Subgroups — C₁₃₉×#37187 #48031783

Order 35584.

2538 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#536×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#124×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2853×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2733×C₁₃₉	C₂	1	4	yes	maximal, complemented
5	#2731×C₁₃₉	C₂	1	4	yes	maximal, complemented
6	#2730×C₁₃₉	C₂	1	8	yes	maximal, complemented
7	#2613×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2482×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2411×C₁₃₉	C₂	1	4	yes	maximal, complemented
10	#2404×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2310×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
13	C₂³×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
15	#536×C₁₃₉	—	2	8	no	—
16	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	complemented
17	C₂×#124×C₁₃₉	—	2	8	no	—
18	C₂×#124×C₁₃₉	C₂²	1	4	yes	—
19	C₂×#124×C₁₃₉	C₂²	1	4	yes	—
20	C₂×#124×C₁₃₉	C₂²	1	2	yes	complemented
21	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	complemented
24	C₂×#120×C₁₃₉	C₂²	1	4	yes	—
25	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
27	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
28	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
29	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
30	#399×C₁₃₉	C₂²	1	4	yes	complemented
31	#397×C₁₃₉	C₂²	1	4	yes	complemented
32	#396×C₁₃₉	C₂²	1	8	yes	complemented
33	#394×C₁₃₉	C₂²	1	8	yes	—
34	#394×C₁₃₉	C₂²	1	8	yes	complemented
35	#393×C₁₃₉	C₂²	1	4	yes	complemented
36	#392×C₁₃₉	C₂²	1	8	yes	—
37	#392×C₁₃₉	C₂²	1	4	yes	complemented
38	#391×C₁₃₉	C₂²	1	4	yes	complemented
39	#391×C₁₃₉	C₂²	1	4	yes	complemented
40	#390×C₁₃₉	C₂²	1	8	yes	complemented
41	#388×C₁₃₉	C₂²	1	8	yes	complemented
42	#388×C₁₃₉	C₂²	1	8	yes	complemented
43	#388×C₁₃₉	C₂²	1	8	yes	complemented
44	#387×C₁₃₉	C₂²	1	8	yes	complemented
45	#386×C₁₃₉	C₂²	1	4	yes	—
46	#386×C₁₃₉	C₂²	1	8	yes	complemented
47	#385×C₁₃₉	C₂²	1	4	yes	—
48	#381×C₁₃₉	C₂²	1	2	yes	—
49	#381×C₁₃₉	C₂²	1	2	yes	—
50	#379×C₁₃₉	C₂²	1	4	yes	—
51	C₂⁵×C₁₃₉	C₂³	1	2	yes	—
52	C₂×#41×C₁₃₉	—	2	4	no	—
53	C₂×#41×C₁₃₉	—	4	4	no	—
54	C₂²×Q₈×C₁₃₉	—	4	4	no	—
55	C₂²×Q₈×C₁₃₉	D₄	1	8	yes	complemented
56	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
57	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
58	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
59	C₂²×D₄×C₁₃₉	—	2	4	no	—
60	C₂²×D₄×C₁₃₉	—	4	4	no	—
61	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
62	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
63	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₁₃₉	C₂³	1	8	yes	—
65	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
69	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
70	C₄⋊Q₈×C₁₃₉	—	2	8	no	—
71	#124×C₁₃₉	—	2	16	no	—
72	#124×C₁₃₉	—	2	16	no	—
73	#124×C₁₃₉	—	2	8	no	—
74	#123×C₁₃₉	—	2	8	no	—
75	#123×C₁₃₉	—	2	8	no	—
76	C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
77	#120×C₁₃₉	—	4	8	no	—
78	#117×C₁₃₉	—	2	4	no	—
79	#117×C₁₃₉	—	4	4	no	—
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	4	yes	—
84	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
85	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
86	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
