Subgroups — C₁₃₉×#35956 #48030552

Order 35584.

2340 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#559×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#556×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2662×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2657×C₁₃₉	C₂	1	1	yes	maximal, characteristic
5	#2610×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2603×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2592×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2554×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#2548×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2548×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#2545×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2461×C₁₃₉	C₂	1	4	yes	maximal, complemented
13	#2399×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2392×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2367×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2366×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	#2276×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	#559×C₁₃₉	—	2	8	no	—
19	#556×C₁₃₉	—	2	8	no	—
20	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×#127×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
23	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
25	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
26	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
27	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
30	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
31	C₂×#123×C₁₃₉	C₂²	1	4	yes	—
32	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
33	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
34	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
35	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
39	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
41	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	—
42	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
43	#398×C₁₃₉	C₂²	1	2	yes	—
44	#398×C₁₃₉	C₂²	1	1	yes	characteristic
45	#398×C₁₃₉	C₂²	1	1	yes	characteristic
46	#397×C₁₃₉	C₂²	1	2	yes	—
47	#396×C₁₃₉	C₂²	1	4	yes	—
48	#396×C₁₃₉	C₂²	1	4	yes	—
49	#395×C₁₃₉	C₂²	1	1	yes	characteristic
50	#395×C₁₃₉	C₂²	1	1	yes	characteristic
51	#395×C₁₃₉	C₂²	1	2	yes	—
52	#394×C₁₃₉	C₂²	1	4	yes	—
53	#394×C₁₃₉	C₂²	1	2	yes	—
54	#394×C₁₃₉	C₂²	1	2	yes	—
55	#394×C₁₃₉	C₂²	1	4	yes	—
56	#393×C₁₃₉	C₂²	1	2	yes	—
57	#392×C₁₃₉	C₂²	1	4	yes	—
58	#392×C₁₃₉	C₂²	1	2	yes	—
59	#392×C₁₃₉	C₂²	1	2	yes	—
60	#391×C₁₃₉	C₂²	1	2	yes	—
61	#390×C₁₃₉	C₂²	1	2	yes	—
62	#390×C₁₃₉	C₂²	1	2	yes	—
63	#390×C₁₃₉	C₂²	1	2	yes	—
64	#390×C₁₃₉	C₂²	1	4	yes	—
65	#390×C₁₃₉	C₂²	1	2	yes	—
66	#390×C₁₃₉	C₂²	1	4	yes	—
67	#390×C₁₃₉	C₂²	1	4	yes	—
68	#388×C₁₃₉	C₂²	1	4	yes	—
69	#388×C₁₃₉	C₂²	1	4	yes	—
70	#388×C₁₃₉	C₂²	1	4	yes	—
71	#388×C₁₃₉	C₂²	1	4	yes	—
72	#388×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	4	yes	—
78	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
79	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
80	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
81	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
82	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
83	#376×C₁₃₉	C₂²	1	2	yes	—
84	#376×C₁₃₉	C₂²	1	1	yes	characteristic
85	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
