Subgroups — C₁₃₉×#36422 #48031018

Order 35584.

2634 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#547×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2854×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2853×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2465×C₁₃₉	C₂	1	4	yes	maximal, complemented
6	#2458×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#2451×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2436×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#2426×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2413×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2409×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#2406×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2367×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2360×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2344×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#123×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	#2297×C₁₃₉	C₂	1	2	yes	maximal, complemented
18	C₂²×#41×C₁₃₉	C₂²	1	2	yes	—
19	C₂³×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
20	#547×C₁₃₉	—	2	8	no	—
21	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
22	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#123×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
25	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
26	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
27	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
28	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
29	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₁₃₉	—	2	8	no	—
32	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
33	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
34	C₂×C₄×Q₈×C₁₃₉	C₂²	1	4	yes	—
35	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
39	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
40	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
41	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
42	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
43	#398×C₁₃₉	C₂²	1	4	yes	—
44	#396×C₁₃₉	C₂²	1	4	yes	—
45	#395×C₁₃₉	C₂²	1	4	yes	—
46	#395×C₁₃₉	C₂²	1	2	yes	—
47	#394×C₁₃₉	C₂²	1	4	yes	—
48	#393×C₁₃₉	C₂²	1	2	yes	—
49	#393×C₁₃₉	C₂²	1	4	yes	—
50	#391×C₁₃₉	C₂²	1	4	yes	—
51	#391×C₁₃₉	C₂²	1	2	yes	—
52	#391×C₁₃₉	C₂²	1	2	yes	—
53	#390×C₁₃₉	C₂²	1	4	yes	—
54	#390×C₁₃₉	C₂²	1	2	yes	—
55	#389×C₁₃₉	C₂²	1	2	yes	—
56	#389×C₁₃₉	C₂²	1	2	yes	—
57	#389×C₁₃₉	C₂²	1	4	yes	—
58	#388×C₁₃₉	C₂²	1	2	yes	—
59	#388×C₁₃₉	C₂²	1	4	yes	—
60	#388×C₁₃₉	C₂²	1	4	yes	—
61	#388×C₁₃₉	C₂²	1	4	yes	—
62	#388×C₁₃₉	C₂²	1	4	yes	—
63	#387×C₁₃₉	C₂²	1	2	yes	—
64	#387×C₁₃₉	C₂²	1	4	yes	—
65	#387×C₁₃₉	C₂²	1	4	yes	—
66	#387×C₁₃₉	C₂²	1	4	yes	—
67	#386×C₁₃₉	C₂²	1	1	yes	characteristic
68	#386×C₁₃₉	C₂²	1	2	yes	—
69	#386×C₁₃₉	C₂²	1	2	yes	—
70	#386×C₁₃₉	C₂²	1	2	yes	—
71	#386×C₁₃₉	C₂²	1	2	yes	—
72	#385×C₁₃₉	C₂²	1	1	yes	characteristic
73	#385×C₁₃₉	C₂²	1	2	yes	—
74	#385×C₁₃₉	C₂²	1	4	yes	—
75	#385×C₁₃₉	C₂²	1	4	yes	—
76	#381×C₁₃₉	C₂²	1	1	yes	characteristic
77	#381×C₁₃₉	C₂²	1	2	yes	—
78	#380×C₁₃₉	C₂²	1	1	yes	characteristic
79	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
80	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
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	C₂×#41×C₁₃₉	—	2	8	no	—
86	C₂×#41×C₁₃₉	—	2	8	no	—
