Subgroups — C₁₃₉×#34243 #48028839

Order 35584.

2430 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#529×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	#2370×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	#2367×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2359×C₁₃₉	C₂	1	4	yes	maximal, complemented
5	#2355×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2354×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2352×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	Q₈×C₄⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	D₄×C₄⋊C₄×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	D₄×C₄⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#2334×C₁₃₉	C₂	1	4	yes	maximal, complemented
12	#2314×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	C₄×C₂²⋊Q₈×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	C₄×#121×C₁₃₉	C₂	1	2	yes	maximal
15	#2285×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	#2274×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×C₄⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	#529×C₁₃₉	C₄	1	16	yes	complemented
19	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
20	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
22	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	—
28	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
32	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
33	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
34	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
35	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
36	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
37	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
38	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
39	#391×C₁₃₉	C₂²	1	2	yes	—
40	#390×C₁₃₉	C₂²	1	2	yes	—
41	#389×C₁₃₉	C₂²	1	2	yes	—
42	#389×C₁₃₉	C₂²	1	2	yes	—
43	#389×C₁₃₉	C₂²	1	4	yes	—
44	#389×C₁₃₉	C₂²	1	4	yes	—
45	#388×C₁₃₉	C₂²	1	4	yes	—
46	#388×C₁₃₉	C₂²	1	4	yes	—
47	#388×C₁₃₉	C₂²	1	4	yes	—
48	#388×C₁₃₉	C₂²	1	4	yes	—
49	#387×C₁₃₉	C₂²	1	4	yes	—
50	#387×C₁₃₉	C₂²	1	4	yes	—
51	#387×C₁₃₉	C₂²	1	4	yes	—
52	#387×C₁₃₉	C₂²	1	4	yes	—
53	#386×C₁₃₉	C₂²	1	4	yes	—
54	#385×C₁₃₉	C₂²	1	4	yes	—
55	#385×C₁₃₉	C₂²	1	4	yes	—
56	#385×C₁₃₉	C₂²	1	4	yes	—
57	#384×C₁₃₉	C₂²	1	1	yes	characteristic
58	#384×C₁₃₉	C₂²	1	1	yes	characteristic
59	#384×C₁₃₉	C₂²	1	2	yes	—
60	#382×C₁₃₉	C₂²	1	2	yes	—
61	#382×C₁₃₉	C₂²	1	2	yes	—
62	#380×C₁₃₉	C₂²	1	2	yes	—
63	#380×C₁₃₉	C₂²	1	2	yes	—
64	#380×C₁₃₉	C₂²	1	2	yes	—
65	#380×C₁₃₉	C₂²	1	2	yes	—
66	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
67	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
68	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
69	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
70	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
71	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
72	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
73	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
74	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
75	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
76	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
77	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
78	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
79	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
80	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
81	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
82	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
83	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
84	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
86	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
