Subgroups — C₁₃₉×#36163 #48030759

Order 35584.

2808 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#552×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₄⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2849×C₁₃₉	C₂	1	2	yes	maximal
4	#2848×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2503×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2486×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2484×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2481×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#2473×C₁₃₉	C₂	1	4	yes	maximal, complemented
10	#2442×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2417×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2413×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2360×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2352×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2344×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#120×C₁₃₉	C₂	1	1	yes	maximal, characteristic
17	#2280×C₁₃₉	C₂	1	2	yes	maximal, complemented
18	C₂⁴×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₁₃₉	C₂²	1	2	yes	—
20	#552×C₁₃₉	—	2	8	no	—
21	C₂×#126×C₁₃₉	C₂²	1	2	yes	complemented
22	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
23	C₂×#125×C₁₃₉	C₂²	1	2	yes	complemented
24	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
25	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
26	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
27	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
29	C₂×#120×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
34	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
35	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
36	C₂²×C₄⋊C₄×C₁₃₉	—	2	8	no	—
37	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
38	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
39	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
40	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
41	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
42	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
43	#400×C₁₃₉	C₂²	1	4	yes	complemented
44	#400×C₁₃₉	C₂²	1	4	yes	complemented
45	#398×C₁₃₉	C₂²	1	4	yes	complemented
46	#398×C₁₃₉	C₂²	1	4	yes	complemented
47	#398×C₁₃₉	C₂²	1	2	yes	complemented
48	#397×C₁₃₉	C₂²	1	2	yes	complemented
49	#396×C₁₃₉	C₂²	1	4	yes	complemented
50	#391×C₁₃₉	C₂²	1	2	yes	complemented
51	#389×C₁₃₉	C₂²	1	2	yes	complemented
52	#389×C₁₃₉	C₂²	1	4	yes	complemented
53	#389×C₁₃₉	C₂²	1	2	yes	complemented
54	#388×C₁₃₉	C₂²	1	4	yes	complemented
55	#387×C₁₃₉	C₂²	1	4	yes	complemented
56	#387×C₁₃₉	C₂²	1	4	yes	complemented
57	#387×C₁₃₉	C₂²	1	4	yes	complemented
58	#386×C₁₃₉	C₂²	1	1	yes	characteristic
59	#386×C₁₃₉	C₂²	1	2	yes	—
60	#386×C₁₃₉	C₂²	1	4	yes	—
61	#386×C₁₃₉	C₂²	1	4	yes	—
62	#385×C₁₃₉	C₂²	1	2	yes	—
63	#385×C₁₃₉	C₂²	1	1	yes	characteristic
64	#385×C₁₃₉	C₂²	1	2	yes	—
65	#385×C₁₃₉	C₂²	1	4	yes	—
66	#385×C₁₃₉	C₂²	1	4	yes	—
67	#385×C₁₃₉	C₂²	1	4	yes	—
68	#382×C₁₃₉	C₂²	1	2	yes	complemented
69	#381×C₁₃₉	C₂²	1	2	yes	—
70	#381×C₁₃₉	C₂²	1	2	yes	—
71	#381×C₁₃₉	C₂²	1	2	yes	—
72	#381×C₁₃₉	C₂²	1	2	yes	—
73	#380×C₁₃₉	C₂²	1	4	yes	—
74	#380×C₁₃₉	C₂²	1	4	yes	—
75	#380×C₁₃₉	C₂²	1	1	yes	characteristic
76	#380×C₁₃₉	C₂²	1	2	yes	—
77	#380×C₁₃₉	C₂²	1	2	yes	complemented
78	#379×C₁₃₉	C₂²	1	1	yes	characteristic
79	#379×C₁₃₉	C₂²	1	2	yes	—
80	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
81	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
82	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
83	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
84	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
85	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