87	C₂×#41×C₁₃₉	—	4	4	no	—
88	C₂²×Q₈×C₁₃₉	—	2	8	no	—
89	C₂²×Q₈×C₁₃₉	—	2	4	no	—
90	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
91	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
92	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
93	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
94	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
95	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
96	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
100	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
102	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
103	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
104	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
105	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
106	#124×C₁₃₉	—	2	8	no	—
107	#123×C₁₃₉	—	2	4	no	—
108	#123×C₁₃₉	—	2	8	no	—
109	#123×C₁₃₉	—	2	8	no	—
110	#123×C₁₃₉	—	4	4	no	—
111	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
112	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
113	#121×C₁₃₉	—	2	4	no	—
114	#121×C₁₃₉	—	2	4	no	—
115	C₄×Q₈×C₁₃₉	—	2	8	no	—
116	C₄×Q₈×C₁₃₉	—	2	8	no	—
117	C₄×Q₈×C₁₃₉	—	2	16	no	—
118	C₄×D₄×C₁₃₉	—	2	4	no	—
119	C₄×D₄×C₁₃₉	—	2	4	no	—
120	#117×C₁₃₉	—	4	4	no	—
121	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
122	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
123	C₂×C₄⋊C₄×C₁₃₉	D₄	1	8	yes	—
124	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
127	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
128	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
130	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
131	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
135	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
136	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
137	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
140	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
141	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
142	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
147	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
148	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
149	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
151	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
153	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
154	C₂×C₄²×C₁₃₉	—	2	8	no	—
155	C₂×C₄²×C₁₃₉	—	2	4	no	—
156	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
157	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
158	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
159	C₂×C₄²×C₁₃₉	C₂³	1	4	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	2	yes	—
169	#95×C₁₃₉	C₂³	1	4	yes	—
170	#95×C₁₃₉	C₂³	1	4	yes	—
171	#95×C₁₃₉	C₂³	1	2	yes	—
172	#95×C₁₃₉	C₂³	1	2	yes	—
173	#95×C₁₃₉	C₂³	1	4	yes	—
174	#95×C₁₃₉	C₂³	1	2	yes	—
175	#95×C₁₃₉	C₂³	1	4	yes	—
176	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
177	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
178	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
179	#41×C₁₃₉	—	4	32	no	—
180	C₂×Q₈×C₁₃₉	—	2	32	no	—
181	C₂×Q₈×C₁₃₉	—	2	4	no	—
182	C₂×Q₈×C₁₃₉	—	2	4	no	—
183	C₂×Q₈×C₁₃₉	—	2	4	no	—
184	C₂×Q₈×C₁₃₉	—	2	8	no	—
185	C₂×Q₈×C₁₃₉	—	2	4	no	—
186	C₂×Q₈×C₁₃₉	—	2	4	no	—
187	C₂×Q₈×C₁₃₉	—	4	2	no	—
188	C₂×Q₈×C₁₃₉	#41	1	8	yes	complemented
