Subgroups — C₁₃₉×#36129 #48030725

Order 35584.

2454 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#533×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2862×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2857×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2857×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2550×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2492×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2451×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2446×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2442×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2439×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2429×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2417×C₁₃₉	C₂	1	2	yes	maximal
14	#2409×C₁₃₉	C₂	1	2	yes	maximal
15	#2360×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2352×C₁₃₉	C₂	1	2	yes	maximal
17	Q₈×C₂²⋊C₄×C₁₃₉	C₂	1	2	yes	maximal, complemented
18	C₄×C₄⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄²×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic
20	C₂³×Q₈×C₁₃₉	C₂²	1	2	yes	—
21	#533×C₁₃₉	—	2	8	no	—
22	C₂×C₄⋊Q₈×C₁₃₉	—	2	8	no	—
23	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
24	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
27	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
28	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
30	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
31	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
32	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
33	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
34	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
35	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
36	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
40	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
41	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
42	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
43	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
44	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
45	#400×C₁₃₉	C₂²	1	4	yes	—
46	#398×C₁₃₉	C₂²	1	4	yes	—
47	#398×C₁₃₉	C₂²	1	4	yes	—
48	#396×C₁₃₉	C₂²	1	4	yes	—
49	#395×C₁₃₉	C₂²	1	4	yes	—
50	#393×C₁₃₉	C₂²	1	4	yes	—
51	#391×C₁₃₉	C₂²	1	4	yes	—
52	#391×C₁₃₉	C₂²	1	2	yes	—
53	#391×C₁₃₉	C₂²	1	2	yes	—
54	#391×C₁₃₉	C₂²	1	2	yes	—
55	#391×C₁₃₉	C₂²	1	4	yes	—
56	#391×C₁₃₉	C₂²	1	2	yes	—
57	#391×C₁₃₉	C₂²	1	2	yes	—
58	#391×C₁₃₉	C₂²	1	2	yes	—
59	#391×C₁₃₉	C₂²	1	2	yes	—
60	#389×C₁₃₉	C₂²	1	2	yes	—
61	#389×C₁₃₉	C₂²	1	2	yes	—
62	#389×C₁₃₉	C₂²	1	4	yes	—
63	#389×C₁₃₉	C₂²	1	2	yes	—
64	#389×C₁₃₉	C₂²	1	2	yes	—
65	#389×C₁₃₉	C₂²	1	2	yes	—
66	#389×C₁₃₉	C₂²	1	2	yes	—
67	#388×C₁₃₉	C₂²	1	4	yes	—
68	#387×C₁₃₉	C₂²	1	4	yes	—
69	#387×C₁₃₉	C₂²	1	4	yes	—
70	#386×C₁₃₉	C₂²	1	4	yes	—
71	#385×C₁₃₉	C₂²	1	4	yes	—
72	#384×C₁₃₉	C₂²	1	1	yes	characteristic
73	#382×C₁₃₉	C₂²	1	2	yes	—
74	#382×C₁₃₉	C₂²	1	2	yes	—
75	#380×C₁₃₉	C₂²	1	2	yes	—
76	#380×C₁₃₉	C₂²	1	4	yes	—
77	#380×C₁₃₉	C₂²	1	2	yes	—
78	#380×C₁₃₉	C₂²	1	2	yes	—
79	#380×C₁₃₉	C₂²	1	2	yes	—
80	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
81	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
82	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
83	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
84	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
85	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
86	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
87	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
88	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
89	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
90	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
91	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
92	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
93	C₂²×Q₈×C₁₃₉	—	2	8	no	—
94	C₂²×Q₈×C₁₃₉	—	2	8	no	—
95	C₂²×Q₈×C₁₃₉	—	4	4	no	—
96	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
97	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
98	C₂²×Q₈×C₁₃₉	C₂³	1	4	yes	—
