Subgroups — C₁₃₉×#36468 #48031064

Order 35584.

2498 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#553×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	#2859×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2854×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2602×C₁₃₉	C₂	1	4	yes	maximal, complemented
5	#2562×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2559×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#2537×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2537×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#2535×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2496×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2428×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2354×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#2352×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	D₄×C₄⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#127×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#121×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	C₄²×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	#553×C₁₃₉	—	2	16	no	—
19	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
20	C₂×#126×C₁₃₉	C₂²	1	4	yes	—
21	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#123×C₁₃₉	C₂²	1	4	yes	—
23	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
25	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
26	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
27	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	—
34	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
37	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
38	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
39	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
40	#400×C₁₃₉	C₂²	1	4	yes	—
41	#397×C₁₃₉	C₂²	1	4	yes	—
42	#394×C₁₃₉	C₂²	1	4	yes	—
43	#394×C₁₃₉	C₂²	1	4	yes	—
44	#394×C₁₃₉	C₂²	1	4	yes	—
45	#392×C₁₃₉	C₂²	1	4	yes	—
46	#390×C₁₃₉	C₂²	1	1	yes	characteristic
47	#390×C₁₃₉	C₂²	1	2	yes	—
48	#390×C₁₃₉	C₂²	1	1	yes	characteristic
49	#390×C₁₃₉	C₂²	1	2	yes	—
50	#390×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	#389×C₁₃₉	C₂²	1	2	yes	—
56	#388×C₁₃₉	C₂²	1	4	yes	—
57	#388×C₁₃₉	C₂²	1	4	yes	—
58	#388×C₁₃₉	C₂²	1	4	yes	—
59	#388×C₁₃₉	C₂²	1	4	yes	—
60	#387×C₁₃₉	C₂²	1	4	yes	—
61	#386×C₁₃₉	C₂²	1	4	yes	—
62	#386×C₁₃₉	C₂²	1	4	yes	—
63	#386×C₁₃₉	C₂²	1	4	yes	—
64	#385×C₁₃₉	C₂²	1	4	yes	—
65	#384×C₁₃₉	C₂²	1	1	yes	characteristic
66	#384×C₁₃₉	C₂²	1	1	yes	characteristic
67	#384×C₁₃₉	C₂²	1	1	yes	characteristic
68	#382×C₁₃₉	C₂²	1	2	yes	—
69	#380×C₁₃₉	C₂²	1	2	yes	—
70	#380×C₁₃₉	C₂²	1	2	yes	—
71	#380×C₁₃₉	C₂²	1	2	yes	—
72	#380×C₁₃₉	C₂²	1	2	yes	—
73	#380×C₁₃₉	C₂²	1	2	yes	—
74	#380×C₁₃₉	C₂²	1	2	yes	—
75	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
76	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
77	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
78	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
79	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
80	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
81	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
82	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
83	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
84	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
86	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
87	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
88	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
91	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
92	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
