Subgroups — C₁₃₉×#36362 #48030958

Order 35584.

2958 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#553×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#546×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2861×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2856×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	#2554×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	#2544×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#2502×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#2500×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#2464×C₁₃₉	C₂	1	4	yes	maximal, complemented
12	#2433×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#2431×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2424×C₁₃₉	C₂	1	4	yes	maximal, complemented
15	#2358×C₁₃₉	C₂	1	4	yes	maximal, complemented
16	C₄×#127×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	#553×C₁₃₉	—	2	8	no	—
23	#546×C₁₃₉	—	2	8	no	—
24	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×#126×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, complemented
30	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
31	C₂×#123×C₁₃₉	C₂²	1	2	yes	complemented
32	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
34	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
35	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
36	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
37	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
38	C₂×#121×C₁₃₉	C₂²	1	4	yes	complemented
39	C₂×#120×C₁₃₉	C₂²	1	4	yes	—
40	C₂×#120×C₁₃₉	C₂²	1	2	yes	—
41	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
42	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
44	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	complemented
47	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
48	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
49	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
50	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
51	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
52	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
53	#398×C₁₃₉	C₂²	1	4	yes	complemented
54	#396×C₁₃₉	C₂²	1	4	yes	complemented
55	#394×C₁₃₉	C₂²	1	4	yes	complemented
56	#394×C₁₃₉	C₂²	1	4	yes	complemented
57	#392×C₁₃₉	C₂²	1	4	yes	—
58	#392×C₁₃₉	C₂²	1	4	yes	complemented
59	#391×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
60	#391×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
61	#391×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
62	#390×C₁₃₉	C₂²	1	1	yes	characteristic
63	#390×C₁₃₉	C₂²	1	1	yes	characteristic
64	#390×C₁₃₉	C₂²	1	4	yes	—
65	#390×C₁₃₉	C₂²	1	1	yes	characteristic
66	#390×C₁₃₉	C₂²	1	1	yes	characteristic
67	#390×C₁₃₉	C₂²	1	1	yes	characteristic
68	#390×C₁₃₉	C₂²	1	1	yes	characteristic
69	#390×C₁₃₉	C₂²	1	4	yes	complemented
70	#390×C₁₃₉	C₂²	1	4	yes	complemented
71	#390×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
72	#388×C₁₃₉	C₂²	1	4	yes	complemented
73	#388×C₁₃₉	C₂²	1	4	yes	complemented
74	#388×C₁₃₉	C₂²	1	4	yes	complemented
75	#388×C₁₃₉	C₂²	1	4	yes	complemented
76	#386×C₁₃₉	C₂²	1	4	yes	—
77	#386×C₁₃₉	C₂²	1	4	yes	complemented
78	#386×C₁₃₉	C₂²	1	4	yes	complemented
79	#386×C₁₃₉	C₂²	1	4	yes	complemented
80	#385×C₁₃₉	C₂²	1	4	yes	—
81	#385×C₁₃₉	C₂²	1	4	yes	complemented
82	#384×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
83	#384×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
84	#382×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
85	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
86	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
87	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
88	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
89	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
90	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	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×D₄×C₁₃₉	—	2	4	no	—
99	C₂²×D₄×C₁₃₉	—	2	4	no	—
100	C₂²×D₄×C₁₃₉	—	4	2	no	—
101	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
