Subgroups — C₁₃₉×#35639 #48030235

Order 35584.

2294 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#125×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#520×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2579×C₁₃₉	C₂	1	4	yes	maximal, complemented
4	#2487×C₁₃₉	C₂	1	4	yes	maximal, complemented
5	#2454×C₁₃₉	C₂	1	4	yes	maximal, complemented
6	#2453×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#2442×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	#2441×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#2317×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#2316×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#2311×C₁₃₉	C₂	1	1	yes	maximal, characteristic
12	#2297×C₁₃₉	C₂	1	1	yes	maximal, characteristic
13	#2296×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
15	C₂×#125×C₁₃₉	—	2	8	no	—
16	C₂×#125×C₁₃₉	C₂²	1	4	yes	—
17	C₂×#125×C₁₃₉	C₂²	1	4	yes	—
18	#520×C₁₃₉	—	2	8	no	—
19	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
20	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	—
21	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
23	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
26	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
28	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
29	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
30	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
32	#400×C₁₃₉	C₂²	1	8	yes	—
33	#399×C₁₃₉	C₂²	1	8	yes	—
34	#398×C₁₃₉	C₂²	1	8	yes	—
35	#396×C₁₃₉	C₂²	1	8	yes	—
36	#391×C₁₃₉	C₂²	1	2	yes	—
37	#391×C₁₃₉	C₂²	1	2	yes	—
38	#390×C₁₃₉	C₂²	1	2	yes	—
39	#390×C₁₃₉	C₂²	1	2	yes	—
40	#389×C₁₃₉	C₂²	1	2	yes	—
41	#389×C₁₃₉	C₂²	1	2	yes	—
42	#389×C₁₃₉	C₂²	1	4	yes	—
43	#389×C₁₃₉	C₂²	1	4	yes	—
44	#389×C₁₃₉	C₂²	1	4	yes	—
45	#389×C₁₃₉	C₂²	1	8	yes	—
46	#387×C₁₃₉	C₂²	1	8	yes	—
47	#386×C₁₃₉	C₂²	1	2	yes	—
48	#386×C₁₃₉	C₂²	1	2	yes	—
49	#386×C₁₃₉	C₂²	1	4	yes	—
50	#385×C₁₃₉	C₂²	1	2	yes	—
51	#385×C₁₃₉	C₂²	1	2	yes	—
52	#385×C₁₃₉	C₂²	1	4	yes	—
53	#385×C₁₃₉	C₂²	1	8	yes	—
54	#384×C₁₃₉	C₂²	1	2	yes	—
55	#382×C₁₃₉	C₂²	1	2	yes	—
56	#380×C₁₃₉	C₂²	1	4	yes	—
57	#380×C₁₃₉	C₂²	1	4	yes	—
58	#380×C₁₃₉	C₂²	1	8	yes	—
59	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
60	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
61	C₂×#41×C₁₃₉	—	2	4	no	—
62	C₂×#41×C₁₃₉	—	2	4	no	—
63	C₂×#41×C₁₃₉	Q₈	1	8	yes	—
64	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
65	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
66	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
68	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
71	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
72	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
73	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
74	#125×C₁₃₉	—	2	16	no	—
75	#125×C₁₃₉	—	2	16	no	—
76	C₄×Q₈×C₁₃₉	—	2	8	no	—
77	C₄×D₄×C₁₃₉	—	2	16	no	—
78	C₄×D₄×C₁₃₉	—	2	8	no	—
79	#117×C₁₃₉	—	2	4	no	—
80	#117×C₁₃₉	—	2	4	no	—
81	#117×C₁₃₉	—	2	4	no	—
82	#117×C₁₃₉	—	2	8	no	—
83	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
84	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
85	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
86	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
87	C₂×C₄⋊C₄×C₁₃₉	D₄	1	8	yes	—
88	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
89	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
90	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
91	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
93	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
