Subgroups — C₁₃₉×#29597 #48024193

Order 35584.

1442 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂²⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#484×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#451×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2848×C₁₃₉	C₂	1	1	yes	maximal, characteristic
5	#2036×C₁₃₉	C₂	1	4	yes	maximal, complemented
6	#2001×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#1824×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#1787×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#1779×C₁₃₉	C₂	1	1	yes	maximal, characteristic
10	C₂³×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
12	C₂²×Q₁₆×C₁₃₉	C₂²	1	2	yes	complemented
13	C₂×C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
14	C₂×C₂²⋊Q₈×C₁₃₉	—	2	2	no	—
15	C₂×C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
16	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
17	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
19	C₂²×C₄⋊C₄×C₁₃₉	—	2	1	no	—
20	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂²×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
22	#484×C₁₃₉	—	2	4	no	—
23	#451×C₁₃₉	—	2	4	no	—
24	C₂×#107×C₁₃₉	C₂²	1	2	yes	complemented
25	C₂×#103×C₁₃₉	C₂²	1	2	yes	complemented
26	C₂×#103×C₁₃₉	C₂²	1	2	yes	complemented
27	C₂×#103×C₁₃₉	C₂²	1	4	yes	complemented
28	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	4	yes	—
31	#385×C₁₃₉	—	2	1	no	—
32	#385×C₁₃₉	—	2	2	no	—
33	#380×C₁₃₉	C₂²	1	2	yes	—
34	#380×C₁₃₉	C₂²	1	1	yes	characteristic
35	#379×C₁₃₉	—	2	1	no	—
36	#340×C₁₃₉	C₂²	1	4	yes	complemented
37	C₂⁵×C₁₃₉	D₄	1	1	yes	characteristic
38	C₂²×Q₈×C₁₃₉	—	2	2	no	—
39	C₂²×Q₈×C₁₃₉	—	2	1	no	—
40	C₂²×Q₈×C₁₃₉	—	4	4	no	—
41	C₂²×Q₈×C₁₃₉	D₄	1	4	yes	—
42	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
43	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
44	C₂³×C₄×C₁₃₉	—	2	1	no	—
45	C₂³×C₄×C₁₃₉	—	2	1	no	—
46	C₂³×C₄×C₁₃₉	—	2	2	no	—
47	C₂³×C₄×C₁₃₉	—	2	2	no	—
48	C₂³×C₄×C₁₃₉	—	4	4	no	—
49	C₂³×C₄×C₁₃₉	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₁₃₉	D₄	1	2	yes	—
51	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
52	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
53	C₂×Q₁₆×C₁₃₉	—	2	4	no	—
54	C₂×Q₁₆×C₁₃₉	—	4	4	no	—
55	C₂²×C₈×C₁₃₉	C₂³	1	2	yes	—
56	C₂²×C₈×C₁₃₉	C₂³	1	2	yes	—
57	C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
58	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
59	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
60	C₂²⋊Q₈×C₁₃₉	—	2	2	no	—
61	C₂²⋊Q₈×C₁₃₉	—	2	2	no	—
62	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
63	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
