Subgroups — C₁₃₉×#34317 #48028913

Order 35584.

2228 conjugacy classes of subgroups.

The subgroup lattice has 682 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	#2370×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	#2369×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2362×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2362×C₁₃₉	C₂	1	4	yes	maximal, complemented
6	#2357×C₁₃₉	C₂	1	2	yes	maximal
7	#2355×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2354×C₁₃₉	C₂	1	1	yes	maximal, characteristic
9	#2344×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2332×C₁₃₉	C₂	1	4	yes	maximal, complemented
11	#2323×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	C₄×C₄⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×#125×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2293×C₁₃₉	C₂	1	1	yes	maximal, characteristic
15	#2293×C₁₃₉	C₂	1	2	yes	maximal
16	#2274×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	C₄²×Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	#554×C₁₃₉	C₄	1	16	yes	complemented
19	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
20	C₂×#125×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×C₄×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	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
29	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
30	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
31	C₂×#117×C₁₃₉	C₂²	1	4	yes	—
32	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
33	#391×C₁₃₉	C₂²	1	2	yes	—
34	#391×C₁₃₉	C₂²	1	2	yes	—
35	#391×C₁₃₉	C₂²	1	4	yes	—
36	#390×C₁₃₉	C₂²	1	1	yes	characteristic
37	#390×C₁₃₉	C₂²	1	2	yes	—
38	#390×C₁₃₉	C₂²	1	1	yes	characteristic
39	#389×C₁₃₉	C₂²	1	1	yes	characteristic
40	#389×C₁₃₉	C₂²	1	2	yes	—
41	#389×C₁₃₉	C₂²	1	2	yes	—
42	#389×C₁₃₉	C₂²	1	1	yes	characteristic
43	#389×C₁₃₉	C₂²	1	2	yes	—
44	#389×C₁₃₉	C₂²	1	2	yes	—
45	#389×C₁₃₉	C₂²	1	4	yes	—
46	#388×C₁₃₉	C₂²	1	4	yes	—
47	#388×C₁₃₉	C₂²	1	2	yes	—
48	#388×C₁₃₉	C₂²	1	2	yes	—
49	#388×C₁₃₉	C₂²	1	4	yes	—
50	#388×C₁₃₉	C₂²	1	4	yes	—
51	#388×C₁₃₉	C₂²	1	4	yes	—
52	#388×C₁₃₉	C₂²	1	4	yes	—
53	#387×C₁₃₉	C₂²	1	4	yes	—
54	#387×C₁₃₉	C₂²	1	4	yes	—
55	#387×C₁₃₉	C₂²	1	4	yes	—
56	#387×C₁₃₉	C₂²	1	4	yes	—
57	#387×C₁₃₉	C₂²	1	4	yes	—
58	#384×C₁₃₉	C₂²	1	1	yes	characteristic
59	#382×C₁₃₉	C₂²	1	2	yes	—
60	#381×C₁₃₉	C₂²	1	4	yes	—
61	#380×C₁₃₉	C₂²	1	2	yes	—
62	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
63	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
64	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
65	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
66	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
67	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
68	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
69	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
70	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
71	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
72	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
73	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
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	2	yes	—
77	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
78	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
79	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
80	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
81	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
82	C₄³×C₁₃₉	C₂²	1	2	yes	—
83	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
84	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
85	C₂²×Q₈×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	4	yes	—