87	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
88	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
89	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
90	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
91	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	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	8	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×C₄²×C₁₃₉	—	2	4	no	—
99	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
100	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
101	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
102	#95×C₁₃₉	C₂³	1	8	yes	—
103	#95×C₁₃₉	C₂³	1	4	yes	—
104	#95×C₁₃₉	C₂³	1	8	yes	—
105	#95×C₁₃₉	C₂³	1	8	yes	—
106	#95×C₁₃₉	C₂³	1	4	yes	—
107	C₂⁴×C₁₃₉	—	2	4	no	—
108	C₂⁴×C₁₃₉	—	2	8	no	—
109	C₂⁴×C₁₃₉	—	4	4	no	—
110	C₂⁴×C₁₃₉	—	4	4	no	—
111	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
112	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
113	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
114	#41×C₁₃₉	—	4	16	no	—
115	C₂×Q₈×C₁₃₉	—	2	2	no	—
116	C₂×Q₈×C₁₃₉	—	4	16	no	—
117	C₂×Q₈×C₁₃₉	—	4	2	no	—
118	C₂×Q₈×C₁₃₉	—	4	2	no	—
119	C₂×Q₈×C₁₃₉	—	4	2	no	—
120	C₂×Q₈×C₁₃₉	—	4	2	no	—
121	C₂×Q₈×C₁₃₉	—	4	2	no	—
122	C₂×Q₈×C₁₃₉	C₂×D₄	1	8	yes	—
123	C₂×Q₈×C₁₃₉	C₂×D₄	1	8	yes	—
124	C₂×D₄×C₁₃₉	—	2	4	no	—
125	C₂×D₄×C₁₃₉	—	2	8	no	—
126	C₂×D₄×C₁₃₉	—	2	8	no	—
127	C₂×D₄×C₁₃₉	—	2	2	no	—
128	C₂×D₄×C₁₃₉	—	4	4	no	—
129	C₂×D₄×C₁₃₉	—	4	4	no	—
130	C₂×D₄×C₁₃₉	—	4	2	no	—
131	C₂×D₄×C₁₃₉	—	4	16	no	—
132	C₂×D₄×C₁₃₉	—	4	8	no	—
133	C₂×D₄×C₁₃₉	—	4	8	no	—
134	C₂×D₄×C₁₃₉	—	4	8	no	—
135	C₂²×C₄×C₁₃₉	—	2	4	no	—
136	C₂²×C₄×C₁₃₉	—	2	4	no	—
137	C₂²×C₄×C₁₃₉	—	2	4	no	—
138	C₂²×C₄×C₁₃₉	—	2	4	no	—
139	C₂²×C₄×C₁₃₉	—	2	4	no	—
140	C₂²×C₄×C₁₃₉	—	4	4	no	—
141	C₂²×C₄×C₁₃₉	—	4	4	no	—
142	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
143	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
144	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
145	C₂²×C₄×C₁₃₉	C₂⁴	1	8	yes	—
146	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
147	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
148	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
149	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
150	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
151	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
152	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
153	C₄⋊C₄×C₁₃₉	—	2	4	no	—
154	C₄⋊C₄×C₁₃₉	—	2	8	no	—
155	C₄⋊C₄×C₁₃₉	—	2	8	no	—
156	C₄⋊C₄×C₁₃₉	—	4	8	no	—
157	C₄⋊C₄×C₁₃₉	—	4	4	no	—
158	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
159	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
160	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
161	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
162	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
163	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
164	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
165	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
166	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
167	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
168	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
169	C₄²×C₁₃₉	—	2	8	no	—
170	C₄²×C₁₃₉	—	2	4	no	—
