Subgroups — C₁₃₉×#10923 #48005519

Order 35584.

1290 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#104×C₁₃₉	C₂	1	2	yes	maximal
2	#2297×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄³×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#339×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#1728×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
7	C₂²×M₁₆×C₁₃₉	C₂²	1	2	yes	—
8	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
9	C₂²×C₄²×C₁₃₉	—	2	2	no	—
10	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
11	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
12	C₂×#104×C₁₃₉	—	2	4	no	—
13	C₂×#104×C₁₃₉	—	2	4	no	—
14	C₂×#104×C₁₃₉	C₄	1	8	yes	complemented
15	#391×C₁₃₉	C₄	1	2	yes	complemented
16	#390×C₁₃₉	C₄	1	2	yes	complemented
17	#386×C₁₃₉	—	2	2	no	—
18	C₄×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
19	C₄³×C₁₃₉	—	2	4	no	—
20	#339×C₁₃₉	—	2	4	no	—
21	#336×C₁₃₉	—	2	2	no	—
22	C₂×#41×C₁₃₉	—	2	2	no	—
23	C₂×#41×C₁₃₉	—	2	2	no	—
24	C₂×#41×C₁₃₉	—	2	2	no	—
25	C₂×#41×C₁₃₉	—	2	2	no	—
26	C₂×#41×C₁₃₉	—	2	2	no	—
27	C₂×#41×C₁₃₉	C₂×C₄	1	4	yes	—
28	C₂²×Q₈×C₁₃₉	C₂×C₄	1	1	yes	characteristic
29	C₂²×D₄×C₁₃₉	—	2	1	no	—
30	C₂²×D₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
31	C₂³×C₄×C₁₃₉	—	2	2	no	—
32	C₂³×C₄×C₁₃₉	—	2	1	no	—
33	C₂³×C₄×C₁₃₉	D₄	1	2	yes	—
34	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
35	C₂×M₁₆×C₁₃₉	—	2	2	no	—
36	C₂×M₁₆×C₁₃₉	—	2	2	no	—
37	C₂×M₁₆×C₁₃₉	—	2	2	no	—
38	C₂×M₁₆×C₁₃₉	—	2	2	no	—
39	C₂×M₁₆×C₁₃₉	—	2	2	no	—
40	C₂×M₁₆×C₁₃₉	C₂×C₄	1	4	yes	—
41	C₂²×C₈×C₁₃₉	—	2	2	no	—
42	#117×C₁₃₉	—	2	2	no	—
43	#117×C₁₃₉	—	2	2	no	—
44	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	2	yes	—
45	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
46	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
47	C₂×C₄²×C₁₃₉	—	2	16	no	—
48	C₂×C₄²×C₁₃₉	—	2	8	no	—
49	C₂×C₄²×C₁₃₉	—	2	2	no	—
50	C₂×C₄²×C₁₃₉	—	2	2	no	—
51	C₂×C₄²×C₁₃₉	—	2	2	no	—
52	C₂×C₄²×C₁₃₉	—	2	2	no	—
53	C₂×C₄²×C₁₃₉	—	2	2	no	—
54	C₂×C₄²×C₁₃₉	—	2	1	no	—
55	C₂×C₄²×C₁₃₉	C₂×C₄	1	2	yes	—
56	C₂×C₄²×C₁₃₉	C₂×C₄	1	4	yes	—
57	C₂×C₄²×C₁₃₉	D₄	1	2	yes	—
58	C₂×C₄²×C₁₃₉	D₄	1	4	yes	—
59	C₂×C₄²×C₁₃₉	D₄	1	4	yes	—
60	#104×C₁₃₉	—	2	16	no	—
61	#95×C₁₃₉	—	2	4	no	—
62	C₂⁴×C₁₃₉	—	2	1	no	—
