Subgroups — C₁₃₉×#35678 #48030274

Order 35584.

2314 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#540×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#519×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2565×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2548×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2500×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2476×C₁₃₉	C₂	1	8	yes	maximal, complemented
7	#2458×C₁₃₉	C₂	1	8	yes	maximal, complemented
8	#2436×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2326×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	C₄×#124×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2298×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
13	#540×C₁₃₉	—	2	8	no	—
14	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
15	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
16	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
17	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
18	C₂×#123×C₁₃₉	C₂²	1	4	yes	—
19	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
20	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
21	#519×C₁₃₉	—	2	8	no	—
22	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
23	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
24	C₂×C₄×Q₈×C₁₃₉	C₂²	1	4	yes	—
25	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
26	C₂×#117×C₁₃₉	C₂²	1	4	yes	—
27	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
29	#398×C₁₃₉	C₂²	1	8	yes	—
30	#394×C₁₃₉	C₂²	1	8	yes	—
31	#394×C₁₃₉	C₂²	1	8	yes	—
32	#393×C₁₃₉	C₂²	1	8	yes	—
33	#391×C₁₃₉	C₂²	1	2	yes	—
34	#391×C₁₃₉	C₂²	1	2	yes	—
35	#390×C₁₃₉	C₂²	1	2	yes	—
36	#390×C₁₃₉	C₂²	1	2	yes	—
37	#390×C₁₃₉	C₂²	1	8	yes	—
38	#388×C₁₃₉	C₂²	1	4	yes	—
39	#388×C₁₃₉	C₂²	1	8	yes	—
40	#388×C₁₃₉	C₂²	1	8	yes	—
41	#388×C₁₃₉	C₂²	1	8	yes	—
42	#387×C₁₃₉	C₂²	1	4	yes	—
43	#387×C₁₃₉	C₂²	1	8	yes	—
44	#386×C₁₃₉	C₂²	1	8	yes	—
45	#385×C₁₃₉	C₂²	1	8	yes	—
46	#384×C₁₃₉	C₂²	1	2	yes	—
47	#382×C₁₃₉	C₂²	1	2	yes	—
48	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
49	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
50	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	8	yes	—
51	#376×C₁₃₉	C₂²	1	1	yes	characteristic
52	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
53	C₂²×Q₈×C₁₃₉	—	2	8	no	—
54	C₂²×Q₈×C₁₃₉	—	2	4	no	—
55	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
56	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
57	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
58	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
59	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
60	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
61	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
63	#127×C₁₃₉	—	2	4	no	—
64	#125×C₁₃₉	—	2	4	no	—
65	#124×C₁₃₉	—	2	8	no	—
66	#124×C₁₃₉	—	2	8	no	—
67	#123×C₁₃₉	—	2	16	no	—
68	#121×C₁₃₉	—	2	8	no	—
69	#121×C₁₃₉	—	2	16	no	—
70	C₄×Q₈×C₁₃₉	—	2	16	no	—
71	C₄×Q₈×C₁₃₉	—	2	8	no	—
72	C₄×Q₈×C₁₃₉	—	2	8	no	—
73	C₄×D₄×C₁₃₉	—	2	8	no	—
74	#117×C₁₃₉	—	2	4	no	—
75	#117×C₁₃₉	—	2	16	no	—
76	#117×C₁₃₉	D₄	1	8	yes	—
77	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
78	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
79	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
80	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
81	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
83	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
84	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
85	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
86	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