171	C₄²×C₁₃₉	—	4	4	no	—
172	C₂³×C₁₃₉	—	2	4	no	—
173	C₂³×C₁₃₉	—	2	2	no	—
174	C₂³×C₁₃₉	—	2	4	no	—
175	C₂³×C₁₃₉	—	2	8	no	—
176	C₂³×C₁₃₉	—	2	4	no	—
177	C₂³×C₁₃₉	—	2	4	no	—
178	C₂³×C₁₃₉	—	2	8	no	—
179	C₂³×C₁₃₉	—	2	8	no	—
180	C₂³×C₁₃₉	—	2	4	no	—
181	C₂³×C₁₃₉	—	4	8	no	—
182	C₂³×C₁₃₉	—	4	8	no	—
183	C₂³×C₁₃₉	—	4	8	no	—
184	C₂³×C₁₃₉	—	8	16	no	—
185	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
186	C₂³×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
187	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
188	Q₈×C₁₃₉	—	4	8	no	—
189	Q₈×C₁₃₉	—	4	8	no	—
190	Q₈×C₁₃₉	—	4	4	no	—
191	D₄×C₁₃₉	—	4	16	no	—
192	D₄×C₁₃₉	—	4	4	no	—
193	D₄×C₁₃₉	—	4	8	no	—
194	D₄×C₁₃₉	—	8	16	no	—
195	C₂×C₄×C₁₃₉	—	2	8	no	—
196	C₂×C₄×C₁₃₉	—	2	8	no	—
197	C₂×C₄×C₁₃₉	—	2	8	no	—
198	C₂×C₄×C₁₃₉	—	2	2	no	—
199	C₂×C₄×C₁₃₉	—	2	2	no	—
200	C₂×C₄×C₁₃₉	—	2	2	no	—
201	C₂×C₄×C₁₃₉	—	2	2	no	—
202	C₂×C₄×C₁₃₉	—	2	2	no	—
203	C₂×C₄×C₁₃₉	—	2	2	no	—
204	C₂×C₄×C₁₃₉	—	2	4	no	—
205	C₂×C₄×C₁₃₉	—	2	4	no	—
206	C₂×C₄×C₁₃₉	—	2	2	no	—
207	C₂×C₄×C₁₃₉	—	2	8	no	—
208	C₂×C₄×C₁₃₉	—	2	4	no	—
209	C₂×C₄×C₁₃₉	—	2	8	no	—
210	C₂×C₄×C₁₃₉	—	2	8	no	—
211	C₂×C₄×C₁₃₉	—	2	8	no	—
212	C₂×C₄×C₁₃₉	—	2	8	no	—
213	C₂×C₄×C₁₃₉	—	4	8	no	—
214	C₂×C₄×C₁₃₉	—	4	8	no	—
215	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
216	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
217	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
218	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
219	C₂²×C₁₃₉	—	2	4	no	—
220	C₂²×C₁₃₉	—	2	8	no	—
221	C₂²×C₁₃₉	—	4	2	no	—
222	C₂²×C₁₃₉	—	4	4	no	—
223	C₂²×C₁₃₉	—	4	4	no	—
224	C₂²×C₁₃₉	—	4	4	no	—
225	C₂²×C₁₃₉	—	4	4	no	—
226	C₂²×C₁₃₉	—	4	8	no	—
227	C₂²×C₁₃₉	—	4	8	no	—
228	C₂²×C₁₃₉	—	4	8	no	—
229	C₂²×C₁₃₉	—	8	16	no	—
230	C₂²×C₁₃₉	#534	1	4	yes	—
231	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
232	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
233	C₂²×C₁₃₉	#585	1	4	yes	—
234	C₄×C₁₃₉	—	2	2	no	—
235	C₄×C₁₃₉	—	2	4	no	—
236	C₄×C₁₃₉	—	2	2	no	—
237	C₄×C₁₃₉	—	2	4	no	—
238	C₄×C₁₃₉	—	4	2	no	—
239	C₄×C₁₃₉	—	4	4	no	—
240	C₄×C₁₃₉	—	4	4	no	—
241	C₄×C₁₃₉	—	4	8	no	—
242	C₂×C₁₃₉	—	2	4	no	—
243	C₂×C₁₃₉	—	8	2	no	—
244	C₂×C₁₃₉	—	8	4	no	—
245	C₂×C₁₃₉	C₂×#534	1	1	yes	characteristic
246	C₂×C₁₃₉	#3487	1	2	yes	—
247	C₂×C₁₃₉	#3545	1	4	yes	—
248	#37187	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
249	C₁₃₉	#37187	1	1	yes	characteristic, direct product factor, Sylow
250	C₂×#536	C₂×C₁₃₉	1	1	yes	characteristic, complemented
251	C₂²×#124	C₂×C₁₃₉	1	1	yes	characteristic, complemented
252	#2853	C₂×C₁₃₉	1	2	yes	complemented
253	#2733	C₂×C₁₃₉	1	4	yes	complemented
254	#2731	C₂×C₁₃₉	1	4	yes	complemented
255	#2730	C₂×C₁₃₉	1	8	yes	complemented
256	#2613	C₂×C₁₃₉	1	2	yes	complemented
257	#2482	C₂×C₁₃₉	1	2	yes	complemented
258	#2411	C₂×C₁₃₉	1	4	yes	complemented
259	#2404	C₂×C₁₃₉	1	2	yes	complemented
260	#2310	C₂×C₁₃₉	1	1	yes	characteristic, complemented
261	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
262	C₂³×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
263	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
264	#536	—	2	8	no	—
265	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	complemented
266	C₂×#124	—	2	8	no	—
267	C₂×#124	C₂²×C₁₃₉	1	4	yes	—
268	C₂×#124	C₂²×C₁₃₉	1	4	yes	—
