Subgroups — C₁₃₉×#37191 #48031787

Order 35584.

1856 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#541×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	#2860×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2859×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2734×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2732×C₁₃₉	C₂	1	1	yes	maximal, characteristic
6	#2729×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2727×C₁₃₉	C₂	1	1	yes	maximal, characteristic
8	#2726×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#2725×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2723×C₁₃₉	C₂	1	2	yes	maximal
11	#2721×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2720×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2719×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2664×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2611×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2604×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	#2601×C₁₃₉	C₂	1	2	yes	maximal
18	#2584×C₁₃₉	C₂	1	2	yes	maximal, complemented
19	#2295×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	#541×C₁₃₉	—	2	16	no	—
21	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
25	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
26	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
27	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
28	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
29	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
30	C₂×#125×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×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
34	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
35	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
36	#400×C₁₃₉	C₂²	1	2	yes	—
37	#400×C₁₃₉	C₂²	1	2	yes	—
38	#400×C₁₃₉	C₂²	1	2	yes	—
39	#399×C₁₃₉	C₂²	1	2	yes	—
40	#399×C₁₃₉	C₂²	1	2	yes	—
41	#399×C₁₃₉	C₂²	1	2	yes	—
42	#398×C₁₃₉	C₂²	1	2	yes	—
43	#398×C₁₃₉	C₂²	1	2	yes	—
44	#398×C₁₃₉	C₂²	1	2	yes	—
45	#398×C₁₃₉	C₂²	1	2	yes	—
46	#398×C₁₃₉	C₂²	1	2	yes	—
47	#398×C₁₃₉	C₂²	1	2	yes	—
48	#398×C₁₃₉	C₂²	1	2	yes	—
49	#397×C₁₃₉	C₂²	1	2	yes	—
50	#397×C₁₃₉	C₂²	1	2	yes	—
51	#396×C₁₃₉	C₂²	1	2	yes	—
52	#396×C₁₃₉	C₂²	1	2	yes	—
53	#396×C₁₃₉	C₂²	1	2	yes	—
54	#396×C₁₃₉	C₂²	1	2	yes	—
55	#395×C₁₃₉	C₂²	1	2	yes	—
56	#395×C₁₃₉	C₂²	1	2	yes	—
57	#395×C₁₃₉	C₂²	1	2	yes	—
58	#394×C₁₃₉	C₂²	1	2	yes	—
59	#393×C₁₃₉	C₂²	1	2	yes	—
60	#391×C₁₃₉	C₂²	1	1	yes	characteristic
61	#391×C₁₃₉	C₂²	1	1	yes	characteristic
62	#390×C₁₃₉	C₂²	1	1	yes	characteristic
63	#390×C₁₃₉	C₂²	1	1	yes	characteristic
64	#390×C₁₃₉	C₂²	1	1	yes	characteristic
65	#389×C₁₃₉	C₂²	1	1	yes	characteristic
66	#389×C₁₃₉	C₂²	1	1	yes	characteristic
67	#389×C₁₃₉	C₂²	1	1	yes	characteristic
68	#389×C₁₃₉	C₂²	1	2	yes	—
69	#389×C₁₃₉	C₂²	1	2	yes	—
70	#389×C₁₃₉	C₂²	1	2	yes	—
71	#389×C₁₃₉	C₂²	1	2	yes	—
72	#389×C₁₃₉	C₂²	1	2	yes	—
73	#389×C₁₃₉	C₂²	1	2	yes	—
74	#389×C₁₃₉	C₂²	1	2	yes	—
75	#389×C₁₃₉	C₂²	1	1	yes	characteristic
76	#389×C₁₃₉	C₂²	1	1	yes	characteristic
77	#389×C₁₃₉	C₂²	1	2	yes	—
78	#389×C₁₃₉	C₂²	1	1	yes	characteristic
79	#389×C₁₃₉	C₂²	1	1	yes	characteristic
80	#389×C₁₃₉	C₂²	1	1	yes	characteristic
81	#389×C₁₃₉	C₂²	1	1	yes	characteristic
82	#388×C₁₃₉	C₂²	1	2	yes	—
83	#388×C₁₃₉	C₂²	1	2	yes	—
84	#388×C₁₃₉	C₂²	1	2	yes	—
85	#388×C₁₃₉	C₂²	1	2	yes	—
86	#388×C₁₃₉	C₂²	1	2	yes	—
87	#388×C₁₃₉	C₂²	1	2	yes	—
