Subgroups — C₁₃₉×#36465 #48031061

Order 35584.

3666 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#550×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄×Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#548×C₁₃₉	C₂	1	4	yes	maximal, complemented
4	#2858×C₁₃₉	C₂	1	3	yes	maximal, complemented
5	#2542×C₁₃₉	C₂	1	3	yes	maximal, complemented
6	#2541×C₁₃₉	C₂	1	3	yes	maximal, complemented
7	#2540×C₁₃₉	C₂	1	12	yes	maximal, complemented
8	C₄×#127×C₁₃₉	C₂	1	3	yes	maximal, complemented
9	C₄²×Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₁₃₉	C₂²	1	2	yes	—
11	C₂³×Q₈×C₁₃₉	C₂²	1	2	yes	—
12	#550×C₁₃₉	—	2	8	no	—
13	D₄×Q₈×C₁₃₉	—	2	8	no	—
14	#548×C₁₃₉	—	2	32	no	—
15	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	3	yes	—
16	C₂×#127×C₁₃₉	C₂²	1	3	yes	—
17	C₂×#127×C₁₃₉	C₂²	1	3	yes	—
18	C₂×#124×C₁₃₉	C₂²	1	12	yes	—
19	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	6	yes	—
20	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	12	yes	—
21	C₂×#121×C₁₃₉	C₂²	1	6	yes	—
22	C₂×#121×C₁₃₉	C₂²	1	12	yes	—
23	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
24	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₁₃₉	C₂²	1	12	yes	—
26	C₂×C₄×D₄×C₁₃₉	C₂²	1	3	yes	—
27	C₂×C₄×D₄×C₁₃₉	C₂²	1	3	yes	—
28	#399×C₁₃₉	C₂²	1	12	yes	—
29	#392×C₁₃₉	C₂²	1	12	yes	—
30	#390×C₁₃₉	C₂²	1	12	yes	—
31	#390×C₁₃₉	C₂²	1	12	yes	—
32	#390×C₁₃₉	C₂²	1	6	yes	—
33	#390×C₁₃₉	C₂²	1	1	yes	characteristic
34	#390×C₁₃₉	C₂²	1	3	yes	—
35	#384×C₁₃₉	C₂²	1	3	yes	—
36	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	6	yes	—
37	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	3	yes	—
38	C₄³×C₁₃₉	C₂²	1	3	yes	—
39	C₂×#41×C₁₃₉	—	2	16	no	—
40	C₂×#41×C₁₃₉	—	2	8	no	—
41	C₂²×Q₈×C₁₃₉	—	2	16	no	—
42	C₂²×Q₈×C₁₃₉	—	2	8	no	—
43	C₂²×Q₈×C₁₃₉	C₂³	1	6	yes	—
44	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₁₃₉	C₂³	1	3	yes	—
46	C₂²×D₄×C₁₃₉	C₂³	1	6	yes	—
47	C₂²×D₄×C₁₃₉	C₂³	1	12	yes	—
48	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
49	C₂²×D₄×C₁₃₉	C₂³	1	6	yes	—
50	C₂³×C₄×C₁₃₉	C₂³	1	6	yes	—
51	C₂³×C₄×C₁₃₉	C₂³	1	6	yes	—
52	C₄⋊Q₈×C₁₃₉	—	2	12	no	—
53	#127×C₁₃₉	—	2	12	no	—
54	#127×C₁₃₉	—	2	12	no	—
55	#124×C₁₃₉	—	2	48	no	—
56	C₂²⋊Q₈×C₁₃₉	—	2	48	no	—
57	C₂²⋊Q₈×C₁₃₉	—	2	24	no	—
58	#121×C₁₃₉	—	2	48	no	—
59	#121×C₁₃₉	—	2	24	no	—
60	C₄×Q₈×C₁₃₉	D₄	1	16	yes	complemented
61	C₄×Q₈×C₁₃₉	D₄	1	8	yes	complemented
62	C₄×D₄×C₁₃₉	—	2	48	no	—
63	C₄×D₄×C₁₃₉	—	2	12	no	—
64	C₄×D₄×C₁₃₉	—	2	12	no	—
65	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	12	yes	—