86	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
87	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
88	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
91	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
92	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
93	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
94	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
95	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
96	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
97	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
98	#127×C₁₃₉	—	2	4	no	—
99	#127×C₁₃₉	—	2	8	no	—
100	#126×C₁₃₉	—	2	8	no	—
101	#126×C₁₃₉	—	2	8	no	—
102	#124×C₁₃₉	—	2	4	no	—
103	#124×C₁₃₉	—	2	8	no	—
104	#124×C₁₃₉	—	2	4	no	—
105	#124×C₁₃₉	—	2	8	no	—
106	#124×C₁₃₉	—	2	8	no	—
107	#124×C₁₃₉	—	4	4	no	—
108	#123×C₁₃₉	—	2	16	no	—
109	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
110	C₄×Q₈×C₁₃₉	—	2	4	no	—
111	C₄×Q₈×C₁₃₉	—	2	4	no	—
112	C₄×Q₈×C₁₃₉	—	2	4	no	—
113	C₄×Q₈×C₁₃₉	—	2	8	no	—
114	C₄×Q₈×C₁₃₉	D₄	1	8	yes	complemented
115	C₄×D₄×C₁₃₉	—	2	4	no	—
116	C₄×D₄×C₁₃₉	—	2	8	no	—
117	C₄×D₄×C₁₃₉	—	2	8	no	—
118	C₄×D₄×C₁₃₉	—	4	8	no	—
119	#117×C₁₃₉	—	2	8	no	—
120	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
124	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	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	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	2	yes	—
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×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
137	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
138	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
139	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	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	4	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	2	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	4	yes	—
149	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
150	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
151	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
152	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
153	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
154	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
155	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
156	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
157	C₂×C₄²×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	#95×C₁₃₉	C₂³	1	2	yes	—
163	#95×C₁₃₉	C₂³	1	2	yes	—
164	#95×C₁₃₉	C₂³	1	1	yes	characteristic
165	#95×C₁₃₉	C₂³	1	1	yes	characteristic
166	#95×C₁₃₉	C₂³	1	2	yes	—
167	#95×C₁₃₉	C₂³	1	4	yes	—
168	#95×C₁₃₉	C₂³	1	4	yes	—
169	#95×C₁₃₉	C₂³	1	2	yes	—
170	#95×C₁₃₉	C₂³	1	2	yes	—
171	#95×C₁₃₉	C₂³	1	2	yes	—
172	#95×C₁₃₉	C₂³	1	4	yes	—
173	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
174	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
175	C₂×Q₈×C₁₃₉	—	2	2	no	—
176	C₂×Q₈×C₁₃₉	—	2	2	no	—
177	C₂×Q₈×C₁₃₉	—	2	2	no	—
178	C₂×Q₈×C₁₃₉	—	2	4	no	—
179	C₂×Q₈×C₁₃₉	—	2	4	no	—
180	C₂×Q₈×C₁₃₉	—	2	2	no	—
181	C₂×Q₈×C₁₃₉	—	4	1	no	—
182	C₂×Q₈×C₁₃₉	—	4	2	no	—
183	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	—
184	C₂×D₄×C₁₃₉	—	2	2	no	—
185	C₂×D₄×C₁₃₉	—	2	4	no	—
186	C₂×D₄×C₁₃₉	—	2	4	no	—
187	C₂×D₄×C₁₃₉	—	2	4	no	—
188	C₂×D₄×C₁₃₉	—	2	4	no	—
189	C₂×D₄×C₁₃₉	—	2	8	no	—