63	C₂⁴×C₁₃₉	C₂×D₄	1	1	yes	characteristic
64	#41×C₁₃₉	—	2	4	no	—
65	#41×C₁₃₉	—	2	4	no	—
66	#41×C₁₃₉	—	2	4	no	—
67	#41×C₁₃₉	—	2	4	no	—
68	#41×C₁₃₉	—	4	2	no	—
69	#41×C₁₃₉	—	4	2	no	—
70	#41×C₁₃₉	—	4	2	no	—
71	#41×C₁₃₉	—	4	2	no	—
72	C₂×Q₈×C₁₃₉	—	2	1	no	—
73	C₂×Q₈×C₁₃₉	—	2	2	no	—
74	C₂×Q₈×C₁₃₉	—	2	2	no	—
75	C₂×Q₈×C₁₃₉	C₄²	1	2	yes	complemented
76	C₂×D₄×C₁₃₉	—	2	4	no	—
77	C₂×D₄×C₁₃₉	—	2	1	no	—
78	C₂×D₄×C₁₃₉	—	2	2	no	—
79	C₂×D₄×C₁₃₉	—	2	2	no	—
80	C₂×D₄×C₁₃₉	—	4	1	no	—
81	C₂×D₄×C₁₃₉	—	4	2	no	—
82	C₂×D₄×C₁₃₉	—	4	1	no	—
83	C₂×D₄×C₁₃₉	C₄²	1	2	yes	complemented
84	C₂²×C₄×C₁₃₉	—	2	16	no	—
85	C₂²×C₄×C₁₃₉	—	2	4	no	—
86	C₂²×C₄×C₁₃₉	—	2	2	no	—
87	C₂²×C₄×C₁₃₉	—	2	4	no	—
88	C₂²×C₄×C₁₃₉	—	2	4	no	—
89	C₂²×C₄×C₁₃₉	—	2	2	no	—
90	C₂²×C₄×C₁₃₉	—	2	8	no	—
91	C₂²×C₄×C₁₃₉	—	2	1	no	—
92	C₂²×C₄×C₁₃₉	—	2	4	no	—
93	C₂²×C₄×C₁₃₉	—	2	2	no	—
94	C₂²×C₄×C₁₃₉	—	4	2	no	—
95	C₂²×C₄×C₁₃₉	—	4	1	no	—
96	C₂²×C₄×C₁₃₉	—	4	1	no	—
97	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	4	yes	—
98	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
104	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
105	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
106	M₁₆×C₁₃₉	—	2	4	no	—
107	M₁₆×C₁₃₉	—	2	4	no	—
108	M₁₆×C₁₃₉	—	4	2	no	—
109	M₁₆×C₁₃₉	—	4	2	no	—
110	C₂×C₈×C₁₃₉	—	2	4	no	—
111	C₂×C₈×C₁₃₉	—	4	2	no	—
112	C₂×C₈×C₁₃₉	—	4	2	no	—
113	C₄⋊C₄×C₁₃₉	—	2	4	no	—
114	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
115	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
116	C₄²×C₁₃₉	—	2	32	no	—
117	C₄²×C₁₃₉	—	2	4	no	—
118	C₄²×C₁₃₉	—	2	4	no	—
119	C₄²×C₁₃₉	—	2	4	no	—
120	C₄²×C₁₃₉	—	2	4	no	—
121	C₄²×C₁₃₉	—	2	4	no	—
122	C₄²×C₁₃₉	—	4	1	no	—
123	C₄²×C₁₃₉	—	4	1	no	—
124	C₄²×C₁₃₉	C₂²⋊C₄	1	8	yes	complemented
125	C₂³×C₁₃₉	—	2	4	no	—
126	C₂³×C₁₃₉	—	2	2	no	—
127	C₂³×C₁₃₉	—	4	1	no	—
128	C₂³×C₁₃₉	—	4	1	no	—
129	C₂³×C₁₃₉	—	4	4	no	—
130	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
131	C₂³×C₁₃₉	C₄×D₄	1	2	yes	—
132	C₂³×C₁₃₉	#120	1	1	yes	characteristic
133	C₂³×C₁₃₉	#121	1	2	yes	—
134	C₂³×C₁₃₉	#123	1	1	yes	characteristic
135	Q₈×C₁₃₉	—	2	4	no	—
136	Q₈×C₁₃₉	—	4	2	no	—
137	D₄×C₁₃₉	—	2	4	no	—
138	D₄×C₁₃₉	—	4	4	no	—
139	D₄×C₁₃₉	—	4	4	no	—
140	D₄×C₁₃₉	—	4	2	no	—
141	C₂×C₄×C₁₃₉	—	2	16	no	—
142	C₂×C₄×C₁₃₉	—	2	8	no	—
143	C₂×C₄×C₁₃₉	—	2	16	no	—
