Subgroups — C₁₃₉×#36100 #48030696

Order 35584.

3552 conjugacy classes of subgroups.

The subgroup lattice has 922 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#547×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#525×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	C₂²×C₄×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2857×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2848×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2542×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2537×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2455×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#2422×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2418×C₁₃₉	C₂	1	4	yes	maximal, complemented
11	#2415×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2408×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2407×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2361×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2354×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	D₄×C₄⋊C₄×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	C₄×#121×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₁₃₉	C₂²	1	2	yes	complemented
19	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
20	C₂⁴×C₄×C₁₃₉	C₂²	1	2	yes	—
21	#547×C₁₃₉	—	2	8	no	—
22	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
23	#525×C₁₃₉	—	2	16	no	—
24	C₂×#123×C₁₃₉	C₂²	1	4	yes	complemented
25	C₂×#123×C₁₃₉	C₂²	1	4	yes	complemented
26	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
27	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	complemented
28	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	complemented
29	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	complemented
30	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
31	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
32	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂×#121×C₁₃₉	C₂²	1	2	yes	complemented
34	C₂×#120×C₁₃₉	C₂²	1	4	yes	—
35	C₂×C₄×D₄×C₁₃₉	—	2	8	no	—
36	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
38	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	—
39	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
41	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
43	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	complemented
46	C₂×#117×C₁₃₉	C₂²	1	2	yes	complemented
47	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
48	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
49	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
50	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
51	#399×C₁₃₉	C₂²	1	4	yes	complemented
52	#397×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	#392×C₁₃₉	C₂²	1	4	yes	—
57	#391×C₁₃₉	C₂²	1	2	yes	complemented
58	#390×C₁₃₉	C₂²	1	2	yes	—
59	#390×C₁₃₉	C₂²	1	2	yes	—
60	#390×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
61	#389×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
62	#389×C₁₃₉	C₂²	1	2	yes	complemented
63	#389×C₁₃₉	C₂²	1	2	yes	complemented
64	#389×C₁₃₉	C₂²	1	4	yes	complemented
65	#388×C₁₃₉	C₂²	1	2	yes	complemented
66	#388×C₁₃₉	C₂²	1	4	yes	complemented
67	#388×C₁₃₉	C₂²	1	4	yes	complemented
68	#386×C₁₃₉	C₂²	1	2	yes	—
69	#386×C₁₃₉	C₂²	1	4	yes	complemented
70	#385×C₁₃₉	C₂²	1	4	yes	—
71	#385×C₁₃₉	C₂²	1	4	yes	complemented
72	#385×C₁₃₉	C₂²	1	4	yes	complemented
73	#385×C₁₃₉	C₂²	1	4	yes	complemented
74	#384×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
75	#384×C₁₃₉	C₂²	1	2	yes	complemented
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	complemented
80	#380×C₁₃₉	C₂²	1	2	yes	complemented
81	#380×C₁₃₉	C₂²	1	2	yes	complemented
82	#379×C₁₃₉	C₂²	1	4	yes	—
83	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
84	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
85	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
86	C₂⁵×C₁₃₉	C₂³	1	2	yes	—
87	C₂×#41×C₁₃₉	—	2	8	no	—
88	C₂×#41×C₁₃₉	—	2	8	no	—
89	C₂×#41×C₁₃₉	—	4	4	no	—
90	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
91	C₂²×D₄×C₁₃₉	—	2	4	no	—
92	C₂²×D₄×C₁₃₉	—	2	4	no	—
93	C₂²×D₄×C₁₃₉	—	2	4	no	—
94	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
95	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
96	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
97	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
98	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
99	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
100	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₁₃₉	—	2	8	no	—
102	C₂³×C₄×C₁₃₉	—	2	8	no	—
103	C₂³×C₄×C₁₃₉	—	4	4	no	—
104	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