190	C₂×D₄×C₁₃₉	—	2	4	no	—
191	C₂×D₄×C₁₃₉	—	2	4	no	—
192	C₂×D₄×C₁₃₉	—	2	8	no	—
193	C₂×D₄×C₁₃₉	—	4	4	no	—
194	C₂×D₄×C₁₃₉	—	4	4	no	—
195	C₂×D₄×C₁₃₉	—	4	4	no	—
196	C₂×D₄×C₁₃₉	—	4	2	no	—
197	C₂×D₄×C₁₃₉	—	4	4	no	—
198	C₂×D₄×C₁₃₉	—	4	4	no	—
199	C₂×D₄×C₁₃₉	—	4	2	no	—
200	C₂²×C₄×C₁₃₉	—	2	4	no	—
201	C₂²×C₄×C₁₃₉	—	2	4	no	—
202	C₂²×C₄×C₁₃₉	—	2	8	no	—
203	C₂²×C₄×C₁₃₉	—	4	2	no	—
204	C₂²×C₄×C₁₃₉	—	4	4	no	—
205	C₂²×C₄×C₁₃₉	—	4	4	no	—
206	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
207	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
208	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
209	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
211	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
212	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
213	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
214	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
216	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₁₃₉	C₂⁴	1	2	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	C₄⋊C₄×C₁₃₉	—	2	2	no	—
222	C₄⋊C₄×C₁₃₉	—	2	4	no	—
223	C₄⋊C₄×C₁₃₉	—	2	2	no	—
224	C₄⋊C₄×C₁₃₉	—	2	4	no	—
225	C₄⋊C₄×C₁₃₉	—	2	4	no	—
226	C₄⋊C₄×C₁₃₉	—	2	2	no	—
227	C₄⋊C₄×C₁₃₉	—	2	2	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	4	no	—
232	C₄⋊C₄×C₁₃₉	—	4	2	no	—
233	C₄⋊C₄×C₁₃₉	—	4	2	no	—
234	C₄⋊C₄×C₁₃₉	—	4	2	no	—
235	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
236	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
237	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
238	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
239	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
240	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
241	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
242	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
243	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
244	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
245	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
246	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
247	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
248	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
249	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
250	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
251	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
252	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
253	C₄²×C₁₃₉	—	2	4	no	—
254	C₄²×C₁₃₉	—	2	4	no	—
255	C₄²×C₁₃₉	—	2	2	no	—
256	C₄²×C₁₃₉	—	2	2	no	—
257	C₄²×C₁₃₉	—	2	8	no	—
258	C₄²×C₁₃₉	—	4	4	no	—
259	C₄²×C₁₃₉	—	4	2	no	—
260	C₄²×C₁₃₉	C₂×D₄	1	8	yes	—
261	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
262	C₄²×C₁₃₉	#41	1	8	yes	—
263	C₂³×C₁₃₉	—	2	2	no	—
264	C₂³×C₁₃₉	—	2	4	no	—
265	C₂³×C₁₃₉	—	2	4	no	—
266	C₂³×C₁₃₉	—	2	4	no	—
267	C₂³×C₁₃₉	—	2	4	no	—
268	C₂³×C₁₃₉	—	2	4	no	—
269	C₂³×C₁₃₉	—	2	2	no	—
270	C₂³×C₁₃₉	—	2	4	no	—
271	C₂³×C₁₃₉	—	2	4	no	—
272	C₂³×C₁₃₉	—	2	4	no	—
273	C₂³×C₁₃₉	—	2	2	no	—
274	C₂³×C₁₃₉	—	2	4	no	—
275	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
276	Q₈×C₁₃₉	—	2	8	no	—
277	Q₈×C₁₃₉	—	4	4	no	—
278	Q₈×C₁₃₉	—	4	4	no	—
279	Q₈×C₁₃₉	—	4	4	no	—
280	D₄×C₁₃₉	—	4	8	no	—
281	D₄×C₁₃₉	—	4	16	no	—
282	D₄×C₁₃₉	—	4	4	no	—
283	D₄×C₁₃₉	—	4	8	no	—
284	D₄×C₁₃₉	—	8	4	no	—
285	D₄×C₁₃₉	—	8	8	no	—
286	C₂×C₄×C₁₃₉	—	2	1	no	—