189	C₂×D₄×C₁₃₉	—	2	2	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	2	no	—
196	C₂×D₄×C₁₃₉	—	2	4	no	—
197	C₂×D₄×C₁₃₉	—	2	4	no	—
198	C₂×D₄×C₁₃₉	—	4	2	no	—
199	C₂×D₄×C₁₃₉	#41	1	4	yes	—
200	C₂²×C₄×C₁₃₉	—	2	2	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	4	no	—
206	C₂²×C₄×C₁₃₉	—	2	4	no	—
207	C₂²×C₄×C₁₃₉	—	2	2	no	—
208	C₂²×C₄×C₁₃₉	—	2	2	no	—
209	C₂²×C₄×C₁₃₉	—	2	4	no	—
210	C₂²×C₄×C₁₃₉	—	2	2	no	—
211	C₂²×C₄×C₁₃₉	—	2	2	no	—
212	C₂²×C₄×C₁₃₉	—	2	4	no	—
213	C₂²×C₄×C₁₃₉	—	2	4	no	—
214	C₂²×C₄×C₁₃₉	—	2	4	no	—
215	C₂²×C₄×C₁₃₉	—	2	4	no	—
216	C₂²×C₄×C₁₃₉	—	4	2	no	—
217	C₂²×C₄×C₁₃₉	—	4	2	no	—
218	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
219	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
220	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
224	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
226	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
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	1	yes	characteristic
231	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
232	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
234	C₄⋊C₄×C₁₃₉	—	2	8	no	—
235	C₄⋊C₄×C₁₃₉	—	2	8	no	—
236	C₄⋊C₄×C₁₃₉	—	2	2	no	—
237	C₄⋊C₄×C₁₃₉	—	2	4	no	—
238	C₄⋊C₄×C₁₃₉	—	2	2	no	—
239	C₄⋊C₄×C₁₃₉	—	2	4	no	—
240	C₄⋊C₄×C₁₃₉	—	2	4	no	—
241	C₄⋊C₄×C₁₃₉	—	2	8	no	—
242	C₄⋊C₄×C₁₃₉	—	2	4	no	—
243	C₄⋊C₄×C₁₃₉	—	2	4	no	—
244	C₄⋊C₄×C₁₃₉	—	4	4	no	—
245	C₄⋊C₄×C₁₃₉	—	4	4	no	—
246	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
247	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
248	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
249	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
250	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
251	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
252	C₂²⋊C₄×C₁₃₉	—	2	2	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	4	no	—
257	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
258	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
259	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
260	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
261	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
262	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
263	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
264	C₄²×C₁₃₉	—	2	8	no	—
265	C₄²×C₁₃₉	—	2	8	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	2	no	—
272	C₂³×C₁₃₉	—	2	2	no	—
273	C₂³×C₁₃₉	—	2	1	no	—
274	C₂³×C₁₃₉	—	2	2	no	—
275	C₂³×C₁₃₉	—	2	1	no	—
276	C₂³×C₁₃₉	—	2	2	no	—
277	C₂³×C₁₃₉	—	2	2	no	—
278	C₂³×C₁₃₉	—	2	4	no	—
279	C₂³×C₁₃₉	—	2	2	no	—
280	C₂³×C₁₃₉	—	2	2	no	—
281	C₂³×C₁₃₉	—	2	4	no	—
282	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
283	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
284	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
285	C₂³×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
286	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
287	Q₈×C₁₃₉	—	2	16	no	—
288	Q₈×C₁₃₉	—	2	16	no	—
289	Q₈×C₁₃₉	—	4	8	no	—
290	D₄×C₁₃₉	—	2	8	no	—
291	D₄×C₁₃₉	—	4	8	no	—
292	D₄×C₁₃₉	—	4	8	no	—
293	D₄×C₁₃₉	—	4	4	no	—
294	C₂×C₄×C₁₃₉	—	2	8	no	—
295	C₂×C₄×C₁₃₉	—	2	16	no	—
296	C₂×C₄×C₁₃₉	—	2	16	no	—
297	C₂×C₄×C₁₃₉	—	2	2	no	—
298	C₂×C₄×C₁₃₉	—	2	4	no	—
299	C₂×C₄×C₁₃₉	—	2	1	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	4	no	—
304	C₂×C₄×C₁₃₉	—	2	2	no	—
305	C₂×C₄×C₁₃₉	—	2	2	no	—
