Subgroups — C₁₃₉×#35928 #48030524

Order 35584.

2444 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#554×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×D₄×Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2660×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2659×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2584×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2583×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2567×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2551×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2550×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2549×C₁₃₉	C₂	1	4	yes	maximal, complemented
11	#2440×C₁₃₉	C₂	1	4	yes	maximal, complemented
12	#2434×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2399×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#395×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2349×C₁₃₉	C₂	1	2	yes	maximal
16	D₄×C₄⋊C₄×C₁₃₉	C₂	1	2	yes	maximal
17	#2275×C₁₃₉	C₂	1	1	yes	maximal, characteristic
18	C₂³×Q₈×C₁₃₉	C₂²	1	2	yes	—
19	#554×C₁₃₉	—	2	8	no	—
20	D₄×Q₈×C₁₃₉	—	2	8	no	—
21	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
22	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
25	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
28	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
29	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
30	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
31	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
32	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
39	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
40	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
41	#398×C₁₃₉	C₂²	1	4	yes	—
42	#398×C₁₃₉	C₂²	1	4	yes	—
43	#398×C₁₃₉	C₂²	1	1	yes	characteristic
44	#398×C₁₃₉	C₂²	1	2	yes	—
45	#398×C₁₃₉	C₂²	1	1	yes	characteristic
46	#398×C₁₃₉	C₂²	1	2	yes	—
47	#395×C₁₃₉	C₂²	1	2	yes	—
48	#395×C₁₃₉	C₂²	1	4	yes	—
49	#395×C₁₃₉	C₂²	1	4	yes	—
50	#395×C₁₃₉	C₂²	1	4	yes	—
51	#395×C₁₃₉	C₂²	1	2	yes	—
52	#395×C₁₃₉	C₂²	1	2	yes	—
53	#395×C₁₃₉	C₂²	1	2	yes	—
54	#395×C₁₃₉	C₂²	1	2	yes	—
55	#395×C₁₃₉	C₂²	1	1	yes	characteristic
56	#395×C₁₃₉	C₂²	1	2	yes	—
57	#395×C₁₃₉	C₂²	1	1	yes	characteristic
58	#391×C₁₃₉	C₂²	1	2	yes	—
59	#391×C₁₃₉	C₂²	1	4	yes	—
60	#389×C₁₃₉	C₂²	1	4	yes	—
61	#389×C₁₃₉	C₂²	1	4	yes	—
62	#389×C₁₃₉	C₂²	1	2	yes	—
63	#389×C₁₃₉	C₂²	1	4	yes	—
64	#389×C₁₃₉	C₂²	1	2	yes	—
65	#389×C₁₃₉	C₂²	1	2	yes	—
66	#389×C₁₃₉	C₂²	1	2	yes	—
67	#385×C₁₃₉	C₂²	1	4	yes	—
68	#385×C₁₃₉	C₂²	1	4	yes	—
69	#385×C₁₃₉	C₂²	1	4	yes	—
70	#385×C₁₃₉	C₂²	1	4	yes	—
71	#384×C₁₃₉	C₂²	1	2	yes	—
72	#384×C₁₃₉	C₂²	1	2	yes	—
73	#382×C₁₃₉	C₂²	1	2	yes	—
74	#380×C₁₃₉	C₂²	1	4	yes	—
75	#380×C₁₃₉	C₂²	1	4	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	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	#376×C₁₃₉	C₂²	1	1	yes	characteristic
83	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
84	C₂×#95×C₁₃₉	C₂²	1	4	yes	—
85	C₂²×Q₈×C₁₃₉	—	2	8	no	—
86	C₂²×Q₈×C₁₃₉	—	4	8	no	—
87	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