87	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
88	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
89	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
90	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
91	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
92	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
93	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
94	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
95	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
96	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
97	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
98	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
99	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
100	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
102	#95×C₁₃₉	C₂³	1	8	yes	—
103	#95×C₁₃₉	C₂³	1	8	yes	—
104	#95×C₁₃₉	C₂³	1	8	yes	—
105	#95×C₁₃₉	C₂³	1	4	yes	—
106	#95×C₁₃₉	C₂³	1	4	yes	—
107	#95×C₁₃₉	C₂³	1	4	yes	—
108	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
109	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
110	C₂×Q₈×C₁₃₉	—	2	32	no	—
111	C₂×Q₈×C₁₃₉	—	2	4	no	—
112	C₂×Q₈×C₁₃₉	—	2	4	no	—
113	C₂×Q₈×C₁₃₉	—	2	8	no	—
114	C₂×Q₈×C₁₃₉	—	2	4	no	—
115	C₂×Q₈×C₁₃₉	#41	1	8	yes	—
116	C₂×D₄×C₁₃₉	—	2	8	no	—
117	C₂×D₄×C₁₃₉	—	2	4	no	—
118	C₂×D₄×C₁₃₉	—	2	8	no	—
119	C₂×D₄×C₁₃₉	—	2	4	no	—
120	C₂×D₄×C₁₃₉	—	2	4	no	—
121	C₂×D₄×C₁₃₉	—	4	8	no	—
122	C₂×D₄×C₁₃₉	—	4	8	no	—
123	C₂²×C₄×C₁₃₉	—	2	4	no	—
124	C₂²×C₄×C₁₃₉	—	2	8	no	—
125	C₂²×C₄×C₁₃₉	—	2	4	no	—
126	C₂²×C₄×C₁₃₉	—	2	8	no	—
127	C₂²×C₄×C₁₃₉	—	4	8	no	—
128	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
129	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
130	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
131	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
132	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
133	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
134	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
135	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
136	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
137	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
138	C₄⋊C₄×C₁₃₉	—	2	8	no	—
139	C₄⋊C₄×C₁₃₉	—	2	8	no	—
140	C₄⋊C₄×C₁₃₉	—	2	4	no	—
141	C₄⋊C₄×C₁₃₉	—	2	4	no	—
142	C₄⋊C₄×C₁₃₉	—	2	8	no	—
143	C₄⋊C₄×C₁₃₉	—	4	4	no	—
144	C₄⋊C₄×C₁₃₉	—	4	8	no	—
145	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
146	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
147	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
148	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
149	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
150	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
151	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
152	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
153	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
154	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
155	C₄²×C₁₃₉	—	2	8	no	—
156	C₄²×C₁₃₉	—	2	8	no	—
157	C₄²×C₁₃₉	—	2	4	no	—
158	C₄²×C₁₃₉	—	2	4	no	—
159	C₄²×C₁₃₉	—	2	4	no	—
160	C₄²×C₁₃₉	—	4	4	no	—
161	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
162	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
163	C₂³×C₁₃₉	—	2	2	no	—
164	C₂³×C₁₃₉	—	2	4	no	—
165	C₂³×C₁₃₉	—	2	4	no	—
166	C₂³×C₁₃₉	—	2	4	no	—
167	C₂³×C₁₃₉	—	2	4	no	—
168	C₂³×C₁₃₉	—	2	8	no	—
169	C₂³×C₁₃₉	—	2	8	no	—
170	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
171	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
172	Q₈×C₁₃₉	—	2	16	no	—
173	Q₈×C₁₃₉	—	2	16	no	—
