Subgroups — C₁₃₉×#36958 #48031554

Order 35584.

2314 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#537×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×#125×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2854×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2720×C₁₃₉	C₂	1	8	yes	maximal, complemented
5	#2711×C₁₃₉	C₂	1	8	yes	maximal, complemented
6	#2618×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2591×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2501×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2406×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2406×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2313×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₁₃₉	C₂²	1	2	yes	—
13	#537×C₁₃₉	—	2	8	no	—
14	C₂×#125×C₁₃₉	—	2	8	no	—
15	C₂×#125×C₁₃₉	C₂²	1	8	yes	—
16	C₂×#123×C₁₃₉	C₂²	1	4	yes	—
17	C₂×#123×C₁₃₉	C₂²	1	4	yes	—
18	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
19	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
20	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
21	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
22	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
29	#400×C₁₃₉	C₂²	1	4	yes	—
30	#399×C₁₃₉	C₂²	1	8	yes	—
31	#398×C₁₃₉	C₂²	1	4	yes	—
32	#396×C₁₃₉	C₂²	1	8	yes	—
33	#395×C₁₃₉	C₂²	1	4	yes	—
34	#395×C₁₃₉	C₂²	1	4	yes	—
35	#394×C₁₃₉	C₂²	1	4	yes	—
36	#394×C₁₃₉	C₂²	1	4	yes	—
37	#394×C₁₃₉	C₂²	1	4	yes	—
38	#394×C₁₃₉	C₂²	1	4	yes	—
39	#390×C₁₃₉	C₂²	1	4	yes	—
40	#390×C₁₃₉	C₂²	1	4	yes	—
41	#389×C₁₃₉	C₂²	1	4	yes	—
42	#388×C₁₃₉	C₂²	1	8	yes	—
43	#388×C₁₃₉	C₂²	1	8	yes	—
44	#387×C₁₃₉	C₂²	1	8	yes	—
45	#386×C₁₃₉	C₂²	1	4	yes	—
46	#386×C₁₃₉	C₂²	1	4	yes	—
47	#385×C₁₃₉	C₂²	1	8	yes	—
48	#385×C₁₃₉	C₂²	1	8	yes	—
49	#384×C₁₃₉	C₂²	1	4	yes	—
50	#381×C₁₃₉	C₂²	1	2	yes	—
51	#380×C₁₃₉	C₂²	1	2	yes	—
52	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
53	C₂×#41×C₁₃₉	—	2	8	no	—
54	C₂×#41×C₁₃₉	—	4	8	no	—
55	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
56	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
57	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
58	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
59	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
60	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
66	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
68	#125×C₁₃₉	—	2	32	no	—
69	#123×C₁₃₉	—	4	8	no	—
70	#123×C₁₃₉	—	4	8	no	—
71	C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
72	#121×C₁₃₉	—	2	8	no	—
73	#121×C₁₃₉	—	2	8	no	—
74	#121×C₁₃₉	—	2	16	no	—
75	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
76	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
77	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
78	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
79	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
80	C₂×C₄⋊C₄×C₁₃₉	D₄	1	8	yes	—
81	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
82	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
83	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
84	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
85	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
86	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
87	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
88	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
89	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
90	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
91	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
92	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
93	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