102	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
103	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
104	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
105	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
106	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
107	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
108	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
109	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
110	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
111	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
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	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
118	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
119	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
120	#127×C₁₃₉	—	2	4	no	—
121	#127×C₁₃₉	—	4	2	no	—
122	#126×C₁₃₉	—	2	8	no	—
123	#125×C₁₃₉	—	2	4	no	—
124	#124×C₁₃₉	—	2	4	no	—
125	#124×C₁₃₉	—	4	2	no	—
126	#123×C₁₃₉	—	2	8	no	—
127	#123×C₁₃₉	—	2	8	no	—
128	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
129	#121×C₁₃₉	—	2	8	no	—
130	#121×C₁₃₉	—	2	4	no	—
131	#121×C₁₃₉	—	2	4	no	—
132	#121×C₁₃₉	—	2	4	no	—
133	#121×C₁₃₉	—	2	8	no	—
134	#121×C₁₃₉	—	4	8	no	—
135	#120×C₁₃₉	—	2	8	no	—
136	#120×C₁₃₉	—	2	16	no	—
137	C₄×D₄×C₁₃₉	—	2	8	no	—
138	C₄×D₄×C₁₃₉	—	2	8	no	—
139	C₄×D₄×C₁₃₉	—	2	4	no	—
140	C₄×D₄×C₁₃₉	—	2	4	no	—
141	C₄×D₄×C₁₃₉	—	4	8	no	—
142	C₄×D₄×C₁₃₉	D₄	1	8	yes	complemented
143	#117×C₁₃₉	—	2	4	no	—
144	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
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	1	yes	characteristic
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	1	yes	characteristic
153	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
155	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
156	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
157	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
158	C₂×C₂²⋊C₄×C₁₃₉	—	4	8	no	—
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	4	yes	—
162	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	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	4	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	4	yes	—
171	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
173	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
175	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
176	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
177	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
178	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
179	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
180	C₂×C₄²×C₁₃₉	—	4	2	no	—
181	C₂×C₄²×C₁₃₉	—	4	2	no	—
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	2	yes	—
188	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
190	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
191	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
192	#95×C₁₃₉	C₂³	1	4	yes	—
193	#95×C₁₃₉	C₂³	1	2	yes	—
194	#95×C₁₃₉	C₂³	1	4	yes	—
195	#95×C₁₃₉	C₂³	1	4	yes	—
196	#95×C₁₃₉	C₂³	1	2	yes	—
197	#95×C₁₃₉	C₂³	1	2	yes	—
198	#95×C₁₃₉	C₂³	1	4	yes	—
199	C₂⁴×C₁₃₉	—	2	4	no	—
200	C₂⁴×C₁₃₉	—	2	4	no	—
201	C₂⁴×C₁₃₉	—	2	8	no	—
202	C₂⁴×C₁₃₉	—	4	4	no	—
203	C₂⁴×C₁₃₉	—	4	2	no	—
204	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
205	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
206	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
207	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
208	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
209	#41×C₁₃₉	—	4	16	no	—
210	C₂×Q₈×C₁₃₉	—	2	2	no	—
211	C₂×Q₈×C₁₃₉	—	2	2	no	—
212	C₂×Q₈×C₁₃₉	—	2	2	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	8	no	—
217	C₂×D₄×C₁₃₉	—	2	8	no	—
218	C₂×D₄×C₁₃₉	—	2	4	no	—
219	C₂×D₄×C₁₃₉	—	2	4	no	—
220	C₂×D₄×C₁₃₉	—	2	4	no	—
221	C₂×D₄×C₁₃₉	—	2	4	no	—
222	C₂×D₄×C₁₃₉	—	2	2	no	—
223	C₂×D₄×C₁₃₉	—	2	2	no	—
224	C₂×D₄×C₁₃₉	—	2	4	no	—
225	C₂×D₄×C₁₃₉	—	2	2	no	—
226	C₂×D₄×C₁₃₉	—	2	8	no	—
227	C₂×D₄×C₁₃₉	—	2	2	no	—
228	C₂×D₄×C₁₃₉	—	2	2	no	—
229	C₂×D₄×C₁₃₉	—	2	8	no	—
230	C₂×D₄×C₁₃₉	—	2	2	no	—
231	C₂×D₄×C₁₃₉	—	2	2	no	—
