Subgroups — C₁₃₉×#36411 #48031007

Order 35584.

2552 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×#555×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×#41×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2857×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2854×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2567×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2538×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2485×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2474×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#2461×C₁₃₉	C₂	1	4	yes	maximal, complemented
10	#2422×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2414×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2407×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2362×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2354×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#2354×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	C₄×#121×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	#2296×C₁₃₉	C₂	1	2	yes	maximal, complemented
18	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
19	#555×C₁₃₉	—	2	8	no	—
20	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×#124×C₁₃₉	C₂²	1	4	yes	—
22	C₂×#123×C₁₃₉	C₂²	1	4	yes	—
23	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
24	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
25	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
27	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
28	C₄×#41×C₁₃₉	—	2	8	no	—
29	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
37	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
38	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
39	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
40	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
41	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
42	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
43	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
44	#397×C₁₃₉	C₂²	1	4	yes	—
45	#396×C₁₃₉	C₂²	1	4	yes	—
46	#395×C₁₃₉	C₂²	1	4	yes	—
47	#394×C₁₃₉	C₂²	1	4	yes	—
48	#394×C₁₃₉	C₂²	1	4	yes	—
49	#392×C₁₃₉	C₂²	1	4	yes	—
50	#391×C₁₃₉	C₂²	1	2	yes	—
51	#391×C₁₃₉	C₂²	1	2	yes	—
52	#390×C₁₃₉	C₂²	1	2	yes	—
53	#390×C₁₃₉	C₂²	1	1	yes	characteristic
54	#390×C₁₃₉	C₂²	1	2	yes	—
55	#390×C₁₃₉	C₂²	1	4	yes	—
56	#389×C₁₃₉	C₂²	1	2	yes	—
57	#389×C₁₃₉	C₂²	1	1	yes	characteristic
58	#389×C₁₃₉	C₂²	1	2	yes	—
59	#389×C₁₃₉	C₂²	1	2	yes	—
60	#389×C₁₃₉	C₂²	1	2	yes	—
61	#389×C₁₃₉	C₂²	1	2	yes	—
62	#388×C₁₃₉	C₂²	1	2	yes	—
63	#388×C₁₃₉	C₂²	1	4	yes	—
64	#388×C₁₃₉	C₂²	1	4	yes	—
65	#388×C₁₃₉	C₂²	1	4	yes	—
66	#388×C₁₃₉	C₂²	1	4	yes	—
67	#388×C₁₃₉	C₂²	1	4	yes	—
68	#387×C₁₃₉	C₂²	1	4	yes	—
69	#386×C₁₃₉	C₂²	1	2	yes	—
70	#386×C₁₃₉	C₂²	1	4	yes	—
71	#385×C₁₃₉	C₂²	1	4	yes	—
72	#385×C₁₃₉	C₂²	1	4	yes	—
73	#384×C₁₃₉	C₂²	1	1	yes	characteristic
74	#384×C₁₃₉	C₂²	1	2	yes	—
75	#380×C₁₃₉	C₂²	1	2	yes	—
76	#380×C₁₃₉	C₂²	1	1	yes	characteristic
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	4	yes	—
81	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
82	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
83	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
84	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
85	C₂×#41×C₁₃₉	—	2	4	no	—
86	C₂×#41×C₁₃₉	—	2	4	no	—
87	C₂×#41×C₁₃₉	—	2	4	no	—
88	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
89	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
90	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
91	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
92	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
