Subgroups — C₁₃₉×#35941 #48030537

Order 35584.

2750 conjugacy classes of subgroups.

The subgroup lattice has 800 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	1	yes	maximal, characteristic, complemented
2	C₂×#550×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2661×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2641×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2584×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2559×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#2543×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2541×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#2430×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2428×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2428×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2428×C₁₃₉	C₂	1	4	yes	maximal, complemented
13	#2398×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2388×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2363×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2361×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	#2275×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₁₃₉	C₂²	1	2	yes	—
19	#553×C₁₃₉	—	2	8	no	—
20	#550×C₁₃₉	—	2	8	no	—
21	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
22	C₂×#127×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#127×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
25	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
27	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
28	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
29	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
30	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
31	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
32	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
34	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
35	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
36	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
38	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
40	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
41	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	—
42	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
43	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
44	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
45	#400×C₁₃₉	C₂²	1	2	yes	—
46	#398×C₁₃₉	C₂²	1	2	yes	—
47	#397×C₁₃₉	C₂²	1	1	yes	characteristic
48	#397×C₁₃₉	C₂²	1	1	yes	characteristic
49	#395×C₁₃₉	C₂²	1	2	yes	—
50	#394×C₁₃₉	C₂²	1	2	yes	—
51	#394×C₁₃₉	C₂²	1	4	yes	—
52	#394×C₁₃₉	C₂²	1	4	yes	—
53	#394×C₁₃₉	C₂²	1	4	yes	—
54	#394×C₁₃₉	C₂²	1	2	yes	—
55	#394×C₁₃₉	C₂²	1	2	yes	—
56	#393×C₁₃₉	C₂²	1	1	yes	characteristic
57	#393×C₁₃₉	C₂²	1	1	yes	characteristic
58	#392×C₁₃₉	C₂²	1	2	yes	—
59	#392×C₁₃₉	C₂²	1	2	yes	—
60	#392×C₁₃₉	C₂²	1	4	yes	—
61	#392×C₁₃₉	C₂²	1	4	yes	—
62	#390×C₁₃₉	C₂²	1	2	yes	—
63	#390×C₁₃₉	C₂²	1	2	yes	—
64	#390×C₁₃₉	C₂²	1	2	yes	—
65	#390×C₁₃₉	C₂²	1	4	yes	—
66	#389×C₁₃₉	C₂²	1	4	yes	—
67	#389×C₁₃₉	C₂²	1	2	yes	—
68	#389×C₁₃₉	C₂²	1	2	yes	—
69	#388×C₁₃₉	C₂²	1	4	yes	—
70	#388×C₁₃₉	C₂²	1	4	yes	—
71	#386×C₁₃₉	C₂²	1	4	yes	—
72	#386×C₁₃₉	C₂²	1	4	yes	—
73	#386×C₁₃₉	C₂²	1	4	yes	—
74	#386×C₁₃₉	C₂²	1	4	yes	—
75	#385×C₁₃₉	C₂²	1	4	yes	—
76	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
77	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
78	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
79	C₄×C₂²⋊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	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
83	#376×C₁₃₉	C₂²	1	1	yes	characteristic