88	#388×C₁₃₉	C₂²	1	2	yes	—
89	#388×C₁₃₉	C₂²	1	2	yes	—
90	#387×C₁₃₉	C₂²	1	2	yes	—
91	#387×C₁₃₉	C₂²	1	2	yes	—
92	#387×C₁₃₉	C₂²	1	2	yes	—
93	#387×C₁₃₉	C₂²	1	2	yes	—
94	#387×C₁₃₉	C₂²	1	2	yes	—
95	#387×C₁₃₉	C₂²	1	2	yes	—
96	#387×C₁₃₉	C₂²	1	2	yes	—
97	#386×C₁₃₉	C₂²	1	2	yes	—
98	#385×C₁₃₉	C₂²	1	2	yes	—
99	#385×C₁₃₉	C₂²	1	2	yes	—
100	#385×C₁₃₉	C₂²	1	2	yes	—
101	#384×C₁₃₉	C₂²	1	1	yes	characteristic
102	#384×C₁₃₉	C₂²	1	1	yes	characteristic
103	#382×C₁₃₉	C₂²	1	2	yes	—
104	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
105	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
106	#376×C₁₃₉	C₂²	1	2	yes	—
107	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
108	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
109	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
112	C₄⋊Q₈×C₁₃₉	—	2	8	no	—
113	#126×C₁₃₉	—	2	8	no	—
114	#126×C₁₃₉	—	2	8	no	—
115	#126×C₁₃₉	—	2	8	no	—
116	#126×C₁₃₉	—	2	8	no	—
117	#125×C₁₃₉	—	2	8	no	—
118	#125×C₁₃₉	—	2	8	no	—
119	#125×C₁₃₉	—	2	8	no	—
120	#125×C₁₃₉	—	2	8	no	—
121	#125×C₁₃₉	—	2	8	no	—
122	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
123	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
124	C₄×Q₈×C₁₃₉	—	2	8	no	—
125	C₄×Q₈×C₁₃₉	D₄	1	8	yes	complemented
126	#117×C₁₃₉	—	2	8	no	—
127	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	2	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	1	yes	characteristic
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	1	yes	characteristic
143	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
147	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
163	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
176	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
177	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
178	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
179	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
180	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
181	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
182	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
184	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
186	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
187	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
188	#95×C₁₃₉	C₂³	1	2	yes	—
189	#95×C₁₃₉	C₂³	1	2	yes	—
190	#95×C₁₃₉	C₂³	1	2	yes	—
191	#95×C₁₃₉	C₂³	1	2	yes	—
192	#95×C₁₃₉	C₂³	1	2	yes	—
193	#95×C₁₃₉	C₂³	1	2	yes	—
194	#95×C₁₃₉	C₂³	1	2	yes	—
195	#95×C₁₃₉	C₂³	1	2	yes	—
196	#95×C₁₃₉	C₂³	1	2	yes	—
197	#95×C₁₃₉	C₂³	1	2	yes	—
198	#95×C₁₃₉	C₂³	1	2	yes	—
199	#95×C₁₃₉	C₂³	1	2	yes	—
200	#95×C₁₃₉	C₂³	1	2	yes	—
201	#95×C₁₃₉	C₂³	1	2	yes	—
202	#95×C₁₃₉	C₂³	1	2	yes	—
203	#95×C₁₃₉	C₂³	1	2	yes	—
204	#95×C₁₃₉	C₂³	1	2	yes	—
205	#95×C₁₃₉	C₂³	1	2	yes	—
206	#95×C₁₃₉	C₂³	1	2	yes	—
207	#95×C₁₃₉	C₂³	1	2	yes	—
208	#95×C₁₃₉	C₂³	1	2	yes	—
209	#95×C₁₃₉	C₂³	1	2	yes	—
210	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
211	C₂×Q₈×C₁₃₉	—	2	4	no	—
212	C₂×Q₈×C₁₃₉	—	4	1	no	—
213	C₂×Q₈×C₁₃₉	—	4	1	no	—
214	C₂×Q₈×C₁₃₉	—	4	2	no	—
215	C₂×Q₈×C₁₃₉	—	4	2	no	—
216	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	—
217	C₂×D₄×C₁₃₉	—	2	2	no	—
218	C₂×D₄×C₁₃₉	—	4	1	no	—
219	C₂×D₄×C₁₃₉	—	4	1	no	—
220	C₂²×C₄×C₁₃₉	—	2	4	no	—
221	C₂²×C₄×C₁₃₉	—	4	2	no	—
222	C₂²×C₄×C₁₃₉	—	4	2	no	—
223	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
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	2	yes	—