93	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
94	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
95	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
96	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
97	#127×C₁₃₉	—	2	4	no	—
98	#126×C₁₃₉	—	2	16	no	—
99	#125×C₁₃₉	—	2	8	no	—
100	#123×C₁₃₉	—	2	16	no	—
101	#121×C₁₃₉	—	2	8	no	—
102	#121×C₁₃₉	—	2	8	no	—
103	#121×C₁₃₉	—	2	8	no	—
104	#121×C₁₃₉	—	2	16	no	—
105	#121×C₁₃₉	—	4	4	no	—
106	C₄×D₄×C₁₃₉	—	2	16	no	—
107	C₄×D₄×C₁₃₉	—	2	8	no	—
108	C₄×D₄×C₁₃₉	—	2	4	no	—
109	C₄×D₄×C₁₃₉	—	2	4	no	—
110	C₄×D₄×C₁₃₉	—	2	4	no	—
111	C₄×D₄×C₁₃₉	—	2	8	no	—
112	C₄×D₄×C₁₃₉	—	2	4	no	—
113	C₄×D₄×C₁₃₉	—	4	4	no	—
114	C₄×D₄×C₁₃₉	D₄	1	8	yes	complemented
115	#117×C₁₃₉	—	2	8	no	—
116	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
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	4	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	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	1	yes	characteristic
126	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
131	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
133	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	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×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
145	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
146	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
147	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
148	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
149	C₂×C₄²×C₁₃₉	—	4	4	no	—
150	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
151	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
152	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
153	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
154	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
155	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
156	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
157	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
158	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
159	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
160	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
165	#95×C₁₃₉	C₂³	1	4	yes	—
166	#95×C₁₃₉	C₂³	1	4	yes	—
167	#95×C₁₃₉	C₂³	1	2	yes	—
168	#95×C₁₃₉	C₂³	1	2	yes	—
169	#95×C₁₃₉	C₂³	1	4	yes	—
170	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
171	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
172	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
173	C₂×D₄×C₁₃₉	—	2	8	no	—
174	C₂×D₄×C₁₃₉	—	2	8	no	—
175	C₂×D₄×C₁₃₉	—	2	4	no	—
176	C₂×D₄×C₁₃₉	—	2	4	no	—
177	C₂×D₄×C₁₃₉	—	2	8	no	—
178	C₂×D₄×C₁₃₉	—	2	4	no	—
179	C₂×D₄×C₁₃₉	—	2	2	no	—
180	C₂×D₄×C₁₃₉	—	2	2	no	—
181	C₂×D₄×C₁₃₉	—	2	2	no	—
182	C₂×D₄×C₁₃₉	—	2	4	no	—
183	C₂×D₄×C₁₃₉	—	2	2	no	—
184	C₂×D₄×C₁₃₉	—	2	2	no	—
185	C₂×D₄×C₁₃₉	—	2	2	no	—
186	C₂×D₄×C₁₃₉	—	2	2	no	—
187	C₂×D₄×C₁₃₉	—	4	2	no	—
188	C₂×D₄×C₁₃₉	—	4	2	no	—
189	C₂×D₄×C₁₃₉	—	4	4	no	—
190	C₂×D₄×C₁₃₉	—	4	4	no	—
191	C₂×D₄×C₁₃₉	—	4	4	no	—
192	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
193	C₂×D₄×C₁₃₉	#41	1	4	yes	—
194	C₂²×C₄×C₁₃₉	—	2	4	no	—
195	C₂²×C₄×C₁₃₉	—	2	4	no	—
196	C₂²×C₄×C₁₃₉	—	2	4	no	—
197	C₂²×C₄×C₁₃₉	—	2	4	no	—
198	C₂²×C₄×C₁₃₉	—	2	4	no	—
199	C₂²×C₄×C₁₃₉	—	2	4	no	—
200	C₂²×C₄×C₁₃₉	—	2	4	no	—
201	C₂²×C₄×C₁₃₉	—	2	4	no	—
202	C₂²×C₄×C₁₃₉	—	2	4	no	—
203	C₂²×C₄×C₁₃₉	—	2	4	no	—
204	C₂²×C₄×C₁₃₉	—	2	8	no	—
205	C₂²×C₄×C₁₃₉	—	4	2	no	—
206	C₂²×C₄×C₁₃₉	—	4	2	no	—
207	C₂²×C₄×C₁₃₉	—	4	2	no	—
208	C₂²×C₄×C₁₃₉	—	4	2	no	—
209	C₂²×C₄×C₁₃₉	—	4	4	no	—
210	C₂²×C₄×C₁₃₉	—	4	4	no	—
211	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