105	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
106	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
108	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
109	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
110	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
111	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
113	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
114	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
115	#123×C₁₃₉	—	2	16	no	—
116	#123×C₁₃₉	—	2	16	no	—
117	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
118	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
119	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
120	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
121	#121×C₁₃₉	—	2	8	no	—
122	#121×C₁₃₉	—	2	8	no	—
123	#121×C₁₃₉	—	2	8	no	—
124	#121×C₁₃₉	D₄	1	8	yes	complemented
125	#120×C₁₃₉	—	2	16	no	—
126	C₄×D₄×C₁₃₉	—	2	4	no	—
127	C₄×D₄×C₁₃₉	—	2	16	no	—
128	C₄×D₄×C₁₃₉	—	2	8	no	—
129	C₄×D₄×C₁₃₉	—	2	8	no	—
130	C₄×D₄×C₁₃₉	—	2	4	no	—
131	C₄×D₄×C₁₃₉	—	2	8	no	—
132	C₄×D₄×C₁₃₉	—	2	16	no	—
133	C₄×D₄×C₁₃₉	—	2	4	no	—
134	C₄×D₄×C₁₃₉	—	2	4	no	—
135	C₄×D₄×C₁₃₉	D₄	1	8	yes	complemented
136	#117×C₁₃₉	—	2	8	no	—
137	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
138	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
139	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
140	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	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	4	yes	—
148	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	4	yes	—
152	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
154	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
155	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
156	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
158	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
159	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
161	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
163	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	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	4	yes	—
168	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
169	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
171	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
173	C₂×C₄²×C₁₃₉	—	2	4	no	—
174	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
175	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
177	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
178	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
179	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
180	#95×C₁₃₉	C₂³	1	2	yes	—
181	#95×C₁₃₉	C₂³	1	4	yes	—
182	#95×C₁₃₉	C₂³	1	4	yes	—
183	#95×C₁₃₉	C₂³	1	2	yes	—
184	#95×C₁₃₉	C₂³	1	2	yes	—
185	#95×C₁₃₉	C₂³	1	4	yes	—
186	#95×C₁₃₉	C₂³	1	4	yes	—
187	C₂⁴×C₁₃₉	—	2	4	no	—
188	C₂⁴×C₁₃₉	—	2	4	no	—
189	C₂⁴×C₁₃₉	—	2	4	no	—
190	C₂⁴×C₁₃₉	—	2	4	no	—
191	C₂⁴×C₁₃₉	—	2	4	no	—
192	C₂⁴×C₁₃₉	—	4	2	no	—
193	C₂⁴×C₁₃₉	—	4	2	no	—
194	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
195	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
196	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
197	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
198	#41×C₁₃₉	—	4	32	no	—
199	C₂×Q₈×C₁₃₉	—	2	4	no	—
200	C₂×Q₈×C₁₃₉	—	2	4	no	—
201	C₂×Q₈×C₁₃₉	—	2	4	no	—
202	C₂×D₄×C₁₃₉	—	2	32	no	—
203	C₂×D₄×C₁₃₉	—	2	4	no	—
204	C₂×D₄×C₁₃₉	—	2	4	no	—
205	C₂×D₄×C₁₃₉	—	2	4	no	—
206	C₂×D₄×C₁₃₉	—	2	4	no	—
207	C₂×D₄×C₁₃₉	—	2	8	no	—
208	C₂×D₄×C₁₃₉	—	2	8	no	—
209	C₂×D₄×C₁₃₉	—	2	8	no	—
210	C₂×D₄×C₁₃₉	—	2	8	no	—
211	C₂×D₄×C₁₃₉	—	2	2	no	—
212	C₂×D₄×C₁₃₉	—	2	2	no	—
213	C₂×D₄×C₁₃₉	—	2	4	no	—
214	C₂×D₄×C₁₃₉	—	2	2	no	—
215	C₂×D₄×C₁₃₉	—	2	2	no	—
216	C₂×D₄×C₁₃₉	—	2	2	no	—
217	C₂×D₄×C₁₃₉	—	2	2	no	—
218	C₂×D₄×C₁₃₉	—	4	4	no	—
219	C₂×D₄×C₁₃₉	—	4	4	no	—
220	C₂×D₄×C₁₃₉	C₂×D₄	1	8	yes	—
221	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
222	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	complemented
223	C₂×D₄×C₁₃₉	#41	1	4	yes	complemented
224	C₂²×C₄×C₁₃₉	—	2	2	no	—
225	C₂²×C₄×C₁₃₉	—	2	2	no	—
226	C₂²×C₄×C₁₃₉	—	2	4	no	—
227	C₂²×C₄×C₁₃₉	—	2	2	no	—
228	C₂²×C₄×C₁₃₉	—	2	2	no	—
229	C₂²×C₄×C₁₃₉	—	2	4	no	—
230	C₂²×C₄×C₁₃₉	—	2	4	no	—
231	C₂²×C₄×C₁₃₉	—	2	4	no	—
232	C₂²×C₄×C₁₃₉	—	2	8	no	—
233	C₂²×C₄×C₁₃₉	—	2	2	no	—
234	C₂²×C₄×C₁₃₉	—	2	2	no	—
235	C₂²×C₄×C₁₃₉	—	2	4	no	—
236	C₂²×C₄×C₁₃₉	—	2	4	no	—
237	C₂²×C₄×C₁₃₉	—	2	8	no	—
238	C₂²×C₄×C₁₃₉	—	2	4	no	—
239	C₂²×C₄×C₁₃₉	—	2	4	no	—
240	C₂²×C₄×C₁₃₉	—	2	4	no	—
241	C₂²×C₄×C₁₃₉	—	2	4	no	—
242	C₂²×C₄×C₁₃₉	—	2	4	no	—
243	C₂²×C₄×C₁₃₉	—	2	4	no	—
244	C₂²×C₄×C₁₃₉	—	2	4	no	—
245	C₂²×C₄×C₁₃₉	—	2	4	no	—
246	C₂²×C₄×C₁₃₉	—	4	2	no	—
