Subgroups — C₁₃₉×#36386 #48030982

Order 35584.

2678 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#552×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#546×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2861×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2857×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2850×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2566×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2559×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	#2558×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#2545×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#2534×C₁₃₉	C₂	1	4	yes	maximal, complemented
11	#2503×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#2500×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#2435×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2432×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#2342×C₁₃₉	C₂	1	4	yes	maximal, complemented
16	C₄×#124×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	#2297×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#390×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄²×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
22	#552×C₁₃₉	—	2	8	no	—
23	#546×C₁₃₉	—	2	8	no	—
24	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
25	C₂×#126×C₁₃₉	C₂²	1	2	yes	complemented
26	C₂×#125×C₁₃₉	C₂²	1	2	yes	complemented
27	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
28	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
32	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
33	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
36	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
37	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
38	C₂×#120×C₁₃₉	C₂²	1	2	yes	—
39	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
41	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
43	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
44	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
45	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
46	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
47	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
48	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
49	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
50	#400×C₁₃₉	C₂²	1	4	yes	complemented
51	#396×C₁₃₉	C₂²	1	4	yes	complemented
52	#396×C₁₃₉	C₂²	1	4	yes	complemented
53	#394×C₁₃₉	C₂²	1	4	yes	—
54	#394×C₁₃₉	C₂²	1	4	yes	complemented
55	#394×C₁₃₉	C₂²	1	4	yes	complemented
56	#391×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
57	#391×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
58	#391×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
59	#391×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
60	#390×C₁₃₉	C₂²	1	1	yes	characteristic
61	#390×C₁₃₉	C₂²	1	1	yes	characteristic
62	#390×C₁₃₉	C₂²	1	4	yes	—
63	#390×C₁₃₉	C₂²	1	1	yes	characteristic
64	#390×C₁₃₉	C₂²	1	1	yes	characteristic
65	#390×C₁₃₉	C₂²	1	1	yes	characteristic
66	#390×C₁₃₉	C₂²	1	1	yes	characteristic
67	#389×C₁₃₉	C₂²	1	4	yes	complemented
68	#388×C₁₃₉	C₂²	1	4	yes	complemented
69	#388×C₁₃₉	C₂²	1	4	yes	complemented
70	#388×C₁₃₉	C₂²	1	4	yes	complemented
71	#388×C₁₃₉	C₂²	1	4	yes	complemented
72	#388×C₁₃₉	C₂²	1	4	yes	complemented
73	#388×C₁₃₉	C₂²	1	4	yes	complemented
74	#386×C₁₃₉	C₂²	1	4	yes	complemented
75	#386×C₁₃₉	C₂²	1	4	yes	complemented
76	#385×C₁₃₉	C₂²	1	4	yes	complemented
77	#385×C₁₃₉	C₂²	1	4	yes	complemented
78	#384×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
79	#382×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
80	#382×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
81	#381×C₁₃₉	C₂²	1	4	yes	—
82	#380×C₁₃₉	C₂²	1	4	yes	—
83	#379×C₁₃₉	C₂²	1	4	yes	—
84	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
85	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
86	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
87	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
88	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
89	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
90	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	complemented
91	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	complemented
92	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
93	C₂⁵×C₁₃₉	C₂³	1	2	yes	—
94	C₂×#41×C₁₃₉	—	2	4	no	—