212	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
216	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
218	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
220	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
221	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
222	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
226	C₄⋊C₄×C₁₃₉	—	2	4	no	—
227	C₄⋊C₄×C₁₃₉	—	2	8	no	—
228	C₄⋊C₄×C₁₃₉	—	2	4	no	—
229	C₄⋊C₄×C₁₃₉	—	2	8	no	—
230	C₄⋊C₄×C₁₃₉	—	2	4	no	—
231	C₄⋊C₄×C₁₃₉	—	2	8	no	—
232	C₄⋊C₄×C₁₃₉	—	2	4	no	—
233	C₄⋊C₄×C₁₃₉	—	2	2	no	—
234	C₄⋊C₄×C₁₃₉	—	2	2	no	—
235	C₄⋊C₄×C₁₃₉	—	2	2	no	—
236	C₄⋊C₄×C₁₃₉	—	2	2	no	—
237	C₄⋊C₄×C₁₃₉	—	2	4	no	—
238	C₄⋊C₄×C₁₃₉	—	2	4	no	—
239	C₄⋊C₄×C₁₃₉	—	4	2	no	—
240	C₄⋊C₄×C₁₃₉	—	4	2	no	—
241	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
242	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
243	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
244	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
245	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
246	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
247	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
248	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
249	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
250	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
251	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
252	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
253	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
254	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
255	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
256	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
257	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
258	C₄²×C₁₃₉	—	2	8	no	—
259	C₄²×C₁₃₉	—	2	2	no	—
260	C₄²×C₁₃₉	—	2	2	no	—
261	C₄²×C₁₃₉	—	2	4	no	—
262	C₄²×C₁₃₉	—	4	2	no	—
263	C₄²×C₁₃₉	—	4	2	no	—
264	C₄²×C₁₃₉	—	4	1	no	—
265	C₄²×C₁₃₉	—	4	1	no	—
266	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
267	C₄²×C₁₃₉	#41	1	4	yes	—
268	C₄²×C₁₃₉	#41	1	4	yes	—
269	C₂³×C₁₃₉	—	2	2	no	—
270	C₂³×C₁₃₉	—	2	2	no	—
271	C₂³×C₁₃₉	—	2	2	no	—
272	C₂³×C₁₃₉	—	2	2	no	—
273	C₂³×C₁₃₉	—	2	2	no	—
274	C₂³×C₁₃₉	—	2	2	no	—
275	C₂³×C₁₃₉	—	2	2	no	—
276	C₂³×C₁₃₉	—	2	2	no	—
277	C₂³×C₁₃₉	—	2	2	no	—
278	C₂³×C₁₃₉	—	2	2	no	—
279	C₂³×C₁₃₉	—	2	2	no	—
280	C₂³×C₁₃₉	—	2	2	no	—
281	C₂³×C₁₃₉	—	2	2	no	—
282	C₂³×C₁₃₉	—	2	2	no	—
283	C₂³×C₁₃₉	—	2	2	no	—
284	C₂³×C₁₃₉	—	2	2	no	—
285	C₂³×C₁₃₉	—	2	2	no	—
286	C₂³×C₁₃₉	—	2	2	no	—
287	C₂³×C₁₃₉	—	2	2	no	—
288	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
289	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
290	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
291	D₄×C₁₃₉	—	2	8	no	—
292	D₄×C₁₃₉	—	2	8	no	—
293	D₄×C₁₃₉	—	4	8	no	—
294	D₄×C₁₃₉	—	4	8	no	—
295	D₄×C₁₃₉	—	4	16	no	—
296	D₄×C₁₃₉	—	4	4	no	—
297	D₄×C₁₃₉	—	8	8	no	—
298	C₂×C₄×C₁₃₉	—	2	1	no	—
299	C₂×C₄×C₁₃₉	—	2	1	no	—
300	C₂×C₄×C₁₃₉	—	2	1	no	—
301	C₂×C₄×C₁₃₉	—	2	1	no	—
302	C₂×C₄×C₁₃₉	—	2	2	no	—
303	C₂×C₄×C₁₃₉	—	2	1	no	—
304	C₂×C₄×C₁₃₉	—	2	1	no	—
305	C₂×C₄×C₁₃₉	—	2	1	no	—
306	C₂×C₄×C₁₃₉	—	2	1	no	—
307	C₂×C₄×C₁₃₉	—	2	1	no	—
308	C₂×C₄×C₁₃₉	—	2	1	no	—
309	C₂×C₄×C₁₃₉	—	2	2	no	—
310	C₂×C₄×C₁₃₉	—	2	2	no	—
311	C₂×C₄×C₁₃₉	—	2	4	no	—
312	C₂×C₄×C₁₃₉	—	2	2	no	—
313	C₂×C₄×C₁₃₉	—	2	4	no	—
314	C₂×C₄×C₁₃₉	—	2	2	no	—
315	C₂×C₄×C₁₃₉	—	2	2	no	—
316	C₂×C₄×C₁₃₉	—	2	2	no	—
317	C₂×C₄×C₁₃₉	—	2	2	no	—
318	C₂×C₄×C₁₃₉	—	2	2	no	—
319	C₂×C₄×C₁₃₉	—	2	2	no	—
320	C₂×C₄×C₁₃₉	—	2	2	no	—
321	C₂×C₄×C₁₃₉	—	2	4	no	—
322	C₂×C₄×C₁₃₉	—	2	2	no	—
323	C₂×C₄×C₁₃₉	—	2	2	no	—
324	C₂×C₄×C₁₃₉	—	2	4	no	—
325	C₂×C₄×C₁₃₉	—	2	2	no	—
326	C₂×C₄×C₁₃₉	—	2	4	no	—