88	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
89	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
93	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
94	#126×C₁₃₉	C₂×C₄	1	16	yes	complemented
95	#125×C₁₃₉	C₂×C₄	1	8	yes	complemented
96	#124×C₁₃₉	C₂×C₄	1	8	yes	complemented
97	#123×C₁₃₉	C₂×C₄	1	16	yes	complemented
98	C₂²⋊Q₈×C₁₃₉	C₂×C₄	1	8	yes	complemented
99	#121×C₁₃₉	C₂×C₄	1	8	yes	—
100	C₄×Q₈×C₁₃₉	—	4	4	no	—
101	C₄×Q₈×C₁₃₉	C₂×C₄	1	8	yes	complemented
102	C₄×D₄×C₁₃₉	—	4	4	no	—
103	C₄×D₄×C₁₃₉	—	4	8	no	—
104	C₄×D₄×C₁₃₉	C₂×C₄	1	8	yes	complemented
105	C₄×D₄×C₁₃₉	C₂×C₄	1	16	yes	complemented
106	#117×C₁₃₉	—	2	8	no	—
107	#117×C₁₃₉	—	4	4	no	—
108	#117×C₁₃₉	C₂×C₄	1	16	yes	complemented
109	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
110	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
111	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
112	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
115	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
117	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
124	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
125	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
128	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
130	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
132	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
133	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
134	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
135	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
136	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
137	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
140	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
142	C₂×C₄²×C₁₃₉	—	4	4	no	—
143	C₂×C₄²×C₁₃₉	C₂×C₄	1	8	yes	complemented
144	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
145	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
146	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
147	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
148	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
149	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
150	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
151	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
152	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
153	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
154	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
155	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
156	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
157	#95×C₁₃₉	C₂³	1	2	yes	—
158	#95×C₁₃₉	C₂³	1	2	yes	—
159	#95×C₁₃₉	C₂³	1	2	yes	—
160	#95×C₁₃₉	C₂³	1	2	yes	—
161	#95×C₁₃₉	C₂³	1	4	yes	—
162	#95×C₁₃₉	C₂³	1	4	yes	—
163	#95×C₁₃₉	C₂³	1	4	yes	—
164	#95×C₁₃₉	C₂³	1	4	yes	—
165	#95×C₁₃₉	C₂³	1	4	yes	—
166	#95×C₁₃₉	C₂³	1	4	yes	—
167	#95×C₁₃₉	C₂³	1	4	yes	—
168	#95×C₁₃₉	C₂³	1	4	yes	—
169	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
170	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
171	C₂×Q₈×C₁₃₉	—	2	2	no	—
172	C₂×Q₈×C₁₃₉	—	2	2	no	—
173	C₂×Q₈×C₁₃₉	C₂²×C₄	1	4	yes	—
174	C₂×D₄×C₁₃₉	—	2	4	no	—
175	C₂×D₄×C₁₃₉	—	2	4	no	—
176	C₂×D₄×C₁₃₉	—	2	2	no	—
177	C₂×D₄×C₁₃₉	—	2	2	no	—
178	C₂×D₄×C₁₃₉	C₂²×C₄	1	8	yes	—
179	C₂×D₄×C₁₃₉	C₂²×C₄	1	4	yes	—
180	C₂²×C₄×C₁₃₉	—	2	2	no	—
181	C₂²×C₄×C₁₃₉	—	2	2	no	—
182	C₂²×C₄×C₁₃₉	—	2	2	no	—
183	C₂²×C₄×C₁₃₉	—	2	2	no	—
184	C₂²×C₄×C₁₃₉	—	2	4	no	—
185	C₂²×C₄×C₁₃₉	—	2	4	no	—
186	C₂²×C₄×C₁₃₉	—	2	2	no	—
187	C₂²×C₄×C₁₃₉	—	2	2	no	—
188	C₂²×C₄×C₁₃₉	—	2	4	no	—
189	C₂²×C₄×C₁₃₉	—	2	4	no	—
190	C₂²×C₄×C₁₃₉	—	2	4	no	—
191	C₂²×C₄×C₁₃₉	—	2	4	no	—
192	C₂²×C₄×C₁₃₉	—	2	8	no	—
193	C₂²×C₄×C₁₃₉	—	4	2	no	—
194	C₂²×C₄×C₁₃₉	—	4	2	no	—
195	C₂²×C₄×C₁₃₉	—	4	4	no	—