306	C₂×C₄×C₁₃₉	—	2	1	no	—
307	C₂×C₄×C₁₃₉	—	2	2	no	—
308	C₂×C₄×C₁₃₉	—	2	8	no	—
309	C₂×C₄×C₁₃₉	—	2	2	no	—
310	C₂×C₄×C₁₃₉	—	2	1	no	—
311	C₂×C₄×C₁₃₉	—	2	1	no	—
312	C₂×C₄×C₁₃₉	—	2	2	no	—
313	C₂×C₄×C₁₃₉	—	2	2	no	—
314	C₂×C₄×C₁₃₉	—	2	2	no	—
315	C₂×C₄×C₁₃₉	—	2	2	no	—
316	C₂×C₄×C₁₃₉	—	2	4	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	2	no	—
325	C₂×C₄×C₁₃₉	—	2	4	no	—
326	C₂×C₄×C₁₃₉	—	2	2	no	—
327	C₂×C₄×C₁₃₉	—	2	2	no	—
328	C₂×C₄×C₁₃₉	—	4	8	no	—
329	C₂×C₄×C₁₃₉	—	4	8	no	—
330	C₂×C₄×C₁₃₉	—	4	4	no	—
331	C₂×C₄×C₁₃₉	—	4	4	no	—
332	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
333	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
334	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
335	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
336	C₂×C₄×C₁₃₉	C₂×#41	1	8	yes	—
337	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
338	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
339	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	4	yes	—
340	C₂²×C₁₃₉	—	2	2	no	—
341	C₂²×C₁₃₉	—	2	4	no	—
342	C₂²×C₁₃₉	—	2	2	no	—
343	C₂²×C₁₃₉	—	2	4	no	—
344	C₂²×C₁₃₉	—	2	2	no	—
345	C₂²×C₁₃₉	—	2	4	no	—
346	C₂²×C₁₃₉	—	4	1	no	—
347	C₂²×C₁₃₉	—	4	1	no	—
348	C₂²×C₁₃₉	—	4	2	no	—
349	C₂²×C₁₃₉	—	4	2	no	—
350	C₂²×C₁₃₉	—	4	2	no	—
351	C₂²×C₁₃₉	—	4	4	no	—
352	C₂²×C₁₃₉	—	4	2	no	—
353	C₂²×C₁₃₉	—	4	4	no	—
354	C₂²×C₁₃₉	#546	1	4	yes	—
355	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
356	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
357	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
358	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
359	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	2	yes	—
360	C₄×C₁₃₉	—	2	2	no	—
361	C₄×C₁₃₉	—	2	8	no	—
362	C₄×C₁₃₉	—	2	4	no	—
363	C₄×C₁₃₉	—	2	4	no	—
364	C₄×C₁₃₉	—	2	2	no	—
365	C₄×C₁₃₉	—	2	4	no	—
366	C₄×C₁₃₉	—	4	1	no	—
367	C₄×C₁₃₉	—	4	2	no	—
368	C₄×C₁₃₉	—	4	2	no	—
369	C₄×C₁₃₉	—	4	2	no	—
370	C₄×C₁₃₉	—	4	1	no	—
371	C₄×C₁₃₉	—	4	2	no	—
372	C₄×C₁₃₉	—	4	4	no	—
373	C₄×C₁₃₉	#525	1	4	yes	—
374	C₂×C₁₃₉	—	2	4	no	—
375	C₂×C₁₃₉	—	4	2	no	—
376	C₂×C₁₃₉	—	8	2	no	—
377	C₂×C₁₃₉	C₂×#525	1	1	yes	characteristic
378	C₂×C₁₃₉	C₂×#546	1	1	yes	characteristic
379	C₂×C₁₃₉	#3482	1	2	yes	—
380	C₂×C₁₃₉	#3486	1	1	yes	characteristic
381	C₂×C₁₃₉	#3522	1	2	yes	—
382	#36422	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
383	C₁₃₉	#36422	1	1	yes	characteristic, direct product factor, Sylow
384	C₂×#547	C₂×C₁₃₉	1	1	yes	characteristic
385	C₂²×C₄×Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
386	#2854	C₂×C₁₃₉	1	1	yes	characteristic, complemented
387	#2853	C₂×C₁₃₉	1	2	yes	complemented
388	#2465	C₂×C₁₃₉	1	4	yes	complemented
389	#2458	C₂×C₁₃₉	1	4	yes	complemented
390	#2451	C₂×C₁₃₉	1	2	yes	complemented
391	#2436	C₂×C₁₃₉	1	1	yes	characteristic, complemented
392	#2426	C₂×C₁₃₉	1	2	yes	complemented
393	#2413	C₂×C₁₃₉	1	2	yes	complemented
394	#2409	C₂×C₁₃₉	1	1	yes	characteristic, complemented
395	#2406	C₂×C₁₃₉	1	2	yes	complemented
396	#2367	C₂×C₁₃₉	1	2	yes	complemented
397	#2360	C₂×C₁₃₉	1	2	yes	complemented
398	#2344	C₂×C₁₃₉	1	1	yes	characteristic, complemented
399	C₄×#123	C₂×C₁₃₉	1	1	yes	characteristic, complemented
400	#2297	C₂×C₁₃₉	1	2	yes	complemented
401	C₂²×#41	C₂²×C₁₃₉	1	2	yes	—
402	C₂³×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
403	#547	—	2	8	no	—
404	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