327	C₂×C₄×C₁₃₉	—	2	4	no	—
328	C₂×C₄×C₁₃₉	—	4	8	no	—
329	C₂×C₄×C₁₃₉	—	4	8	no	—
330	C₂×C₄×C₁₃₉	—	4	8	no	—
331	C₂×C₄×C₁₃₉	—	4	8	no	—
332	C₂×C₄×C₁₃₉	—	4	8	no	—
333	C₂×C₄×C₁₃₉	—	8	8	no	—
334	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
335	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
336	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
337	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
338	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
339	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
340	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
341	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
342	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
343	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
344	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
345	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
346	C₂²×C₁₃₉	—	2	4	no	—
347	C₂²×C₁₃₉	—	2	4	no	—
348	C₂²×C₁₃₉	—	2	4	no	—
349	C₂²×C₁₃₉	—	2	4	no	—
350	C₂²×C₁₃₉	—	2	4	no	—
351	C₂²×C₁₃₉	—	2	4	no	—
352	C₂²×C₁₃₉	—	4	2	no	—
353	C₂²×C₁₃₉	—	4	2	no	—
354	C₂²×C₁₃₉	—	4	2	no	—
355	C₂²×C₁₃₉	—	4	2	no	—
356	C₂²×C₁₃₉	—	4	2	no	—
357	C₂²×C₁₃₉	—	4	2	no	—
358	C₂²×C₁₃₉	—	4	2	no	—
359	C₂²×C₁₃₉	—	4	2	no	—
360	C₂²×C₁₃₉	—	4	2	no	—
361	C₂²×C₁₃₉	—	4	2	no	—
362	C₂²×C₁₃₉	—	4	2	no	—
363	C₂²×C₁₃₉	—	4	2	no	—
364	C₂²×C₁₃₉	—	4	2	no	—
365	C₂²×C₁₃₉	—	4	2	no	—
366	C₂²×C₁₃₉	—	4	2	no	—
367	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
368	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
369	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
370	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
371	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
372	C₂²×C₁₃₉	#585	1	1	yes	characteristic
373	C₂²×C₁₃₉	#585	1	1	yes	characteristic
374	C₄×C₁₃₉	—	2	2	no	—
375	C₄×C₁₃₉	—	2	2	no	—
376	C₄×C₁₃₉	—	2	2	no	—
377	C₄×C₁₃₉	—	2	4	no	—
378	C₄×C₁₃₉	—	2	2	no	—
379	C₄×C₁₃₉	—	2	2	no	—
380	C₄×C₁₃₉	—	4	2	no	—
381	C₄×C₁₃₉	—	4	2	no	—
382	C₄×C₁₃₉	—	4	4	no	—
383	C₄×C₁₃₉	—	4	2	no	—
384	C₄×C₁₃₉	—	4	4	no	—
385	C₄×C₁₃₉	—	4	2	no	—
386	C₄×C₁₃₉	#532	1	4	yes	—
387	C₄×C₁₃₉	#553	1	4	yes	complemented
388	C₂×C₁₃₉	—	4	4	no	—
389	C₂×C₁₃₉	—	4	4	no	—
390	C₂×C₁₃₉	—	8	2	no	—
391	C₂×C₁₃₉	C₂×#532	1	1	yes	characteristic
392	C₂×C₁₃₉	D₄×#41	1	1	yes	characteristic
393	C₂×C₁₃₉	C₂×#553	1	1	yes	characteristic
394	C₂×C₁₃₉	#3475	1	1	yes	characteristic
395	C₂×C₁₃₉	#3496	1	1	yes	characteristic
396	C₂×C₁₃₉	#3506	1	1	yes	characteristic
397	C₂×C₁₃₉	#3512	1	1	yes	characteristic
398	#36468	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
399	C₁₃₉	#36468	1	1	yes	characteristic, direct product factor, Sylow
400	C₂×#553	C₂×C₁₃₉	1	2	yes	complemented
401	#2859	C₂×C₁₃₉	1	1	yes	characteristic, complemented
402	#2854	C₂×C₁₃₉	1	2	yes	complemented
403	#2602	C₂×C₁₃₉	1	4	yes	complemented
404	#2562	C₂×C₁₃₉	1	2	yes	complemented
405	#2559	C₂×C₁₃₉	1	4	yes	complemented
406	#2537	C₂×C₁₃₉	1	1	yes	characteristic, complemented
407	#2537	C₂×C₁₃₉	1	1	yes	characteristic, complemented
408	#2535	C₂×C₁₃₉	1	2	yes	complemented
409	#2496	C₂×C₁₃₉	1	2	yes	complemented
410	#2428	C₂×C₁₃₉	1	2	yes	complemented
411	#2354	C₂×C₁₃₉	1	1	yes	characteristic, complemented
412	#2352	C₂×C₁₃₉	1	2	yes	complemented
413	D₄×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
414	C₄×#127	C₂×C₁₃₉	1	1	yes	characteristic, complemented
415	C₄×#121	C₂×C₁₃₉	1	2	yes	complemented
416	C₄²×D₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
417	#553	—	2	16	no	—
418	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
419	C₂×#126	C₂²×C₁₃₉	1	4	yes	—
420	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