94	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
95	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
96	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
97	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
98	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
99	C₂×C₄²×C₁₃₉	—	2	4	no	—
100	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
101	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
102	#95×C₁₃₉	C₂³	1	8	yes	—
103	#95×C₁₃₉	C₂³	1	8	yes	—
104	#95×C₁₃₉	C₂³	1	4	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	#41×C₁₃₉	—	4	32	no	—
111	C₂×Q₈×C₁₃₉	—	2	4	no	—
112	C₂×Q₈×C₁₃₉	—	4	4	no	—
113	C₂×D₄×C₁₃₉	—	2	8	no	—
114	C₂×D₄×C₁₃₉	—	2	8	no	—
115	C₂×D₄×C₁₃₉	—	2	8	no	—
116	C₂×D₄×C₁₃₉	—	2	4	no	—
117	C₂×D₄×C₁₃₉	—	2	4	no	—
118	C₂×D₄×C₁₃₉	—	2	4	no	—
119	C₂×D₄×C₁₃₉	—	4	4	no	—
120	C₂×D₄×C₁₃₉	—	4	4	no	—
121	C₂×D₄×C₁₃₉	—	4	4	no	—
122	C₂²×C₄×C₁₃₉	—	2	2	no	—
123	C₂²×C₄×C₁₃₉	—	2	4	no	—
124	C₂²×C₄×C₁₃₉	—	2	4	no	—
125	C₂²×C₄×C₁₃₉	—	2	2	no	—
126	C₂²×C₄×C₁₃₉	—	2	2	no	—
127	C₂²×C₄×C₁₃₉	—	2	2	no	—
128	C₂²×C₄×C₁₃₉	—	2	4	no	—
129	C₂²×C₄×C₁₃₉	—	2	4	no	—
130	C₂²×C₄×C₁₃₉	—	2	8	no	—
131	C₂²×C₄×C₁₃₉	—	4	2	no	—
132	C₂²×C₄×C₁₃₉	—	4	2	no	—
133	C₂²×C₄×C₁₃₉	—	4	2	no	—
134	C₂²×C₄×C₁₃₉	—	4	4	no	—
135	C₂²×C₄×C₁₃₉	—	4	4	no	—
136	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
137	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
138	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
139	C₂²×C₄×C₁₃₉	C₂⁴	1	8	yes	—
140	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
141	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
142	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
143	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
144	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
145	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
146	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
147	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
148	C₄⋊C₄×C₁₃₉	—	2	8	no	—
149	C₄⋊C₄×C₁₃₉	—	2	8	no	—
150	C₄⋊C₄×C₁₃₉	—	2	8	no	—
151	C₄⋊C₄×C₁₃₉	—	2	8	no	—
152	C₄⋊C₄×C₁₃₉	—	2	8	no	—
153	C₄⋊C₄×C₁₃₉	—	2	4	no	—
154	C₄⋊C₄×C₁₃₉	—	2	4	no	—
155	C₄⋊C₄×C₁₃₉	—	4	4	no	—
156	C₄⋊C₄×C₁₃₉	—	4	8	no	—
157	C₄⋊C₄×C₁₃₉	—	4	8	no	—
158	C₄⋊C₄×C₁₃₉	C₂×D₄	1	16	yes	—
159	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
160	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
161	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
162	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
163	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
164	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
165	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
166	C₄²×C₁₃₉	—	2	8	no	—
167	C₄²×C₁₃₉	—	4	4	no	—
168	C₂³×C₁₃₉	—	2	2	no	—
169	C₂³×C₁₃₉	—	2	2	no	—
170	C₂³×C₁₃₉	—	2	4	no	—
171	C₂³×C₁₃₉	—	2	4	no	—
172	C₂³×C₁₃₉	—	2	4	no	—
173	C₂³×C₁₃₉	—	2	8	no	—
174	C₂³×C₁₃₉	—	2	8	no	—
175	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
176	C₂³×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
177	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
178	Q₈×C₁₃₉	—	4	8	no	—
179	D₄×C₁₃₉	—	4	8	no	—
180	D₄×C₁₃₉	—	4	16	no	—
181	D₄×C₁₃₉	—	8	4	no	—
182	D₄×C₁₃₉	—	8	4	no	—
183	C₂×C₄×C₁₃₉	—	2	8	no	—
184	C₂×C₄×C₁₃₉	—	2	8	no	—
185	C₂×C₄×C₁₃₉	—	2	2	no	—
186	C₂×C₄×C₁₃₉	—	2	4	no	—
187	C₂×C₄×C₁₃₉	—	2	2	no	—
188	C₂×C₄×C₁₃₉	—	2	4	no	—
189	C₂×C₄×C₁₃₉	—	2	4	no	—
190	C₂×C₄×C₁₃₉	—	2	2	no	—
191	C₂×C₄×C₁₃₉	—	2	4	no	—
192	C₂×C₄×C₁₃₉	—	2	2	no	—
193	C₂×C₄×C₁₃₉	—	2	2	no	—
194	C₂×C₄×C₁₃₉	—	2	8	no	—
195	C₂×C₄×C₁₃₉	—	2	4	no	—
196	C₂×C₄×C₁₃₉	—	2	4	no	—
197	C₂×C₄×C₁₃₉	—	2	4	no	—