99	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
100	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
103	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
104	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
108	C₄⋊Q₈×C₁₃₉	—	2	8	no	—
109	C₄⋊Q₈×C₁₃₉	—	2	8	no	—
110	C₄⋊Q₈×C₁₃₉	—	2	8	no	—
111	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
112	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
113	C₄⋊Q₈×C₁₃₉	D₄	1	8	yes	complemented
114	#125×C₁₃₉	—	2	8	no	—
115	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
116	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
117	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
118	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
119	C₄×Q₈×C₁₃₉	—	2	8	no	—
120	C₄×Q₈×C₁₃₉	—	2	8	no	—
121	C₄×Q₈×C₁₃₉	—	4	4	no	—
122	C₄×D₄×C₁₃₉	—	2	4	no	—
123	C₄×D₄×C₁₃₉	—	2	4	no	—
124	C₄×D₄×C₁₃₉	Q₈	1	8	yes	complemented
125	#117×C₁₃₉	—	2	8	no	—
126	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
127	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
128	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
129	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
130	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
131	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
132	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
133	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
134	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
135	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	2	yes	—
139	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
143	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
144	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
147	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
148	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
149	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
150	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
151	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
152	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
153	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
154	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
155	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
156	C₂×C₄²×C₁₃₉	—	2	4	no	—
157	C₂×C₄²×C₁₃₉	—	2	4	no	—
158	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
159	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
160	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
165	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
167	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
168	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
169	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
170	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
171	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
172	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
173	#95×C₁₃₉	C₂³	1	4	yes	—
174	#95×C₁₃₉	C₂³	1	4	yes	—
175	#95×C₁₃₉	C₂³	1	4	yes	—
176	#95×C₁₃₉	C₂³	1	4	yes	—
177	#95×C₁₃₉	C₂³	1	1	yes	characteristic
178	#95×C₁₃₉	C₂³	1	4	yes	—
179	#95×C₁₃₉	C₂³	1	4	yes	—
180	#95×C₁₃₉	C₂³	1	1	yes	characteristic
181	#95×C₁₃₉	C₂³	1	4	yes	—
182	#95×C₁₃₉	C₂³	1	4	yes	—
183	#95×C₁₃₉	C₂³	1	1	yes	characteristic
184	#95×C₁₃₉	C₂³	1	1	yes	characteristic
185	#95×C₁₃₉	C₂³	1	1	yes	characteristic
186	#95×C₁₃₉	C₂³	1	1	yes	characteristic
187	#95×C₁₃₉	C₂³	1	4	yes	—
188	#95×C₁₃₉	C₂³	1	4	yes	—
189	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
190	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
191	C₂×Q₈×C₁₃₉	—	2	4	no	—
192	C₂×Q₈×C₁₃₉	—	2	8	no	—
193	C₂×Q₈×C₁₃₉	—	2	4	no	—
194	C₂×Q₈×C₁₃₉	—	2	4	no	—
195	C₂×Q₈×C₁₃₉	—	2	4	no	—
196	C₂×Q₈×C₁₃₉	—	2	8	no	—
197	C₂×Q₈×C₁₃₉	—	2	4	no	—
198	C₂×Q₈×C₁₃₉	—	2	4	no	—
199	C₂×Q₈×C₁₃₉	—	2	4	no	—
200	C₂×Q₈×C₁₃₉	—	2	4	no	—
201	C₂×Q₈×C₁₃₉	—	4	4	no	—
202	C₂×Q₈×C₁₃₉	—	4	32	no	—
203	C₂×Q₈×C₁₃₉	C₂×D₄	1	8	yes	—
204	C₂×D₄×C₁₃₉	—	2	2	no	—
205	C₂×D₄×C₁₃₉	—	2	2	no	—
206	C₂×D₄×C₁₃₉	C₂×Q₈	1	4	yes	—
207	C₂²×C₄×C₁₃₉	—	2	2	no	—
208	C₂²×C₄×C₁₃₉	—	2	2	no	—
209	C₂²×C₄×C₁₃₉	—	2	2	no	—