89	C₄⋊Q₈×C₁₃₉	C₂×C₄	1	8	yes	—
90	#125×C₁₃₉	C₂×C₄	1	16	yes	—
91	C₂²⋊Q₈×C₁₃₉	C₂×C₄	1	32	yes	—
92	C₂²⋊Q₈×C₁₃₉	C₂×C₄	1	16	yes	—
93	C₄×Q₈×C₁₃₉	—	2	4	no	—
94	C₄×Q₈×C₁₃₉	—	2	4	no	—
95	C₄×Q₈×C₁₃₉	—	4	4	no	—
96	C₄×Q₈×C₁₃₉	C₂×C₄	1	8	yes	—
97	C₄×D₄×C₁₃₉	C₂×C₄	1	16	yes	—
98	C₄×D₄×C₁₃₉	C₂×C₄	1	8	yes	—
99	#117×C₁₃₉	—	2	8	no	—
100	#117×C₁₃₉	—	2	8	no	—
101	#117×C₁₃₉	—	4	8	no	—
102	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	16	yes	—
103	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
104	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
105	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
106	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	1	yes	characteristic
111	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
112	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
114	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
115	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	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	4	yes	—
122	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
123	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
124	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
125	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
126	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
127	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
128	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
129	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
130	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
131	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
132	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
133	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
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	1	yes	characteristic
139	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
141	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
142	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
143	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
144	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
145	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
146	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
147	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
148	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
149	#95×C₁₃₉	C₂³	1	2	yes	—
150	#95×C₁₃₉	C₂³	1	4	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	2	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	4	yes	—
161	#95×C₁₃₉	C₂³	1	4	yes	—
162	#95×C₁₃₉	C₂³	1	2	yes	—
163	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
164	C₂×Q₈×C₁₃₉	—	2	2	no	—
165	C₂×Q₈×C₁₃₉	—	2	2	no	—
166	C₂×Q₈×C₁₃₉	—	4	2	no	—
167	C₂×Q₈×C₁₃₉	—	4	2	no	—
168	C₂×Q₈×C₁₃₉	C₂²×C₄	1	4	yes	—
169	C₂×Q₈×C₁₃₉	C₂²×C₄	1	8	yes	—
170	C₂×D₄×C₁₃₉	—	2	2	no	—
171	C₂×D₄×C₁₃₉	—	2	2	no	—
172	C₂×D₄×C₁₃₉	C₂²×C₄	1	4	yes	—
173	C₂²×C₄×C₁₃₉	—	2	4	no	—
174	C₂²×C₄×C₁₃₉	—	2	4	no	—
175	C₂²×C₄×C₁₃₉	—	4	4	no	—
176	C₂²×C₄×C₁₃₉	—	4	4	no	—
177	C₂²×C₄×C₁₃₉	C₂²×C₄	1	8	yes	—
178	C₂²×C₄×C₁₃₉	C₂²×C₄	1	16	yes	—
179	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
180	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
181	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
183	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
184	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
185	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
186	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
187	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
188	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