405	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
406	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
407	C₂×#123	C₂²×C₁₃₉	1	1	yes	characteristic
408	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
409	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
410	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
411	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
412	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
413	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
414	C₂×C₄×Q₈	—	2	8	no	—
415	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
416	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
417	C₂×C₄×Q₈	C₂²×C₁₃₉	1	4	yes	—
418	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
419	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
420	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
421	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
422	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
423	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
424	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
425	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
426	#398	C₂²×C₁₃₉	1	4	yes	—
427	#396	C₂²×C₁₃₉	1	4	yes	—
428	#395	C₂²×C₁₃₉	1	4	yes	—
429	#395	C₂²×C₁₃₉	1	2	yes	—
430	#394	C₂²×C₁₃₉	1	4	yes	—
431	#393	C₂²×C₁₃₉	1	2	yes	—
432	#393	C₂²×C₁₃₉	1	4	yes	—
433	#391	C₂²×C₁₃₉	1	2	yes	—
434	#391	C₂²×C₁₃₉	1	2	yes	—
435	#391	C₂²×C₁₃₉	1	4	yes	—
436	#390	C₂²×C₁₃₉	1	2	yes	—
437	#390	C₂²×C₁₃₉	1	4	yes	—
438	#389	C₂²×C₁₃₉	1	2	yes	—
439	#389	C₂²×C₁₃₉	1	2	yes	—
440	#389	C₂²×C₁₃₉	1	4	yes	—
441	#388	C₂²×C₁₃₉	1	4	yes	—
442	#388	C₂²×C₁₃₉	1	4	yes	—
443	#388	C₂²×C₁₃₉	1	4	yes	—
444	#388	C₂²×C₁₃₉	1	4	yes	—
445	#388	C₂²×C₁₃₉	1	2	yes	—
446	#387	C₂²×C₁₃₉	1	4	yes	—
447	#387	C₂²×C₁₃₉	1	4	yes	—
448	#387	C₂²×C₁₃₉	1	4	yes	—
449	#387	C₂²×C₁₃₉	1	2	yes	—
450	#386	C₂²×C₁₃₉	1	2	yes	—
451	#386	C₂²×C₁₃₉	1	2	yes	—
452	#386	C₂²×C₁₃₉	1	2	yes	—
453	#386	C₂²×C₁₃₉	1	2	yes	—
454	#386	C₂²×C₁₃₉	1	1	yes	characteristic
455	#385	C₂²×C₁₃₉	1	1	yes	characteristic
456	#385	C₂²×C₁₃₉	1	2	yes	—
457	#385	C₂²×C₁₃₉	1	4	yes	—
458	#385	C₂²×C₁₃₉	1	4	yes	—
459	#381	C₂²×C₁₃₉	1	2	yes	—
460	#381	C₂²×C₁₃₉	1	1	yes	characteristic
461	#380	C₂²×C₁₃₉	1	1	yes	characteristic
462	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
463	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
464	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
465	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
466	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
467	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
468	C₂×#41	—	2	8	no	—
469	C₂×#41	—	2	8	no	—
470	C₂×#41	—	4	4	no	—
471	C₂²×Q₈	—	2	8	no	—
472	C₂²×Q₈	—	2	4	no	—
473	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
474	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
475	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
476	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
477	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
478	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
479	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
480	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
481	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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	2	yes	—