232	C₂×D₄×C₁₃₉	—	2	2	no	—
233	C₂×D₄×C₁₃₉	—	4	16	no	—
234	C₂×D₄×C₁₃₉	—	4	4	no	—
235	C₂×D₄×C₁₃₉	—	4	2	no	—
236	C₂×D₄×C₁₃₉	—	4	2	no	—
237	C₂×D₄×C₁₃₉	—	4	4	no	—
238	C₂×D₄×C₁₃₉	—	4	4	no	—
239	C₂×D₄×C₁₃₉	—	4	4	no	—
240	C₂×D₄×C₁₃₉	—	4	4	no	—
241	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
242	C₂×D₄×C₁₃₉	#41	1	4	yes	—
243	C₂²×C₄×C₁₃₉	—	2	2	no	—
244	C₂²×C₄×C₁₃₉	—	2	2	no	—
245	C₂²×C₄×C₁₃₉	—	2	2	no	—
246	C₂²×C₄×C₁₃₉	—	2	2	no	—
247	C₂²×C₄×C₁₃₉	—	2	4	no	—
248	C₂²×C₄×C₁₃₉	—	2	4	no	—
249	C₂²×C₄×C₁₃₉	—	2	4	no	—
250	C₂²×C₄×C₁₃₉	—	2	4	no	—
251	C₂²×C₄×C₁₃₉	—	2	4	no	—
252	C₂²×C₄×C₁₃₉	—	2	4	no	—
253	C₂²×C₄×C₁₃₉	—	2	4	no	—
254	C₂²×C₄×C₁₃₉	—	2	4	no	—
255	C₂²×C₄×C₁₃₉	—	2	4	no	—
256	C₂²×C₄×C₁₃₉	—	4	2	no	—
257	C₂²×C₄×C₁₃₉	—	4	2	no	—
258	C₂²×C₄×C₁₃₉	—	4	2	no	—
259	C₂²×C₄×C₁₃₉	—	4	4	no	—
260	C₂²×C₄×C₁₃₉	—	4	4	no	—
261	C₂²×C₄×C₁₃₉	—	4	4	no	—
262	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
263	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
264	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
278	C₄⋊C₄×C₁₃₉	—	2	2	no	—
279	C₄⋊C₄×C₁₃₉	—	2	2	no	—
280	C₄⋊C₄×C₁₃₉	—	2	4	no	—
281	C₄⋊C₄×C₁₃₉	—	2	2	no	—
282	C₄⋊C₄×C₁₃₉	—	2	2	no	—
283	C₄⋊C₄×C₁₃₉	—	2	4	no	—
284	C₄⋊C₄×C₁₃₉	—	2	4	no	—
285	C₄⋊C₄×C₁₃₉	—	2	4	no	—
286	C₄⋊C₄×C₁₃₉	—	2	4	no	—
287	C₄⋊C₄×C₁₃₉	—	4	4	no	—
288	C₄⋊C₄×C₁₃₉	—	4	4	no	—
289	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
290	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
291	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
292	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
293	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
294	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
295	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
296	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
297	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
298	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
299	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
300	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
301	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
302	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
303	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
304	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
305	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
306	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
307	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
308	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
309	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
310	C₂²⋊C₄×C₁₃₉	#41	1	8	yes	complemented
311	C₄²×C₁₃₉	—	2	4	no	—
312	C₄²×C₁₃₉	—	2	4	no	—
313	C₄²×C₁₃₉	—	2	2	no	—
314	C₄²×C₁₃₉	—	2	2	no	—
315	C₄²×C₁₃₉	—	2	2	no	—
316	C₄²×C₁₃₉	—	2	2	no	—
317	C₄²×C₁₃₉	—	2	4	no	—
318	C₄²×C₁₃₉	—	4	2	no	—
319	C₄²×C₁₃₉	—	4	2	no	—
320	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
321	C₂³×C₁₃₉	—	2	1	no	—
322	C₂³×C₁₃₉	—	2	1	no	—
323	C₂³×C₁₃₉	—	2	2	no	—
324	C₂³×C₁₃₉	—	2	2	no	—
325	C₂³×C₁₃₉	—	2	2	no	—
326	C₂³×C₁₃₉	—	2	4	no	—
327	C₂³×C₁₃₉	—	2	1	no	—
328	C₂³×C₁₃₉	—	2	4	no	—
329	C₂³×C₁₃₉	—	2	1	no	—
330	C₂³×C₁₃₉	—	2	2	no	—
331	C₂³×C₁₃₉	—	2	2	no	—
332	C₂³×C₁₃₉	—	2	2	no	—
333	C₂³×C₁₃₉	—	2	2	no	—
334	C₂³×C₁₃₉	—	2	4	no	—
335	C₂³×C₁₃₉	—	2	4	no	—
336	C₂³×C₁₃₉	—	2	2	no	—
337	C₂³×C₁₃₉	—	2	2	no	—
338	C₂³×C₁₃₉	—	2	4	no	—
339	C₂³×C₁₃₉	—	2	4	no	—
340	C₂³×C₁₃₉	—	2	2	no	—
341	C₂³×C₁₃₉	—	2	2	no	—
342	C₂³×C₁₃₉	—	4	8	no	—
343	C₂³×C₁₃₉	—	4	16	no	—
344	C₂³×C₁₃₉	—	4	8	no	—
345	C₂³×C₁₃₉	—	8	4	no	—
346	C₂³×C₁₃₉	—	8	8	no	—
347	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
348	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
349	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
350	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
351	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
352	Q₈×C₁₃₉	—	4	4	no	—
353	D₄×C₁₃₉	—	2	8	no	—
354	D₄×C₁₃₉	—	2	8	no	—
355	D₄×C₁₃₉	—	4	16	no	—
356	D₄×C₁₃₉	—	4	8	no	—
357	D₄×C₁₃₉	—	4	8	no	—
358	D₄×C₁₃₉	—	4	8	no	—
359	D₄×C₁₃₉	—	4	4	no	—
360	D₄×C₁₃₉	—	4	4	no	—
361	D₄×C₁₃₉	—	8	8	no	—
362	D₄×C₁₃₉	—	8	4	no	—