210	C₂²×C₄×C₁₃₉	—	2	2	no	—
211	C₂²×C₄×C₁₃₉	—	2	2	no	—
212	C₂²×C₄×C₁₃₉	—	2	2	no	—
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	2	no	—
217	C₂²×C₄×C₁₃₉	—	2	2	no	—
218	C₂²×C₄×C₁₃₉	—	2	8	no	—
219	C₂²×C₄×C₁₃₉	—	2	2	no	—
220	C₂²×C₄×C₁₃₉	—	2	2	no	—
221	C₂²×C₄×C₁₃₉	—	2	2	no	—
222	C₂²×C₄×C₁₃₉	—	2	2	no	—
223	C₂²×C₄×C₁₃₉	—	4	4	no	—
224	C₂²×C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
225	C₂²×C₄×C₁₃₉	C₂×Q₈	1	4	yes	complemented
226	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
227	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
228	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
230	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
231	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
232	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
233	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
234	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
235	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
236	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
237	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
238	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
239	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
240	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
245	C₄⋊C₄×C₁₃₉	—	2	8	no	—
246	C₄⋊C₄×C₁₃₉	—	2	8	no	—
247	C₄⋊C₄×C₁₃₉	—	2	4	no	—
248	C₄⋊C₄×C₁₃₉	—	2	4	no	—
249	C₄⋊C₄×C₁₃₉	—	2	4	no	—
250	C₄⋊C₄×C₁₃₉	—	2	8	no	—
251	C₄⋊C₄×C₁₃₉	—	2	8	no	—
252	C₄⋊C₄×C₁₃₉	—	2	4	no	—
253	C₄⋊C₄×C₁₃₉	—	2	2	no	—
254	C₄⋊C₄×C₁₃₉	—	2	2	no	—
255	C₄⋊C₄×C₁₃₉	—	2	4	no	—
256	C₄⋊C₄×C₁₃₉	—	2	8	no	—
257	C₄⋊C₄×C₁₃₉	—	2	4	no	—
258	C₄⋊C₄×C₁₃₉	—	2	4	no	—
259	C₄⋊C₄×C₁₃₉	—	4	4	no	—
260	C₄⋊C₄×C₁₃₉	—	4	4	no	—
261	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
262	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
263	C₄⋊C₄×C₁₃₉	C₂×Q₈	1	4	yes	complemented
264	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
265	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
266	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
267	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
268	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
269	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
270	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
271	C₂²⋊C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
272	C₂²⋊C₄×C₁₃₉	C₂×Q₈	1	4	yes	complemented
273	C₄²×C₁₃₉	—	2	2	no	—
274	C₄²×C₁₃₉	—	2	2	no	—
275	C₄²×C₁₃₉	—	2	2	no	—
276	C₄²×C₁₃₉	—	2	2	no	—
277	C₄²×C₁₃₉	—	2	2	no	—
278	C₄²×C₁₃₉	—	2	2	no	—
279	C₄²×C₁₃₉	—	2	8	no	—
280	C₄²×C₁₃₉	—	2	2	no	—
281	C₄²×C₁₃₉	—	2	2	no	—
282	C₄²×C₁₃₉	—	2	2	no	—
283	C₄²×C₁₃₉	—	2	2	no	—
284	C₄²×C₁₃₉	—	2	2	no	—
285	C₄²×C₁₃₉	—	4	4	no	—
286	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
287	C₄²×C₁₃₉	C₂×Q₈	1	4	yes	complemented
288	C₂³×C₁₃₉	—	2	1	no	—
289	C₂³×C₁₃₉	—	2	1	no	—
290	C₂³×C₁₃₉	—	2	1	no	—
291	C₂³×C₁₃₉	—	2	1	no	—
292	C₂³×C₁₃₉	—	2	1	no	—
293	C₂³×C₁₃₉	—	2	1	no	—
294	C₂³×C₁₃₉	—	2	1	no	—
295	C₂³×C₁₃₉	—	2	1	no	—
296	C₂³×C₁₃₉	—	2	1	no	—
297	C₂³×C₁₃₉	—	2	1	no	—
298	C₂³×C₁₃₉	C₂²×Q₈	1	2	yes	—
299	C₂³×C₁₃₉	C₂²×Q₈	1	2	yes	—
300	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
301	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
302	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
303	Q₈×C₁₃₉	—	2	16	no	—
304	Q₈×C₁₃₉	—	4	16	no	—
305	Q₈×C₁₃₉	—	4	8	no	—
306	Q₈×C₁₃₉	—	4	8	no	—
307	D₄×C₁₃₉	—	2	8	no	—
308	C₂×C₄×C₁₃₉	—	2	1	no	—
309	C₂×C₄×C₁₃₉	—	2	1	no	—
310	C₂×C₄×C₁₃₉	—	2	1	no	—
311	C₂×C₄×C₁₃₉	—	2	1	no	—
312	C₂×C₄×C₁₃₉	—	2	1	no	—
313	C₂×C₄×C₁₃₉	—	2	1	no	—
314	C₂×C₄×C₁₃₉	—	2	4	no	—
315	C₂×C₄×C₁₃₉	—	2	1	no	—
316	C₂×C₄×C₁₃₉	—	2	4	no	—
317	C₂×C₄×C₁₃₉	—	2	1	no	—
318	C₂×C₄×C₁₃₉	—	2	1	no	—
319	C₂×C₄×C₁₃₉	—	2	1	no	—
320	C₂×C₄×C₁₃₉	—	2	1	no	—
321	C₂×C₄×C₁₃₉	—	2	1	no	—
322	C₂×C₄×C₁₃₉	—	2	8	no	—
323	C₂×C₄×C₁₃₉	—	2	8	no	—
324	C₂×C₄×C₁₃₉	—	2	8	no	—
325	C₂×C₄×C₁₃₉	—	2	8	no	—
326	C₂×C₄×C₁₃₉	—	2	1	no	—
327	C₂×C₄×C₁₃₉	—	2	1	no	—
328	C₂×C₄×C₁₃₉	—	2	4	no	—
329	C₂×C₄×C₁₃₉	—	2	4	no	—
330	C₂×C₄×C₁₃₉	—	2	1	no	—
331	C₂×C₄×C₁₃₉	—	2	1	no	—