189	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
190	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
191	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
192	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
193	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
194	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
195	C₄⋊C₄×C₁₃₉	—	2	4	no	—
196	C₄⋊C₄×C₁₃₉	—	2	4	no	—
197	C₄⋊C₄×C₁₃₉	—	2	4	no	—
198	C₄⋊C₄×C₁₃₉	—	2	4	no	—
199	C₄⋊C₄×C₁₃₉	—	2	4	no	—
200	C₄⋊C₄×C₁₃₉	—	2	2	no	—
201	C₄⋊C₄×C₁₃₉	—	2	8	no	—
202	C₄⋊C₄×C₁₃₉	—	2	2	no	—
203	C₄⋊C₄×C₁₃₉	—	2	2	no	—
204	C₄⋊C₄×C₁₃₉	—	2	4	no	—
205	C₄⋊C₄×C₁₃₉	—	4	4	no	—
206	C₄⋊C₄×C₁₃₉	—	4	2	no	—
207	C₄⋊C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
208	C₄⋊C₄×C₁₃₉	C₂²×C₄	1	16	yes	—
209	C₄⋊C₄×C₁₃₉	C₂²×C₄	1	8	yes	—
210	C₄⋊C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
211	C₄⋊C₄×C₁₃₉	C₂²×C₄	1	8	yes	—
212	C₄⋊C₄×C₁₃₉	C₂²×C₄	1	8	yes	—
213	C₄⋊C₄×C₁₃₉	C₂²×C₄	1	16	yes	—
214	C₄⋊C₄×C₁₃₉	#41	1	4	yes	—
215	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
216	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
217	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
218	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
219	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
220	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
221	C₂²⋊C₄×C₁₃₉	C₂²×C₄	1	16	yes	—
222	C₂²⋊C₄×C₁₃₉	C₂²×C₄	1	8	yes	—
223	C₄²×C₁₃₉	—	2	8	no	—
224	C₄²×C₁₃₉	—	2	4	no	—
225	C₄²×C₁₃₉	—	2	4	no	—
226	C₄²×C₁₃₉	—	2	2	no	—
227	C₄²×C₁₃₉	—	2	4	no	—
228	C₄²×C₁₃₉	—	2	4	no	—
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	—	4	2	no	—
234	C₄²×C₁₃₉	—	4	4	no	—
235	C₄²×C₁₃₉	—	4	1	no	—
236	C₄²×C₁₃₉	—	4	4	no	—
237	C₄²×C₁₃₉	—	4	4	no	—
238	C₄²×C₁₃₉	C₂²×C₄	1	8	yes	—
239	C₄²×C₁₃₉	C₂²×C₄	1	4	yes	—
240	C₄²×C₁₃₉	#41	1	4	yes	—
241	C₂³×C₁₃₉	—	2	2	no	—
242	C₂³×C₁₃₉	—	2	2	no	—
243	C₂³×C₁₃₉	—	2	2	no	—
244	C₂³×C₁₃₉	—	2	2	no	—
245	C₂³×C₁₃₉	—	2	2	no	—
246	C₂³×C₁₃₉	—	2	2	no	—
247	C₂³×C₁₃₉	C₂³×C₄	1	4	yes	—
248	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
249	Q₈×C₁₃₉	—	2	8	no	—
250	Q₈×C₁₃₉	—	4	8	no	—
251	D₄×C₁₃₉	—	2	8	no	—
252	C₂×C₄×C₁₃₉	—	2	1	no	—
253	C₂×C₄×C₁₃₉	—	2	2	no	—
254	C₂×C₄×C₁₃₉	—	2	2	no	—
255	C₂×C₄×C₁₃₉	—	2	2	no	—
256	C₂×C₄×C₁₃₉	—	2	2	no	—
257	C₂×C₄×C₁₃₉	—	2	1	no	—
258	C₂×C₄×C₁₃₉	—	2	2	no	—
259	C₂×C₄×C₁₃₉	—	2	1	no	—
260	C₂×C₄×C₁₃₉	—	2	4	no	—
261	C₂×C₄×C₁₃₉	—	2	1	no	—
262	C₂×C₄×C₁₃₉	—	2	1	no	—
263	C₂×C₄×C₁₃₉	—	2	2	no	—
264	C₂×C₄×C₁₃₉	—	2	1	no	—
265	C₂×C₄×C₁₃₉	—	2	1	no	—
266	C₂×C₄×C₁₃₉	—	2	2	no	—
267	C₂×C₄×C₁₃₉	—	2	2	no	—
268	C₂×C₄×C₁₃₉	—	2	4	no	—
269	C₂×C₄×C₁₃₉	—	2	1	no	—
270	C₂×C₄×C₁₃₉	—	2	16	no	—
271	C₂×C₄×C₁₃₉	—	2	2	no	—
272	C₂×C₄×C₁₃₉	—	2	2	no	—
273	C₂×C₄×C₁₃₉	—	2	4	no	—
274	C₂×C₄×C₁₃₉	—	2	2	no	—
275	C₂×C₄×C₁₃₉	—	2	1	no	—
276	C₂×C₄×C₁₃₉	—	2	2	no	—
277	C₂×C₄×C₁₃₉	—	2	2	no	—
278	C₂×C₄×C₁₃₉	—	2	4	no	—
279	C₂×C₄×C₁₃₉	—	2	2	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	4	no	—
284	C₂×C₄×C₁₃₉	—	2	2	no	—
285	C₂×C₄×C₁₃₉	—	2	1	no	—
286	C₂×C₄×C₁₃₉	—	4	16	no	—
287	C₂×C₄×C₁₃₉	C₂³×C₄	1	4	yes	—
288	C₂×C₄×C₁₃₉	C₂³×C₄	1	2	yes	—
289	C₂×C₄×C₁₃₉	C₂³×C₄	1	4	yes	—
290	C₂×C₄×C₁₃₉	C₂³×C₄	1	4	yes	—
291	C₂×C₄×C₁₃₉	C₂³×C₄	1	8	yes	—
292	C₂×C₄×C₁₃₉	C₂³×C₄	1	2	yes	—
293	C₂×C₄×C₁₃₉	C₂³×C₄	1	2	yes	—
294	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
295	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
296	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
297	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
298	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
299	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
300	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