95	C₂×#41×C₁₃₉	—	2	4	no	—
96	C₂×#41×C₁₃₉	—	4	2	no	—
97	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
98	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
99	C₂²×D₄×C₁₃₉	—	2	4	no	—
100	C₂²×D₄×C₁₃₉	—	2	4	no	—
101	C₂²×D₄×C₁₃₉	—	4	2	no	—
102	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
103	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
104	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
105	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
106	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
107	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
108	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
109	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
110	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
113	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
114	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
115	C₄⋊Q₈×C₁₃₉	—	4	2	no	—
116	#126×C₁₃₉	—	2	8	no	—
117	#125×C₁₃₉	—	2	8	no	—
118	#125×C₁₃₉	—	2	4	no	—
119	#124×C₁₃₉	—	2	4	no	—
120	#124×C₁₃₉	—	2	4	no	—
121	#124×C₁₃₉	—	4	2	no	—
122	#123×C₁₃₉	—	2	8	no	—
123	#123×C₁₃₉	—	2	8	no	—
124	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
125	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
126	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
127	#121×C₁₃₉	—	2	4	no	—
128	#121×C₁₃₉	—	2	8	no	—
129	#120×C₁₃₉	—	2	8	no	—
130	C₄×Q₈×C₁₃₉	—	2	4	no	—
131	C₄×D₄×C₁₃₉	—	2	8	no	—
132	C₄×D₄×C₁₃₉	—	2	4	no	—
133	C₄×D₄×C₁₃₉	D₄	1	8	yes	—
134	#117×C₁₃₉	—	2	4	no	—
135	#117×C₁₃₉	—	2	8	no	—
136	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
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	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	1	yes	characteristic
147	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
150	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
151	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
152	C₂×C₂²⋊C₄×C₁₃₉	—	2	16	no	—
153	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
154	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
157	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
158	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
162	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
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	4	yes	—
169	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
170	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
171	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
172	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
173	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₁₃₉	—	4	2	no	—
175	C₂×C₄²×C₁₃₉	—	4	2	no	—
176	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
177	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
180	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
181	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
182	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
184	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
185	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
186	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
187	#95×C₁₃₉	C₂³	1	4	yes	—
188	#95×C₁₃₉	C₂³	1	4	yes	—
189	#95×C₁₃₉	C₂³	1	2	yes	—
190	#95×C₁₃₉	C₂³	1	4	yes	—
191	#95×C₁₃₉	C₂³	1	4	yes	—
192	#95×C₁₃₉	C₂³	1	2	yes	—
193	#95×C₁₃₉	C₂³	1	2	yes	—
194	#95×C₁₃₉	C₂³	1	4	yes	—
195	#95×C₁₃₉	C₂³	1	4	yes	—
196	C₂⁴×C₁₃₉	—	2	4	no	—
197	C₂⁴×C₁₃₉	—	2	4	no	—
198	C₂⁴×C₁₃₉	—	2	8	no	—
199	C₂⁴×C₁₃₉	—	4	2	no	—
200	C₂⁴×C₁₃₉	—	4	4	no	—
201	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
202	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
203	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
204	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
205	#41×C₁₃₉	—	4	16	no	—
206	C₂×Q₈×C₁₃₉	—	2	2	no	—
207	C₂×Q₈×C₁₃₉	—	2	2	no	—
208	C₂×Q₈×C₁₃₉	—	2	2	no	—
209	C₂×Q₈×C₁₃₉	—	2	2	no	—
210	C₂×Q₈×C₁₃₉	—	2	2	no	—
211	C₂×Q₈×C₁₃₉	—	2	2	no	—
212	C₂×D₄×C₁₃₉	—	2	4	no	—
213	C₂×D₄×C₁₃₉	—	2	4	no	—
214	C₂×D₄×C₁₃₉	—	2	4	no	—
215	C₂×D₄×C₁₃₉	—	2	4	no	—
216	C₂×D₄×C₁₃₉	—	2	4	no	—
217	C₂×D₄×C₁₃₉	—	2	2	no	—
218	C₂×D₄×C₁₃₉	—	2	4	no	—
219	C₂×D₄×C₁₃₉	—	2	2	no	—
220	C₂×D₄×C₁₃₉	—	2	2	no	—
221	C₂×D₄×C₁₃₉	—	2	2	no	—
222	C₂×D₄×C₁₃₉	—	2	2	no	—
223	C₂×D₄×C₁₃₉	—	4	16	no	—
224	C₂×D₄×C₁₃₉	—	4	2	no	—
225	C₂×D₄×C₁₃₉	—	4	2	no	—
226	C₂×D₄×C₁₃₉	—	4	4	no	—
227	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