86	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
88	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
89	C₂³×C₄×C₁₃₉	—	2	4	no	—
90	C₂³×C₄×C₁₃₉	—	2	8	no	—
91	C₂³×C₄×C₁₃₉	—	2	8	no	—
92	C₂³×C₄×C₁₃₉	—	2	8	no	—
93	C₂³×C₄×C₁₃₉	—	4	4	no	—
94	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
95	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
97	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
99	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
100	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
101	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
103	#126×C₁₃₉	—	2	8	no	—
104	#125×C₁₃₉	—	2	8	no	—
105	#125×C₁₃₉	—	2	4	no	—
106	#123×C₁₃₉	—	2	8	no	—
107	#123×C₁₃₉	—	4	4	no	—
108	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
109	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
110	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
111	#120×C₁₃₉	—	2	4	no	—
112	C₄×Q₈×C₁₃₉	—	2	4	no	—
113	C₄×D₄×C₁₃₉	—	2	4	no	—
114	C₄×D₄×C₁₃₉	—	2	8	no	—
115	#117×C₁₃₉	—	2	8	no	—
116	#117×C₁₃₉	—	2	4	no	—
117	#117×C₁₃₉	—	4	4	no	—
118	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
119	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
120	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
121	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
122	C₂×C₄⋊C₄×C₁₃₉	—	2	16	no	—
123	C₂×C₄⋊C₄×C₁₃₉	D₄	1	8	yes	complemented
124	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
125	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
126	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	2	yes	—
133	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
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	2	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	1	yes	characteristic
141	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	1	yes	characteristic
146	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
147	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
148	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	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	2	yes	—
152	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
156	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
157	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
158	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
159	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
160	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
162	C₂×C₄²×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	4	yes	—
169	#95×C₁₃₉	C₂³	1	4	yes	—
170	#95×C₁₃₉	C₂³	1	4	yes	—
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	4	yes	—
175	#95×C₁₃₉	C₂³	1	4	yes	—
176	C₂⁴×C₁₃₉	—	2	2	no	—
177	C₂⁴×C₁₃₉	—	2	4	no	—
178	C₂⁴×C₁₃₉	—	2	2	no	—
179	C₂⁴×C₁₃₉	—	2	4	no	—
180	C₂⁴×C₁₃₉	#41	1	4	yes	—
181	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
182	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
183	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
184	C₂×Q₈×C₁₃₉	—	2	2	no	—
185	C₂×Q₈×C₁₃₉	—	2	4	no	—
186	C₂×D₄×C₁₃₉	—	2	2	no	—
187	C₂×D₄×C₁₃₉	—	2	4	no	—
188	C₂×D₄×C₁₃₉	—	2	2	no	—
189	C₂×D₄×C₁₃₉	—	2	4	no	—
190	C₂×D₄×C₁₃₉	—	2	2	no	—
191	C₂×D₄×C₁₃₉	—	2	4	no	—
192	C₂²×C₄×C₁₃₉	—	2	32	no	—
193	C₂²×C₄×C₁₃₉	—	2	2	no	—
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	—	2	8	no	—
206	C₂²×C₄×C₁₃₉	—	2	4	no	—
207	C₂²×C₄×C₁₃₉	—	2	4	no	—
208	C₂²×C₄×C₁₃₉	—	2	8	no	—
209	C₂²×C₄×C₁₃₉	—	2	8	no	—
210	C₂²×C₄×C₁₃₉	—	2	2	no	—
211	C₂²×C₄×C₁₃₉	—	2	4	no	—
212	C₂²×C₄×C₁₃₉	—	4	4	no	—
213	C₂²×C₄×C₁₃₉	—	4	4	no	—
214	C₂²×C₄×C₁₃₉	—	4	32	no	—
215	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
216	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