196	C₂²×C₄×C₁₃₉	—	4	4	no	—
197	C₂²×C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
198	C₂²×C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
199	C₂²×C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
200	C₂²×C₄×C₁₃₉	C₂²×C₄	1	8	yes	—
201	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
202	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
203	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
204	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
205	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
206	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
207	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
208	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
209	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
211	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
212	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
215	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
216	C₄⋊C₄×C₁₃₉	—	2	4	no	—
217	C₄⋊C₄×C₁₃₉	—	2	4	no	—
218	C₄⋊C₄×C₁₃₉	—	2	8	no	—
219	C₄⋊C₄×C₁₃₉	—	2	2	no	—
220	C₄⋊C₄×C₁₃₉	—	2	2	no	—
221	C₄⋊C₄×C₁₃₉	—	2	4	no	—
222	C₄⋊C₄×C₁₃₉	—	2	4	no	—
223	C₄⋊C₄×C₁₃₉	—	2	4	no	—
224	C₄⋊C₄×C₁₃₉	—	2	4	no	—
225	C₄⋊C₄×C₁₃₉	—	4	2	no	—
226	C₄⋊C₄×C₁₃₉	—	4	2	no	—
227	C₄⋊C₄×C₁₃₉	—	4	4	no	—
228	C₄⋊C₄×C₁₃₉	—	4	4	no	—
229	C₄⋊C₄×C₁₃₉	C₂²×C₄	1	8	yes	—
230	C₄⋊C₄×C₁₃₉	C₂²×C₄	1	8	yes	—
231	C₄⋊C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
232	C₄⋊C₄×C₁₃₉	C₂²×C₄	1	8	yes	—
233	C₄⋊C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
234	C₄⋊C₄×C₁₃₉	C₂²×C₄	1	8	yes	—
235	C₄⋊C₄×C₁₃₉	#41	1	4	yes	—
236	C₄⋊C₄×C₁₃₉	#41	1	4	yes	—
237	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
238	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
239	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
240	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
241	C₂²⋊C₄×C₁₃₉	C₂²×C₄	1	8	yes	—
242	C₂²⋊C₄×C₁₃₉	C₂²×C₄	1	8	yes	—
243	C₂²⋊C₄×C₁₃₉	C₂²×C₄	1	8	yes	—
244	C₂²⋊C₄×C₁₃₉	C₂²×C₄	1	8	yes	—
245	C₂²⋊C₄×C₁₃₉	C₂²×C₄	1	8	yes	—
246	C₄²×C₁₃₉	—	2	8	no	—
247	C₄²×C₁₃₉	—	2	4	no	—
248	C₄²×C₁₃₉	—	2	4	no	—
249	C₄²×C₁₃₉	—	4	2	no	—
250	C₄²×C₁₃₉	—	4	2	no	—
251	C₄²×C₁₃₉	—	4	4	no	—
252	C₄²×C₁₃₉	—	4	4	no	—
253	C₄²×C₁₃₉	—	4	4	no	—
254	C₄²×C₁₃₉	C₂²×C₄	1	4	yes	—
255	C₄²×C₁₃₉	C₂²×C₄	1	4	yes	—
256	C₄²×C₁₃₉	C₂²×C₄	1	4	yes	—
257	C₄²×C₁₃₉	C₂²×C₄	1	4	yes	—
258	C₄²×C₁₃₉	C₂²×C₄	1	8	yes	—
259	C₂³×C₁₃₉	—	2	1	no	—
260	C₂³×C₁₃₉	—	2	1	no	—
261	C₂³×C₁₃₉	—	2	1	no	—
262	C₂³×C₁₃₉	—	2	1	no	—
263	C₂³×C₁₃₉	—	2	2	no	—
264	C₂³×C₁₃₉	—	2	2	no	—
265	C₂³×C₁₃₉	—	2	2	no	—
266	C₂³×C₁₃₉	—	2	2	no	—
267	C₂³×C₁₃₉	—	2	2	no	—
268	C₂³×C₁₃₉	—	2	2	no	—
269	C₂³×C₁₃₉	C₂³×C₄	1	4	yes	—
270	C₂³×C₁₃₉	C₂³×C₄	1	2	yes	—
271	C₂³×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
272	C₂³×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
273	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
274	Q₈×C₁₃₉	—	2	8	no	—
275	D₄×C₁₃₉	—	2	16	no	—
276	D₄×C₁₃₉	—	2	8	no	—
277	C₂×C₄×C₁₃₉	—	2	8	no	—
278	C₂×C₄×C₁₃₉	—	2	2	no	—
279	C₂×C₄×C₁₃₉	—	2	2	no	—
280	C₂×C₄×C₁₃₉	—	2	1	no	—
281	C₂×C₄×C₁₃₉	—	2	1	no	—
282	C₂×C₄×C₁₃₉	—	2	2	no	—
283	C₂×C₄×C₁₃₉	—	2	2	no	—
284	C₂×C₄×C₁₃₉	—	2	1	no	—
285	C₂×C₄×C₁₃₉	—	2	1	no	—
286	C₂×C₄×C₁₃₉	—	2	2	no	—
287	C₂×C₄×C₁₃₉	—	2	2	no	—
288	C₂×C₄×C₁₃₉	—	2	2	no	—
289	C₂×C₄×C₁₃₉	—	2	1	no	—
290	C₂×C₄×C₁₃₉	—	2	1	no	—
291	C₂×C₄×C₁₃₉	—	2	1	no	—
292	C₂×C₄×C₁₃₉	—	2	1	no	—
293	C₂×C₄×C₁₃₉	—	2	2	no	—
294	C₂×C₄×C₁₃₉	—	2	2	no	—
295	C₂×C₄×C₁₃₉	—	2	2	no	—
296	C₂×C₄×C₁₃₉	—	2	8	no	—
297	C₂×C₄×C₁₃₉	—	2	16	no	—
298	C₂×C₄×C₁₃₉	—	2	8	no	—
299	C₂×C₄×C₁₃₉	—	2	4	no	—
300	C₂×C₄×C₁₃₉	—	2	2	no	—
301	C₂×C₄×C₁₃₉	—	2	4	no	—
302	C₂×C₄×C₁₃₉	—	2	2	no	—
303	C₂×C₄×C₁₃₉	—	2	2	no	—
304	C₂×C₄×C₁₃₉	—	2	2	no	—
305	C₂×C₄×C₁₃₉	—	2	4	no	—