228	C₂×D₄×C₁₃₉	#41	1	4	yes	—
229	C₂²×C₄×C₁₃₉	—	2	2	no	—
230	C₂²×C₄×C₁₃₉	—	2	2	no	—
231	C₂²×C₄×C₁₃₉	—	2	2	no	—
232	C₂²×C₄×C₁₃₉	—	2	2	no	—
233	C₂²×C₄×C₁₃₉	—	2	4	no	—
234	C₂²×C₄×C₁₃₉	—	2	8	no	—
235	C₂²×C₄×C₁₃₉	—	2	4	no	—
236	C₂²×C₄×C₁₃₉	—	2	4	no	—
237	C₂²×C₄×C₁₃₉	—	2	4	no	—
238	C₂²×C₄×C₁₃₉	—	2	4	no	—
239	C₂²×C₄×C₁₃₉	—	4	2	no	—
240	C₂²×C₄×C₁₃₉	—	4	2	no	—
241	C₂²×C₄×C₁₃₉	—	4	2	no	—
242	C₂²×C₄×C₁₃₉	—	4	2	no	—
243	C₂²×C₄×C₁₃₉	—	4	2	no	—
244	C₂²×C₄×C₁₃₉	—	4	4	no	—
245	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
246	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
247	C₂²×C₄×C₁₃₉	#41	1	8	yes	complemented
248	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
263	C₄⋊C₄×C₁₃₉	—	2	2	no	—
264	C₄⋊C₄×C₁₃₉	—	2	2	no	—
265	C₄⋊C₄×C₁₃₉	—	2	4	no	—
266	C₄⋊C₄×C₁₃₉	—	2	2	no	—
267	C₄⋊C₄×C₁₃₉	—	2	4	no	—
268	C₄⋊C₄×C₁₃₉	—	2	4	no	—
269	C₄⋊C₄×C₁₃₉	—	2	2	no	—
270	C₄⋊C₄×C₁₃₉	—	2	4	no	—
271	C₄⋊C₄×C₁₃₉	—	2	4	no	—
272	C₄⋊C₄×C₁₃₉	—	2	4	no	—
273	C₄⋊C₄×C₁₃₉	—	2	4	no	—
274	C₄⋊C₄×C₁₃₉	—	2	4	no	—
275	C₄⋊C₄×C₁₃₉	—	4	4	no	—
276	C₄⋊C₄×C₁₃₉	—	4	4	no	—
277	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
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	8	no	—
284	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
285	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
286	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
287	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
288	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
289	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
290	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
291	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
292	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
293	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
294	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
295	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
296	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
297	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
298	C₄²×C₁₃₉	—	2	4	no	—
299	C₄²×C₁₃₉	—	2	4	no	—
300	C₄²×C₁₃₉	—	2	4	no	—
301	C₄²×C₁₃₉	—	2	2	no	—
302	C₄²×C₁₃₉	—	2	2	no	—
303	C₄²×C₁₃₉	—	2	2	no	—
304	C₄²×C₁₃₉	—	2	2	no	—
305	C₄²×C₁₃₉	—	4	2	no	—
306	C₄²×C₁₃₉	—	4	2	no	—
307	C₄²×C₁₃₉	—	4	2	no	—
308	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
309	C₂³×C₁₃₉	—	2	1	no	—
310	C₂³×C₁₃₉	—	2	1	no	—
311	C₂³×C₁₃₉	—	2	2	no	—
312	C₂³×C₁₃₉	—	2	2	no	—
313	C₂³×C₁₃₉	—	2	4	no	—
314	C₂³×C₁₃₉	—	2	2	no	—
315	C₂³×C₁₃₉	—	2	1	no	—
316	C₂³×C₁₃₉	—	2	1	no	—
317	C₂³×C₁₃₉	—	2	2	no	—
318	C₂³×C₁₃₉	—	2	4	no	—
319	C₂³×C₁₃₉	—	2	2	no	—
320	C₂³×C₁₃₉	—	2	2	no	—
321	C₂³×C₁₃₉	—	2	4	no	—
322	C₂³×C₁₃₉	—	2	2	no	—
323	C₂³×C₁₃₉	—	2	2	no	—
324	C₂³×C₁₃₉	—	2	4	no	—
325	C₂³×C₁₃₉	—	4	8	no	—
326	C₂³×C₁₃₉	—	4	16	no	—
327	C₂³×C₁₃₉	—	4	8	no	—
328	C₂³×C₁₃₉	—	8	4	no	—
329	C₂³×C₁₃₉	—	8	8	no	—
330	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
331	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
332	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
333	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
334	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
335	Q₈×C₁₃₉	—	4	4	no	—
336	Q₈×C₁₃₉	—	4	4	no	—
337	D₄×C₁₃₉	—	2	8	no	—
338	D₄×C₁₃₉	—	2	8	no	—
339	D₄×C₁₃₉	—	4	8	no	—
340	D₄×C₁₃₉	—	4	8	no	—
341	D₄×C₁₃₉	—	4	4	no	—
342	D₄×C₁₃₉	—	8	4	no	—
343	C₂×C₄×C₁₃₉	—	2	2	no	—
344	C₂×C₄×C₁₃₉	—	2	1	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	1	no	—
349	C₂×C₄×C₁₃₉	—	2	1	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	8	no	—
354	C₂×C₄×C₁₃₉	—	2	8	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	—	2	2	no	—
360	C₂×C₄×C₁₃₉	—	2	2	no	—
361	C₂×C₄×C₁₃₉	—	2	2	no	—
362	C₂×C₄×C₁₃₉	—	2	2	no	—
363	C₂×C₄×C₁₃₉	—	2	4	no	—
364	C₂×C₄×C₁₃₉	—	2	4	no	—
365	C₂×C₄×C₁₃₉	—	2	2	no	—
366	C₂×C₄×C₁₃₉	—	2	2	no	—
367	C₂×C₄×C₁₃₉	—	2	2	no	—
368	C₂×C₄×C₁₃₉	—	2	2	no	—
369	C₂×C₄×C₁₃₉	—	2	2	no	—
370	C₂×C₄×C₁₃₉	—	2	2	no	—
371	C₂×C₄×C₁₃₉	—	2	2	no	—
372	C₂×C₄×C₁₃₉	—	2	4	no	—
373	C₂×C₄×C₁₃₉	—	2	2	no	—
374	C₂×C₄×C₁₃₉	—	2	4	no	—
375	C₂×C₄×C₁₃₉	—	4	8	no	—
376	C₂×C₄×C₁₃₉	—	4	8	no	—
377	C₂×C₄×C₁₃₉	—	4	8	no	—
378	C₂×C₄×C₁₃₉	—	4	8	no	—
379	C₂×C₄×C₁₃₉	—	8	4	no	—
380	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
381	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
382	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
383	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