217	C₂²×C₄×C₁₃₉	#41	1	8	yes	—
218	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
220	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
223	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
224	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
227	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
232	C₄⋊C₄×C₁₃₉	—	2	8	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	—	2	4	no	—
237	C₄⋊C₄×C₁₃₉	—	2	2	no	—
238	C₄⋊C₄×C₁₃₉	—	2	4	no	—
239	C₄⋊C₄×C₁₃₉	—	2	2	no	—
240	C₄⋊C₄×C₁₃₉	—	2	4	no	—
241	C₄⋊C₄×C₁₃₉	—	2	4	no	—
242	C₄⋊C₄×C₁₃₉	—	2	4	no	—
243	C₄⋊C₄×C₁₃₉	—	2	4	no	—
244	C₄⋊C₄×C₁₃₉	—	2	4	no	—
245	C₄⋊C₄×C₁₃₉	—	2	8	no	—
246	C₄⋊C₄×C₁₃₉	—	4	4	no	—
247	C₄⋊C₄×C₁₃₉	—	4	4	no	—
248	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
249	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
250	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
251	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
252	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
253	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
254	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
255	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
256	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
257	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
258	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
259	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
260	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
261	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
262	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
263	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
264	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
265	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
266	C₄²×C₁₃₉	—	2	4	no	—
267	C₄²×C₁₃₉	—	2	4	no	—
268	C₄²×C₁₃₉	—	2	2	no	—
269	C₄²×C₁₃₉	—	2	4	no	—
270	C₄²×C₁₃₉	—	4	4	no	—
271	C₂³×C₁₃₉	—	2	8	no	—
272	C₂³×C₁₃₉	—	2	8	no	—
273	C₂³×C₁₃₉	—	2	16	no	—
274	C₂³×C₁₃₉	—	2	8	no	—
275	C₂³×C₁₃₉	—	2	16	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	1	no	—
283	C₂³×C₁₃₉	—	2	2	no	—
284	C₂³×C₁₃₉	—	2	1	no	—
285	C₂³×C₁₃₉	—	2	1	no	—
286	C₂³×C₁₃₉	—	2	2	no	—
287	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
288	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
289	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
290	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
291	C₂³×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
292	C₂³×C₁₃₉	2₋¹⁺⁴	1	4	yes	—
293	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
294	Q₈×C₁₃₉	—	4	4	no	—
295	D₄×C₁₃₉	—	4	4	no	—
296	D₄×C₁₃₉	—	4	8	no	—
297	C₂×C₄×C₁₃₉	—	2	16	no	—
298	C₂×C₄×C₁₃₉	—	2	8	no	—
299	C₂×C₄×C₁₃₉	—	2	16	no	—
300	C₂×C₄×C₁₃₉	—	2	2	no	—
301	C₂×C₄×C₁₃₉	—	2	2	no	—
302	C₂×C₄×C₁₃₉	—	2	2	no	—
303	C₂×C₄×C₁₃₉	—	2	2	no	—
304	C₂×C₄×C₁₃₉	—	2	2	no	—
305	C₂×C₄×C₁₃₉	—	2	2	no	—
306	C₂×C₄×C₁₃₉	—	2	2	no	—
307	C₂×C₄×C₁₃₉	—	2	8	no	—
308	C₂×C₄×C₁₃₉	—	2	16	no	—
309	C₂×C₄×C₁₃₉	—	2	1	no	—
310	C₂×C₄×C₁₃₉	—	2	1	no	—
311	C₂×C₄×C₁₃₉	—	2	2	no	—
312	C₂×C₄×C₁₃₉	—	2	2	no	—
313	C₂×C₄×C₁₃₉	—	2	1	no	—
314	C₂×C₄×C₁₃₉	—	2	4	no	—
315	C₂×C₄×C₁₃₉	—	2	2	no	—
316	C₂×C₄×C₁₃₉	—	2	2	no	—
317	C₂×C₄×C₁₃₉	—	2	1	no	—
318	C₂×C₄×C₁₃₉	—	2	2	no	—
319	C₂×C₄×C₁₃₉	—	2	4	no	—
320	C₂×C₄×C₁₃₉	—	2	2	no	—
321	C₂×C₄×C₁₃₉	—	2	4	no	—
322	C₂×C₄×C₁₃₉	—	2	4	no	—
323	C₂×C₄×C₁₃₉	—	2	2	no	—
324	C₂×C₄×C₁₃₉	—	2	4	no	—
325	C₂×C₄×C₁₃₉	—	2	4	no	—
326	C₂×C₄×C₁₃₉	—	2	1	no	—
327	C₂×C₄×C₁₃₉	—	2	2	no	—
328	C₂×C₄×C₁₃₉	—	2	4	no	—
329	C₂×C₄×C₁₃₉	—	2	2	no	—
330	C₂×C₄×C₁₃₉	—	2	4	no	—
331	C₂×C₄×C₁₃₉	—	2	2	no	—
332	C₂×C₄×C₁₃₉	—	4	16	no	—
333	C₂×C₄×C₁₃₉	—	4	16	no	—
334	C₂×C₄×C₁₃₉	—	4	8	no	—
335	C₂×C₄×C₁₃₉	—	4	4	no	—