306	C₂×C₄×C₁₃₉	—	2	4	no	—
307	C₂×C₄×C₁₃₉	—	2	4	no	—
308	C₂×C₄×C₁₃₉	—	2	2	no	—
309	C₂×C₄×C₁₃₉	—	2	4	no	—
310	C₂×C₄×C₁₃₉	—	2	2	no	—
311	C₂×C₄×C₁₃₉	—	4	8	no	—
312	C₂×C₄×C₁₃₉	—	4	8	no	—
313	C₂×C₄×C₁₃₉	—	8	8	no	—
314	C₂×C₄×C₁₃₉	C₂³×C₄	1	2	yes	—
315	C₂×C₄×C₁₃₉	C₂³×C₄	1	2	yes	—
316	C₂×C₄×C₁₃₉	C₂³×C₄	1	2	yes	—
317	C₂×C₄×C₁₃₉	C₂³×C₄	1	2	yes	—
318	C₂×C₄×C₁₃₉	C₂³×C₄	1	4	yes	—
319	C₂×C₄×C₁₃₉	C₂³×C₄	1	4	yes	—
320	C₂×C₄×C₁₃₉	C₂³×C₄	1	4	yes	—
321	C₂×C₄×C₁₃₉	C₂³×C₄	1	2	yes	—
322	C₂×C₄×C₁₃₉	C₂³×C₄	1	2	yes	—
323	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
324	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
325	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
326	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
327	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
328	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
329	C₂²×C₁₃₉	—	2	2	no	—
330	C₂²×C₁₃₉	—	2	2	no	—
331	C₂²×C₁₃₉	—	2	2	no	—
332	C₂²×C₁₃₉	—	2	2	no	—
333	C₂²×C₁₃₉	—	2	2	no	—
334	C₂²×C₁₃₉	—	2	2	no	—
335	C₂²×C₁₃₉	—	2	4	no	—
336	C₂²×C₁₃₉	—	2	4	no	—
337	C₂²×C₁₃₉	—	2	4	no	—
338	C₂²×C₁₃₉	—	4	2	no	—
339	C₂²×C₁₃₉	—	4	2	no	—
340	C₂²×C₁₃₉	—	4	2	no	—
341	C₂²×C₁₃₉	—	4	2	no	—
342	C₂²×C₁₃₉	#520	1	4	yes	—
343	C₂²×C₁₃₉	C₂⁴×C₄	1	1	yes	characteristic
344	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
345	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
346	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
347	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
348	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
349	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
350	C₄×C₁₃₉	—	2	4	no	—
351	C₄×C₁₃₉	—	2	2	no	—
352	C₄×C₁₃₉	—	2	2	no	—
353	C₄×C₁₃₉	—	2	2	no	—
354	C₄×C₁₃₉	—	2	2	no	—
355	C₄×C₁₃₉	—	2	4	no	—
356	C₄×C₁₃₉	—	2	4	no	—
357	C₄×C₁₃₉	—	2	4	no	—
358	C₄×C₁₃₉	—	2	4	no	—
359	C₄×C₁₃₉	—	4	2	no	—
360	C₄×C₁₃₉	—	4	4	no	—
361	C₄×C₁₃₉	—	4	2	no	—
362	C₄×C₁₃₉	—	4	4	no	—
363	C₄×C₁₃₉	C₄×#41	1	4	yes	—
364	C₄×C₁₃₉	#520	1	4	yes	—
365	C₂×C₁₃₉	—	2	4	no	—
366	C₂×C₁₃₉	—	4	4	no	—
367	C₂×C₁₃₉	C₂×C₄×#41	1	1	yes	characteristic
368	C₂×C₁₃₉	C₂×#520	1	1	yes	characteristic
369	C₂×C₁₃₉	C₂×#520	1	1	yes	characteristic
370	C₂×C₁₃₉	#3519	1	1	yes	characteristic
371	C₂×C₁₃₉	#3520	1	1	yes	characteristic
372	C₂×C₁₃₉	#3522	1	1	yes	characteristic
373	C₂×C₁₃₉	#3523	1	1	yes	characteristic
374	#34243	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
375	C₁₃₉	#34243	1	1	yes	characteristic, direct product factor, Sylow
376	C₂×#529	C₂×C₁₃₉	1	1	yes	characteristic
377	#2370	C₂×C₁₃₉	1	2	yes	complemented
378	#2367	C₂×C₁₃₉	1	2	yes	complemented
379	#2359	C₂×C₁₃₉	1	4	yes	complemented
380	#2355	C₂×C₁₃₉	1	1	yes	characteristic, complemented
381	#2354	C₂×C₁₃₉	1	1	yes	characteristic, complemented
382	#2352	C₂×C₁₃₉	1	2	yes	complemented
383	Q₈×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
384	D₄×C₄⋊C₄	C₂×C₁₃₉	1	2	yes	complemented
385	D₄×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
386	#2334	C₂×C₁₃₉	1	4	yes	complemented
387	#2314	C₂×C₁₃₉	1	2	yes	complemented
388	C₄×C₂²⋊Q₈	C₂×C₁₃₉	1	2	yes	complemented
389	C₄×#121	C₂×C₁₃₉	1	2	yes	—
390	#2285	C₂×C₁₃₉	1	1	yes	characteristic, complemented
391	#2274	C₂×C₁₃₉	1	2	yes	complemented
392	C₂×C₄×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
393	#529	C₄×C₁₃₉	1	16	yes	complemented
394	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
395	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
396	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
397	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
398	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
399	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
400	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