421	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
422	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
423	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
424	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
425	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
426	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
427	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
428	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
429	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
430	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
431	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	—
432	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
433	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
434	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
435	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
436	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
437	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
438	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
439	#400	C₂²×C₁₃₉	1	4	yes	—
440	#397	C₂²×C₁₃₉	1	4	yes	—
441	#394	C₂²×C₁₃₉	1	4	yes	—
442	#394	C₂²×C₁₃₉	1	4	yes	—
443	#394	C₂²×C₁₃₉	1	4	yes	—
444	#392	C₂²×C₁₃₉	1	4	yes	—
445	#390	C₂²×C₁₃₉	1	1	yes	characteristic
446	#390	C₂²×C₁₃₉	1	2	yes	—
447	#390	C₂²×C₁₃₉	1	1	yes	characteristic
448	#390	C₂²×C₁₃₉	1	2	yes	—
449	#390	C₂²×C₁₃₉	1	2	yes	—
450	#389	C₂²×C₁₃₉	1	2	yes	—
451	#389	C₂²×C₁₃₉	1	2	yes	—
452	#389	C₂²×C₁₃₉	1	2	yes	—
453	#389	C₂²×C₁₃₉	1	2	yes	—
454	#389	C₂²×C₁₃₉	1	2	yes	—
455	#388	C₂²×C₁₃₉	1	4	yes	—
456	#388	C₂²×C₁₃₉	1	4	yes	—
457	#388	C₂²×C₁₃₉	1	4	yes	—
458	#388	C₂²×C₁₃₉	1	4	yes	—
459	#387	C₂²×C₁₃₉	1	4	yes	—
460	#386	C₂²×C₁₃₉	1	4	yes	—
461	#386	C₂²×C₁₃₉	1	4	yes	—
462	#386	C₂²×C₁₃₉	1	4	yes	—
463	#385	C₂²×C₁₃₉	1	4	yes	—
464	#384	C₂²×C₁₃₉	1	1	yes	characteristic
465	#384	C₂²×C₁₃₉	1	1	yes	characteristic
466	#384	C₂²×C₁₃₉	1	1	yes	characteristic
467	#382	C₂²×C₁₃₉	1	2	yes	—
468	#380	C₂²×C₁₃₉	1	2	yes	—
469	#380	C₂²×C₁₃₉	1	2	yes	—
470	#380	C₂²×C₁₃₉	1	2	yes	—
471	#380	C₂²×C₁₃₉	1	2	yes	—
472	#380	C₂²×C₁₃₉	1	2	yes	—
473	#380	C₂²×C₁₃₉	1	2	yes	—
474	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
475	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
476	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
477	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
478	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
479	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
480	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
481	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
482	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
483	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
484	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
485	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
486	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
487	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
488	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
489	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
490	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
491	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
492	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
493	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
494	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
495	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
496	#127	—	2	4	no	—
497	#126	—	2	16	no	—
498	#125	—	2	8	no	—
499	#123	—	2	16	no	—
500	#121	—	2	8	no	—
501	#121	—	2	8	no	—
502	#121	—	2	8	no	—
503	#121	—	2	16	no	—
