Subgroups — C₁₃₉×#36133 #48030729

Order 35584.

2208 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#533×C₁₃₉	C₂	1	2	yes	maximal
2	#2857×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2855×C₁₃₉	C₂	1	2	yes	maximal
4	#2551×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2546×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2506×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2462×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	#2451×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2446×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2440×C₁₃₉	C₂	1	2	yes	maximal
11	#2438×C₁₃₉	C₂	1	4	yes	maximal
12	#2365×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#2365×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	Q₈×C₄⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#2344×C₁₃₉	C₂	1	2	yes	maximal
16	C₄×C₂²⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic
17	C₂×C₄×C₄⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic
18	#533×C₁₃₉	—	2	16	no	—
19	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
21	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
22	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#125×C₁₃₉	C₂²	1	4	yes	—
24	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
25	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
26	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
29	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
30	C₂×C₄×Q₈×C₁₃₉	C₂²	1	4	yes	—
31	C₂×#117×C₁₃₉	C₂²	1	4	yes	—
32	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
34	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
36	#400×C₁₃₉	C₂²	1	4	yes	—
37	#398×C₁₃₉	C₂²	1	4	yes	—
38	#398×C₁₃₉	C₂²	1	4	yes	—
39	#398×C₁₃₉	C₂²	1	4	yes	—
40	#395×C₁₃₉	C₂²	1	4	yes	—
41	#395×C₁₃₉	C₂²	1	4	yes	—
42	#391×C₁₃₉	C₂²	1	2	yes	—
43	#391×C₁₃₉	C₂²	1	1	yes	characteristic
44	#391×C₁₃₉	C₂²	1	2	yes	—
45	#391×C₁₃₉	C₂²	1	2	yes	—
46	#391×C₁₃₉	C₂²	1	4	yes	—
47	#389×C₁₃₉	C₂²	1	2	yes	—
48	#389×C₁₃₉	C₂²	1	2	yes	—
49	#389×C₁₃₉	C₂²	1	2	yes	—
50	#389×C₁₃₉	C₂²	1	2	yes	—
51	#389×C₁₃₉	C₂²	1	1	yes	characteristic
52	#389×C₁₃₉	C₂²	1	2	yes	—
53	#389×C₁₃₉	C₂²	1	2	yes	—
54	#389×C₁₃₉	C₂²	1	2	yes	—
55	#389×C₁₃₉	C₂²	1	4	yes	—
56	#389×C₁₃₉	C₂²	1	2	yes	—
57	#387×C₁₃₉	C₂²	1	2	yes	—
58	#387×C₁₃₉	C₂²	1	4	yes	—
59	#387×C₁₃₉	C₂²	1	4	yes	—
60	#387×C₁₃₉	C₂²	1	4	yes	—
61	#387×C₁₃₉	C₂²	1	4	yes	—
62	#387×C₁₃₉	C₂²	1	4	yes	—
63	#387×C₁₃₉	C₂²	1	4	yes	—
64	#385×C₁₃₉	C₂²	1	2	yes	—
65	#385×C₁₃₉	C₂²	1	4	yes	—
66	#384×C₁₃₉	C₂²	1	1	yes	characteristic
67	#384×C₁₃₉	C₂²	1	2	yes	—
68	#381×C₁₃₉	C₂²	1	4	yes	—
69	#380×C₁₃₉	C₂²	1	1	yes	characteristic
70	#380×C₁₃₉	C₂²	1	2	yes	—
71	#380×C₁₃₉	C₂²	1	2	yes	—
72	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
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	2	yes	—
76	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
77	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
78	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
79	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
80	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
81	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
82	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
83	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