198	C₂×C₄×C₁₃₉	—	2	4	no	—
199	C₂×C₄×C₁₃₉	—	2	8	no	—
200	C₂×C₄×C₁₃₉	—	2	8	no	—
201	C₂×C₄×C₁₃₉	—	2	4	no	—
202	C₂×C₄×C₁₃₉	—	4	4	no	—
203	C₂×C₄×C₁₃₉	—	4	4	no	—
204	C₂×C₄×C₁₃₉	—	4	16	no	—
205	C₂×C₄×C₁₃₉	—	4	4	no	—
206	C₂×C₄×C₁₃₉	—	4	4	no	—
207	C₂×C₄×C₁₃₉	—	4	4	no	—
208	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
209	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
210	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
211	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	4	yes	—
212	C₂²×C₁₃₉	—	2	2	no	—
213	C₂²×C₁₃₉	—	2	2	no	—
214	C₂²×C₁₃₉	—	2	8	no	—
215	C₂²×C₁₃₉	—	4	4	no	—
216	C₂²×C₁₃₉	—	4	4	no	—
217	C₂²×C₁₃₉	—	4	4	no	—
218	C₂²×C₁₃₉	—	4	8	no	—
219	C₂²×C₁₃₉	—	4	8	no	—
220	C₂²×C₁₃₉	#535	1	4	yes	—
221	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
222	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
223	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	2	yes	—
224	C₂²×C₁₃₉	#585	1	2	yes	—
225	C₄×C₁₃₉	—	2	4	no	—
226	C₄×C₁₃₉	—	2	4	no	—
227	C₄×C₁₃₉	—	2	4	no	—
228	C₄×C₁₃₉	—	2	4	no	—
229	C₄×C₁₃₉	—	4	2	no	—
230	C₄×C₁₃₉	—	4	2	no	—
231	C₄×C₁₃₉	—	4	4	no	—
232	C₄×C₁₃₉	—	4	2	no	—
233	C₄×C₁₃₉	—	4	8	no	—
234	C₂×C₁₃₉	—	2	4	no	—
235	C₂×C₁₃₉	—	8	4	no	—
236	C₂×C₁₃₉	C₂×#535	1	1	yes	characteristic
237	C₂×C₁₃₉	#3485	1	1	yes	characteristic
238	C₂×C₁₃₉	#3486	1	1	yes	characteristic
239	C₂×C₁₃₉	#3559	1	4	yes	—
240	#36958	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
241	C₁₃₉	#36958	1	1	yes	characteristic, direct product factor, Sylow
242	C₂×#537	C₂×C₁₃₉	1	1	yes	characteristic
243	C₂²×#125	C₂×C₁₃₉	1	1	yes	characteristic, complemented
244	#2854	C₂×C₁₃₉	1	2	yes	complemented
245	#2720	C₂×C₁₃₉	1	8	yes	complemented
246	#2711	C₂×C₁₃₉	1	8	yes	complemented
247	#2618	C₂×C₁₃₉	1	2	yes	complemented
248	#2591	C₂×C₁₃₉	1	2	yes	complemented
249	#2501	C₂×C₁₃₉	1	2	yes	complemented
250	#2406	C₂×C₁₃₉	1	2	yes	complemented
251	#2406	C₂×C₁₃₉	1	2	yes	complemented
252	#2313	C₂×C₁₃₉	1	1	yes	characteristic, complemented
253	C₂²×#41	C₂²×C₁₃₉	1	2	yes	—
254	#537	—	2	8	no	—
255	C₂×#125	—	2	8	no	—
256	C₂×#125	C₂²×C₁₃₉	1	8	yes	—
257	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
258	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
259	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
260	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
261	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
262	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
263	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
264	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
265	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
266	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
267	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
268	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
269	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
270	#400	C₂²×C₁₃₉	1	4	yes	—
271	#399	C₂²×C₁₃₉	1	8	yes	—
272	#398	C₂²×C₁₃₉	1	4	yes	—
273	#396	C₂²×C₁₃₉	1	8	yes	—
274	#395	C₂²×C₁₃₉	1	4	yes	—
275	#395	C₂²×C₁₃₉	1	4	yes	—
276	#394	C₂²×C₁₃₉	1	4	yes	—
277	#394	C₂²×C₁₃₉	1	4	yes	—
278	#394	C₂²×C₁₃₉	1	4	yes	—
279	#394	C₂²×C₁₃₉	1	4	yes	—
280	#390	C₂²×C₁₃₉	1	4	yes	—
281	#390	C₂²×C₁₃₉	1	4	yes	—
282	#389	C₂²×C₁₃₉	1	4	yes	—
283	#388	C₂²×C₁₃₉	1	8	yes	—
284	#388	C₂²×C₁₃₉	1	8	yes	—
285	#387	C₂²×C₁₃₉	1	8	yes	—
286	#386	C₂²×C₁₃₉	1	4	yes	—
287	#386	C₂²×C₁₃₉	1	4	yes	—
288	#385	C₂²×C₁₃₉	1	8	yes	—
289	#385	C₂²×C₁₃₉	1	8	yes	—
290	#384	C₂²×C₁₃₉	1	4	yes	—
291	#381	C₂²×C₁₃₉	1	2	yes	—
292	#380	C₂²×C₁₃₉	1	2	yes	—
293	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
294	C₂×#41	—	2	8	no	—
295	C₂×#41	—	4	8	no	—
