Subgroups — C₁₃₉×#36564 #48031160

Order 35584.

1864 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2857×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	#2857×C₁₃₉	C₂	1	2	yes	maximal
3	#2586×C₁₃₉	C₂	1	4	yes	maximal, complemented
4	#2567×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2551×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2549×C₁₃₉	C₂	1	4	yes	maximal
7	#2507×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2507×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2451×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2440×C₁₃₉	C₂	1	2	yes	maximal
11	#2369×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2369×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	Q₈×C₄⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2345×C₁₃₉	C₂	1	2	yes	maximal
15	C₄×C₂²⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic
16	C₄×C₂²⋊Q₈×C₁₃₉	C₂	1	2	yes	maximal
17	C₂×C₄×C₄⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic
18	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
19	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
21	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
22	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
23	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
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	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
30	#398×C₁₃₉	C₂²	1	4	yes	—
31	#398×C₁₃₉	C₂²	1	4	yes	—
32	#398×C₁₃₉	C₂²	1	4	yes	—
33	#395×C₁₃₉	C₂²	1	4	yes	—
34	#395×C₁₃₉	C₂²	1	4	yes	—
35	#395×C₁₃₉	C₂²	1	4	yes	—
36	#391×C₁₃₉	C₂²	1	4	yes	—
37	#391×C₁₃₉	C₂²	1	4	yes	—
38	#391×C₁₃₉	C₂²	1	2	yes	—
39	#391×C₁₃₉	C₂²	1	1	yes	characteristic
40	#391×C₁₃₉	C₂²	1	2	yes	—
41	#391×C₁₃₉	C₂²	1	4	yes	—
42	#389×C₁₃₉	C₂²	1	4	yes	—
43	#389×C₁₃₉	C₂²	1	4	yes	—
44	#389×C₁₃₉	C₂²	1	2	yes	—
45	#389×C₁₃₉	C₂²	1	2	yes	—
46	#389×C₁₃₉	C₂²	1	1	yes	characteristic
47	#389×C₁₃₉	C₂²	1	2	yes	—
48	#389×C₁₃₉	C₂²	1	2	yes	—
49	#389×C₁₃₉	C₂²	1	4	yes	—
50	#389×C₁₃₉	C₂²	1	2	yes	—
51	#389×C₁₃₉	C₂²	1	2	yes	—
52	#389×C₁₃₉	C₂²	1	2	yes	—
53	#389×C₁₃₉	C₂²	1	2	yes	—
54	#389×C₁₃₉	C₂²	1	2	yes	—
55	#387×C₁₃₉	C₂²	1	2	yes	—
56	#387×C₁₃₉	C₂²	1	4	yes	—
57	#387×C₁₃₉	C₂²	1	4	yes	—
58	#387×C₁₃₉	C₂²	1	4	yes	—
59	#385×C₁₃₉	C₂²	1	2	yes	—
60	#385×C₁₃₉	C₂²	1	4	yes	—
61	#384×C₁₃₉	C₂²	1	1	yes	characteristic
62	#384×C₁₃₉	C₂²	1	2	yes	—
63	#384×C₁₃₉	C₂²	1	2	yes	—
64	#380×C₁₃₉	C₂²	1	4	yes	—
65	#380×C₁₃₉	C₂²	1	2	yes	—
66	#380×C₁₃₉	C₂²	1	1	yes	characteristic
67	#380×C₁₃₉	C₂²	1	2	yes	—
68	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
69	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
70	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
71	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
72	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
73	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
74	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
75	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
76	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	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	2	yes	—
82	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
83	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
84	C₂²×Q₈×C₁₃₉	C₂³	1	4	yes	—
85	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