64	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
65	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
66	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
67	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
68	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
69	C₂×C₄⋊C₄×C₁₃₉	D₄	1	4	yes	—
70	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
73	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
74	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
75	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
79	#107×C₁₃₉	—	2	4	no	—
80	#103×C₁₃₉	—	2	4	no	—
81	#103×C₁₃₉	—	2	4	no	—
82	#103×C₁₃₉	—	4	4	no	—
83	C₂²⋊C₈×C₁₃₉	—	2	2	no	—
84	C₂²⋊C₈×C₁₃₉	—	2	2	no	—
85	C₂²⋊C₈×C₁₃₉	—	4	4	no	—
86	#95×C₁₃₉	—	2	2	no	—
87	#95×C₁₃₉	—	2	1	no	—
88	C₂⁴×C₁₃₉	—	2	2	no	—
89	C₂⁴×C₁₃₉	—	2	2	no	—
90	C₂⁴×C₁₃₉	—	4	2	no	—
91	C₂⁴×C₁₃₉	—	4	2	no	—
92	C₂⁴×C₁₃₉	Q₁₆	1	4	yes	complemented
93	C₂⁴×C₁₃₉	C₂×D₄	1	2	yes	—
94	C₂⁴×C₁₃₉	C₂×D₄	1	1	yes	characteristic
95	C₂×Q₈×C₁₃₉	—	2	4	no	—
96	C₂×Q₈×C₁₃₉	—	2	2	no	—
97	C₂×Q₈×C₁₃₉	—	2	1	no	—
98	C₂×Q₈×C₁₃₉	—	2	1	no	—
99	C₂×Q₈×C₁₃₉	—	2	4	no	—
100	C₂×Q₈×C₁₃₉	—	2	4	no	—
101	C₂×Q₈×C₁₃₉	—	2	4	no	—
102	C₂×Q₈×C₁₃₉	—	4	8	no	—
103	C₂×Q₈×C₁₃₉	—	4	4	no	—
104	C₂×Q₈×C₁₃₉	—	4	8	no	—
105	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	—
106	C₂²×C₄×C₁₃₉	—	2	4	no	—
107	C₂²×C₄×C₁₃₉	—	2	4	no	—
108	C₂²×C₄×C₁₃₉	—	2	4	no	—
109	C₂²×C₄×C₁₃₉	—	2	2	no	—
110	C₂²×C₄×C₁₃₉	—	2	2	no	—
111	C₂²×C₄×C₁₃₉	—	2	2	no	—
112	C₂²×C₄×C₁₃₉	—	2	4	no	—
113	C₂²×C₄×C₁₃₉	—	2	2	no	—
114	C₂²×C₄×C₁₃₉	—	2	2	no	—
115	C₂²×C₄×C₁₃₉	—	2	4	no	—
116	C₂²×C₄×C₁₃₉	—	2	4	no	—
117	C₂²×C₄×C₁₃₉	—	2	1	no	—
118	C₂²×C₄×C₁₃₉	—	2	2	no	—
119	C₂²×C₄×C₁₃₉	—	2	1	no	—
120	C₂²×C₄×C₁₃₉	—	4	2	no	—
121	C₂²×C₄×C₁₃₉	—	4	2	no	—
122	C₂²×C₄×C₁₃₉	—	4	2	no	—
123	C₂²×C₄×C₁₃₉	—	4	8	no	—
124	C₂²×C₄×C₁₃₉	—	4	8	no	—
125	C₂²×C₄×C₁₃₉	—	4	4	no	—
126	C₂²×C₄×C₁₃₉	—	4	4	no	—
127	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
132	Q₁₆×C₁₃₉	—	4	8	no	—
133	C₂×C₈×C₁₃₉	—	2	2	no	—
134	C₂×C₈×C₁₃₉	—	2	2	no	—
135	C₂×C₈×C₁₃₉	—	2	4	no	—
136	C₂×C₈×C₁₃₉	—	2	4	no	—
137	C₄⋊C₄×C₁₃₉	—	2	16	no	—
138	C₄⋊C₄×C₁₃₉	—	2	4	no	—
139	C₄⋊C₄×C₁₃₉	—	2	2	no	—
140	C₄⋊C₄×C₁₃₉	—	2	1	no	—
141	C₄⋊C₄×C₁₃₉	—	2	1	no	—
142	C₄⋊C₄×C₁₃₉	—	2	4	no	—
143	C₄⋊C₄×C₁₃₉	—	4	4	no	—
144	C₄⋊C₄×C₁₃₉	—	4	2	no	—
145	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
146	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
147	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
148	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
149	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