401	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
402	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	—
403	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
404	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
405	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
406	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
407	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
408	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
409	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
410	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
411	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
412	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
413	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
414	#391	C₂²×C₁₃₉	1	2	yes	—
415	#390	C₂²×C₁₃₉	1	2	yes	—
416	#389	C₂²×C₁₃₉	1	4	yes	—
417	#389	C₂²×C₁₃₉	1	4	yes	—
418	#389	C₂²×C₁₃₉	1	2	yes	—
419	#389	C₂²×C₁₃₉	1	2	yes	—
420	#388	C₂²×C₁₃₉	1	4	yes	—
421	#388	C₂²×C₁₃₉	1	4	yes	—
422	#388	C₂²×C₁₃₉	1	4	yes	—
423	#388	C₂²×C₁₃₉	1	4	yes	—
424	#387	C₂²×C₁₃₉	1	4	yes	—
425	#387	C₂²×C₁₃₉	1	4	yes	—
426	#387	C₂²×C₁₃₉	1	4	yes	—
427	#387	C₂²×C₁₃₉	1	4	yes	—
428	#386	C₂²×C₁₃₉	1	4	yes	—
429	#385	C₂²×C₁₃₉	1	4	yes	—
430	#385	C₂²×C₁₃₉	1	4	yes	—
431	#385	C₂²×C₁₃₉	1	4	yes	—
432	#384	C₂²×C₁₃₉	1	2	yes	—
433	#384	C₂²×C₁₃₉	1	1	yes	characteristic
434	#384	C₂²×C₁₃₉	1	1	yes	characteristic
435	#382	C₂²×C₁₃₉	1	2	yes	—
436	#382	C₂²×C₁₃₉	1	2	yes	—
437	#380	C₂²×C₁₃₉	1	2	yes	—
438	#380	C₂²×C₁₃₉	1	2	yes	—
439	#380	C₂²×C₁₃₉	1	2	yes	—
440	#380	C₂²×C₁₃₉	1	2	yes	—
441	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
442	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
443	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
444	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
445	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
446	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
447	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
448	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
449	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
450	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
451	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
452	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
453	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
454	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
455	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
456	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
457	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
458	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
459	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
460	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
461	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
462	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
463	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
464	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
465	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
466	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
467	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
468	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
469	#126	C₂×C₄×C₁₃₉	1	16	yes	complemented
470	#125	C₂×C₄×C₁₃₉	1	8	yes	complemented
471	#124	C₂×C₄×C₁₃₉	1	8	yes	complemented
472	#123	C₂×C₄×C₁₃₉	1	16	yes	complemented
473	C₂²⋊Q₈	C₂×C₄×C₁₃₉	1	8	yes	complemented
474	#121	C₂×C₄×C₁₃₉	1	8	yes	—
475	C₄×Q₈	—	4	4	no	—
476	C₄×Q₈	C₂×C₄×C₁₃₉	1	8	yes	complemented
477	C₄×D₄	—	4	4	no	—
478	C₄×D₄	—	4	8	no	—
479	C₄×D₄	C₂×C₄×C₁₃₉	1	8	yes	complemented
480	C₄×D₄	C₂×C₄×C₁₃₉	1	16	yes	complemented
481	#117	—	2	8	no	—
482	#117	—	4	4	no	—