88	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
89	C₂²×Q₈×C₁₃₉	C₂³	1	4	yes	—
90	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
91	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
92	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
94	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
95	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
96	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
97	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
98	C₄⋊Q₈×C₁₃₉	—	2	8	no	—
99	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
100	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
101	C₄⋊Q₈×C₁₃₉	—	4	8	no	—
102	#125×C₁₃₉	—	2	4	no	—
103	#125×C₁₃₉	—	2	4	no	—
104	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
105	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
106	C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
107	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
108	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
109	C₄×Q₈×C₁₃₉	—	2	4	no	—
110	C₄×Q₈×C₁₃₉	—	2	4	no	—
111	C₄×D₄×C₁₃₉	—	2	8	no	—
112	C₄×D₄×C₁₃₉	—	2	4	no	—
113	C₄×D₄×C₁₃₉	—	2	4	no	—
114	C₄×D₄×C₁₃₉	D₄	1	8	yes	—
115	C₄×D₄×C₁₃₉	Q₈	1	16	yes	complemented
116	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
117	C₂×C₄⋊C₄×C₁₃₉	—	4	8	no	—
118	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
122	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	4	yes	—
127	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	1	yes	characteristic
131	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
135	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
138	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
139	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
140	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
142	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
143	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
148	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
150	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
151	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
152	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
153	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
154	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
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	1	yes	characteristic
159	#95×C₁₃₉	C₂³	1	2	yes	—
160	#95×C₁₃₉	C₂³	1	4	yes	—
161	#95×C₁₃₉	C₂³	1	1	yes	characteristic
162	#95×C₁₃₉	C₂³	1	4	yes	—
163	#95×C₁₃₉	C₂³	1	2	yes	—
164	#95×C₁₃₉	C₂³	1	4	yes	—
165	#95×C₁₃₉	C₂³	1	4	yes	—
166	#95×C₁₃₉	C₂³	1	2	yes	—
167	#95×C₁₃₉	C₂³	1	2	yes	—
168	#95×C₁₃₉	C₂³	1	4	yes	—
169	#95×C₁₃₉	C₂³	1	4	yes	—
170	#95×C₁₃₉	C₂³	1	4	yes	—
171	#95×C₁₃₉	C₂³	1	2	yes	—
172	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
173	C₂×Q₈×C₁₃₉	—	2	2	no	—
174	C₂×Q₈×C₁₃₉	—	2	2	no	—
175	C₂×Q₈×C₁₃₉	—	2	8	no	—
176	C₂×Q₈×C₁₃₉	—	2	4	no	—
177	C₂×Q₈×C₁₃₉	—	2	4	no	—
178	C₂×Q₈×C₁₃₉	—	2	4	no	—
179	C₂×Q₈×C₁₃₉	—	2	8	no	—
180	C₂×Q₈×C₁₃₉	—	2	2	no	—
181	C₂×Q₈×C₁₃₉	—	4	4	no	—
182	C₂×Q₈×C₁₃₉	—	4	4	no	—