287	C₂×C₄×C₁₃₉	—	2	4	no	—
288	C₂×C₄×C₁₃₉	—	2	2	no	—
289	C₂×C₄×C₁₃₉	—	2	2	no	—
290	C₂×C₄×C₁₃₉	—	2	1	no	—
291	C₂×C₄×C₁₃₉	—	2	2	no	—
292	C₂×C₄×C₁₃₉	—	2	2	no	—
293	C₂×C₄×C₁₃₉	—	2	2	no	—
294	C₂×C₄×C₁₃₉	—	2	2	no	—
295	C₂×C₄×C₁₃₉	—	2	1	no	—
296	C₂×C₄×C₁₃₉	—	2	2	no	—
297	C₂×C₄×C₁₃₉	—	2	1	no	—
298	C₂×C₄×C₁₃₉	—	2	1	no	—
299	C₂×C₄×C₁₃₉	—	2	2	no	—
300	C₂×C₄×C₁₃₉	—	2	1	no	—
301	C₂×C₄×C₁₃₉	—	2	2	no	—
302	C₂×C₄×C₁₃₉	—	2	1	no	—
303	C₂×C₄×C₁₃₉	—	2	2	no	—
304	C₂×C₄×C₁₃₉	—	2	4	no	—
305	C₂×C₄×C₁₃₉	—	2	4	no	—
306	C₂×C₄×C₁₃₉	—	2	4	no	—
307	C₂×C₄×C₁₃₉	—	2	1	no	—
308	C₂×C₄×C₁₃₉	—	2	2	no	—
309	C₂×C₄×C₁₃₉	—	2	4	no	—
310	C₂×C₄×C₁₃₉	—	2	2	no	—
311	C₂×C₄×C₁₃₉	—	2	2	no	—
312	C₂×C₄×C₁₃₉	—	2	2	no	—
313	C₂×C₄×C₁₃₉	—	2	2	no	—
314	C₂×C₄×C₁₃₉	—	2	1	no	—
315	C₂×C₄×C₁₃₉	—	2	2	no	—
316	C₂×C₄×C₁₃₉	—	4	8	no	—
317	C₂×C₄×C₁₃₉	—	8	8	no	—
318	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
319	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
320	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
321	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
322	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
323	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
324	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
325	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
326	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
327	C₂²×C₁₃₉	—	4	2	no	—
328	C₂²×C₁₃₉	—	4	4	no	—
329	C₂²×C₁₃₉	—	4	4	no	—
330	C₂²×C₁₃₉	—	4	2	no	—
331	C₂²×C₁₃₉	—	4	2	no	—
332	C₂²×C₁₃₉	—	4	4	no	—
333	C₂²×C₁₃₉	—	4	4	no	—
334	C₂²×C₁₃₉	—	4	4	no	—
335	C₂²×C₁₃₉	—	4	4	no	—
336	C₂²×C₁₃₉	—	4	4	no	—
337	C₂²×C₁₃₉	—	4	4	no	—
338	C₂²×C₁₃₉	—	4	4	no	—
339	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
340	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
341	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
342	C₂²×C₁₃₉	#585	1	2	yes	—
343	C₂²×C₁₃₉	#585	1	1	yes	characteristic
344	C₄×C₁₃₉	—	2	4	no	—
345	C₄×C₁₃₉	—	2	2	no	—
346	C₄×C₁₃₉	—	2	2	no	—
347	C₄×C₁₃₉	—	2	4	no	—
348	C₄×C₁₃₉	—	2	2	no	—
349	C₄×C₁₃₉	—	2	4	no	—
350	C₄×C₁₃₉	—	2	4	no	—
351	C₄×C₁₃₉	—	4	2	no	—
352	C₄×C₁₃₉	—	4	1	no	—
353	C₄×C₁₃₉	—	4	1	no	—
354	C₄×C₁₃₉	—	4	2	no	—
355	C₄×C₁₃₉	—	4	2	no	—
356	C₄×C₁₃₉	—	4	1	no	—
357	C₄×C₁₃₉	—	4	4	no	—
358	C₄×C₁₃₉	#532	1	4	yes	—
359	C₂×C₁₃₉	—	8	4	no	—
360	C₂×C₁₃₉	—	8	2	no	—
361	C₂×C₁₃₉	C₂×#532	1	1	yes	characteristic
362	C₂×C₁₃₉	#3487	1	1	yes	characteristic
363	C₂×C₁₃₉	#3488	1	1	yes	characteristic
364	C₂×C₁₃₉	#3506	1	2	yes	—
365	C₂×C₁₃₉	#3510	1	2	yes	—
366	#35956	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
367	C₁₃₉	#35956	1	1	yes	characteristic, direct product factor, Sylow
368	C₂×#559	C₂×C₁₃₉	1	1	yes	characteristic, complemented
369	C₂×#556	C₂×C₁₃₉	1	1	yes	characteristic, complemented
370	#2662	C₂×C₁₃₉	1	2	yes	complemented
371	#2657	C₂×C₁₃₉	1	1	yes	characteristic
372	#2610	C₂×C₁₃₉	1	2	yes	complemented
373	#2603	C₂×C₁₃₉	1	2	yes	complemented
374	#2592	C₂×C₁₃₉	1	1	yes	characteristic, complemented
375	#2554	C₂×C₁₃₉	1	4	yes	complemented
376	#2548	C₂×C₁₃₉	1	1	yes	characteristic, complemented
377	#2548	C₂×C₁₃₉	1	2	yes	complemented
378	#2545	C₂×C₁₃₉	1	2	yes	complemented
379	#2461	C₂×C₁₃₉	1	4	yes	complemented
380	#2399	C₂×C₁₃₉	1	1	yes	characteristic, complemented
381	#2392	C₂×C₁₃₉	1	2	yes	complemented
382	#2367	C₂×C₁₃₉	1	2	yes	complemented