247	C₂²×C₄×C₁₃₉	—	4	2	no	—
248	C₂²×C₄×C₁₃₉	—	4	2	no	—
249	C₂²×C₄×C₁₃₉	—	4	1	no	—
250	C₂²×C₄×C₁₃₉	—	4	4	no	—
251	C₂²×C₄×C₁₃₉	—	4	32	no	—
252	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
253	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
254	C₂²×C₄×C₁₃₉	#41	1	4	yes	complemented
255	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
258	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
261	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
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	8	no	—
272	C₄⋊C₄×C₁₃₉	—	2	4	no	—
273	C₄⋊C₄×C₁₃₉	—	2	2	no	—
274	C₄⋊C₄×C₁₃₉	—	2	8	no	—
275	C₄⋊C₄×C₁₃₉	—	2	8	no	—
276	C₄⋊C₄×C₁₃₉	—	2	4	no	—
277	C₄⋊C₄×C₁₃₉	—	2	4	no	—
278	C₄⋊C₄×C₁₃₉	—	2	4	no	—
279	C₄⋊C₄×C₁₃₉	—	2	2	no	—
280	C₄⋊C₄×C₁₃₉	—	4	2	no	—
281	C₄⋊C₄×C₁₃₉	—	4	4	no	—
282	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
283	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	complemented
284	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
285	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
286	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
287	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
288	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
289	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
290	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
291	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
292	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
293	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
294	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
295	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
296	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
297	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
298	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
299	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
300	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	complemented
301	C₄²×C₁₃₉	—	2	2	no	—
302	C₄²×C₁₃₉	—	2	2	no	—
303	C₄²×C₁₃₉	—	2	2	no	—
304	C₄²×C₁₃₉	—	2	8	no	—
305	C₄²×C₁₃₉	—	2	4	no	—
306	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
307	C₂³×C₁₃₉	—	2	1	no	—
308	C₂³×C₁₃₉	—	2	1	no	—
309	C₂³×C₁₃₉	—	2	1	no	—
310	C₂³×C₁₃₉	—	2	1	no	—
311	C₂³×C₁₃₉	—	2	16	no	—
312	C₂³×C₁₃₉	—	2	2	no	—
313	C₂³×C₁₃₉	—	2	2	no	—
314	C₂³×C₁₃₉	—	2	2	no	—
315	C₂³×C₁₃₉	—	2	2	no	—
316	C₂³×C₁₃₉	—	2	2	no	—
317	C₂³×C₁₃₉	—	2	2	no	—
318	C₂³×C₁₃₉	—	2	2	no	—
319	C₂³×C₁₃₉	—	2	2	no	—
320	C₂³×C₁₃₉	—	2	2	no	—
321	C₂³×C₁₃₉	—	2	2	no	—
322	C₂³×C₁₃₉	—	2	2	no	—
323	C₂³×C₁₃₉	—	2	2	no	—
324	C₂³×C₁₃₉	—	2	2	no	—
325	C₂³×C₁₃₉	—	2	2	no	—
326	C₂³×C₁₃₉	—	2	2	no	—
327	C₂³×C₁₃₉	—	2	2	no	—
328	C₂³×C₁₃₉	—	2	2	no	—
329	C₂³×C₁₃₉	—	2	2	no	—
330	C₂³×C₁₃₉	—	4	8	no	—
331	C₂³×C₁₃₉	—	4	8	no	—
332	C₂³×C₁₃₉	—	4	8	no	—
333	C₂³×C₁₃₉	—	4	8	no	—
334	C₂³×C₁₃₉	—	4	8	no	—
335	C₂³×C₁₃₉	—	4	8	no	—
336	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
337	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
338	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
339	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
340	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
341	C₂³×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
342	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
343	Q₈×C₁₃₉	—	4	8	no	—
344	D₄×C₁₃₉	—	2	16	no	—
345	D₄×C₁₃₉	—	2	16	no	—
346	D₄×C₁₃₉	—	2	8	no	—
347	D₄×C₁₃₉	—	2	8	no	—
348	D₄×C₁₃₉	—	2	8	no	—
349	D₄×C₁₃₉	—	4	16	no	—
350	D₄×C₁₃₉	—	4	16	no	—
351	C₂×C₄×C₁₃₉	—	2	1	no	—
352	C₂×C₄×C₁₃₉	—	2	1	no	—
353	C₂×C₄×C₁₃₉	—	2	2	no	—
354	C₂×C₄×C₁₃₉	—	2	2	no	—
355	C₂×C₄×C₁₃₉	—	2	1	no	—
356	C₂×C₄×C₁₃₉	—	2	1	no	—
357	C₂×C₄×C₁₃₉	—	2	2	no	—
358	C₂×C₄×C₁₃₉	—	2	1	no	—
359	C₂×C₄×C₁₃₉	—	2	2	no	—
360	C₂×C₄×C₁₃₉	—	2	1	no	—
361	C₂×C₄×C₁₃₉	—	2	8	no	—
362	C₂×C₄×C₁₃₉	—	2	8	no	—
363	C₂×C₄×C₁₃₉	—	2	16	no	—
364	C₂×C₄×C₁₃₉	—	2	1	no	—
365	C₂×C₄×C₁₃₉	—	2	4	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	4	no	—
370	C₂×C₄×C₁₃₉	—	2	4	no	—
371	C₂×C₄×C₁₃₉	—	2	2	no	—
372	C₂×C₄×C₁₃₉	—	2	2	no	—
373	C₂×C₄×C₁₃₉	—	2	2	no	—
374	C₂×C₄×C₁₃₉	—	2	4	no	—
375	C₂×C₄×C₁₃₉	—	2	2	no	—
376	C₂×C₄×C₁₃₉	—	2	4	no	—
377	C₂×C₄×C₁₃₉	—	2	2	no	—
378	C₂×C₄×C₁₃₉	—	2	1	no	—
379	C₂×C₄×C₁₃₉	—	2	2	no	—
380	C₂×C₄×C₁₃₉	—	2	1	no	—
381	C₂×C₄×C₁₃₉	—	2	4	no	—
382	C₂×C₄×C₁₃₉	—	4	8	no	—
383	C₂×C₄×C₁₃₉	—	4	4	no	—
384	C₂×C₄×C₁₃₉	—	4	8	no	—
385	C₂×C₄×C₁₃₉	—	4	8	no	—
386	C₂×C₄×C₁₃₉	—	4	16	no	—
387	C₂×C₄×C₁₃₉	—	4	8	no	—
388	C₂×C₄×C₁₃₉	—	4	8	no	—
389	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
390	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
391	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