183	C₂×Q₈×C₁₃₉	—	4	1	no	—
184	C₂×Q₈×C₁₃₉	—	4	4	no	—
185	C₂×Q₈×C₁₃₉	—	4	32	no	—
186	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
187	C₂×D₄×C₁₃₉	C₂×Q₈	1	8	yes	—
188	C₂²×C₄×C₁₃₉	—	2	4	no	—
189	C₂²×C₄×C₁₃₉	—	2	8	no	—
190	C₂²×C₄×C₁₃₉	—	2	4	no	—
191	C₂²×C₄×C₁₃₉	—	2	8	no	—
192	C₂²×C₄×C₁₃₉	—	2	4	no	—
193	C₂²×C₄×C₁₃₉	—	4	4	no	—
194	C₂²×C₄×C₁₃₉	—	4	4	no	—
195	C₂²×C₄×C₁₃₉	—	4	2	no	—
196	C₂²×C₄×C₁₃₉	—	4	4	no	—
197	C₂²×C₄×C₁₃₉	—	4	4	no	—
198	C₂²×C₄×C₁₃₉	—	4	4	no	—
199	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
200	C₂²×C₄×C₁₃₉	C₂×Q₈	1	16	yes	complemented
201	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
202	C₂²×C₄×C₁₃₉	C₂⁴	1	2	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	1	yes	characteristic
209	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
210	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
214	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
216	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
217	C₄⋊C₄×C₁₃₉	—	2	2	no	—
218	C₄⋊C₄×C₁₃₉	—	2	4	no	—
219	C₄⋊C₄×C₁₃₉	—	2	4	no	—
220	C₄⋊C₄×C₁₃₉	—	2	4	no	—
221	C₄⋊C₄×C₁₃₉	—	2	2	no	—
222	C₄⋊C₄×C₁₃₉	—	2	2	no	—
223	C₄⋊C₄×C₁₃₉	—	2	4	no	—
224	C₄⋊C₄×C₁₃₉	—	2	4	no	—
225	C₄⋊C₄×C₁₃₉	—	2	2	no	—
226	C₄⋊C₄×C₁₃₉	—	2	2	no	—
227	C₄⋊C₄×C₁₃₉	—	2	2	no	—
228	C₄⋊C₄×C₁₃₉	—	2	4	no	—
229	C₄⋊C₄×C₁₃₉	—	2	4	no	—
230	C₄⋊C₄×C₁₃₉	—	2	8	no	—
231	C₄⋊C₄×C₁₃₉	—	2	4	no	—
232	C₄⋊C₄×C₁₃₉	—	2	4	no	—
233	C₄⋊C₄×C₁₃₉	—	2	8	no	—
234	C₄⋊C₄×C₁₃₉	—	2	4	no	—
235	C₄⋊C₄×C₁₃₉	—	2	4	no	—
236	C₄⋊C₄×C₁₃₉	—	4	4	no	—
237	C₄⋊C₄×C₁₃₉	—	4	4	no	—
238	C₄⋊C₄×C₁₃₉	—	4	4	no	—
239	C₄⋊C₄×C₁₃₉	—	4	2	no	—
240	C₄⋊C₄×C₁₃₉	—	4	4	no	—
241	C₄⋊C₄×C₁₃₉	—	4	4	no	—
242	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
243	C₄⋊C₄×C₁₃₉	C₂×Q₈	1	8	yes	complemented
244	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
245	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
246	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
247	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
248	C₂²⋊C₄×C₁₃₉	C₂×Q₈	1	16	yes	complemented
249	C₄²×C₁₃₉	—	2	2	no	—
250	C₄²×C₁₃₉	—	2	2	no	—
251	C₄²×C₁₃₉	—	2	4	no	—
252	C₄²×C₁₃₉	—	4	2	no	—
253	C₄²×C₁₃₉	—	4	4	no	—
254	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
255	C₄²×C₁₃₉	C₂×Q₈	1	8	yes	complemented
256	C₂³×C₁₃₉	—	2	4	no	—
257	C₂³×C₁₃₉	—	2	2	no	—
258	C₂³×C₁₃₉	—	2	2	no	—
259	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
260	C₂³×C₁₃₉	C₂²×Q₈	1	8	yes	—
261	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
262	Q₈×C₁₃₉	—	2	8	no	—
263	Q₈×C₁₃₉	—	4	4	no	—
264	Q₈×C₁₃₉	—	4	16	no	—
265	Q₈×C₁₃₉	—	4	8	no	—
266	Q₈×C₁₃₉	—	8	4	no	—
267	D₄×C₁₃₉	C₄⋊Q₈	1	16	yes	complemented
268	C₂×C₄×C₁₃₉	—	2	1	no	—
269	C₂×C₄×C₁₃₉	—	2	2	no	—
270	C₂×C₄×C₁₃₉	—	2	2	no	—
271	C₂×C₄×C₁₃₉	—	2	4	no	—
272	C₂×C₄×C₁₃₉	—	2	4	no	—
273	C₂×C₄×C₁₃₉	—	2	2	no	—
274	C₂×C₄×C₁₃₉	—	2	2	no	—
275	C₂×C₄×C₁₃₉	—	2	2	no	—
276	C₂×C₄×C₁₃₉	—	2	2	no	—
277	C₂×C₄×C₁₃₉	—	2	1	no	—
278	C₂×C₄×C₁₃₉	—	2	1	no	—
279	C₂×C₄×C₁₃₉	—	2	4	no	—
280	C₂×C₄×C₁₃₉	—	2	2	no	—
281	C₂×C₄×C₁₃₉	—	2	1	no	—
282	C₂×C₄×C₁₃₉	—	2	2	no	—