93	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
94	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
95	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
96	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
98	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
100	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
101	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
102	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
103	#124×C₁₃₉	—	2	16	no	—
104	#123×C₁₃₉	—	4	8	no	—
105	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
106	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
107	#121×C₁₃₉	—	2	8	no	—
108	#121×C₁₃₉	—	2	8	no	—
109	#121×C₁₃₉	—	2	4	no	—
110	C₄×Q₈×C₁₃₉	—	2	4	no	—
111	C₄×Q₈×C₁₃₉	—	2	4	no	—
112	C₄×D₄×C₁₃₉	—	2	4	no	—
113	C₄×D₄×C₁₃₉	—	2	8	no	—
114	C₄×D₄×C₁₃₉	—	2	8	no	—
115	C₄×D₄×C₁₃₉	—	2	8	no	—
116	C₄×D₄×C₁₃₉	—	2	4	no	—
117	C₄×D₄×C₁₃₉	D₄	1	8	yes	complemented
118	#117×C₁₃₉	—	2	8	no	—
119	#117×C₁₃₉	—	2	4	no	—
120	#117×C₁₃₉	—	2	8	no	—
121	#117×C₁₃₉	—	2	8	no	—
122	#117×C₁₃₉	—	2	8	no	—
123	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
125	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	4	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	4	yes	—
136	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
137	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
139	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
142	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
144	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
146	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
147	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
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	2	yes	—
155	C₂×C₄²×C₁₃₉	—	2	8	no	—
156	C₂×C₄²×C₁₃₉	—	2	4	no	—
157	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
158	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
159	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
160	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
162	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
163	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
164	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
165	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
166	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
167	#95×C₁₃₉	C₂³	1	2	yes	—
168	#95×C₁₃₉	C₂³	1	4	yes	—
169	#95×C₁₃₉	C₂³	1	4	yes	—
170	#95×C₁₃₉	C₂³	1	4	yes	—
171	#95×C₁₃₉	C₂³	1	2	yes	—
172	#95×C₁₃₉	C₂³	1	4	yes	—
173	#95×C₁₃₉	C₂³	1	2	yes	—
174	#95×C₁₃₉	C₂³	1	4	yes	—
175	#95×C₁₃₉	C₂³	1	4	yes	—
176	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
177	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
178	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
179	#41×C₁₃₉	—	2	32	no	—
180	C₂×Q₈×C₁₃₉	—	2	2	no	—
181	C₂×Q₈×C₁₃₉	—	2	4	no	—
182	C₂×Q₈×C₁₃₉	—	2	2	no	—
183	C₂×Q₈×C₁₃₉	—	4	2	no	—
184	C₂×Q₈×C₁₃₉	—	4	2	no	—
185	C₂×Q₈×C₁₃₉	#41	1	4	yes	—
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	2	no	—
191	C₂×D₄×C₁₃₉	—	2	4	no	—
192	C₂×D₄×C₁₃₉	—	2	2	no	—
193	C₂×D₄×C₁₃₉	—	2	2	no	—
194	C₂×D₄×C₁₃₉	—	2	4	no	—
195	C₂×D₄×C₁₃₉	—	2	2	no	—
196	C₂×D₄×C₁₃₉	—	2	2	no	—
197	C₂×D₄×C₁₃₉	—	4	2	no	—
198	C₂×D₄×C₁₃₉	—	4	4	no	—
199	C₂×D₄×C₁₃₉	—	4	4	no	—
200	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
201	C₂²×C₄×C₁₃₉	—	2	4	no	—
202	C₂²×C₄×C₁₃₉	—	2	2	no	—
203	C₂²×C₄×C₁₃₉	—	2	4	no	—
204	C₂²×C₄×C₁₃₉	—	2	4	no	—
205	C₂²×C₄×C₁₃₉	—	2	4	no	—
206	C₂²×C₄×C₁₃₉	—	2	2	no	—
207	C₂²×C₄×C₁₃₉	—	2	4	no	—
208	C₂²×C₄×C₁₃₉	—	2	4	no	—
209	C₂²×C₄×C₁₃₉	—	2	2	no	—
210	C₂²×C₄×C₁₃₉	—	2	2	no	—
211	C₂²×C₄×C₁₃₉	—	2	4	no	—
212	C₂²×C₄×C₁₃₉	—	2	4	no	—