332	C₂×C₄×C₁₃₉	—	2	4	no	—
333	C₂×C₄×C₁₃₉	—	2	1	no	—
334	C₂×C₄×C₁₃₉	—	2	1	no	—
335	C₂×C₄×C₁₃₉	—	2	4	no	—
336	C₂×C₄×C₁₃₉	—	2	4	no	—
337	C₂×C₄×C₁₃₉	—	2	1	no	—
338	C₂×C₄×C₁₃₉	—	2	4	no	—
339	C₂×C₄×C₁₃₉	—	2	4	no	—
340	C₂×C₄×C₁₃₉	—	2	1	no	—
341	C₂×C₄×C₁₃₉	—	2	1	no	—
342	C₂×C₄×C₁₃₉	—	2	1	no	—
343	C₂×C₄×C₁₃₉	—	2	1	no	—
344	C₂×C₄×C₁₃₉	—	2	4	no	—
345	C₂×C₄×C₁₃₉	—	2	1	no	—
346	C₂×C₄×C₁₃₉	—	2	4	no	—
347	C₂×C₄×C₁₃₉	—	4	16	no	—
348	C₂×C₄×C₁₃₉	—	4	4	no	—
349	C₂×C₄×C₁₃₉	—	4	4	no	—
350	C₂×C₄×C₁₃₉	C₂²×D₄	1	8	yes	—
351	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
352	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
353	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
354	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
355	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
356	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
357	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
358	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
359	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
360	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
361	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
362	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
363	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
364	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
365	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
366	C₂²×C₁₃₉	—	2	2	no	—
367	C₂²×C₁₃₉	—	2	2	no	—
368	C₂²×C₁₃₉	—	2	2	no	—
369	C₂²×C₁₃₉	—	2	2	no	—
370	C₂²×C₁₃₉	—	2	2	no	—
371	C₂²×C₁₃₉	—	2	2	no	—
372	C₂²×C₁₃₉	—	2	2	no	—
373	C₂²×C₁₃₉	—	2	2	no	—
374	C₂²×C₁₃₉	—	2	2	no	—
375	C₂²×C₁₃₉	—	4	1	no	—
376	C₂²×C₁₃₉	—	4	1	no	—
377	C₂²×C₁₃₉	—	4	1	no	—
378	C₂²×C₁₃₉	—	4	1	no	—
379	C₂²×C₁₃₉	#533	1	4	yes	complemented
380	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
381	C₂²×C₁₃₉	C₂³×Q₈	1	1	yes	characteristic
382	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
383	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
384	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
385	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
386	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
387	C₄×C₁₃₉	—	2	2	no	—
388	C₄×C₁₃₉	—	2	2	no	—
389	C₄×C₁₃₉	—	2	8	no	—
390	C₄×C₁₃₉	—	2	2	no	—
391	C₄×C₁₃₉	—	2	2	no	—
392	C₄×C₁₃₉	—	2	2	no	—
393	C₄×C₁₃₉	—	2	2	no	—
394	C₄×C₁₃₉	—	4	1	no	—
395	C₄×C₁₃₉	—	4	4	no	—
396	C₄×C₁₃₉	—	4	1	no	—
397	C₄×C₁₃₉	—	4	4	no	—
398	C₄×C₁₃₉	—	4	1	no	—
399	C₄×C₁₃₉	—	4	1	no	—
400	C₄×C₁₃₉	—	4	4	no	—
401	C₄×C₁₃₉	#546	1	4	yes	—
402	C₄×C₁₃₉	#548	1	4	yes	—
403	C₄×C₁₃₉	D₄×Q₈	1	4	yes	—
404	C₂×C₁₃₉	—	2	4	no	—
405	C₂×C₁₃₉	—	4	2	no	—
406	C₂×C₁₃₉	C₂×#533	1	1	yes	characteristic
407	C₂×C₁₃₉	C₂×#546	1	1	yes	characteristic
408	C₂×C₁₃₉	C₂×#548	1	1	yes	characteristic
409	C₂×C₁₃₉	C₂×D₄×Q₈	1	1	yes	characteristic
410	C₂×C₁₃₉	#3503	1	1	yes	characteristic
411	C₂×C₁₃₉	#3509	1	1	yes	characteristic
412	C₂×C₁₃₉	#3511	1	1	yes	characteristic
413	#36129	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
414	C₁₃₉	#36129	1	1	yes	characteristic, direct product factor, Sylow
415	C₂×#533	C₂×C₁₃₉	1	1	yes	characteristic, complemented
416	C₂²×C₄⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
417	#2862	C₂×C₁₃₉	1	1	yes	characteristic, complemented
418	#2857	C₂×C₁₃₉	1	1	yes	characteristic, complemented
419	#2857	C₂×C₁₃₉	1	1	yes	characteristic, complemented
420	#2550	C₂×C₁₃₉	1	2	yes	complemented
421	#2492	C₂×C₁₃₉	1	2	yes	complemented
422	#2451	C₂×C₁₃₉	1	2	yes	complemented
423	#2446	C₂×C₁₃₉	1	2	yes	complemented
424	#2442	C₂×C₁₃₉	1	2	yes	complemented
425	#2439	C₂×C₁₃₉	1	2	yes	complemented
426	#2429	C₂×C₁₃₉	1	2	yes	complemented
427	#2417	C₂×C₁₃₉	1	2	yes	—
428	#2409	C₂×C₁₃₉	1	2	yes	—
429	#2360	C₂×C₁₃₉	1	2	yes	complemented
430	#2352	C₂×C₁₃₉	1	2	yes	—
431	Q₈×C₂²⋊C₄	C₂×C₁₃₉	1	2	yes	complemented
432	C₄×C₄⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
433	C₄²×D₄	C₂×C₁₃₉	1	1	yes	characteristic
434	C₂³×Q₈	C₂²×C₁₃₉	1	2	yes	—
435	#533	—	2	8	no	—
436	C₂×C₄⋊Q₈	—	2	8	no	—
437	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