483	#117	C₂×C₄×C₁₃₉	1	16	yes	complemented
484	C₂×C₄⋊C₄	—	2	4	no	—
485	C₂×C₄⋊C₄	—	2	8	no	—
486	C₂×C₄⋊C₄	—	2	4	no	—
487	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
488	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
489	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
490	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
491	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
492	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
493	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
494	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
495	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
496	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
497	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
498	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
499	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
500	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
501	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
502	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
503	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
504	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
505	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
506	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
507	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
508	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
509	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
510	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
511	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
513	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
514	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
515	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
517	C₂×C₄²	—	4	4	no	—
518	C₂×C₄²	C₂×C₄×C₁₃₉	1	8	yes	complemented
519	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
520	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
521	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
522	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
523	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
524	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
525	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
526	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
527	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
528	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
529	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
530	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
531	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
532	#95	C₂³×C₁₃₉	1	2	yes	—
533	#95	C₂³×C₁₃₉	1	2	yes	—
534	#95	C₂³×C₁₃₉	1	2	yes	—
535	#95	C₂³×C₁₃₉	1	2	yes	—
536	#95	C₂³×C₁₃₉	1	4	yes	—
537	#95	C₂³×C₁₃₉	1	4	yes	—
538	#95	C₂³×C₁₃₉	1	4	yes	—
539	#95	C₂³×C₁₃₉	1	4	yes	—
540	#95	C₂³×C₁₃₉	1	4	yes	—
541	#95	C₂³×C₁₃₉	1	4	yes	—
542	#95	C₂³×C₁₃₉	1	4	yes	—
543	#95	C₂³×C₁₃₉	1	4	yes	—
544	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
545	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
546	C₂×Q₈	—	2	2	no	—
547	C₂×Q₈	—	2	2	no	—
548	C₂×Q₈	C₂²×C₄×C₁₃₉	1	4	yes	—
549	C₂×D₄	—	2	4	no	—
550	C₂×D₄	—	2	4	no	—
551	C₂×D₄	—	2	2	no	—
552	C₂×D₄	—	2	2	no	—
553	C₂×D₄	C₂²×C₄×C₁₃₉	1	8	yes	—
554	C₂×D₄	C₂²×C₄×C₁₃₉	1	4	yes	—
555	C₂²×C₄	—	2	2	no	—
556	C₂²×C₄	—	2	2	no	—
557	C₂²×C₄	—	2	2	no	—
558	C₂²×C₄	—	2	2	no	—
559	C₂²×C₄	—	2	4	no	—
560	C₂²×C₄	—	2	4	no	—
561	C₂²×C₄	—	2	2	no	—
562	C₂²×C₄	—	2	2	no	—
563	C₂²×C₄	—	2	4	no	—
564	C₂²×C₄	—	2	4	no	—
565	C₂²×C₄	—	2	4	no	—
566	C₂²×C₄	—	2	4	no	—
567	C₂²×C₄	—	2	8	no	—
568	C₂²×C₄	—	4	2	no	—
569	C₂²×C₄	—	4	2	no	—
570	C₂²×C₄	—	4	4	no	—
571	C₂²×C₄	—	4	4	no	—
572	C₂²×C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