283	C₂×C₄×C₁₃₉	—	2	1	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	4	no	—
289	C₂×C₄×C₁₃₉	—	2	2	no	—
290	C₂×C₄×C₁₃₉	—	2	4	no	—
291	C₂×C₄×C₁₃₉	—	2	2	no	—
292	C₂×C₄×C₁₃₉	—	2	4	no	—
293	C₂×C₄×C₁₃₉	—	2	4	no	—
294	C₂×C₄×C₁₃₉	—	2	2	no	—
295	C₂×C₄×C₁₃₉	—	2	2	no	—
296	C₂×C₄×C₁₃₉	—	2	1	no	—
297	C₂×C₄×C₁₃₉	—	2	2	no	—
298	C₂×C₄×C₁₃₉	—	2	2	no	—
299	C₂×C₄×C₁₃₉	—	2	1	no	—
300	C₂×C₄×C₁₃₉	—	4	8	no	—
301	C₂×C₄×C₁₃₉	—	4	16	no	—
302	C₂×C₄×C₁₃₉	—	4	8	no	—
303	C₂×C₄×C₁₃₉	—	4	16	no	—
304	C₂×C₄×C₁₃₉	—	8	4	no	—
305	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
306	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
307	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
308	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
309	C₂×C₄×C₁₃₉	C₂²×Q₈	1	4	yes	—
310	C₂×C₄×C₁₃₉	C₂²×Q₈	1	4	yes	—
311	C₂×C₄×C₁₃₉	C₂²×Q₈	1	8	yes	—
312	C₂×C₄×C₁₃₉	C₂²×Q₈	1	4	yes	—
313	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
314	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
315	C₂²×C₁₃₉	—	2	4	no	—
316	C₂²×C₁₃₉	—	2	4	no	—
317	C₂²×C₁₃₉	—	2	8	no	—
318	C₂²×C₁₃₉	—	2	8	no	—
319	C₂²×C₁₃₉	C₂×C₄⋊Q₈	1	8	yes	—
320	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
321	C₂²×C₁₃₉	C₂³×Q₈	1	2	yes	—
322	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
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	4	no	—
327	C₄×C₁₃₉	—	2	4	no	—
328	C₄×C₁₃₉	—	2	2	no	—
329	C₄×C₁₃₉	—	2	2	no	—
330	C₄×C₁₃₉	—	2	4	no	—
331	C₄×C₁₃₉	—	2	8	no	—
332	C₄×C₁₃₉	—	2	4	no	—
333	C₄×C₁₃₉	—	4	4	no	—
334	C₄×C₁₃₉	—	4	1	no	—
335	C₄×C₁₃₉	—	4	2	no	—
336	C₄×C₁₃₉	—	4	1	no	—
337	C₄×C₁₃₉	—	4	2	no	—
338	C₄×C₁₃₉	—	4	2	no	—
339	C₄×C₁₃₉	—	4	1	no	—
340	C₄×C₁₃₉	C₂×C₄⋊Q₈	1	4	yes	—
341	C₂×C₁₃₉	—	2	8	no	—
342	C₂×C₁₃₉	C₂²×C₄⋊Q₈	1	1	yes	characteristic
343	C₂×C₁₃₉	#3484	1	1	yes	characteristic
344	C₂×C₁₃₉	#3489	1	1	yes	characteristic
345	C₂×C₁₃₉	#3501	1	2	yes	—
346	C₂×C₁₃₉	#3503	1	2	yes	—
347	#35928	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
348	C₁₃₉	#35928	1	1	yes	characteristic, direct product factor, Sylow
349	C₂×#554	C₂×C₁₃₉	1	1	yes	characteristic
350	C₂×D₄×Q₈	C₂×C₁₃₉	1	1	yes	characteristic
351	#2660	C₂×C₁₃₉	1	1	yes	characteristic, complemented
352	#2659	C₂×C₁₃₉	1	2	yes	complemented
353	#2584	C₂×C₁₃₉	1	1	yes	characteristic, complemented
354	#2583	C₂×C₁₃₉	1	2	yes	complemented
355	#2567	C₂×C₁₃₉	1	1	yes	characteristic, complemented
356	#2551	C₂×C₁₃₉	1	2	yes	complemented
357	#2550	C₂×C₁₃₉	1	2	yes	complemented
358	#2549	C₂×C₁₃₉	1	4	yes	complemented
359	#2440	C₂×C₁₃₉	1	4	yes	complemented
360	#2434	C₂×C₁₃₉	1	2	yes	complemented
361	#2399	C₂×C₁₃₉	1	1	yes	characteristic, complemented
362	C₂×#395	C₂×C₁₃₉	1	2	yes	complemented
363	#2349	C₂×C₁₃₉	1	2	yes	—
364	D₄×C₄⋊C₄	C₂×C₁₃₉	1	2	yes	—
365	#2275	C₂×C₁₃₉	1	1	yes	characteristic
366	C₂³×Q₈	C₂²×C₁₃₉	1	2	yes	—
367	#554	—	2	8	no	—
368	D₄×Q₈	—	2	8	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	1	yes	characteristic
372	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
373	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
374	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