383	#2366	C₂×C₁₃₉	1	2	yes	complemented
384	#2276	C₂×C₁₃₉	1	1	yes	characteristic, complemented
385	#559	—	2	8	no	—
386	#556	—	2	8	no	—
387	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
388	C₂×#127	C₂²×C₁₃₉	1	2	yes	—
389	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
390	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
391	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
392	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
393	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
394	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
395	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
396	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
397	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
398	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
399	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
400	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
401	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
402	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
403	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
404	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
405	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
406	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
407	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
408	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	—
409	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
410	#398	C₂²×C₁₃₉	1	1	yes	characteristic
411	#398	C₂²×C₁₃₉	1	1	yes	characteristic
412	#398	C₂²×C₁₃₉	1	2	yes	—
413	#397	C₂²×C₁₃₉	1	2	yes	—
414	#396	C₂²×C₁₃₉	1	4	yes	—
415	#396	C₂²×C₁₃₉	1	4	yes	—
416	#395	C₂²×C₁₃₉	1	1	yes	characteristic
417	#395	C₂²×C₁₃₉	1	1	yes	characteristic
418	#395	C₂²×C₁₃₉	1	2	yes	—
419	#394	C₂²×C₁₃₉	1	2	yes	—
420	#394	C₂²×C₁₃₉	1	2	yes	—
421	#394	C₂²×C₁₃₉	1	4	yes	—
422	#394	C₂²×C₁₃₉	1	4	yes	—
423	#393	C₂²×C₁₃₉	1	2	yes	—
424	#392	C₂²×C₁₃₉	1	2	yes	—
425	#392	C₂²×C₁₃₉	1	2	yes	—
426	#392	C₂²×C₁₃₉	1	4	yes	—
427	#391	C₂²×C₁₃₉	1	2	yes	—
428	#390	C₂²×C₁₃₉	1	2	yes	—
429	#390	C₂²×C₁₃₉	1	4	yes	—
430	#390	C₂²×C₁₃₉	1	4	yes	—
431	#390	C₂²×C₁₃₉	1	4	yes	—
432	#390	C₂²×C₁₃₉	1	2	yes	—
433	#390	C₂²×C₁₃₉	1	2	yes	—
434	#390	C₂²×C₁₃₉	1	2	yes	—
435	#388	C₂²×C₁₃₉	1	4	yes	—
436	#388	C₂²×C₁₃₉	1	4	yes	—
437	#388	C₂²×C₁₃₉	1	4	yes	—
438	#388	C₂²×C₁₃₉	1	4	yes	—
439	#388	C₂²×C₁₃₉	1	4	yes	—
440	#386	C₂²×C₁₃₉	1	4	yes	—
441	#386	C₂²×C₁₃₉	1	4	yes	—
442	#385	C₂²×C₁₃₉	1	4	yes	—
443	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
444	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
445	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
446	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
447	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
448	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
449	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
450	#376	C₂²×C₁₃₉	1	2	yes	—
451	#376	C₂²×C₁₃₉	1	1	yes	characteristic
452	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
453	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
454	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
455	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
456	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
457	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
458	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