86	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
87	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
91	C₄⋊Q₈×C₁₃₉	—	2	8	no	—
92	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
93	C₄⋊Q₈×C₁₃₉	—	4	4	no	—
94	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
95	C₂²⋊Q₈×C₁₃₉	—	4	8	no	—
96	C₂²⋊Q₈×C₁₃₉	Q₈	1	8	yes	complemented
97	C₄×Q₈×C₁₃₉	—	2	4	no	—
98	C₄×Q₈×C₁₃₉	—	4	4	no	—
99	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
100	C₂×C₄⋊C₄×C₁₃₉	Q₈	1	8	yes	complemented
101	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
102	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
103	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
104	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
106	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
109	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
110	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
112	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
113	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
114	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
115	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
116	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
117	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
118	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
119	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
123	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
126	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
127	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
128	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
129	C₂×C₄²×C₁₃₉	—	2	4	no	—
130	C₂×C₄²×C₁₃₉	—	4	4	no	—
131	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
132	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
133	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
134	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
135	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
136	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
137	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
138	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
139	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
140	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
141	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
142	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
143	#95×C₁₃₉	C₂³	1	2	yes	—
144	#95×C₁₃₉	C₂³	1	2	yes	—
145	#95×C₁₃₉	C₂³	1	2	yes	—
146	#95×C₁₃₉	C₂³	1	4	yes	—
147	#95×C₁₃₉	C₂³	1	4	yes	—
148	#95×C₁₃₉	C₂³	1	4	yes	—
149	#95×C₁₃₉	C₂³	1	4	yes	—
150	#95×C₁₃₉	C₂³	1	2	yes	—
151	#95×C₁₃₉	C₂³	1	2	yes	—
152	#95×C₁₃₉	C₂³	1	4	yes	—
153	#95×C₁₃₉	C₂³	1	2	yes	—
154	#95×C₁₃₉	C₂³	1	2	yes	—
155	#95×C₁₃₉	C₂³	1	2	yes	—
156	#95×C₁₃₉	C₂³	1	4	yes	—
157	#95×C₁₃₉	C₂³	1	4	yes	—
158	#95×C₁₃₉	C₂³	1	2	yes	—
159	#95×C₁₃₉	C₂³	1	4	yes	—
160	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
161	C₂×Q₈×C₁₃₉	—	2	2	no	—
162	C₂×Q₈×C₁₃₉	—	2	8	no	—
163	C₂×Q₈×C₁₃₉	—	2	4	no	—
164	C₂×Q₈×C₁₃₉	—	2	2	no	—
165	C₂×Q₈×C₁₃₉	—	4	2	no	—
166	C₂×Q₈×C₁₃₉	—	4	4	no	—
167	C₂×Q₈×C₁₃₉	—	4	4	no	—
168	C₂×Q₈×C₁₃₉	—	4	2	no	—
169	C₂×Q₈×C₁₃₉	C₂×Q₈	1	4	yes	—
170	C₂²×C₄×C₁₃₉	—	2	2	no	—
171	C₂²×C₄×C₁₃₉	—	2	2	no	—
172	C₂²×C₄×C₁₃₉	—	2	2	no	—