486	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
487	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
488	C₄⋊Q₈	—	2	4	no	—
489	#124	—	2	8	no	—
490	#123	—	2	4	no	—
491	#123	—	2	8	no	—
492	#123	—	2	8	no	—
493	#123	—	4	4	no	—
494	C₂²⋊Q₈	—	2	8	no	—
495	C₂²⋊Q₈	—	2	8	no	—
496	#121	—	2	4	no	—
497	#121	—	2	4	no	—
498	C₄×Q₈	—	2	8	no	—
499	C₄×Q₈	—	2	8	no	—
500	C₄×Q₈	—	2	16	no	—
501	C₄×D₄	—	2	4	no	—
502	C₄×D₄	—	2	4	no	—
503	#117	—	4	4	no	—
504	C₂×C₄⋊C₄	—	2	8	no	—
505	C₂×C₄⋊C₄	—	2	4	no	—
506	C₂×C₄⋊C₄	D₄×C₁₃₉	1	8	yes	—
507	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
508	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
509	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
510	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
511	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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	2	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	4	yes	—
518	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
519	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
520	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
521	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
523	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
525	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
526	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
527	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
528	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
529	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
530	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
531	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
532	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
533	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
534	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
535	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
536	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
537	C₂×C₄²	—	2	8	no	—
538	C₂×C₄²	—	2	4	no	—
539	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
540	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
541	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
542	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
543	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
544	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
545	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
546	#95	C₂³×C₁₃₉	1	2	yes	—
547	#95	C₂³×C₁₃₉	1	2	yes	—
548	#95	C₂³×C₁₃₉	1	4	yes	—
549	#95	C₂³×C₁₃₉	1	2	yes	—
550	#95	C₂³×C₁₃₉	1	4	yes	—
551	#95	C₂³×C₁₃₉	1	4	yes	—
552	#95	C₂³×C₁₃₉	1	2	yes	—
553	#95	C₂³×C₁₃₉	1	4	yes	—
554	#95	C₂³×C₁₃₉	1	2	yes	—
555	#95	C₂³×C₁₃₉	1	2	yes	—
556	#95	C₂³×C₁₃₉	1	4	yes	—
557	#95	C₂³×C₁₃₉	1	4	yes	—
558	#95	C₂³×C₁₃₉	1	4	yes	—
559	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
560	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
561	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
562	#41	—	4	32	no	—
563	C₂×Q₈	—	2	32	no	—
564	C₂×Q₈	—	2	4	no	—
565	C₂×Q₈	—	2	4	no	—
566	C₂×Q₈	—	2	4	no	—
567	C₂×Q₈	—	2	8	no	—
568	C₂×Q₈	—	2	4	no	—
569	C₂×Q₈	—	2	4	no	—
570	C₂×Q₈	—	4	2	no	—
571	C₂×Q₈	#41×C₁₃₉	1	8	yes	complemented
572	C₂×D₄	—	2	2	no	—
573	C₂×D₄	—	2	2	no	—
574	C₂×D₄	—	2	4	no	—
575	C₂×D₄	—	2	4	no	—
576	C₂×D₄	—	2	4	no	—
577	C₂×D₄	—	2	4	no	—
578	C₂×D₄	—	2	2	no	—
579	C₂×D₄	—	2	4	no	—