392	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
393	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
394	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
395	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
396	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
397	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
398	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
399	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
400	C₂²×C₁₃₉	—	2	2	no	—
401	C₂²×C₁₃₉	—	2	2	no	—
402	C₂²×C₁₃₉	—	2	2	no	—
403	C₂²×C₁₃₉	—	2	2	no	—
404	C₂²×C₁₃₉	—	2	2	no	—
405	C₂²×C₁₃₉	—	2	2	no	—
406	C₂²×C₁₃₉	—	2	4	no	—
407	C₂²×C₁₃₉	—	2	4	no	—
408	C₂²×C₁₃₉	—	2	4	no	—
409	C₂²×C₁₃₉	—	2	4	no	—
410	C₂²×C₁₃₉	—	2	4	no	—
411	C₂²×C₁₃₉	—	2	4	no	—
412	C₂²×C₁₃₉	—	2	4	no	—
413	C₂²×C₁₃₉	—	2	4	no	—
414	C₂²×C₁₃₉	—	2	4	no	—
415	C₂²×C₁₃₉	—	4	32	no	—
416	C₂²×C₁₃₉	—	4	2	no	—
417	C₂²×C₁₃₉	—	4	2	no	—
418	C₂²×C₁₃₉	—	4	2	no	—
419	C₂²×C₁₃₉	—	4	2	no	—
420	C₂²×C₁₃₉	—	4	2	no	—
421	C₂²×C₁₃₉	—	4	2	no	—
422	C₂²×C₁₃₉	—	4	2	no	—
423	C₂²×C₁₃₉	—	4	2	no	—
424	C₂²×C₁₃₉	—	4	2	no	—
425	C₂²×C₁₃₉	—	4	2	no	—
426	C₂²×C₁₃₉	—	4	2	no	—
427	C₂²×C₁₃₉	—	4	2	no	—
428	C₂²×C₁₃₉	#547	1	4	yes	complemented
429	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
430	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
431	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
432	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
433	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
434	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
435	C₂²×C₁₃₉	#585	1	1	yes	characteristic
436	C₄×C₁₃₉	—	2	2	no	—
437	C₄×C₁₃₉	—	2	2	no	—
438	C₄×C₁₃₉	—	2	4	no	—
439	C₄×C₁₃₉	—	2	4	no	—
440	C₄×C₁₃₉	—	2	2	no	—
441	C₄×C₁₃₉	—	4	2	no	—
442	C₄×C₁₃₉	—	4	2	no	—
443	C₄×C₁₃₉	—	4	4	no	—
444	C₄×C₁₃₉	—	4	4	no	—
445	C₄×C₁₃₉	—	4	1	no	—
446	C₄×C₁₃₉	—	4	2	no	—
447	C₄×C₁₃₉	#525	1	4	yes	complemented
448	C₄×C₁₃₉	D₄²	1	4	yes	—
449	C₂×C₁₃₉	—	2	4	no	—
450	C₂×C₁₃₉	—	4	4	no	—
451	C₂×C₁₃₉	—	4	4	no	—
452	C₂×C₁₃₉	—	4	4	no	—
453	C₂×C₁₃₉	C₂×#525	1	1	yes	characteristic
454	C₂×C₁₃₉	C₂×D₄²	1	1	yes	characteristic
455	C₂×C₁₃₉	C₂×#547	1	1	yes	characteristic
456	C₂×C₁₃₉	D₄×#41	1	1	yes	characteristic
457	C₂×C₁₃₉	#3489	1	1	yes	characteristic
458	C₂×C₁₃₉	#3506	1	1	yes	characteristic
459	C₂×C₁₃₉	#3520	1	1	yes	characteristic
460	#36100	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
461	C₁₃₉	#36100	1	1	yes	characteristic, direct product factor, Sylow
462	C₂×#547	C₂×C₁₃₉	1	1	yes	characteristic, complemented
463	C₂×#525	C₂×C₁₃₉	1	2	yes	complemented
464	C₂²×C₄×D₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
465	#2857	C₂×C₁₃₉	1	1	yes	characteristic, complemented
466	#2848	C₂×C₁₃₉	1	2	yes	complemented
467	#2542	C₂×C₁₃₉	1	1	yes	characteristic, complemented
468	#2537	C₂×C₁₃₉	1	1	yes	characteristic, complemented
469	#2455	C₂×C₁₃₉	1	4	yes	complemented
470	#2422	C₂×C₁₃₉	1	2	yes	complemented
471	#2418	C₂×C₁₃₉	1	4	yes	complemented
472	#2415	C₂×C₁₃₉	1	2	yes	complemented
473	#2408	C₂×C₁₃₉	1	2	yes	complemented
474	#2407	C₂×C₁₃₉	1	2	yes	complemented
475	#2361	C₂×C₁₃₉	1	2	yes	complemented
476	#2354	C₂×C₁₃₉	1	1	yes	characteristic, complemented
477	D₄×C₄⋊C₄	C₂×C₁₃₉	1	2	yes	complemented
478	C₄×#121	C₂×C₁₃₉	1	1	yes	characteristic, complemented
479	C₂²×#41	C₂²×C₁₃₉	1	2	yes	complemented
480	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
481	C₂⁴×C₄	C₂²×C₁₃₉	1	2	yes	—
482	#547	—	2	8	no	—
483	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
484	#525	—	2	16	no	—
485	C₂×#123	C₂²×C₁₃₉	1	4	yes	complemented
486	C₂×#123	C₂²×C₁₃₉	1	4	yes	complemented
487	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
488	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	complemented
489	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	complemented
490	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	complemented
491	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
492	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
493	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
494	C₂×#121	C₂²×C₁₃₉	1	2	yes	complemented
495	C₂×#120	C₂²×C₁₃₉	1	4	yes	—
496	C₂×C₄×D₄	—	2	8	no	—
497	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
498	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	—
499	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
500	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
501	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
502	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
503	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
504	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
505	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	complemented