336	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
337	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
338	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
339	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
340	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
341	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
342	C₂²×C₁₃₉	—	2	32	no	—
343	C₂²×C₁₃₉	—	2	2	no	—
344	C₂²×C₁₃₉	—	2	4	no	—
345	C₂²×C₁₃₉	—	2	4	no	—
346	C₂²×C₁₃₉	—	2	4	no	—
347	C₂²×C₁₃₉	—	2	4	no	—
348	C₂²×C₁₃₉	—	2	2	no	—
349	C₂²×C₁₃₉	—	2	4	no	—
350	C₂²×C₁₃₉	—	2	4	no	—
351	C₂²×C₁₃₉	—	2	4	no	—
352	C₂²×C₁₃₉	—	2	4	no	—
353	C₂²×C₁₃₉	—	4	1	no	—
354	C₂²×C₁₃₉	—	4	1	no	—
355	C₂²×C₁₃₉	—	4	2	no	—
356	C₂²×C₁₃₉	—	4	1	no	—
357	C₂²×C₁₃₉	—	4	2	no	—
358	C₂²×C₁₃₉	#546	1	4	yes	—
359	C₂²×C₁₃₉	#552	1	8	yes	complemented
360	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
361	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
362	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
363	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
364	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	2	yes	—
365	C₄×C₁₃₉	—	2	2	no	—
366	C₄×C₁₃₉	—	2	4	no	—
367	C₄×C₁₃₉	—	2	4	no	—
368	C₄×C₁₃₉	—	2	4	no	—
369	C₄×C₁₃₉	—	4	1	no	—
370	C₄×C₁₃₉	—	4	2	no	—
371	C₄×C₁₃₉	—	4	4	no	—
372	C₄×C₁₃₉	—	4	1	no	—
373	C₄×C₁₃₉	—	4	2	no	—
374	C₄×C₁₃₉	—	4	1	no	—
375	C₄×C₁₃₉	—	4	2	no	—
376	C₄×C₁₃₉	—	4	2	no	—
377	C₄×C₁₃₉	—	4	4	no	—
378	C₄×C₁₃₉	#525	1	4	yes	—
379	C₂×C₁₃₉	—	2	4	no	—
380	C₂×C₁₃₉	—	2	8	no	—
381	C₂×C₁₃₉	—	8	1	no	—
382	C₂×C₁₃₉	C₂×#525	1	1	yes	characteristic
383	C₂×C₁₃₉	C₂×#546	1	1	yes	characteristic
384	C₂×C₁₃₉	C₂×#552	1	2	yes	—
385	C₂×C₁₃₉	#3486	1	1	yes	characteristic
386	C₂×C₁₃₉	#3492	1	2	yes	—
387	#36163	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
388	C₁₃₉	#36163	1	1	yes	characteristic, direct product factor, Sylow
389	C₂×#552	C₂×C₁₃₉	1	1	yes	characteristic, complemented
390	C₂³×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
391	#2849	C₂×C₁₃₉	1	2	yes	—
392	#2848	C₂×C₁₃₉	1	1	yes	characteristic, complemented
393	#2503	C₂×C₁₃₉	1	1	yes	characteristic, complemented
394	#2486	C₂×C₁₃₉	1	1	yes	characteristic, complemented
395	#2484	C₂×C₁₃₉	1	2	yes	complemented
396	#2481	C₂×C₁₃₉	1	4	yes	complemented
397	#2473	C₂×C₁₃₉	1	4	yes	complemented
398	#2442	C₂×C₁₃₉	1	2	yes	complemented
399	#2417	C₂×C₁₃₉	1	2	yes	complemented
400	#2413	C₂×C₁₃₉	1	2	yes	complemented
401	#2360	C₂×C₁₃₉	1	2	yes	complemented
402	#2352	C₂×C₁₃₉	1	2	yes	complemented
403	#2344	C₂×C₁₃₉	1	1	yes	characteristic, complemented
404	C₄×#120	C₂×C₁₃₉	1	1	yes	characteristic
405	#2280	C₂×C₁₃₉	1	2	yes	complemented
406	C₂⁴×C₄	C₂²×C₁₃₉	1	1	yes	characteristic
407	C₂⁴×C₄	C₂²×C₁₃₉	1	2	yes	—
408	#552	—	2	8	no	—
409	C₂×#126	C₂²×C₁₃₉	1	2	yes	complemented
410	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
411	C₂×#125	C₂²×C₁₃₉	1	2	yes	complemented
412	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
413	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
414	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
415	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
416	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
417	C₂×#120	C₂²×C₁₃₉	1	1	yes	characteristic
418	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
419	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
420	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
421	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
422	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
423	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
424	C₂²×C₄⋊C₄	—	2	8	no	—
425	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