363	D₄×C₁₃₉	—	8	4	no	—
364	C₂×C₄×C₁₃₉	—	2	2	no	—
365	C₂×C₄×C₁₃₉	—	2	2	no	—
366	C₂×C₄×C₁₃₉	—	2	2	no	—
367	C₂×C₄×C₁₃₉	—	2	1	no	—
368	C₂×C₄×C₁₃₉	—	2	1	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	2	no	—
373	C₂×C₄×C₁₃₉	—	2	1	no	—
374	C₂×C₄×C₁₃₉	—	2	1	no	—
375	C₂×C₄×C₁₃₉	—	2	2	no	—
376	C₂×C₄×C₁₃₉	—	2	8	no	—
377	C₂×C₄×C₁₃₉	—	2	8	no	—
378	C₂×C₄×C₁₃₉	—	2	2	no	—
379	C₂×C₄×C₁₃₉	—	2	2	no	—
380	C₂×C₄×C₁₃₉	—	2	2	no	—
381	C₂×C₄×C₁₃₉	—	2	2	no	—
382	C₂×C₄×C₁₃₉	—	2	2	no	—
383	C₂×C₄×C₁₃₉	—	2	4	no	—
384	C₂×C₄×C₁₃₉	—	2	2	no	—
385	C₂×C₄×C₁₃₉	—	2	2	no	—
386	C₂×C₄×C₁₃₉	—	2	2	no	—
387	C₂×C₄×C₁₃₉	—	2	4	no	—
388	C₂×C₄×C₁₃₉	—	2	4	no	—
389	C₂×C₄×C₁₃₉	—	2	4	no	—
390	C₂×C₄×C₁₃₉	—	2	2	no	—
391	C₂×C₄×C₁₃₉	—	2	2	no	—
392	C₂×C₄×C₁₃₉	—	4	8	no	—
393	C₂×C₄×C₁₃₉	—	4	8	no	—
394	C₂×C₄×C₁₃₉	—	4	8	no	—
395	C₂×C₄×C₁₃₉	—	8	4	no	—
396	C₂×C₄×C₁₃₉	—	8	4	no	—
397	C₂×C₄×C₁₃₉	—	8	4	no	—
398	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
399	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
400	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
401	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
402	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
403	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
404	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
405	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
406	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
407	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
408	C₂²×C₁₃₉	—	2	2	no	—
409	C₂²×C₁₃₉	—	2	4	no	—
410	C₂²×C₁₃₉	—	2	2	no	—
411	C₂²×C₁₃₉	—	2	4	no	—
412	C₂²×C₁₃₉	—	2	2	no	—
413	C₂²×C₁₃₉	—	2	2	no	—
414	C₂²×C₁₃₉	—	2	4	no	—
415	C₂²×C₁₃₉	—	2	8	no	—
416	C₂²×C₁₃₉	—	2	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	4	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	4	no	—
427	C₂²×C₁₃₉	—	4	4	no	—
428	C₂²×C₁₃₉	—	4	2	no	—
429	C₂²×C₁₃₉	—	4	2	no	—
430	C₂²×C₁₃₉	—	4	4	no	—
431	C₂²×C₁₃₉	—	4	4	no	—
432	C₂²×C₁₃₉	—	8	16	no	—
433	C₂²×C₁₃₉	#532	1	4	yes	—
434	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
435	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
436	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
437	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
438	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
439	C₄×C₁₃₉	—	2	2	no	—
440	C₄×C₁₃₉	—	2	2	no	—
441	C₄×C₁₃₉	—	2	2	no	—
442	C₄×C₁₃₉	—	2	4	no	—
443	C₄×C₁₃₉	—	2	2	no	—
444	C₄×C₁₃₉	—	2	4	no	—
445	C₄×C₁₃₉	—	2	4	no	—
446	C₄×C₁₃₉	—	4	2	no	—
447	C₄×C₁₃₉	—	4	2	no	—
448	C₄×C₁₃₉	—	4	2	no	—
449	C₄×C₁₃₉	—	4	2	no	—
450	C₄×C₁₃₉	—	4	2	no	—
451	C₄×C₁₃₉	—	4	2	no	—
452	C₄×C₁₃₉	#546	1	4	yes	—
453	C₂×C₁₃₉	—	2	4	no	—
454	C₂×C₁₃₉	—	4	2	no	—
455	C₂×C₁₃₉	—	4	4	no	—
456	C₂×C₁₃₉	—	8	2	no	—
457	C₂×C₁₃₉	—	8	2	no	—
458	C₂×C₁₃₉	C₂×#532	1	1	yes	characteristic
459	C₂×C₁₃₉	C₂×#546	1	1	yes	characteristic
460	C₂×C₁₃₉	#3481	1	2	yes	—
461	C₂×C₁₃₉	#3498	1	1	yes	characteristic
462	C₂×C₁₃₉	#3519	1	2	yes	—
463	#36362	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
464	C₁₃₉	#36362	1	1	yes	characteristic, direct product factor, Sylow
465	C₂×#553	C₂×C₁₃₉	1	1	yes	characteristic, complemented
466	C₂×#546	C₂×C₁₃₉	1	1	yes	characteristic, complemented
467	#2861	C₂×C₁₃₉	1	1	yes	characteristic, complemented
468	#2856	C₂×C₁₃₉	1	1	yes	characteristic, complemented
469	#2850	C₂×C₁₃₉	1	1	yes	characteristic, complemented
470	#2566	C₂×C₁₃₉	1	1	yes	characteristic, complemented
471	#2554	C₂×C₁₃₉	1	4	yes	complemented
472	#2544	C₂×C₁₃₉	1	1	yes	characteristic, complemented
473	#2502	C₂×C₁₃₉	1	1	yes	characteristic, complemented
474	#2500	C₂×C₁₃₉	1	1	yes	characteristic, complemented
475	#2464	C₂×C₁₃₉	1	4	yes	complemented
476	#2433	C₂×C₁₃₉	1	1	yes	characteristic, complemented
477	#2431	C₂×C₁₃₉	1	1	yes	characteristic, complemented
478	#2424	C₂×C₁₃₉	1	4	yes	complemented
479	#2358	C₂×C₁₃₉	1	4	yes	complemented
480	C₄×#127	C₂×C₁₃₉	1	1	yes	characteristic, complemented
481	#2297	C₂×C₁₃₉	1	1	yes	characteristic, complemented
482	C₂×#390	C₂×C₁₃₉	1	1	yes	characteristic, complemented
483	C₄²×D₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
