₃₉	C₂³	1	2	yes	—
52	C₂×M₁₆×C₁₃₉	C₂³	1	2	yes	—
53	C₂×M₁₆×C₁₃₉	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
56	C₄⋊Q₈×C₁₃₉	—	2	1	no	—
57	#125×C₁₃₉	—	2	1	no	—
58	C₂²⋊Q₈×C₁₃₉	—	2	2	no	—
59	C₄×Q₈×C₁₃₉	—	2	2	no	—
60	#117×C₁₃₉	C₂³	1	2	yes	—
61	#117×C₁₃₉	C₂³	1	1	yes	characteristic
62	#117×C₁₃₉	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
64	#108×C₁₃₉	—	2	1	no	—
65	#108×C₁₃₉	—	2	1	no	—
66	#108×C₁₃₉	—	2	1	no	—
67	#108×C₁₃₉	—	2	1	no	—
68	#108×C₁₃₉	—	4	2	no	—
69	#107×C₁₃₉	—	2	1	no	—
70	#106×C₁₃₉	—	2	1	no	—
71	C₄⋊C₈×C₁₃₉	—	2	2	no	—
72	C₄⋊C₈×C₁₃₉	—	2	2	no	—
73	C₄⋊C₈×C₁₃₉	—	2	2	no	—
74	C₄⋊C₈×C₁₃₉	—	4	2	no	—
75	#104×C₁₃₉	—	2	4	no	—
76	#104×C₁₃₉	—	2	2	no	—
77	#104×C₁₃₉	—	2	2	no	—
78	#104×C₁₃₉	—	4	2	no	—
79	#99×C₁₃₉	—	2	4	no	—
80	C₂²⋊C₈×C₁₃₉	—	4	2	no	—
81	#97×C₁₃₉	—	2	1	no	—
82	#97×C₁₃₉	D₄	1	2	yes	—
83	C₄×C₈×C₁₃₉	—	2	1	no	—
84	C₄×C₈×C₁₃₉	—	2	1	no	—
85	C₄×C₈×C₁₃₉	—	2	1	no	—
86	C₄×C₈×C₁₃₉	D₄	1	2	yes	—
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	—	2	2	no	—
92	C₂×Q₈×C₁₃₉	C₂×Q₈	1	2	yes	—
93	C₂×D₄×C₁₃₉	—	2	2	no	—
94	C₂×D₄×C₁₃₉	C₂×Q₈	1	2	yes	—
95	C₂²×C₄×C₁₃₉	—	2	1	no	—
96	C₂²×C₄×C₁₃₉	—	2	2	no	—
97	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
98	Q₁₆×C₁₃₉	—	2	1	no	—
99	Q₁₆×C₁₃₉	—	2	1	no	—
100	SD₁₆×C₁₃₉	—	2	2	no	—
101	SD₁₆×C₁₃₉	—	2	2	no	—
102	D₈×C₁₃₉	—	2	1	no	—
103	D₈×C₁₃₉	—	2	1	no	—
104	M₁₆×C₁₃₉	—	2	1	no	—
105	M₁₆×C₁₃₉	—	2	1	no	—
106	M₁₆×C₁₃₉	—	2	2	no	—
107	M₁₆×C₁₃₉	—	2	2	no	—
108	M₁₆×C₁₃₉	—	2	2	no	—
109	M₁₆×C₁₃₉	—	2	1	no	—
110	M₁₆×C₁₃₉	—	2	1	no	—
111	M₁₆×C₁₃₉	—	2	2	no	—
112	M₁₆×C₁₃₉	—	4	4	no	—
113	C₂×C₈×C₁₃₉	—	2	1	no	—
114	C₂×C₈×C₁₃₉	—	2	1	no	—
115	C₂×C₈×C₁₃₉	—	2	1	no	—
116	C₂×C₈×C₁₃₉	—	2	2	no	—
117	C₂×C₈×C₁₃₉	—	2	1	no	—
118	C₂×C₈×C₁₃₉	—	2	2	no	—
119	C₂×C₈×C₁₃₉	—	4	4	no	—
120	C₂×C₈×C₁₃₉	C₂×D₄	1	2	yes	—
121	C₂×C₈×C₁₃₉	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₁₃₉	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₁₃₉	C₂×Q₈	1	1	yes	characteristic
124	C₂×C₈×C₁₃₉	C₂×Q₈	1	1	yes	characteristic
125	C₂×C₈×C₁₃₉	#41	1	1	yes	characteristic
126	C₂×C₈×C₁₃₉	#41	1	1	yes	characteristic
127	C₄⋊C₄×C₁₃₉	—	2	4	no	—
128	C₄⋊C₄×C₁₃₉	—	2	2	no	—
129	C₄⋊C₄×C₁₃₉	—	2	1	no	—
130	C₄⋊C₄×C₁₃₉	—	2	1	no	—
131	C₄⋊C₄×C₁₃₉	—	2	2	no	—
132	C₂²⋊C₄×C₁₃₉	—	2	1	no	—