174	D₄×C₁₃₉	—	4	8	no	—
175	D₄×C₁₃₉	—	8	8	no	—
176	D₄×C₁₃₉	—	8	8	no	—
177	C₂×C₄×C₁₃₉	—	2	16	no	—
178	C₂×C₄×C₁₃₉	—	2	4	no	—
179	C₂×C₄×C₁₃₉	—	2	2	no	—
180	C₂×C₄×C₁₃₉	—	2	4	no	—
181	C₂×C₄×C₁₃₉	—	2	4	no	—
182	C₂×C₄×C₁₃₉	—	2	4	no	—
183	C₂×C₄×C₁₃₉	—	2	8	no	—
184	C₂×C₄×C₁₃₉	—	2	4	no	—
185	C₂×C₄×C₁₃₉	—	2	4	no	—
186	C₂×C₄×C₁₃₉	—	2	4	no	—
187	C₂×C₄×C₁₃₉	—	2	4	no	—
188	C₂×C₄×C₁₃₉	—	2	4	no	—
189	C₂×C₄×C₁₃₉	—	2	4	no	—
190	C₂×C₄×C₁₃₉	—	2	4	no	—
191	C₂×C₄×C₁₃₉	—	2	8	no	—
192	C₂×C₄×C₁₃₉	—	2	4	no	—
193	C₂×C₄×C₁₃₉	—	2	8	no	—
194	C₂×C₄×C₁₃₉	—	8	8	no	—
195	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
196	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
197	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
198	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
199	C₂×C₄×C₁₃₉	C₂×#41	1	8	yes	—
200	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
201	C₂²×C₁₃₉	—	2	2	no	—
202	C₂²×C₁₃₉	—	2	4	no	—
203	C₂²×C₁₃₉	—	4	4	no	—
204	C₂²×C₁₃₉	—	4	4	no	—
205	C₂²×C₁₃₉	—	4	4	no	—
206	C₂²×C₁₃₉	—	4	4	no	—
207	C₂²×C₁₃₉	—	4	8	no	—
208	C₂²×C₁₃₉	—	4	8	no	—
209	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
210	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
211	C₂²×C₁₃₉	#585	1	4	yes	—
212	C₄×C₁₃₉	—	2	2	no	—
213	C₄×C₁₃₉	—	2	8	no	—
214	C₄×C₁₃₉	—	2	4	no	—
215	C₄×C₁₃₉	—	2	4	no	—
216	C₄×C₁₃₉	—	4	4	no	—
217	C₄×C₁₃₉	—	4	4	no	—
218	C₄×C₁₃₉	—	4	4	no	—
219	C₄×C₁₃₉	—	4	4	no	—
220	C₄×C₁₃₉	#525	1	4	yes	—
221	C₂×C₁₃₉	—	4	2	no	—
222	C₂×C₁₃₉	—	8	4	no	—
223	C₂×C₁₃₉	C₂×#525	1	1	yes	characteristic
224	C₂×C₁₃₉	#3500	1	2	yes	—
225	C₂×C₁₃₉	#3524	1	4	yes	—
226	#35678	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
227	C₁₃₉	#35678	1	1	yes	characteristic, direct product factor, Sylow
228	C₂×#540	C₂×C₁₃₉	1	1	yes	characteristic
229	C₂×#519	C₂×C₁₃₉	1	1	yes	characteristic, complemented
230	#2565	C₂×C₁₃₉	1	2	yes	complemented
231	#2548	C₂×C₁₃₉	1	2	yes	complemented
232	#2500	C₂×C₁₃₉	1	2	yes	complemented
233	#2476	C₂×C₁₃₉	1	8	yes	complemented
234	#2458	C₂×C₁₃₉	1	8	yes	complemented
235	#2436	C₂×C₁₃₉	1	2	yes	complemented
236	#2326	C₂×C₁₃₉	1	2	yes	complemented
237	C₄×#124	C₂×C₁₃₉	1	2	yes	complemented
238	#2298	C₂×C₁₃₉	1	1	yes	characteristic, complemented
239	C₂³×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
240	#540	—	2	8	no	—
241	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
242	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
243	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
244	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
245	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
246	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
247	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
248	#519	—	2	8	no	—
249	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
250	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
251	C₂×C₄×Q₈	C₂²×C₁₃₉	1	4	yes	—
252	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
253	C₂×#117	C₂²×C₁₃₉	1	4	yes	—
254	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
255	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
256	#398	C₂²×C₁₃₉	1	8	yes	—
257	#394	C₂²×C₁₃₉	1	8	yes	—
258	#394	C₂²×C₁₃₉	1	8	yes	—
259	#393	C₂²×C₁₃₉	1	8	yes	—
260	#391	C₂²×C₁₃₉	1	2	yes	—
261	#391	C₂²×C₁₃₉	1	2	yes	—
262	#390	C₂²×C₁₃₉	1	2	yes	—
263	#390	C₂²×C₁₃₉	1	8	yes	—
264	#390	C₂²×C₁₃₉	1	2	yes	—
265	#388	C₂²×C₁₃₉	1	8	yes	—
266	#388	C₂²×C₁₃₉	1	8	yes	—
267	#388	C₂²×C₁₃₉	1	8	yes	—
268	#388	C₂²×C₁₃₉	1	4	yes	—
269	#387	C₂²×C₁₃₉	1	8	yes	—
270	#387	C₂²×C₁₃₉	1	4	yes	—
271	#386	C₂²×C₁₃₉	1	8	yes	—
272	#385	C₂²×C₁₃₉	1	8	yes	—