232	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
235	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
237	C₂²×C₄×C₁₃₉	C₂⁴	1	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	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	4	no	—
246	C₄⋊C₄×C₁₃₉	—	2	4	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	4	no	—
251	C₄⋊C₄×C₁₃₉	—	2	4	no	—
252	C₄⋊C₄×C₁₃₉	—	2	4	no	—
253	C₄⋊C₄×C₁₃₉	—	2	4	no	—
254	C₄⋊C₄×C₁₃₉	—	2	4	no	—
255	C₄⋊C₄×C₁₃₉	—	2	4	no	—
256	C₄⋊C₄×C₁₃₉	—	2	4	no	—
257	C₄⋊C₄×C₁₃₉	—	2	4	no	—
258	C₄⋊C₄×C₁₃₉	—	2	4	no	—
259	C₄⋊C₄×C₁₃₉	—	2	4	no	—
260	C₄⋊C₄×C₁₃₉	—	2	2	no	—
261	C₄⋊C₄×C₁₃₉	—	2	2	no	—
262	C₄⋊C₄×C₁₃₉	—	2	2	no	—
263	C₄⋊C₄×C₁₃₉	—	4	2	no	—
264	C₄⋊C₄×C₁₃₉	—	4	2	no	—
265	C₄⋊C₄×C₁₃₉	—	4	1	no	—
266	C₄⋊C₄×C₁₃₉	—	4	1	no	—
267	C₄⋊C₄×C₁₃₉	—	4	1	no	—
268	C₄⋊C₄×C₁₃₉	—	4	1	no	—
269	C₄⋊C₄×C₁₃₉	—	4	1	no	—
270	C₄⋊C₄×C₁₃₉	—	4	1	no	—
271	C₄⋊C₄×C₁₃₉	—	4	2	no	—
272	C₄⋊C₄×C₁₃₉	—	4	2	no	—
273	C₄⋊C₄×C₁₃₉	—	4	2	no	—
274	C₄⋊C₄×C₁₃₉	—	4	2	no	—
275	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
276	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
277	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
278	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
279	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
280	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
281	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
282	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
283	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
284	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
285	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
286	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
287	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
288	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
289	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
290	C₄²×C₁₃₉	—	2	4	no	—
291	C₄²×C₁₃₉	—	2	4	no	—
292	C₄²×C₁₃₉	—	2	4	no	—
293	C₄²×C₁₃₉	—	2	2	no	—
294	C₄²×C₁₃₉	—	2	2	no	—
295	C₄²×C₁₃₉	—	2	2	no	—
296	C₄²×C₁₃₉	—	4	1	no	—
297	C₄²×C₁₃₉	—	4	2	no	—
298	C₄²×C₁₃₉	—	4	1	no	—
299	C₄²×C₁₃₉	—	4	1	no	—
300	C₄²×C₁₃₉	C₂×D₄	1	8	yes	—
301	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
302	C₂³×C₁₃₉	—	2	2	no	—
303	C₂³×C₁₃₉	—	2	2	no	—
304	C₂³×C₁₃₉	—	2	2	no	—
305	C₂³×C₁₃₉	—	2	2	no	—
306	C₂³×C₁₃₉	—	2	2	no	—
307	C₂³×C₁₃₉	—	2	2	no	—
308	C₂³×C₁₃₉	—	2	2	no	—
309	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
310	Q₈×C₁₃₉	—	4	4	no	—
311	Q₈×C₁₃₉	—	4	8	no	—
312	D₄×C₁₃₉	—	8	2	no	—
313	C₂×C₄×C₁₃₉	—	2	1	no	—
314	C₂×C₄×C₁₃₉	—	2	1	no	—
315	C₂×C₄×C₁₃₉	—	2	1	no	—
316	C₂×C₄×C₁₃₉	—	2	1	no	—
317	C₂×C₄×C₁₃₉	—	2	2	no	—
318	C₂×C₄×C₁₃₉	—	2	2	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	1	no	—
323	C₂×C₄×C₁₃₉	—	2	1	no	—
324	C₂×C₄×C₁₃₉	—	2	1	no	—
325	C₂×C₄×C₁₃₉	—	2	1	no	—
326	C₂×C₄×C₁₃₉	—	2	1	no	—
327	C₂×C₄×C₁₃₉	—	2	2	no	—
328	C₂×C₄×C₁₃₉	—	2	2	no	—
329	C₂×C₄×C₁₃₉	—	2	2	no	—
330	C₂×C₄×C₁₃₉	—	2	2	no	—
331	C₂×C₄×C₁₃₉	—	2	2	no	—
332	C₂×C₄×C₁₃₉	—	2	2	no	—
333	C₂×C₄×C₁₃₉	—	2	2	no	—
334	C₂×C₄×C₁₃₉	—	2	2	no	—
335	C₂×C₄×C₁₃₉	—	2	2	no	—
336	C₂×C₄×C₁₃₉	—	2	1	no	—
337	C₂×C₄×C₁₃₉	—	2	1	no	—
338	C₂×C₄×C₁₃₉	—	2	2	no	—
339	C₂×C₄×C₁₃₉	—	2	2	no	—
340	C₂×C₄×C₁₃₉	—	2	2	no	—
341	C₂×C₄×C₁₃₉	—	2	2	no	—
342	C₂×C₄×C₁₃₉	—	2	2	no	—
343	C₂×C₄×C₁₃₉	—	2	2	no	—
344	C₂×C₄×C₁₃₉	—	2	2	no	—
345	C₂×C₄×C₁₃₉	—	2	1	no	—
346	C₂×C₄×C₁₃₉	—	2	2	no	—
347	C₂×C₄×C₁₃₉	—	2	2	no	—