301	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
302	C₂²×C₁₃₉	—	2	4	no	—
303	C₂²×C₁₃₉	—	2	4	no	—
304	C₂²×C₁₃₉	—	2	4	no	—
305	C₂²×C₁₃₉	—	4	2	no	—
306	C₂²×C₁₃₉	—	4	2	no	—
307	C₂²×C₁₃₉	—	4	2	no	—
308	C₂²×C₁₃₉	—	4	2	no	—
309	C₂²×C₁₃₉	C₂⁴×C₄	1	1	yes	characteristic
310	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
311	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
312	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
313	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
314	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
315	C₂²×C₁₃₉	#585	1	1	yes	characteristic
316	C₄×C₁₃₉	—	2	4	no	—
317	C₄×C₁₃₉	—	2	4	no	—
318	C₄×C₁₃₉	—	2	4	no	—
319	C₄×C₁₃₉	—	2	8	no	—
320	C₄×C₁₃₉	—	2	2	no	—
321	C₄×C₁₃₉	—	2	2	no	—
322	C₄×C₁₃₉	—	2	2	no	—
323	C₄×C₁₃₉	—	2	4	no	—
324	C₄×C₁₃₉	—	2	2	no	—
325	C₄×C₁₃₉	—	4	2	no	—
326	C₄×C₁₃₉	—	4	2	no	—
327	C₄×C₁₃₉	—	4	2	no	—
328	C₄×C₁₃₉	—	4	1	no	—
329	C₄×C₁₃₉	—	4	4	no	—
330	C₄×C₁₃₉	C₄×#41	1	4	yes	—
331	C₄×C₁₃₉	#519	1	4	yes	—
332	C₂×C₁₃₉	—	4	4	no	—
333	C₂×C₁₃₉	C₂×C₄×#41	1	1	yes	characteristic
334	C₂×C₁₃₉	C₂×#519	1	1	yes	characteristic
335	C₂×C₁₃₉	C₄×H(5,𝔽₂)	1	1	yes	characteristic
336	C₂×C₁₃₉	#3507	1	1	yes	characteristic
337	C₂×C₁₃₉	#3511	1	1	yes	characteristic
338	C₂×C₁₃₉	#3515	1	1	yes	characteristic
339	C₂×C₁₃₉	#3522	1	1	yes	characteristic
340	#34317	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
341	C₁₃₉	#34317	1	1	yes	characteristic, direct product factor, Sylow
342	C₂×#554	C₂×C₁₃₉	1	1	yes	characteristic
343	#2370	C₂×C₁₃₉	1	2	yes	complemented
344	#2369	C₂×C₁₃₉	1	1	yes	characteristic, complemented
345	#2362	C₂×C₁₃₉	1	2	yes	complemented
346	#2362	C₂×C₁₃₉	1	4	yes	complemented
347	#2357	C₂×C₁₃₉	1	2	yes	—
348	#2355	C₂×C₁₃₉	1	1	yes	characteristic, complemented
349	#2354	C₂×C₁₃₉	1	1	yes	characteristic
350	#2344	C₂×C₁₃₉	1	2	yes	complemented
351	#2332	C₂×C₁₃₉	1	4	yes	complemented
352	#2323	C₂×C₁₃₉	1	2	yes	complemented
353	C₄×C₄⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
354	C₄×#125	C₂×C₁₃₉	1	2	yes	complemented
355	#2293	C₂×C₁₃₉	1	1	yes	characteristic
356	#2293	C₂×C₁₃₉	1	2	yes	—
357	#2274	C₂×C₁₃₉	1	2	yes	complemented
358	C₄²×Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
359	#554	C₄×C₁₃₉	1	16	yes	complemented
360	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
361	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
362	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
363	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
364	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
365	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
366	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
367	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
368	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
369	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
370	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
371	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
372	C₂×#117	C₂²×C₁₃₉	1	4	yes	—
373	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
374	#391	C₂²×C₁₃₉	1	2	yes	—
375	#391	C₂²×C₁₃₉	1	2	yes	—
376	#391	C₂²×C₁₃₉	1	4	yes	—
377	#390	C₂²×C₁₃₉	1	2	yes	—
378	#390	C₂²×C₁₃₉	1	1	yes	characteristic
379	#390	C₂²×C₁₃₉	1	1	yes	characteristic
380	#389	C₂²×C₁₃₉	1	1	yes	characteristic
381	#389	C₂²×C₁₃₉	1	2	yes	—
382	#389	C₂²×C₁₃₉	1	2	yes	—
383	#389	C₂²×C₁₃₉	1	2	yes	—
384	#389	C₂²×C₁₃₉	1	4	yes	—
385	#389	C₂²×C₁₃₉	1	2	yes	—
386	#389	C₂²×C₁₃₉	1	1	yes	characteristic
387	#388	C₂²×C₁₃₉	1	4	yes	—
388	#388	C₂²×C₁₃₉	1	4	yes	—
389	#388	C₂²×C₁₃₉	1	2	yes	—
390	#388	C₂²×C₁₃₉	1	4	yes	—