94	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
96	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
97	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
98	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
99	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
100	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
101	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
102	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
103	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
104	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
105	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
106	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
107	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
108	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
109	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
110	C₂×C₄²×C₁₃₉	—	2	4	no	—
111	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
112	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
113	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
114	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
115	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
116	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
117	#95×C₁₃₉	C₂³	1	4	yes	—
118	#95×C₁₃₉	C₂³	1	4	yes	—
119	#95×C₁₃₉	C₂³	1	8	yes	—
120	#95×C₁₃₉	C₂³	1	8	yes	—
121	#95×C₁₃₉	C₂³	1	8	yes	—
122	#95×C₁₃₉	C₂³	1	4	yes	—
123	#95×C₁₃₉	C₂³	1	4	yes	—
124	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
125	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
126	#41×C₁₃₉	—	2	32	no	—
127	C₂×Q₈×C₁₃₉	—	2	2	no	—
128	C₂×Q₈×C₁₃₉	—	2	2	no	—
129	C₂×Q₈×C₁₃₉	C₂×Q₈	1	4	yes	—
130	C₂×D₄×C₁₃₉	—	2	4	no	—
131	C₂×D₄×C₁₃₉	—	2	4	no	—
132	C₂×D₄×C₁₃₉	—	2	2	no	—
133	C₂×D₄×C₁₃₉	—	2	2	no	—
134	C₂×D₄×C₁₃₉	C₂×Q₈	1	8	yes	—
135	C₂×D₄×C₁₃₉	C₂×Q₈	1	4	yes	—
136	C₂²×C₄×C₁₃₉	—	2	4	no	—
137	C₂²×C₄×C₁₃₉	—	2	4	no	—
138	C₂²×C₄×C₁₃₉	—	2	2	no	—
139	C₂²×C₄×C₁₃₉	—	2	2	no	—
140	C₂²×C₄×C₁₃₉	—	2	4	no	—
141	C₂²×C₄×C₁₃₉	—	2	8	no	—
142	C₂²×C₄×C₁₃₉	—	4	4	no	—
143	C₂²×C₄×C₁₃₉	—	4	2	no	—
144	C₂²×C₄×C₁₃₉	—	4	2	no	—
145	C₂²×C₄×C₁₃₉	—	4	4	no	—
146	C₂²×C₄×C₁₃₉	—	4	8	no	—
147	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
148	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
149	C₂²×C₄×C₁₃₉	C₂×Q₈	1	8	yes	—
150	C₂²×C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
151	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
152	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
153	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
154	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
155	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
156	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
157	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
158	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
159	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
160	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
161	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
162	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
163	C₄⋊C₄×C₁₃₉	—	2	2	no	—
164	C₄⋊C₄×C₁₃₉	—	2	8	no	—
165	C₄⋊C₄×C₁₃₉	—	2	16	no	—
166	C₄⋊C₄×C₁₃₉	—	2	16	no	—
167	C₄⋊C₄×C₁₃₉	—	2	4	no	—
168	C₄⋊C₄×C₁₃₉	—	2	4	no	—
169	C₄⋊C₄×C₁₃₉	—	2	2	no	—
170	C₄⋊C₄×C₁₃₉	—	2	4	no	—
171	C₄⋊C₄×C₁₃₉	—	2	4	no	—
172	C₄⋊C₄×C₁₃₉	—	4	8	no	—
173	C₄⋊C₄×C₁₃₉	—	4	4	no	—
174	C₄⋊C₄×C₁₃₉	—	4	8	no	—
175	C₄⋊C₄×C₁₃₉	—	4	4	no	—
176	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