84	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
85	C₂²×Q₈×C₁₃₉	C₂³	1	4	yes	—
86	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
88	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
92	C₄⋊Q₈×C₁₃₉	—	2	8	no	—
93	C₄⋊Q₈×C₁₃₉	—	2	8	no	—
94	C₄⋊Q₈×C₁₃₉	—	2	8	no	—
95	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
96	#125×C₁₃₉	—	2	16	no	—
97	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
98	C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
99	C₂²⋊Q₈×C₁₃₉	D₄	1	8	yes	—
100	C₄×Q₈×C₁₃₉	—	2	8	no	—
101	C₄×Q₈×C₁₃₉	—	2	8	no	—
102	C₄×Q₈×C₁₃₉	—	2	16	no	—
103	C₄×Q₈×C₁₃₉	—	2	4	no	—
104	#117×C₁₃₉	—	2	16	no	—
105	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
106	C₂×C₄⋊C₄×C₁₃₉	Q₈	1	8	yes	complemented
107	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
108	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
109	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
110	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
111	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
112	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
113	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	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	1	yes	characteristic
117	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
118	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
123	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	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	1	yes	characteristic
129	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
131	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
132	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
133	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
134	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
135	C₂×C₄²×C₁₃₉	—	2	8	no	—
136	C₂×C₄²×C₁₃₉	—	2	4	no	—
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	2	yes	—
141	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
142	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
143	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
144	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
145	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
146	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
147	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
148	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
149	#95×C₁₃₉	C₂³	1	2	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	4	yes	—
154	#95×C₁₃₉	C₂³	1	4	yes	—
155	#95×C₁₃₉	C₂³	1	2	yes	—
156	#95×C₁₃₉	C₂³	1	2	yes	—
157	#95×C₁₃₉	C₂³	1	4	yes	—
158	#95×C₁₃₉	C₂³	1	4	yes	—
159	#95×C₁₃₉	C₂³	1	4	yes	—
160	#95×C₁₃₉	C₂³	1	2	yes	—
161	#95×C₁₃₉	C₂³	1	2	yes	—
162	#95×C₁₃₉	C₂³	1	2	yes	—
163	#95×C₁₃₉	C₂³	1	2	yes	—
164	#95×C₁₃₉	C₂³	1	4	yes	—
165	#95×C₁₃₉	C₂³	1	4	yes	—
166	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
167	C₂×Q₈×C₁₃₉	—	2	8	no	—
168	C₂×Q₈×C₁₃₉	—	2	4	no	—
169	C₂×Q₈×C₁₃₉	—	2	2	no	—
170	C₂×Q₈×C₁₃₉	—	2	8	no	—
171	C₂×Q₈×C₁₃₉	—	2	4	no	—
172	C₂×Q₈×C₁₃₉	—	2	2	no	—
173	C₂×Q₈×C₁₃₉	—	2	4	no	—
174	C₂×Q₈×C₁₃₉	—	4	4	no	—
175	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	—
176	C₂²×C₄×C₁₃₉	—	2	4	no	—
177	C₂²×C₄×C₁₃₉	—	2	4	no	—
178	C₂²×C₄×C₁₃₉	—	2	2	no	—
179	C₂²×C₄×C₁₃₉	—	2	2	no	—