375	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
376	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
377	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
378	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
379	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
380	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
381	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
382	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
383	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
384	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
385	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
386	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
387	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
388	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
389	#398	C₂²×C₁₃₉	1	1	yes	characteristic
390	#398	C₂²×C₁₃₉	1	2	yes	—
391	#398	C₂²×C₁₃₉	1	1	yes	characteristic
392	#398	C₂²×C₁₃₉	1	2	yes	—
393	#398	C₂²×C₁₃₉	1	4	yes	—
394	#398	C₂²×C₁₃₉	1	4	yes	—
395	#395	C₂²×C₁₃₉	1	2	yes	—
396	#395	C₂²×C₁₃₉	1	2	yes	—
397	#395	C₂²×C₁₃₉	1	2	yes	—
398	#395	C₂²×C₁₃₉	1	2	yes	—
399	#395	C₂²×C₁₃₉	1	1	yes	characteristic
400	#395	C₂²×C₁₃₉	1	2	yes	—
401	#395	C₂²×C₁₃₉	1	4	yes	—
402	#395	C₂²×C₁₃₉	1	4	yes	—
403	#395	C₂²×C₁₃₉	1	1	yes	characteristic
404	#395	C₂²×C₁₃₉	1	2	yes	—
405	#395	C₂²×C₁₃₉	1	4	yes	—
406	#391	C₂²×C₁₃₉	1	2	yes	—
407	#391	C₂²×C₁₃₉	1	4	yes	—
408	#389	C₂²×C₁₃₉	1	2	yes	—
409	#389	C₂²×C₁₃₉	1	2	yes	—
410	#389	C₂²×C₁₃₉	1	4	yes	—
411	#389	C₂²×C₁₃₉	1	4	yes	—
412	#389	C₂²×C₁₃₉	1	2	yes	—
413	#389	C₂²×C₁₃₉	1	2	yes	—
414	#389	C₂²×C₁₃₉	1	4	yes	—
415	#385	C₂²×C₁₃₉	1	4	yes	—
416	#385	C₂²×C₁₃₉	1	4	yes	—
417	#385	C₂²×C₁₃₉	1	4	yes	—
418	#385	C₂²×C₁₃₉	1	4	yes	—
419	#384	C₂²×C₁₃₉	1	2	yes	—
420	#384	C₂²×C₁₃₉	1	2	yes	—
421	#382	C₂²×C₁₃₉	1	2	yes	—
422	#380	C₂²×C₁₃₉	1	4	yes	—
423	#380	C₂²×C₁₃₉	1	4	yes	—
424	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
425	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
426	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
427	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
428	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
429	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
430	#376	C₂²×C₁₃₉	1	1	yes	characteristic
431	C₂×#95	C₂²×C₁₃₉	1	4	yes	—
432	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
433	C₂²×Q₈	—	2	8	no	—
434	C₂²×Q₈	—	4	8	no	—
435	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
436	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
437	C₂²×Q₈	C₂³×C₁₃₉	1	4	yes	—
438	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
439	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
440	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
441	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
442	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
443	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
444	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
445	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
446	C₄⋊Q₈	—	2	8	no	—