213	C₂²×C₄×C₁₃₉	—	2	2	no	—
214	C₂²×C₄×C₁₃₉	—	2	4	no	—
215	C₂²×C₄×C₁₃₉	—	2	2	no	—
216	C₂²×C₄×C₁₃₉	—	2	4	no	—
217	C₂²×C₄×C₁₃₉	—	2	2	no	—
218	C₂²×C₄×C₁₃₉	—	4	1	no	—
219	C₂²×C₄×C₁₃₉	—	4	2	no	—
220	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
221	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
222	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
226	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
227	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
230	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
231	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
234	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
235	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
236	C₄⋊C₄×C₁₃₉	—	2	2	no	—
237	C₄⋊C₄×C₁₃₉	—	2	4	no	—
238	C₄⋊C₄×C₁₃₉	—	2	4	no	—
239	C₄⋊C₄×C₁₃₉	—	2	2	no	—
240	C₄⋊C₄×C₁₃₉	—	2	4	no	—
241	C₄⋊C₄×C₁₃₉	—	2	4	no	—
242	C₄⋊C₄×C₁₃₉	—	2	4	no	—
243	C₄⋊C₄×C₁₃₉	—	2	4	no	—
244	C₄⋊C₄×C₁₃₉	—	2	4	no	—
245	C₄⋊C₄×C₁₃₉	—	2	8	no	—
246	C₄⋊C₄×C₁₃₉	—	2	8	no	—
247	C₄⋊C₄×C₁₃₉	—	2	2	no	—
248	C₄⋊C₄×C₁₃₉	—	4	4	no	—
249	C₄⋊C₄×C₁₃₉	—	4	2	no	—
250	C₄⋊C₄×C₁₃₉	—	4	4	no	—
251	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
252	C₄⋊C₄×C₁₃₉	#41	1	4	yes	complemented
253	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
254	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
255	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
256	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
257	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
258	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
259	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
260	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
261	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
262	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
263	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
264	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
265	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
266	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
267	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
268	C₄²×C₁₃₉	—	2	2	no	—
269	C₄²×C₁₃₉	—	2	4	no	—
270	C₄²×C₁₃₉	—	2	2	no	—
271	C₄²×C₁₃₉	—	2	4	no	—
272	C₄²×C₁₃₉	—	2	2	no	—
273	C₄²×C₁₃₉	—	2	4	no	—
274	C₄²×C₁₃₉	—	2	8	no	—
275	C₄²×C₁₃₉	—	2	8	no	—
276	C₄²×C₁₃₉	—	2	4	no	—
277	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
278	C₂³×C₁₃₉	—	2	1	no	—
279	C₂³×C₁₃₉	—	2	2	no	—
280	C₂³×C₁₃₉	—	2	2	no	—
281	C₂³×C₁₃₉	—	2	2	no	—
282	C₂³×C₁₃₉	—	2	1	no	—
283	C₂³×C₁₃₉	—	2	1	no	—
284	C₂³×C₁₃₉	—	2	1	no	—
285	C₂³×C₁₃₉	—	2	2	no	—
286	C₂³×C₁₃₉	—	2	2	no	—
287	C₂³×C₁₃₉	—	2	1	no	—
288	C₂³×C₁₃₉	—	2	1	no	—
289	C₂³×C₁₃₉	—	2	2	no	—
290	C₂³×C₁₃₉	—	2	2	no	—
291	C₂³×C₁₃₉	—	2	2	no	—
292	C₂³×C₁₃₉	—	2	2	no	—
293	C₂³×C₁₃₉	—	2	2	no	—
294	C₂³×C₁₃₉	—	2	2	no	—
295	C₂³×C₁₃₉	—	2	2	no	—
296	C₂³×C₁₃₉	—	2	2	no	—
297	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
298	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
299	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
300	Q₈×C₁₃₉	—	2	8	no	—
301	Q₈×C₁₃₉	—	8	4	no	—
302	D₄×C₁₃₉	—	2	16	no	—
303	D₄×C₁₃₉	—	2	8	no	—
304	D₄×C₁₃₉	—	4	8	no	—
305	D₄×C₁₃₉	—	4	4	no	—
306	D₄×C₁₃₉	—	8	8	no	—
307	C₂×C₄×C₁₃₉	—	2	16	no	—
308	C₂×C₄×C₁₃₉	—	2	1	no	—
309	C₂×C₄×C₁₃₉	—	2	1	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	1	no	—
314	C₂×C₄×C₁₃₉	—	2	2	no	—
315	C₂×C₄×C₁₃₉	—	2	1	no	—
316	C₂×C₄×C₁₃₉	—	2	2	no	—
317	C₂×C₄×C₁₃₉	—	2	2	no	—
318	C₂×C₄×C₁₃₉	—	2	1	no	—
319	C₂×C₄×C₁₃₉	—	2	1	no	—
320	C₂×C₄×C₁₃₉	—	2	8	no	—
321	C₂×C₄×C₁₃₉	—	2	16	no	—
322	C₂×C₄×C₁₃₉	—	2	2	no	—