84	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
85	C₂×#41×C₁₃₉	—	2	8	no	—
86	C₂×#41×C₁₃₉	—	4	8	no	—
87	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
88	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
89	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
90	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
92	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
93	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
94	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
95	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
96	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
97	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
98	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
99	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
102	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
103	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
104	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
105	#127×C₁₃₉	—	2	8	no	—
106	#127×C₁₃₉	—	2	4	no	—
107	#127×C₁₃₉	—	4	4	no	—
108	#126×C₁₃₉	—	2	8	no	—
109	#125×C₁₃₉	—	2	4	no	—
110	#123×C₁₃₉	—	2	8	no	—
111	#121×C₁₃₉	—	2	4	no	—
112	#121×C₁₃₉	—	2	4	no	—
113	#121×C₁₃₉	—	2	8	no	—
114	#121×C₁₃₉	—	2	8	no	—
115	#121×C₁₃₉	—	2	8	no	—
116	#121×C₁₃₉	—	2	16	no	—
117	#121×C₁₃₉	—	2	8	no	—
118	#121×C₁₃₉	—	4	8	no	—
119	#121×C₁₃₉	—	4	8	no	—
120	C₄×Q₈×C₁₃₉	—	2	4	no	—
121	C₄×D₄×C₁₃₉	—	2	8	no	—
122	C₄×D₄×C₁₃₉	—	2	8	no	—
123	C₄×D₄×C₁₃₉	—	2	8	no	—
124	C₄×D₄×C₁₃₉	—	2	4	no	—
125	C₄×D₄×C₁₃₉	—	4	8	no	—
126	C₄×D₄×C₁₃₉	D₄	1	8	yes	complemented
127	#117×C₁₃₉	—	2	4	no	—
128	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
129	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
131	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
132	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
136	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
137	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
139	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
142	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
147	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
149	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
152	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
153	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
155	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
156	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
157	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
158	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
159	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
160	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
161	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
162	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
163	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
164	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
165	#95×C₁₃₉	C₂³	1	2	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	1	yes	characteristic
170	#95×C₁₃₉	C₂³	1	1	yes	characteristic
171	#95×C₁₃₉	C₂³	1	4	yes	—
172	#95×C₁₃₉	C₂³	1	2	yes	—
173	#95×C₁₃₉	C₂³	1	2	yes	—
174	#95×C₁₃₉	C₂³	1	2	yes	—
175	#95×C₁₃₉	C₂³	1	4	yes	—
176	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
177	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
178	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
179	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
180	#41×C₁₃₉	—	4	32	no	—
181	C₂×Q₈×C₁₃₉	—	2	2	no	—
182	C₂×Q₈×C₁₃₉	—	2	4	no	—
183	C₂×D₄×C₁₃₉	—	2	4	no	—
184	C₂×D₄×C₁₃₉	—	2	8	no	—
185	C₂×D₄×C₁₃₉	—	2	4	no	—