173	C₂²×C₄×C₁₃₉	—	2	2	no	—
174	C₂²×C₄×C₁₃₉	—	2	4	no	—
175	C₂²×C₄×C₁₃₉	—	2	2	no	—
176	C₂²×C₄×C₁₃₉	—	2	2	no	—
177	C₂²×C₄×C₁₃₉	—	2	4	no	—
178	C₂²×C₄×C₁₃₉	—	4	2	no	—
179	C₂²×C₄×C₁₃₉	—	4	2	no	—
180	C₂²×C₄×C₁₃₉	—	4	2	no	—
181	C₂²×C₄×C₁₃₉	—	4	1	no	—
182	C₂²×C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
183	C₂²×C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
184	C₂²×C₄×C₁₃₉	C₂×Q₈	1	8	yes	—
185	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
186	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
187	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
188	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
189	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
190	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
191	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
192	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
193	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
194	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
195	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
196	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
197	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
198	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
199	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
200	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
201	C₄⋊C₄×C₁₃₉	—	2	4	no	—
202	C₄⋊C₄×C₁₃₉	—	2	2	no	—
203	C₄⋊C₄×C₁₃₉	—	2	4	no	—
204	C₄⋊C₄×C₁₃₉	—	2	2	no	—
205	C₄⋊C₄×C₁₃₉	—	2	8	no	—
206	C₄⋊C₄×C₁₃₉	—	2	4	no	—
207	C₄⋊C₄×C₁₃₉	—	2	4	no	—
208	C₄⋊C₄×C₁₃₉	—	2	4	no	—
209	C₄⋊C₄×C₁₃₉	—	2	4	no	—
210	C₄⋊C₄×C₁₃₉	—	2	2	no	—
211	C₄⋊C₄×C₁₃₉	—	4	2	no	—
212	C₄⋊C₄×C₁₃₉	—	4	4	no	—
213	C₄⋊C₄×C₁₃₉	—	4	4	no	—
214	C₄⋊C₄×C₁₃₉	—	4	4	no	—
215	C₄⋊C₄×C₁₃₉	—	4	2	no	—
216	C₄⋊C₄×C₁₃₉	—	4	4	no	—
217	C₄⋊C₄×C₁₃₉	—	4	4	no	—
218	C₄⋊C₄×C₁₃₉	—	4	4	no	—
219	C₄⋊C₄×C₁₃₉	—	4	4	no	—
220	C₄⋊C₄×C₁₃₉	C₂×Q₈	1	8	yes	—
221	C₄⋊C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
222	C₄⋊C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
223	C₄⋊C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
224	C₄⋊C₄×C₁₃₉	C₂×Q₈	1	8	yes	—
225	C₄⋊C₄×C₁₃₉	#41	1	4	yes	—
226	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
227	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
228	C₂²⋊C₄×C₁₃₉	C₂×Q₈	1	8	yes	—
229	C₄²×C₁₃₉	—	2	2	no	—
230	C₄²×C₁₃₉	—	2	2	no	—
231	C₄²×C₁₃₉	—	2	2	no	—
232	C₄²×C₁₃₉	—	2	4	no	—
233	C₄²×C₁₃₉	—	2	4	no	—
234	C₄²×C₁₃₉	—	2	4	no	—
235	C₄²×C₁₃₉	—	2	4	no	—
236	C₄²×C₁₃₉	—	4	2	no	—
237	C₄²×C₁₃₉	—	4	2	no	—
238	C₄²×C₁₃₉	—	4	4	no	—
239	C₄²×C₁₃₉	—	4	4	no	—
240	C₄²×C₁₃₉	#41	1	4	yes	—
241	C₂³×C₁₃₉	—	2	1	no	—
242	C₂³×C₁₃₉	—	2	1	no	—
243	C₂³×C₁₃₉	—	2	1	no	—
244	C₂³×C₁₃₉	—	2	1	no	—
245	C₂³×C₁₃₉	C₂²×Q₈	1	2	yes	—
246	C₂³×C₁₃₉	C₂²×Q₈	1	2	yes	—
247	C₂³×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
248	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
249	Q₈×C₁₃₉	—	2	8	no	—
250	Q₈×C₁₃₉	—	8	4	no	—
251	Q₈×C₁₃₉	—	8	8	no	—
252	C₂×C₄×C₁₃₉	—	2	1	no	—
253	C₂×C₄×C₁₃₉	—	2	1	no	—
254	C₂×C₄×C₁₃₉	—	2	2	no	—
255	C₂×C₄×C₁₃₉	—	2	2	no	—
256	C₂×C₄×C₁₃₉	—	2	1	no	—
257	C₂×C₄×C₁₃₉	—	2	2	no	—
258	C₂×C₄×C₁₃₉	—	2	2	no	—
259	C₂×C₄×C₁₃₉	—	2	2	no	—
260	C₂×C₄×C₁₃₉	—	2	1	no	—
261	C₂×C₄×C₁₃₉	—	2	2	no	—
262	C₂×C₄×C₁₃₉	—	2	1	no	—
263	C₂×C₄×C₁₃₉	—	2	2	no	—