484	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
485	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
486	#553	—	2	8	no	—
487	#546	—	2	8	no	—
488	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
489	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
490	C₂×#126	C₂²×C₁₃₉	1	2	yes	complemented
491	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
492	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
493	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
494	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
495	C₂×#123	C₂²×C₁₃₉	1	2	yes	complemented
496	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
497	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
498	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
499	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
500	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
501	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
502	C₂×#121	C₂²×C₁₃₉	1	4	yes	complemented
503	C₂×#120	C₂²×C₁₃₉	1	4	yes	—
504	C₂×#120	C₂²×C₁₃₉	1	2	yes	—
505	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
506	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
507	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
508	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
509	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
510	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	complemented
511	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
512	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
513	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
514	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
515	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
516	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
517	#398	C₂²×C₁₃₉	1	4	yes	complemented
518	#396	C₂²×C₁₃₉	1	4	yes	complemented
519	#394	C₂²×C₁₃₉	1	4	yes	complemented
520	#394	C₂²×C₁₃₉	1	4	yes	complemented
521	#392	C₂²×C₁₃₉	1	4	yes	—
522	#392	C₂²×C₁₃₉	1	4	yes	complemented
523	#391	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
524	#391	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
525	#391	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
526	#390	C₂²×C₁₃₉	1	1	yes	characteristic
527	#390	C₂²×C₁₃₉	1	1	yes	characteristic
528	#390	C₂²×C₁₃₉	1	1	yes	characteristic
529	#390	C₂²×C₁₃₉	1	1	yes	characteristic
530	#390	C₂²×C₁₃₉	1	1	yes	characteristic
531	#390	C₂²×C₁₃₉	1	4	yes	—
532	#390	C₂²×C₁₃₉	1	1	yes	characteristic
533	#390	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
534	#390	C₂²×C₁₃₉	1	4	yes	complemented
535	#390	C₂²×C₁₃₉	1	4	yes	complemented
536	#388	C₂²×C₁₃₉	1	4	yes	complemented
537	#388	C₂²×C₁₃₉	1	4	yes	complemented
538	#388	C₂²×C₁₃₉	1	4	yes	complemented
539	#388	C₂²×C₁₃₉	1	4	yes	complemented
540	#386	C₂²×C₁₃₉	1	4	yes	—
541	#386	C₂²×C₁₃₉	1	4	yes	complemented
542	#386	C₂²×C₁₃₉	1	4	yes	complemented
543	#386	C₂²×C₁₃₉	1	4	yes	complemented
544	#385	C₂²×C₁₃₉	1	4	yes	—
545	#385	C₂²×C₁₃₉	1	4	yes	complemented
546	#384	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
547	#384	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
548	#382	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
549	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
550	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
551	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
552	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
553	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	complemented
554	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
555	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
556	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
557	C₂⁵	C₂³×C₁₃₉	1	2	yes	—
558	C₂×#41	—	2	4	no	—
559	C₂×#41	—	2	4	no	—
560	C₂×#41	—	4	2	no	—
561	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
562	C₂²×D₄	—	2	4	no	—
563	C₂²×D₄	—	2	4	no	—
564	C₂²×D₄	—	4	2	no	—
565	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
566	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
567	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