269	C₂×#124	C₂²×C₁₃₉	1	2	yes	complemented
270	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
271	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
272	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	complemented
273	C₂×#120	C₂²×C₁₃₉	1	4	yes	—
274	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
275	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
276	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
277	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
278	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
279	#399	C₂²×C₁₃₉	1	4	yes	complemented
280	#397	C₂²×C₁₃₉	1	4	yes	complemented
281	#396	C₂²×C₁₃₉	1	8	yes	complemented
282	#394	C₂²×C₁₃₉	1	8	yes	—
283	#394	C₂²×C₁₃₉	1	8	yes	complemented
284	#393	C₂²×C₁₃₉	1	4	yes	complemented
285	#392	C₂²×C₁₃₉	1	8	yes	—
286	#392	C₂²×C₁₃₉	1	4	yes	complemented
287	#391	C₂²×C₁₃₉	1	4	yes	complemented
288	#391	C₂²×C₁₃₉	1	4	yes	complemented
289	#390	C₂²×C₁₃₉	1	8	yes	complemented
290	#388	C₂²×C₁₃₉	1	8	yes	complemented
291	#388	C₂²×C₁₃₉	1	8	yes	complemented
292	#388	C₂²×C₁₃₉	1	8	yes	complemented
293	#387	C₂²×C₁₃₉	1	8	yes	complemented
294	#386	C₂²×C₁₃₉	1	4	yes	—
295	#386	C₂²×C₁₃₉	1	8	yes	complemented
296	#385	C₂²×C₁₃₉	1	4	yes	—
297	#381	C₂²×C₁₃₉	1	2	yes	—
298	#381	C₂²×C₁₃₉	1	2	yes	—
299	#379	C₂²×C₁₃₉	1	4	yes	—
300	C₂⁵	C₂³×C₁₃₉	1	2	yes	—
301	C₂×#41	—	2	4	no	—
302	C₂×#41	—	4	4	no	—
303	C₂²×Q₈	—	4	4	no	—
304	C₂²×Q₈	D₄×C₁₃₉	1	8	yes	complemented
305	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
306	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
307	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
308	C₂²×D₄	—	2	4	no	—
309	C₂²×D₄	—	4	4	no	—
310	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
311	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
312	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
313	C₂²×D₄	C₂³×C₁₃₉	1	8	yes	—
314	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
315	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
316	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
317	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
318	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
319	C₄⋊Q₈	—	2	8	no	—
320	#124	—	2	16	no	—
321	#124	—	2	16	no	—
322	#124	—	2	8	no	—
323	#123	—	2	8	no	—
324	#123	—	2	8	no	—
325	C₂²⋊Q₈	—	2	16	no	—
326	#120	—	4	8	no	—
327	#117	—	2	4	no	—
328	#117	—	4	4	no	—
329	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
330	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
331	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
332	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
333	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
334	C₂×C₂²⋊C₄	—	2	8	no	—
335	C₂×C₂²⋊C₄	—	2	8	no	—
336	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
337	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
338	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
339	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
340	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
341	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
342	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
343	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