180	C₂²×C₄×C₁₃₉	—	2	2	no	—
181	C₂²×C₄×C₁₃₉	—	2	2	no	—
182	C₂²×C₄×C₁₃₉	—	2	4	no	—
183	C₂²×C₄×C₁₃₉	—	2	2	no	—
184	C₂²×C₄×C₁₃₉	—	2	2	no	—
185	C₂²×C₄×C₁₃₉	—	2	4	no	—
186	C₂²×C₄×C₁₃₉	—	4	1	no	—
187	C₂²×C₄×C₁₃₉	—	4	2	no	—
188	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
189	C₂²×C₄×C₁₃₉	C₂×Q₈	1	8	yes	—
190	C₂²×C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
191	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
192	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
193	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
194	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
195	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
196	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
197	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
198	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
199	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
200	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
201	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
202	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
203	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
204	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
206	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
207	C₄⋊C₄×C₁₃₉	—	2	8	no	—
208	C₄⋊C₄×C₁₃₉	—	2	8	no	—
209	C₄⋊C₄×C₁₃₉	—	2	8	no	—
210	C₄⋊C₄×C₁₃₉	—	2	8	no	—
211	C₄⋊C₄×C₁₃₉	—	2	8	no	—
212	C₄⋊C₄×C₁₃₉	—	2	8	no	—
213	C₄⋊C₄×C₁₃₉	—	2	4	no	—
214	C₄⋊C₄×C₁₃₉	—	2	4	no	—
215	C₄⋊C₄×C₁₃₉	—	2	2	no	—
216	C₄⋊C₄×C₁₃₉	—	2	4	no	—
217	C₄⋊C₄×C₁₃₉	—	2	2	no	—
218	C₄⋊C₄×C₁₃₉	—	2	8	no	—
219	C₄⋊C₄×C₁₃₉	—	2	4	no	—
220	C₄⋊C₄×C₁₃₉	—	2	4	no	—
221	C₄⋊C₄×C₁₃₉	—	2	4	no	—
222	C₄⋊C₄×C₁₃₉	—	2	2	no	—
223	C₄⋊C₄×C₁₃₉	—	4	2	no	—
224	C₄⋊C₄×C₁₃₉	—	4	2	no	—
225	C₄⋊C₄×C₁₃₉	—	4	4	no	—
226	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
227	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
228	C₄⋊C₄×C₁₃₉	C₂×Q₈	1	8	yes	—
229	C₄⋊C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
230	C₄⋊C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
231	C₄⋊C₄×C₁₃₉	#41	1	4	yes	—
232	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
233	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
234	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
235	C₄²×C₁₃₉	—	2	4	no	—
236	C₄²×C₁₃₉	—	2	4	no	—
237	C₄²×C₁₃₉	—	2	4	no	—
238	C₄²×C₁₃₉	—	2	4	no	—
239	C₄²×C₁₃₉	—	2	8	no	—
240	C₄²×C₁₃₉	—	2	8	no	—
241	C₄²×C₁₃₉	—	2	2	no	—
242	C₄²×C₁₃₉	—	2	2	no	—
243	C₄²×C₁₃₉	—	2	2	no	—
244	C₄²×C₁₃₉	—	2	4	no	—
245	C₄²×C₁₃₉	—	2	4	no	—
246	C₄²×C₁₃₉	#41	1	4	yes	—
247	C₂³×C₁₃₉	—	2	1	no	—
248	C₂³×C₁₃₉	—	2	1	no	—
249	C₂³×C₁₃₉	—	2	1	no	—
250	C₂³×C₁₃₉	—	2	1	no	—
251	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
252	C₂³×C₁₃₉	C₂²×Q₈	1	2	yes	—
253	C₂³×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
254	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
255	Q₈×C₁₃₉	—	2	8	no	—
256	Q₈×C₁₃₉	—	4	16	no	—
257	Q₈×C₁₃₉	—	4	8	no	—
258	C₂×C₄×C₁₃₉	—	2	16	no	—
259	C₂×C₄×C₁₃₉	—	2	2	no	—
260	C₂×C₄×C₁₃₉	—	2	2	no	—
261	C₂×C₄×C₁₃₉	—	2	2	no	—
262	C₂×C₄×C₁₃₉	—	2	1	no	—
263	C₂×C₄×C₁₃₉	—	2	1	no	—
264	C₂×C₄×C₁₃₉	—	2	2	no	—
265	C₂×C₄×C₁₃₉	—	2	2	no	—
266	C₂×C₄×C₁₃₉	—	2	1	no	—
267	C₂×C₄×C₁₃₉	—	2	1	no	—
268	C₂×C₄×C₁₃₉	—	2	2	no	—
269	C₂×C₄×C₁₃₉	—	2	2	no	—