177	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
178	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
179	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
180	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
181	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
182	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
183	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
184	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
185	C₄²×C₁₃₉	—	2	4	no	—
186	C₄²×C₁₃₉	—	2	4	no	—
187	C₄²×C₁₃₉	—	2	8	no	—
188	C₄²×C₁₃₉	—	2	4	no	—
189	C₄²×C₁₃₉	—	2	4	no	—
190	C₄²×C₁₃₉	—	2	4	no	—
191	C₂³×C₁₃₉	—	2	2	no	—
192	C₂³×C₁₃₉	—	2	2	no	—
193	C₂³×C₁₃₉	—	2	2	no	—
194	C₂³×C₁₃₉	—	2	2	no	—
195	C₂³×C₁₃₉	—	2	4	no	—
196	C₂³×C₁₃₉	—	2	4	no	—
197	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
198	C₂³×C₁₃₉	C₂²×Q₈	1	4	yes	—
199	C₂³×C₁₃₉	C₂²×Q₈	1	2	yes	—
200	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
201	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
202	Q₈×C₁₃₉	—	2	8	no	—
203	D₄×C₁₃₉	—	2	16	no	—
204	D₄×C₁₃₉	—	2	8	no	—
205	C₂×C₄×C₁₃₉	—	2	2	no	—
206	C₂×C₄×C₁₃₉	—	2	2	no	—
207	C₂×C₄×C₁₃₉	—	2	8	no	—
208	C₂×C₄×C₁₃₉	—	2	16	no	—
209	C₂×C₄×C₁₃₉	—	2	2	no	—
210	C₂×C₄×C₁₃₉	—	2	2	no	—
211	C₂×C₄×C₁₃₉	—	2	2	no	—
212	C₂×C₄×C₁₃₉	—	2	2	no	—
213	C₂×C₄×C₁₃₉	—	2	4	no	—
214	C₂×C₄×C₁₃₉	—	2	4	no	—
215	C₂×C₄×C₁₃₉	—	2	4	no	—
216	C₂×C₄×C₁₃₉	—	2	4	no	—
217	C₂×C₄×C₁₃₉	—	2	2	no	—
218	C₂×C₄×C₁₃₉	—	2	2	no	—
219	C₂×C₄×C₁₃₉	—	2	4	no	—
220	C₂×C₄×C₁₃₉	—	2	4	no	—
221	C₂×C₄×C₁₃₉	—	2	8	no	—
222	C₂×C₄×C₁₃₉	—	2	4	no	—
223	C₂×C₄×C₁₃₉	—	2	4	no	—
224	C₂×C₄×C₁₃₉	—	2	2	no	—
225	C₂×C₄×C₁₃₉	—	2	2	no	—
226	C₂×C₄×C₁₃₉	—	2	4	no	—
227	C₂×C₄×C₁₃₉	—	4	8	no	—
228	C₂×C₄×C₁₃₉	—	4	4	no	—
229	C₂×C₄×C₁₃₉	—	4	4	no	—
230	C₂×C₄×C₁₃₉	—	4	8	no	—
231	C₂×C₄×C₁₃₉	—	8	8	no	—
232	C₂×C₄×C₁₃₉	C₂²⋊Q₈	1	16	yes	—
233	C₂×C₄×C₁₃₉	C₂²×D₄	1	8	yes	—
234	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
235	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
236	C₂×C₄×C₁₃₉	C₂²×Q₈	1	4	yes	—
237	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
238	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
239	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
240	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
241	C₂²×C₁₃₉	—	2	2	no	—
242	C₂²×C₁₃₉	—	2	2	no	—
243	C₂²×C₁₃₉	—	2	4	no	—
244	C₂²×C₁₃₉	—	2	4	no	—
245	C₂²×C₁₃₉	—	2	4	no	—
246	C₂²×C₁₃₉	—	2	8	no	—
247	C₂²×C₁₃₉	—	4	2	no	—
248	C₂²×C₁₃₉	—	4	2	no	—
249	C₂²×C₁₃₉	—	4	4	no	—
250	C₂²×C₁₃₉	C₂×C₂²⋊Q₈	1	4	yes	—
251	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
252	C₂²×C₁₃₉	C₂³×Q₈	1	1	yes	characteristic
253	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
254	C₂²×C₁₃₉	#585	1	2	yes	—
255	C₂²×C₁₃₉	#585	1	2	yes	—
256	C₄×C₁₃₉	—	2	4	no	—
257	C₄×C₁₃₉	—	2	8	no	—
258	C₄×C₁₃₉	—	4	2	no	—
259	C₄×C₁₃₉	—	4	2	no	—
260	C₄×C₁₃₉	—	4	2	no	—
261	C₄×C₁₃₉	—	4	2	no	—
262	C₄×C₁₃₉	—	4	4	no	—
263	C₄×C₁₃₉	—	4	4	no	—
264	C₄×C₁₃₉	—	4	4	no	—
265	C₄×C₁₃₉	C₂×C₂²⋊Q₈	1	4	yes	—
266	C₄×C₁₃₉	C₂×C₂²⋊Q₈	1	4	yes	—
267	C₂×C₁₃₉	—	2	4	no	—
268	C₂×C₁₃₉	—	4	4	no	—
269	C₂×C₁₃₉	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
270	C₂×C₁₃₉	#3485	1	1	yes	characteristic
271	C₂×C₁₃₉	#3487	1	1	yes	characteristic
272	C₂×C₁₃₉	#3504	1	2	yes	—
273	C₂×C₁₃₉	#3512	1	2	yes	—
274	#35639	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
275	C₁₃₉	#35639	1	1	yes	characteristic, direct product factor, Sylow
276	C₂²×#125	C₂×C₁₃₉	1	1	yes	characteristic, complemented
277	C₂×#520	C₂×C₁₃₉	1	1	yes	characteristic
278	#2579	C₂×C₁₃₉	1	4	yes	complemented