264	C₂×C₄×C₁₃₉	—	2	2	no	—
265	C₂×C₄×C₁₃₉	—	2	2	no	—
266	C₂×C₄×C₁₃₉	—	2	2	no	—
267	C₂×C₄×C₁₃₉	—	2	1	no	—
268	C₂×C₄×C₁₃₉	—	2	8	no	—
269	C₂×C₄×C₁₃₉	—	2	8	no	—
270	C₂×C₄×C₁₃₉	—	2	1	no	—
271	C₂×C₄×C₁₃₉	—	2	2	no	—
272	C₂×C₄×C₁₃₉	—	2	2	no	—
273	C₂×C₄×C₁₃₉	—	2	2	no	—
274	C₂×C₄×C₁₃₉	—	2	4	no	—
275	C₂×C₄×C₁₃₉	—	2	4	no	—
276	C₂×C₄×C₁₃₉	—	2	2	no	—
277	C₂×C₄×C₁₃₉	—	2	4	no	—
278	C₂×C₄×C₁₃₉	—	2	2	no	—
279	C₂×C₄×C₁₃₉	—	2	4	no	—
280	C₂×C₄×C₁₃₉	—	2	4	no	—
281	C₂×C₄×C₁₃₉	—	2	2	no	—
282	C₂×C₄×C₁₃₉	—	2	2	no	—
283	C₂×C₄×C₁₃₉	—	2	1	no	—
284	C₂×C₄×C₁₃₉	—	2	2	no	—
285	C₂×C₄×C₁₃₉	—	2	4	no	—
286	C₂×C₄×C₁₃₉	—	2	2	no	—
287	C₂×C₄×C₁₃₉	—	2	1	no	—
288	C₂×C₄×C₁₃₉	—	4	8	no	—
289	C₂×C₄×C₁₃₉	—	4	4	no	—
290	C₂×C₄×C₁₃₉	—	4	8	no	—
291	C₂×C₄×C₁₃₉	C₂²×Q₈	1	4	yes	—
292	C₂×C₄×C₁₃₉	C₂²×Q₈	1	4	yes	—
293	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
294	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
295	C₂×C₄×C₁₃₉	C₂²×Q₈	1	4	yes	—
296	C₂×C₄×C₁₃₉	C₂²×Q₈	1	4	yes	—
297	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
298	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
299	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
300	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
301	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
302	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
303	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
304	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
305	C₂²×C₁₃₉	—	2	2	no	—
306	C₂²×C₁₃₉	—	2	2	no	—
307	C₂²×C₁₃₉	—	2	2	no	—
308	C₂²×C₁₃₉	—	2	2	no	—
309	C₂²×C₁₃₉	—	2	2	no	—
310	C₂²×C₁₃₉	—	2	2	no	—
311	C₂²×C₁₃₉	Q₈²	1	4	yes	—
312	C₂²×C₁₃₉	C₂³×Q₈	1	1	yes	characteristic
313	C₂²×C₁₃₉	C₂³×Q₈	1	1	yes	characteristic
314	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
315	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
316	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
317	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
318	C₂²×C₁₃₉	#585	1	1	yes	characteristic
319	C₄×C₁₃₉	—	2	2	no	—
320	C₄×C₁₃₉	—	2	2	no	—
321	C₄×C₁₃₉	—	2	4	no	—
322	C₄×C₁₃₉	—	2	4	no	—
323	C₄×C₁₃₉	—	2	2	no	—
324	C₄×C₁₃₉	—	2	4	no	—
325	C₄×C₁₃₉	—	2	4	no	—
326	C₄×C₁₃₉	—	2	4	no	—
327	C₄×C₁₃₉	—	4	2	no	—
328	C₄×C₁₃₉	—	4	1	no	—
329	C₄×C₁₃₉	—	4	4	no	—
330	C₄×C₁₃₉	—	4	2	no	—
331	C₄×C₁₃₉	—	4	4	no	—
332	C₄×C₁₃₉	—	4	2	no	—
333	C₄×C₁₃₉	#533	1	4	yes	—
334	C₄×C₁₃₉	#554	1	4	yes	—
335	C₂×C₁₃₉	—	2	4	no	—
336	C₂×C₁₃₉	C₂×#533	1	1	yes	characteristic
337	C₂×C₁₃₉	C₂×#554	1	1	yes	characteristic
338	C₂×C₁₃₉	C₂×Q₈²	1	1	yes	characteristic
339	C₂×C₁₃₉	Q₈×#41	1	1	yes	characteristic
340	C₂×C₁₃₉	#3494	1	1	yes	characteristic
341	C₂×C₁₃₉	#3501	1	1	yes	characteristic
342	C₂×C₁₃₉	#3519	1	1	yes	characteristic
343	#36564	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
344	C₁₃₉	#36564	1	1	yes	characteristic, direct product factor, Sylow
345	#2857	C₂×C₁₃₉	1	2	yes	—
346	#2857	C₂×C₁₃₉	1	1	yes	characteristic
347	#2586	C₂×C₁₃₉	1	4	yes	complemented
348	#2567	C₂×C₁₃₉	1	1	yes	characteristic, complemented
349	#2551	C₂×C₁₃₉	1	1	yes	characteristic, complemented
350	#2549	C₂×C₁₃₉	1	4	yes	—
351	#2507	C₂×C₁₃₉	1	2	yes	complemented
352	#2507	C₂×C₁₃₉	1	2	yes	complemented
353	#2451	C₂×C₁₃₉	1	2	yes	complemented
354	#2440	C₂×C₁₃₉	1	2	yes	—
355	#2369	C₂×C₁₃₉	1	1	yes	characteristic, complemented