447	C₄⋊Q₈	—	2	4	no	—
448	C₄⋊Q₈	—	2	4	no	—
449	C₄⋊Q₈	—	4	8	no	—
450	#125	—	2	4	no	—
451	#125	—	2	4	no	—
452	C₂²⋊Q₈	—	2	8	no	—
453	C₂²⋊Q₈	—	2	8	no	—
454	C₂²⋊Q₈	—	2	16	no	—
455	C₂²⋊Q₈	—	2	8	no	—
456	C₂²⋊Q₈	—	2	8	no	—
457	C₄×Q₈	—	2	4	no	—
458	C₄×Q₈	—	2	4	no	—
459	C₄×D₄	—	2	8	no	—
460	C₄×D₄	—	2	4	no	—
461	C₄×D₄	—	2	4	no	—
462	C₄×D₄	D₄×C₁₃₉	1	8	yes	—
463	C₄×D₄	Q₈×C₁₃₉	1	16	yes	complemented
464	C₂×C₄⋊C₄	—	2	8	no	—
465	C₂×C₄⋊C₄	—	4	8	no	—
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	1	yes	characteristic
474	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
475	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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	2	yes	—
481	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
482	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
483	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
484	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
485	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
486	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
487	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
488	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
489	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
490	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
491	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
492	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
493	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
494	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
495	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
496	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
497	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
498	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
499	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
500	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
501	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
502	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
503	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
504	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
505	#95	C₂³×C₁₃₉	1	1	yes	characteristic
506	#95	C₂³×C₁₃₉	1	2	yes	—
507	#95	C₂³×C₁₃₉	1	2	yes	—
508	#95	C₂³×C₁₃₉	1	4	yes	—
509	#95	C₂³×C₁₃₉	1	4	yes	—
510	#95	C₂³×C₁₃₉	1	4	yes	—
511	#95	C₂³×C₁₃₉	1	4	yes	—
512	#95	C₂³×C₁₃₉	1	1	yes	characteristic
513	#95	C₂³×C₁₃₉	1	2	yes	—
514	#95	C₂³×C₁₃₉	1	2	yes	—
515	#95	C₂³×C₁₃₉	1	2	yes	—
516	#95	C₂³×C₁₃₉	1	2	yes	—
517	#95	C₂³×C₁₃₉	1	4	yes	—
518	#95	C₂³×C₁₃₉	1	4	yes	—
519	#95	C₂³×C₁₃₉	1	4	yes	—
520	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
521	C₂×Q₈	—	2	2	no	—
522	C₂×Q₈	—	2	2	no	—
523	C₂×Q₈	—	2	8	no	—
524	C₂×Q₈	—	2	4	no	—
525	C₂×Q₈	—	2	4	no	—
526	C₂×Q₈	—	2	4	no	—
527	C₂×Q₈	—	2	8	no	—
528	C₂×Q₈	—	2	2	no	—
529	C₂×Q₈	—	4	4	no	—
530	C₂×Q₈	—	4	4	no	—
531	C₂×Q₈	—	4	1	no	—
532	C₂×Q₈	—	4	4	no	—
533	C₂×Q₈	—	4	32	no	—
534	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
535	C₂×D₄	C₂×Q₈×C₁₃₉	1	8	yes	—
536	C₂²×C₄	—	2	4	no	—
537	C₂²×C₄	—	2	8	no	—