568	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
569	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
570	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
571	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
572	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
573	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
574	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
575	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
576	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
577	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
578	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
579	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
580	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
581	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
582	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
583	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
584	#127	—	2	4	no	—
585	#127	—	4	2	no	—
586	#126	—	2	8	no	—
587	#125	—	2	4	no	—
588	#124	—	2	4	no	—
589	#124	—	4	2	no	—
590	#123	—	2	8	no	—
591	#123	—	2	8	no	—
592	C₂²⋊Q₈	—	2	4	no	—
593	#121	—	2	8	no	—
594	#121	—	2	4	no	—
595	#121	—	2	4	no	—
596	#121	—	2	4	no	—
597	#121	—	2	8	no	—
598	#121	—	4	8	no	—
599	#120	—	2	8	no	—
600	#120	—	2	16	no	—
601	C₄×D₄	—	2	8	no	—
602	C₄×D₄	—	2	8	no	—
603	C₄×D₄	—	2	4	no	—
604	C₄×D₄	—	2	4	no	—
605	C₄×D₄	—	4	8	no	—
606	C₄×D₄	D₄×C₁₃₉	1	8	yes	complemented
607	#117	—	2	4	no	—
608	C₂×C₄⋊C₄	—	2	4	no	—
609	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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	1	yes	characteristic
613	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
614	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
615	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
616	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
617	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
618	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
619	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
620	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
621	C₂×C₂²⋊C₄	—	2	8	no	—
622	C₂×C₂²⋊C₄	—	4	8	no	—
623	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
624	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
625	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	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	2	yes	—
629	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
630	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
631	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
632	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
633	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
634	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
635	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
637	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
638	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
639	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
640	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
641	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
642	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
643	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
644	C₂×C₄²	—	4	2	no	—
645	C₂×C₄²	—	4	2	no	—
646	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
647	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
648	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
649	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
650	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
651	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
652	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
653	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
654	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
655	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
656	#95	C₂³×C₁₃₉	1	2	yes	—
657	#95	C₂³×C₁₃₉	1	2	yes	—
658	#95	C₂³×C₁₃₉	1	2	yes	—
659	#95	C₂³×C₁₃₉	1	4	yes	—
660	#95	C₂³×C₁₃₉	1	4	yes	—
661	#95	C₂³×C₁₃₉	1	4	yes	—
662	#95	C₂³×C₁₃₉	1	4	yes	—