186	C₂×D₄×C₁₃₉	—	2	8	no	—
187	C₂×D₄×C₁₃₉	—	2	2	no	—
188	C₂×D₄×C₁₃₉	—	2	4	no	—
189	C₂×D₄×C₁₃₉	—	2	8	no	—
190	C₂×D₄×C₁₃₉	—	2	2	no	—
191	C₂×D₄×C₁₃₉	—	2	4	no	—
192	C₂×D₄×C₁₃₉	—	2	4	no	—
193	C₂×D₄×C₁₃₉	—	2	4	no	—
194	C₂×D₄×C₁₃₉	—	2	4	no	—
195	C₂×D₄×C₁₃₉	—	2	8	no	—
196	C₂×D₄×C₁₃₉	—	2	4	no	—
197	C₂×D₄×C₁₃₉	—	2	4	no	—
198	C₂×D₄×C₁₃₉	—	2	8	no	—
199	C₂×D₄×C₁₃₉	—	2	8	no	—
200	C₂×D₄×C₁₃₉	—	4	4	no	—
201	C₂×D₄×C₁₃₉	—	4	1	no	—
202	C₂×D₄×C₁₃₉	—	4	2	no	—
203	C₂×D₄×C₁₃₉	—	4	4	no	—
204	C₂×D₄×C₁₃₉	—	4	4	no	—
205	C₂×D₄×C₁₃₉	—	4	4	no	—
206	C₂×D₄×C₁₃₉	—	4	4	no	—
207	C₂×D₄×C₁₃₉	—	4	4	no	—
208	C₂×D₄×C₁₃₉	—	4	2	no	—
209	C₂×D₄×C₁₃₉	—	4	4	no	—
210	C₂×D₄×C₁₃₉	—	4	2	no	—
211	C₂×D₄×C₁₃₉	—	4	4	no	—
212	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
213	C₂²×C₄×C₁₃₉	—	2	2	no	—
214	C₂²×C₄×C₁₃₉	—	2	2	no	—
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	8	no	—
219	C₂²×C₄×C₁₃₉	—	2	4	no	—
220	C₂²×C₄×C₁₃₉	—	2	8	no	—
221	C₂²×C₄×C₁₃₉	—	4	4	no	—
222	C₂²×C₄×C₁₃₉	—	4	4	no	—
223	C₂²×C₄×C₁₃₉	—	4	4	no	—
224	C₂²×C₄×C₁₃₉	—	4	4	no	—
225	C₂²×C₄×C₁₃₉	—	4	4	no	—
226	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
227	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
230	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
232	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
235	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
237	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
238	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
240	C₄⋊C₄×C₁₃₉	—	2	2	no	—
241	C₄⋊C₄×C₁₃₉	—	2	4	no	—
242	C₄⋊C₄×C₁₃₉	—	2	2	no	—
243	C₄⋊C₄×C₁₃₉	—	2	4	no	—
244	C₄⋊C₄×C₁₃₉	—	2	2	no	—
245	C₄⋊C₄×C₁₃₉	—	2	4	no	—
246	C₄⋊C₄×C₁₃₉	—	2	2	no	—
247	C₄⋊C₄×C₁₃₉	—	2	4	no	—
248	C₄⋊C₄×C₁₃₉	—	2	8	no	—
249	C₄⋊C₄×C₁₃₉	—	4	4	no	—
250	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
251	C₄⋊C₄×C₁₃₉	#41	1	8	yes	complemented
252	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
253	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
254	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
255	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
256	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
257	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
258	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
259	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
260	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
261	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
262	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
263	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
264	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
265	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
266	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
267	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
268	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
269	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
270	C₄²×C₁₃₉	—	2	4	no	—
271	C₄²×C₁₃₉	—	2	4	no	—
272	C₄²×C₁₃₉	—	2	4	no	—
273	C₄²×C₁₃₉	—	4	4	no	—
274	C₄²×C₁₃₉	—	4	2	no	—
275	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
276	C₂³×C₁₃₉	—	2	1	no	—
277	C₂³×C₁₃₉	—	2	4	no	—
278	C₂³×C₁₃₉	—	2	2	no	—
279	C₂³×C₁₃₉	—	2	2	no	—
280	C₂³×C₁₃₉	—	2	4	no	—
281	C₂³×C₁₃₉	—	2	2	no	—
282	C₂³×C₁₃₉	—	2	1	no	—
283	C₂³×C₁₃₉	—	2	2	no	—
284	C₂³×C₁₃₉	—	2	1	no	—
285	C₂³×C₁₃₉	—	2	4	no	—
286	C₂³×C₁₃₉	—	2	4	no	—
287	C₂³×C₁₃₉	—	2	4	no	—
288	C₂³×C₁₃₉	—	2	2	no	—
289	C₂³×C₁₃₉	—	2	2	no	—
290	C₂³×C₁₃₉	—	2	4	no	—
291	C₂³×C₁₃₉	—	2	4	no	—
292	C₂³×C₁₃₉	—	2	4	no	—
293	C₂³×C₁₃₉	—	2	1	no	—
294	C₂³×C₁₃₉	—	2	1	no	—
295	C₂³×C₁₃₉	—	2	4	no	—