438	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
439	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
440	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
441	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
442	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
443	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
444	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
445	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
446	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
447	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
448	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
449	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
450	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
451	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
452	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
453	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
454	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
455	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
456	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
457	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
458	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
459	#400	C₂²×C₁₃₉	1	4	yes	—
460	#398	C₂²×C₁₃₉	1	4	yes	—
461	#398	C₂²×C₁₃₉	1	4	yes	—
462	#396	C₂²×C₁₃₉	1	4	yes	—
463	#395	C₂²×C₁₃₉	1	4	yes	—
464	#393	C₂²×C₁₃₉	1	4	yes	—
465	#391	C₂²×C₁₃₉	1	2	yes	—
466	#391	C₂²×C₁₃₉	1	2	yes	—
467	#391	C₂²×C₁₃₉	1	2	yes	—
468	#391	C₂²×C₁₃₉	1	4	yes	—
469	#391	C₂²×C₁₃₉	1	4	yes	—
470	#391	C₂²×C₁₃₉	1	2	yes	—
471	#391	C₂²×C₁₃₉	1	2	yes	—
472	#391	C₂²×C₁₃₉	1	2	yes	—
473	#391	C₂²×C₁₃₉	1	2	yes	—
474	#389	C₂²×C₁₃₉	1	2	yes	—
475	#389	C₂²×C₁₃₉	1	2	yes	—
476	#389	C₂²×C₁₃₉	1	2	yes	—
477	#389	C₂²×C₁₃₉	1	2	yes	—
478	#389	C₂²×C₁₃₉	1	2	yes	—
479	#389	C₂²×C₁₃₉	1	2	yes	—
480	#389	C₂²×C₁₃₉	1	4	yes	—
481	#388	C₂²×C₁₃₉	1	4	yes	—
482	#387	C₂²×C₁₃₉	1	4	yes	—
483	#387	C₂²×C₁₃₉	1	4	yes	—
484	#386	C₂²×C₁₃₉	1	4	yes	—
485	#385	C₂²×C₁₃₉	1	4	yes	—
486	#384	C₂²×C₁₃₉	1	1	yes	characteristic
487	#382	C₂²×C₁₃₉	1	2	yes	—
488	#382	C₂²×C₁₃₉	1	2	yes	—
489	#380	C₂²×C₁₃₉	1	2	yes	—
490	#380	C₂²×C₁₃₉	1	4	yes	—
491	#380	C₂²×C₁₃₉	1	2	yes	—
492	#380	C₂²×C₁₃₉	1	2	yes	—
493	#380	C₂²×C₁₃₉	1	2	yes	—
494	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
495	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
496	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
497	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
498	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
499	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
500	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
501	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
502	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
503	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
504	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
505	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
506	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
507	C₂²×Q₈	—	2	8	no	—
508	C₂²×Q₈	—	2	8	no	—
509	C₂²×Q₈	—	4	4	no	—
510	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
511	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
512	C₂²×Q₈	C₂³×C₁₃₉	1	4	yes	—
513	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
514	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
515	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
516	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
517	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
518	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
519	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
520	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
521	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
522	C₄⋊Q₈	—	2	8	no	—
523	C₄⋊Q₈	—	2	8	no	—
524	C₄⋊Q₈	—	2	8	no	—
525	C₄⋊Q₈	—	2	4	no	—
526	C₄⋊Q₈	—	2	4	no	—
527	C₄⋊Q₈	D₄×C₁₃₉	1	8	yes	complemented
528	#125	—	2	8	no	—
529	C₂²⋊Q₈	—	2	8	no	—
530	C₂²⋊Q₈	—	2	8	no	—
531	C₂²⋊Q₈	—	2	8	no	—
532	C₂²⋊Q₈	—	4	4	no	—
533	C₄×Q₈	—	2	8	no	—
534	C₄×Q₈	—	2	8	no	—