391	#388	C₂²×C₁₃₉	1	4	yes	—
392	#388	C₂²×C₁₃₉	1	2	yes	—
393	#388	C₂²×C₁₃₉	1	4	yes	—
394	#387	C₂²×C₁₃₉	1	4	yes	—
395	#387	C₂²×C₁₃₉	1	4	yes	—
396	#387	C₂²×C₁₃₉	1	4	yes	—
397	#387	C₂²×C₁₃₉	1	4	yes	—
398	#387	C₂²×C₁₃₉	1	4	yes	—
399	#384	C₂²×C₁₃₉	1	1	yes	characteristic
400	#382	C₂²×C₁₃₉	1	2	yes	—
401	#381	C₂²×C₁₃₉	1	4	yes	—
402	#380	C₂²×C₁₃₉	1	2	yes	—
403	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
404	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
405	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
406	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
407	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
408	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
409	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
410	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
411	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
412	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
413	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
414	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	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	2	yes	—
418	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
419	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
420	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
421	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
422	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
423	C₄³	C₂²×C₁₃₉	1	2	yes	—
424	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
425	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
426	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
427	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
428	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
429	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
430	C₄⋊Q₈	C₂×C₄×C₁₃₉	1	8	yes	—
431	#125	C₂×C₄×C₁₃₉	1	16	yes	—
432	C₂²⋊Q₈	C₂×C₄×C₁₃₉	1	32	yes	—
433	C₂²⋊Q₈	C₂×C₄×C₁₃₉	1	16	yes	—
434	C₄×Q₈	—	2	4	no	—
435	C₄×Q₈	—	2	4	no	—
436	C₄×Q₈	—	4	4	no	—
437	C₄×Q₈	C₂×C₄×C₁₃₉	1	8	yes	—
438	C₄×D₄	C₂×C₄×C₁₃₉	1	16	yes	—
439	C₄×D₄	C₂×C₄×C₁₃₉	1	8	yes	—
440	#117	—	2	8	no	—
441	#117	—	2	8	no	—
442	#117	—	4	8	no	—
443	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	16	yes	—
444	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
445	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
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	2	yes	—
451	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
452	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
453	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
454	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
455	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
456	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
457	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
458	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
459	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
460	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
461	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
462	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
463	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
464	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
465	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
466	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
467	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
468	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
469	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
470	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
471	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