663	C₂⁴	—	2	4	no	—
664	C₂⁴	—	2	4	no	—
665	C₂⁴	—	2	8	no	—
666	C₂⁴	—	4	4	no	—
667	C₂⁴	—	4	2	no	—
668	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
669	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
670	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
671	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
672	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
673	#41	—	4	16	no	—
674	C₂×Q₈	—	2	2	no	—
675	C₂×Q₈	—	2	2	no	—
676	C₂×Q₈	—	2	2	no	—
677	C₂×D₄	—	2	4	no	—
678	C₂×D₄	—	2	4	no	—
679	C₂×D₄	—	2	4	no	—
680	C₂×D₄	—	2	8	no	—
681	C₂×D₄	—	2	8	no	—
682	C₂×D₄	—	2	4	no	—
683	C₂×D₄	—	2	4	no	—
684	C₂×D₄	—	2	4	no	—
685	C₂×D₄	—	2	4	no	—
686	C₂×D₄	—	2	2	no	—
687	C₂×D₄	—	2	2	no	—
688	C₂×D₄	—	2	4	no	—
689	C₂×D₄	—	2	2	no	—
690	C₂×D₄	—	2	8	no	—
691	C₂×D₄	—	2	2	no	—
692	C₂×D₄	—	2	2	no	—
693	C₂×D₄	—	2	8	no	—
694	C₂×D₄	—	2	2	no	—
695	C₂×D₄	—	2	2	no	—
696	C₂×D₄	—	2	2	no	—
697	C₂×D₄	—	4	16	no	—
698	C₂×D₄	—	4	4	no	—
699	C₂×D₄	—	4	2	no	—
700	C₂×D₄	—	4	2	no	—
701	C₂×D₄	—	4	4	no	—
702	C₂×D₄	—	4	4	no	—
703	C₂×D₄	—	4	4	no	—
704	C₂×D₄	—	4	4	no	—
705	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
706	C₂×D₄	#41×C₁₃₉	1	4	yes	—
707	C₂²×C₄	—	2	2	no	—
708	C₂²×C₄	—	2	2	no	—
709	C₂²×C₄	—	2	2	no	—
710	C₂²×C₄	—	2	2	no	—
711	C₂²×C₄	—	2	4	no	—
712	C₂²×C₄	—	2	4	no	—
713	C₂²×C₄	—	2	4	no	—
714	C₂²×C₄	—	2	4	no	—
715	C₂²×C₄	—	2	4	no	—
716	C₂²×C₄	—	2	4	no	—
717	C₂²×C₄	—	2	4	no	—
718	C₂²×C₄	—	2	4	no	—
719	C₂²×C₄	—	2	4	no	—
720	C₂²×C₄	—	4	2	no	—
721	C₂²×C₄	—	4	2	no	—
722	C₂²×C₄	—	4	2	no	—
723	C₂²×C₄	—	4	4	no	—
724	C₂²×C₄	—	4	4	no	—
725	C₂²×C₄	—	4	4	no	—
726	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
727	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
728	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
729	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
730	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
731	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
732	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
733	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
734	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
735	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
736	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
737	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
738	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
739	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
740	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
741	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	4	no	—
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	4	no	—
748	C₄⋊C₄	—	2	4	no	—
749	C₄⋊C₄	—	2	4	no	—
750	C₄⋊C₄	—	2	4	no	—
751	C₄⋊C₄	—	4	4	no	—
752	C₄⋊C₄	—	4	4	no	—
753	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
754	C₂²⋊C₄	—	2	4	no	—
755	C₂²⋊C₄	—	2	4	no	—
756	C₂²⋊C₄	—	2	4	no	—
757	C₂²⋊C₄	—	2	4	no	—
758	C₂²⋊C₄	—	2	4	no	—
759	C₂²⋊C₄	—	2	4	no	—
760	C₂²⋊C₄	—	2	4	no	—
761	C₂²⋊C₄	—	2	4	no	—
762	C₂²⋊C₄	—	2	4	no	—
763	C₂²⋊C₄	—	2	4	no	—
764	C₂²⋊C₄	—	2	8	no	—
765	C₂²⋊C₄	—	2	8	no	—
766	C₂²⋊C₄	—	2	8	no	—
767	C₂²⋊C₄	—	2	8	no	—
768	C₂²⋊C₄	—	2	8	no	—
769	C₂²⋊C₄	—	4	4	no	—
770	C₂²⋊C₄	—	4	4	no	—
771	C₂²⋊C₄	—	4	4	no	—
772	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
773	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
774	C₂²⋊C₄	#41×C₁₃₉	1	8	yes	complemented
775	C₄²	—	2	4	no	—
776	C₄²	—	2	4	no	—
777	C₄²	—	2	2	no	—
778	C₄²	—	2	2	no	—
779	C₄²	—	2	2	no	—
780	C₄²	—	2	2	no	—
781	C₄²	—	2	4	no	—
782	C₄²	—	4	2	no	—
783	C₄²	—	4	2	no	—
784	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
785	C₂³	—	2	1	no	—
786	C₂³	—	2	1	no	—
787	C₂³	—	2	2	no	—
788	C₂³	—	2	2	no	—
789	C₂³	—	2	2	no	—
790	C₂³	—	2	4	no	—
791	C₂³	—	2	1	no	—
792	C₂³	—	2	4	no	—
793	C₂³	—	2	1	no	—
794	C₂³	—	2	2	no	—
795	C₂³	—	2	2	no	—
796	C₂³	—	2	2	no	—
797	C₂³	—	2	2	no	—
798	C₂³	—	2	4	no	—
799	C₂³	—	2	4	no	—
800	C₂³	—	2	2	no	—
801	C₂³	—	2	2	no	—
802	C₂³	—	2	4	no	—
803	C₂³	—	2	4	no	—
804	C₂³	—	2	2	no	—
805	C₂³	—	2	2	no	—
806	C₂³	—	4	8	no	—
807	C₂³	—	4	16	no	—
808	C₂³	—	4	8	no	—
809	C₂³	—	8	4	no	—
810	C₂³	—	8	8	no	—