538	C₂²×C₄	—	2	4	no	—
539	C₂²×C₄	—	2	8	no	—
540	C₂²×C₄	—	2	4	no	—
541	C₂²×C₄	—	4	4	no	—
542	C₂²×C₄	—	4	4	no	—
543	C₂²×C₄	—	4	2	no	—
544	C₂²×C₄	—	4	4	no	—
545	C₂²×C₄	—	4	4	no	—
546	C₂²×C₄	—	4	4	no	—
547	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
548	C₂²×C₄	C₂×Q₈×C₁₃₉	1	16	yes	complemented
549	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
550	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
551	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
552	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
553	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
554	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
555	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
556	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
557	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
558	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
559	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
560	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
561	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
562	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
563	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
564	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
565	C₄⋊C₄	—	2	2	no	—
566	C₄⋊C₄	—	2	4	no	—
567	C₄⋊C₄	—	2	4	no	—
568	C₄⋊C₄	—	2	4	no	—
569	C₄⋊C₄	—	2	2	no	—
570	C₄⋊C₄	—	2	2	no	—
571	C₄⋊C₄	—	2	4	no	—
572	C₄⋊C₄	—	2	4	no	—
573	C₄⋊C₄	—	2	2	no	—
574	C₄⋊C₄	—	2	2	no	—
575	C₄⋊C₄	—	2	2	no	—
576	C₄⋊C₄	—	2	4	no	—
577	C₄⋊C₄	—	2	4	no	—
578	C₄⋊C₄	—	2	8	no	—
579	C₄⋊C₄	—	2	4	no	—
580	C₄⋊C₄	—	2	4	no	—
581	C₄⋊C₄	—	2	8	no	—
582	C₄⋊C₄	—	2	4	no	—
583	C₄⋊C₄	—	2	4	no	—
584	C₄⋊C₄	—	4	4	no	—
585	C₄⋊C₄	—	4	4	no	—
586	C₄⋊C₄	—	4	4	no	—
587	C₄⋊C₄	—	4	2	no	—
588	C₄⋊C₄	—	4	4	no	—
589	C₄⋊C₄	—	4	4	no	—
590	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
591	C₄⋊C₄	C₂×Q₈×C₁₃₉	1	8	yes	complemented
592	C₂²⋊C₄	—	2	8	no	—
593	C₂²⋊C₄	—	2	4	no	—
594	C₂²⋊C₄	—	2	4	no	—
595	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
596	C₂²⋊C₄	C₂×Q₈×C₁₃₉	1	16	yes	complemented
597	C₄²	—	2	2	no	—
598	C₄²	—	2	2	no	—
599	C₄²	—	2	4	no	—
600	C₄²	—	4	2	no	—
601	C₄²	—	4	4	no	—
602	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
603	C₄²	C₂×Q₈×C₁₃₉	1	8	yes	complemented
604	C₂³	—	2	4	no	—
605	C₂³	—	2	2	no	—
606	C₂³	—	2	2	no	—
607	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
608	C₂³	C₂²×Q₈×C₁₃₉	1	8	yes	—
609	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
610	Q₈	—	2	8	no	—
611	Q₈	—	4	16	no	—
612	Q₈	—	4	4	no	—
613	Q₈	—	4	8	no	—
614	Q₈	—	8	4	no	—
615	D₄	C₄⋊Q₈×C₁₃₉	1	16	yes	complemented
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	4	no	—
620	C₂×C₄	—	2	4	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	4	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	4	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	4	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	4	no	—
641	C₂×C₄	—	2	4	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	4	8	no	—
649	C₂×C₄	—	4	16	no	—
650	C₂×C₄	—	4	16	no	—
651	C₂×C₄	—	4	8	no	—