273	#384	C₂²×C₁₃₉	1	2	yes	—
274	#382	C₂²×C₁₃₉	1	2	yes	—
275	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
276	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
277	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	8	yes	—
278	#376	C₂²×C₁₃₉	1	1	yes	characteristic
279	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
280	C₂²×Q₈	—	2	8	no	—
281	C₂²×Q₈	—	2	4	no	—
282	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
283	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
284	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
285	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
286	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
287	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
288	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
289	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
290	#127	—	2	4	no	—
291	#125	—	2	4	no	—
292	#124	—	2	8	no	—
293	#124	—	2	8	no	—
294	#123	—	2	16	no	—
295	#121	—	2	8	no	—
296	#121	—	2	16	no	—
297	C₄×Q₈	—	2	16	no	—
298	C₄×Q₈	—	2	8	no	—
299	C₄×Q₈	—	2	8	no	—
300	C₄×D₄	—	2	8	no	—
301	#117	—	2	4	no	—
302	#117	—	2	16	no	—
303	#117	D₄×C₁₃₉	1	8	yes	—
304	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
305	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
306	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
307	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
308	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
309	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
310	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
311	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
312	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
313	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
314	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
315	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
316	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
317	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
318	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
319	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
320	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
321	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
322	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
323	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
324	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
325	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
326	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
327	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
328	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
329	#95	C₂³×C₁₃₉	1	4	yes	—
330	#95	C₂³×C₁₃₉	1	8	yes	—
331	#95	C₂³×C₁₃₉	1	8	yes	—
332	#95	C₂³×C₁₃₉	1	4	yes	—
333	#95	C₂³×C₁₃₉	1	4	yes	—
334	#95	C₂³×C₁₃₉	1	8	yes	—
335	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
336	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
337	C₂×Q₈	—	2	32	no	—
338	C₂×Q₈	—	2	4	no	—
339	C₂×Q₈	—	2	4	no	—
340	C₂×Q₈	—	2	8	no	—
341	C₂×Q₈	—	2	4	no	—
342	C₂×Q₈	#41×C₁₃₉	1	8	yes	—
343	C₂×D₄	—	2	8	no	—
344	C₂×D₄	—	2	4	no	—
345	C₂×D₄	—	2	8	no	—
346	C₂×D₄	—	2	4	no	—
347	C₂×D₄	—	2	4	no	—
348	C₂×D₄	—	4	8	no	—
349	C₂×D₄	—	4	8	no	—
350	C₂²×C₄	—	2	4	no	—
351	C₂²×C₄	—	2	8	no	—
352	C₂²×C₄	—	2	4	no	—
353	C₂²×C₄	—	2	8	no	—
354	C₂²×C₄	—	4	8	no	—
355	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
356	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
357	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
358	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