535	C₄×Q₈	—	4	4	no	—
536	C₄×D₄	—	2	4	no	—
537	C₄×D₄	—	2	4	no	—
538	C₄×D₄	Q₈×C₁₃₉	1	8	yes	complemented
539	#117	—	2	8	no	—
540	C₂×C₄⋊C₄	—	2	8	no	—
541	C₂×C₄⋊C₄	—	2	8	no	—
542	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
543	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
544	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
545	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
546	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
547	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
548	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
549	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
550	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
551	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
552	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
553	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
554	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
555	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
556	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
557	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
558	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
559	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
560	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
561	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
562	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
563	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
564	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
565	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
566	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
567	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
568	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
569	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
570	C₂×C₄²	—	2	4	no	—
571	C₂×C₄²	—	2	4	no	—
572	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
573	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
574	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
575	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
576	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
577	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
578	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
579	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
580	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
581	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
582	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
583	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
584	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
585	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
586	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
587	#95	C₂³×C₁₃₉	1	1	yes	characteristic
588	#95	C₂³×C₁₃₉	1	1	yes	characteristic
589	#95	C₂³×C₁₃₉	1	1	yes	characteristic
590	#95	C₂³×C₁₃₉	1	1	yes	characteristic
591	#95	C₂³×C₁₃₉	1	1	yes	characteristic
592	#95	C₂³×C₁₃₉	1	1	yes	characteristic
593	#95	C₂³×C₁₃₉	1	4	yes	—
594	#95	C₂³×C₁₃₉	1	4	yes	—
595	#95	C₂³×C₁₃₉	1	4	yes	—
596	#95	C₂³×C₁₃₉	1	4	yes	—
597	#95	C₂³×C₁₃₉	1	4	yes	—
598	#95	C₂³×C₁₃₉	1	4	yes	—
599	#95	C₂³×C₁₃₉	1	4	yes	—
600	#95	C₂³×C₁₃₉	1	4	yes	—
601	#95	C₂³×C₁₃₉	1	4	yes	—
602	#95	C₂³×C₁₃₉	1	4	yes	—
603	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
604	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
605	C₂×Q₈	—	2	4	no	—
606	C₂×Q₈	—	2	8	no	—
607	C₂×Q₈	—	2	4	no	—
608	C₂×Q₈	—	2	4	no	—
609	C₂×Q₈	—	2	4	no	—
610	C₂×Q₈	—	2	8	no	—
611	C₂×Q₈	—	2	4	no	—
612	C₂×Q₈	—	2	4	no	—
613	C₂×Q₈	—	2	4	no	—
614	C₂×Q₈	—	2	4	no	—
615	C₂×Q₈	—	4	4	no	—
616	C₂×Q₈	—	4	32	no	—
617	C₂×Q₈	C₂×D₄×C₁₃₉	1	8	yes	—
618	C₂×D₄	—	2	2	no	—
619	C₂×D₄	—	2	2	no	—
620	C₂×D₄	C₂×Q₈×C₁₃₉	1	4	yes	—
621	C₂²×C₄	—	2	2	no	—
622	C₂²×C₄	—	2	2	no	—
623	C₂²×C₄	—	2	2	no	—
624	C₂²×C₄	—	2	2	no	—
625	C₂²×C₄	—	2	2	no	—
626	C₂²×C₄	—	2	2	no	—
627	C₂²×C₄	—	2	2	no	—
628	C₂²×C₄	—	2	2	no	—
629	C₂²×C₄	—	2	8	no	—
630	C₂²×C₄	—	2	2	no	—
631	C₂²×C₄	—	2	2	no	—
632	C₂²×C₄	—	2	8	no	—
633	C₂²×C₄	—	2	2	no	—