348	C₂×C₄×C₁₃₉	—	2	2	no	—
349	C₂×C₄×C₁₃₉	—	2	2	no	—
350	C₂×C₄×C₁₃₉	—	2	2	no	—
351	C₂×C₄×C₁₃₉	—	2	2	no	—
352	C₂×C₄×C₁₃₉	—	2	2	no	—
353	C₂×C₄×C₁₃₉	—	2	2	no	—
354	C₂×C₄×C₁₃₉	—	2	2	no	—
355	C₂×C₄×C₁₃₉	—	2	2	no	—
356	C₂×C₄×C₁₃₉	—	2	2	no	—
357	C₂×C₄×C₁₃₉	—	2	2	no	—
358	C₂×C₄×C₁₃₉	—	2	2	no	—
359	C₂×C₄×C₁₃₉	—	4	8	no	—
360	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
361	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
362	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
363	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
364	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
365	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
366	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
367	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
368	C₂²×C₁₃₉	—	4	2	no	—
369	C₂²×C₁₃₉	—	4	2	no	—
370	C₂²×C₁₃₉	—	4	2	no	—
371	C₂²×C₁₃₉	—	4	2	no	—
372	C₂²×C₁₃₉	—	4	2	no	—
373	C₂²×C₁₃₉	—	4	2	no	—
374	C₂²×C₁₃₉	—	4	2	no	—
375	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
376	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
377	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
378	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
379	C₂²×C₁₃₉	#585	1	1	yes	characteristic
380	C₂²×C₁₃₉	#585	1	1	yes	characteristic
381	C₂²×C₁₃₉	#585	1	1	yes	characteristic
382	C₄×C₁₃₉	—	2	4	no	—
383	C₄×C₁₃₉	—	2	2	no	—
384	C₄×C₁₃₉	—	2	2	no	—
385	C₄×C₁₃₉	—	2	2	no	—
386	C₄×C₁₃₉	—	2	4	no	—
387	C₄×C₁₃₉	—	2	2	no	—
388	C₄×C₁₃₉	—	2	2	no	—
389	C₄×C₁₃₉	—	2	2	no	—
390	C₄×C₁₃₉	—	4	2	no	—
391	C₄×C₁₃₉	—	4	2	no	—
392	C₄×C₁₃₉	—	4	2	no	—
393	C₄×C₁₃₉	—	4	2	no	—
394	C₄×C₁₃₉	—	4	2	no	—
395	C₄×C₁₃₉	—	4	2	no	—
396	C₄×C₁₃₉	—	4	2	no	—
397	C₄×C₁₃₉	—	4	2	no	—
398	C₄×C₁₃₉	—	4	1	no	—
399	C₄×C₁₃₉	—	4	2	no	—
400	C₂×C₁₃₉	—	8	2	no	—
401	C₂×C₁₃₉	#3449	1	1	yes	characteristic
402	C₂×C₁₃₉	#3497	1	1	yes	characteristic
403	C₂×C₁₃₉	#3499	1	1	yes	characteristic
404	C₂×C₁₃₉	#3553	1	1	yes	characteristic
405	C₂×C₁₃₉	#3555	1	1	yes	characteristic
406	C₂×C₁₃₉	#3563	1	1	yes	characteristic
407	C₂×C₁₃₉	#3564	1	1	yes	characteristic
408	#37191	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
409	C₁₃₉	#37191	1	1	yes	characteristic, direct product factor, Sylow
410	C₂×#541	C₂×C₁₃₉	1	2	yes	complemented
411	#2860	C₂×C₁₃₉	1	1	yes	characteristic
412	#2859	C₂×C₁₃₉	1	1	yes	characteristic, complemented
413	#2734	C₂×C₁₃₉	1	1	yes	characteristic, complemented
414	#2732	C₂×C₁₃₉	1	1	yes	characteristic
415	#2729	C₂×C₁₃₉	1	2	yes	complemented
416	#2727	C₂×C₁₃₉	1	1	yes	characteristic
417	#2726	C₂×C₁₃₉	1	1	yes	characteristic, complemented
418	#2725	C₂×C₁₃₉	1	2	yes	complemented
419	#2723	C₂×C₁₃₉	1	2	yes	—
420	#2721	C₂×C₁₃₉	1	2	yes	complemented
421	#2720	C₂×C₁₃₉	1	2	yes	complemented
422	#2719	C₂×C₁₃₉	1	2	yes	complemented
423	#2664	C₂×C₁₃₉	1	2	yes	complemented
424	#2611	C₂×C₁₃₉	1	2	yes	complemented
425	#2604	C₂×C₁₃₉	1	2	yes	complemented
426	#2601	C₂×C₁₃₉	1	2	yes	—
427	#2584	C₂×C₁₃₉	1	2	yes	complemented
428	#2295	C₂×C₁₃₉	1	1	yes	characteristic, complemented
429	#541	—	2	16	no	—
430	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
431	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
432	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
433	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
434	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
435	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