356	#2369	C₂×C₁₃₉	1	2	yes	complemented
357	Q₈×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
358	#2345	C₂×C₁₃₉	1	2	yes	—
359	C₄×C₂²⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic
360	C₄×C₂²⋊Q₈	C₂×C₁₃₉	1	2	yes	—
361	C₂×C₄×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic
362	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
363	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
364	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
365	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
366	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
367	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
368	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
369	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
370	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
371	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
372	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
373	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
374	#398	C₂²×C₁₃₉	1	4	yes	—
375	#398	C₂²×C₁₃₉	1	4	yes	—
376	#398	C₂²×C₁₃₉	1	4	yes	—
377	#395	C₂²×C₁₃₉	1	4	yes	—
378	#395	C₂²×C₁₃₉	1	4	yes	—
379	#395	C₂²×C₁₃₉	1	4	yes	—
380	#391	C₂²×C₁₃₉	1	2	yes	—
381	#391	C₂²×C₁₃₉	1	2	yes	—
382	#391	C₂²×C₁₃₉	1	4	yes	—
383	#391	C₂²×C₁₃₉	1	4	yes	—
384	#391	C₂²×C₁₃₉	1	4	yes	—
385	#391	C₂²×C₁₃₉	1	1	yes	characteristic
386	#389	C₂²×C₁₃₉	1	2	yes	—
387	#389	C₂²×C₁₃₉	1	2	yes	—
388	#389	C₂²×C₁₃₉	1	4	yes	—
389	#389	C₂²×C₁₃₉	1	4	yes	—
390	#389	C₂²×C₁₃₉	1	2	yes	—
391	#389	C₂²×C₁₃₉	1	2	yes	—
392	#389	C₂²×C₁₃₉	1	2	yes	—
393	#389	C₂²×C₁₃₉	1	2	yes	—
394	#389	C₂²×C₁₃₉	1	2	yes	—
395	#389	C₂²×C₁₃₉	1	2	yes	—
396	#389	C₂²×C₁₃₉	1	4	yes	—
397	#389	C₂²×C₁₃₉	1	1	yes	characteristic
398	#389	C₂²×C₁₃₉	1	2	yes	—
399	#387	C₂²×C₁₃₉	1	2	yes	—
400	#387	C₂²×C₁₃₉	1	4	yes	—
401	#387	C₂²×C₁₃₉	1	4	yes	—
402	#387	C₂²×C₁₃₉	1	4	yes	—
403	#385	C₂²×C₁₃₉	1	4	yes	—
404	#385	C₂²×C₁₃₉	1	2	yes	—
405	#384	C₂²×C₁₃₉	1	2	yes	—
406	#384	C₂²×C₁₃₉	1	1	yes	characteristic
407	#384	C₂²×C₁₃₉	1	2	yes	—
408	#380	C₂²×C₁₃₉	1	2	yes	—
409	#380	C₂²×C₁₃₉	1	4	yes	—
410	#380	C₂²×C₁₃₉	1	2	yes	—
411	#380	C₂²×C₁₃₉	1	1	yes	characteristic
412	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
413	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
414	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
415	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
416	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
417	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
418	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
419	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
420	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
421	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
422	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
423	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
424	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
425	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
426	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
427	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
428	C₂²×Q₈	C₂³×C₁₃₉	1	4	yes	—
429	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
430	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