296	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
297	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
298	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
299	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
300	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
301	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
302	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
303	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
304	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
305	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
306	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
307	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
308	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
309	#125	—	2	32	no	—
310	#123	—	4	8	no	—
311	#123	—	4	8	no	—
312	C₂²⋊Q₈	—	2	16	no	—
313	#121	—	2	8	no	—
314	#121	—	2	8	no	—
315	#121	—	2	16	no	—
316	C₂×C₄⋊C₄	—	2	4	no	—
317	C₂×C₄⋊C₄	—	2	4	no	—
318	C₂×C₄⋊C₄	—	2	4	no	—
319	C₂×C₄⋊C₄	—	2	4	no	—
320	C₂×C₄⋊C₄	—	2	4	no	—
321	C₂×C₄⋊C₄	D₄×C₁₃₉	1	8	yes	—
322	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
323	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
324	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
325	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
326	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
327	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
328	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
329	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
330	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
331	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
332	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
333	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
334	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
335	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
336	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
337	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
338	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
339	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
340	C₂×C₄²	—	2	4	no	—
341	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
342	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
343	#95	C₂³×C₁₃₉	1	4	yes	—
344	#95	C₂³×C₁₃₉	1	4	yes	—
345	#95	C₂³×C₁₃₉	1	4	yes	—
346	#95	C₂³×C₁₃₉	1	4	yes	—
347	#95	C₂³×C₁₃₉	1	8	yes	—
348	#95	C₂³×C₁₃₉	1	8	yes	—
349	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
350	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
351	#41	—	4	32	no	—
352	C₂×Q₈	—	2	4	no	—
353	C₂×Q₈	—	4	4	no	—
354	C₂×D₄	—	2	8	no	—
355	C₂×D₄	—	2	8	no	—
356	C₂×D₄	—	2	8	no	—
357	C₂×D₄	—	2	4	no	—
358	C₂×D₄	—	2	4	no	—
359	C₂×D₄	—	2	4	no	—
360	C₂×D₄	—	4	4	no	—
361	C₂×D₄	—	4	4	no	—
362	C₂×D₄	—	4	4	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	4	no	—
365	C₂²×C₄	—	2	4	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	4	no	—
370	C₂²×C₄	—	2	4	no	—
371	C₂²×C₄	—	2	8	no	—
372	C₂²×C₄	—	4	2	no	—
373	C₂²×C₄	—	4	2	no	—
374	C₂²×C₄	—	4	2	no	—
375	C₂²×C₄	—	4	4	no	—
376	C₂²×C₄	—	4	4	no	—
377	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
378	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
379	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
380	C₂²×C₄	C₂⁴×C₁₃₉	1	8	yes	—
381	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
382	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
383	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
384	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
385	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