133	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
134	C₂²⋊C₄×C₁₃₉	#41	1	2	yes	—
135	C₄²×C₁₃₉	—	2	1	no	—
136	C₄²×C₁₃₉	—	2	1	no	—
137	C₄²×C₁₃₉	—	2	2	no	—
138	C₄²×C₁₃₉	C₂×D₄	1	2	yes	—
139	C₄²×C₁₃₉	#41	1	1	yes	characteristic
140	C₄²×C₁₃₉	#41	1	1	yes	characteristic
141	C₂³×C₁₃₉	—	2	2	no	—
142	C₂³×C₁₃₉	C₂×#41	1	1	yes	characteristic
143	Q₈×C₁₃₉	—	2	2	no	—
144	Q₈×C₁₃₉	—	2	2	no	—
145	Q₈×C₁₃₉	—	4	4	no	—
146	D₄×C₁₃₉	—	2	2	no	—
147	D₄×C₁₃₉	—	2	2	no	—
148	D₄×C₁₃₉	—	4	2	no	—
149	D₄×C₁₃₉	—	4	2	no	—
150	C₂×C₄×C₁₃₉	—	2	1	no	—
151	C₂×C₄×C₁₃₉	—	2	1	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	2	no	—
156	C₂×C₄×C₁₃₉	—	4	2	no	—
157	C₂×C₄×C₁₃₉	—	4	2	no	—
158	C₂×C₄×C₁₃₉	—	4	2	no	—
159	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₁₃₉	C₂²×Q₈	1	1	yes	characteristic
161	C₂×C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
162	C₂×C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
163	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	1	yes	characteristic
164	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	1	yes	characteristic
165	C₈×C₁₃₉	—	2	2	no	—
166	C₈×C₁₃₉	—	4	1	no	—
167	C₈×C₁₃₉	—	4	2	no	—
168	C₈×C₁₃₉	—	4	1	no	—
169	C₈×C₁₃₉	—	4	2	no	—
170	C₈×C₁₃₉	C₂²⋊Q₈	1	1	yes	characteristic
171	C₈×C₁₃₉	C₂²⋊Q₈	1	1	yes	characteristic
172	C₈×C₁₃₉	C₂²⋊Q₈	1	1	yes	characteristic
173	C₈×C₁₃₉	C₂²⋊Q₈	1	1	yes	characteristic
174	C₂²×C₁₃₉	—	4	1	no	—
175	C₂²×C₁₃₉	—	4	2	no	—
176	C₂²×C₁₃₉	—	8	2	no	—
177	C₂²×C₁₃₉	#525	1	1	yes	characteristic
178	C₂²×C₁₃₉	#554	1	1	yes	characteristic
179	C₂²×C₁₃₉	#559	1	1	yes	characteristic
180	C₄×C₁₃₉	—	2	2	no	—
181	C₄×C₁₃₉	—	4	1	no	—
182	C₄×C₁₃₉	—	4	2	no	—
183	C₄×C₁₃₉	—	4	2	no	—
184	C₄×C₁₃₉	—	4	2	no	—
185	C₄×C₁₃₉	—	8	2	no	—
186	C₄×C₁₃₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
187	C₄×C₁₃₉	#535	1	1	yes	characteristic
188	C₄×C₁₃₉	#554	1	1	yes	characteristic
189	C₄×C₁₃₉	#559	1	1	yes	characteristic
190	C₂×C₁₃₉	—	2	1	no	—
191	C₂×C₁₃₉	—	2	1	no	—
192	C₂×C₁₃₉	—	2	1	no	—
193	C₂×C₁₃₉	—	8	2	no	—
194	C₂×C₁₃₉	#2580	1	1	yes	characteristic
195	#29270	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
196	C₁₃₉	#29270	1	1	yes	characteristic, direct product factor, Sylow
197	#2960	C₂×C₁₃₉	1	1	yes	characteristic, complemented