66	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
67	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
69	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
70	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
71	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
72	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	24	yes	—
73	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
74	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
75	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	12	yes	—
76	C₂×C₄²×C₁₃₉	C₂³	1	3	yes	—
77	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₁₃₉	C₂³	1	6	yes	—
79	C₂×C₄²×C₁₃₉	C₂³	1	6	yes	—
80	C₂×C₄²×C₁₃₉	C₂³	1	3	yes	—
81	#95×C₁₃₉	C₂³	1	6	yes	—
82	C₂⁴×C₁₃₉	C₂⁴	1	6	yes	—
83	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
84	#41×C₁₃₉	—	4	32	no	—
85	C₂×Q₈×C₁₃₉	—	2	24	no	—
86	C₂×Q₈×C₁₃₉	—	2	12	no	—
87	C₂×Q₈×C₁₃₉	—	4	32	no	—
88	C₂×Q₈×C₁₃₉	C₂×D₄	1	8	yes	—
89	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	—
90	C₂×D₄×C₁₃₉	—	2	24	no	—
91	C₂×D₄×C₁₃₉	—	2	2	no	—
92	C₂×D₄×C₁₃₉	—	2	24	no	—
93	C₂×D₄×C₁₃₉	—	2	6	no	—
94	C₂×D₄×C₁₃₉	—	2	24	no	—
95	C₂×D₄×C₁₃₉	—	2	12	no	—
96	C₂×D₄×C₁₃₉	—	2	12	no	—
97	C₂×D₄×C₁₃₉	—	2	6	no	—
98	C₂×D₄×C₁₃₉	—	2	2	no	—
99	C₂×D₄×C₁₃₉	—	2	6	no	—
100	C₂×D₄×C₁₃₉	—	4	12	no	—
101	C₂×D₄×C₁₃₉	—	4	12	no	—
102	C₂×D₄×C₁₃₉	#41	1	4	yes	complemented
103	C₂²×C₄×C₁₃₉	—	2	24	no	—
104	C₂²×C₄×C₁₃₉	—	2	12	no	—
105	C₂²×C₄×C₁₃₉	—	2	12	no	—
106	C₂²×C₄×C₁₃₉	—	2	24	no	—
107	C₂²×C₄×C₁₃₉	C₂⁴	1	6	yes	—
108	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
109	C₂²×C₄×C₁₃₉	C₂⁴	1	6	yes	—
110	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
111	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
112	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
113	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
114	C₄⋊C₄×C₁₃₉	—	2	2	no	—
115	C₄⋊C₄×C₁₃₉	—	2	24	no	—
116	C₄⋊C₄×C₁₃₉	—	2	6	no	—
117	C₄⋊C₄×C₁₃₉	—	2	12	no	—
118	C₄⋊C₄×C₁₃₉	C₂×D₄	1	24	yes	—
119	C₄⋊C₄×C₁₃₉	C₂×D₄	1	12	yes	—
120	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
121	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
122	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
123	C₂²⋊C₄×C₁₃₉	—	2	24	no	—
124	C₂²⋊C₄×C₁₃₉	—	2	48	no	—
125	C₄²×C₁₃₉	—	2	6	no	—
126	C₄²×C₁₃₉	—	2	2	no	—
127	C₄²×C₁₃₉	—	4	6	no	—
128	C₄²×C₁₃₉	C₂×D₄	1	24	yes	—
129	C₄²×C₁₃₉	C₂×D₄	1	12	yes	—
130	C₂³×C₁₃₉	—	2	2	no	—
131	C₂³×C₁₃₉	—	2	4	no	—