426	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
427	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
428	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
429	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
430	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
431	#400	C₂²×C₁₃₉	1	4	yes	complemented
432	#400	C₂²×C₁₃₉	1	4	yes	complemented
433	#398	C₂²×C₁₃₉	1	4	yes	complemented
434	#398	C₂²×C₁₃₉	1	4	yes	complemented
435	#398	C₂²×C₁₃₉	1	2	yes	complemented
436	#397	C₂²×C₁₃₉	1	2	yes	complemented
437	#396	C₂²×C₁₃₉	1	4	yes	complemented
438	#391	C₂²×C₁₃₉	1	2	yes	complemented
439	#389	C₂²×C₁₃₉	1	2	yes	complemented
440	#389	C₂²×C₁₃₉	1	4	yes	complemented
441	#389	C₂²×C₁₃₉	1	2	yes	complemented
442	#388	C₂²×C₁₃₉	1	4	yes	complemented
443	#387	C₂²×C₁₃₉	1	4	yes	complemented
444	#387	C₂²×C₁₃₉	1	4	yes	complemented
445	#387	C₂²×C₁₃₉	1	4	yes	complemented
446	#386	C₂²×C₁₃₉	1	4	yes	—
447	#386	C₂²×C₁₃₉	1	4	yes	—
448	#386	C₂²×C₁₃₉	1	1	yes	characteristic
449	#386	C₂²×C₁₃₉	1	2	yes	—
450	#385	C₂²×C₁₃₉	1	2	yes	—
451	#385	C₂²×C₁₃₉	1	4	yes	—
452	#385	C₂²×C₁₃₉	1	4	yes	—
453	#385	C₂²×C₁₃₉	1	4	yes	—
454	#385	C₂²×C₁₃₉	1	2	yes	—
455	#385	C₂²×C₁₃₉	1	1	yes	characteristic
456	#382	C₂²×C₁₃₉	1	2	yes	complemented
457	#381	C₂²×C₁₃₉	1	2	yes	—
458	#381	C₂²×C₁₃₉	1	2	yes	—
459	#381	C₂²×C₁₃₉	1	2	yes	—
460	#381	C₂²×C₁₃₉	1	2	yes	—
461	#380	C₂²×C₁₃₉	1	1	yes	characteristic
462	#380	C₂²×C₁₃₉	1	2	yes	—
463	#380	C₂²×C₁₃₉	1	4	yes	—
464	#380	C₂²×C₁₃₉	1	4	yes	—
465	#380	C₂²×C₁₃₉	1	2	yes	complemented
466	#379	C₂²×C₁₃₉	1	2	yes	—
467	#379	C₂²×C₁₃₉	1	1	yes	characteristic
468	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
469	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
470	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
471	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
472	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
473	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
474	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
475	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
476	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
477	C₂³×C₄	—	2	4	no	—
478	C₂³×C₄	—	2	8	no	—
479	C₂³×C₄	—	2	8	no	—
480	C₂³×C₄	—	2	8	no	—
481	C₂³×C₄	—	4	4	no	—
482	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
483	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
484	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
485	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
486	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
487	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
488	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
489	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
490	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
491	#126	—	2	8	no	—
492	#125	—	2	8	no	—
493	#125	—	2	4	no	—
494	#123	—	2	8	no	—
495	#123	—	4	4	no	—
496	C₂²⋊Q₈	—	2	4	no	—
497	C₂²⋊Q₈	—	2	8	no	—
498	C₂²⋊Q₈	—	2	4	no	—
499	#120	—	2	4	no	—
500	C₄×Q₈	—	2	4	no	—
501	C₄×D₄	—	2	4	no	—
502	C₄×D₄	—	2	8	no	—
503	#117	—	2	8	no	—
504	#117	—	2	4	no	—
505	#117	—	4	4	no	—
506	C₂×C₄⋊C₄	—	2	8	no	—
507	C₂×C₄⋊C₄	—	2	4	no	—
508	C₂×C₄⋊C₄	—	2	8	no	—
509	C₂×C₄⋊C₄	—	2	8	no	—
510	C₂×C₄⋊C₄	—	2	16	no	—
511	C₂×C₄⋊C₄	D₄×C₁₃₉	1	8	yes	complemented
512	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
513	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
514	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
515	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
516	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
517	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
518	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
519	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