198	#2957	C₂×C₁₃₉	1	1	yes	characteristic
199	#2098	C₂×C₁₃₉	1	2	yes	complemented
200	#2031	C₂×C₁₃₉	1	2	yes	complemented
201	#1976	C₂×C₁₃₉	1	1	yes	characteristic
202	#1974	C₂×C₁₃₉	1	1	yes	characteristic
203	#1953	C₂×C₁₃₉	1	1	yes	characteristic, complemented
204	#1945	C₂×C₁₃₉	1	1	yes	characteristic, complemented
205	#1868	C₂×C₁₃₉	1	2	yes	complemented
206	#1861	C₂×C₁₃₉	1	2	yes	complemented
207	#1833	C₂×C₁₃₉	1	1	yes	characteristic, complemented
208	C₂×#135	C₂²×C₁₃₉	1	1	yes	characteristic
209	#568	C₂²×C₁₃₉	1	2	yes	—
210	#533	C₂²×C₁₃₉	1	1	yes	characteristic
211	#446	—	2	2	no	—
212	C₈×Q₈	—	2	2	no	—
213	#444	—	2	2	no	—
214	#443	—	2	2	no	—
215	#430	C₂²×C₁₃₉	1	2	yes	—
216	C₂×#108	C₂²×C₁₃₉	1	1	yes	characteristic
217	C₂×#108	C₂²×C₁₃₉	1	1	yes	characteristic
218	#427	C₂²×C₁₃₉	1	1	yes	characteristic
219	#424	C₂²×C₁₃₉	1	1	yes	characteristic
220	#424	C₂²×C₁₃₉	1	1	yes	characteristic
221	#424	C₂²×C₁₃₉	1	2	yes	—
222	#423	C₂²×C₁₃₉	1	1	yes	characteristic
223	#421	C₂²×C₁₃₉	1	2	yes	—
224	#421	C₂²×C₁₃₉	1	2	yes	—
225	C₂×#104	C₂²×C₁₃₉	1	2	yes	—
226	#410	C₂²×C₁₃₉	1	2	yes	—
227	#408	C₂²×C₁₃₉	1	2	yes	—
228	#405	C₂²×C₁₃₉	1	1	yes	characteristic
229	#405	C₂²×C₁₃₉	1	1	yes	characteristic
230	C₂×C₄×C₈	C₂²×C₁₃₉	1	1	yes	characteristic
231	#344	C₂²×C₁₃₉	1	2	yes	—
232	#344	C₂²×C₁₃₉	1	2	yes	—
233	#339	C₂²×C₁₃₉	1	2	yes	—
234	H(3,ℤ/4)	C₂²×C₁₃₉	1	2	yes	—
235	C₂×#41	C₂³×C₁₃₉	1	2	yes	—
236	#135	—	2	1	no	—
237	#135	—	2	1	no	—
238	#135	—	2	1	no	—
239	#135	—	2	1	no	—
240	C₂×Q₁₆	Q₈×C₁₃₉	1	1	yes	characteristic, complemented
241	C₂×SD₁₆	Q₈×C₁₃₉	1	2	yes	complemented
242	C₂×D₈	Q₈×C₁₃₉	1	1	yes	characteristic, complemented
243	#131	—	2	4	no	—
244	#131	—	4	2	no	—
245	C₂×M₁₆	—	4	2	no	—
246	C₂×M₁₆	C₂³×C₁₃₉	1	2	yes	—
247	C₂×M₁₆	C₂³×C₁₃₉	1	2	yes	—
248	C₂×M₁₆	C₂³×C₁₃₉	1	1	yes	characteristic
249	C₂×M₁₆	C₂³×C₁₃₉	1	1	yes	characteristic
250	C₂²×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
251	C₂²×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
252	C₄⋊Q₈	—	2	1	no	—
253	#125	—	2	1	no	—
254	C₂²⋊Q₈	—	2	2	no	—
255	C₄×Q₈	—	2	2	no	—
256	#117	C₂³×C₁₃₉	1	2	yes	—
257	#117	C₂³×C₁₃₉	1	1	yes	characteristic
258	#117	C₂³×C₁₃₉	1	1	yes	characteristic
259	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