431	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
432	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
433	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
434	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
435	C₄⋊Q₈	—	2	8	no	—
436	C₄⋊Q₈	—	2	4	no	—
437	C₄⋊Q₈	—	4	4	no	—
438	C₂²⋊Q₈	—	4	8	no	—
439	C₂²⋊Q₈	—	4	4	no	—
440	C₂²⋊Q₈	Q₈×C₁₃₉	1	8	yes	complemented
441	C₄×Q₈	—	2	4	no	—
442	C₄×Q₈	—	4	4	no	—
443	C₂×C₄⋊C₄	—	2	4	no	—
444	C₂×C₄⋊C₄	Q₈×C₁₃₉	1	8	yes	complemented
445	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
446	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
447	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
448	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
449	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
450	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
451	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
452	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
453	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
454	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
455	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
456	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
457	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
458	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
459	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
460	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
461	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
462	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
463	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
464	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
465	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
466	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
467	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
468	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
469	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
470	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
471	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
472	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
473	C₂×C₄²	—	2	4	no	—
474	C₂×C₄²	—	4	4	no	—
475	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
476	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
477	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
478	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
479	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
480	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
481	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
482	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
483	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
484	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
485	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
486	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
487	#95	C₂³×C₁₃₉	1	2	yes	—
488	#95	C₂³×C₁₃₉	1	2	yes	—
489	#95	C₂³×C₁₃₉	1	2	yes	—
490	#95	C₂³×C₁₃₉	1	2	yes	—
491	#95	C₂³×C₁₃₉	1	2	yes	—
492	#95	C₂³×C₁₃₉	1	2	yes	—
493	#95	C₂³×C₁₃₉	1	4	yes	—
494	#95	C₂³×C₁₃₉	1	4	yes	—
495	#95	C₂³×C₁₃₉	1	4	yes	—
496	#95	C₂³×C₁₃₉	1	4	yes	—
497	#95	C₂³×C₁₃₉	1	2	yes	—
498	#95	C₂³×C₁₃₉	1	4	yes	—
499	#95	C₂³×C₁₃₉	1	4	yes	—
500	#95	C₂³×C₁₃₉	1	2	yes	—