652	C₂×C₄	—	8	4	no	—
653	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
654	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
655	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
656	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
657	C₂×C₄	C₂²×Q₈×C₁₃₉	1	4	yes	—
658	C₂×C₄	C₂²×Q₈×C₁₃₉	1	4	yes	—
659	C₂×C₄	C₂²×Q₈×C₁₃₉	1	8	yes	—
660	C₂×C₄	C₂²×Q₈×C₁₃₉	1	4	yes	—
661	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
662	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
663	C₂²	—	2	4	no	—
664	C₂²	—	2	4	no	—
665	C₂²	—	2	8	no	—
666	C₂²	—	2	8	no	—
667	C₂²	C₂×C₄⋊Q₈×C₁₃₉	1	8	yes	—
668	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
669	C₂²	C₂³×Q₈×C₁₃₉	1	2	yes	—
670	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
671	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
672	C₂²	#585×C₁₃₉	1	1	yes	characteristic
673	C₄	—	2	2	no	—
674	C₄	—	2	4	no	—
675	C₄	—	2	4	no	—
676	C₄	—	2	2	no	—
677	C₄	—	2	2	no	—
678	C₄	—	2	4	no	—
679	C₄	—	2	8	no	—
680	C₄	—	2	4	no	—
681	C₄	—	4	4	no	—
682	C₄	—	4	1	no	—
683	C₄	—	4	2	no	—
684	C₄	—	4	1	no	—
685	C₄	—	4	2	no	—
686	C₄	—	4	1	no	—
687	C₄	—	4	2	no	—
688	C₄	C₂×C₄⋊Q₈×C₁₃₉	1	4	yes	—
689	C₂	—	2	8	no	—
690	C₂	C₂²×C₄⋊Q₈×C₁₃₉	1	1	yes	characteristic
691	C₂	#3484×C₁₃₉	1	1	yes	characteristic
692	C₂	#3489×C₁₃₉	1	1	yes	characteristic
693	C₂	#3501×C₁₃₉	1	2	yes	—
694	C₂	#3503×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂²×D₄×C₁₃₉	C₂³
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. #2660×C₁₃₉	C₂	semidirect
4. #2659×C₁₃₉	C₂	semidirect
5. #2584×C₁₃₉	C₂	semidirect
6. #2583×C₁₃₉	C₂	semidirect
7. #2567×C₁₃₉	C₂	semidirect
8. #2551×C₁₃₉	C₂	semidirect
9. #2550×C₁₃₉	C₂	semidirect
10. #2549×C₁₃₉	C₂	semidirect
11. #2440×C₁₃₉	C₂	semidirect
12. #2434×C₁₃₉	C₂	semidirect
13. #2399×C₁₃₉	C₂	semidirect
14. C₂×#395×C₁₃₉	C₂	semidirect
115. C₄×D₄×C₁₃₉	Q₈	semidirect
200. C₂²×C₄×C₁₃₉	C₂×Q₈	semidirect
243. C₄⋊C₄×C₁₃₉	C₂×Q₈	semidirect
248. C₂²⋊C₄×C₁₃₉	C₂×Q₈	semidirect
255. C₄²×C₁₃₉	C₂×Q₈	semidirect
267. D₄×C₁₃₉	C₄⋊Q₈	semidirect
347. #35928	C₁₃₉	direct (N × H)
348. C₁₃₉	#35928	direct (N × H)
351. #2660	C₂×C₁₃₉	semidirect
352. #2659	C₂×C₁₃₉	semidirect
353. #2584	C₂×C₁₃₉	semidirect
354. #2583	C₂×C₁₃₉	semidirect
355. #2567	C₂×C₁₃₉	semidirect
356. #2551	C₂×C₁₃₉	semidirect
357. #2550	C₂×C₁₃₉	semidirect
358. #2549	C₂×C₁₃₉	semidirect
359. #2440	C₂×C₁₃₉	semidirect
360. #2434	C₂×C₁₃₉	semidirect
361. #2399	C₂×C₁₃₉	semidirect
362. C₂×#395	C₂×C₁₃₉	semidirect
463. C₄×D₄	Q₈×C₁₃₉	semidirect
548. C₂²×C₄	C₂×Q₈×C₁₃₉	semidirect
591. C₄⋊C₄	C₂×Q₈×C₁₃₉	semidirect
596. C₂²⋊C₄	C₂×Q₈×C₁₃₉	semidirect
603. C₄²	C₂×Q₈×C₁₃₉	semidirect
615. D₄	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
C₂×#554×C₁₃₉	2
C₂×D₄×Q₈×C₁₃₉	2
#2660×C₁₃₉	2
#2659×C₁₃₉	2
#2584×C₁₃₉	2
#2583×C₁₃₉	2
#2567×C₁₃₉	2
#2551×C₁₃₉	2
#2550×C₁₃₉	2
#2549×C₁₃₉	2
#2440×C₁₃₉	2
#2434×C₁₃₉	2
#2399×C₁₃₉	2
C₂×#395×C₁₃₉	2
#2349×C₁₃₉	2
D₄×C₄⋊C₄×C₁₃₉	2
#2275×C₁₃₉	2
#35928	139

Subgroups — C139×#35928 #48030524

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#35928 #48030524