279	#2487	C₂×C₁₃₉	1	4	yes	complemented
280	#2454	C₂×C₁₃₉	1	4	yes	complemented
281	#2453	C₂×C₁₃₉	1	4	yes	complemented
282	#2442	C₂×C₁₃₉	1	4	yes	complemented
283	#2441	C₂×C₁₃₉	1	4	yes	complemented
284	#2317	C₂×C₁₃₉	1	1	yes	characteristic, complemented
285	#2316	C₂×C₁₃₉	1	1	yes	characteristic, complemented
286	#2311	C₂×C₁₃₉	1	1	yes	characteristic
287	#2297	C₂×C₁₃₉	1	1	yes	characteristic
288	#2296	C₂×C₁₃₉	1	1	yes	characteristic, complemented
289	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
290	C₂×#125	—	2	8	no	—
291	C₂×#125	C₂²×C₁₃₉	1	4	yes	—
292	C₂×#125	C₂²×C₁₃₉	1	4	yes	—
293	#520	—	2	8	no	—
294	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
295	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	—
296	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
297	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
298	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
299	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
300	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
301	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
302	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
303	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
304	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
305	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
306	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
307	#400	C₂²×C₁₃₉	1	8	yes	—
308	#399	C₂²×C₁₃₉	1	8	yes	—
309	#398	C₂²×C₁₃₉	1	8	yes	—
310	#396	C₂²×C₁₃₉	1	8	yes	—
311	#391	C₂²×C₁₃₉	1	2	yes	—
312	#391	C₂²×C₁₃₉	1	2	yes	—
313	#390	C₂²×C₁₃₉	1	2	yes	—
314	#390	C₂²×C₁₃₉	1	2	yes	—
315	#389	C₂²×C₁₃₉	1	4	yes	—
316	#389	C₂²×C₁₃₉	1	4	yes	—
317	#389	C₂²×C₁₃₉	1	4	yes	—
318	#389	C₂²×C₁₃₉	1	2	yes	—
319	#389	C₂²×C₁₃₉	1	8	yes	—
320	#389	C₂²×C₁₃₉	1	2	yes	—
321	#387	C₂²×C₁₃₉	1	8	yes	—
322	#386	C₂²×C₁₃₉	1	4	yes	—
323	#386	C₂²×C₁₃₉	1	2	yes	—
324	#386	C₂²×C₁₃₉	1	2	yes	—
325	#385	C₂²×C₁₃₉	1	4	yes	—
326	#385	C₂²×C₁₃₉	1	2	yes	—
327	#385	C₂²×C₁₃₉	1	8	yes	—
328	#385	C₂²×C₁₃₉	1	2	yes	—
329	#384	C₂²×C₁₃₉	1	2	yes	—
330	#382	C₂²×C₁₃₉	1	2	yes	—
331	#380	C₂²×C₁₃₉	1	4	yes	—
332	#380	C₂²×C₁₃₉	1	4	yes	—
333	#380	C₂²×C₁₃₉	1	8	yes	—
334	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
335	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
336	C₂×#41	—	2	4	no	—
337	C₂×#41	—	2	4	no	—
338	C₂×#41	Q₈×C₁₃₉	1	8	yes	—
339	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
340	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
341	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
342	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
343	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
344	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
345	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
346	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
347	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
348	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
349	#125	—	2	16	no	—
350	#125	—	2	16	no	—
351	C₄×Q₈	—	2	8	no	—
352	C₄×D₄	—	2	16	no	—
353	C₄×D₄	—	2	8	no	—
354	#117	—	2	4	no	—
355	#117	—	2	4	no	—
356	#117	—	2	4	no	—
357	#117	—	2	8	no	—
358	C₂×C₄⋊C₄	—	2	8	no	—
359	C₂×C₄⋊C₄	—	2	8	no	—
360	C₂×C₄⋊C₄	—	2	4	no	—
361	C₂×C₄⋊C₄	—	2	8	no	—
362	C₂×C₄⋊C₄	D₄×C₁₃₉	1	8	yes	—
363	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
364	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
365	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
366	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