270	C₂×C₄×C₁₃₉	—	2	1	no	—
271	C₂×C₄×C₁₃₉	—	2	2	no	—
272	C₂×C₄×C₁₃₉	—	2	1	no	—
273	C₂×C₄×C₁₃₉	—	2	2	no	—
274	C₂×C₄×C₁₃₉	—	2	2	no	—
275	C₂×C₄×C₁₃₉	—	2	8	no	—
276	C₂×C₄×C₁₃₉	—	2	8	no	—
277	C₂×C₄×C₁₃₉	—	2	2	no	—
278	C₂×C₄×C₁₃₉	—	2	4	no	—
279	C₂×C₄×C₁₃₉	—	2	4	no	—
280	C₂×C₄×C₁₃₉	—	2	1	no	—
281	C₂×C₄×C₁₃₉	—	2	2	no	—
282	C₂×C₄×C₁₃₉	—	2	2	no	—
283	C₂×C₄×C₁₃₉	—	2	2	no	—
284	C₂×C₄×C₁₃₉	—	2	4	no	—
285	C₂×C₄×C₁₃₉	—	2	4	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	4	no	—
291	C₂×C₄×C₁₃₉	—	2	2	no	—
292	C₂×C₄×C₁₃₉	—	2	2	no	—
293	C₂×C₄×C₁₃₉	—	2	1	no	—
294	C₂×C₄×C₁₃₉	—	2	4	no	—
295	C₂×C₄×C₁₃₉	—	4	8	no	—
296	C₂×C₄×C₁₃₉	—	4	4	no	—
297	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
298	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
299	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
300	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
301	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
302	C₂×C₄×C₁₃₉	C₂²×Q₈	1	4	yes	—
303	C₂×C₄×C₁₃₉	C₂²×Q₈	1	4	yes	—
304	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
305	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
306	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
307	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
308	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
309	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
310	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
311	C₂²×C₁₃₉	—	2	2	no	—
312	C₂²×C₁₃₉	—	2	2	no	—
313	C₂²×C₁₃₉	—	2	2	no	—
314	C₂²×C₁₃₉	—	2	2	no	—
315	C₂²×C₁₃₉	—	2	2	no	—
316	C₂²×C₁₃₉	—	2	2	no	—
317	C₂²×C₁₃₉	D₄×Q₈	1	4	yes	—
318	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
319	C₂²×C₁₃₉	C₂³×Q₈	1	1	yes	characteristic
320	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
321	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
322	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
323	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
324	C₂²×C₁₃₉	#585	1	1	yes	characteristic
325	C₄×C₁₃₉	—	2	2	no	—
326	C₄×C₁₃₉	—	2	2	no	—
327	C₄×C₁₃₉	—	2	4	no	—
328	C₄×C₁₃₉	—	2	4	no	—
329	C₄×C₁₃₉	—	2	4	no	—
330	C₄×C₁₃₉	—	2	4	no	—
331	C₄×C₁₃₉	—	2	4	no	—
332	C₄×C₁₃₉	—	2	2	no	—
333	C₄×C₁₃₉	—	4	4	no	—
334	C₄×C₁₃₉	—	4	2	no	—
335	C₄×C₁₃₉	—	4	4	no	—
336	C₄×C₁₃₉	—	4	2	no	—
337	C₄×C₁₃₉	—	4	1	no	—
338	C₄×C₁₃₉	—	4	2	no	—
339	C₄×C₁₃₉	#533	1	4	yes	complemented
340	C₄×C₁₃₉	#547	1	4	yes	—
341	C₂×C₁₃₉	—	2	4	no	—
342	C₂×C₁₃₉	C₂×#533	1	1	yes	characteristic
343	C₂×C₁₃₉	C₂×#547	1	1	yes	characteristic
344	C₂×C₁₃₉	C₂×D₄×Q₈	1	1	yes	characteristic
345	C₂×C₁₃₉	D₄×#41	1	1	yes	characteristic
346	C₂×C₁₃₉	#3495	1	1	yes	characteristic
347	C₂×C₁₃₉	#3502	1	1	yes	characteristic
348	C₂×C₁₃₉	#3523	1	1	yes	characteristic
349	#36133	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
350	C₁₃₉	#36133	1	1	yes	characteristic, direct product factor, Sylow
351	C₂×#533	C₂×C₁₃₉	1	2	yes	—
352	#2857	C₂×C₁₃₉	1	1	yes	characteristic
353	#2855	C₂×C₁₃₉	1	2	yes	—
354	#2551	C₂×C₁₃₉	1	1	yes	characteristic, complemented
355	#2546	C₂×C₁₃₉	1	1	yes	characteristic, complemented
356	#2506	C₂×C₁₃₉	1	2	yes	complemented
357	#2462	C₂×C₁₃₉	1	4	yes	complemented
358	#2451	C₂×C₁₃₉	1	2	yes	complemented
359	#2446	C₂×C₁₃₉	1	2	yes	complemented
360	#2440	C₂×C₁₃₉	1	2	yes	—
361	#2438	C₂×C₁₃₉	1	4	yes	—