573	C₂²×C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
574	C₂²×C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
575	C₂²×C₄	C₂²×C₄×C₁₃₉	1	8	yes	—
576	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
577	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
578	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
579	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
580	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
581	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
582	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
583	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
584	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
585	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
586	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
587	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
588	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
589	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
590	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
591	C₄⋊C₄	—	2	4	no	—
592	C₄⋊C₄	—	2	4	no	—
593	C₄⋊C₄	—	2	8	no	—
594	C₄⋊C₄	—	2	2	no	—
595	C₄⋊C₄	—	2	2	no	—
596	C₄⋊C₄	—	2	4	no	—
597	C₄⋊C₄	—	2	4	no	—
598	C₄⋊C₄	—	2	4	no	—
599	C₄⋊C₄	—	2	4	no	—
600	C₄⋊C₄	—	4	2	no	—
601	C₄⋊C₄	—	4	2	no	—
602	C₄⋊C₄	—	4	4	no	—
603	C₄⋊C₄	—	4	4	no	—
604	C₄⋊C₄	C₂²×C₄×C₁₃₉	1	8	yes	—
605	C₄⋊C₄	C₂²×C₄×C₁₃₉	1	8	yes	—
606	C₄⋊C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
607	C₄⋊C₄	C₂²×C₄×C₁₃₉	1	8	yes	—
608	C₄⋊C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
609	C₄⋊C₄	C₂²×C₄×C₁₃₉	1	8	yes	—
610	C₄⋊C₄	#41×C₁₃₉	1	4	yes	—
611	C₄⋊C₄	#41×C₁₃₉	1	4	yes	—
612	C₂²⋊C₄	—	2	8	no	—
613	C₂²⋊C₄	—	2	8	no	—
614	C₂²⋊C₄	—	4	4	no	—
615	C₂²⋊C₄	—	4	4	no	—
616	C₂²⋊C₄	C₂²×C₄×C₁₃₉	1	8	yes	—
617	C₂²⋊C₄	C₂²×C₄×C₁₃₉	1	8	yes	—
618	C₂²⋊C₄	C₂²×C₄×C₁₃₉	1	8	yes	—
619	C₂²⋊C₄	C₂²×C₄×C₁₃₉	1	8	yes	—
620	C₂²⋊C₄	C₂²×C₄×C₁₃₉	1	8	yes	—
621	C₄²	—	2	8	no	—
622	C₄²	—	2	4	no	—
623	C₄²	—	2	4	no	—
624	C₄²	—	4	2	no	—
625	C₄²	—	4	2	no	—
626	C₄²	—	4	4	no	—
627	C₄²	—	4	4	no	—
628	C₄²	—	4	4	no	—
629	C₄²	C₂²×C₄×C₁₃₉	1	4	yes	—
630	C₄²	C₂²×C₄×C₁₃₉	1	4	yes	—
631	C₄²	C₂²×C₄×C₁₃₉	1	4	yes	—
632	C₄²	C₂²×C₄×C₁₃₉	1	4	yes	—
633	C₄²	C₂²×C₄×C₁₃₉	1	8	yes	—
634	C₂³	—	2	1	no	—
635	C₂³	—	2	1	no	—
636	C₂³	—	2	1	no	—
637	C₂³	—	2	1	no	—
638	C₂³	—	2	2	no	—
639	C₂³	—	2	2	no	—
640	C₂³	—	2	2	no	—
641	C₂³	—	2	2	no	—
642	C₂³	—	2	2	no	—
643	C₂³	—	2	2	no	—
644	C₂³	C₂³×C₄×C₁₃₉	1	4	yes	—
645	C₂³	C₂³×C₄×C₁₃₉	1	2	yes	—
646	C₂³	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
647	C₂³	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
648	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
649	Q₈	—	2	8	no	—
650	D₄	—	2	16	no	—
651	D₄	—	2	8	no	—
652	C₂×C₄	—	2	8	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	8	no	—
672	C₂×C₄	—	2	16	no	—
673	C₂×C₄	—	2	8	no	—
674	C₂×C₄	—	2	4	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	4	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	4	no	—
681	C₂×C₄	—	2	4	no	—
682	C₂×C₄	—	2	4	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	4	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	4	8	no	—
687	C₂×C₄	—	4	8	no	—
688	C₂×C₄	—	8	8	no	—
689	C₂×C₄	C₂³×C₄×C₁₃₉	1	2	yes	—
690	C₂×C₄	C₂³×C₄×C₁₃₉	1	2	yes	—
691	C₂×C₄	C₂³×C₄×C₁₃₉	1	2	yes	—
692	C₂×C₄	C₂³×C₄×C₁₃₉	1	2	yes	—
693	C₂×C₄	C₂³×C₄×C₁₃₉	1	4	yes	—
694	C₂×C₄	C₂³×C₄×C₁₃₉	1	4	yes	—
695	C₂×C₄	C₂³×C₄×C₁₃₉	1	4	yes	—
696	C₂×C₄	C₂³×C₄×C₁₃₉	1	2	yes	—
697	C₂×C₄	C₂³×C₄×C₁₃₉	1	2	yes	—
698	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
699	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
700	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
701	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