634	C₂²×C₄	—	2	2	no	—
635	C₂²×C₄	—	2	2	no	—
636	C₂²×C₄	—	2	2	no	—
637	C₂²×C₄	—	4	4	no	—
638	C₂²×C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
639	C₂²×C₄	C₂×Q₈×C₁₃₉	1	4	yes	complemented
640	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
641	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
642	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
643	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
644	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
645	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
646	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
647	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
648	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
649	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
650	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
651	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
652	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
653	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
654	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
655	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
656	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
657	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
658	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
659	C₄⋊C₄	—	2	8	no	—
660	C₄⋊C₄	—	2	8	no	—
661	C₄⋊C₄	—	2	4	no	—
662	C₄⋊C₄	—	2	4	no	—
663	C₄⋊C₄	—	2	4	no	—
664	C₄⋊C₄	—	2	8	no	—
665	C₄⋊C₄	—	2	8	no	—
666	C₄⋊C₄	—	2	4	no	—
667	C₄⋊C₄	—	2	2	no	—
668	C₄⋊C₄	—	2	2	no	—
669	C₄⋊C₄	—	2	4	no	—
670	C₄⋊C₄	—	2	8	no	—
671	C₄⋊C₄	—	2	4	no	—
672	C₄⋊C₄	—	2	4	no	—
673	C₄⋊C₄	—	4	4	no	—
674	C₄⋊C₄	—	4	4	no	—
675	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
676	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
677	C₄⋊C₄	C₂×Q₈×C₁₃₉	1	4	yes	complemented
678	C₂²⋊C₄	—	2	2	no	—
679	C₂²⋊C₄	—	2	2	no	—
680	C₂²⋊C₄	—	2	8	no	—
681	C₂²⋊C₄	—	2	8	no	—
682	C₂²⋊C₄	—	2	2	no	—
683	C₂²⋊C₄	—	2	2	no	—
684	C₂²⋊C₄	—	4	4	no	—
685	C₂²⋊C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
686	C₂²⋊C₄	C₂×Q₈×C₁₃₉	1	4	yes	complemented
687	C₄²	—	2	2	no	—
688	C₄²	—	2	2	no	—
689	C₄²	—	2	2	no	—
690	C₄²	—	2	2	no	—
691	C₄²	—	2	2	no	—
692	C₄²	—	2	2	no	—
693	C₄²	—	2	8	no	—
694	C₄²	—	2	2	no	—
695	C₄²	—	2	2	no	—
696	C₄²	—	2	2	no	—
697	C₄²	—	2	2	no	—
698	C₄²	—	2	2	no	—
699	C₄²	—	4	4	no	—
700	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
701	C₄²	C₂×Q₈×C₁₃₉	1	4	yes	complemented
702	C₂³	—	2	1	no	—
703	C₂³	—	2	1	no	—
704	C₂³	—	2	1	no	—
705	C₂³	—	2	1	no	—
706	C₂³	—	2	1	no	—
707	C₂³	—	2	1	no	—
708	C₂³	—	2	1	no	—
709	C₂³	—	2	1	no	—
710	C₂³	—	2	1	no	—
711	C₂³	—	2	1	no	—
712	C₂³	C₂²×Q₈×C₁₃₉	1	2	yes	—
713	C₂³	C₂²×Q₈×C₁₃₉	1	2	yes	—
714	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
715	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
716	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
717	Q₈	—	2	16	no	—
718	Q₈	—	4	16	no	—
719	Q₈	—	4	8	no	—
720	Q₈	—	4	8	no	—
721	D₄	—	2	8	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	2	1	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	1	no	—
727	C₂×C₄	—	2	1	no	—
728	C₂×C₄	—	2	4	no	—
729	C₂×C₄	—	2	1	no	—
730	C₂×C₄	—	2	4	no	—
731	C₂×C₄	—	2	1	no	—
732	C₂×C₄	—	2	1	no	—
733	C₂×C₄	—	2	1	no	—
734	C₂×C₄	—	2	1	no	—
735	C₂×C₄	—	2	1	no	—
736	C₂×C₄	—	2	8	no	—
737	C₂×C₄	—	2	8	no	—
738	C₂×C₄	—	2	8	no	—
739	C₂×C₄	—	2	8	no	—
740	C₂×C₄	—	2	1	no	—
741	C₂×C₄	—	2	1	no	—
742	C₂×C₄	—	2	4	no	—
743	C₂×C₄	—	2	4	no	—
744	C₂×C₄	—	2	1	no	—
745	C₂×C₄	—	2	1	no	—
746	C₂×C₄	—	2	4	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	2	1	no	—
749	C₂×C₄	—	2	4	no	—
750	C₂×C₄	—	2	4	no	—
751	C₂×C₄	—	2	1	no	—
752	C₂×C₄	—	2	4	no	—
753	C₂×C₄	—	2	4	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	1	no	—
758	C₂×C₄	—	2	4	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	4	no	—
761	C₂×C₄	—	4	16	no	—
762	C₂×C₄	—	4	4	no	—
763	C₂×C₄	—	4	4	no	—
764	C₂×C₄	C₂²×D₄×C₁₃₉	1	8	yes	—
765	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
766	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