506	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
507	C₂×#117	C₂²×C₁₃₉	1	2	yes	complemented
508	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
509	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
510	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
511	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
512	#399	C₂²×C₁₃₉	1	4	yes	complemented
513	#397	C₂²×C₁₃₉	1	4	yes	complemented
514	#394	C₂²×C₁₃₉	1	4	yes	—
515	#394	C₂²×C₁₃₉	1	4	yes	complemented
516	#394	C₂²×C₁₃₉	1	4	yes	complemented
517	#392	C₂²×C₁₃₉	1	4	yes	—
518	#391	C₂²×C₁₃₉	1	2	yes	complemented
519	#390	C₂²×C₁₃₉	1	2	yes	—
520	#390	C₂²×C₁₃₉	1	2	yes	—
521	#390	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
522	#389	C₂²×C₁₃₉	1	2	yes	complemented
523	#389	C₂²×C₁₃₉	1	2	yes	complemented
524	#389	C₂²×C₁₃₉	1	4	yes	complemented
525	#389	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
526	#388	C₂²×C₁₃₉	1	4	yes	complemented
527	#388	C₂²×C₁₃₉	1	4	yes	complemented
528	#388	C₂²×C₁₃₉	1	2	yes	complemented
529	#386	C₂²×C₁₃₉	1	2	yes	—
530	#386	C₂²×C₁₃₉	1	4	yes	complemented
531	#385	C₂²×C₁₃₉	1	4	yes	—
532	#385	C₂²×C₁₃₉	1	4	yes	complemented
533	#385	C₂²×C₁₃₉	1	4	yes	complemented
534	#385	C₂²×C₁₃₉	1	4	yes	complemented
535	#384	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
536	#384	C₂²×C₁₃₉	1	2	yes	complemented
537	#380	C₂²×C₁₃₉	1	1	yes	characteristic
538	#380	C₂²×C₁₃₉	1	2	yes	—
539	#380	C₂²×C₁₃₉	1	2	yes	—
540	#380	C₂²×C₁₃₉	1	2	yes	complemented
541	#380	C₂²×C₁₃₉	1	2	yes	complemented
542	#380	C₂²×C₁₃₉	1	2	yes	complemented
543	#379	C₂²×C₁₃₉	1	4	yes	—
544	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
545	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
546	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
547	C₂⁵	C₂³×C₁₃₉	1	2	yes	—
548	C₂×#41	—	2	8	no	—
549	C₂×#41	—	2	8	no	—
550	C₂×#41	—	4	4	no	—
551	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
552	C₂²×D₄	—	2	4	no	—
553	C₂²×D₄	—	2	4	no	—
554	C₂²×D₄	—	2	4	no	—
555	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
556	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
557	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
558	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
559	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
560	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
561	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
562	C₂³×C₄	—	2	8	no	—
563	C₂³×C₄	—	2	8	no	—
564	C₂³×C₄	—	4	4	no	—
565	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
566	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
567	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
568	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
569	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
570	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
571	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
572	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
573	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
574	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
575	C₄⋊Q₈	—	2	4	no	—
576	#123	—	2	16	no	—
577	#123	—	2	16	no	—
578	C₂²⋊Q₈	—	2	8	no	—
579	C₂²⋊Q₈	—	2	8	no	—
580	C₂²⋊Q₈	—	2	8	no	—
581	C₂²⋊Q₈	—	4	4	no	—
582	#121	—	2	8	no	—
583	#121	—	2	8	no	—
584	#121	—	2	8	no	—
585	#121	D₄×C₁₃₉	1	8	yes	complemented
586	#120	—	2	16	no	—
587	C₄×D₄	—	2	4	no	—
588	C₄×D₄	—	2	16	no	—
589	C₄×D₄	—	2	8	no	—
590	C₄×D₄	—	2	8	no	—
591	C₄×D₄	—	2	4	no	—
592	C₄×D₄	—	2	8	no	—
593	C₄×D₄	—	2	16	no	—
594	C₄×D₄	—	2	4	no	—
595	C₄×D₄	—	2	4	no	—
596	C₄×D₄	D₄×C₁₃₉	1	8	yes	complemented
597	#117	—	2	8	no	—
598	C₂×C₄⋊C₄	—	2	4	no	—
599	C₂×C₄⋊C₄	—	2	8	no	—
600	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
601	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
602	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
603	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
604	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
605	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
606	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
607	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
608	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
609	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
610	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
612	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
613	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
614	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
615	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
616	C₂×C₂²⋊C₄	—	2	8	no	—
617	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