504	#121	—	4	4	no	—
505	C₄×D₄	—	2	16	no	—
506	C₄×D₄	—	2	8	no	—
507	C₄×D₄	—	2	4	no	—
508	C₄×D₄	—	2	4	no	—
509	C₄×D₄	—	2	4	no	—
510	C₄×D₄	—	2	8	no	—
511	C₄×D₄	—	2	4	no	—
512	C₄×D₄	—	4	4	no	—
513	C₄×D₄	D₄×C₁₃₉	1	8	yes	complemented
514	#117	—	2	8	no	—
515	C₂×C₄⋊C₄	—	2	8	no	—
516	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
517	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
518	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
519	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
520	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
521	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
522	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
523	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
524	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
525	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
526	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
527	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
528	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
529	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
530	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
531	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
532	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
533	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
534	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
535	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
536	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
537	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
538	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
539	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
540	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
541	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
542	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
545	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
546	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
547	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
548	C₂×C₄²	—	4	4	no	—
549	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
550	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
551	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
552	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
553	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
554	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
555	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
556	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
557	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
558	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
559	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
560	#95	C₂³×C₁₃₉	1	2	yes	—
561	#95	C₂³×C₁₃₉	1	2	yes	—
562	#95	C₂³×C₁₃₉	1	2	yes	—
563	#95	C₂³×C₁₃₉	1	4	yes	—
564	#95	C₂³×C₁₃₉	1	4	yes	—
565	#95	C₂³×C₁₃₉	1	4	yes	—
566	#95	C₂³×C₁₃₉	1	4	yes	—
567	#95	C₂³×C₁₃₉	1	4	yes	—
568	#95	C₂³×C₁₃₉	1	4	yes	—
569	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
570	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
571	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
572	C₂×D₄	—	2	8	no	—
573	C₂×D₄	—	2	8	no	—
574	C₂×D₄	—	2	4	no	—
575	C₂×D₄	—	2	4	no	—
576	C₂×D₄	—	2	8	no	—
577	C₂×D₄	—	2	4	no	—
578	C₂×D₄	—	2	2	no	—
579	C₂×D₄	—	2	2	no	—
580	C₂×D₄	—	2	2	no	—
581	C₂×D₄	—	2	4	no	—
582	C₂×D₄	—	2	2	no	—
583	C₂×D₄	—	2	2	no	—
584	C₂×D₄	—	2	2	no	—
585	C₂×D₄	—	2	2	no	—
586	C₂×D₄	—	4	2	no	—
587	C₂×D₄	—	4	2	no	—
588	C₂×D₄	—	4	4	no	—
589	C₂×D₄	—	4	4	no	—
590	C₂×D₄	—	4	4	no	—
591	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