323	C₂×C₄×C₁₃₉	—	2	1	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	4	no	—
328	C₂×C₄×C₁₃₉	—	2	1	no	—
329	C₂×C₄×C₁₃₉	—	2	4	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	4	no	—
334	C₂×C₄×C₁₃₉	—	2	2	no	—
335	C₂×C₄×C₁₃₉	—	2	4	no	—
336	C₂×C₄×C₁₃₉	—	2	2	no	—
337	C₂×C₄×C₁₃₉	—	2	1	no	—
338	C₂×C₄×C₁₃₉	—	2	2	no	—
339	C₂×C₄×C₁₃₉	—	2	4	no	—
340	C₂×C₄×C₁₃₉	—	4	4	no	—
341	C₂×C₄×C₁₃₉	—	4	8	no	—
342	C₂×C₄×C₁₃₉	—	4	8	no	—
343	C₂×C₄×C₁₃₉	—	4	4	no	—
344	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
345	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
346	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
347	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
348	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
349	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
350	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
351	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
352	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
353	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
354	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
355	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
356	C₂²×C₁₃₉	—	2	4	no	—
357	C₂²×C₁₃₉	—	2	2	no	—
358	C₂²×C₁₃₉	—	2	4	no	—
359	C₂²×C₁₃₉	—	2	2	no	—
360	C₂²×C₁₃₉	—	2	4	no	—
361	C₂²×C₁₃₉	—	2	2	no	—
362	C₂²×C₁₃₉	—	4	1	no	—
363	C₂²×C₁₃₉	—	4	2	no	—
364	C₂²×C₁₃₉	—	4	2	no	—
365	C₂²×C₁₃₉	—	4	1	no	—
366	C₂²×C₁₃₉	—	4	1	no	—
367	C₂²×C₁₃₉	—	4	2	no	—
368	C₂²×C₁₃₉	—	4	2	no	—
369	C₂²×C₁₃₉	—	4	1	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	—	4	2	no	—
376	C₂²×C₁₃₉	—	4	2	no	—
377	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
378	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
379	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
380	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
381	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
382	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
383	C₂²×C₁₃₉	#585	1	1	yes	characteristic
384	C₄×C₁₃₉	—	2	2	no	—
385	C₄×C₁₃₉	—	2	4	no	—
386	C₄×C₁₃₉	—	2	4	no	—
387	C₄×C₁₃₉	—	2	4	no	—
388	C₄×C₁₃₉	—	2	2	no	—
389	C₄×C₁₃₉	—	2	2	no	—
390	C₄×C₁₃₉	—	4	2	no	—
391	C₄×C₁₃₉	—	4	1	no	—
392	C₄×C₁₃₉	—	4	4	no	—
393	C₄×C₁₃₉	—	4	2	no	—
394	C₄×C₁₃₉	—	4	4	no	—
395	C₄×C₁₃₉	—	4	2	no	—
396	C₄×C₁₃₉	#525	1	4	yes	—
397	C₄×C₁₃₉	#547	1	4	yes	—
398	C₂×C₁₃₉	—	4	4	no	—
399	C₂×C₁₃₉	—	4	2	no	—
400	C₂×C₁₃₉	—	8	2	no	—
401	C₂×C₁₃₉	C₂×#525	1	1	yes	characteristic
402	C₂×C₁₃₉	C₂×#547	1	1	yes	characteristic
403	C₂×C₁₃₉	#3475	1	1	yes	characteristic
404	C₂×C₁₃₉	#3483	1	1	yes	characteristic
405	C₂×C₁₃₉	#3488	1	1	yes	characteristic
406	C₂×C₁₃₉	#3511	1	1	yes	characteristic
407	C₂×C₁₃₉	#3518	1	1	yes	characteristic
408	#36411	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
409	C₁₃₉	#36411	1	1	yes	characteristic, direct product factor, Sylow
410	C₂×#555	C₂×C₁₃₉	1	1	yes	characteristic, complemented
411	C₂×C₄×#41	C₂×C₁₃₉	1	1	yes	characteristic, complemented
412	#2857	C₂×C₁₃₉	1	1	yes	characteristic, complemented
413	#2854	C₂×C₁₃₉	1	2	yes	complemented
414	#2567	C₂×C₁₃₉	1	1	yes	characteristic, complemented
415	#2538	C₂×C₁₃₉	1	1	yes	characteristic, complemented
416	#2485	C₂×C₁₃₉	1	2	yes	complemented
417	#2474	C₂×C₁₃₉	1	4	yes	complemented
418	#2461	C₂×C₁₃₉	1	4	yes	complemented
419	#2422	C₂×C₁₃₉	1	2	yes	complemented
420	#2414	C₂×C₁₃₉	1	2	yes	complemented
421	#2407	C₂×C₁₃₉	1	2	yes	complemented
422	#2362	C₂×C₁₃₉	1	2	yes	complemented
423	#2354	C₂×C₁₃₉	1	2	yes	complemented
424	#2354	C₂×C₁₃₉	1	1	yes	characteristic, complemented
425	C₄×#121	C₂×C₁₃₉	1	1	yes	characteristic, complemented
426	#2296	C₂×C₁₃₉	1	2	yes	complemented
427	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