618	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
619	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
620	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
623	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
624	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
625	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
626	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
627	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
628	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
629	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
630	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
631	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
632	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
633	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
634	C₂×C₄²	—	2	4	no	—
635	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
636	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
637	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
638	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
639	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
640	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
641	#95	C₂³×C₁₃₉	1	2	yes	—
642	#95	C₂³×C₁₃₉	1	2	yes	—
643	#95	C₂³×C₁₃₉	1	4	yes	—
644	#95	C₂³×C₁₃₉	1	2	yes	—
645	#95	C₂³×C₁₃₉	1	4	yes	—
646	#95	C₂³×C₁₃₉	1	4	yes	—
647	#95	C₂³×C₁₃₉	1	4	yes	—
648	C₂⁴	—	2	4	no	—
649	C₂⁴	—	2	4	no	—
650	C₂⁴	—	2	4	no	—
651	C₂⁴	—	2	4	no	—
652	C₂⁴	—	2	4	no	—
653	C₂⁴	—	4	2	no	—
654	C₂⁴	—	4	2	no	—
655	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
656	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
657	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
658	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
659	#41	—	4	32	no	—
660	C₂×Q₈	—	2	4	no	—
661	C₂×Q₈	—	2	4	no	—
662	C₂×Q₈	—	2	4	no	—
663	C₂×D₄	—	2	32	no	—
664	C₂×D₄	—	2	4	no	—
665	C₂×D₄	—	2	4	no	—
666	C₂×D₄	—	2	4	no	—
667	C₂×D₄	—	2	4	no	—
668	C₂×D₄	—	2	8	no	—
669	C₂×D₄	—	2	8	no	—
670	C₂×D₄	—	2	8	no	—
671	C₂×D₄	—	2	8	no	—
672	C₂×D₄	—	2	2	no	—
673	C₂×D₄	—	2	2	no	—
674	C₂×D₄	—	2	4	no	—
675	C₂×D₄	—	2	2	no	—
676	C₂×D₄	—	2	2	no	—
677	C₂×D₄	—	2	2	no	—
678	C₂×D₄	—	2	2	no	—
679	C₂×D₄	—	4	4	no	—
680	C₂×D₄	—	4	4	no	—
681	C₂×D₄	C₂×D₄×C₁₃₉	1	8	yes	—
682	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
683	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	complemented
684	C₂×D₄	#41×C₁₃₉	1	4	yes	complemented
685	C₂²×C₄	—	2	2	no	—
686	C₂²×C₄	—	2	2	no	—
687	C₂²×C₄	—	2	4	no	—
688	C₂²×C₄	—	2	2	no	—
689	C₂²×C₄	—	2	2	no	—
690	C₂²×C₄	—	2	4	no	—
691	C₂²×C₄	—	2	4	no	—
692	C₂²×C₄	—	2	4	no	—
693	C₂²×C₄	—	2	8	no	—
694	C₂²×C₄	—	2	2	no	—
695	C₂²×C₄	—	2	2	no	—
696	C₂²×C₄	—	2	4	no	—
697	C₂²×C₄	—	2	4	no	—
698	C₂²×C₄	—	2	8	no	—
699	C₂²×C₄	—	2	4	no	—
700	C₂²×C₄	—	2	4	no	—
701	C₂²×C₄	—	2	4	no	—
702	C₂²×C₄	—	2	4	no	—
703	C₂²×C₄	—	2	4	no	—
704	C₂²×C₄	—	2	4	no	—
705	C₂²×C₄	—	2	4	no	—
706	C₂²×C₄	—	2	4	no	—
707	C₂²×C₄	—	4	2	no	—
708	C₂²×C₄	—	4	2	no	—
709	C₂²×C₄	—	4	2	no	—
710	C₂²×C₄	—	4	1	no	—
711	C₂²×C₄	—	4	4	no	—
712	C₂²×C₄	—	4	32	no	—
713	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
714	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
715	C₂²×C₄	#41×C₁₃₉	1	4	yes	complemented
716	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
717	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
718	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
719	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
720	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
721	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
722	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
723	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
724	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
725	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
726	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
727	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
728	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
729	C₄⋊C₄	—	2	4	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	4	no	—
732	C₄⋊C₄	—	2	8	no	—
733	C₄⋊C₄	—	2	4	no	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	8	no	—
736	C₄⋊C₄	—	2	8	no	—
737	C₄⋊C₄	—	2	4	no	—
738	C₄⋊C₄	—	2	4	no	—
739	C₄⋊C₄	—	2	4	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	4	2	no	—
742	C₄⋊C₄	—	4	4	no	—
743	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
744	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	complemented
745	C₂²⋊C₄	—	2	4	no	—
746	C₂²⋊C₄	—	2	8	no	—
747	C₂²⋊C₄	—	2	8	no	—
748	C₂²⋊C₄	—	2	8	no	—
749	C₂²⋊C₄	—	2	4	no	—
750	C₂²⋊C₄	—	2	8	no	—
751	C₂²⋊C₄	—	2	4	no	—