501	#95	C₂³×C₁₃₉	1	4	yes	—
502	#95	C₂³×C₁₃₉	1	2	yes	—
503	#95	C₂³×C₁₃₉	1	4	yes	—
504	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
505	C₂×Q₈	—	2	2	no	—
506	C₂×Q₈	—	2	8	no	—
507	C₂×Q₈	—	2	4	no	—
508	C₂×Q₈	—	2	2	no	—
509	C₂×Q₈	—	4	2	no	—
510	C₂×Q₈	—	4	4	no	—
511	C₂×Q₈	—	4	4	no	—
512	C₂×Q₈	—	4	2	no	—
513	C₂×Q₈	C₂×Q₈×C₁₃₉	1	4	yes	—
514	C₂²×C₄	—	2	2	no	—
515	C₂²×C₄	—	2	2	no	—
516	C₂²×C₄	—	2	2	no	—
517	C₂²×C₄	—	2	2	no	—
518	C₂²×C₄	—	2	4	no	—
519	C₂²×C₄	—	2	2	no	—
520	C₂²×C₄	—	2	2	no	—
521	C₂²×C₄	—	2	4	no	—
522	C₂²×C₄	—	4	2	no	—
523	C₂²×C₄	—	4	2	no	—
524	C₂²×C₄	—	4	2	no	—
525	C₂²×C₄	—	4	1	no	—
526	C₂²×C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
527	C₂²×C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
528	C₂²×C₄	C₂×Q₈×C₁₃₉	1	8	yes	—
529	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
530	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
531	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
532	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
533	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
534	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
535	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
536	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
537	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
538	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
539	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
540	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
541	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
542	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
543	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
544	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
545	C₄⋊C₄	—	2	4	no	—
546	C₄⋊C₄	—	2	2	no	—
547	C₄⋊C₄	—	2	4	no	—
548	C₄⋊C₄	—	2	2	no	—
549	C₄⋊C₄	—	2	8	no	—
550	C₄⋊C₄	—	2	4	no	—
551	C₄⋊C₄	—	2	4	no	—
552	C₄⋊C₄	—	2	4	no	—
553	C₄⋊C₄	—	2	4	no	—
554	C₄⋊C₄	—	2	2	no	—
555	C₄⋊C₄	—	4	2	no	—
556	C₄⋊C₄	—	4	4	no	—
557	C₄⋊C₄	—	4	4	no	—
558	C₄⋊C₄	—	4	4	no	—
559	C₄⋊C₄	—	4	2	no	—
560	C₄⋊C₄	—	4	4	no	—
561	C₄⋊C₄	—	4	4	no	—
562	C₄⋊C₄	—	4	4	no	—
563	C₄⋊C₄	—	4	4	no	—
564	C₄⋊C₄	C₂×Q₈×C₁₃₉	1	8	yes	—
565	C₄⋊C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
566	C₄⋊C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
567	C₄⋊C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
568	C₄⋊C₄	C₂×Q₈×C₁₃₉	1	8	yes	—
569	C₄⋊C₄	#41×C₁₃₉	1	4	yes	—
570	C₂²⋊C₄	—	2	4	no	—
571	C₂²⋊C₄	—	2	8	no	—
572	C₂²⋊C₄	C₂×Q₈×C₁₃₉	1	8	yes	—
573	C₄²	—	2	2	no	—
574	C₄²	—	2	2	no	—
575	C₄²	—	2	2	no	—
576	C₄²	—	2	4	no	—
577	C₄²	—	2	4	no	—
578	C₄²	—	2	4	no	—
579	C₄²	—	2	4	no	—
580	C₄²	—	4	2	no	—
581	C₄²	—	4	2	no	—
582	C₄²	—	4	4	no	—
583	C₄²	—	4	4	no	—
584	C₄²	#41×C₁₃₉	1	4	yes	—
585	C₂³	—	2	1	no	—
586	C₂³	—	2	1	no	—
587	C₂³	—	2	1	no	—
588	C₂³	—	2	1	no	—
589	C₂³	C₂²×Q₈×C₁₃₉	1	2	yes	—
590	C₂³	C₂²×Q₈×C₁₃₉	1	2	yes	—
591	C₂³	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
592	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
593	Q₈	—	2	8	no	—
594	Q₈	—	8	4	no	—
595	Q₈	—	8	8	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	8	no	—
613	C₂×C₄	—	2	8	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	4	no	—
619	C₂×C₄	—	2	4	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	4	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	4	no	—