436	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
437	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
438	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
439	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
440	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
441	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
442	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
443	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
444	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
445	#400	C₂²×C₁₃₉	1	2	yes	—
446	#400	C₂²×C₁₃₉	1	2	yes	—
447	#400	C₂²×C₁₃₉	1	2	yes	—
448	#399	C₂²×C₁₃₉	1	2	yes	—
449	#399	C₂²×C₁₃₉	1	2	yes	—
450	#399	C₂²×C₁₃₉	1	2	yes	—
451	#398	C₂²×C₁₃₉	1	2	yes	—
452	#398	C₂²×C₁₃₉	1	2	yes	—
453	#398	C₂²×C₁₃₉	1	2	yes	—
454	#398	C₂²×C₁₃₉	1	2	yes	—
455	#398	C₂²×C₁₃₉	1	2	yes	—
456	#398	C₂²×C₁₃₉	1	2	yes	—
457	#398	C₂²×C₁₃₉	1	2	yes	—
458	#397	C₂²×C₁₃₉	1	2	yes	—
459	#397	C₂²×C₁₃₉	1	2	yes	—
460	#396	C₂²×C₁₃₉	1	2	yes	—
461	#396	C₂²×C₁₃₉	1	2	yes	—
462	#396	C₂²×C₁₃₉	1	2	yes	—
463	#396	C₂²×C₁₃₉	1	2	yes	—
464	#395	C₂²×C₁₃₉	1	2	yes	—
465	#395	C₂²×C₁₃₉	1	2	yes	—
466	#395	C₂²×C₁₃₉	1	2	yes	—
467	#394	C₂²×C₁₃₉	1	2	yes	—
468	#393	C₂²×C₁₃₉	1	2	yes	—
469	#391	C₂²×C₁₃₉	1	1	yes	characteristic
470	#391	C₂²×C₁₃₉	1	1	yes	characteristic
471	#390	C₂²×C₁₃₉	1	1	yes	characteristic
472	#390	C₂²×C₁₃₉	1	1	yes	characteristic
473	#390	C₂²×C₁₃₉	1	1	yes	characteristic
474	#389	C₂²×C₁₃₉	1	1	yes	characteristic
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	2	yes	—
481	#389	C₂²×C₁₃₉	1	2	yes	—
482	#389	C₂²×C₁₃₉	1	1	yes	characteristic
483	#389	C₂²×C₁₃₉	1	1	yes	characteristic
484	#389	C₂²×C₁₃₉	1	2	yes	—
485	#389	C₂²×C₁₃₉	1	1	yes	characteristic
486	#389	C₂²×C₁₃₉	1	1	yes	characteristic
487	#389	C₂²×C₁₃₉	1	1	yes	characteristic
488	#389	C₂²×C₁₃₉	1	1	yes	characteristic
489	#389	C₂²×C₁₃₉	1	1	yes	characteristic
490	#389	C₂²×C₁₃₉	1	1	yes	characteristic
491	#388	C₂²×C₁₃₉	1	2	yes	—
492	#388	C₂²×C₁₃₉	1	2	yes	—
493	#388	C₂²×C₁₃₉	1	2	yes	—
494	#388	C₂²×C₁₃₉	1	2	yes	—
495	#388	C₂²×C₁₃₉	1	2	yes	—
496	#388	C₂²×C₁₃₉	1	2	yes	—
497	#388	C₂²×C₁₃₉	1	2	yes	—
498	#388	C₂²×C₁₃₉	1	2	yes	—
499	#387	C₂²×C₁₃₉	1	2	yes	—
500	#387	C₂²×C₁₃₉	1	2	yes	—
501	#387	C₂²×C₁₃₉	1	2	yes	—
502	#387	C₂²×C₁₃₉	1	2	yes	—
503	#387	C₂²×C₁₃₉	1	2	yes	—
504	#387	C₂²×C₁₃₉	1	2	yes	—
505	#387	C₂²×C₁₃₉	1	2	yes	—
506	#386	C₂²×C₁₃₉	1	2	yes	—
507	#385	C₂²×C₁₃₉	1	2	yes	—
508	#385	C₂²×C₁₃₉	1	2	yes	—
509	#385	C₂²×C₁₃₉	1	2	yes	—
510	#384	C₂²×C₁₃₉	1	1	yes	characteristic
511	#384	C₂²×C₁₃₉	1	1	yes	characteristic
512	#382	C₂²×C₁₃₉	1	2	yes	—
513	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
514	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
515	#376	C₂²×C₁₃₉	1	2	yes	—
516	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
517	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
518	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
519	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
520	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
521	C₄⋊Q₈	—	2	8	no	—
522	#126	—	2	8	no	—
523	#126	—	2	8	no	—
524	#126	—	2	8	no	—
525	#126	—	2	8	no	—
526	#125	—	2	8	no	—
527	#125	—	2	8	no	—
528	#125	—	2	8	no	—
529	#125	—	2	8	no	—
530	#125	—	2	8	no	—
531	C₂²⋊Q₈	—	2	8	no	—
532	C₂²⋊Q₈	—	2	8	no	—
533	C₄×Q₈	—	2	8	no	—
534	C₄×Q₈	D₄×C₁₃₉	1	8	yes	complemented
535	#117	—	2	8	no	—
536	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