296	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
297	C₂³×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
298	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
299	Q₈×C₁₃₉	—	2	8	no	—
300	D₄×C₁₃₉	—	2	8	no	—
301	D₄×C₁₃₉	—	4	4	no	—
302	D₄×C₁₃₉	—	4	16	no	—
303	D₄×C₁₃₉	—	4	16	no	—
304	D₄×C₁₃₉	—	4	8	no	—
305	D₄×C₁₃₉	—	4	8	no	—
306	D₄×C₁₃₉	—	4	8	no	—
307	D₄×C₁₃₉	—	8	4	no	—
308	D₄×C₁₃₉	—	8	8	no	—
309	D₄×C₁₃₉	—	8	4	no	—
310	D₄×C₁₃₉	—	8	8	no	—
311	C₂×C₄×C₁₃₉	—	2	2	no	—
312	C₂×C₄×C₁₃₉	—	2	1	no	—
313	C₂×C₄×C₁₃₉	—	2	4	no	—
314	C₂×C₄×C₁₃₉	—	2	4	no	—
315	C₂×C₄×C₁₃₉	—	2	4	no	—
316	C₂×C₄×C₁₃₉	—	2	2	no	—
317	C₂×C₄×C₁₃₉	—	2	2	no	—
318	C₂×C₄×C₁₃₉	—	2	1	no	—
319	C₂×C₄×C₁₃₉	—	2	1	no	—
320	C₂×C₄×C₁₃₉	—	2	2	no	—
321	C₂×C₄×C₁₃₉	—	2	2	no	—
322	C₂×C₄×C₁₃₉	—	2	1	no	—
323	C₂×C₄×C₁₃₉	—	2	2	no	—
324	C₂×C₄×C₁₃₉	—	2	2	no	—
325	C₂×C₄×C₁₃₉	—	2	2	no	—
326	C₂×C₄×C₁₃₉	—	2	2	no	—
327	C₂×C₄×C₁₃₉	—	2	2	no	—
328	C₂×C₄×C₁₃₉	—	2	2	no	—
329	C₂×C₄×C₁₃₉	—	2	2	no	—
330	C₂×C₄×C₁₃₉	—	2	2	no	—
331	C₂×C₄×C₁₃₉	—	2	2	no	—
332	C₂×C₄×C₁₃₉	—	2	4	no	—
333	C₂×C₄×C₁₃₉	—	2	2	no	—
334	C₂×C₄×C₁₃₉	—	2	2	no	—
335	C₂×C₄×C₁₃₉	—	2	2	no	—
336	C₂×C₄×C₁₃₉	—	2	2	no	—
337	C₂×C₄×C₁₃₉	—	4	8	no	—
338	C₂×C₄×C₁₃₉	—	4	16	no	—
339	C₂×C₄×C₁₃₉	—	4	4	no	—
340	C₂×C₄×C₁₃₉	—	4	4	no	—
341	C₂×C₄×C₁₃₉	—	8	4	no	—
342	C₂×C₄×C₁₃₉	—	8	8	no	—
343	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
344	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
345	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
346	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
347	C₂×C₄×C₁₃₉	C₂×#41	1	8	yes	—
348	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
349	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
350	C₂²×C₁₃₉	—	2	4	no	—
351	C₂²×C₁₃₉	—	2	4	no	—
352	C₂²×C₁₃₉	—	2	2	no	—
353	C₂²×C₁₃₉	—	2	4	no	—
354	C₂²×C₁₃₉	—	2	4	no	—
355	C₂²×C₁₃₉	—	4	1	no	—
356	C₂²×C₁₃₉	—	4	1	no	—
357	C₂²×C₁₃₉	—	4	4	no	—
358	C₂²×C₁₃₉	—	4	2	no	—
359	C₂²×C₁₃₉	—	4	4	no	—
360	C₂²×C₁₃₉	—	4	1	no	—
361	C₂²×C₁₃₉	—	4	4	no	—
362	C₂²×C₁₃₉	—	4	4	no	—
363	C₂²×C₁₃₉	—	4	1	no	—
364	C₂²×C₁₃₉	—	4	1	no	—
365	C₂²×C₁₃₉	—	4	4	no	—
366	C₂²×C₁₃₉	—	4	4	no	—
367	C₂²×C₁₃₉	—	4	4	no	—
368	C₂²×C₁₃₉	—	4	2	no	—
369	C₂²×C₁₃₉	—	4	4	no	—
370	C₂²×C₁₃₉	—	4	2	no	—
371	C₂²×C₁₃₉	—	4	4	no	—
372	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
373	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
374	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
375	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
376	C₂²×C₁₃₉	#585	1	1	yes	characteristic
377	C₄×C₁₃₉	—	2	4	no	—
378	C₄×C₁₃₉	—	2	2	no	—
379	C₄×C₁₃₉	—	2	4	no	—
380	C₄×C₁₃₉	—	2	2	no	—
381	C₄×C₁₃₉	—	2	8	no	—
382	C₄×C₁₃₉	—	4	1	no	—
383	C₄×C₁₃₉	—	4	1	no	—
384	C₄×C₁₃₉	—	4	2	no	—
385	C₄×C₁₃₉	—	4	2	no	—
386	C₄×C₁₃₉	—	4	2	no	—
387	C₄×C₁₃₉	—	4	2	no	—
388	C₄×C₁₃₉	—	4	2	no	—
389	C₄×C₁₃₉	#532	1	4	yes	—
390	C₂×C₁₃₉	—	4	4	no	—
391	C₂×C₁₃₉	—	4	2	no	—
392	C₂×C₁₃₉	—	8	1	no	—
393	C₂×C₁₃₉	—	8	4	no	—
394	C₂×C₁₃₉	C₂×#532	1	1	yes	characteristic
395	C₂×C₁₃₉	#3484	1	1	yes	characteristic
396	C₂×C₁₃₉	#3488	1	1	yes	characteristic
397	C₂×C₁₃₉	#3517	1	2	yes	—
398	C₂×C₁₃₉	#3519	1	2	yes	—
399	#35941	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
400	C₁₃₉	#35941	1	1	yes	characteristic, direct product factor, Sylow
401	C₂×#553	C₂×C₁₃₉	1	1	yes	characteristic, complemented
402	C₂×#550	C₂×C₁₃₉	1	1	yes	characteristic, complemented
403	#2661	C₂×C₁₃₉	1	2	yes	complemented
404	#2641	C₂×C₁₃₉	1	1	yes	characteristic, complemented
405	#2584	C₂×C₁₃₉	1	1	yes	characteristic, complemented
406	#2559	C₂×C₁₃₉	1	4	yes	complemented