428	#555	—	2	8	no	—
429	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
430	C₂×#124	C₂²×C₁₃₉	1	4	yes	—
431	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
432	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
433	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
434	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
435	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
436	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
437	C₄×#41	—	2	8	no	—
438	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
439	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
440	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
441	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
442	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
443	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
444	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
445	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
446	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
447	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
448	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
449	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
450	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
451	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
452	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
453	#397	C₂²×C₁₃₉	1	4	yes	—
454	#396	C₂²×C₁₃₉	1	4	yes	—
455	#395	C₂²×C₁₃₉	1	4	yes	—
456	#394	C₂²×C₁₃₉	1	4	yes	—
457	#394	C₂²×C₁₃₉	1	4	yes	—
458	#392	C₂²×C₁₃₉	1	4	yes	—
459	#391	C₂²×C₁₃₉	1	2	yes	—
460	#391	C₂²×C₁₃₉	1	2	yes	—
461	#390	C₂²×C₁₃₉	1	1	yes	characteristic
462	#390	C₂²×C₁₃₉	1	2	yes	—
463	#390	C₂²×C₁₃₉	1	2	yes	—
464	#390	C₂²×C₁₃₉	1	4	yes	—
465	#389	C₂²×C₁₃₉	1	2	yes	—
466	#389	C₂²×C₁₃₉	1	2	yes	—
467	#389	C₂²×C₁₃₉	1	2	yes	—
468	#389	C₂²×C₁₃₉	1	2	yes	—
469	#389	C₂²×C₁₃₉	1	2	yes	—
470	#389	C₂²×C₁₃₉	1	1	yes	characteristic
471	#388	C₂²×C₁₃₉	1	4	yes	—
472	#388	C₂²×C₁₃₉	1	4	yes	—
473	#388	C₂²×C₁₃₉	1	4	yes	—
474	#388	C₂²×C₁₃₉	1	4	yes	—
475	#388	C₂²×C₁₃₉	1	4	yes	—
476	#388	C₂²×C₁₃₉	1	2	yes	—
477	#387	C₂²×C₁₃₉	1	4	yes	—
478	#386	C₂²×C₁₃₉	1	4	yes	—
479	#386	C₂²×C₁₃₉	1	2	yes	—
480	#385	C₂²×C₁₃₉	1	4	yes	—
481	#385	C₂²×C₁₃₉	1	4	yes	—
482	#384	C₂²×C₁₃₉	1	2	yes	—
483	#384	C₂²×C₁₃₉	1	1	yes	characteristic
484	#380	C₂²×C₁₃₉	1	2	yes	—
485	#380	C₂²×C₁₃₉	1	2	yes	—
486	#380	C₂²×C₁₃₉	1	2	yes	—
487	#380	C₂²×C₁₃₉	1	2	yes	—
488	#380	C₂²×C₁₃₉	1	1	yes	characteristic
489	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
490	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
491	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
492	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
493	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
494	C₂×#41	—	2	4	no	—
495	C₂×#41	—	2	4	no	—
496	C₂×#41	—	2	4	no	—
497	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
498	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
499	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
500	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
501	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
502	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
503	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
504	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
505	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
506	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
507	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
508	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
509	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