367	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
368	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
369	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
370	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
371	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
372	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
373	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
374	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
375	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
376	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
377	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
378	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
379	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
380	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
381	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
382	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
383	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
384	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
385	C₂×C₄²	—	2	4	no	—
386	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
387	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
388	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
389	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
390	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
391	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
392	#95	C₂³×C₁₃₉	1	4	yes	—
393	#95	C₂³×C₁₃₉	1	4	yes	—
394	#95	C₂³×C₁₃₉	1	4	yes	—
395	#95	C₂³×C₁₃₉	1	4	yes	—
396	#95	C₂³×C₁₃₉	1	8	yes	—
397	#95	C₂³×C₁₃₉	1	8	yes	—
398	#95	C₂³×C₁₃₉	1	8	yes	—
399	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
400	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
401	#41	—	2	32	no	—
402	C₂×Q₈	—	2	2	no	—
403	C₂×Q₈	—	2	2	no	—
404	C₂×Q₈	C₂×Q₈×C₁₃₉	1	4	yes	—
405	C₂×D₄	—	2	4	no	—
406	C₂×D₄	—	2	4	no	—
407	C₂×D₄	—	2	2	no	—
408	C₂×D₄	—	2	2	no	—
409	C₂×D₄	C₂×Q₈×C₁₃₉	1	8	yes	—
410	C₂×D₄	C₂×Q₈×C₁₃₉	1	4	yes	—
411	C₂²×C₄	—	2	4	no	—
412	C₂²×C₄	—	2	4	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	4	no	—
416	C₂²×C₄	—	2	8	no	—
417	C₂²×C₄	—	4	4	no	—
418	C₂²×C₄	—	4	2	no	—
419	C₂²×C₄	—	4	2	no	—
420	C₂²×C₄	—	4	4	no	—
421	C₂²×C₄	—	4	8	no	—
422	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
423	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
424	C₂²×C₄	C₂×Q₈×C₁₃₉	1	8	yes	—
425	C₂²×C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
426	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
427	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
428	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
429	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
430	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
431	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
432	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
433	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
434	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
435	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
436	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
437	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	2	8	no	—
440	C₄⋊C₄	—	2	16	no	—
441	C₄⋊C₄	—	2	16	no	—
442	C₄⋊C₄	—	2	4	no	—
443	C₄⋊C₄	—	2	4	no	—
444	C₄⋊C₄	—	2	2	no	—
445	C₄⋊C₄	—	2	4	no	—
446	C₄⋊C₄	—	2	4	no	—
447	C₄⋊C₄	—	4	8	no	—
448	C₄⋊C₄	—	4	4	no	—
449	C₄⋊C₄	—	4	8	no	—
450	C₄⋊C₄	—	4	4	no	—
451	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
452	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
453	C₂²⋊C₄	—	2	4	no	—