407	#2543	C₂×C₁₃₉	1	2	yes	complemented
408	#2541	C₂×C₁₃₉	1	1	yes	characteristic, complemented
409	#2430	C₂×C₁₃₉	1	2	yes	complemented
410	#2428	C₂×C₁₃₉	1	2	yes	complemented
411	#2428	C₂×C₁₃₉	1	2	yes	complemented
412	#2428	C₂×C₁₃₉	1	4	yes	complemented
413	#2398	C₂×C₁₃₉	1	1	yes	characteristic, complemented
414	#2388	C₂×C₁₃₉	1	2	yes	complemented
415	#2363	C₂×C₁₃₉	1	2	yes	complemented
416	#2361	C₂×C₁₃₉	1	2	yes	complemented
417	#2275	C₂×C₁₃₉	1	1	yes	characteristic, complemented
418	C₂²×#41	C₂²×C₁₃₉	1	2	yes	—
419	#553	—	2	8	no	—
420	#550	—	2	8	no	—
421	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
422	C₂×#127	C₂²×C₁₃₉	1	2	yes	—
423	C₂×#127	C₂²×C₁₃₉	1	2	yes	—
424	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
425	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
426	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
427	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
428	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
429	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
430	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
431	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
432	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
433	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
434	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
435	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
436	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
437	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
438	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
439	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
440	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
441	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	—
442	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
443	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
444	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
445	#400	C₂²×C₁₃₉	1	2	yes	—
446	#398	C₂²×C₁₃₉	1	2	yes	—
447	#397	C₂²×C₁₃₉	1	1	yes	characteristic
448	#397	C₂²×C₁₃₉	1	1	yes	characteristic
449	#395	C₂²×C₁₃₉	1	2	yes	—
450	#394	C₂²×C₁₃₉	1	2	yes	—
451	#394	C₂²×C₁₃₉	1	4	yes	—
452	#394	C₂²×C₁₃₉	1	2	yes	—
453	#394	C₂²×C₁₃₉	1	4	yes	—
454	#394	C₂²×C₁₃₉	1	2	yes	—
455	#394	C₂²×C₁₃₉	1	4	yes	—
456	#393	C₂²×C₁₃₉	1	1	yes	characteristic
457	#393	C₂²×C₁₃₉	1	1	yes	characteristic
458	#392	C₂²×C₁₃₉	1	4	yes	—
459	#392	C₂²×C₁₃₉	1	2	yes	—
460	#392	C₂²×C₁₃₉	1	4	yes	—
461	#392	C₂²×C₁₃₉	1	2	yes	—
462	#390	C₂²×C₁₃₉	1	2	yes	—
463	#390	C₂²×C₁₃₉	1	2	yes	—
464	#390	C₂²×C₁₃₉	1	4	yes	—
465	#390	C₂²×C₁₃₉	1	2	yes	—
466	#389	C₂²×C₁₃₉	1	2	yes	—
467	#389	C₂²×C₁₃₉	1	2	yes	—
468	#389	C₂²×C₁₃₉	1	4	yes	—
469	#388	C₂²×C₁₃₉	1	4	yes	—
470	#388	C₂²×C₁₃₉	1	4	yes	—
471	#386	C₂²×C₁₃₉	1	4	yes	—
472	#386	C₂²×C₁₃₉	1	4	yes	—
473	#386	C₂²×C₁₃₉	1	4	yes	—
474	#386	C₂²×C₁₃₉	1	4	yes	—
475	#385	C₂²×C₁₃₉	1	4	yes	—
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	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
483	#376	C₂²×C₁₃₉	1	1	yes	characteristic
484	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
485	C₂×#41	—	2	8	no	—
486	C₂×#41	—	4	8	no	—
487	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
488	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
489	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
490	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
491	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
492	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
493	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
494	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