459	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
460	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
461	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
462	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
463	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
464	C₄⋊Q₈	—	2	4	no	—
465	#127	—	2	4	no	—
466	#127	—	2	8	no	—
467	#126	—	2	8	no	—
468	#126	—	2	8	no	—
469	#124	—	2	4	no	—
470	#124	—	2	8	no	—
471	#124	—	2	4	no	—
472	#124	—	2	8	no	—
473	#124	—	2	8	no	—
474	#124	—	4	4	no	—
475	#123	—	2	16	no	—
476	C₂²⋊Q₈	—	2	8	no	—
477	C₄×Q₈	—	2	4	no	—
478	C₄×Q₈	—	2	4	no	—
479	C₄×Q₈	—	2	4	no	—
480	C₄×Q₈	—	2	8	no	—
481	C₄×Q₈	D₄×C₁₃₉	1	8	yes	complemented
482	C₄×D₄	—	2	4	no	—
483	C₄×D₄	—	2	8	no	—
484	C₄×D₄	—	2	8	no	—
485	C₄×D₄	—	4	8	no	—
486	#117	—	2	8	no	—
487	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
488	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
489	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
490	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
491	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
492	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
493	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
494	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
495	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
496	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
497	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
498	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
499	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
500	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
501	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
502	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
503	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
504	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
505	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
506	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
507	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
508	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
509	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
510	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
511	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
513	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
514	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
515	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
519	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
520	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
521	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
522	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
523	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
524	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
525	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
526	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
527	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
528	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
529	#95	C₂³×C₁₃₉	1	1	yes	characteristic
530	#95	C₂³×C₁₃₉	1	4	yes	—
531	#95	C₂³×C₁₃₉	1	1	yes	characteristic
532	#95	C₂³×C₁₃₉	1	2	yes	—
533	#95	C₂³×C₁₃₉	1	2	yes	—
534	#95	C₂³×C₁₃₉	1	2	yes	—
535	#95	C₂³×C₁₃₉	1	4	yes	—
536	#95	C₂³×C₁₃₉	1	2	yes	—