520	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
521	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
522	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
523	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
524	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
525	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
526	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
527	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
528	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
529	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
530	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
531	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
532	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
533	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
534	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
535	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
536	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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	1	yes	characteristic
540	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
541	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
542	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
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	4	yes	—
546	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
547	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
548	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
549	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
550	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
551	#95	C₂³×C₁₃₉	1	4	yes	—
552	#95	C₂³×C₁₃₉	1	4	yes	—
553	#95	C₂³×C₁₃₉	1	4	yes	—
554	#95	C₂³×C₁₃₉	1	4	yes	—
555	#95	C₂³×C₁₃₉	1	2	yes	—
556	#95	C₂³×C₁₃₉	1	2	yes	—
557	#95	C₂³×C₁₃₉	1	2	yes	—
558	#95	C₂³×C₁₃₉	1	4	yes	—
559	#95	C₂³×C₁₃₉	1	2	yes	—
560	#95	C₂³×C₁₃₉	1	4	yes	—
561	#95	C₂³×C₁₃₉	1	4	yes	—
562	#95	C₂³×C₁₃₉	1	4	yes	—
563	#95	C₂³×C₁₃₉	1	4	yes	—
564	C₂⁴	—	2	2	no	—
565	C₂⁴	—	2	4	no	—
566	C₂⁴	—	2	2	no	—
567	C₂⁴	—	2	4	no	—
568	C₂⁴	#41×C₁₃₉	1	4	yes	—
569	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
570	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
571	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
572	C₂×Q₈	—	2	2	no	—
573	C₂×Q₈	—	2	4	no	—
574	C₂×D₄	—	2	2	no	—
575	C₂×D₄	—	2	4	no	—
576	C₂×D₄	—	2	2	no	—
577	C₂×D₄	—	2	4	no	—
578	C₂×D₄	—	2	2	no	—
579	C₂×D₄	—	2	4	no	—
580	C₂²×C₄	—	2	32	no	—
581	C₂²×C₄	—	2	2	no	—
582	C₂²×C₄	—	2	4	no	—
583	C₂²×C₄	—	2	4	no	—
584	C₂²×C₄	—	2	4	no	—
585	C₂²×C₄	—	2	4	no	—
586	C₂²×C₄	—	2	4	no	—
587	C₂²×C₄	—	2	4	no	—
588	C₂²×C₄	—	2	4	no	—
589	C₂²×C₄	—	2	4	no	—
590	C₂²×C₄	—	2	4	no	—
591	C₂²×C₄	—	2	4	no	—
592	C₂²×C₄	—	2	8	no	—
593	C₂²×C₄	—	2	8	no	—
594	C₂²×C₄	—	2	4	no	—
595	C₂²×C₄	—	2	4	no	—
596	C₂²×C₄	—	2	8	no	—
597	C₂²×C₄	—	2	8	no	—
598	C₂²×C₄	—	2	2	no	—
599	C₂²×C₄	—	2	4	no	—
600	C₂²×C₄	—	4	4	no	—
601	C₂²×C₄	—	4	4	no	—
602	C₂²×C₄	—	4	32	no	—
603	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
604	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
605	C₂²×C₄	#41×C₁₃₉	1	8	yes	—
606	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
607	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
608	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
609	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
610	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
611	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
612	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
613	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
614	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