472	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
473	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
474	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
475	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
476	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
486	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
487	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
488	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
489	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
490	#95	C₂³×C₁₃₉	1	2	yes	—
491	#95	C₂³×C₁₃₉	1	4	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	2	yes	—
496	#95	C₂³×C₁₃₉	1	2	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	4	yes	—
501	#95	C₂³×C₁₃₉	1	4	yes	—
502	#95	C₂³×C₁₃₉	1	4	yes	—
503	#95	C₂³×C₁₃₉	1	2	yes	—
504	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
505	C₂×Q₈	—	2	2	no	—
506	C₂×Q₈	—	2	2	no	—
507	C₂×Q₈	—	4	2	no	—
508	C₂×Q₈	—	4	2	no	—
509	C₂×Q₈	C₂²×C₄×C₁₃₉	1	4	yes	—
510	C₂×Q₈	C₂²×C₄×C₁₃₉	1	8	yes	—
511	C₂×D₄	—	2	2	no	—
512	C₂×D₄	—	2	2	no	—
513	C₂×D₄	C₂²×C₄×C₁₃₉	1	4	yes	—
514	C₂²×C₄	—	2	4	no	—
515	C₂²×C₄	—	2	4	no	—
516	C₂²×C₄	—	4	4	no	—
517	C₂²×C₄	—	4	4	no	—
518	C₂²×C₄	C₂²×C₄×C₁₃₉	1	8	yes	—
519	C₂²×C₄	C₂²×C₄×C₁₃₉	1	16	yes	—
520	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
521	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
522	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
523	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
524	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
525	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
526	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
527	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
528	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
529	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
530	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
531	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
532	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
533	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
534	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
535	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
536	C₄⋊C₄	—	2	4	no	—
537	C₄⋊C₄	—	2	4	no	—
538	C₄⋊C₄	—	2	4	no	—
539	C₄⋊C₄	—	2	4	no	—
540	C₄⋊C₄	—	2	4	no	—
541	C₄⋊C₄	—	2	2	no	—
542	C₄⋊C₄	—	2	8	no	—
543	C₄⋊C₄	—	2	2	no	—
544	C₄⋊C₄	—	2	2	no	—
545	C₄⋊C₄	—	2	4	no	—
546	C₄⋊C₄	—	4	4	no	—
547	C₄⋊C₄	—	4	2	no	—
548	C₄⋊C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
549	C₄⋊C₄	C₂²×C₄×C₁₃₉	1	16	yes	—
550	C₄⋊C₄	C₂²×C₄×C₁₃₉	1	8	yes	—
551	C₄⋊C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
552	C₄⋊C₄	C₂²×C₄×C₁₃₉	1	8	yes	—
553	C₄⋊C₄	C₂²×C₄×C₁₃₉	1	8	yes	—
554	C₄⋊C₄	C₂²×C₄×C₁₃₉	1	16	yes	—
555	C₄⋊C₄	#41×C₁₃₉	1	4	yes	—
556	C₂²⋊C₄	—	2	8	no	—
557	C₂²⋊C₄	—	2	4	no	—
558	C₂²⋊C₄	—	2	4	no	—
559	C₂²⋊C₄	—	2	4	no	—
560	C₂²⋊C₄	—	4	2	no	—
561	C₂²⋊C₄	—	4	4	no	—
562	C₂²⋊C₄	C₂²×C₄×C₁₃₉	1	16	yes	—
563	C₂²⋊C₄	C₂²×C₄×C₁₃₉	1	8	yes	—
564	C₄²	—	2	8	no	—
565	C₄²	—	2	4	no	—
566	C₄²	—	2	4	no	—
567	C₄²	—	2	2	no	—
568	C₄²	—	2	4	no	—
569	C₄²	—	2	4	no	—
570	C₄²	—	2	2	no	—
571	C₄²	—	2	2	no	—
572	C₄²	—	2	2	no	—
573	C₄²	—	2	4	no	—
574	C₄²	—	4	2	no	—
575	C₄²	—	4	4	no	—
576	C₄²	—	4	1	no	—
577	C₄²	—	4	4	no	—
578	C₄²	—	4	4	no	—
579	C₄²	C₂²×C₄×C₁₃₉	1	8	yes	—
580	C₄²	C₂²×C₄×C₁₃₉	1	4	yes	—
581	C₄²	#41×C₁₃₉	1	4	yes	—
582	C₂³	—	2	2	no	—
583	C₂³	—	2	2	no	—
584	C₂³	—	2	2	no	—
585	C₂³	—	2	2	no	—
586	C₂³	—	2	2	no	—
587	C₂³	—	2	2	no	—
588	C₂³	C₂³×C₄×C₁₃₉	1	4	yes	—
589	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
590	Q₈	—	2	8	no	—