132	C₂³×C₁₃₉	—	2	2	no	—
133	C₂³×C₁₃₉	—	2	4	no	—
134	C₂³×C₁₃₉	—	2	12	no	—
135	C₂³×C₁₃₉	—	2	6	no	—
136	C₂³×C₁₃₉	—	2	6	no	—
137	C₂³×C₁₃₉	—	2	6	no	—
138	C₂³×C₁₃₉	—	2	12	no	—
139	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
140	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
141	Q₈×C₁₃₉	—	4	24	no	—
142	Q₈×C₁₃₉	#127	1	16	yes	complemented
143	D₄×C₁₃₉	—	2	8	no	—
144	D₄×C₁₃₉	—	4	48	no	—
145	D₄×C₁₃₉	—	4	24	no	—
146	D₄×C₁₃₉	—	4	12	no	—
147	D₄×C₁₃₉	—	8	12	no	—
148	C₂×C₄×C₁₃₉	—	2	6	no	—
149	C₂×C₄×C₁₃₉	—	2	2	no	—
150	C₂×C₄×C₁₃₉	—	2	2	no	—
151	C₂×C₄×C₁₃₉	—	2	6	no	—
152	C₂×C₄×C₁₃₉	—	2	6	no	—
153	C₂×C₄×C₁₃₉	—	2	2	no	—
154	C₂×C₄×C₁₃₉	—	2	12	no	—
155	C₂×C₄×C₁₃₉	—	2	4	no	—
156	C₂×C₄×C₁₃₉	—	2	6	no	—
157	C₂×C₄×C₁₃₉	—	4	24	no	—
158	C₂×C₄×C₁₃₉	—	4	24	no	—
159	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
160	C₂×C₄×C₁₃₉	C₂²×D₄	1	12	yes	—
161	C₂×C₄×C₁₃₉	C₂²×D₄	1	6	yes	—
162	C₂×C₄×C₁₃₉	C₂²×D₄	1	6	yes	—
163	C₂×C₄×C₁₃₉	C₂²×D₄	1	12	yes	—
164	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
165	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
166	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
167	C₂²×C₁₃₉	—	2	4	no	—
168	C₂²×C₁₃₉	—	2	8	no	—
169	C₂²×C₁₃₉	—	4	2	no	—
170	C₂²×C₁₃₉	—	4	4	no	—
171	C₂²×C₁₃₉	—	4	2	no	—
172	C₂²×C₁₃₉	—	4	6	no	—
173	C₂²×C₁₃₉	—	4	6	no	—
174	C₂²×C₁₃₉	—	4	12	no	—
175	C₂²×C₁₃₉	—	4	12	no	—
176	C₂²×C₁₃₉	—	4	6	no	—
177	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
178	C₂²×C₁₃₉	C₂³×D₄	1	2	yes	—
179	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
180	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
181	C₂²×C₁₃₉	#585	1	2	yes	—
182	C₄×C₁₃₉	—	2	12	no	—
183	C₄×C₁₃₉	—	2	4	no	—
184	C₄×C₁₃₉	—	2	6	no	—
185	C₄×C₁₃₉	—	4	2	no	—
186	C₄×C₁₃₉	—	4	6	no	—
187	C₄×C₁₃₉	C₂×#127	1	12	yes	—
188	C₄×C₁₃₉	#548	1	4	yes	complemented
189	C₂×C₁₃₉	—	4	4	no	—
190	C₂×C₁₃₉	—	8	6	no	—
191	C₂×C₁₃₉	C₂²×#127	1	1	yes	characteristic
192	C₂×C₁₃₉	C₂×#548	1	1	yes	characteristic
193	C₂×C₁₃₉	D₄×#41	1	2	yes	—
194	C₂×C₁₃₉	#3497	1	2	yes	—
195	C₂×C₁₃₉	#3500	1	1	yes	characteristic
196	#36465	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
197	C₁₃₉	#36465	1	1	yes	characteristic, direct product factor, Sylow
198	C₂×#550	C₂×C₁₃₉	1	1	yes	characteristic, complemented
199	C₂×D₄×Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
200	C₂×#548	C₂×C₁₃₉	1	4	yes	complemented
201	#2858	C₂×C₁₃₉	1	3	yes	complemented
202	#2542	C₂×C₁₃₉	1	3	yes	complemented
203	#2541	C₂×C₁₃₉	1	3	yes	complemented