537	#95	C₂³×C₁₃₉	1	2	yes	—
538	#95	C₂³×C₁₃₉	1	2	yes	—
539	#95	C₂³×C₁₃₉	1	4	yes	—
540	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
541	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
542	C₂×Q₈	—	2	2	no	—
543	C₂×Q₈	—	2	2	no	—
544	C₂×Q₈	—	2	2	no	—
545	C₂×Q₈	—	2	4	no	—
546	C₂×Q₈	—	2	4	no	—
547	C₂×Q₈	—	2	2	no	—
548	C₂×Q₈	—	4	1	no	—
549	C₂×Q₈	—	4	2	no	—
550	C₂×Q₈	C₂×D₄×C₁₃₉	1	4	yes	—
551	C₂×D₄	—	2	2	no	—
552	C₂×D₄	—	2	4	no	—
553	C₂×D₄	—	2	4	no	—
554	C₂×D₄	—	2	4	no	—
555	C₂×D₄	—	2	4	no	—
556	C₂×D₄	—	2	8	no	—
557	C₂×D₄	—	2	4	no	—
558	C₂×D₄	—	2	4	no	—
559	C₂×D₄	—	2	8	no	—
560	C₂×D₄	—	4	4	no	—
561	C₂×D₄	—	4	4	no	—
562	C₂×D₄	—	4	4	no	—
563	C₂×D₄	—	4	2	no	—
564	C₂×D₄	—	4	4	no	—
565	C₂×D₄	—	4	4	no	—
566	C₂×D₄	—	4	2	no	—
567	C₂²×C₄	—	2	4	no	—
568	C₂²×C₄	—	2	4	no	—
569	C₂²×C₄	—	2	8	no	—
570	C₂²×C₄	—	4	2	no	—
571	C₂²×C₄	—	4	4	no	—
572	C₂²×C₄	—	4	4	no	—
573	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
574	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
575	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
576	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
577	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
578	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
579	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
580	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
581	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
582	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
583	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
584	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
585	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
586	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
587	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
588	C₄⋊C₄	—	2	2	no	—
589	C₄⋊C₄	—	2	4	no	—
590	C₄⋊C₄	—	2	2	no	—
591	C₄⋊C₄	—	2	4	no	—
592	C₄⋊C₄	—	2	4	no	—
593	C₄⋊C₄	—	2	2	no	—
594	C₄⋊C₄	—	2	2	no	—
595	C₄⋊C₄	—	2	4	no	—
596	C₄⋊C₄	—	2	8	no	—
597	C₄⋊C₄	—	2	4	no	—
598	C₄⋊C₄	—	2	4	no	—
599	C₄⋊C₄	—	4	2	no	—
600	C₄⋊C₄	—	4	2	no	—
601	C₄⋊C₄	—	4	2	no	—
602	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
603	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
604	C₂²⋊C₄	—	2	4	no	—
605	C₂²⋊C₄	—	2	4	no	—
606	C₂²⋊C₄	—	2	8	no	—
607	C₂²⋊C₄	—	2	8	no	—
608	C₂²⋊C₄	—	2	4	no	—
609	C₂²⋊C₄	—	2	4	no	—
610	C₂²⋊C₄	—	2	4	no	—
611	C₂²⋊C₄	—	2	8	no	—
612	C₂²⋊C₄	—	2	8	no	—
613	C₂²⋊C₄	—	2	8	no	—
614	C₂²⋊C₄	—	2	8	no	—
615	C₂²⋊C₄	—	4	4	no	—
616	C₂²⋊C₄	—	4	4	no	—
617	C₂²⋊C₄	—	4	4	no	—
618	C₂²⋊C₄	—	4	4	no	—
619	C₂²⋊C₄	—	4	4	no	—
620	C₄²	—	2	4	no	—
621	C₄²	—	2	4	no	—
622	C₄²	—	2	2	no	—
623	C₄²	—	2	2	no	—
624	C₄²	—	2	8	no	—
625	C₄²	—	4	4	no	—
626	C₄²	—	4	2	no	—
627	C₄²	C₂×D₄×C₁₃₉	1	8	yes	—
628	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
629	C₄²	#41×C₁₃₉	1	8	yes	—
630	C₂³	—	2	2	no	—
631	C₂³	—	2	4	no	—
632	C₂³	—	2	4	no	—
633	C₂³	—	2	4	no	—
634	C₂³	—	2	4	no	—
635	C₂³	—	2	4	no	—
636	C₂³	—	2	2	no	—
637	C₂³	—	2	4	no	—
638	C₂³	—	2	4	no	—
639	C₂³	—	2	4	no	—
640	C₂³	—	2	2	no	—
641	C₂³	—	2	4	no	—
642	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
643	Q₈	—	2	8	no	—
644	Q₈	—	4	4	no	—
645	Q₈	—	4	4	no	—
646	Q₈	—	4	4	no	—
647	D₄	—	4	8	no	—
648	D₄	—	4	16	no	—
649	D₄	—	4	4	no	—
650	D₄	—	4	8	no	—
651	D₄	—	8	4	no	—
652	D₄	—	8	8	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	4	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	4	no	—