362	#2365	C₂×C₁₃₉	1	1	yes	characteristic, complemented
363	#2365	C₂×C₁₃₉	1	2	yes	complemented
364	Q₈×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
365	#2344	C₂×C₁₃₉	1	2	yes	—
366	C₄×C₂²⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic
367	C₂×C₄×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic
368	#533	—	2	16	no	—
369	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
370	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
371	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
372	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
373	C₂×#125	C₂²×C₁₃₉	1	4	yes	—
374	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
375	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
376	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
377	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
378	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
379	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
380	C₂×C₄×Q₈	C₂²×C₁₃₉	1	4	yes	—
381	C₂×#117	C₂²×C₁₃₉	1	4	yes	—
382	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
383	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
384	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
385	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
386	#400	C₂²×C₁₃₉	1	4	yes	—
387	#398	C₂²×C₁₃₉	1	4	yes	—
388	#398	C₂²×C₁₃₉	1	4	yes	—
389	#398	C₂²×C₁₃₉	1	4	yes	—
390	#395	C₂²×C₁₃₉	1	4	yes	—
391	#395	C₂²×C₁₃₉	1	4	yes	—
392	#391	C₂²×C₁₃₉	1	2	yes	—
393	#391	C₂²×C₁₃₉	1	2	yes	—
394	#391	C₂²×C₁₃₉	1	2	yes	—
395	#391	C₂²×C₁₃₉	1	4	yes	—
396	#391	C₂²×C₁₃₉	1	1	yes	characteristic
397	#389	C₂²×C₁₃₉	1	2	yes	—
398	#389	C₂²×C₁₃₉	1	2	yes	—
399	#389	C₂²×C₁₃₉	1	2	yes	—
400	#389	C₂²×C₁₃₉	1	2	yes	—
401	#389	C₂²×C₁₃₉	1	2	yes	—
402	#389	C₂²×C₁₃₉	1	2	yes	—
403	#389	C₂²×C₁₃₉	1	4	yes	—
404	#389	C₂²×C₁₃₉	1	2	yes	—
405	#389	C₂²×C₁₃₉	1	2	yes	—
406	#389	C₂²×C₁₃₉	1	1	yes	characteristic
407	#387	C₂²×C₁₃₉	1	4	yes	—
408	#387	C₂²×C₁₃₉	1	4	yes	—
409	#387	C₂²×C₁₃₉	1	4	yes	—
410	#387	C₂²×C₁₃₉	1	4	yes	—
411	#387	C₂²×C₁₃₉	1	4	yes	—
412	#387	C₂²×C₁₃₉	1	4	yes	—
413	#387	C₂²×C₁₃₉	1	2	yes	—
414	#385	C₂²×C₁₃₉	1	4	yes	—
415	#385	C₂²×C₁₃₉	1	2	yes	—
416	#384	C₂²×C₁₃₉	1	1	yes	characteristic
417	#384	C₂²×C₁₃₉	1	2	yes	—
418	#381	C₂²×C₁₃₉	1	4	yes	—
419	#380	C₂²×C₁₃₉	1	1	yes	characteristic
420	#380	C₂²×C₁₃₉	1	2	yes	—
421	#380	C₂²×C₁₃₉	1	2	yes	—
422	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
423	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
424	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
425	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
426	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
427	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
428	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
429	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
430	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
431	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
432	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
433	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
434	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
435	C₂²×Q₈	C₂³×C₁₃₉	1	4	yes	—
436	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
437	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