204	#2540	C₂×C₁₃₉	1	12	yes	complemented
205	C₄×#127	C₂×C₁₃₉	1	3	yes	complemented
206	C₄²×Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
207	C₂²×#41	C₂²×C₁₃₉	1	2	yes	—
208	C₂³×Q₈	C₂²×C₁₃₉	1	2	yes	—
209	#550	—	2	8	no	—
210	D₄×Q₈	—	2	8	no	—
211	#548	—	2	32	no	—
212	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	3	yes	—
213	C₂×#127	C₂²×C₁₃₉	1	3	yes	—
214	C₂×#127	C₂²×C₁₃₉	1	3	yes	—
215	C₂×#124	C₂²×C₁₃₉	1	12	yes	—
216	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	12	yes	—
217	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	6	yes	—
218	C₂×#121	C₂²×C₁₃₉	1	12	yes	—
219	C₂×#121	C₂²×C₁₃₉	1	6	yes	—
220	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
221	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
222	C₂×C₄×D₄	C₂²×C₁₃₉	1	12	yes	—
223	C₂×C₄×D₄	C₂²×C₁₃₉	1	3	yes	—
224	C₂×C₄×D₄	C₂²×C₁₃₉	1	3	yes	—
225	#399	C₂²×C₁₃₉	1	12	yes	—
226	#392	C₂²×C₁₃₉	1	12	yes	—
227	#390	C₂²×C₁₃₉	1	1	yes	characteristic
228	#390	C₂²×C₁₃₉	1	3	yes	—
229	#390	C₂²×C₁₃₉	1	12	yes	—
230	#390	C₂²×C₁₃₉	1	12	yes	—
231	#390	C₂²×C₁₃₉	1	6	yes	—
232	#384	C₂²×C₁₃₉	1	3	yes	—
233	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	6	yes	—
234	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	3	yes	—
235	C₄³	C₂²×C₁₃₉	1	3	yes	—
236	C₂×#41	—	2	16	no	—
237	C₂×#41	—	2	8	no	—
238	C₂²×Q₈	—	2	16	no	—
239	C₂²×Q₈	—	2	8	no	—
240	C₂²×Q₈	C₂³×C₁₃₉	1	6	yes	—
241	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
242	C₂²×D₄	C₂³×C₁₃₉	1	3	yes	—
243	C₂²×D₄	C₂³×C₁₃₉	1	6	yes	—
244	C₂²×D₄	C₂³×C₁₃₉	1	12	yes	—
245	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
246	C₂²×D₄	C₂³×C₁₃₉	1	6	yes	—
247	C₂³×C₄	C₂³×C₁₃₉	1	6	yes	—
248	C₂³×C₄	C₂³×C₁₃₉	1	6	yes	—
249	C₄⋊Q₈	—	2	12	no	—
250	#127	—	2	12	no	—
251	#127	—	2	12	no	—
252	#124	—	2	48	no	—
253	C₂²⋊Q₈	—	2	48	no	—
254	C₂²⋊Q₈	—	2	24	no	—
255	#121	—	2	48	no	—
256	#121	—	2	24	no	—
257	C₄×Q₈	D₄×C₁₃₉	1	16	yes	complemented
258	C₄×Q₈	D₄×C₁₃₉	1	8	yes	complemented
259	C₄×D₄	—	2	48	no	—
260	C₄×D₄	—	2	12	no	—
261	C₄×D₄	—	2	12	no	—
262	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
263	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	12	yes	—
264	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
265	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
266	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
267	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
268	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
269	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