672	C₂×C₄	—	2	4	no	—
673	C₂×C₄	—	2	4	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	4	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	4	8	no	—
684	C₂×C₄	—	8	8	no	—
685	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
686	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
687	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
688	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
689	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
690	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
691	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
692	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
693	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
694	C₂²	—	4	2	no	—
695	C₂²	—	4	4	no	—
696	C₂²	—	4	4	no	—
697	C₂²	—	4	2	no	—
698	C₂²	—	4	2	no	—
699	C₂²	—	4	4	no	—
700	C₂²	—	4	4	no	—
701	C₂²	—	4	4	no	—
702	C₂²	—	4	4	no	—
703	C₂²	—	4	4	no	—
704	C₂²	—	4	4	no	—
705	C₂²	—	4	4	no	—
706	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
707	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
708	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
709	C₂²	#585×C₁₃₉	1	2	yes	—
710	C₂²	#585×C₁₃₉	1	1	yes	characteristic
711	C₄	—	2	4	no	—
712	C₄	—	2	2	no	—
713	C₄	—	2	2	no	—
714	C₄	—	2	4	no	—
715	C₄	—	2	2	no	—
716	C₄	—	2	4	no	—
717	C₄	—	2	4	no	—
718	C₄	—	4	2	no	—
719	C₄	—	4	2	no	—
720	C₄	—	4	1	no	—
721	C₄	—	4	1	no	—
722	C₄	—	4	2	no	—
723	C₄	—	4	1	no	—
724	C₄	—	4	4	no	—
725	C₄	#532×C₁₃₉	1	4	yes	—
726	C₂	—	8	4	no	—
727	C₂	—	8	2	no	—
728	C₂	C₂×#532×C₁₃₉	1	1	yes	characteristic
729	C₂	#3487×C₁₃₉	1	1	yes	characteristic
730	C₂	#3488×C₁₃₉	1	1	yes	characteristic
731	C₂	#3506×C₁₃₉	1	2	yes	—
732	C₂	#3510×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	#2657×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
1. C₂×#559×C₁₃₉	C₂	semidirect
2. C₂×#556×C₁₃₉	C₂	semidirect
3. #2662×C₁₃₉	C₂	semidirect
5. #2610×C₁₃₉	C₂	semidirect
6. #2603×C₁₃₉	C₂	semidirect
7. #2592×C₁₃₉	C₂	semidirect
8. #2554×C₁₃₉	C₂	semidirect
9. #2548×C₁₃₉	C₂	semidirect
10. #2548×C₁₃₉	C₂	semidirect
11. #2545×C₁₃₉	C₂	semidirect
12. #2461×C₁₃₉	C₂	semidirect
13. #2399×C₁₃₉	C₂	semidirect
14. #2392×C₁₃₉	C₂	semidirect
15. #2367×C₁₃₉	C₂	semidirect
16. #2366×C₁₃₉	C₂	semidirect
17. #2276×C₁₃₉	C₂	semidirect
114. C₄×Q₈×C₁₃₉	D₄	semidirect
366. #35956	C₁₃₉	direct (N × H)
367. C₁₃₉	#35956	direct (N × H)
368. C₂×#559	C₂×C₁₃₉	semidirect
369. C₂×#556	C₂×C₁₃₉	semidirect
370. #2662	C₂×C₁₃₉	semidirect
372. #2610	C₂×C₁₃₉	semidirect
373. #2603	C₂×C₁₃₉	semidirect
374. #2592	C₂×C₁₃₉	semidirect
375. #2554	C₂×C₁₃₉	semidirect
376. #2548	C₂×C₁₃₉	semidirect
377. #2548	C₂×C₁₃₉	semidirect
378. #2545	C₂×C₁₃₉	semidirect
379. #2461	C₂×C₁₃₉	semidirect
380. #2399	C₂×C₁₃₉	semidirect
381. #2392	C₂×C₁₃₉	semidirect
382. #2367	C₂×C₁₃₉	semidirect
383. #2366	C₂×C₁₃₉	semidirect
384. #2276	C₂×C₁₃₉	semidirect
481. C₄×Q₈	D₄×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#559×C₁₃₉	2
C₂×#556×C₁₃₉	2
#2662×C₁₃₉	2
#2657×C₁₃₉	2
#2610×C₁₃₉	2
#2603×C₁₃₉	2
#2592×C₁₃₉	2
#2554×C₁₃₉	2
#2548×C₁₃₉	2
#2545×C₁₃₉	2
#2461×C₁₃₉	2
#2399×C₁₃₉	2
#2392×C₁₃₉	2
#2367×C₁₃₉	2
#2366×C₁₃₉	2
#2276×C₁₃₉	2
#35956	139

Subgroups — C139×#35956 #48030552

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#35956 #48030552