144	C₂×C₄×C₁₃₉	—	2	16	no	—
145	C₂×C₄×C₁₃₉	—	2	8	no	—
146	C₂×C₄×C₁₃₉	—	2	4	no	—
147	C₂×C₄×C₁₃₉	—	2	8	no	—
148	C₂×C₄×C₁₃₉	—	2	4	no	—
149	C₂×C₄×C₁₃₉	—	2	2	no	—
150	C₂×C₄×C₁₃₉	—	4	1	no	—
151	C₂×C₄×C₁₃₉	—	4	1	no	—
152	C₂×C₄×C₁₃₉	—	4	4	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	#104	1	8	yes	complemented
157	C₂×C₄×C₁₃₉	C₂×C₄²	1	1	yes	characteristic
158	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
159	C₂×C₄×C₁₃₉	#117	1	2	yes	—
160	C₂×C₄×C₁₃₉	#117	1	1	yes	characteristic
161	C₂×C₄×C₁₃₉	C₄×D₄	1	2	yes	—
162	C₂×C₄×C₁₃₉	C₄×D₄	1	2	yes	—
163	C₂×C₄×C₁₃₉	C₄×D₄	1	2	yes	—
164	C₂×C₄×C₁₃₉	C₄×D₄	1	2	yes	—
165	C₂×C₄×C₁₃₉	C₄×D₄	1	2	yes	—
166	C₂×C₄×C₁₃₉	#121	1	2	yes	—
167	C₂×C₄×C₁₃₉	#121	1	2	yes	—
168	C₂×C₄×C₁₃₉	#123	1	2	yes	—
169	C₂×C₄×C₁₃₉	#124	1	1	yes	characteristic
170	C₂×C₄×C₁₃₉	#124	1	2	yes	—
171	C₂×C₄×C₁₃₉	#126	1	2	yes	—
172	C₂×C₄×C₁₃₉	#127	1	1	yes	characteristic
173	C₈×C₁₃₉	—	4	4	no	—
174	C₂²×C₁₃₉	—	2	2	no	—
175	C₂²×C₁₃₉	—	2	2	no	—
176	C₂²×C₁₃₉	—	2	4	no	—
177	C₂²×C₁₃₉	—	2	4	no	—
178	C₂²×C₁₃₉	—	4	2	no	—
179	C₂²×C₁₃₉	—	4	4	no	—
180	C₂²×C₁₃₉	—	8	2	no	—
181	C₂²×C₁₃₉	—	8	2	no	—
182	C₂²×C₁₃₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
183	C₂²×C₁₃₉	#386	1	2	yes	—
184	C₂²×C₁₃₉	#386	1	1	yes	characteristic
185	C₂²×C₁₃₉	#388	1	2	yes	—
186	C₂²×C₁₃₉	#390	1	1	yes	characteristic
187	C₂²×C₁₃₉	C₂×#104	1	4	yes	—
188	C₄×C₁₃₉	—	2	16	no	—
189	C₄×C₁₃₉	—	2	8	no	—
190	C₄×C₁₃₉	—	4	2	no	—
191	C₄×C₁₃₉	—	8	2	no	—
192	C₄×C₁₃₉	C₄×C₂²⋊C₄	1	2	yes	—
193	C₄×C₁₃₉	#388	1	2	yes	—
194	C₄×C₁₃₉	#388	1	2	yes	—
195	C₄×C₁₃₉	#390	1	2	yes	—
196	C₂×C₁₃₉	—	2	2	no	—
197	C₂×C₁₃₉	—	2	2	no	—
198	C₂×C₁₃₉	—	8	2	no	—
199	C₂×C₁₃₉	#1437	1	1	yes	characteristic
200	C₂×C₁₃₉	C₄×#104	1	2	yes	—
201	C₂×C₁₃₉	#1896	1	2	yes	—
202	C₂×C₁₃₉	#1962	1	2	yes	—
203	#10923	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
204	C₁₃₉	#10923	1	1	yes	characteristic, direct product factor, Sylow
205	C₂²×#104	C₂×C₁₃₉	1	2	yes	—
206	#2297	C₂×C₁₃₉	1	1	yes	characteristic
207	C₂×C₄³	C₂×C₁₃₉	1	1	yes	characteristic, complemented
208	C₂×#339	C₂×C₁₃₉	1	2	yes	complemented
209	#1728	C₂×C₁₃₉	1	1	yes	characteristic, complemented
210	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
211	C₂²×M₁₆	C₂²×C₁₃₉	1	2	yes	—