386	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
387	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
388	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
389	C₄⋊C₄	—	2	8	no	—
390	C₄⋊C₄	—	2	8	no	—
391	C₄⋊C₄	—	2	8	no	—
392	C₄⋊C₄	—	2	8	no	—
393	C₄⋊C₄	—	2	8	no	—
394	C₄⋊C₄	—	2	4	no	—
395	C₄⋊C₄	—	2	4	no	—
396	C₄⋊C₄	—	4	4	no	—
397	C₄⋊C₄	—	4	8	no	—
398	C₄⋊C₄	—	4	8	no	—
399	C₄⋊C₄	C₂×D₄×C₁₃₉	1	16	yes	—
400	C₂²⋊C₄	—	2	8	no	—
401	C₂²⋊C₄	—	2	8	no	—
402	C₂²⋊C₄	—	2	8	no	—
403	C₂²⋊C₄	—	2	16	no	—
404	C₂²⋊C₄	—	4	8	no	—
405	C₂²⋊C₄	—	4	8	no	—
406	C₂²⋊C₄	—	4	8	no	—
407	C₄²	—	2	8	no	—
408	C₄²	—	4	4	no	—
409	C₂³	—	2	2	no	—
410	C₂³	—	2	2	no	—
411	C₂³	—	2	4	no	—
412	C₂³	—	2	4	no	—
413	C₂³	—	2	4	no	—
414	C₂³	—	2	8	no	—
415	C₂³	—	2	8	no	—
416	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
417	C₂³	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
418	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
419	Q₈	—	4	8	no	—
420	D₄	—	4	8	no	—
421	D₄	—	4	16	no	—
422	D₄	—	8	4	no	—
423	D₄	—	8	4	no	—
424	C₂×C₄	—	2	8	no	—
425	C₂×C₄	—	2	8	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	4	no	—
430	C₂×C₄	—	2	4	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	4	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	8	no	—
436	C₂×C₄	—	2	4	no	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	8	no	—
441	C₂×C₄	—	2	8	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	4	4	no	—
444	C₂×C₄	—	4	4	no	—
445	C₂×C₄	—	4	16	no	—
446	C₂×C₄	—	4	4	no	—
447	C₂×C₄	—	4	4	no	—
448	C₂×C₄	—	4	4	no	—
449	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
450	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
451	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
452	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	4	yes	—
453	C₂²	—	2	8	no	—
454	C₂²	—	2	2	no	—
455	C₂²	—	2	2	no	—
456	C₂²	—	4	8	no	—
457	C₂²	—	4	8	no	—
458	C₂²	—	4	4	no	—
459	C₂²	—	4	4	no	—
460	C₂²	—	4	4	no	—
461	C₂²	#535×C₁₃₉	1	4	yes	—
462	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
463	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
464	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	2	yes	—
465	C₂²	#585×C₁₃₉	1	2	yes	—
466	C₄	—	2	4	no	—
467	C₄	—	2	4	no	—
468	C₄	—	2	4	no	—
469	C₄	—	2	4	no	—
470	C₄	—	4	8	no	—
471	C₄	—	4	4	no	—
472	C₄	—	4	2	no	—
473	C₄	—	4	2	no	—
474	C₄	—	4	2	no	—
475	C₂	—	2	4	no	—
476	C₂	—	8	4	no	—
477	C₂	C₂×#535×C₁₃₉	1	1	yes	characteristic
478	C₂	#3485×C₁₃₉	1	1	yes	characteristic
479	C₂	#3486×C₁₃₉	1	1	yes	characteristic
480	C₂	#3559×C₁₃₉	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂×#537×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. C₂²×#125×C₁₃₉	C₂	semidirect
3. #2854×C₁₃₉	C₂	semidirect
4. #2720×C₁₃₉	C₂	semidirect
5. #2711×C₁₃₉	C₂	semidirect
6. #2618×C₁₃₉	C₂	semidirect
7. #2591×C₁₃₉	C₂	semidirect
8. #2501×C₁₃₉	C₂	semidirect
9. #2406×C₁₃₉	C₂	semidirect
10. #2406×C₁₃₉	C₂	semidirect
11. #2313×C₁₃₉	C₂	semidirect
240. #36958	C₁₃₉	direct (N × H)
241. C₁₃₉	#36958	direct (N × H)
243. C₂²×#125	C₂×C₁₃₉	semidirect
244. #2854	C₂×C₁₃₉	semidirect
245. #2720	C₂×C₁₃₉	semidirect
246. #2711	C₂×C₁₃₉	semidirect
247. #2618	C₂×C₁₃₉	semidirect
248. #2591	C₂×C₁₃₉	semidirect
249. #2501	C₂×C₁₃₉	semidirect
250. #2406	C₂×C₁₃₉	semidirect
251. #2406	C₂×C₁₃₉	semidirect
252. #2313	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×#537×C₁₃₉	2
C₂²×#125×C₁₃₉	2
#2854×C₁₃₉	2
#2720×C₁₃₉	2
#2711×C₁₃₉	2
#2618×C₁₃₉	2
#2591×C₁₃₉	2
#2501×C₁₃₉	2
#2406×C₁₃₉	2
#2313×C₁₃₉	2
#36958	139

Subgroups — C139×#36958 #48031554

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36958 #48031554