359	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
360	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
361	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
362	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
363	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
364	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
365	C₄⋊C₄	—	2	8	no	—
366	C₄⋊C₄	—	2	8	no	—
367	C₄⋊C₄	—	2	4	no	—
368	C₄⋊C₄	—	2	4	no	—
369	C₄⋊C₄	—	2	8	no	—
370	C₄⋊C₄	—	4	4	no	—
371	C₄⋊C₄	—	4	8	no	—
372	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
373	C₂²⋊C₄	—	2	4	no	—
374	C₂²⋊C₄	—	2	8	no	—
375	C₂²⋊C₄	—	2	8	no	—
376	C₂²⋊C₄	—	2	16	no	—
377	C₂²⋊C₄	—	2	16	no	—
378	C₂²⋊C₄	—	4	8	no	—
379	C₂²⋊C₄	—	4	4	no	—
380	C₂²⋊C₄	—	4	8	no	—
381	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
382	C₄²	—	2	8	no	—
383	C₄²	—	2	8	no	—
384	C₄²	—	2	4	no	—
385	C₄²	—	2	4	no	—
386	C₄²	—	2	4	no	—
387	C₄²	—	4	4	no	—
388	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
389	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
390	C₂³	—	2	2	no	—
391	C₂³	—	2	4	no	—
392	C₂³	—	2	4	no	—
393	C₂³	—	2	4	no	—
394	C₂³	—	2	4	no	—
395	C₂³	—	2	8	no	—
396	C₂³	—	2	8	no	—
397	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
398	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
399	Q₈	—	2	16	no	—
400	Q₈	—	2	16	no	—
401	D₄	—	4	8	no	—
402	D₄	—	8	8	no	—
403	D₄	—	8	8	no	—
404	C₂×C₄	—	2	16	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	8	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	8	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	8	no	—
421	C₂×C₄	—	8	8	no	—
422	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
423	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
424	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
425	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
426	C₂×C₄	C₂×#41×C₁₃₉	1	8	yes	—
427	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	4	no	—
430	C₂²	—	4	4	no	—
431	C₂²	—	4	4	no	—
432	C₂²	—	4	4	no	—
433	C₂²	—	4	4	no	—
434	C₂²	—	4	8	no	—
435	C₂²	—	4	8	no	—
436	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
437	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
438	C₂²	#585×C₁₃₉	1	4	yes	—
439	C₄	—	2	2	no	—
440	C₄	—	2	8	no	—
441	C₄	—	2	4	no	—
442	C₄	—	2	4	no	—
443	C₄	—	4	4	no	—
444	C₄	—	4	4	no	—
445	C₄	—	4	4	no	—
446	C₄	—	4	4	no	—
447	C₄	#525×C₁₃₉	1	4	yes	—
448	C₂	—	4	2	no	—
449	C₂	—	8	4	no	—
450	C₂	C₂×#525×C₁₃₉	1	1	yes	characteristic
451	C₂	#3500×C₁₃₉	1	2	yes	—
452	C₂	#3524×C₁₃₉	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂×#540×C₁₃₉	C₂
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
2. C₂×#519×C₁₃₉	C₂	semidirect
3. #2565×C₁₃₉	C₂	semidirect
4. #2548×C₁₃₉	C₂	semidirect
5. #2500×C₁₃₉	C₂	semidirect
6. #2476×C₁₃₉	C₂	semidirect
7. #2458×C₁₃₉	C₂	semidirect
8. #2436×C₁₃₉	C₂	semidirect
9. #2326×C₁₃₉	C₂	semidirect
10. C₄×#124×C₁₃₉	C₂	semidirect
11. #2298×C₁₃₉	C₂	semidirect
226. #35678	C₁₃₉	direct (N × H)
227. C₁₃₉	#35678	direct (N × H)
229. C₂×#519	C₂×C₁₃₉	semidirect
230. #2565	C₂×C₁₃₉	semidirect
231. #2548	C₂×C₁₃₉	semidirect
232. #2500	C₂×C₁₃₉	semidirect
233. #2476	C₂×C₁₃₉	semidirect
234. #2458	C₂×C₁₃₉	semidirect
235. #2436	C₂×C₁₃₉	semidirect
236. #2326	C₂×C₁₃₉	semidirect
237. C₄×#124	C₂×C₁₃₉	semidirect
238. #2298	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#540×C₁₃₉	2
C₂×#519×C₁₃₉	2
#2565×C₁₃₉	2
#2548×C₁₃₉	2
#2500×C₁₃₉	2
#2476×C₁₃₉	2
#2458×C₁₃₉	2
#2436×C₁₃₉	2
#2326×C₁₃₉	2
C₄×#124×C₁₃₉	2
#2298×C₁₃₉	2
#35678	139

Subgroups — C139×#35678 #48030274

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#35678 #48030274