150	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
151	C₂³×C₁₃₉	—	2	2	no	—
152	C₂³×C₁₃₉	—	2	2	no	—
153	C₂³×C₁₃₉	—	2	2	no	—
154	C₂³×C₁₃₉	—	2	2	no	—
155	C₂³×C₁₃₉	—	2	2	no	—
156	C₂³×C₁₃₉	—	2	2	no	—
157	C₂³×C₁₃₉	—	2	2	no	—
158	C₂³×C₁₃₉	—	2	2	no	—
159	C₂³×C₁₃₉	—	2	8	no	—
160	C₂³×C₁₃₉	—	4	8	no	—
161	C₂³×C₁₃₉	—	4	4	no	—
162	C₂³×C₁₃₉	—	4	8	no	—
163	C₂³×C₁₃₉	—	4	4	no	—
164	C₂³×C₁₃₉	#120	1	2	yes	—
165	C₂³×C₁₃₉	C₂×Q₁₆	1	4	yes	—
166	C₂³×C₁₃₉	C₂×Q₁₆	1	2	yes	—
167	C₂³×C₁₃₉	#137	1	2	yes	—
168	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
169	Q₈×C₁₃₉	—	2	4	no	—
170	Q₈×C₁₃₉	—	2	4	no	—
171	Q₈×C₁₃₉	—	4	8	no	—
172	Q₈×C₁₃₉	—	4	4	no	—
173	Q₈×C₁₃₉	—	4	2	no	—
174	Q₈×C₁₃₉	—	4	2	no	—
175	C₂×C₄×C₁₃₉	—	2	2	no	—
176	C₂×C₄×C₁₃₉	—	2	4	no	—
177	C₂×C₄×C₁₃₉	—	2	4	no	—
178	C₂×C₄×C₁₃₉	—	2	4	no	—
179	C₂×C₄×C₁₃₉	—	2	4	no	—
180	C₂×C₄×C₁₃₉	—	2	2	no	—
181	C₂×C₄×C₁₃₉	—	2	2	no	—
182	C₂×C₄×C₁₃₉	—	2	2	no	—
183	C₂×C₄×C₁₃₉	—	4	8	no	—
184	C₂×C₄×C₁₃₉	—	4	8	no	—
185	C₂×C₄×C₁₃₉	—	4	4	no	—
186	C₂×C₄×C₁₃₉	—	4	8	no	—
187	C₂×C₄×C₁₃₉	—	4	4	no	—
188	C₂×C₄×C₁₃₉	—	4	4	no	—
189	C₂×C₄×C₁₃₉	—	4	4	no	—
190	C₂×C₄×C₁₃₉	—	4	4	no	—
191	C₂×C₄×C₁₃₉	—	4	1	no	—
192	C₂×C₄×C₁₃₉	—	4	1	no	—
193	C₂×C₄×C₁₃₉	—	4	2	no	—
194	C₂×C₄×C₁₃₉	—	4	2	no	—
195	C₂×C₄×C₁₃₉	—	4	2	no	—
196	C₂×C₄×C₁₃₉	—	4	2	no	—
197	C₂×C₄×C₁₃₉	—	4	2	no	—
198	C₂×C₄×C₁₃₉	#120	1	2	yes	—
199	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
202	C₈×C₁₃₉	—	4	2	no	—
203	C₈×C₁₃₉	—	4	2	no	—
204	C₂²×C₁₃₉	—	2	2	no	—
205	C₂²×C₁₃₉	—	2	4	no	—
206	C₂²×C₁₃₉	—	2	4	no	—
207	C₂²×C₁₃₉	—	2	2	no	—
208	C₂²×C₁₃₉	—	2	4	no	—
209	C₂²×C₁₃₉	—	2	4	no	—
210	C₂²×C₁₃₉	—	2	4	no	—
211	C₂²×C₁₃₉	—	4	16	no	—
212	C₂²×C₁₃₉	—	4	2	no	—
213	C₂²×C₁₃₉	—	4	2	no	—
214	C₂²×C₁₃₉	—	4	2	no	—
215	C₂²×C₁₃₉	—	4	2	no	—
216	C₂²×C₁₃₉	#451	1	4	yes	—
217	C₂²×C₁₃₉	C₂×#120	1	1	yes	characteristic
218	C₂²×C₁₃₉	#534	1	2	yes	—
219	C₂²×C₁₃₉	C₂²×Q₁₆	1	1	yes	characteristic
220	C₂²×C₁₃₉	C₂×#137	1	1	yes	characteristic
221	C₂²×C₁₃₉	#575	1	2	yes	—
222	C₄×C₁₃₉	—	2	2	no	—
223	C₄×C₁₃₉	—	4	2	no	—
224	C₄×C₁₃₉	—	4	4	no	—
225	C₄×C₁₃₉	—	4	4	no	—
226	C₄×C₁₃₉	—	8	1	no	—
227	C₄×C₁₃₉	—	8	2	no	—
228	C₄×C₁₃₉	—	8	1	no	—
229	C₄×C₁₃₉	#534	1	2	yes	—
230	C₄×C₁₃₉	#535	1	2	yes	—
231	C₂×C₁₃₉	—	2	4	no	—
232	C₂×C₁₃₉	—	4	4	no	—
233	C₂×C₁₃₉	#2613	1	1	yes	characteristic
234	C₂×C₁₃₉	C₂×#451	1	1	yes	characteristic
235	C₂×C₁₃₉	#3005	1	1	yes	characteristic
236	C₂×C₁₃₉	#3189	1	2	yes	—
237	C₂×C₁₃₉	#3196	1	2	yes	—
238	#29597	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
239	C₁₃₉	#29597	1	1	yes	characteristic, direct product factor, Sylow
240	C₂²×C₂²⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic
241	C₂×#484	C₂×C₁₃₉	1	1	yes	characteristic, complemented