260	#108	—	2	1	no	—
261	#108	—	2	1	no	—
262	#108	—	2	1	no	—
263	#108	—	2	1	no	—
264	#108	—	4	2	no	—
265	#107	—	2	1	no	—
266	#106	—	2	1	no	—
267	C₄⋊C₈	—	2	2	no	—
268	C₄⋊C₈	—	2	2	no	—
269	C₄⋊C₈	—	2	2	no	—
270	C₄⋊C₈	—	4	2	no	—
271	#104	—	2	4	no	—
272	#104	—	2	2	no	—
273	#104	—	2	2	no	—
274	#104	—	4	2	no	—
275	#99	—	2	4	no	—
276	C₂²⋊C₈	—	4	2	no	—
277	#97	—	2	1	no	—
278	#97	D₄×C₁₃₉	1	2	yes	—
279	C₄×C₈	—	2	1	no	—
280	C₄×C₈	—	2	1	no	—
281	C₄×C₈	—	2	1	no	—
282	C₄×C₈	D₄×C₁₃₉	1	2	yes	—
283	#41	—	2	2	no	—
284	#41	—	2	2	no	—
285	#41	—	2	2	no	—
286	#41	—	2	2	no	—
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	C₂×Q₈×C₁₃₉	1	2	yes	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	C₂×Q₈×C₁₃₉	1	2	yes	—
291	C₂²×C₄	—	2	1	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
294	Q₁₆	—	2	1	no	—
295	Q₁₆	—	2	1	no	—
296	SD₁₆	—	2	2	no	—
297	SD₁₆	—	2	2	no	—
298	D₈	—	2	1	no	—
299	D₈	—	2	1	no	—
300	M₁₆	—	2	1	no	—
301	M₁₆	—	2	1	no	—
302	M₁₆	—	2	2	no	—
303	M₁₆	—	2	2	no	—
304	M₁₆	—	2	2	no	—
305	M₁₆	—	2	1	no	—
306	M₁₆	—	2	1	no	—
307	M₁₆	—	2	2	no	—
308	M₁₆	—	4	4	no	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	4	4	no	—
316	C₂×C₈	C₂×D₄×C₁₃₉	1	2	yes	—
317	C₂×C₈	C₂×D₄×C₁₃₉	1	1	yes	characteristic
318	C₂×C₈	C₂×D₄×C₁₃₉	1	1	yes	characteristic
319	C₂×C₈	C₂×Q₈×C₁₃₉	1	1	yes	characteristic
320	C₂×C₈	C₂×Q₈×C₁₃₉	1	1	yes	characteristic
321	C₂×C₈	#41×C₁₃₉	1	1	yes	characteristic
322	C₂×C₈	#41×C₁₃₉	1	1	yes	characteristic
323	C₄⋊C₄	—	2	4	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	1	no	—
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₂²⋊C₄	—	2	1	no	—
329	C₂²⋊C₄	—	2	2	no	—
330	C₂²⋊C₄	#41×C₁₃₉	1	2	yes	—
331	C₄²	—	2	1	no	—
332	C₄²	—	2	1	no	—
333	C₄²	—	2	2	no	—
334	C₄²	C₂×D₄×C₁₃₉	1	2	yes	—
335	C₄²	#41×C₁₃₉	1	1	yes	characteristic
336	C₄²	#41×C₁₃₉	1	1	yes	characteristic
337	C₂³	—	2	2	no	—
338	C₂³	C₂×#41×C₁₃₉	1	1	yes	characteristic
339	Q₈	—	2	2	no	—
340	Q₈	—	2	2	no	—
341	Q₈	—	4	4	no	—
342	D₄	—	2	2	no	—
343	D₄	—	2	2	no	—
344	D₄	—	4	2	no	—
345	D₄	—	4	2	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
356	C₂×C₄	C₂²×Q₈×C₁₃₉	1	1	yes	characteristic
357	C₂×C₄	C₂×#41×C₁₃₉	1	1	yes	characteristic
358	C₂×C₄	C₂×#41×C₁₃₉	1	1	yes	characteristic