580	C₂×D₄	—	2	4	no	—
581	C₂×D₄	—	4	2	no	—
582	C₂×D₄	#41×C₁₃₉	1	4	yes	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	2	4	no	—
585	C₂²×C₄	—	2	4	no	—
586	C₂²×C₄	—	2	4	no	—
587	C₂²×C₄	—	2	8	no	—
588	C₂²×C₄	—	2	4	no	—
589	C₂²×C₄	—	2	4	no	—
590	C₂²×C₄	—	2	2	no	—
591	C₂²×C₄	—	2	2	no	—
592	C₂²×C₄	—	2	4	no	—
593	C₂²×C₄	—	2	2	no	—
594	C₂²×C₄	—	2	2	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	—	4	2	no	—
600	C₂²×C₄	—	4	2	no	—
601	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
602	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
603	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
604	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
605	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
606	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
607	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
608	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
609	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
610	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
611	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
612	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
613	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
614	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
615	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
616	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
617	C₄⋊C₄	—	2	8	no	—
618	C₄⋊C₄	—	2	8	no	—
619	C₄⋊C₄	—	2	2	no	—
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	—	2	2	no	—
622	C₄⋊C₄	—	2	4	no	—
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	8	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	4	4	no	—
628	C₄⋊C₄	—	4	4	no	—
629	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
630	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
631	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
632	C₂²⋊C₄	—	2	2	no	—
633	C₂²⋊C₄	—	2	2	no	—
634	C₂²⋊C₄	—	2	4	no	—
635	C₂²⋊C₄	—	2	2	no	—
636	C₂²⋊C₄	—	2	4	no	—
637	C₂²⋊C₄	—	2	2	no	—
638	C₂²⋊C₄	—	2	4	no	—
639	C₂²⋊C₄	—	2	4	no	—
640	C₂²⋊C₄	—	2	4	no	—
641	C₂²⋊C₄	—	2	8	no	—
642	C₂²⋊C₄	—	2	8	no	—
643	C₂²⋊C₄	—	2	8	no	—
644	C₂²⋊C₄	—	2	4	no	—
645	C₂²⋊C₄	—	2	8	no	—
646	C₂²⋊C₄	—	4	4	no	—
647	C₄²	—	2	8	no	—
648	C₄²	—	2	8	no	—
649	C₄²	—	2	4	no	—
650	C₄²	—	2	4	no	—
651	C₄²	—	2	2	no	—
652	C₄²	—	2	4	no	—
653	C₄²	—	4	4	no	—
654	C₂³	—	2	2	no	—
655	C₂³	—	2	2	no	—
656	C₂³	—	2	1	no	—
657	C₂³	—	2	2	no	—
658	C₂³	—	2	1	no	—
659	C₂³	—	2	2	no	—
660	C₂³	—	2	2	no	—
661	C₂³	—	2	4	no	—
662	C₂³	—	2	2	no	—
663	C₂³	—	2	2	no	—
664	C₂³	—	2	4	no	—
665	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
666	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
667	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
668	C₂³	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
669	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
670	Q₈	—	2	16	no	—
671	Q₈	—	2	16	no	—
672	Q₈	—	4	8	no	—
673	D₄	—	2	8	no	—
674	D₄	—	4	8	no	—
675	D₄	—	4	8	no	—
676	D₄	—	4	4	no	—
677	C₂×C₄	—	2	16	no	—
678	C₂×C₄	—	2	8	no	—
679	C₂×C₄	—	2	16	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	4	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	4	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	8	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	4	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	4	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	4	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	4	8	no	—