270	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
271	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	12	yes	—
272	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	24	yes	—
273	C₂×C₄²	C₂³×C₁₃₉	1	3	yes	—
274	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
275	C₂×C₄²	C₂³×C₁₃₉	1	6	yes	—
276	C₂×C₄²	C₂³×C₁₃₉	1	6	yes	—
277	C₂×C₄²	C₂³×C₁₃₉	1	3	yes	—
278	#95	C₂³×C₁₃₉	1	6	yes	—
279	C₂⁴	C₂⁴×C₁₃₉	1	6	yes	—
280	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
281	#41	—	4	32	no	—
282	C₂×Q₈	—	2	24	no	—
283	C₂×Q₈	—	2	12	no	—
284	C₂×Q₈	—	4	32	no	—
285	C₂×Q₈	C₂×D₄×C₁₃₉	1	8	yes	—
286	C₂×Q₈	C₂×D₄×C₁₃₉	1	4	yes	—
287	C₂×D₄	—	2	24	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	2	24	no	—
290	C₂×D₄	—	2	6	no	—
291	C₂×D₄	—	2	24	no	—
292	C₂×D₄	—	2	12	no	—
293	C₂×D₄	—	2	12	no	—
294	C₂×D₄	—	2	6	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	2	6	no	—
297	C₂×D₄	—	4	12	no	—
298	C₂×D₄	—	4	12	no	—
299	C₂×D₄	#41×C₁₃₉	1	4	yes	complemented
300	C₂²×C₄	—	2	24	no	—
301	C₂²×C₄	—	2	12	no	—
302	C₂²×C₄	—	2	12	no	—
303	C₂²×C₄	—	2	24	no	—
304	C₂²×C₄	C₂⁴×C₁₃₉	1	6	yes	—
305	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
306	C₂²×C₄	C₂⁴×C₁₃₉	1	6	yes	—
307	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
308	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
309	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
310	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	24	no	—
313	C₄⋊C₄	—	2	6	no	—
314	C₄⋊C₄	—	2	12	no	—
315	C₄⋊C₄	C₂×D₄×C₁₃₉	1	24	yes	—
316	C₄⋊C₄	C₂×D₄×C₁₃₉	1	12	yes	—
317	C₂²⋊C₄	—	2	8	no	—
318	C₂²⋊C₄	—	2	12	no	—
319	C₂²⋊C₄	—	2	12	no	—
320	C₂²⋊C₄	—	2	24	no	—
321	C₂²⋊C₄	—	2	48	no	—
322	C₄²	—	2	6	no	—
323	C₄²	—	2	2	no	—
324	C₄²	—	4	6	no	—
325	C₄²	C₂×D₄×C₁₃₉	1	24	yes	—
326	C₄²	C₂×D₄×C₁₃₉	1	12	yes	—
327	C₂³	—	2	2	no	—
328	C₂³	—	2	4	no	—
329	C₂³	—	2	2	no	—
330	C₂³	—	2	4	no	—
331	C₂³	—	2	12	no	—
332	C₂³	—	2	6	no	—
333	C₂³	—	2	6	no	—
334	C₂³	—	2	6	no	—
335	C₂³	—	2	12	no	—
336	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
337	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
338	Q₈	—	4	24	no	—
339	Q₈	#127×C₁₃₉	1	16	yes	complemented
340	D₄	—	2	8	no	—
341	D₄	—	4	48	no	—
342	D₄	—	4	24	no	—
343	D₄	—	4	12	no	—
344	D₄	—	8	12	no	—
345	C₂×C₄	—	2	6	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	6	no	—
349	C₂×C₄	—	2	6	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	12	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	6	no	—