537	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
538	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
539	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
540	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
541	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
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	2	yes	—
545	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
546	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
547	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
548	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
549	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
550	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	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	2	yes	—
555	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
556	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
557	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
558	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
559	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
560	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
561	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
562	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
563	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
564	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
565	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
566	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
567	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
568	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
569	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
570	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
571	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
572	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
574	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
576	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
577	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
578	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
579	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
580	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
581	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
582	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
583	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
584	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
585	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
586	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
587	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
588	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
589	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
590	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
591	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
592	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
593	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
594	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
595	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
596	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
597	#95	C₂³×C₁₃₉	1	2	yes	—
598	#95	C₂³×C₁₃₉	1	2	yes	—
599	#95	C₂³×C₁₃₉	1	2	yes	—
600	#95	C₂³×C₁₃₉	1	2	yes	—
601	#95	C₂³×C₁₃₉	1	2	yes	—
602	#95	C₂³×C₁₃₉	1	2	yes	—
603	#95	C₂³×C₁₃₉	1	2	yes	—
604	#95	C₂³×C₁₃₉	1	2	yes	—
605	#95	C₂³×C₁₃₉	1	2	yes	—
606	#95	C₂³×C₁₃₉	1	2	yes	—
607	#95	C₂³×C₁₃₉	1	2	yes	—
608	#95	C₂³×C₁₃₉	1	2	yes	—
609	#95	C₂³×C₁₃₉	1	2	yes	—
610	#95	C₂³×C₁₃₉	1	2	yes	—
611	#95	C₂³×C₁₃₉	1	2	yes	—
612	#95	C₂³×C₁₃₉	1	2	yes	—
613	#95	C₂³×C₁₃₉	1	2	yes	—
614	#95	C₂³×C₁₃₉	1	2	yes	—
615	#95	C₂³×C₁₃₉	1	2	yes	—
616	#95	C₂³×C₁₃₉	1	2	yes	—
617	#95	C₂³×C₁₃₉	1	2	yes	—
618	#95	C₂³×C₁₃₉	1	2	yes	—
619	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
620	C₂×Q₈	—	2	4	no	—
621	C₂×Q₈	—	4	1	no	—
622	C₂×Q₈	—	4	1	no	—
623	C₂×Q₈	—	4	2	no	—
624	C₂×Q₈	—	4	2	no	—
625	C₂×Q₈	C₂×D₄×C₁₃₉	1	4	yes	—
626	C₂×D₄	—	2	2	no	—
627	C₂×D₄	—	4	1	no	—
628	C₂×D₄	—	4	1	no	—
629	C₂²×C₄	—	2	4	no	—
630	C₂²×C₄	—	4	2	no	—
631	C₂²×C₄	—	4	2	no	—
632	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
633	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
634	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
635	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
636	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
637	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
638	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
639	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
640	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
641	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
642	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
643	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
644	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
645	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
646	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
647	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
648	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
649	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
650	C₄⋊C₄	—	2	4	no	—
651	C₄⋊C₄	—	2	4	no	—
652	C₄⋊C₄	—	2	4	no	—
653	C₄⋊C₄	—	2	4	no	—
654	C₄⋊C₄	—	2	4	no	—
655	C₄⋊C₄	—	2	4	no	—
656	C₄⋊C₄	—	2	4	no	—
657	C₄⋊C₄	—	2	4	no	—
658	C₄⋊C₄	—	2	4	no	—
659	C₄⋊C₄	—	2	4	no	—
660	C₄⋊C₄	—	2	4	no	—
661	C₄⋊C₄	—	2	4	no	—
662	C₄⋊C₄	—	2	4	no	—
663	C₄⋊C₄	—	2	4	no	—
664	C₄⋊C₄	—	2	4	no	—
665	C₄⋊C₄	—	2	4	no	—
666	C₄⋊C₄	—	2	4	no	—
667	C₄⋊C₄	—	2	4	no	—
668	C₄⋊C₄	—	2	4	no	—
669	C₄⋊C₄	—	2	2	no	—
670	C₄⋊C₄	—	2	2	no	—
671	C₄⋊C₄	—	2	2	no	—
672	C₄⋊C₄	—	4	2	no	—
673	C₄⋊C₄	—	4	2	no	—
674	C₄⋊C₄	—	4	1	no	—
675	C₄⋊C₄	—	4	1	no	—
676	C₄⋊C₄	—	4	1	no	—
677	C₄⋊C₄	—	4	1	no	—
678	C₄⋊C₄	—	4	1	no	—
679	C₄⋊C₄	—	4	1	no	—
680	C₄⋊C₄	—	4	2	no	—
681	C₄⋊C₄	—	4	2	no	—
682	C₄⋊C₄	—	4	2	no	—
683	C₄⋊C₄	—	4	2	no	—
684	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
685	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
686	C₂²⋊C₄	—	2	4	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	—	2	4	no	—
689	C₂²⋊C₄	—	2	4	no	—
690	C₂²⋊C₄	—	2	4	no	—
691	C₂²⋊C₄	—	2	4	no	—
692	C₂²⋊C₄	—	2	4	no	—
693	C₂²⋊C₄	—	2	4	no	—
694	C₂²⋊C₄	—	4	2	no	—
695	C₂²⋊C₄	—	4	2	no	—
696	C₂²⋊C₄	—	4	2	no	—
697	C₂²⋊C₄	—	4	2	no	—
698	C₂²⋊C₄	—	4	2	no	—
699	C₄²	—	2	4	no	—
700	C₄²	—	2	4	no	—
701	C₄²	—	2	4	no	—
702	C₄²	—	2	2	no	—
703	C₄²	—	2	2	no	—
704	C₄²	—	2	2	no	—
705	C₄²	—	4	1	no	—
706	C₄²	—	4	2	no	—
707	C₄²	—	4	1	no	—
708	C₄²	—	4	1	no	—
709	C₄²	C₂×D₄×C₁₃₉	1	8	yes	—
710	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
711	C₂³	—	2	2	no	—
712	C₂³	—	2	2	no	—
713	C₂³	—	2	2	no	—
714	C₂³	—	2	2	no	—
715	C₂³	—	2	2	no	—
716	C₂³	—	2	2	no	—
717	C₂³	—	2	2	no	—
718	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