624	C₂×C₄	—	2	4	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	4	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	4	8	no	—
633	C₂×C₄	—	4	4	no	—
634	C₂×C₄	—	4	8	no	—
635	C₂×C₄	C₂²×Q₈×C₁₃₉	1	4	yes	—
636	C₂×C₄	C₂²×Q₈×C₁₃₉	1	4	yes	—
637	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
638	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
639	C₂×C₄	C₂²×Q₈×C₁₃₉	1	4	yes	—
640	C₂×C₄	C₂²×Q₈×C₁₃₉	1	4	yes	—
641	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
642	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
643	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
644	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
645	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
646	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
647	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
648	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
649	C₂²	—	2	2	no	—
650	C₂²	—	2	2	no	—
651	C₂²	—	2	2	no	—
652	C₂²	—	2	2	no	—
653	C₂²	—	2	2	no	—
654	C₂²	—	2	2	no	—
655	C₂²	Q₈²×C₁₃₉	1	4	yes	—
656	C₂²	C₂³×Q₈×C₁₃₉	1	1	yes	characteristic
657	C₂²	C₂³×Q₈×C₁₃₉	1	1	yes	characteristic
658	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
659	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
660	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
661	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
662	C₂²	#585×C₁₃₉	1	1	yes	characteristic
663	C₄	—	2	2	no	—
664	C₄	—	2	2	no	—
665	C₄	—	2	4	no	—
666	C₄	—	2	4	no	—
667	C₄	—	2	2	no	—
668	C₄	—	2	4	no	—
669	C₄	—	2	4	no	—
670	C₄	—	2	4	no	—
671	C₄	—	4	1	no	—
672	C₄	—	4	4	no	—
673	C₄	—	4	2	no	—
674	C₄	—	4	2	no	—
675	C₄	—	4	2	no	—
676	C₄	—	4	4	no	—
677	C₄	#533×C₁₃₉	1	4	yes	—
678	C₄	#554×C₁₃₉	1	4	yes	—
679	C₂	—	2	4	no	—
680	C₂	C₂×#533×C₁₃₉	1	1	yes	characteristic
681	C₂	C₂×#554×C₁₃₉	1	1	yes	characteristic
682	C₂	C₂×Q₈²×C₁₃₉	1	1	yes	characteristic
683	C₂	Q₈×#41×C₁₃₉	1	1	yes	characteristic
684	C₂	#3494×C₁₃₉	1	1	yes	characteristic
685	C₂	#3501×C₁₃₉	1	1	yes	characteristic
686	C₂	#3519×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂⁴×C₁₃₉	C₂⁴
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
3. #2586×C₁₃₉	C₂	semidirect
4. #2567×C₁₃₉	C₂	semidirect
5. #2551×C₁₃₉	C₂	semidirect
7. #2507×C₁₃₉	C₂	semidirect
8. #2507×C₁₃₉	C₂	semidirect
9. #2451×C₁₃₉	C₂	semidirect
11. #2369×C₁₃₉	C₂	semidirect
12. #2369×C₁₃₉	C₂	semidirect
13. Q₈×C₄⋊C₄×C₁₃₉	C₂	semidirect
96. C₂²⋊Q₈×C₁₃₉	Q₈	semidirect
100. C₂×C₄⋊C₄×C₁₃₉	Q₈	semidirect
343. #36564	C₁₃₉	direct (N × H)
344. C₁₃₉	#36564	direct (N × H)
347. #2586	C₂×C₁₃₉	semidirect
348. #2567	C₂×C₁₃₉	semidirect
349. #2551	C₂×C₁₃₉	semidirect
351. #2507	C₂×C₁₃₉	semidirect
352. #2507	C₂×C₁₃₉	semidirect
353. #2451	C₂×C₁₃₉	semidirect
355. #2369	C₂×C₁₃₉	semidirect
356. #2369	C₂×C₁₃₉	semidirect
357. Q₈×C₄⋊C₄	C₂×C₁₃₉	semidirect
440. C₂²⋊Q₈	Q₈×C₁₃₉	semidirect
444. C₂×C₄⋊C₄	Q₈×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2857×C₁₃₉	2
#2586×C₁₃₉	2
#2567×C₁₃₉	2
#2551×C₁₃₉	2
#2549×C₁₃₉	2
#2507×C₁₃₉	2
#2451×C₁₃₉	2
#2440×C₁₃₉	2
#2369×C₁₃₉	2
Q₈×C₄⋊C₄×C₁₃₉	2
#2345×C₁₃₉	2
C₄×C₂²⋊Q₈×C₁₃₉	2
C₂×C₄×C₄⋊C₄×C₁₃₉	2
#36564	139

Subgroups — C139×#36564 #48031160

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36564 #48031160