344	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
345	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
346	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
347	C₂×C₄²	—	2	4	no	—
348	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
349	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
350	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
351	#95	C₂³×C₁₃₉	1	4	yes	—
352	#95	C₂³×C₁₃₉	1	8	yes	—
353	#95	C₂³×C₁₃₉	1	4	yes	—
354	#95	C₂³×C₁₃₉	1	8	yes	—
355	#95	C₂³×C₁₃₉	1	8	yes	—
356	C₂⁴	—	2	4	no	—
357	C₂⁴	—	2	8	no	—
358	C₂⁴	—	4	4	no	—
359	C₂⁴	—	4	4	no	—
360	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
361	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
362	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
363	#41	—	4	16	no	—
364	C₂×Q₈	—	2	2	no	—
365	C₂×Q₈	—	4	16	no	—
366	C₂×Q₈	—	4	2	no	—
367	C₂×Q₈	—	4	2	no	—
368	C₂×Q₈	—	4	2	no	—
369	C₂×Q₈	—	4	2	no	—
370	C₂×Q₈	—	4	2	no	—
371	C₂×Q₈	C₂×D₄×C₁₃₉	1	8	yes	—
372	C₂×Q₈	C₂×D₄×C₁₃₉	1	8	yes	—
373	C₂×D₄	—	2	4	no	—
374	C₂×D₄	—	2	8	no	—
375	C₂×D₄	—	2	8	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	4	4	no	—
378	C₂×D₄	—	4	4	no	—
379	C₂×D₄	—	4	2	no	—
380	C₂×D₄	—	4	16	no	—
381	C₂×D₄	—	4	8	no	—
382	C₂×D₄	—	4	8	no	—
383	C₂×D₄	—	4	8	no	—
384	C₂²×C₄	—	2	4	no	—
385	C₂²×C₄	—	2	4	no	—
386	C₂²×C₄	—	2	4	no	—
387	C₂²×C₄	—	2	4	no	—
388	C₂²×C₄	—	2	4	no	—
389	C₂²×C₄	—	4	4	no	—
390	C₂²×C₄	—	4	4	no	—
391	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
392	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
393	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
394	C₂²×C₄	C₂⁴×C₁₃₉	1	8	yes	—
395	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
396	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
397	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
398	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
399	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
400	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
401	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
402	C₄⋊C₄	—	2	4	no	—
403	C₄⋊C₄	—	2	8	no	—
404	C₄⋊C₄	—	2	8	no	—
405	C₄⋊C₄	—	4	8	no	—
406	C₄⋊C₄	—	4	4	no	—
407	C₂²⋊C₄	—	2	4	no	—
408	C₂²⋊C₄	—	2	8	no	—
409	C₂²⋊C₄	—	2	8	no	—
410	C₂²⋊C₄	—	2	16	no	—
411	C₂²⋊C₄	—	2	8	no	—
412	C₂²⋊C₄	—	2	8	no	—
413	C₂²⋊C₄	—	2	8	no	—
414	C₂²⋊C₄	—	4	8	no	—
415	C₂²⋊C₄	—	4	8	no	—
416	C₂²⋊C₄	—	4	8	no	—
417	C₂²⋊C₄	—	4	8	no	—
418	C₄²	—	2	8	no	—
419	C₄²	—	2	4	no	—
420	C₄²	—	4	4	no	—
421	C₂³	—	2	4	no	—
422	C₂³	—	2	2	no	—
423	C₂³	—	2	4	no	—
424	C₂³	—	2	8	no	—
425	C₂³	—	2	4	no	—
426	C₂³	—	2	4	no	—
427	C₂³	—	2	8	no	—
428	C₂³	—	2	8	no	—
429	C₂³	—	2	4	no	—
430	C₂³	—	4	8	no	—
431	C₂³	—	4	8	no	—
432	C₂³	—	4	8	no	—
433	C₂³	—	8	16	no	—
434	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
435	C₂³	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
436	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
437	Q₈	—	4	8	no	—
438	Q₈	—	4	8	no	—
439	Q₈	—	4	4	no	—
440	D₄	—	4	16	no	—
441	D₄	—	4	4	no	—
442	D₄	—	4	8	no	—
443	D₄	—	8	16	no	—
444	C₂×C₄	—	2	8	no	—
445	C₂×C₄	—	2	8	no	—
446	C₂×C₄	—	2	8	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	4	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	8	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	8	no	—
459	C₂×C₄	—	2	8	no	—