752	C₂²⋊C₄	—	2	4	no	—
753	C₂²⋊C₄	—	2	8	no	—
754	C₂²⋊C₄	—	2	8	no	—
755	C₂²⋊C₄	—	2	4	no	—
756	C₂²⋊C₄	—	2	4	no	—
757	C₂²⋊C₄	—	4	2	no	—
758	C₂²⋊C₄	—	4	4	no	—
759	C₂²⋊C₄	—	4	4	no	—
760	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
761	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	complemented
762	C₄²	—	2	2	no	—
763	C₄²	—	2	2	no	—
764	C₄²	—	2	2	no	—
765	C₄²	—	2	8	no	—
766	C₄²	—	2	4	no	—
767	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
768	C₂³	—	2	1	no	—
769	C₂³	—	2	1	no	—
770	C₂³	—	2	1	no	—
771	C₂³	—	2	1	no	—
772	C₂³	—	2	16	no	—
773	C₂³	—	2	2	no	—
774	C₂³	—	2	2	no	—
775	C₂³	—	2	2	no	—
776	C₂³	—	2	2	no	—
777	C₂³	—	2	2	no	—
778	C₂³	—	2	2	no	—
779	C₂³	—	2	2	no	—
780	C₂³	—	2	2	no	—
781	C₂³	—	2	2	no	—
782	C₂³	—	2	2	no	—
783	C₂³	—	2	2	no	—
784	C₂³	—	2	2	no	—
785	C₂³	—	2	2	no	—
786	C₂³	—	2	2	no	—
787	C₂³	—	2	2	no	—
788	C₂³	—	2	2	no	—
789	C₂³	—	2	2	no	—
790	C₂³	—	2	2	no	—
791	C₂³	—	4	8	no	—
792	C₂³	—	4	8	no	—
793	C₂³	—	4	8	no	—
794	C₂³	—	4	8	no	—
795	C₂³	—	4	8	no	—
796	C₂³	—	4	8	no	—
797	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
798	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
799	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
800	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
801	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
802	C₂³	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
803	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
804	Q₈	—	4	8	no	—
805	D₄	—	2	16	no	—
806	D₄	—	2	16	no	—
807	D₄	—	2	8	no	—
808	D₄	—	2	8	no	—
809	D₄	—	2	8	no	—
810	D₄	—	4	16	no	—
811	D₄	—	4	16	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	8	no	—
823	C₂×C₄	—	2	8	no	—
824	C₂×C₄	—	2	16	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	4	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	4	no	—
831	C₂×C₄	—	2	4	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	4	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	4	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	4	no	—
843	C₂×C₄	—	4	8	no	—
844	C₂×C₄	—	4	8	no	—
845	C₂×C₄	—	4	8	no	—
846	C₂×C₄	—	4	16	no	—
847	C₂×C₄	—	4	4	no	—
848	C₂×C₄	—	4	8	no	—
849	C₂×C₄	—	4	8	no	—
850	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
851	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
852	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
853	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
854	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
855	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
856	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
857	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
858	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
859	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
860	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
861	C₂²	—	2	2	no	—
862	C₂²	—	2	2	no	—
863	C₂²	—	2	2	no	—
864	C₂²	—	2	2	no	—
865	C₂²	—	2	2	no	—
866	C₂²	—	2	2	no	—
867	C₂²	—	2	4	no	—
868	C₂²	—	2	4	no	—
869	C₂²	—	2	4	no	—
870	C₂²	—	2	4	no	—
871	C₂²	—	2	4	no	—
872	C₂²	—	2	4	no	—
873	C₂²	—	2	4	no	—
874	C₂²	—	2	4	no	—
875	C₂²	—	2	4	no	—
876	C₂²	—	4	32	no	—
877	C₂²	—	4	2	no	—
878	C₂²	—	4	2	no	—
879	C₂²	—	4	2	no	—
880	C₂²	—	4	2	no	—
881	C₂²	—	4	2	no	—
882	C₂²	—	4	2	no	—
883	C₂²	—	4	2	no	—
884	C₂²	—	4	2	no	—
885	C₂²	—	4	2	no	—
886	C₂²	—	4	2	no	—
887	C₂²	—	4	2	no	—
888	C₂²	—	4	2	no	—
889	C₂²	#547×C₁₃₉	1	4	yes	complemented
890	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
891	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
892	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
893	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
894	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
895	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
896	C₂²	#585×C₁₃₉	1	1	yes	characteristic
897	C₄	—	2	2	no	—
898	C₄	—	2	2	no	—
899	C₄	—	2	4	no	—
900	C₄	—	2	4	no	—
901	C₄	—	2	2	no	—
902	C₄	—	4	2	no	—
903	C₄	—	4	2	no	—
904	C₄	—	4	4	no	—
905	C₄	—	4	4	no	—
906	C₄	—	4	1	no	—
907	C₄	—	4	2	no	—
908	C₄	#525×C₁₃₉	1	4	yes	complemented
909	C₄	D₄²×C₁₃₉	1	4	yes	—
910	C₂	—	2	4	no	—
911	C₂	—	4	4	no	—
912	C₂	—	4	4	no	—
913	C₂	—	4	4	no	—
914	C₂	C₂×#525×C₁₃₉	1	1	yes	characteristic
915	C₂	C₂×D₄²×C₁₃₉	1	1	yes	characteristic
916	C₂	C₂×#547×C₁₃₉	1	1	yes	characteristic
917	C₂	D₄×#41×C₁₃₉	1	1	yes	characteristic
918	C₂	#3489×C₁₃₉	1	1	yes	characteristic
919	C₂	#3506×C₁₃₉	1	1	yes	characteristic
920	C₂	#3520×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×#547×C₁₃₉	C₂	semidirect
2. C₂×#525×C₁₃₉	C₂	semidirect
3. C₂²×C₄×D₄×C₁₃₉	C₂	semidirect
4. #2857×C₁₃₉	C₂	semidirect
5. #2848×C₁₃₉	C₂	semidirect
6. #2542×C₁₃₉	C₂	semidirect