702	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
703	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
704	C₂²	—	2	2	no	—
705	C₂²	—	2	2	no	—
706	C₂²	—	2	2	no	—
707	C₂²	—	2	2	no	—
708	C₂²	—	2	2	no	—
709	C₂²	—	2	2	no	—
710	C₂²	—	2	4	no	—
711	C₂²	—	2	4	no	—
712	C₂²	—	2	4	no	—
713	C₂²	—	4	2	no	—
714	C₂²	—	4	2	no	—
715	C₂²	—	4	2	no	—
716	C₂²	—	4	2	no	—
717	C₂²	#520×C₁₃₉	1	4	yes	—
718	C₂²	C₂⁴×C₄×C₁₃₉	1	1	yes	characteristic
719	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
720	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
721	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
722	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
723	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
724	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
725	C₄	—	2	4	no	—
726	C₄	—	2	2	no	—
727	C₄	—	2	2	no	—
728	C₄	—	2	2	no	—
729	C₄	—	2	2	no	—
730	C₄	—	2	4	no	—
731	C₄	—	2	4	no	—
732	C₄	—	2	4	no	—
733	C₄	—	2	4	no	—
734	C₄	—	4	2	no	—
735	C₄	—	4	4	no	—
736	C₄	—	4	2	no	—
737	C₄	—	4	4	no	—
738	C₄	C₄×#41×C₁₃₉	1	4	yes	—
739	C₄	#520×C₁₃₉	1	4	yes	—
740	C₂	—	2	4	no	—
741	C₂	—	4	4	no	—
742	C₂	C₂×C₄×#41×C₁₃₉	1	1	yes	characteristic
743	C₂	C₂×#520×C₁₃₉	1	1	yes	characteristic
744	C₂	C₂×#520×C₁₃₉	1	1	yes	characteristic
745	C₂	#3519×C₁₃₉	1	1	yes	characteristic
746	C₂	#3520×C₁₃₉	1	1	yes	characteristic
747	C₂	#3522×C₁₃₉	1	1	yes	characteristic
748	C₂	#3523×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃₉
Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂×#121×C₁₃₉	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2370×C₁₃₉	C₂	semidirect
3. #2367×C₁₃₉	C₂	semidirect
4. #2359×C₁₃₉	C₂	semidirect
5. #2355×C₁₃₉	C₂	semidirect
6. #2354×C₁₃₉	C₂	semidirect
7. #2352×C₁₃₉	C₂	semidirect
8. Q₈×C₄⋊C₄×C₁₃₉	C₂	semidirect
9. D₄×C₄⋊C₄×C₁₃₉	C₂	semidirect
10. D₄×C₄⋊C₄×C₁₃₉	C₂	semidirect
11. #2334×C₁₃₉	C₂	semidirect
12. #2314×C₁₃₉	C₂	semidirect
13. C₄×C₂²⋊Q₈×C₁₃₉	C₂	semidirect
15. #2285×C₁₃₉	C₂	semidirect
16. #2274×C₁₃₉	C₂	semidirect
17. C₂×C₄×C₄⋊C₄×C₁₃₉	C₂	semidirect
18. #529×C₁₃₉	C₄	semidirect
94. #126×C₁₃₉	C₂×C₄	semidirect
95. #125×C₁₃₉	C₂×C₄	semidirect
96. #124×C₁₃₉	C₂×C₄	semidirect
97. #123×C₁₃₉	C₂×C₄	semidirect
98. C₂²⋊Q₈×C₁₃₉	C₂×C₄	semidirect
101. C₄×Q₈×C₁₃₉	C₂×C₄	semidirect
104. C₄×D₄×C₁₃₉	C₂×C₄	semidirect
105. C₄×D₄×C₁₃₉	C₂×C₄	semidirect
108. #117×C₁₃₉	C₂×C₄	semidirect
143. C₂×C₄²×C₁₃₉	C₂×C₄	semidirect
374. #34243	C₁₃₉	direct (N × H)
375. C₁₃₉	#34243	direct (N × H)
377. #2370	C₂×C₁₃₉	semidirect
378. #2367	C₂×C₁₃₉	semidirect
379. #2359	C₂×C₁₃₉	semidirect
380. #2355	C₂×C₁₃₉	semidirect
381. #2354	C₂×C₁₃₉	semidirect
382. #2352	C₂×C₁₃₉	semidirect
383. Q₈×C₄⋊C₄	C₂×C₁₃₉	semidirect
384. D₄×C₄⋊C₄	C₂×C₁₃₉	semidirect
385. D₄×C₄⋊C₄	C₂×C₁₃₉	semidirect
386. #2334	C₂×C₁₃₉	semidirect
387. #2314	C₂×C₁₃₉	semidirect
388. C₄×C₂²⋊Q₈	C₂×C₁₃₉	semidirect
390. #2285	C₂×C₁₃₉	semidirect
391. #2274	C₂×C₁₃₉	semidirect
392. C₂×C₄×C₄⋊C₄	C₂×C₁₃₉	semidirect
393. #529	C₄×C₁₃₉	semidirect
469. #126	C₂×C₄×C₁₃₉	semidirect
470. #125	C₂×C₄×C₁₃₉	semidirect
471. #124	C₂×C₄×C₁₃₉	semidirect
472. #123	C₂×C₄×C₁₃₉	semidirect
473. C₂²⋊Q₈	C₂×C₄×C₁₃₉	semidirect
476. C₄×Q₈	C₂×C₄×C₁₃₉	semidirect
479. C₄×D₄	C₂×C₄×C₁₃₉	semidirect
480. C₄×D₄	C₂×C₄×C₁₃₉	semidirect
483. #117	C₂×C₄×C₁₃₉	semidirect
518. C₂×C₄²	C₂×C₄×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#529×C₁₃₉	2
#2370×C₁₃₉	2
#2367×C₁₃₉	2
#2359×C₁₃₉	2
#2355×C₁₃₉	2
#2354×C₁₃₉	2
#2352×C₁₃₉	2
Q₈×C₄⋊C₄×C₁₃₉	2
D₄×C₄⋊C₄×C₁₃₉	2
#2334×C₁₃₉	2
#2314×C₁₃₉	2
C₄×C₂²⋊Q₈×C₁₃₉	2
C₄×#121×C₁₃₉	2
#2285×C₁₃₉	2
#2274×C₁₃₉	2
C₂×C₄×C₄⋊C₄×C₁₃₉	2
#34243	139

Subgroups — C139×#34243 #48028839

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#34243 #48028839