438	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
439	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
440	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
441	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
442	C₄⋊Q₈	—	2	8	no	—
443	C₄⋊Q₈	—	2	8	no	—
444	C₄⋊Q₈	—	2	8	no	—
445	C₄⋊Q₈	—	2	4	no	—
446	#125	—	2	16	no	—
447	C₂²⋊Q₈	—	2	8	no	—
448	C₂²⋊Q₈	—	2	16	no	—
449	C₂²⋊Q₈	D₄×C₁₃₉	1	8	yes	—
450	C₄×Q₈	—	2	8	no	—
451	C₄×Q₈	—	2	8	no	—
452	C₄×Q₈	—	2	16	no	—
453	C₄×Q₈	—	2	4	no	—
454	#117	—	2	16	no	—
455	C₂×C₄⋊C₄	—	2	4	no	—
456	C₂×C₄⋊C₄	Q₈×C₁₃₉	1	8	yes	complemented
457	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
458	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	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	4	yes	—
463	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
464	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
465	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	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	2	yes	—
469	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
470	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
471	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
472	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
473	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
474	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
475	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
476	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
477	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
478	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
479	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
480	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
481	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
482	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
483	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
484	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
485	C₂×C₄²	—	2	8	no	—
486	C₂×C₄²	—	2	4	no	—
487	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
488	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
489	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
490	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
491	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
492	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
493	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
494	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
495	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
496	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
497	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
498	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
499	#95	C₂³×C₁₃₉	1	2	yes	—
500	#95	C₂³×C₁₃₉	1	2	yes	—
501	#95	C₂³×C₁₃₉	1	2	yes	—
502	#95	C₂³×C₁₃₉	1	2	yes	—
503	#95	C₂³×C₁₃₉	1	2	yes	—
504	#95	C₂³×C₁₃₉	1	2	yes	—
505	#95	C₂³×C₁₃₉	1	2	yes	—
506	#95	C₂³×C₁₃₉	1	4	yes	—
507	#95	C₂³×C₁₃₉	1	4	yes	—
508	#95	C₂³×C₁₃₉	1	2	yes	—
509	#95	C₂³×C₁₃₉	1	2	yes	—
510	#95	C₂³×C₁₃₉	1	4	yes	—
511	#95	C₂³×C₁₃₉	1	4	yes	—
512	#95	C₂³×C₁₃₉	1	4	yes	—
513	#95	C₂³×C₁₃₉	1	4	yes	—
514	#95	C₂³×C₁₃₉	1	4	yes	—
515	#95	C₂³×C₁₃₉	1	4	yes	—
516	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