384	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
385	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
386	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
387	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
388	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
389	C₂²×C₁₃₉	—	2	2	no	—
390	C₂²×C₁₃₉	—	2	4	no	—
391	C₂²×C₁₃₉	—	2	2	no	—
392	C₂²×C₁₃₉	—	2	4	no	—
393	C₂²×C₁₃₉	—	2	2	no	—
394	C₂²×C₁₃₉	—	2	2	no	—
395	C₂²×C₁₃₉	—	2	4	no	—
396	C₂²×C₁₃₉	—	2	8	no	—
397	C₂²×C₁₃₉	—	2	2	no	—
398	C₂²×C₁₃₉	—	4	2	no	—
399	C₂²×C₁₃₉	—	4	2	no	—
400	C₂²×C₁₃₉	—	4	2	no	—
401	C₂²×C₁₃₉	—	4	2	no	—
402	C₂²×C₁₃₉	—	4	4	no	—
403	C₂²×C₁₃₉	—	4	2	no	—
404	C₂²×C₁₃₉	—	4	2	no	—
405	C₂²×C₁₃₉	—	4	4	no	—
406	C₂²×C₁₃₉	—	4	2	no	—
407	C₂²×C₁₃₉	—	4	4	no	—
408	C₂²×C₁₃₉	—	8	16	no	—
409	C₂²×C₁₃₉	#532	1	4	yes	—
410	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
411	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
412	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
413	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
414	C₂²×C₁₃₉	#585	1	2	yes	—
415	C₄×C₁₃₉	—	2	2	no	—
416	C₄×C₁₃₉	—	2	2	no	—
417	C₄×C₁₃₉	—	2	2	no	—
418	C₄×C₁₃₉	—	2	2	no	—
419	C₄×C₁₃₉	—	2	4	no	—
420	C₄×C₁₃₉	—	2	4	no	—
421	C₄×C₁₃₉	—	4	2	no	—
422	C₄×C₁₃₉	—	4	2	no	—
423	C₄×C₁₃₉	—	4	2	no	—
424	C₄×C₁₃₉	—	4	2	no	—
425	C₄×C₁₃₉	—	4	2	no	—
426	C₄×C₁₃₉	—	4	2	no	—
427	C₄×C₁₃₉	—	4	2	no	—
428	C₄×C₁₃₉	—	4	2	no	—
429	C₄×C₁₃₉	#546	1	4	yes	—
430	C₂×C₁₃₉	—	2	4	no	—
431	C₂×C₁₃₉	—	4	2	no	—
432	C₂×C₁₃₉	—	4	4	no	—
433	C₂×C₁₃₉	—	8	2	no	—
434	C₂×C₁₃₉	C₂×#532	1	1	yes	characteristic
435	C₂×C₁₃₉	C₂×#546	1	1	yes	characteristic
436	C₂×C₁₃₉	#3475	1	2	yes	—
437	C₂×C₁₃₉	#3500	1	1	yes	characteristic
438	C₂×C₁₃₉	#3505	1	2	yes	—
439	#36386	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
440	C₁₃₉	#36386	1	1	yes	characteristic, direct product factor, Sylow
441	C₂×#552	C₂×C₁₃₉	1	1	yes	characteristic, complemented
442	C₂×#546	C₂×C₁₃₉	1	1	yes	characteristic
443	#2861	C₂×C₁₃₉	1	1	yes	characteristic, complemented
444	#2857	C₂×C₁₃₉	1	1	yes	characteristic, complemented
445	#2850	C₂×C₁₃₉	1	1	yes	characteristic, complemented
446	#2566	C₂×C₁₃₉	1	1	yes	characteristic, complemented
447	#2559	C₂×C₁₃₉	1	4	yes	complemented
448	#2558	C₂×C₁₃₉	1	4	yes	complemented
449	#2545	C₂×C₁₃₉	1	1	yes	characteristic, complemented
450	#2534	C₂×C₁₃₉	1	4	yes	complemented
451	#2503	C₂×C₁₃₉	1	1	yes	characteristic, complemented
452	#2500	C₂×C₁₃₉	1	1	yes	characteristic, complemented
453	#2435	C₂×C₁₃₉	1	1	yes	characteristic, complemented
454	#2432	C₂×C₁₃₉	1	1	yes	characteristic, complemented
455	#2342	C₂×C₁₃₉	1	4	yes	complemented
456	C₄×#124	C₂×C₁₃₉	1	1	yes	characteristic, complemented
457	#2297	C₂×C₁₃₉	1	1	yes	characteristic, complemented
458	C₂×#390	C₂×C₁₃₉	1	1	yes	characteristic, complemented
459	C₄²×D₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
460	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
461	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
462	#552	—	2	8	no	—
463	#546	—	2	8	no	—
464	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
465	C₂×#126	C₂²×C₁₃₉	1	2	yes	complemented
466	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
467	C₂×#125	C₂²×C₁₃₉	1	2	yes	complemented
468	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
469	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
470	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
471	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
472	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
473	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
474	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
475	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
476	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
477	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
478	C₂×#120	C₂²×C₁₃₉	1	2	yes	—
479	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
480	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
481	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
482	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
483	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
484	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
485	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
486	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
487	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