592	C₂×D₄	#41×C₁₃₉	1	4	yes	—
593	C₂²×C₄	—	2	4	no	—
594	C₂²×C₄	—	2	4	no	—
595	C₂²×C₄	—	2	4	no	—
596	C₂²×C₄	—	2	4	no	—
597	C₂²×C₄	—	2	4	no	—
598	C₂²×C₄	—	2	4	no	—
599	C₂²×C₄	—	2	4	no	—
600	C₂²×C₄	—	2	4	no	—
601	C₂²×C₄	—	2	4	no	—
602	C₂²×C₄	—	2	4	no	—
603	C₂²×C₄	—	2	8	no	—
604	C₂²×C₄	—	4	2	no	—
605	C₂²×C₄	—	4	2	no	—
606	C₂²×C₄	—	4	2	no	—
607	C₂²×C₄	—	4	2	no	—
608	C₂²×C₄	—	4	4	no	—
609	C₂²×C₄	—	4	4	no	—
610	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
611	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
612	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
613	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
614	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
615	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
616	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
617	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
618	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
619	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
620	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
621	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
622	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
623	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
624	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	8	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	8	no	—
629	C₄⋊C₄	—	2	4	no	—
630	C₄⋊C₄	—	2	8	no	—
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	—	2	2	no	—
633	C₄⋊C₄	—	2	2	no	—
634	C₄⋊C₄	—	2	2	no	—
635	C₄⋊C₄	—	2	2	no	—
636	C₄⋊C₄	—	2	4	no	—
637	C₄⋊C₄	—	2	4	no	—
638	C₄⋊C₄	—	4	2	no	—
639	C₄⋊C₄	—	4	2	no	—
640	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
641	C₂²⋊C₄	—	2	8	no	—
642	C₂²⋊C₄	—	2	8	no	—
643	C₂²⋊C₄	—	2	8	no	—
644	C₂²⋊C₄	—	2	8	no	—
645	C₂²⋊C₄	—	2	4	no	—
646	C₂²⋊C₄	—	2	4	no	—
647	C₂²⋊C₄	—	2	4	no	—
648	C₂²⋊C₄	—	2	4	no	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	—	2	4	no	—
653	C₂²⋊C₄	—	4	4	no	—
654	C₂²⋊C₄	—	4	4	no	—
655	C₂²⋊C₄	—	4	4	no	—
656	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
657	C₄²	—	2	8	no	—
658	C₄²	—	2	2	no	—
659	C₄²	—	2	2	no	—
660	C₄²	—	2	4	no	—
661	C₄²	—	4	2	no	—
662	C₄²	—	4	2	no	—
663	C₄²	—	4	1	no	—
664	C₄²	—	4	1	no	—
665	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
666	C₄²	#41×C₁₃₉	1	4	yes	—
667	C₄²	#41×C₁₃₉	1	4	yes	—
668	C₂³	—	2	2	no	—
669	C₂³	—	2	2	no	—
670	C₂³	—	2	2	no	—
671	C₂³	—	2	2	no	—
672	C₂³	—	2	2	no	—
673	C₂³	—	2	2	no	—
674	C₂³	—	2	2	no	—
675	C₂³	—	2	2	no	—
676	C₂³	—	2	2	no	—
677	C₂³	—	2	2	no	—
678	C₂³	—	2	2	no	—
679	C₂³	—	2	2	no	—
680	C₂³	—	2	2	no	—
681	C₂³	—	2	2	no	—
682	C₂³	—	2	2	no	—
683	C₂³	—	2	2	no	—
684	C₂³	—	2	2	no	—
685	C₂³	—	2	2	no	—
686	C₂³	—	2	2	no	—
687	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
688	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
689	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
690	D₄	—	2	8	no	—
691	D₄	—	2	8	no	—
692	D₄	—	4	8	no	—
693	D₄	—	4	8	no	—
694	D₄	—	4	16	no	—
695	D₄	—	4	4	no	—
696	D₄	—	8	8	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	4	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	4	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	4	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	4	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	4	no	—
726	C₂×C₄	—	2	4	no	—
727	C₂×C₄	—	4	8	no	—
728	C₂×C₄	—	4	8	no	—
729	C₂×C₄	—	4	8	no	—
730	C₂×C₄	—	4	8	no	—
731	C₂×C₄	—	4	8	no	—
732	C₂×C₄	—	8	8	no	—
733	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
734	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
735	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