454	C₂²⋊C₄	—	2	4	no	—
455	C₂²⋊C₄	—	2	4	no	—
456	C₂²⋊C₄	—	2	8	no	—
457	C₂²⋊C₄	—	4	8	no	—
458	C₂²⋊C₄	—	4	4	no	—
459	C₂²⋊C₄	—	4	4	no	—
460	C₄²	—	2	4	no	—
461	C₄²	—	2	4	no	—
462	C₄²	—	2	8	no	—
463	C₄²	—	2	4	no	—
464	C₄²	—	2	4	no	—
465	C₄²	—	2	4	no	—
466	C₂³	—	2	2	no	—
467	C₂³	—	2	2	no	—
468	C₂³	—	2	2	no	—
469	C₂³	—	2	2	no	—
470	C₂³	—	2	4	no	—
471	C₂³	—	2	4	no	—
472	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
473	C₂³	C₂²×Q₈×C₁₃₉	1	4	yes	—
474	C₂³	C₂²×Q₈×C₁₃₉	1	2	yes	—
475	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
476	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
477	Q₈	—	2	8	no	—
478	D₄	—	2	16	no	—
479	D₄	—	2	8	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	8	no	—
483	C₂×C₄	—	2	16	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	4	no	—
489	C₂×C₄	—	2	4	no	—
490	C₂×C₄	—	2	4	no	—
491	C₂×C₄	—	2	4	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	8	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	4	no	—
502	C₂×C₄	—	4	8	no	—
503	C₂×C₄	—	4	4	no	—
504	C₂×C₄	—	4	4	no	—
505	C₂×C₄	—	4	8	no	—
506	C₂×C₄	—	8	8	no	—
507	C₂×C₄	C₂²⋊Q₈×C₁₃₉	1	16	yes	—
508	C₂×C₄	C₂²×D₄×C₁₃₉	1	8	yes	—
509	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
510	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
511	C₂×C₄	C₂²×Q₈×C₁₃₉	1	4	yes	—
512	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
513	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
514	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
515	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
516	C₂²	—	2	2	no	—
517	C₂²	—	2	2	no	—
518	C₂²	—	2	4	no	—
519	C₂²	—	2	4	no	—
520	C₂²	—	2	4	no	—
521	C₂²	—	2	8	no	—
522	C₂²	—	4	2	no	—
523	C₂²	—	4	2	no	—
524	C₂²	—	4	4	no	—
525	C₂²	C₂×C₂²⋊Q₈×C₁₃₉	1	4	yes	—
526	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
527	C₂²	C₂³×Q₈×C₁₃₉	1	1	yes	characteristic
528	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
529	C₂²	#585×C₁₃₉	1	2	yes	—
530	C₂²	#585×C₁₃₉	1	2	yes	—
531	C₄	—	2	4	no	—
532	C₄	—	2	8	no	—
533	C₄	—	4	2	no	—
534	C₄	—	4	2	no	—
535	C₄	—	4	2	no	—
536	C₄	—	4	4	no	—
537	C₄	—	4	2	no	—
538	C₄	—	4	4	no	—
539	C₄	—	4	4	no	—
540	C₄	C₂×C₂²⋊Q₈×C₁₃₉	1	4	yes	—
541	C₄	C₂×C₂²⋊Q₈×C₁₃₉	1	4	yes	—
542	C₂	—	2	4	no	—
543	C₂	—	4	4	no	—
544	C₂	C₂²×C₂²⋊Q₈×C₁₃₉	1	1	yes	characteristic
545	C₂	#3485×C₁₃₉	1	1	yes	characteristic
546	C₂	#3487×C₁₃₉	1	1	yes	characteristic
547	C₂	#3504×C₁₃₉	1	2	yes	—
548	C₂	#3512×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂²×#41×C₁₃₉	C₂²
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. C₂²×#125×C₁₃₉	C₂	semidirect
3. #2579×C₁₃₉	C₂	semidirect
4. #2487×C₁₃₉	C₂	semidirect
5. #2454×C₁₃₉	C₂	semidirect
6. #2453×C₁₃₉	C₂	semidirect
7. #2442×C₁₃₉	C₂	semidirect
8. #2441×C₁₃₉	C₂	semidirect
9. #2317×C₁₃₉	C₂	semidirect
10. #2316×C₁₃₉	C₂	semidirect
13. #2296×C₁₃₉	C₂	semidirect
274. #35639	C₁₃₉	direct (N × H)
275. C₁₃₉	#35639	direct (N × H)
276. C₂²×#125	C₂×C₁₃₉	semidirect
278. #2579	C₂×C₁₃₉	semidirect
279. #2487	C₂×C₁₃₉	semidirect
280. #2454	C₂×C₁₃₉	semidirect
281. #2453	C₂×C₁₃₉	semidirect
282. #2442	C₂×C₁₃₉	semidirect
283. #2441	C₂×C₁₃₉	semidirect
284. #2317	C₂×C₁₃₉	semidirect
285. #2316	C₂×C₁₃₉	semidirect
288. #2296	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#125×C₁₃₉	2
C₂×#520×C₁₃₉	2
#2579×C₁₃₉	2
#2487×C₁₃₉	2
#2454×C₁₃₉	2
#2453×C₁₃₉	2
#2442×C₁₃₉	2
#2441×C₁₃₉	2
#2317×C₁₃₉	2
#2316×C₁₃₉	2
#2311×C₁₃₉	2
#2297×C₁₃₉	2
#2296×C₁₃₉	2
#35639	139

Subgroups — C139×#35639 #48030235

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#35639 #48030235