488	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
489	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
490	#400	C₂²×C₁₃₉	1	4	yes	complemented
491	#396	C₂²×C₁₃₉	1	4	yes	complemented
492	#396	C₂²×C₁₃₉	1	4	yes	complemented
493	#394	C₂²×C₁₃₉	1	4	yes	—
494	#394	C₂²×C₁₃₉	1	4	yes	complemented
495	#394	C₂²×C₁₃₉	1	4	yes	complemented
496	#391	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
497	#391	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
498	#391	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
499	#391	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
500	#390	C₂²×C₁₃₉	1	1	yes	characteristic
501	#390	C₂²×C₁₃₉	1	1	yes	characteristic
502	#390	C₂²×C₁₃₉	1	1	yes	characteristic
503	#390	C₂²×C₁₃₉	1	1	yes	characteristic
504	#390	C₂²×C₁₃₉	1	1	yes	characteristic
505	#390	C₂²×C₁₃₉	1	1	yes	characteristic
506	#390	C₂²×C₁₃₉	1	4	yes	—
507	#389	C₂²×C₁₃₉	1	4	yes	complemented
508	#388	C₂²×C₁₃₉	1	4	yes	complemented
509	#388	C₂²×C₁₃₉	1	4	yes	complemented
510	#388	C₂²×C₁₃₉	1	4	yes	complemented
511	#388	C₂²×C₁₃₉	1	4	yes	complemented
512	#388	C₂²×C₁₃₉	1	4	yes	complemented
513	#388	C₂²×C₁₃₉	1	4	yes	complemented
514	#386	C₂²×C₁₃₉	1	4	yes	complemented
515	#386	C₂²×C₁₃₉	1	4	yes	complemented
516	#385	C₂²×C₁₃₉	1	4	yes	complemented
517	#385	C₂²×C₁₃₉	1	4	yes	complemented
518	#384	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
519	#382	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
520	#382	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
521	#381	C₂²×C₁₃₉	1	4	yes	—
522	#380	C₂²×C₁₃₉	1	4	yes	—
523	#379	C₂²×C₁₃₉	1	4	yes	—
524	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
525	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
526	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
527	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
528	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	complemented
529	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	complemented
530	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
531	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
532	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
533	C₂⁵	C₂³×C₁₃₉	1	2	yes	—
534	C₂×#41	—	2	4	no	—
535	C₂×#41	—	2	4	no	—
536	C₂×#41	—	4	2	no	—
537	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
538	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
539	C₂²×D₄	—	2	4	no	—
540	C₂²×D₄	—	2	4	no	—
541	C₂²×D₄	—	4	2	no	—
542	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
543	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
544	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
545	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
546	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
547	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
548	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
549	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
550	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
551	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
552	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
553	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
554	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
555	C₄⋊Q₈	—	4	2	no	—
556	#126	—	2	8	no	—
557	#125	—	2	8	no	—
558	#125	—	2	4	no	—
559	#124	—	2	4	no	—
560	#124	—	2	4	no	—
561	#124	—	4	2	no	—
562	#123	—	2	8	no	—
563	#123	—	2	8	no	—
564	C₂²⋊Q₈	—	2	4	no	—
565	C₂²⋊Q₈	—	2	4	no	—
566	C₂²⋊Q₈	—	2	4	no	—
567	#121	—	2	4	no	—
568	#121	—	2	8	no	—
569	#120	—	2	8	no	—
570	C₄×Q₈	—	2	4	no	—
571	C₄×D₄	—	2	8	no	—
572	C₄×D₄	—	2	4	no	—
573	C₄×D₄	D₄×C₁₃₉	1	8	yes	—
574	#117	—	2	4	no	—
575	#117	—	2	8	no	—
576	C₂×C₄⋊C₄	—	2	4	no	—
577	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
578	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
579	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
580	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
581	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
582	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
583	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
584	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
585	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
586	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
587	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
588	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