736	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
737	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
738	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
739	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
740	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
741	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
742	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
743	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
744	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
745	C₂²	—	2	4	no	—
746	C₂²	—	2	4	no	—
747	C₂²	—	2	4	no	—
748	C₂²	—	2	4	no	—
749	C₂²	—	2	4	no	—
750	C₂²	—	2	4	no	—
751	C₂²	—	4	2	no	—
752	C₂²	—	4	2	no	—
753	C₂²	—	4	2	no	—
754	C₂²	—	4	2	no	—
755	C₂²	—	4	2	no	—
756	C₂²	—	4	2	no	—
757	C₂²	—	4	2	no	—
758	C₂²	—	4	2	no	—
759	C₂²	—	4	2	no	—
760	C₂²	—	4	2	no	—
761	C₂²	—	4	2	no	—
762	C₂²	—	4	2	no	—
763	C₂²	—	4	2	no	—
764	C₂²	—	4	2	no	—
765	C₂²	—	4	2	no	—
766	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
767	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
768	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
769	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
770	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
771	C₂²	#585×C₁₃₉	1	1	yes	characteristic
772	C₂²	#585×C₁₃₉	1	1	yes	characteristic
773	C₄	—	2	2	no	—
774	C₄	—	2	2	no	—
775	C₄	—	2	2	no	—
776	C₄	—	2	4	no	—
777	C₄	—	2	2	no	—
778	C₄	—	2	2	no	—
779	C₄	—	4	2	no	—
780	C₄	—	4	2	no	—
781	C₄	—	4	4	no	—
782	C₄	—	4	2	no	—
783	C₄	—	4	4	no	—
784	C₄	—	4	2	no	—
785	C₄	#532×C₁₃₉	1	4	yes	—
786	C₄	#553×C₁₃₉	1	4	yes	complemented
787	C₂	—	4	4	no	—
788	C₂	—	4	4	no	—
789	C₂	—	8	2	no	—
790	C₂	C₂×#532×C₁₃₉	1	1	yes	characteristic
791	C₂	D₄×#41×C₁₃₉	1	1	yes	characteristic
792	C₂	C₂×#553×C₁₃₉	1	1	yes	characteristic
793	C₂	#3475×C₁₃₉	1	1	yes	characteristic
794	C₂	#3496×C₁₃₉	1	1	yes	characteristic
795	C₂	#3506×C₁₃₉	1	1	yes	characteristic
796	C₂	#3512×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
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
1. C₂×#553×C₁₃₉	C₂	semidirect
2. #2859×C₁₃₉	C₂	semidirect
3. #2854×C₁₃₉	C₂	semidirect
4. #2602×C₁₃₉	C₂	semidirect
5. #2562×C₁₃₉	C₂	semidirect
6. #2559×C₁₃₉	C₂	semidirect
7. #2537×C₁₃₉	C₂	semidirect
8. #2537×C₁₃₉	C₂	semidirect
9. #2535×C₁₃₉	C₂	semidirect
10. #2496×C₁₃₉	C₂	semidirect
11. #2428×C₁₃₉	C₂	semidirect
12. #2354×C₁₃₉	C₂	semidirect
13. #2352×C₁₃₉	C₂	semidirect
14. D₄×C₄⋊C₄×C₁₃₉	C₂	semidirect
15. C₄×#127×C₁₃₉	C₂	semidirect
16. C₄×#121×C₁₃₉	C₂	semidirect
17. C₄²×D₄×C₁₃₉	C₂	semidirect
114. C₄×D₄×C₁₃₉	D₄	semidirect
387. C₄×C₁₃₉	#553	semidirect
398. #36468	C₁₃₉	direct (N × H)
399. C₁₃₉	#36468	direct (N × H)
400. C₂×#553	C₂×C₁₃₉	semidirect
401. #2859	C₂×C₁₃₉	semidirect
402. #2854	C₂×C₁₃₉	semidirect
403. #2602	C₂×C₁₃₉	semidirect
404. #2562	C₂×C₁₃₉	semidirect
405. #2559	C₂×C₁₃₉	semidirect
406. #2537	C₂×C₁₃₉	semidirect
407. #2537	C₂×C₁₃₉	semidirect
408. #2535	C₂×C₁₃₉	semidirect
409. #2496	C₂×C₁₃₉	semidirect
410. #2428	C₂×C₁₃₉	semidirect
411. #2354	C₂×C₁₃₉	semidirect
412. #2352	C₂×C₁₃₉	semidirect
413. D₄×C₄⋊C₄	C₂×C₁₃₉	semidirect
414. C₄×#127	C₂×C₁₃₉	semidirect
415. C₄×#121	C₂×C₁₃₉	semidirect
416. C₄²×D₄	C₂×C₁₃₉	semidirect
513. C₄×D₄	D₄×C₁₃₉	semidirect
786. C₄	#553×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#553×C₁₃₉	2
#2859×C₁₃₉	2
#2854×C₁₃₉	2
#2602×C₁₃₉	2
#2562×C₁₃₉	2
#2559×C₁₃₉	2
#2537×C₁₃₉	2
#2535×C₁₃₉	2
#2496×C₁₃₉	2
#2428×C₁₃₉	2
#2354×C₁₃₉	2
#2352×C₁₃₉	2
D₄×C₄⋊C₄×C₁₃₉	2
C₄×#127×C₁₃₉	2
C₄×#121×C₁₃₉	2
C₄²×D₄×C₁₃₉	2
#36468	139

Subgroups — C139×#36468 #48031064

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36468 #48031064