495	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
496	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
497	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
498	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
499	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
500	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
501	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
502	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
503	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
504	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
505	#127	—	2	8	no	—
506	#127	—	2	4	no	—
507	#127	—	4	4	no	—
508	#126	—	2	8	no	—
509	#125	—	2	4	no	—
510	#123	—	2	8	no	—
511	#121	—	2	4	no	—
512	#121	—	2	4	no	—
513	#121	—	2	8	no	—
514	#121	—	2	8	no	—
515	#121	—	2	8	no	—
516	#121	—	2	16	no	—
517	#121	—	2	8	no	—
518	#121	—	4	8	no	—
519	#121	—	4	8	no	—
520	C₄×Q₈	—	2	4	no	—
521	C₄×D₄	—	2	8	no	—
522	C₄×D₄	—	2	8	no	—
523	C₄×D₄	—	2	8	no	—
524	C₄×D₄	—	2	4	no	—
525	C₄×D₄	—	4	8	no	—
526	C₄×D₄	D₄×C₁₃₉	1	8	yes	complemented
527	#117	—	2	4	no	—
528	C₂×C₄⋊C₄	—	2	4	no	—
529	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
530	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
531	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
532	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
533	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
534	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
535	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
536	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
537	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
538	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
539	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
540	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
541	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
542	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
543	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
545	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
546	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
547	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
548	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
549	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
550	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
553	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
555	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
556	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
557	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
558	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
559	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
560	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
561	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
562	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
563	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
564	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
565	#95	C₂³×C₁₃₉	1	1	yes	characteristic
566	#95	C₂³×C₁₃₉	1	4	yes	—
567	#95	C₂³×C₁₃₉	1	2	yes	—
568	#95	C₂³×C₁₃₉	1	1	yes	characteristic
569	#95	C₂³×C₁₃₉	1	2	yes	—
570	#95	C₂³×C₁₃₉	1	2	yes	—
571	#95	C₂³×C₁₃₉	1	2	yes	—
572	#95	C₂³×C₁₃₉	1	2	yes	—
573	#95	C₂³×C₁₃₉	1	4	yes	—
574	#95	C₂³×C₁₃₉	1	2	yes	—
575	#95	C₂³×C₁₃₉	1	4	yes	—
576	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
577	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
578	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
579	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