212	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
213	C₂²×C₄²	—	2	2	no	—
214	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
215	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
216	C₂×#104	—	2	4	no	—
217	C₂×#104	—	2	4	no	—
218	C₂×#104	C₄×C₁₃₉	1	8	yes	complemented
219	#391	C₄×C₁₃₉	1	2	yes	complemented
220	#390	C₄×C₁₃₉	1	2	yes	complemented
221	#386	—	2	2	no	—
222	C₄×C₂²⋊C₄	—	2	2	no	—
223	C₄³	—	2	4	no	—
224	#339	—	2	4	no	—
225	#336	—	2	2	no	—
226	C₂×#41	—	2	2	no	—
227	C₂×#41	—	2	2	no	—
228	C₂×#41	—	2	2	no	—
229	C₂×#41	—	2	2	no	—
230	C₂×#41	—	2	2	no	—
231	C₂×#41	C₂×C₄×C₁₃₉	1	4	yes	—
232	C₂²×Q₈	C₂×C₄×C₁₃₉	1	1	yes	characteristic
233	C₂²×D₄	—	2	1	no	—
234	C₂²×D₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
235	C₂³×C₄	—	2	2	no	—
236	C₂³×C₄	—	2	1	no	—
237	C₂³×C₄	D₄×C₁₃₉	1	2	yes	—
238	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
239	C₂×M₁₆	—	2	2	no	—
240	C₂×M₁₆	—	2	2	no	—
241	C₂×M₁₆	—	2	2	no	—
242	C₂×M₁₆	—	2	2	no	—
243	C₂×M₁₆	—	2	2	no	—
244	C₂×M₁₆	C₂×C₄×C₁₃₉	1	4	yes	—
245	C₂²×C₈	—	2	2	no	—
246	#117	—	2	2	no	—
247	#117	—	2	2	no	—
248	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	2	yes	—
249	C₂×C₂²⋊C₄	—	2	1	no	—
250	C₂×C₂²⋊C₄	—	2	4	no	—
251	C₂×C₄²	—	2	8	no	—
252	C₂×C₄²	—	2	16	no	—
253	C₂×C₄²	—	2	2	no	—
254	C₂×C₄²	—	2	2	no	—
255	C₂×C₄²	—	2	2	no	—
256	C₂×C₄²	—	2	2	no	—
257	C₂×C₄²	—	2	2	no	—
258	C₂×C₄²	—	2	1	no	—
259	C₂×C₄²	C₂×C₄×C₁₃₉	1	2	yes	—
260	C₂×C₄²	C₂×C₄×C₁₃₉	1	4	yes	—
261	C₂×C₄²	D₄×C₁₃₉	1	2	yes	—
262	C₂×C₄²	D₄×C₁₃₉	1	4	yes	—
263	C₂×C₄²	D₄×C₁₃₉	1	4	yes	—
264	#104	—	2	16	no	—
265	#95	—	2	4	no	—
266	C₂⁴	—	2	1	no	—
267	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
268	#41	—	2	4	no	—
269	#41	—	2	4	no	—
270	#41	—	2	4	no	—
271	#41	—	2	4	no	—
272	#41	—	4	2	no	—
273	#41	—	4	2	no	—
274	#41	—	4	2	no	—
275	#41	—	4	2	no	—
276	C₂×Q₈	—	2	1	no	—
277	C₂×Q₈	—	2	2	no	—
278	C₂×Q₈	—	2	2	no	—
279	C₂×Q₈	C₄²×C₁₃₉	1	2	yes	complemented
280	C₂×D₄	—	2	4	no	—
281	C₂×D₄	—	2	1	no	—
282	C₂×D₄	—	2	2	no	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	4	1	no	—
285	C₂×D₄	—	4	2	no	—
286	C₂×D₄	—	4	1	no	—
287	C₂×D₄	C₄²×C₁₃₉	1	2	yes	complemented
288	C₂²×C₄	—	2	16	no	—
289	C₂²×C₄	—	2	4	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	4	no	—