510	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
511	C₄⋊Q₈	—	2	4	no	—
512	#124	—	2	16	no	—
513	#123	—	4	8	no	—
514	C₂²⋊Q₈	—	2	8	no	—
515	C₂²⋊Q₈	—	4	4	no	—
516	#121	—	2	8	no	—
517	#121	—	2	8	no	—
518	#121	—	2	4	no	—
519	C₄×Q₈	—	2	4	no	—
520	C₄×Q₈	—	2	4	no	—
521	C₄×D₄	—	2	4	no	—
522	C₄×D₄	—	2	8	no	—
523	C₄×D₄	—	2	8	no	—
524	C₄×D₄	—	2	8	no	—
525	C₄×D₄	—	2	4	no	—
526	C₄×D₄	D₄×C₁₃₉	1	8	yes	complemented
527	#117	—	2	8	no	—
528	#117	—	2	4	no	—
529	#117	—	2	8	no	—
530	#117	—	2	8	no	—
531	#117	—	2	8	no	—
532	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
533	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
534	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
535	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
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	4	yes	—
541	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
542	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
543	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
544	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
545	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
546	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
547	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
548	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
549	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
550	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
553	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
555	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
556	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
557	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
558	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
559	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
560	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
561	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
562	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
563	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
564	C₂×C₄²	—	2	8	no	—
565	C₂×C₄²	—	2	4	no	—
566	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
567	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
568	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
569	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
570	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
571	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
572	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
573	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
574	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
575	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
576	#95	C₂³×C₁₃₉	1	2	yes	—
577	#95	C₂³×C₁₃₉	1	2	yes	—
578	#95	C₂³×C₁₃₉	1	4	yes	—
579	#95	C₂³×C₁₃₉	1	4	yes	—
580	#95	C₂³×C₁₃₉	1	4	yes	—
581	#95	C₂³×C₁₃₉	1	4	yes	—
582	#95	C₂³×C₁₃₉	1	2	yes	—
583	#95	C₂³×C₁₃₉	1	4	yes	—
584	#95	C₂³×C₁₃₉	1	4	yes	—
585	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
586	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
587	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
588	#41	—	2	32	no	—
589	C₂×Q₈	—	2	2	no	—
590	C₂×Q₈	—	2	4	no	—
591	C₂×Q₈	—	2	2	no	—
592	C₂×Q₈	—	4	2	no	—
593	C₂×Q₈	—	4	2	no	—
594	C₂×Q₈	#41×C₁₃₉	1	4	yes	—
595	C₂×D₄	—	2	4	no	—
596	C₂×D₄	—	2	4	no	—
597	C₂×D₄	—	2	4	no	—
598	C₂×D₄	—	2	8	no	—
599	C₂×D₄	—	2	2	no	—
600	C₂×D₄	—	2	4	no	—
601	C₂×D₄	—	2	2	no	—
602	C₂×D₄	—	2	2	no	—
603	C₂×D₄	—	2	4	no	—
604	C₂×D₄	—	2	2	no	—
605	C₂×D₄	—	2	2	no	—
606	C₂×D₄	—	4	2	no	—
607	C₂×D₄	—	4	4	no	—
608	C₂×D₄	—	4	4	no	—
609	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
610	C₂²×C₄	—	2	4	no	—
611	C₂²×C₄	—	2	2	no	—