517	C₂×Q₈	—	2	8	no	—
518	C₂×Q₈	—	2	4	no	—
519	C₂×Q₈	—	2	2	no	—
520	C₂×Q₈	—	2	8	no	—
521	C₂×Q₈	—	2	4	no	—
522	C₂×Q₈	—	2	2	no	—
523	C₂×Q₈	—	2	4	no	—
524	C₂×Q₈	—	4	4	no	—
525	C₂×Q₈	C₂×D₄×C₁₃₉	1	4	yes	—
526	C₂²×C₄	—	2	4	no	—
527	C₂²×C₄	—	2	4	no	—
528	C₂²×C₄	—	2	2	no	—
529	C₂²×C₄	—	2	2	no	—
530	C₂²×C₄	—	2	2	no	—
531	C₂²×C₄	—	2	2	no	—
532	C₂²×C₄	—	2	4	no	—
533	C₂²×C₄	—	2	2	no	—
534	C₂²×C₄	—	2	2	no	—
535	C₂²×C₄	—	2	4	no	—
536	C₂²×C₄	—	4	1	no	—
537	C₂²×C₄	—	4	2	no	—
538	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
539	C₂²×C₄	C₂×Q₈×C₁₃₉	1	8	yes	—
540	C₂²×C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
541	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
542	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
543	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
544	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
545	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
546	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
547	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
548	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
549	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
550	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
551	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
552	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
553	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
554	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
555	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
556	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
557	C₄⋊C₄	—	2	8	no	—
558	C₄⋊C₄	—	2	8	no	—
559	C₄⋊C₄	—	2	8	no	—
560	C₄⋊C₄	—	2	8	no	—
561	C₄⋊C₄	—	2	8	no	—
562	C₄⋊C₄	—	2	8	no	—
563	C₄⋊C₄	—	2	4	no	—
564	C₄⋊C₄	—	2	4	no	—
565	C₄⋊C₄	—	2	2	no	—
566	C₄⋊C₄	—	2	4	no	—
567	C₄⋊C₄	—	2	2	no	—
568	C₄⋊C₄	—	2	8	no	—
569	C₄⋊C₄	—	2	4	no	—
570	C₄⋊C₄	—	2	4	no	—
571	C₄⋊C₄	—	2	4	no	—
572	C₄⋊C₄	—	2	2	no	—
573	C₄⋊C₄	—	4	2	no	—
574	C₄⋊C₄	—	4	2	no	—
575	C₄⋊C₄	—	4	4	no	—
576	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
577	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
578	C₄⋊C₄	C₂×Q₈×C₁₃₉	1	8	yes	—
579	C₄⋊C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
580	C₄⋊C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
581	C₄⋊C₄	#41×C₁₃₉	1	4	yes	—
582	C₂²⋊C₄	—	2	8	no	—
583	C₂²⋊C₄	—	2	4	no	—
584	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
585	C₄²	—	2	4	no	—
586	C₄²	—	2	4	no	—
587	C₄²	—	2	4	no	—
588	C₄²	—	2	4	no	—
589	C₄²	—	2	8	no	—
590	C₄²	—	2	8	no	—
591	C₄²	—	2	2	no	—
592	C₄²	—	2	2	no	—
593	C₄²	—	2	2	no	—
594	C₄²	—	2	4	no	—
595	C₄²	—	2	4	no	—
596	C₄²	#41×C₁₃₉	1	4	yes	—
597	C₂³	—	2	1	no	—
598	C₂³	—	2	1	no	—
599	C₂³	—	2	1	no	—
600	C₂³	—	2	1	no	—
601	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
602	C₂³	C₂²×Q₈×C₁₃₉	1	2	yes	—
603	C₂³	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
604	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
605	Q₈	—	2	8	no	—
606	Q₈	—	4	16	no	—
607	Q₈	—	4	8	no	—
608	C₂×C₄	—	2	16	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	8	no	—
626	C₂×C₄	—	2	8	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	4	no	—
629	C₂×C₄	—	2	4	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	4	no	—