591	Q₈	—	4	8	no	—
592	D₄	—	2	8	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	4	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	4	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	16	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	4	no	—
615	C₂×C₄	—	2	2	no	—
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	2	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	4	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	4	16	no	—
628	C₂×C₄	C₂³×C₄×C₁₃₉	1	4	yes	—
629	C₂×C₄	C₂³×C₄×C₁₃₉	1	2	yes	—
630	C₂×C₄	C₂³×C₄×C₁₃₉	1	4	yes	—
631	C₂×C₄	C₂³×C₄×C₁₃₉	1	4	yes	—
632	C₂×C₄	C₂³×C₄×C₁₃₉	1	8	yes	—
633	C₂×C₄	C₂³×C₄×C₁₃₉	1	2	yes	—
634	C₂×C₄	C₂³×C₄×C₁₃₉	1	2	yes	—
635	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
636	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
637	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
638	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
639	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
640	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
641	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
642	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
643	C₂²	—	2	4	no	—
644	C₂²	—	2	4	no	—
645	C₂²	—	2	4	no	—
646	C₂²	—	4	2	no	—
647	C₂²	—	4	2	no	—
648	C₂²	—	4	2	no	—
649	C₂²	—	4	2	no	—
650	C₂²	C₂⁴×C₄×C₁₃₉	1	1	yes	characteristic
651	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
652	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
653	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
654	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
655	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
656	C₂²	#585×C₁₃₉	1	1	yes	characteristic
657	C₄	—	2	4	no	—
658	C₄	—	2	4	no	—
659	C₄	—	2	4	no	—
660	C₄	—	2	8	no	—
661	C₄	—	2	2	no	—
662	C₄	—	2	2	no	—
663	C₄	—	2	2	no	—
664	C₄	—	2	4	no	—
665	C₄	—	2	2	no	—
666	C₄	—	4	2	no	—
667	C₄	—	4	2	no	—
668	C₄	—	4	2	no	—
669	C₄	—	4	1	no	—
670	C₄	—	4	4	no	—
671	C₄	C₄×#41×C₁₃₉	1	4	yes	—
672	C₄	#519×C₁₃₉	1	4	yes	—
673	C₂	—	4	4	no	—
674	C₂	C₂×C₄×#41×C₁₃₉	1	1	yes	characteristic
675	C₂	C₂×#519×C₁₃₉	1	1	yes	characteristic
676	C₂	C₄×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
677	C₂	#3507×C₁₃₉	1	1	yes	characteristic
678	C₂	#3511×C₁₃₉	1	1	yes	characteristic
679	C₂	#3515×C₁₃₉	1	1	yes	characteristic
680	C₂	#3522×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	C₂²×D₄×C₁₃₉	C₂³
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. #2369×C₁₃₉	C₂	semidirect
4. #2362×C₁₃₉	C₂	semidirect
5. #2362×C₁₃₉	C₂	semidirect
7. #2355×C₁₃₉	C₂	semidirect
9. #2344×C₁₃₉	C₂	semidirect
10. #2332×C₁₃₉	C₂	semidirect
11. #2323×C₁₃₉	C₂	semidirect
12. C₄×C₄⋊Q₈×C₁₃₉	C₂	semidirect
13. C₄×#125×C₁₃₉	C₂	semidirect
16. #2274×C₁₃₉	C₂	semidirect
17. C₄²×Q₈×C₁₃₉	C₂	semidirect
18. #554×C₁₃₉	C₄	semidirect
340. #34317	C₁₃₉	direct (N × H)
341. C₁₃₉	#34317	direct (N × H)
343. #2370	C₂×C₁₃₉	semidirect
344. #2369	C₂×C₁₃₉	semidirect
345. #2362	C₂×C₁₃₉	semidirect
346. #2362	C₂×C₁₃₉	semidirect
348. #2355	C₂×C₁₃₉	semidirect
350. #2344	C₂×C₁₃₉	semidirect
351. #2332	C₂×C₁₃₉	semidirect
352. #2323	C₂×C₁₃₉	semidirect
353. C₄×C₄⋊Q₈	C₂×C₁₃₉	semidirect
354. C₄×#125	C₂×C₁₃₉	semidirect
357. #2274	C₂×C₁₃₉	semidirect
358. C₄²×Q₈	C₂×C₁₃₉	semidirect
359. #554	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×#554×C₁₃₉	2
#2370×C₁₃₉	2
#2369×C₁₃₉	2
#2362×C₁₃₉	2
#2357×C₁₃₉	2
#2355×C₁₃₉	2
#2354×C₁₃₉	2
#2344×C₁₃₉	2
#2332×C₁₃₉	2
#2323×C₁₃₉	2
C₄×C₄⋊Q₈×C₁₃₉	2
C₄×#125×C₁₃₉	2
#2293×C₁₃₉	2
#2274×C₁₃₉	2
C₄²×Q₈×C₁₃₉	2
#34317	139

Subgroups — C139×#34317 #48028913

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#34317 #48028913