612	C₂²×C₄	—	2	4	no	—
613	C₂²×C₄	—	2	4	no	—
614	C₂²×C₄	—	2	4	no	—
615	C₂²×C₄	—	2	2	no	—
616	C₂²×C₄	—	2	4	no	—
617	C₂²×C₄	—	2	4	no	—
618	C₂²×C₄	—	2	2	no	—
619	C₂²×C₄	—	2	2	no	—
620	C₂²×C₄	—	2	4	no	—
621	C₂²×C₄	—	2	4	no	—
622	C₂²×C₄	—	2	2	no	—
623	C₂²×C₄	—	2	4	no	—
624	C₂²×C₄	—	2	2	no	—
625	C₂²×C₄	—	2	4	no	—
626	C₂²×C₄	—	2	2	no	—
627	C₂²×C₄	—	4	1	no	—
628	C₂²×C₄	—	4	2	no	—
629	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
630	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
631	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
632	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
633	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
634	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
635	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
636	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
637	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
638	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
639	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
640	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
641	C₂²×C₄	C₂⁴×C₁₃₉	1	2	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	C₄⋊C₄	—	2	2	no	—
646	C₄⋊C₄	—	2	4	no	—
647	C₄⋊C₄	—	2	4	no	—
648	C₄⋊C₄	—	2	2	no	—
649	C₄⋊C₄	—	2	4	no	—
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	8	no	—
655	C₄⋊C₄	—	2	8	no	—
656	C₄⋊C₄	—	2	2	no	—
657	C₄⋊C₄	—	4	4	no	—
658	C₄⋊C₄	—	4	2	no	—
659	C₄⋊C₄	—	4	4	no	—
660	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
661	C₄⋊C₄	#41×C₁₃₉	1	4	yes	complemented
662	C₂²⋊C₄	—	2	4	no	—
663	C₂²⋊C₄	—	2	8	no	—
664	C₂²⋊C₄	—	2	4	no	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₂²⋊C₄	—	2	8	no	—
667	C₂²⋊C₄	—	2	4	no	—
668	C₂²⋊C₄	—	2	8	no	—
669	C₂²⋊C₄	—	2	4	no	—
670	C₂²⋊C₄	—	2	4	no	—
671	C₂²⋊C₄	—	2	8	no	—
672	C₂²⋊C₄	—	2	4	no	—
673	C₂²⋊C₄	—	4	4	no	—
674	C₂²⋊C₄	—	4	4	no	—
675	C₂²⋊C₄	—	4	4	no	—
676	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
677	C₄²	—	2	2	no	—
678	C₄²	—	2	4	no	—
679	C₄²	—	2	2	no	—
680	C₄²	—	2	4	no	—
681	C₄²	—	2	2	no	—
682	C₄²	—	2	4	no	—
683	C₄²	—	2	8	no	—
684	C₄²	—	2	8	no	—
685	C₄²	—	2	4	no	—
686	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
687	C₂³	—	2	1	no	—
688	C₂³	—	2	2	no	—
689	C₂³	—	2	2	no	—
690	C₂³	—	2	2	no	—
691	C₂³	—	2	1	no	—
692	C₂³	—	2	1	no	—
693	C₂³	—	2	1	no	—
694	C₂³	—	2	2	no	—
695	C₂³	—	2	2	no	—
696	C₂³	—	2	1	no	—
697	C₂³	—	2	1	no	—
698	C₂³	—	2	2	no	—
699	C₂³	—	2	2	no	—
700	C₂³	—	2	2	no	—
701	C₂³	—	2	2	no	—
702	C₂³	—	2	2	no	—
703	C₂³	—	2	2	no	—
704	C₂³	—	2	2	no	—
705	C₂³	—	2	2	no	—
706	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
707	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
708	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
709	Q₈	—	2	8	no	—
710	Q₈	—	8	4	no	—
711	D₄	—	2	16	no	—
712	D₄	—	2	8	no	—
713	D₄	—	4	8	no	—
714	D₄	—	4	4	no	—
715	D₄	—	8	8	no	—
716	C₂×C₄	—	2	16	no	—
717	C₂×C₄	—	2	1	no	—
718	C₂×C₄	—	2	1	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	1	no	—
728	C₂×C₄	—	2	1	no	—
729	C₂×C₄	—	2	8	no	—
730	C₂×C₄	—	2	16	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	1	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	4	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	4	no	—
737	C₂×C₄	—	2	1	no	—
738	C₂×C₄	—	2	4	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	4	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	4	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	4	no	—
749	C₂×C₄	—	4	4	no	—
750	C₂×C₄	—	4	8	no	—
751	C₂×C₄	—	4	8	no	—
752	C₂×C₄	—	4	4	no	—
753	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
754	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