242	C₂×#451	C₂×C₁₃₉	1	1	yes	characteristic, complemented
243	#2848	C₂×C₁₃₉	1	1	yes	characteristic
244	#2036	C₂×C₁₃₉	1	4	yes	complemented
245	#2001	C₂×C₁₃₉	1	4	yes	complemented
246	#1824	C₂×C₁₃₉	1	1	yes	characteristic, complemented
247	#1787	C₂×C₁₃₉	1	1	yes	characteristic, complemented
248	#1779	C₂×C₁₃₉	1	1	yes	characteristic
249	C₂³×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
250	C₂⁴×C₄	C₂²×C₁₃₉	1	1	yes	characteristic
251	C₂²×Q₁₆	C₂²×C₁₃₉	1	2	yes	complemented
252	C₂×C₂²⋊Q₈	—	2	4	no	—
253	C₂×C₂²⋊Q₈	—	2	2	no	—
254	C₂×C₂²⋊Q₈	—	2	4	no	—
255	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
256	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
257	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
258	C₂²×C₄⋊C₄	—	2	1	no	—
259	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
260	C₂²×C₂²⋊C₄	—	2	1	no	—
261	#484	—	2	4	no	—
262	#451	—	2	4	no	—
263	C₂×#107	C₂²×C₁₃₉	1	2	yes	complemented
264	C₂×#103	C₂²×C₁₃₉	1	2	yes	complemented
265	C₂×#103	C₂²×C₁₃₉	1	2	yes	complemented
266	C₂×#103	C₂²×C₁₃₉	1	4	yes	complemented
267	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	1	yes	characteristic
268	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	1	yes	characteristic
269	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	4	yes	—
270	#385	—	2	1	no	—
271	#385	—	2	2	no	—
272	#380	C₂²×C₁₃₉	1	1	yes	characteristic
273	#380	C₂²×C₁₃₉	1	2	yes	—
274	#379	—	2	1	no	—
275	#340	C₂²×C₁₃₉	1	4	yes	complemented
276	C₂⁵	D₄×C₁₃₉	1	1	yes	characteristic
277	C₂²×Q₈	—	2	2	no	—
278	C₂²×Q₈	—	2	1	no	—
279	C₂²×Q₈	—	4	4	no	—
280	C₂²×Q₈	D₄×C₁₃₉	1	4	yes	—
281	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
282	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
283	C₂³×C₄	—	2	1	no	—
284	C₂³×C₄	—	2	1	no	—
285	C₂³×C₄	—	2	2	no	—
286	C₂³×C₄	—	2	2	no	—
287	C₂³×C₄	—	4	4	no	—
288	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
289	C₂³×C₄	D₄×C₁₃₉	1	2	yes	—
290	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
291	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
292	C₂×Q₁₆	—	2	4	no	—
293	C₂×Q₁₆	—	4	4	no	—
294	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
295	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
296	C₂²⋊Q₈	—	2	16	no	—
297	C₂²⋊Q₈	—	2	8	no	—
298	C₂²⋊Q₈	—	2	8	no	—
299	C₂²⋊Q₈	—	2	2	no	—
300	C₂²⋊Q₈	—	2	2	no	—
301	C₂²⋊Q₈	—	4	4	no	—
302	C₂×C₄⋊C₄	—	2	8	no	—
303	C₂×C₄⋊C₄	—	2	4	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	—	2	2	no	—
306	C₂×C₄⋊C₄	—	2	2	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	D₄×C₁₃₉	1	4	yes	—
309	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