615	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
616	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
617	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
618	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
619	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
620	C₄⋊C₄	—	2	8	no	—
621	C₄⋊C₄	—	2	8	no	—
622	C₄⋊C₄	—	2	4	no	—
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	2	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	2	no	—
628	C₄⋊C₄	—	2	4	no	—
629	C₄⋊C₄	—	2	4	no	—
630	C₄⋊C₄	—	2	4	no	—
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	—	2	8	no	—
634	C₄⋊C₄	—	4	4	no	—
635	C₄⋊C₄	—	4	4	no	—
636	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
637	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
638	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
639	C₂²⋊C₄	—	2	2	no	—
640	C₂²⋊C₄	—	2	4	no	—
641	C₂²⋊C₄	—	2	4	no	—
642	C₂²⋊C₄	—	2	2	no	—
643	C₂²⋊C₄	—	2	4	no	—
644	C₂²⋊C₄	—	2	8	no	—
645	C₂²⋊C₄	—	2	2	no	—
646	C₂²⋊C₄	—	2	4	no	—
647	C₂²⋊C₄	—	2	4	no	—
648	C₂²⋊C₄	—	2	8	no	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	—	2	2	no	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	—	2	4	no	—
653	C₂²⋊C₄	—	4	4	no	—
654	C₄²	—	2	4	no	—
655	C₄²	—	2	4	no	—
656	C₄²	—	2	2	no	—
657	C₄²	—	2	4	no	—
658	C₄²	—	4	4	no	—
659	C₂³	—	2	8	no	—
660	C₂³	—	2	8	no	—
661	C₂³	—	2	16	no	—
662	C₂³	—	2	8	no	—
663	C₂³	—	2	16	no	—
664	C₂³	—	2	2	no	—
665	C₂³	—	2	2	no	—
666	C₂³	—	2	2	no	—
667	C₂³	—	2	2	no	—
668	C₂³	—	2	2	no	—
669	C₂³	—	2	2	no	—
670	C₂³	—	2	1	no	—
671	C₂³	—	2	2	no	—
672	C₂³	—	2	1	no	—
673	C₂³	—	2	1	no	—
674	C₂³	—	2	2	no	—
675	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
676	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
677	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
678	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
679	C₂³	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
680	C₂³	2₋¹⁺⁴×C₁₃₉	1	4	yes	—
681	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
682	Q₈	—	4	4	no	—
683	D₄	—	4	4	no	—
684	D₄	—	4	8	no	—
685	C₂×C₄	—	2	16	no	—
686	C₂×C₄	—	2	8	no	—
687	C₂×C₄	—	2	16	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	8	no	—
696	C₂×C₄	—	2	16	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	4	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	4	no	—
710	C₂×C₄	—	2	4	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	4	no	—
713	C₂×C₄	—	2	4	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	4	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	4	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	4	16	no	—
721	C₂×C₄	—	4	16	no	—
722	C₂×C₄	—	4	8	no	—
723	C₂×C₄	—	4	4	no	—
724	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
725	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
726	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
727	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
728	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
729	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
730	C₂²	—	2	32	no	—
731	C₂²	—	2	2	no	—
732	C₂²	—	2	4	no	—
733	C₂²	—	2	4	no	—
734	C₂²	—	2	4	no	—
735	C₂²	—	2	4	no	—
736	C₂²	—	2	2	no	—
737	C₂²	—	2	4	no	—
738	C₂²	—	2	4	no	—
739	C₂²	—	2	4	no	—
740	C₂²	—	2	4	no	—
741	C₂²	—	4	1	no	—
742	C₂²	—	4	1	no	—
743	C₂²	—	4	2	no	—
744	C₂²	—	4	1	no	—
745	C₂²	—	4	2	no	—
746	C₂²	#546×C₁₃₉	1	4	yes	—
747	C₂²	#552×C₁₃₉	1	8	yes	complemented
748	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
749	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
750	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
751	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
752	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	2	yes	—
753	C₄	—	2	2	no	—