589	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
590	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
591	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
592	C₂×C₂²⋊C₄	—	2	16	no	—
593	C₂×C₂²⋊C₄	—	2	8	no	—
594	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
597	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
598	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
599	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
600	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
601	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
602	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
603	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
605	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
606	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
607	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
608	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
611	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
612	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
613	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
614	C₂×C₄²	—	4	2	no	—
615	C₂×C₄²	—	4	2	no	—
616	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
617	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
618	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
619	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
620	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
621	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
622	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
623	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
624	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
625	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
626	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
627	#95	C₂³×C₁₃₉	1	2	yes	—
628	#95	C₂³×C₁₃₉	1	2	yes	—
629	#95	C₂³×C₁₃₉	1	2	yes	—
630	#95	C₂³×C₁₃₉	1	4	yes	—
631	#95	C₂³×C₁₃₉	1	4	yes	—
632	#95	C₂³×C₁₃₉	1	4	yes	—
633	#95	C₂³×C₁₃₉	1	4	yes	—
634	#95	C₂³×C₁₃₉	1	4	yes	—
635	#95	C₂³×C₁₃₉	1	4	yes	—
636	C₂⁴	—	2	4	no	—
637	C₂⁴	—	2	4	no	—
638	C₂⁴	—	2	8	no	—
639	C₂⁴	—	4	2	no	—
640	C₂⁴	—	4	4	no	—
641	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
642	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
643	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
644	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
645	#41	—	4	16	no	—
646	C₂×Q₈	—	2	2	no	—
647	C₂×Q₈	—	2	2	no	—
648	C₂×Q₈	—	2	2	no	—
649	C₂×Q₈	—	2	2	no	—
650	C₂×Q₈	—	2	2	no	—
651	C₂×Q₈	—	2	2	no	—
652	C₂×D₄	—	2	4	no	—
653	C₂×D₄	—	2	4	no	—
654	C₂×D₄	—	2	4	no	—
655	C₂×D₄	—	2	4	no	—
656	C₂×D₄	—	2	4	no	—
657	C₂×D₄	—	2	2	no	—
658	C₂×D₄	—	2	4	no	—
659	C₂×D₄	—	2	2	no	—
660	C₂×D₄	—	2	2	no	—
661	C₂×D₄	—	2	2	no	—
662	C₂×D₄	—	2	2	no	—
663	C₂×D₄	—	4	16	no	—
664	C₂×D₄	—	4	2	no	—
665	C₂×D₄	—	4	2	no	—
666	C₂×D₄	—	4	4	no	—
667	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
668	C₂×D₄	#41×C₁₃₉	1	4	yes	—
669	C₂²×C₄	—	2	2	no	—
670	C₂²×C₄	—	2	2	no	—
671	C₂²×C₄	—	2	2	no	—
672	C₂²×C₄	—	2	2	no	—
673	C₂²×C₄	—	2	4	no	—
674	C₂²×C₄	—	2	8	no	—
675	C₂²×C₄	—	2	4	no	—
676	C₂²×C₄	—	2	4	no	—
677	C₂²×C₄	—	2	4	no	—
678	C₂²×C₄	—	2	4	no	—
679	C₂²×C₄	—	4	2	no	—
680	C₂²×C₄	—	4	2	no	—
681	C₂²×C₄	—	4	2	no	—
682	C₂²×C₄	—	4	2	no	—
683	C₂²×C₄	—	4	2	no	—
684	C₂²×C₄	—	4	4	no	—
685	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
686	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
687	C₂²×C₄	#41×C₁₃₉	1	8	yes	complemented
688	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
689	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
690	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
691	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
692	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
693	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
694	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
695	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
696	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
697	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
698	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
699	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
700	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
701	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
702	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