359	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
360	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
361	C₈	—	2	2	no	—
362	C₈	—	4	1	no	—
363	C₈	—	4	2	no	—
364	C₈	—	4	1	no	—
365	C₈	—	4	2	no	—
366	C₈	C₂²⋊Q₈×C₁₃₉	1	1	yes	characteristic
367	C₈	C₂²⋊Q₈×C₁₃₉	1	1	yes	characteristic
368	C₈	C₂²⋊Q₈×C₁₃₉	1	1	yes	characteristic
369	C₈	C₂²⋊Q₈×C₁₃₉	1	1	yes	characteristic
370	C₂²	—	4	1	no	—
371	C₂²	—	4	2	no	—
372	C₂²	—	8	2	no	—
373	C₂²	#525×C₁₃₉	1	1	yes	characteristic
374	C₂²	#554×C₁₃₉	1	1	yes	characteristic
375	C₂²	#559×C₁₃₉	1	1	yes	characteristic
376	C₄	—	2	2	no	—
377	C₄	—	4	1	no	—
378	C₄	—	4	2	no	—
379	C₄	—	4	2	no	—
380	C₄	—	4	2	no	—
381	C₄	—	8	2	no	—
382	C₄	C₂×C₂²⋊Q₈×C₁₃₉	1	1	yes	characteristic
383	C₄	#535×C₁₃₉	1	1	yes	characteristic
384	C₄	#554×C₁₃₉	1	1	yes	characteristic
385	C₄	#559×C₁₃₉	1	1	yes	characteristic
386	C₂	—	2	1	no	—
387	C₂	—	2	1	no	—
388	C₂	—	2	1	no	—
389	C₂	—	8	2	no	—
390	C₂	#2580×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₃₉	#535
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
socle	C₂×C₁₃₉	#2580
prime radical	C₂×#135×C₁₃₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃₉ ◁ C₂²×C₄×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. #2960×C₁₃₉	C₂	semidirect
3. #2098×C₁₃₉	C₂	semidirect
4. #2031×C₁₃₉	C₂	semidirect
7. #1953×C₁₃₉	C₂	semidirect
8. #1945×C₁₃₉	C₂	semidirect
9. #1868×C₁₃₉	C₂	semidirect
10. #1861×C₁₃₉	C₂	semidirect
11. #1833×C₁₃₉	C₂	semidirect
44. C₂×Q₁₆×C₁₃₉	Q₈	semidirect
45. C₂×SD₁₆×C₁₃₉	Q₈	semidirect
46. C₂×D₈×C₁₃₉	Q₈	semidirect
195. #29270	C₁₃₉	direct (N × H)
196. C₁₃₉	#29270	direct (N × H)
197. #2960	C₂×C₁₃₉	semidirect
199. #2098	C₂×C₁₃₉	semidirect
200. #2031	C₂×C₁₃₉	semidirect
203. #1953	C₂×C₁₃₉	semidirect
204. #1945	C₂×C₁₃₉	semidirect
205. #1868	C₂×C₁₃₉	semidirect
206. #1861	C₂×C₁₃₉	semidirect
207. #1833	C₂×C₁₃₉	semidirect
240. C₂×Q₁₆	Q₈×C₁₃₉	semidirect
241. C₂×SD₁₆	Q₈×C₁₃₉	semidirect
242. C₂×D₈	Q₈×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2960×C₁₃₉	2
#2957×C₁₃₉	2
#2098×C₁₃₉	2
#2031×C₁₃₉	2
#1976×C₁₃₉	2
#1974×C₁₃₉	2
#1953×C₁₃₉	2
#1945×C₁₃₉	2
#1868×C₁₃₉	2
#1861×C₁₃₉	2
#1833×C₁₃₉	2
#29270	139

Subgroups — C139×#29270 #48023866

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#29270 #48023866