310	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
311	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
312	C₂×C₂²⋊C₄	—	2	8	no	—
313	C₂×C₂²⋊C₄	—	2	4	no	—
314	C₂×C₂²⋊C₄	—	2	2	no	—
315	C₂×C₂²⋊C₄	—	2	1	no	—
316	C₂×C₂²⋊C₄	—	2	2	no	—
317	C₂×C₂²⋊C₄	—	2	1	no	—
318	#107	—	2	4	no	—
319	#103	—	2	4	no	—
320	#103	—	2	4	no	—
321	#103	—	4	4	no	—
322	C₂²⋊C₈	—	2	2	no	—
323	C₂²⋊C₈	—	2	2	no	—
324	C₂²⋊C₈	—	4	4	no	—
325	#95	—	2	2	no	—
326	#95	—	2	1	no	—
327	C₂⁴	—	2	2	no	—
328	C₂⁴	—	2	2	no	—
329	C₂⁴	—	4	2	no	—
330	C₂⁴	—	4	2	no	—
331	C₂⁴	Q₁₆×C₁₃₉	1	4	yes	complemented
332	C₂⁴	C₂×D₄×C₁₃₉	1	2	yes	—
333	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
334	C₂×Q₈	—	2	4	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	—	2	1	no	—
337	C₂×Q₈	—	2	1	no	—
338	C₂×Q₈	—	2	4	no	—
339	C₂×Q₈	—	2	4	no	—
340	C₂×Q₈	—	2	4	no	—
341	C₂×Q₈	—	4	8	no	—
342	C₂×Q₈	—	4	4	no	—
343	C₂×Q₈	—	4	8	no	—
344	C₂×Q₈	C₂×D₄×C₁₃₉	1	4	yes	—
345	C₂²×C₄	—	2	4	no	—
346	C₂²×C₄	—	2	4	no	—
347	C₂²×C₄	—	2	4	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	4	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	4	no	—
355	C₂²×C₄	—	2	4	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	4	2	no	—
360	C₂²×C₄	—	4	2	no	—
361	C₂²×C₄	—	4	2	no	—
362	C₂²×C₄	—	4	8	no	—
363	C₂²×C₄	—	4	8	no	—
364	C₂²×C₄	—	4	4	no	—
365	C₂²×C₄	—	4	4	no	—
366	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
367	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
368	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
369	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
370	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
371	Q₁₆	—	4	8	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	4	no	—
375	C₂×C₈	—	2	4	no	—
376	C₄⋊C₄	—	2	16	no	—
377	C₄⋊C₄	—	2	4	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	4	no	—
382	C₄⋊C₄	—	4	4	no	—
383	C₄⋊C₄	—	4	2	no	—
384	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
385	C₂²⋊C₄	—	2	16	no	—
386	C₂²⋊C₄	—	4	4	no	—
387	C₂²⋊C₄	—	4	4	no	—
388	C₂²⋊C₄	—	4	2	no	—
389	C₂²⋊C₄	—	4	2	no	—
390	C₂³	—	2	2	no	—
391	C₂³	—	2	2	no	—
392	C₂³	—	2	8	no	—
393	C₂³	—	2	2	no	—
394	C₂³	—	2	2	no	—
395	C₂³	—	2	2	no	—
396	C₂³	—	2	2	no	—
397	C₂³	—	2	2	no	—
398	C₂³	—	2	2	no	—
399	C₂³	—	4	8	no	—
400	C₂³	—	4	4	no	—
401	C₂³	—	4	8	no	—
402	C₂³	—	4	4	no	—
403	C₂³	#120×C₁₃₉	1	2	yes	—
404	C₂³	C₂×Q₁₆×C₁₃₉	1	4	yes	—
405	C₂³	C₂×Q₁₆×C₁₃₉	1	2	yes	—
406	C₂³	#137×C₁₃₉	1	2	yes	—
407	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
408	Q₈	—	2	4	no	—
409	Q₈	—	2	4	no	—
410	Q₈	—	4	8	no	—
411	Q₈	—	4	4	no	—
412	Q₈	—	4	2	no	—
413	Q₈	—	4	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	4	8	no	—