703	C₄⋊C₄	—	2	2	no	—
704	C₄⋊C₄	—	2	2	no	—
705	C₄⋊C₄	—	2	4	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	4	no	—
708	C₄⋊C₄	—	2	4	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	4	no	—
711	C₄⋊C₄	—	2	4	no	—
712	C₄⋊C₄	—	2	4	no	—
713	C₄⋊C₄	—	2	4	no	—
714	C₄⋊C₄	—	2	4	no	—
715	C₄⋊C₄	—	4	4	no	—
716	C₄⋊C₄	—	4	4	no	—
717	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
718	C₂²⋊C₄	—	2	4	no	—
719	C₂²⋊C₄	—	2	4	no	—
720	C₂²⋊C₄	—	2	4	no	—
721	C₂²⋊C₄	—	2	4	no	—
722	C₂²⋊C₄	—	2	4	no	—
723	C₂²⋊C₄	—	2	8	no	—
724	C₂²⋊C₄	—	2	4	no	—
725	C₂²⋊C₄	—	2	4	no	—
726	C₂²⋊C₄	—	2	4	no	—
727	C₂²⋊C₄	—	2	4	no	—
728	C₂²⋊C₄	—	2	8	no	—
729	C₂²⋊C₄	—	2	8	no	—
730	C₂²⋊C₄	—	2	8	no	—
731	C₂²⋊C₄	—	2	8	no	—
732	C₂²⋊C₄	—	2	4	no	—
733	C₂²⋊C₄	—	4	4	no	—
734	C₂²⋊C₄	—	4	4	no	—
735	C₂²⋊C₄	—	4	4	no	—
736	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
737	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
738	C₄²	—	2	4	no	—
739	C₄²	—	2	4	no	—
740	C₄²	—	2	4	no	—
741	C₄²	—	2	2	no	—
742	C₄²	—	2	2	no	—
743	C₄²	—	2	2	no	—
744	C₄²	—	2	2	no	—
745	C₄²	—	4	2	no	—
746	C₄²	—	4	2	no	—
747	C₄²	—	4	2	no	—
748	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
749	C₂³	—	2	1	no	—
750	C₂³	—	2	1	no	—
751	C₂³	—	2	2	no	—
752	C₂³	—	2	2	no	—
753	C₂³	—	2	4	no	—
754	C₂³	—	2	2	no	—
755	C₂³	—	2	1	no	—
756	C₂³	—	2	1	no	—
757	C₂³	—	2	2	no	—
758	C₂³	—	2	4	no	—
759	C₂³	—	2	2	no	—
760	C₂³	—	2	2	no	—
761	C₂³	—	2	4	no	—
762	C₂³	—	2	2	no	—
763	C₂³	—	2	2	no	—
764	C₂³	—	2	4	no	—
765	C₂³	—	4	8	no	—
766	C₂³	—	4	16	no	—
767	C₂³	—	4	8	no	—
768	C₂³	—	8	4	no	—
769	C₂³	—	8	8	no	—
770	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
771	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
772	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
773	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
774	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
775	Q₈	—	4	4	no	—
776	Q₈	—	4	4	no	—
777	D₄	—	2	8	no	—
778	D₄	—	2	8	no	—
779	D₄	—	4	8	no	—
780	D₄	—	4	8	no	—
781	D₄	—	4	4	no	—
782	D₄	—	8	4	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	1	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	1	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	8	no	—
794	C₂×C₄	—	2	8	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	4	no	—
804	C₂×C₄	—	2	4	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	4	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	4	no	—
815	C₂×C₄	—	4	8	no	—
816	C₂×C₄	—	4	8	no	—
817	C₂×C₄	—	4	8	no	—
818	C₂×C₄	—	4	8	no	—
819	C₂×C₄	—	8	4	no	—
820	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
821	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
822	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
823	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
824	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
825	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
826	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
827	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
828	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
829	C₂²	—	2	2	no	—
830	C₂²	—	2	4	no	—
831	C₂²	—	2	2	no	—
832	C₂²	—	2	4	no	—
833	C₂²	—	2	2	no	—
834	C₂²	—	2	2	no	—
835	C₂²	—	2	4	no	—
836	C₂²	—	2	8	no	—
837	C₂²	—	2	2	no	—
838	C₂²	—	4	2	no	—
839	C₂²	—	4	2	no	—
840	C₂²	—	4	2	no	—
841	C₂²	—	4	2	no	—
842	C₂²	—	4	4	no	—
843	C₂²	—	4	2	no	—
844	C₂²	—	4	2	no	—
845	C₂²	—	4	4	no	—
846	C₂²	—	4	2	no	—
847	C₂²	—	4	4	no	—
848	C₂²	—	8	16	no	—
849	C₂²	#532×C₁₃₉	1	4	yes	—
850	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
851	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
852	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
853	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
854	C₂²	#585×C₁₃₉	1	2	yes	—
855	C₄	—	2	2	no	—
856	C₄	—	2	2	no	—
857	C₄	—	2	2	no	—
858	C₄	—	2	2	no	—
859	C₄	—	2	4	no	—
860	C₄	—	2	4	no	—
861	C₄	—	4	2	no	—
862	C₄	—	4	2	no	—
863	C₄	—	4	2	no	—
864	C₄	—	4	2	no	—
865	C₄	—	4	2	no	—
866	C₄	—	4	2	no	—
867	C₄	—	4	2	no	—
868	C₄	—	4	2	no	—
869	C₄	#546×C₁₃₉	1	4	yes	—
870	C₂	—	2	4	no	—
871	C₂	—	4	4	no	—
872	C₂	—	4	2	no	—
873	C₂	—	8	2	no	—
874	C₂	C₂×#532×C₁₃₉	1	1	yes	characteristic
875	C₂	C₂×#546×C₁₃₉	1	1	yes	characteristic
876	C₂	#3475×C₁₃₉	1	2	yes	—
877	C₂	#3500×C₁₃₉	1	1	yes	characteristic
878	C₂	#3505×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂×#546×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×#552×C₁₃₉	C₂	semidirect