292	C₂²×C₄	—	2	4	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	8	no	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	4	2	no	—
299	C₂²×C₄	—	4	1	no	—
300	C₂²×C₄	—	4	1	no	—
301	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	4	yes	—
302	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
303	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
304	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
305	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
306	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
307	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
308	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
309	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
310	M₁₆	—	2	4	no	—
311	M₁₆	—	2	4	no	—
312	M₁₆	—	4	2	no	—
313	M₁₆	—	4	2	no	—
314	C₂×C₈	—	2	4	no	—
315	C₂×C₈	—	4	2	no	—
316	C₂×C₈	—	4	2	no	—
317	C₄⋊C₄	—	2	4	no	—
318	C₂²⋊C₄	—	4	2	no	—
319	C₂²⋊C₄	—	4	8	no	—
320	C₄²	—	2	32	no	—
321	C₄²	—	2	4	no	—
322	C₄²	—	2	4	no	—
323	C₄²	—	2	4	no	—
324	C₄²	—	2	4	no	—
325	C₄²	—	2	4	no	—
326	C₄²	—	4	1	no	—
327	C₄²	—	4	1	no	—
328	C₄²	C₂²⋊C₄×C₁₃₉	1	8	yes	complemented
329	C₂³	—	2	4	no	—
330	C₂³	—	2	2	no	—
331	C₂³	—	4	4	no	—
332	C₂³	—	4	1	no	—
333	C₂³	—	4	1	no	—
334	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
335	C₂³	C₄×D₄×C₁₃₉	1	2	yes	—
336	C₂³	#120×C₁₃₉	1	1	yes	characteristic
337	C₂³	#121×C₁₃₉	1	2	yes	—
338	C₂³	#123×C₁₃₉	1	1	yes	characteristic
339	Q₈	—	2	4	no	—
340	Q₈	—	4	2	no	—
341	D₄	—	2	4	no	—
342	D₄	—	4	4	no	—
343	D₄	—	4	4	no	—
344	D₄	—	4	2	no	—
345	C₂×C₄	—	2	16	no	—
346	C₂×C₄	—	2	8	no	—
347	C₂×C₄	—	2	16	no	—
348	C₂×C₄	—	2	16	no	—
349	C₂×C₄	—	2	8	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	8	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	4	no	—
357	C₂×C₄	—	4	4	no	—
358	C₂×C₄	—	4	4	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	#104×C₁₃₉	1	8	yes	complemented
361	C₂×C₄	C₂×C₄²×C₁₃₉	1	1	yes	characteristic
362	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
363	C₂×C₄	#117×C₁₃₉	1	2	yes	—
364	C₂×C₄	#117×C₁₃₉	1	1	yes	characteristic
365	C₂×C₄	C₄×D₄×C₁₃₉	1	2	yes	—
366	C₂×C₄	C₄×D₄×C₁₃₉	1	2	yes	—
367	C₂×C₄	C₄×D₄×C₁₃₉	1	2	yes	—
368	C₂×C₄	C₄×D₄×C₁₃₉	1	2	yes	—
369	C₂×C₄	C₄×D₄×C₁₃₉	1	2	yes	—
370	C₂×C₄	#121×C₁₃₉	1	2	yes	—