7. #2537×C₁₃₉	C₂	semidirect
8. #2455×C₁₃₉	C₂	semidirect
9. #2422×C₁₃₉	C₂	semidirect
10. #2418×C₁₃₉	C₂	semidirect
11. #2415×C₁₃₉	C₂	semidirect
12. #2408×C₁₃₉	C₂	semidirect
13. #2407×C₁₃₉	C₂	semidirect
14. #2361×C₁₃₉	C₂	semidirect
15. #2354×C₁₃₉	C₂	semidirect
16. D₄×C₄⋊C₄×C₁₃₉	C₂	semidirect
17. C₄×#121×C₁₃₉	C₂	semidirect
18. C₂²×#41×C₁₃₉	C₂²	semidirect
22. C₂×C₄⋊Q₈×C₁₃₉	C₂²	semidirect
24. C₂×#123×C₁₃₉	C₂²	semidirect
25. C₂×#123×C₁₃₉	C₂²	semidirect
27. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
28. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
29. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
33. C₂×#121×C₁₃₉	C₂²	semidirect
44. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
45. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
46. C₂×#117×C₁₃₉	C₂²	semidirect
48. C₂²×C₄⋊C₄×C₁₃₉	C₂²	semidirect
51. #399×C₁₃₉	C₂²	semidirect
52. #397×C₁₃₉	C₂²	semidirect
54. #394×C₁₃₉	C₂²	semidirect
55. #394×C₁₃₉	C₂²	semidirect
57. #391×C₁₃₉	C₂²	semidirect
60. #390×C₁₃₉	C₂²	semidirect
61. #389×C₁₃₉	C₂²	semidirect
62. #389×C₁₃₉	C₂²	semidirect
63. #389×C₁₃₉	C₂²	semidirect
64. #389×C₁₃₉	C₂²	semidirect
65. #388×C₁₃₉	C₂²	semidirect
66. #388×C₁₃₉	C₂²	semidirect
67. #388×C₁₃₉	C₂²	semidirect
69. #386×C₁₃₉	C₂²	semidirect
71. #385×C₁₃₉	C₂²	semidirect
72. #385×C₁₃₉	C₂²	semidirect
73. #385×C₁₃₉	C₂²	semidirect
74. #384×C₁₃₉	C₂²	semidirect
75. #384×C₁₃₉	C₂²	semidirect
79. #380×C₁₃₉	C₂²	semidirect
80. #380×C₁₃₉	C₂²	semidirect
81. #380×C₁₃₉	C₂²	semidirect
83. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
84. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
85. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
124. #121×C₁₃₉	D₄	semidirect
135. C₄×D₄×C₁₃₉	D₄	semidirect
222. C₂×D₄×C₁₃₉	C₂×D₄	semidirect
223. C₂×D₄×C₁₃₉	#41	semidirect
254. C₂²×C₄×C₁₃₉	#41	semidirect
283. C₄⋊C₄×C₁₃₉	C₂×D₄	semidirect
300. C₂²⋊C₄×C₁₃₉	C₂×D₄	semidirect
428. C₂²×C₁₃₉	#547	semidirect
447. C₄×C₁₃₉	#525	semidirect
460. #36100	C₁₃₉	direct (N × H)
461. C₁₃₉	#36100	direct (N × H)
462. C₂×#547	C₂×C₁₃₉	semidirect
463. C₂×#525	C₂×C₁₃₉	semidirect
464. C₂²×C₄×D₄	C₂×C₁₃₉	semidirect
465. #2857	C₂×C₁₃₉	semidirect
466. #2848	C₂×C₁₃₉	semidirect
467. #2542	C₂×C₁₃₉	semidirect
468. #2537	C₂×C₁₃₉	semidirect
469. #2455	C₂×C₁₃₉	semidirect
470. #2422	C₂×C₁₃₉	semidirect
471. #2418	C₂×C₁₃₉	semidirect
472. #2415	C₂×C₁₃₉	semidirect
473. #2408	C₂×C₁₃₉	semidirect
474. #2407	C₂×C₁₃₉	semidirect
475. #2361	C₂×C₁₃₉	semidirect
476. #2354	C₂×C₁₃₉	semidirect
477. D₄×C₄⋊C₄	C₂×C₁₃₉	semidirect
478. C₄×#121	C₂×C₁₃₉	semidirect
479. C₂²×#41	C₂²×C₁₃₉	semidirect
483. C₂×C₄⋊Q₈	C₂²×C₁₃₉	semidirect
485. C₂×#123	C₂²×C₁₃₉	semidirect
486. C₂×#123	C₂²×C₁₃₉	semidirect
488. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
489. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
490. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
494. C₂×#121	C₂²×C₁₃₉	semidirect
505. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
506. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
507. C₂×#117	C₂²×C₁₃₉	semidirect
509. C₂²×C₄⋊C₄	C₂²×C₁₃₉	semidirect
512. #399	C₂²×C₁₃₉	semidirect
513. #397	C₂²×C₁₃₉	semidirect
515. #394	C₂²×C₁₃₉	semidirect
516. #394	C₂²×C₁₃₉	semidirect
518. #391	C₂²×C₁₃₉	semidirect
521. #390	C₂²×C₁₃₉	semidirect
522. #389	C₂²×C₁₃₉	semidirect
523. #389	C₂²×C₁₃₉	semidirect
524. #389	C₂²×C₁₃₉	semidirect
525. #389	C₂²×C₁₃₉	semidirect
526. #388	C₂²×C₁₃₉	semidirect
527. #388	C₂²×C₁₃₉	semidirect
528. #388	C₂²×C₁₃₉	semidirect
530. #386	C₂²×C₁₃₉	semidirect
532. #385	C₂²×C₁₃₉	semidirect
533. #385	C₂²×C₁₃₉	semidirect
534. #385	C₂²×C₁₃₉	semidirect
535. #384	C₂²×C₁₃₉	semidirect
536. #384	C₂²×C₁₃₉	semidirect
540. #380	C₂²×C₁₃₉	semidirect
541. #380	C₂²×C₁₃₉	semidirect
542. #380	C₂²×C₁₃₉	semidirect
544. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
545. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
546. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
585. #121	D₄×C₁₃₉	semidirect
596. C₄×D₄	D₄×C₁₃₉	semidirect
683. C₂×D₄	C₂×D₄×C₁₃₉	semidirect
684. C₂×D₄	#41×C₁₃₉	semidirect
715. C₂²×C₄	#41×C₁₃₉	semidirect
744. C₄⋊C₄	C₂×D₄×C₁₃₉	semidirect
761. C₂²⋊C₄	C₂×D₄×C₁₃₉	semidirect
889. C₂²	#547×C₁₃₉	semidirect
908. C₄	#525×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#547×C₁₃₉	2
C₂×#525×C₁₃₉	2
C₂²×C₄×D₄×C₁₃₉	2
#2857×C₁₃₉	2
#2848×C₁₃₉	2
#2542×C₁₃₉	2
#2537×C₁₃₉	2
#2455×C₁₃₉	2
#2422×C₁₃₉	2
#2418×C₁₃₉	2
#2415×C₁₃₉	2
#2408×C₁₃₉	2
#2407×C₁₃₉	2
#2361×C₁₃₉	2
#2354×C₁₃₉	2
D₄×C₄⋊C₄×C₁₃₉	2
C₄×#121×C₁₃₉	2
#36100	139

Subgroups — C139×#36100 #48030696

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36100 #48030696