635	C₂×C₄	—	2	4	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	4	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	4	no	—
645	C₂×C₄	—	4	8	no	—
646	C₂×C₄	—	4	4	no	—
647	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
648	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
649	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
650	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
651	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
652	C₂×C₄	C₂²×Q₈×C₁₃₉	1	4	yes	—
653	C₂×C₄	C₂²×Q₈×C₁₃₉	1	4	yes	—
654	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
655	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
656	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
657	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
658	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
659	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
660	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
661	C₂²	—	2	2	no	—
662	C₂²	—	2	2	no	—
663	C₂²	—	2	2	no	—
664	C₂²	—	2	2	no	—
665	C₂²	—	2	2	no	—
666	C₂²	—	2	2	no	—
667	C₂²	D₄×Q₈×C₁₃₉	1	4	yes	—
668	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
669	C₂²	C₂³×Q₈×C₁₃₉	1	1	yes	characteristic
670	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
671	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
672	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
673	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
674	C₂²	#585×C₁₃₉	1	1	yes	characteristic
675	C₄	—	2	2	no	—
676	C₄	—	2	2	no	—
677	C₄	—	2	4	no	—
678	C₄	—	2	4	no	—
679	C₄	—	2	4	no	—
680	C₄	—	2	4	no	—
681	C₄	—	2	4	no	—
682	C₄	—	2	2	no	—
683	C₄	—	4	4	no	—
684	C₄	—	4	2	no	—
685	C₄	—	4	4	no	—
686	C₄	—	4	1	no	—
687	C₄	—	4	2	no	—
688	C₄	—	4	2	no	—
689	C₄	#533×C₁₃₉	1	4	yes	complemented
690	C₄	#547×C₁₃₉	1	4	yes	—
691	C₂	—	2	4	no	—
692	C₂	C₂×#533×C₁₃₉	1	1	yes	characteristic
693	C₂	C₂×#547×C₁₃₉	1	1	yes	characteristic
694	C₂	C₂×D₄×Q₈×C₁₃₉	1	1	yes	characteristic
695	C₂	D₄×#41×C₁₃₉	1	1	yes	characteristic
696	C₂	#3495×C₁₃₉	1	1	yes	characteristic
697	C₂	#3502×C₁₃₉	1	1	yes	characteristic
698	C₂	#3523×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
4. #2551×C₁₃₉	C₂	semidirect
5. #2546×C₁₃₉	C₂	semidirect
6. #2506×C₁₃₉	C₂	semidirect
7. #2462×C₁₃₉	C₂	semidirect
8. #2451×C₁₃₉	C₂	semidirect
9. #2446×C₁₃₉	C₂	semidirect
12. #2365×C₁₃₉	C₂	semidirect
13. #2365×C₁₃₉	C₂	semidirect
14. Q₈×C₄⋊C₄×C₁₃₉	C₂	semidirect
106. C₂×C₄⋊C₄×C₁₃₉	Q₈	semidirect
339. C₄×C₁₃₉	#533	semidirect
349. #36133	C₁₃₉	direct (N × H)
350. C₁₃₉	#36133	direct (N × H)
354. #2551	C₂×C₁₃₉	semidirect
355. #2546	C₂×C₁₃₉	semidirect
356. #2506	C₂×C₁₃₉	semidirect
357. #2462	C₂×C₁₃₉	semidirect
358. #2451	C₂×C₁₃₉	semidirect
359. #2446	C₂×C₁₃₉	semidirect
362. #2365	C₂×C₁₃₉	semidirect
363. #2365	C₂×C₁₃₉	semidirect
364. Q₈×C₄⋊C₄	C₂×C₁₃₉	semidirect
456. C₂×C₄⋊C₄	Q₈×C₁₃₉	semidirect
689. C₄	#533×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#533×C₁₃₉	2
#2857×C₁₃₉	2
#2855×C₁₃₉	2
#2551×C₁₃₉	2
#2546×C₁₃₉	2
#2506×C₁₃₉	2
#2462×C₁₃₉	2
#2451×C₁₃₉	2
#2446×C₁₃₉	2
#2440×C₁₃₉	2
#2438×C₁₃₉	2
#2365×C₁₃₉	2
Q₈×C₄⋊C₄×C₁₃₉	2
#2344×C₁₃₉	2
C₄×C₂²⋊Q₈×C₁₃₉	2
C₂×C₄×C₄⋊C₄×C₁₃₉	2
#36133	139

Subgroups — C139×#36133 #48030729

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36133 #48030729