371	C₂×C₄	#121×C₁₃₉	1	2	yes	—
372	C₂×C₄	#123×C₁₃₉	1	2	yes	—
373	C₂×C₄	#124×C₁₃₉	1	1	yes	characteristic
374	C₂×C₄	#124×C₁₃₉	1	2	yes	—
375	C₂×C₄	#126×C₁₃₉	1	2	yes	—
376	C₂×C₄	#127×C₁₃₉	1	1	yes	characteristic
377	C₈	—	4	4	no	—
378	C₂²	—	2	4	no	—
379	C₂²	—	2	2	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	2	4	no	—
382	C₂²	—	4	4	no	—
383	C₂²	—	4	2	no	—
384	C₂²	—	8	2	no	—
385	C₂²	—	8	2	no	—
386	C₂²	C₄×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
387	C₂²	#386×C₁₃₉	1	2	yes	—
388	C₂²	#386×C₁₃₉	1	1	yes	characteristic
389	C₂²	#388×C₁₃₉	1	2	yes	—
390	C₂²	#390×C₁₃₉	1	1	yes	characteristic
391	C₂²	C₂×#104×C₁₃₉	1	4	yes	—
392	C₄	—	2	16	no	—
393	C₄	—	2	8	no	—
394	C₄	—	4	2	no	—
395	C₄	—	8	2	no	—
396	C₄	C₄×C₂²⋊C₄×C₁₃₉	1	2	yes	—
397	C₄	#388×C₁₃₉	1	2	yes	—
398	C₄	#388×C₁₃₉	1	2	yes	—
399	C₄	#390×C₁₃₉	1	2	yes	—
400	C₂	—	2	2	no	—
401	C₂	—	2	2	no	—
402	C₂	—	8	2	no	—
403	C₂	#1437×C₁₃₉	1	1	yes	characteristic
404	C₂	C₄×#104×C₁₃₉	1	2	yes	—
405	C₂	#1896×C₁₃₉	1	2	yes	—
406	C₂	#1962×C₁₃₉	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃₉	C₂×D₄
commutator	C₂×C₄	C₂×C₄²×C₁₃₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₃₉
socle	C₂³×C₁₃₉	C₂×C₂²⋊C₄
prime radical	C₂²×#41×C₁₃₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃₉ ◁ C₂²×C₄²×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₄³×C₁₃₉	C₂	semidirect
4. C₂×#339×C₁₃₉	C₂	semidirect
5. #1728×C₁₃₉	C₂	semidirect
14. C₂×#104×C₁₃₉	C₄	semidirect
15. #391×C₁₃₉	C₄	semidirect
16. #390×C₁₃₉	C₄	semidirect
75. C₂×Q₈×C₁₃₉	C₄²	semidirect
83. C₂×D₄×C₁₃₉	C₄²	semidirect
124. C₄²×C₁₃₉	C₂²⋊C₄	semidirect
156. C₂×C₄×C₁₃₉	#104	semidirect
203. #10923	C₁₃₉	direct (N × H)
204. C₁₃₉	#10923	direct (N × H)
207. C₂×C₄³	C₂×C₁₃₉	semidirect
208. C₂×#339	C₂×C₁₃₉	semidirect
209. #1728	C₂×C₁₃₉	semidirect
218. C₂×#104	C₄×C₁₃₉	semidirect
219. #391	C₄×C₁₃₉	semidirect
220. #390	C₄×C₁₃₉	semidirect
279. C₂×Q₈	C₄²×C₁₃₉	semidirect
287. C₂×D₄	C₄²×C₁₃₉	semidirect
328. C₄²	C₂²⋊C₄×C₁₃₉	semidirect
360. C₂×C₄	#104×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#104×C₁₃₉	2
#2297×C₁₃₉	2
C₂×C₄³×C₁₃₉	2
C₂×#339×C₁₃₉	2
#1728×C₁₃₉	2
#10923	139

Subgroups — C139×#10923 #48005519

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#10923 #48005519