712	C₂×C₄	—	4	8	no	—
713	C₂×C₄	—	4	4	no	—
714	C₂×C₄	—	4	4	no	—
715	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
716	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
717	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
718	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
719	C₂×C₄	C₂×#41×C₁₃₉	1	8	yes	—
720	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
721	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
722	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	4	yes	—
723	C₂²	—	2	2	no	—
724	C₂²	—	2	4	no	—
725	C₂²	—	2	2	no	—
726	C₂²	—	2	4	no	—
727	C₂²	—	2	2	no	—
728	C₂²	—	2	4	no	—
729	C₂²	—	4	1	no	—
730	C₂²	—	4	1	no	—
731	C₂²	—	4	2	no	—
732	C₂²	—	4	2	no	—
733	C₂²	—	4	2	no	—
734	C₂²	—	4	4	no	—
735	C₂²	—	4	2	no	—
736	C₂²	—	4	4	no	—
737	C₂²	#546×C₁₃₉	1	4	yes	—
738	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
739	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
740	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
741	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
742	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	2	yes	—
743	C₄	—	2	2	no	—
744	C₄	—	2	8	no	—
745	C₄	—	2	4	no	—
746	C₄	—	2	4	no	—
747	C₄	—	2	2	no	—
748	C₄	—	2	4	no	—
749	C₄	—	4	1	no	—
750	C₄	—	4	2	no	—
751	C₄	—	4	2	no	—
752	C₄	—	4	2	no	—
753	C₄	—	4	1	no	—
754	C₄	—	4	2	no	—
755	C₄	—	4	4	no	—
756	C₄	#525×C₁₃₉	1	4	yes	—
757	C₂	—	2	4	no	—
758	C₂	—	4	2	no	—
759	C₂	—	8	2	no	—
760	C₂	C₂×#525×C₁₃₉	1	1	yes	characteristic
761	C₂	C₂×#546×C₁₃₉	1	1	yes	characteristic
762	C₂	#3482×C₁₃₉	1	2	yes	—
763	C₂	#3486×C₁₃₉	1	1	yes	characteristic
764	C₂	#3522×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂×#547×C₁₃₉	C₂
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
2. C₂²×C₄×Q₈×C₁₃₉	C₂	semidirect
3. #2854×C₁₃₉	C₂	semidirect
4. #2853×C₁₃₉	C₂	semidirect
5. #2465×C₁₃₉	C₂	semidirect
6. #2458×C₁₃₉	C₂	semidirect
7. #2451×C₁₃₉	C₂	semidirect
8. #2436×C₁₃₉	C₂	semidirect
9. #2426×C₁₃₉	C₂	semidirect
10. #2413×C₁₃₉	C₂	semidirect
11. #2409×C₁₃₉	C₂	semidirect
12. #2406×C₁₃₉	C₂	semidirect
13. #2367×C₁₃₉	C₂	semidirect
14. #2360×C₁₃₉	C₂	semidirect
15. #2344×C₁₃₉	C₂	semidirect
16. C₄×#123×C₁₃₉	C₂	semidirect
17. #2297×C₁₃₉	C₂	semidirect
188. C₂×Q₈×C₁₃₉	#41	semidirect
382. #36422	C₁₃₉	direct (N × H)
383. C₁₃₉	#36422	direct (N × H)
385. C₂²×C₄×Q₈	C₂×C₁₃₉	semidirect
386. #2854	C₂×C₁₃₉	semidirect
387. #2853	C₂×C₁₃₉	semidirect
388. #2465	C₂×C₁₃₉	semidirect
389. #2458	C₂×C₁₃₉	semidirect
390. #2451	C₂×C₁₃₉	semidirect
391. #2436	C₂×C₁₃₉	semidirect
392. #2426	C₂×C₁₃₉	semidirect
393. #2413	C₂×C₁₃₉	semidirect
394. #2409	C₂×C₁₃₉	semidirect
395. #2406	C₂×C₁₃₉	semidirect
396. #2367	C₂×C₁₃₉	semidirect
397. #2360	C₂×C₁₃₉	semidirect
398. #2344	C₂×C₁₃₉	semidirect
399. C₄×#123	C₂×C₁₃₉	semidirect
400. #2297	C₂×C₁₃₉	semidirect
571. C₂×Q₈	#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×#547×C₁₃₉	2
C₂²×C₄×Q₈×C₁₃₉	2
#2854×C₁₃₉	2
#2853×C₁₃₉	2
#2465×C₁₃₉	2
#2458×C₁₃₉	2
#2451×C₁₃₉	2
#2436×C₁₃₉	2
#2426×C₁₃₉	2
#2413×C₁₃₉	2
#2409×C₁₃₉	2
#2406×C₁₃₉	2
#2367×C₁₃₉	2
#2360×C₁₃₉	2
#2344×C₁₃₉	2
C₄×#123×C₁₃₉	2
#2297×C₁₃₉	2
#36422	139

Subgroups — C139×#36422 #48031018

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36422 #48031018