423	C₂×C₄	—	4	4	no	—
424	C₂×C₄	—	4	8	no	—
425	C₂×C₄	—	4	8	no	—
426	C₂×C₄	—	4	4	no	—
427	C₂×C₄	—	4	4	no	—
428	C₂×C₄	—	4	4	no	—
429	C₂×C₄	—	4	4	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	#120×C₁₃₉	1	2	yes	—
438	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
439	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
440	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
441	C₈	—	4	2	no	—
442	C₈	—	4	2	no	—
443	C₂²	—	2	2	no	—
444	C₂²	—	2	4	no	—
445	C₂²	—	2	4	no	—
446	C₂²	—	2	2	no	—
447	C₂²	—	2	4	no	—
448	C₂²	—	2	4	no	—
449	C₂²	—	2	4	no	—
450	C₂²	—	4	16	no	—
451	C₂²	—	4	2	no	—
452	C₂²	—	4	2	no	—
453	C₂²	—	4	2	no	—
454	C₂²	—	4	2	no	—
455	C₂²	#451×C₁₃₉	1	4	yes	—
456	C₂²	C₂×#120×C₁₃₉	1	1	yes	characteristic
457	C₂²	#534×C₁₃₉	1	2	yes	—
458	C₂²	C₂²×Q₁₆×C₁₃₉	1	1	yes	characteristic
459	C₂²	C₂×#137×C₁₃₉	1	1	yes	characteristic
460	C₂²	#575×C₁₃₉	1	2	yes	—
461	C₄	—	2	2	no	—
462	C₄	—	4	2	no	—
463	C₄	—	4	4	no	—
464	C₄	—	4	4	no	—
465	C₄	—	8	1	no	—
466	C₄	—	8	2	no	—
467	C₄	—	8	1	no	—
468	C₄	#534×C₁₃₉	1	2	yes	—
469	C₄	#535×C₁₃₉	1	2	yes	—
470	C₂	—	2	4	no	—
471	C₂	—	4	4	no	—
472	C₂	#2613×C₁₃₉	1	1	yes	characteristic
473	C₂	C₂×#451×C₁₃₉	1	1	yes	characteristic
474	C₂	#3005×C₁₃₉	1	1	yes	characteristic
475	C₂	#3189×C₁₃₉	1	2	yes	—
476	C₂	#3196×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
prime radical	C₂⁵×C₁₃₉	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ C₂⁴×C₄×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#484×C₁₃₉	C₂	semidirect
3. C₂×#451×C₁₃₉	C₂	semidirect
5. #2036×C₁₃₉	C₂	semidirect
6. #2001×C₁₃₉	C₂	semidirect
7. #1824×C₁₃₉	C₂	semidirect
8. #1787×C₁₃₉	C₂	semidirect
12. C₂²×Q₁₆×C₁₃₉	C₂²	semidirect
24. C₂×#107×C₁₃₉	C₂²	semidirect
25. C₂×#103×C₁₃₉	C₂²	semidirect
26. C₂×#103×C₁₃₉	C₂²	semidirect
27. C₂×#103×C₁₃₉	C₂²	semidirect
36. #340×C₁₃₉	C₂²	semidirect
92. C₂⁴×C₁₃₉	Q₁₆	semidirect
238. #29597	C₁₃₉	direct (N × H)
239. C₁₃₉	#29597	direct (N × H)
241. C₂×#484	C₂×C₁₃₉	semidirect
242. C₂×#451	C₂×C₁₃₉	semidirect
244. #2036	C₂×C₁₃₉	semidirect
245. #2001	C₂×C₁₃₉	semidirect
246. #1824	C₂×C₁₃₉	semidirect
247. #1787	C₂×C₁₃₉	semidirect
251. C₂²×Q₁₆	C₂²×C₁₃₉	semidirect
263. C₂×#107	C₂²×C₁₃₉	semidirect
264. C₂×#103	C₂²×C₁₃₉	semidirect
265. C₂×#103	C₂²×C₁₃₉	semidirect
266. C₂×#103	C₂²×C₁₃₉	semidirect
275. #340	C₂²×C₁₃₉	semidirect
331. C₂⁴	Q₁₆×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₂²⋊Q₈×C₁₃₉	2
C₂×#484×C₁₃₉	2
C₂×#451×C₁₃₉	2
#2848×C₁₃₉	2
#2036×C₁₃₉	2
#2001×C₁₃₉	2
#1824×C₁₃₉	2
#1787×C₁₃₉	2
#1779×C₁₃₉	2
#29597	139

Subgroups — C139×#29597 #48024193

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#29597 #48024193