580	#41	—	4	32	no	—
581	C₂×Q₈	—	2	2	no	—
582	C₂×Q₈	—	2	4	no	—
583	C₂×D₄	—	2	4	no	—
584	C₂×D₄	—	2	8	no	—
585	C₂×D₄	—	2	4	no	—
586	C₂×D₄	—	2	8	no	—
587	C₂×D₄	—	2	2	no	—
588	C₂×D₄	—	2	4	no	—
589	C₂×D₄	—	2	8	no	—
590	C₂×D₄	—	2	2	no	—
591	C₂×D₄	—	2	4	no	—
592	C₂×D₄	—	2	4	no	—
593	C₂×D₄	—	2	4	no	—
594	C₂×D₄	—	2	4	no	—
595	C₂×D₄	—	2	8	no	—
596	C₂×D₄	—	2	4	no	—
597	C₂×D₄	—	2	4	no	—
598	C₂×D₄	—	2	8	no	—
599	C₂×D₄	—	2	8	no	—
600	C₂×D₄	—	4	4	no	—
601	C₂×D₄	—	4	1	no	—
602	C₂×D₄	—	4	2	no	—
603	C₂×D₄	—	4	4	no	—
604	C₂×D₄	—	4	4	no	—
605	C₂×D₄	—	4	4	no	—
606	C₂×D₄	—	4	4	no	—
607	C₂×D₄	—	4	4	no	—
608	C₂×D₄	—	4	2	no	—
609	C₂×D₄	—	4	4	no	—
610	C₂×D₄	—	4	2	no	—
611	C₂×D₄	—	4	4	no	—
612	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
613	C₂²×C₄	—	2	2	no	—
614	C₂²×C₄	—	2	2	no	—
615	C₂²×C₄	—	2	8	no	—
616	C₂²×C₄	—	2	4	no	—
617	C₂²×C₄	—	2	4	no	—
618	C₂²×C₄	—	2	8	no	—
619	C₂²×C₄	—	2	4	no	—
620	C₂²×C₄	—	2	8	no	—
621	C₂²×C₄	—	4	4	no	—
622	C₂²×C₄	—	4	4	no	—
623	C₂²×C₄	—	4	4	no	—
624	C₂²×C₄	—	4	4	no	—
625	C₂²×C₄	—	4	4	no	—
626	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
627	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
628	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
629	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
630	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
631	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
632	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
633	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
634	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
635	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
636	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
637	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
638	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
639	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
640	C₄⋊C₄	—	2	2	no	—
641	C₄⋊C₄	—	2	4	no	—
642	C₄⋊C₄	—	2	2	no	—
643	C₄⋊C₄	—	2	4	no	—
644	C₄⋊C₄	—	2	2	no	—
645	C₄⋊C₄	—	2	4	no	—
646	C₄⋊C₄	—	2	2	no	—
647	C₄⋊C₄	—	2	4	no	—
648	C₄⋊C₄	—	2	8	no	—
649	C₄⋊C₄	—	4	4	no	—
650	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
651	C₄⋊C₄	#41×C₁₃₉	1	8	yes	complemented
652	C₂²⋊C₄	—	2	4	no	—
653	C₂²⋊C₄	—	2	4	no	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	—	2	4	no	—
656	C₂²⋊C₄	—	2	2	no	—
657	C₂²⋊C₄	—	2	8	no	—
658	C₂²⋊C₄	—	2	2	no	—
659	C₂²⋊C₄	—	2	8	no	—
660	C₂²⋊C₄	—	2	8	no	—
661	C₂²⋊C₄	—	2	8	no	—
662	C₂²⋊C₄	—	2	4	no	—
663	C₂²⋊C₄	—	2	4	no	—
664	C₂²⋊C₄	—	4	4	no	—
665	C₂²⋊C₄	—	4	2	no	—
666	C₂²⋊C₄	—	4	4	no	—
667	C₂²⋊C₄	—	4	4	no	—
668	C₂²⋊C₄	—	4	4	no	—
669	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
670	C₄²	—	2	4	no	—
671	C₄²	—	2	4	no	—
672	C₄²	—	2	4	no	—
673	C₄²	—	4	4	no	—
674	C₄²	—	4	2	no	—
675	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
676	C₂³	—	2	1	no	—
677	C₂³	—	2	4	no	—
678	C₂³	—	2	2	no	—
679	C₂³	—	2	2	no	—
680	C₂³	—	2	4	no	—
681	C₂³	—	2	2	no	—
682	C₂³	—	2	1	no	—
683	C₂³	—	2	2	no	—
684	C₂³	—	2	1	no	—
685	C₂³	—	2	4	no	—
686	C₂³	—	2	4	no	—
687	C₂³	—	2	4	no	—
688	C₂³	—	2	2	no	—
689	C₂³	—	2	2	no	—
690	C₂³	—	2	4	no	—
691	C₂³	—	2	4	no	—
692	C₂³	—	2	4	no	—
693	C₂³	—	2	1	no	—
694	C₂³	—	2	1	no	—
695	C₂³	—	2	4	no	—
696	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
697	C₂³	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
698	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
699	Q₈	—	2	8	no	—
700	D₄	—	2	8	no	—
701	D₄	—	4	16	no	—
702	D₄	—	4	4	no	—
703	D₄	—	4	16	no	—
704	D₄	—	4	8	no	—
705	D₄	—	4	8	no	—
706	D₄	—	4	8	no	—
707	D₄	—	8	4	no	—
708	D₄	—	8	8	no	—
709	D₄	—	8	4	no	—