460	C₂×C₄	—	2	8	no	—
461	C₂×C₄	—	2	8	no	—
462	C₂×C₄	—	4	8	no	—
463	C₂×C₄	—	4	8	no	—
464	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
465	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
466	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
467	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
468	C₂²	—	2	8	no	—
469	C₂²	—	2	4	no	—
470	C₂²	—	4	8	no	—
471	C₂²	—	4	8	no	—
472	C₂²	—	4	8	no	—
473	C₂²	—	4	2	no	—
474	C₂²	—	4	4	no	—
475	C₂²	—	4	4	no	—
476	C₂²	—	4	4	no	—
477	C₂²	—	4	4	no	—
478	C₂²	—	8	16	no	—
479	C₂²	#534×C₁₃₉	1	4	yes	—
480	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
481	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
482	C₂²	#585×C₁₃₉	1	4	yes	—
483	C₄	—	2	2	no	—
484	C₄	—	2	4	no	—
485	C₄	—	2	2	no	—
486	C₄	—	2	4	no	—
487	C₄	—	4	8	no	—
488	C₄	—	4	2	no	—
489	C₄	—	4	4	no	—
490	C₄	—	4	4	no	—
491	C₂	—	2	4	no	—
492	C₂	—	8	4	no	—
493	C₂	—	8	2	no	—
494	C₂	C₂×#534×C₁₃₉	1	1	yes	characteristic
495	C₂	#3487×C₁₃₉	1	2	yes	—
496	C₂	#3545×C₁₃₉	1	4	yes	—

	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×#536×C₁₃₉	C₂	semidirect
2. C₂²×#124×C₁₃₉	C₂	semidirect
3. #2853×C₁₃₉	C₂	semidirect
4. #2733×C₁₃₉	C₂	semidirect
5. #2731×C₁₃₉	C₂	semidirect
6. #2730×C₁₃₉	C₂	semidirect
7. #2613×C₁₃₉	C₂	semidirect
8. #2482×C₁₃₉	C₂	semidirect
9. #2411×C₁₃₉	C₂	semidirect
10. #2404×C₁₃₉	C₂	semidirect
11. #2310×C₁₃₉	C₂	semidirect
16. C₂×C₄⋊Q₈×C₁₃₉	C₂²	semidirect
20. C₂×#124×C₁₃₉	C₂²	semidirect
23. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
30. #399×C₁₃₉	C₂²	semidirect
31. #397×C₁₃₉	C₂²	semidirect
32. #396×C₁₃₉	C₂²	semidirect
34. #394×C₁₃₉	C₂²	semidirect
35. #393×C₁₃₉	C₂²	semidirect
37. #392×C₁₃₉	C₂²	semidirect
38. #391×C₁₃₉	C₂²	semidirect
39. #391×C₁₃₉	C₂²	semidirect
40. #390×C₁₃₉	C₂²	semidirect
41. #388×C₁₃₉	C₂²	semidirect
42. #388×C₁₃₉	C₂²	semidirect
43. #388×C₁₃₉	C₂²	semidirect
44. #387×C₁₃₉	C₂²	semidirect
46. #386×C₁₃₉	C₂²	semidirect
55. C₂²×Q₈×C₁₃₉	D₄	semidirect
248. #37187	C₁₃₉	direct (N × H)
249. C₁₃₉	#37187	direct (N × H)
250. C₂×#536	C₂×C₁₃₉	semidirect
251. C₂²×#124	C₂×C₁₃₉	semidirect
252. #2853	C₂×C₁₃₉	semidirect
253. #2733	C₂×C₁₃₉	semidirect
254. #2731	C₂×C₁₃₉	semidirect
255. #2730	C₂×C₁₃₉	semidirect
256. #2613	C₂×C₁₃₉	semidirect
257. #2482	C₂×C₁₃₉	semidirect
258. #2411	C₂×C₁₃₉	semidirect
259. #2404	C₂×C₁₃₉	semidirect
260. #2310	C₂×C₁₃₉	semidirect
265. C₂×C₄⋊Q₈	C₂²×C₁₃₉	semidirect
269. C₂×#124	C₂²×C₁₃₉	semidirect
272. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
279. #399	C₂²×C₁₃₉	semidirect
280. #397	C₂²×C₁₃₉	semidirect
281. #396	C₂²×C₁₃₉	semidirect
283. #394	C₂²×C₁₃₉	semidirect
284. #393	C₂²×C₁₃₉	semidirect
286. #392	C₂²×C₁₃₉	semidirect
287. #391	C₂²×C₁₃₉	semidirect
288. #391	C₂²×C₁₃₉	semidirect
289. #390	C₂²×C₁₃₉	semidirect
290. #388	C₂²×C₁₃₉	semidirect
291. #388	C₂²×C₁₃₉	semidirect
292. #388	C₂²×C₁₃₉	semidirect
293. #387	C₂²×C₁₃₉	semidirect
295. #386	C₂²×C₁₃₉	semidirect
304. C₂²×Q₈	D₄×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#536×C₁₃₉	2
C₂²×#124×C₁₃₉	2
#2853×C₁₃₉	2
#2733×C₁₃₉	2
#2731×C₁₃₉	2
#2730×C₁₃₉	2
#2613×C₁₃₉	2
#2482×C₁₃₉	2
#2411×C₁₃₉	2
#2404×C₁₃₉	2
#2310×C₁₃₉	2
#37187	139

Subgroups — C139×#37187 #48031783

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37187 #48031783