719	Q₈	—	4	4	no	—
720	Q₈	—	4	8	no	—
721	D₄	—	8	2	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	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	1	no	—
729	C₂×C₄	—	2	1	no	—
730	C₂×C₄	—	2	1	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	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	1	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	4	8	no	—
769	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
770	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
771	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
772	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
773	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
774	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
775	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
776	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
777	C₂²	—	4	2	no	—
778	C₂²	—	4	2	no	—
779	C₂²	—	4	2	no	—
780	C₂²	—	4	2	no	—
781	C₂²	—	4	2	no	—
782	C₂²	—	4	2	no	—
783	C₂²	—	4	2	no	—
784	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
785	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
786	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
787	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
788	C₂²	#585×C₁₃₉	1	1	yes	characteristic
789	C₂²	#585×C₁₃₉	1	1	yes	characteristic
790	C₂²	#585×C₁₃₉	1	1	yes	characteristic
791	C₄	—	2	2	no	—
792	C₄	—	2	2	no	—
793	C₄	—	2	2	no	—
794	C₄	—	2	4	no	—
795	C₄	—	2	2	no	—
796	C₄	—	2	2	no	—
797	C₄	—	2	2	no	—
798	C₄	—	2	4	no	—
799	C₄	—	4	2	no	—
800	C₄	—	4	1	no	—
801	C₄	—	4	2	no	—
802	C₄	—	4	2	no	—
803	C₄	—	4	2	no	—
804	C₄	—	4	2	no	—
805	C₄	—	4	2	no	—
806	C₄	—	4	2	no	—
807	C₄	—	4	2	no	—
808	C₄	—	4	2	no	—
809	C₂	—	8	2	no	—
810	C₂	#3449×C₁₃₉	1	1	yes	characteristic
811	C₂	#3497×C₁₃₉	1	1	yes	characteristic
812	C₂	#3499×C₁₃₉	1	1	yes	characteristic
813	C₂	#3553×C₁₃₉	1	1	yes	characteristic
814	C₂	#3555×C₁₃₉	1	1	yes	characteristic
815	C₂	#3563×C₁₃₉	1	1	yes	characteristic
816	C₂	#3564×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×#541×C₁₃₉	C₂	semidirect
3. #2859×C₁₃₉	C₂	semidirect
4. #2734×C₁₃₉	C₂	semidirect
6. #2729×C₁₃₉	C₂	semidirect
8. #2726×C₁₃₉	C₂	semidirect
9. #2725×C₁₃₉	C₂	semidirect
11. #2721×C₁₃₉	C₂	semidirect
12. #2720×C₁₃₉	C₂	semidirect
13. #2719×C₁₃₉	C₂	semidirect
14. #2664×C₁₃₉	C₂	semidirect
15. #2611×C₁₃₉	C₂	semidirect
16. #2604×C₁₃₉	C₂	semidirect
18. #2584×C₁₃₉	C₂	semidirect
19. #2295×C₁₃₉	C₂	semidirect
125. C₄×Q₈×C₁₃₉	D₄	semidirect
408. #37191	C₁₃₉	direct (N × H)
409. C₁₃₉	#37191	direct (N × H)
410. C₂×#541	C₂×C₁₃₉	semidirect
412. #2859	C₂×C₁₃₉	semidirect
413. #2734	C₂×C₁₃₉	semidirect
415. #2729	C₂×C₁₃₉	semidirect
417. #2726	C₂×C₁₃₉	semidirect
418. #2725	C₂×C₁₃₉	semidirect
420. #2721	C₂×C₁₃₉	semidirect
421. #2720	C₂×C₁₃₉	semidirect
422. #2719	C₂×C₁₃₉	semidirect
423. #2664	C₂×C₁₃₉	semidirect
424. #2611	C₂×C₁₃₉	semidirect
425. #2604	C₂×C₁₃₉	semidirect
427. #2584	C₂×C₁₃₉	semidirect
428. #2295	C₂×C₁₃₉	semidirect
534. 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×#541×C₁₃₉	2
#2860×C₁₃₉	2
#2859×C₁₃₉	2
#2734×C₁₃₉	2
#2732×C₁₃₉	2
#2729×C₁₃₉	2
#2727×C₁₃₉	2
#2726×C₁₃₉	2
#2725×C₁₃₉	2
#2723×C₁₃₉	2
#2721×C₁₃₉	2
#2720×C₁₃₉	2
#2719×C₁₃₉	2
#2664×C₁₃₉	2
#2611×C₁₃₉	2
#2604×C₁₃₉	2
#2601×C₁₃₉	2
#2584×C₁₃₉	2
#2295×C₁₃₉	2
#37191	139

Subgroups — C139×#37191 #48031787

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37191 #48031787