3. #2861×C₁₃₉	C₂	semidirect
4. #2857×C₁₃₉	C₂	semidirect
5. #2850×C₁₃₉	C₂	semidirect
6. #2566×C₁₃₉	C₂	semidirect
7. #2559×C₁₃₉	C₂	semidirect
8. #2558×C₁₃₉	C₂	semidirect
9. #2545×C₁₃₉	C₂	semidirect
10. #2534×C₁₃₉	C₂	semidirect
11. #2503×C₁₃₉	C₂	semidirect
12. #2500×C₁₃₉	C₂	semidirect
13. #2435×C₁₃₉	C₂	semidirect
14. #2432×C₁₃₉	C₂	semidirect
15. #2342×C₁₃₉	C₂	semidirect
16. C₄×#124×C₁₃₉	C₂	semidirect
17. #2297×C₁₃₉	C₂	semidirect
18. C₂×#390×C₁₃₉	C₂	semidirect
19. C₄²×D₄×C₁₃₉	C₂	semidirect
24. C₂×C₄⋊Q₈×C₁₃₉	C₂²	semidirect
25. C₂×#126×C₁₃₉	C₂²	semidirect
26. C₂×#125×C₁₃₉	C₂²	semidirect
27. C₂×#125×C₁₃₉	C₂²	semidirect
35. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
39. C₂×C₄×Q₈×C₁₃₉	C₂²	semidirect
44. C₂×#117×C₁₃₉	C₂²	semidirect
49. C₂²×C₄²×C₁₃₉	C₂²	semidirect
50. #400×C₁₃₉	C₂²	semidirect
51. #396×C₁₃₉	C₂²	semidirect
52. #396×C₁₃₉	C₂²	semidirect
54. #394×C₁₃₉	C₂²	semidirect
55. #394×C₁₃₉	C₂²	semidirect
56. #391×C₁₃₉	C₂²	semidirect
57. #391×C₁₃₉	C₂²	semidirect
58. #391×C₁₃₉	C₂²	semidirect
59. #391×C₁₃₉	C₂²	semidirect
67. #389×C₁₃₉	C₂²	semidirect
68. #388×C₁₃₉	C₂²	semidirect
69. #388×C₁₃₉	C₂²	semidirect
70. #388×C₁₃₉	C₂²	semidirect
71. #388×C₁₃₉	C₂²	semidirect
72. #388×C₁₃₉	C₂²	semidirect
73. #388×C₁₃₉	C₂²	semidirect
74. #386×C₁₃₉	C₂²	semidirect
75. #386×C₁₃₉	C₂²	semidirect
76. #385×C₁₃₉	C₂²	semidirect
77. #385×C₁₃₉	C₂²	semidirect
78. #384×C₁₃₉	C₂²	semidirect
79. #382×C₁₃₉	C₂²	semidirect
80. #382×C₁₃₉	C₂²	semidirect
84. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
85. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
88. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
89. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
90. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
91. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
92. C₄³×C₁₃₉	C₂²	semidirect
247. C₂²×C₄×C₁₃₉	#41	semidirect
439. #36386	C₁₃₉	direct (N × H)
440. C₁₃₉	#36386	direct (N × H)
441. C₂×#552	C₂×C₁₃₉	semidirect
443. #2861	C₂×C₁₃₉	semidirect
444. #2857	C₂×C₁₃₉	semidirect
445. #2850	C₂×C₁₃₉	semidirect
446. #2566	C₂×C₁₃₉	semidirect
447. #2559	C₂×C₁₃₉	semidirect
448. #2558	C₂×C₁₃₉	semidirect
449. #2545	C₂×C₁₃₉	semidirect
450. #2534	C₂×C₁₃₉	semidirect
451. #2503	C₂×C₁₃₉	semidirect
452. #2500	C₂×C₁₃₉	semidirect
453. #2435	C₂×C₁₃₉	semidirect
454. #2432	C₂×C₁₃₉	semidirect
455. #2342	C₂×C₁₃₉	semidirect
456. C₄×#124	C₂×C₁₃₉	semidirect
457. #2297	C₂×C₁₃₉	semidirect
458. C₂×#390	C₂×C₁₃₉	semidirect
459. C₄²×D₄	C₂×C₁₃₉	semidirect
464. C₂×C₄⋊Q₈	C₂²×C₁₃₉	semidirect
465. C₂×#126	C₂²×C₁₃₉	semidirect
466. C₂×#125	C₂²×C₁₃₉	semidirect
467. C₂×#125	C₂²×C₁₃₉	semidirect
475. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
479. C₂×C₄×Q₈	C₂²×C₁₃₉	semidirect
484. C₂×#117	C₂²×C₁₃₉	semidirect
489. C₂²×C₄²	C₂²×C₁₃₉	semidirect
490. #400	C₂²×C₁₃₉	semidirect
491. #396	C₂²×C₁₃₉	semidirect
492. #396	C₂²×C₁₃₉	semidirect
494. #394	C₂²×C₁₃₉	semidirect
495. #394	C₂²×C₁₃₉	semidirect
496. #391	C₂²×C₁₃₉	semidirect
497. #391	C₂²×C₁₃₉	semidirect
498. #391	C₂²×C₁₃₉	semidirect
499. #391	C₂²×C₁₃₉	semidirect
507. #389	C₂²×C₁₃₉	semidirect
508. #388	C₂²×C₁₃₉	semidirect
509. #388	C₂²×C₁₃₉	semidirect
510. #388	C₂²×C₁₃₉	semidirect
511. #388	C₂²×C₁₃₉	semidirect
512. #388	C₂²×C₁₃₉	semidirect
513. #388	C₂²×C₁₃₉	semidirect
514. #386	C₂²×C₁₃₉	semidirect
515. #386	C₂²×C₁₃₉	semidirect
516. #385	C₂²×C₁₃₉	semidirect
517. #385	C₂²×C₁₃₉	semidirect
518. #384	C₂²×C₁₃₉	semidirect
519. #382	C₂²×C₁₃₉	semidirect
520. #382	C₂²×C₁₃₉	semidirect
524. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
525. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
528. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
529. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
530. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
531. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
532. C₄³	C₂²×C₁₃₉	semidirect
687. C₂²×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×#552×C₁₃₉	2
C₂×#546×C₁₃₉	2
#2861×C₁₃₉	2
#2857×C₁₃₉	2
#2850×C₁₃₉	2
#2566×C₁₃₉	2
#2559×C₁₃₉	2
#2558×C₁₃₉	2
#2545×C₁₃₉	2
#2534×C₁₃₉	2
#2503×C₁₃₉	2
#2500×C₁₃₉	2
#2435×C₁₃₉	2
#2432×C₁₃₉	2
#2342×C₁₃₉	2
C₄×#124×C₁₃₉	2
#2297×C₁₃₉	2
C₂×#390×C₁₃₉	2
C₄²×D₄×C₁₃₉	2
#36386	139

Subgroups — C139×#36386 #48030982

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36386 #48030982