767	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
768	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
769	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
770	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
771	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
772	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
773	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
774	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
775	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
776	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
777	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
778	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
779	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
780	C₂²	—	2	2	no	—
781	C₂²	—	2	2	no	—
782	C₂²	—	2	2	no	—
783	C₂²	—	2	2	no	—
784	C₂²	—	2	2	no	—
785	C₂²	—	2	2	no	—
786	C₂²	—	2	2	no	—
787	C₂²	—	2	2	no	—
788	C₂²	—	2	2	no	—
789	C₂²	—	4	1	no	—
790	C₂²	—	4	1	no	—
791	C₂²	—	4	1	no	—
792	C₂²	—	4	1	no	—
793	C₂²	#533×C₁₃₉	1	4	yes	complemented
794	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
795	C₂²	C₂³×Q₈×C₁₃₉	1	1	yes	characteristic
796	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
797	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
798	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
799	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
800	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
801	C₄	—	2	2	no	—
802	C₄	—	2	2	no	—
803	C₄	—	2	8	no	—
804	C₄	—	2	2	no	—
805	C₄	—	2	2	no	—
806	C₄	—	2	2	no	—
807	C₄	—	2	2	no	—
808	C₄	—	4	4	no	—
809	C₄	—	4	1	no	—
810	C₄	—	4	1	no	—
811	C₄	—	4	4	no	—
812	C₄	—	4	1	no	—
813	C₄	—	4	1	no	—
814	C₄	—	4	4	no	—
815	C₄	#546×C₁₃₉	1	4	yes	—
816	C₄	#548×C₁₃₉	1	4	yes	—
817	C₄	D₄×Q₈×C₁₃₉	1	4	yes	—
818	C₂	—	2	4	no	—
819	C₂	—	4	2	no	—
820	C₂	C₂×#533×C₁₃₉	1	1	yes	characteristic
821	C₂	C₂×#546×C₁₃₉	1	1	yes	characteristic
822	C₂	C₂×#548×C₁₃₉	1	1	yes	characteristic
823	C₂	C₂×D₄×Q₈×C₁₃₉	1	1	yes	characteristic
824	C₂	#3503×C₁₃₉	1	1	yes	characteristic
825	C₂	#3509×C₁₃₉	1	1	yes	characteristic
826	C₂	#3511×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂²×D₄×C₁₃₉	C₂³
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×#533×C₁₃₉	C₂	semidirect
2. C₂²×C₄⋊Q₈×C₁₃₉	C₂	semidirect
3. #2862×C₁₃₉	C₂	semidirect
4. #2857×C₁₃₉	C₂	semidirect
5. #2857×C₁₃₉	C₂	semidirect
6. #2550×C₁₃₉	C₂	semidirect
7. #2492×C₁₃₉	C₂	semidirect
8. #2451×C₁₃₉	C₂	semidirect
9. #2446×C₁₃₉	C₂	semidirect
10. #2442×C₁₃₉	C₂	semidirect
11. #2439×C₁₃₉	C₂	semidirect
12. #2429×C₁₃₉	C₂	semidirect
15. #2360×C₁₃₉	C₂	semidirect
17. Q₈×C₂²⋊C₄×C₁₃₉	C₂	semidirect
18. C₄×C₄⋊Q₈×C₁₃₉	C₂	semidirect
113. C₄⋊Q₈×C₁₃₉	D₄	semidirect
124. C₄×D₄×C₁₃₉	Q₈	semidirect
225. C₂²×C₄×C₁₃₉	C₂×Q₈	semidirect
263. C₄⋊C₄×C₁₃₉	C₂×Q₈	semidirect
272. C₂²⋊C₄×C₁₃₉	C₂×Q₈	semidirect
287. C₄²×C₁₃₉	C₂×Q₈	semidirect
379. C₂²×C₁₃₉	#533	semidirect
413. #36129	C₁₃₉	direct (N × H)
414. C₁₃₉	#36129	direct (N × H)
415. C₂×#533	C₂×C₁₃₉	semidirect
416. C₂²×C₄⋊Q₈	C₂×C₁₃₉	semidirect
417. #2862	C₂×C₁₃₉	semidirect
418. #2857	C₂×C₁₃₉	semidirect
419. #2857	C₂×C₁₃₉	semidirect
420. #2550	C₂×C₁₃₉	semidirect
421. #2492	C₂×C₁₃₉	semidirect
422. #2451	C₂×C₁₃₉	semidirect
423. #2446	C₂×C₁₃₉	semidirect
424. #2442	C₂×C₁₃₉	semidirect
425. #2439	C₂×C₁₃₉	semidirect
426. #2429	C₂×C₁₃₉	semidirect
429. #2360	C₂×C₁₃₉	semidirect
431. Q₈×C₂²⋊C₄	C₂×C₁₃₉	semidirect
432. C₄×C₄⋊Q₈	C₂×C₁₃₉	semidirect
527. C₄⋊Q₈	D₄×C₁₃₉	semidirect
538. C₄×D₄	Q₈×C₁₃₉	semidirect
639. C₂²×C₄	C₂×Q₈×C₁₃₉	semidirect
677. C₄⋊C₄	C₂×Q₈×C₁₃₉	semidirect
686. C₂²⋊C₄	C₂×Q₈×C₁₃₉	semidirect
701. C₄²	C₂×Q₈×C₁₃₉	semidirect
793. C₂²	#533×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#533×C₁₃₉	2
C₂²×C₄⋊Q₈×C₁₃₉	2
#2862×C₁₃₉	2
#2857×C₁₃₉	2
#2550×C₁₃₉	2
#2492×C₁₃₉	2
#2451×C₁₃₉	2
#2446×C₁₃₉	2
#2442×C₁₃₉	2
#2439×C₁₃₉	2
#2429×C₁₃₉	2
#2417×C₁₃₉	2
#2409×C₁₃₉	2
#2360×C₁₃₉	2
#2352×C₁₃₉	2
Q₈×C₂²⋊C₄×C₁₃₉	2
C₄×C₄⋊Q₈×C₁₃₉	2
C₄²×D₄×C₁₃₉	2
#36129	139

Subgroups — C139×#36129 #48030725

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36129 #48030725