754	C₄	—	2	4	no	—
755	C₄	—	2	4	no	—
756	C₄	—	2	4	no	—
757	C₄	—	4	1	no	—
758	C₄	—	4	2	no	—
759	C₄	—	4	4	no	—
760	C₄	—	4	1	no	—
761	C₄	—	4	2	no	—
762	C₄	—	4	1	no	—
763	C₄	—	4	2	no	—
764	C₄	—	4	2	no	—
765	C₄	—	4	4	no	—
766	C₄	#525×C₁₃₉	1	4	yes	—
767	C₂	—	2	4	no	—
768	C₂	—	2	8	no	—
769	C₂	—	8	1	no	—
770	C₂	C₂×#525×C₁₃₉	1	1	yes	characteristic
771	C₂	C₂×#546×C₁₃₉	1	1	yes	characteristic
772	C₂	C₂×#552×C₁₃₉	1	2	yes	—
773	C₂	#3486×C₁₃₉	1	1	yes	characteristic
774	C₂	#3492×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂×#120×C₁₃₉	C₂²
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×#552×C₁₃₉	C₂	semidirect
2. C₂³×C₄⋊C₄×C₁₃₉	C₂	semidirect
4. #2848×C₁₃₉	C₂	semidirect
5. #2503×C₁₃₉	C₂	semidirect
6. #2486×C₁₃₉	C₂	semidirect
7. #2484×C₁₃₉	C₂	semidirect
8. #2481×C₁₃₉	C₂	semidirect
9. #2473×C₁₃₉	C₂	semidirect
10. #2442×C₁₃₉	C₂	semidirect
11. #2417×C₁₃₉	C₂	semidirect
12. #2413×C₁₃₉	C₂	semidirect
13. #2360×C₁₃₉	C₂	semidirect
14. #2352×C₁₃₉	C₂	semidirect
15. #2344×C₁₃₉	C₂	semidirect
17. #2280×C₁₃₉	C₂	semidirect
21. C₂×#126×C₁₃₉	C₂²	semidirect
22. C₂×#125×C₁₃₉	C₂²	semidirect
23. C₂×#125×C₁₃₉	C₂²	semidirect
28. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
30. C₂×C₄×Q₈×C₁₃₉	C₂²	semidirect
35. C₂×#117×C₁₃₉	C₂²	semidirect
43. #400×C₁₃₉	C₂²	semidirect
44. #400×C₁₃₉	C₂²	semidirect
45. #398×C₁₃₉	C₂²	semidirect
46. #398×C₁₃₉	C₂²	semidirect
47. #398×C₁₃₉	C₂²	semidirect
48. #397×C₁₃₉	C₂²	semidirect
49. #396×C₁₃₉	C₂²	semidirect
50. #391×C₁₃₉	C₂²	semidirect
51. #389×C₁₃₉	C₂²	semidirect
52. #389×C₁₃₉	C₂²	semidirect
53. #389×C₁₃₉	C₂²	semidirect
54. #388×C₁₃₉	C₂²	semidirect
55. #387×C₁₃₉	C₂²	semidirect
56. #387×C₁₃₉	C₂²	semidirect
57. #387×C₁₃₉	C₂²	semidirect
68. #382×C₁₃₉	C₂²	semidirect
77. #380×C₁₃₉	C₂²	semidirect
80. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
123. C₂×C₄⋊C₄×C₁₃₉	D₄	semidirect
359. C₂²×C₁₃₉	#552	semidirect
387. #36163	C₁₃₉	direct (N × H)
388. C₁₃₉	#36163	direct (N × H)
389. C₂×#552	C₂×C₁₃₉	semidirect
390. C₂³×C₄⋊C₄	C₂×C₁₃₉	semidirect
392. #2848	C₂×C₁₃₉	semidirect
393. #2503	C₂×C₁₃₉	semidirect
394. #2486	C₂×C₁₃₉	semidirect
395. #2484	C₂×C₁₃₉	semidirect
396. #2481	C₂×C₁₃₉	semidirect
397. #2473	C₂×C₁₃₉	semidirect
398. #2442	C₂×C₁₃₉	semidirect
399. #2417	C₂×C₁₃₉	semidirect
400. #2413	C₂×C₁₃₉	semidirect
401. #2360	C₂×C₁₃₉	semidirect
402. #2352	C₂×C₁₃₉	semidirect
403. #2344	C₂×C₁₃₉	semidirect
405. #2280	C₂×C₁₃₉	semidirect
409. C₂×#126	C₂²×C₁₃₉	semidirect
410. C₂×#125	C₂²×C₁₃₉	semidirect
411. C₂×#125	C₂²×C₁₃₉	semidirect
416. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
418. C₂×C₄×Q₈	C₂²×C₁₃₉	semidirect
423. C₂×#117	C₂²×C₁₃₉	semidirect
431. #400	C₂²×C₁₃₉	semidirect
432. #400	C₂²×C₁₃₉	semidirect
433. #398	C₂²×C₁₃₉	semidirect
434. #398	C₂²×C₁₃₉	semidirect
435. #398	C₂²×C₁₃₉	semidirect
436. #397	C₂²×C₁₃₉	semidirect
437. #396	C₂²×C₁₃₉	semidirect
438. #391	C₂²×C₁₃₉	semidirect
439. #389	C₂²×C₁₃₉	semidirect
440. #389	C₂²×C₁₃₉	semidirect
441. #389	C₂²×C₁₃₉	semidirect
442. #388	C₂²×C₁₃₉	semidirect
443. #387	C₂²×C₁₃₉	semidirect
444. #387	C₂²×C₁₃₉	semidirect
445. #387	C₂²×C₁₃₉	semidirect
456. #382	C₂²×C₁₃₉	semidirect
465. #380	C₂²×C₁₃₉	semidirect
468. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
511. C₂×C₄⋊C₄	D₄×C₁₃₉	semidirect
747. C₂²	#552×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#552×C₁₃₉	2
C₂³×C₄⋊C₄×C₁₃₉	2
#2849×C₁₃₉	2
#2848×C₁₃₉	2
#2503×C₁₃₉	2
#2486×C₁₃₉	2
#2484×C₁₃₉	2
#2481×C₁₃₉	2
#2473×C₁₃₉	2
#2442×C₁₃₉	2
#2417×C₁₃₉	2
#2413×C₁₃₉	2
#2360×C₁₃₉	2
#2352×C₁₃₉	2
#2344×C₁₃₉	2
C₄×#120×C₁₃₉	2
#2280×C₁₃₉	2
#36163	139

Subgroups — C139×#36163 #48030759

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36163 #48030759