710	D₄	—	8	8	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	4	no	—
714	C₂×C₄	—	2	4	no	—
715	C₂×C₄	—	2	4	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	1	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	4	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	4	8	no	—
738	C₂×C₄	—	4	16	no	—
739	C₂×C₄	—	4	4	no	—
740	C₂×C₄	—	4	4	no	—
741	C₂×C₄	—	8	4	no	—
742	C₂×C₄	—	8	8	no	—
743	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
744	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
745	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
746	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
747	C₂×C₄	C₂×#41×C₁₃₉	1	8	yes	—
748	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
749	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
750	C₂²	—	2	4	no	—
751	C₂²	—	2	4	no	—
752	C₂²	—	2	2	no	—
753	C₂²	—	2	4	no	—
754	C₂²	—	2	4	no	—
755	C₂²	—	4	1	no	—
756	C₂²	—	4	1	no	—
757	C₂²	—	4	4	no	—
758	C₂²	—	4	2	no	—
759	C₂²	—	4	4	no	—
760	C₂²	—	4	1	no	—
761	C₂²	—	4	4	no	—
762	C₂²	—	4	4	no	—
763	C₂²	—	4	1	no	—
764	C₂²	—	4	1	no	—
765	C₂²	—	4	4	no	—
766	C₂²	—	4	4	no	—
767	C₂²	—	4	4	no	—
768	C₂²	—	4	2	no	—
769	C₂²	—	4	4	no	—
770	C₂²	—	4	2	no	—
771	C₂²	—	4	4	no	—
772	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
773	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
774	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
775	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
776	C₂²	#585×C₁₃₉	1	1	yes	characteristic
777	C₄	—	2	4	no	—
778	C₄	—	2	2	no	—
779	C₄	—	2	4	no	—
780	C₄	—	2	2	no	—
781	C₄	—	2	8	no	—
782	C₄	—	4	1	no	—
783	C₄	—	4	1	no	—
784	C₄	—	4	2	no	—
785	C₄	—	4	2	no	—
786	C₄	—	4	2	no	—
787	C₄	—	4	2	no	—
788	C₄	—	4	2	no	—
789	C₄	#532×C₁₃₉	1	4	yes	—
790	C₂	—	4	4	no	—
791	C₂	—	4	2	no	—
792	C₂	—	8	1	no	—
793	C₂	—	8	4	no	—
794	C₂	C₂×#532×C₁₃₉	1	1	yes	characteristic
795	C₂	#3484×C₁₃₉	1	1	yes	characteristic
796	C₂	#3488×C₁₃₉	1	1	yes	characteristic
797	C₂	#3517×C₁₃₉	1	2	yes	—
798	C₂	#3519×C₁₃₉	1	2	yes	—

	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. C₂×#550×C₁₃₉	C₂	semidirect
3. #2661×C₁₃₉	C₂	semidirect
4. #2641×C₁₃₉	C₂	semidirect
5. #2584×C₁₃₉	C₂	semidirect
6. #2559×C₁₃₉	C₂	semidirect
7. #2543×C₁₃₉	C₂	semidirect
8. #2541×C₁₃₉	C₂	semidirect
9. #2430×C₁₃₉	C₂	semidirect
10. #2428×C₁₃₉	C₂	semidirect
11. #2428×C₁₃₉	C₂	semidirect
12. #2428×C₁₃₉	C₂	semidirect
13. #2398×C₁₃₉	C₂	semidirect
14. #2388×C₁₃₉	C₂	semidirect
15. #2363×C₁₃₉	C₂	semidirect
16. #2361×C₁₃₉	C₂	semidirect
17. #2275×C₁₃₉	C₂	semidirect
126. C₄×D₄×C₁₃₉	D₄	semidirect
251. C₄⋊C₄×C₁₃₉	#41	semidirect
399. #35941	C₁₃₉	direct (N × H)
400. C₁₃₉	#35941	direct (N × H)
401. C₂×#553	C₂×C₁₃₉	semidirect
402. C₂×#550	C₂×C₁₃₉	semidirect
403. #2661	C₂×C₁₃₉	semidirect
404. #2641	C₂×C₁₃₉	semidirect
405. #2584	C₂×C₁₃₉	semidirect
406. #2559	C₂×C₁₃₉	semidirect
407. #2543	C₂×C₁₃₉	semidirect
408. #2541	C₂×C₁₃₉	semidirect
409. #2430	C₂×C₁₃₉	semidirect
410. #2428	C₂×C₁₃₉	semidirect
411. #2428	C₂×C₁₃₉	semidirect
412. #2428	C₂×C₁₃₉	semidirect
413. #2398	C₂×C₁₃₉	semidirect
414. #2388	C₂×C₁₃₉	semidirect
415. #2363	C₂×C₁₃₉	semidirect
416. #2361	C₂×C₁₃₉	semidirect
417. #2275	C₂×C₁₃₉	semidirect
526. C₄×D₄	D₄×C₁₃₉	semidirect
651. C₄⋊C₄	#41×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
C₂×#550×C₁₃₉	2
#2661×C₁₃₉	2
#2641×C₁₃₉	2
#2584×C₁₃₉	2
#2559×C₁₃₉	2
#2543×C₁₃₉	2
#2541×C₁₃₉	2
#2430×C₁₃₉	2
#2428×C₁₃₉	2
#2398×C₁₃₉	2
#2388×C₁₃₉	2
#2363×C₁₃₉	2
#2361×C₁₃₉	2
#2275×C₁₃₉	2
#35941	139

Subgroups — C139×#35941 #48030537

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#35941 #48030537