755	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
756	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
757	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
758	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
759	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
760	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
761	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
762	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
763	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
764	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
765	C₂²	—	2	4	no	—
766	C₂²	—	2	2	no	—
767	C₂²	—	2	4	no	—
768	C₂²	—	2	2	no	—
769	C₂²	—	2	4	no	—
770	C₂²	—	2	2	no	—
771	C₂²	—	4	1	no	—
772	C₂²	—	4	2	no	—
773	C₂²	—	4	2	no	—
774	C₂²	—	4	1	no	—
775	C₂²	—	4	1	no	—
776	C₂²	—	4	2	no	—
777	C₂²	—	4	2	no	—
778	C₂²	—	4	1	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	—	4	2	no	—
785	C₂²	—	4	2	no	—
786	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
787	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
788	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
789	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
790	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
791	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
792	C₂²	#585×C₁₃₉	1	1	yes	characteristic
793	C₄	—	2	2	no	—
794	C₄	—	2	4	no	—
795	C₄	—	2	4	no	—
796	C₄	—	2	4	no	—
797	C₄	—	2	2	no	—
798	C₄	—	2	2	no	—
799	C₄	—	4	2	no	—
800	C₄	—	4	1	no	—
801	C₄	—	4	4	no	—
802	C₄	—	4	2	no	—
803	C₄	—	4	4	no	—
804	C₄	—	4	2	no	—
805	C₄	#525×C₁₃₉	1	4	yes	—
806	C₄	#547×C₁₃₉	1	4	yes	—
807	C₂	—	4	4	no	—
808	C₂	—	4	2	no	—
809	C₂	—	8	2	no	—
810	C₂	C₂×#525×C₁₃₉	1	1	yes	characteristic
811	C₂	C₂×#547×C₁₃₉	1	1	yes	characteristic
812	C₂	#3475×C₁₃₉	1	1	yes	characteristic
813	C₂	#3483×C₁₃₉	1	1	yes	characteristic
814	C₂	#3488×C₁₃₉	1	1	yes	characteristic
815	C₂	#3511×C₁₃₉	1	1	yes	characteristic
816	C₂	#3518×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
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×#555×C₁₃₉	C₂	semidirect
2. C₂×C₄×#41×C₁₃₉	C₂	semidirect
3. #2857×C₁₃₉	C₂	semidirect
4. #2854×C₁₃₉	C₂	semidirect
5. #2567×C₁₃₉	C₂	semidirect
6. #2538×C₁₃₉	C₂	semidirect
7. #2485×C₁₃₉	C₂	semidirect
8. #2474×C₁₃₉	C₂	semidirect
9. #2461×C₁₃₉	C₂	semidirect
10. #2422×C₁₃₉	C₂	semidirect
11. #2414×C₁₃₉	C₂	semidirect
12. #2407×C₁₃₉	C₂	semidirect
13. #2362×C₁₃₉	C₂	semidirect
14. #2354×C₁₃₉	C₂	semidirect
15. #2354×C₁₃₉	C₂	semidirect
16. C₄×#121×C₁₃₉	C₂	semidirect
17. #2296×C₁₃₉	C₂	semidirect
117. C₄×D₄×C₁₃₉	D₄	semidirect
252. C₄⋊C₄×C₁₃₉	#41	semidirect
408. #36411	C₁₃₉	direct (N × H)
409. C₁₃₉	#36411	direct (N × H)
410. C₂×#555	C₂×C₁₃₉	semidirect
411. C₂×C₄×#41	C₂×C₁₃₉	semidirect
412. #2857	C₂×C₁₃₉	semidirect
413. #2854	C₂×C₁₃₉	semidirect
414. #2567	C₂×C₁₃₉	semidirect
415. #2538	C₂×C₁₃₉	semidirect
416. #2485	C₂×C₁₃₉	semidirect
417. #2474	C₂×C₁₃₉	semidirect
418. #2461	C₂×C₁₃₉	semidirect
419. #2422	C₂×C₁₃₉	semidirect
420. #2414	C₂×C₁₃₉	semidirect
421. #2407	C₂×C₁₃₉	semidirect
422. #2362	C₂×C₁₃₉	semidirect
423. #2354	C₂×C₁₃₉	semidirect
424. #2354	C₂×C₁₃₉	semidirect
425. C₄×#121	C₂×C₁₃₉	semidirect
426. #2296	C₂×C₁₃₉	semidirect
526. C₄×D₄	D₄×C₁₃₉	semidirect
661. C₄⋊C₄	#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×#555×C₁₃₉	2
C₂×C₄×#41×C₁₃₉	2
#2857×C₁₃₉	2
#2854×C₁₃₉	2
#2567×C₁₃₉	2
#2538×C₁₃₉	2
#2485×C₁₃₉	2
#2474×C₁₃₉	2
#2461×C₁₃₉	2
#2422×C₁₃₉	2
#2414×C₁₃₉	2
#2407×C₁₃₉	2
#2362×C₁₃₉	2
#2354×C₁₃₉	2
C₄×#121×C₁₃₉	2
#2296×C₁₃₉	2
#36411	139

Subgroups — C139×#36411 #48031007

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36411 #48031007