354	C₂×C₄	—	4	24	no	—
355	C₂×C₄	—	4	24	no	—
356	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
357	C₂×C₄	C₂²×D₄×C₁₃₉	1	12	yes	—
358	C₂×C₄	C₂²×D₄×C₁₃₉	1	6	yes	—
359	C₂×C₄	C₂²×D₄×C₁₃₉	1	6	yes	—
360	C₂×C₄	C₂²×D₄×C₁₃₉	1	12	yes	—
361	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
362	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
363	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
364	C₂²	—	2	4	no	—
365	C₂²	—	2	8	no	—
366	C₂²	—	4	2	no	—
367	C₂²	—	4	4	no	—
368	C₂²	—	4	2	no	—
369	C₂²	—	4	6	no	—
370	C₂²	—	4	6	no	—
371	C₂²	—	4	12	no	—
372	C₂²	—	4	12	no	—
373	C₂²	—	4	6	no	—
374	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
375	C₂²	C₂³×D₄×C₁₃₉	1	2	yes	—
376	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
377	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
378	C₂²	#585×C₁₃₉	1	2	yes	—
379	C₄	—	2	12	no	—
380	C₄	—	2	4	no	—
381	C₄	—	2	6	no	—
382	C₄	—	4	2	no	—
383	C₄	—	4	6	no	—
384	C₄	C₂×#127×C₁₃₉	1	12	yes	—
385	C₄	#548×C₁₃₉	1	4	yes	complemented
386	C₂	—	4	4	no	—
387	C₂	—	8	6	no	—
388	C₂	C₂²×#127×C₁₃₉	1	1	yes	characteristic
389	C₂	C₂×#548×C₁₃₉	1	1	yes	characteristic
390	C₂	D₄×#41×C₁₃₉	1	2	yes	—
391	C₂	#3497×C₁₃₉	1	2	yes	—
392	C₂	#3500×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#550×C₁₃₉	C₂	semidirect
2. C₂×D₄×Q₈×C₁₃₉	C₂	semidirect
3. C₂×#548×C₁₃₉	C₂	semidirect
4. #2858×C₁₃₉	C₂	semidirect
5. #2542×C₁₃₉	C₂	semidirect
6. #2541×C₁₃₉	C₂	semidirect
7. #2540×C₁₃₉	C₂	semidirect
8. C₄×#127×C₁₃₉	C₂	semidirect
9. C₄²×Q₈×C₁₃₉	C₂	semidirect
60. C₄×Q₈×C₁₃₉	D₄	semidirect
61. C₄×Q₈×C₁₃₉	D₄	semidirect
102. C₂×D₄×C₁₃₉	#41	semidirect
142. Q₈×C₁₃₉	#127	semidirect
188. C₄×C₁₃₉	#548	semidirect
196. #36465	C₁₃₉	direct (N × H)
197. C₁₃₉	#36465	direct (N × H)
198. C₂×#550	C₂×C₁₃₉	semidirect
199. C₂×D₄×Q₈	C₂×C₁₃₉	semidirect
200. C₂×#548	C₂×C₁₃₉	semidirect
201. #2858	C₂×C₁₃₉	semidirect
202. #2542	C₂×C₁₃₉	semidirect
203. #2541	C₂×C₁₃₉	semidirect
204. #2540	C₂×C₁₃₉	semidirect
205. C₄×#127	C₂×C₁₃₉	semidirect
206. C₄²×Q₈	C₂×C₁₃₉	semidirect
257. C₄×Q₈	D₄×C₁₃₉	semidirect
258. C₄×Q₈	D₄×C₁₃₉	semidirect
299. C₂×D₄	#41×C₁₃₉	semidirect
339. Q₈	#127×C₁₃₉	semidirect
385. C₄	#548×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#550×C₁₃₉	2
C₂×D₄×Q₈×C₁₃₉	2
C₂×#548×C₁₃₉	2
#2858×C₁₃₉	2
#2542×C₁₃₉	2
#2541×C₁₃₉	2
#2540×C₁₃₉	2
C₄×#127×C₁₃₉	2
C₄²×Q₈×C₁₃₉	2
#36465	139

Subgroups — C139×#36465 #48031061

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36465 #48031061