811	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
812	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
813	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
814	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
815	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
816	Q₈	—	4	4	no	—
817	D₄	—	2	8	no	—
818	D₄	—	2	8	no	—
819	D₄	—	4	8	no	—
820	D₄	—	4	16	no	—
821	D₄	—	4	8	no	—
822	D₄	—	4	8	no	—
823	D₄	—	4	4	no	—
824	D₄	—	4	4	no	—
825	D₄	—	8	8	no	—
826	D₄	—	8	4	no	—
827	D₄	—	8	4	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	8	no	—
841	C₂×C₄	—	2	8	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	4	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	4	no	—
852	C₂×C₄	—	2	4	no	—
853	C₂×C₄	—	2	4	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	4	8	no	—
857	C₂×C₄	—	4	8	no	—
858	C₂×C₄	—	4	8	no	—
859	C₂×C₄	—	8	4	no	—
860	C₂×C₄	—	8	4	no	—
861	C₂×C₄	—	8	4	no	—
862	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
863	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
864	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
865	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
866	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
867	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
868	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
869	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
870	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
871	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
872	C₂²	—	2	2	no	—
873	C₂²	—	2	4	no	—
874	C₂²	—	2	2	no	—
875	C₂²	—	2	4	no	—
876	C₂²	—	2	2	no	—
877	C₂²	—	2	2	no	—
878	C₂²	—	2	4	no	—
879	C₂²	—	2	8	no	—
880	C₂²	—	2	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	4	no	—
886	C₂²	—	4	2	no	—
887	C₂²	—	4	2	no	—
888	C₂²	—	4	2	no	—
889	C₂²	—	4	2	no	—
890	C₂²	—	4	4	no	—
891	C₂²	—	4	4	no	—
892	C₂²	—	4	2	no	—
893	C₂²	—	4	2	no	—
894	C₂²	—	4	4	no	—
895	C₂²	—	4	4	no	—
896	C₂²	—	8	16	no	—
897	C₂²	#532×C₁₃₉	1	4	yes	—
898	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
899	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
900	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
901	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
902	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
903	C₄	—	2	2	no	—
904	C₄	—	2	2	no	—
905	C₄	—	2	2	no	—
906	C₄	—	2	4	no	—
907	C₄	—	2	2	no	—
908	C₄	—	2	4	no	—
909	C₄	—	2	4	no	—
910	C₄	—	4	2	no	—
911	C₄	—	4	2	no	—
912	C₄	—	4	2	no	—
913	C₄	—	4	2	no	—
914	C₄	—	4	2	no	—
915	C₄	—	4	2	no	—
916	C₄	#546×C₁₃₉	1	4	yes	—
917	C₂	—	2	4	no	—
918	C₂	—	4	4	no	—
919	C₂	—	4	2	no	—
920	C₂	—	8	2	no	—
921	C₂	—	8	2	no	—
922	C₂	C₂×#532×C₁₃₉	1	1	yes	characteristic
923	C₂	C₂×#546×C₁₃₉	1	1	yes	characteristic
924	C₂	#3481×C₁₃₉	1	2	yes	—
925	C₂	#3498×C₁₃₉	1	1	yes	characteristic
926	C₂	#3519×C₁₃₉	1	2	yes	—

	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×#553×C₁₃₉	C₂	semidirect
2. C₂×#546×C₁₃₉	C₂	semidirect
3. #2861×C₁₃₉	C₂	semidirect
4. #2856×C₁₃₉	C₂	semidirect
5. #2850×C₁₃₉	C₂	semidirect
6. #2566×C₁₃₉	C₂	semidirect
7. #2554×C₁₃₉	C₂	semidirect
8. #2544×C₁₃₉	C₂	semidirect
9. #2502×C₁₃₉	C₂	semidirect
10. #2500×C₁₃₉	C₂	semidirect
11. #2464×C₁₃₉	C₂	semidirect
12. #2433×C₁₃₉	C₂	semidirect
13. #2431×C₁₃₉	C₂	semidirect
14. #2424×C₁₃₉	C₂	semidirect
15. #2358×C₁₃₉	C₂	semidirect
16. C₄×#127×C₁₃₉	C₂	semidirect
17. #2297×C₁₃₉	C₂	semidirect
18. C₂×#390×C₁₃₉	C₂	semidirect
19. C₄²×D₄×C₁₃₉	C₂	semidirect
26. C₂×#126×C₁₃₉	C₂²	semidirect
27. C₂×#125×C₁₃₉	C₂²	semidirect
29. C₂×#124×C₁₃₉	C₂²	semidirect
31. C₂×#123×C₁₃₉	C₂²	semidirect
37. C₂×#121×C₁₃₉	C₂²	semidirect
38. C₂×#121×C₁₃₉	C₂²	semidirect
45. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
46. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
47. C₂×#117×C₁₃₉	C₂²	semidirect
52. C₂²×C₄²×C₁₃₉	C₂²	semidirect
53. #398×C₁₃₉	C₂²	semidirect
54. #396×C₁₃₉	C₂²	semidirect
55. #394×C₁₃₉	C₂²	semidirect
56. #394×C₁₃₉	C₂²	semidirect
58. #392×C₁₃₉	C₂²	semidirect
59. #391×C₁₃₉	C₂²	semidirect
60. #391×C₁₃₉	C₂²	semidirect
61. #391×C₁₃₉	C₂²	semidirect
69. #390×C₁₃₉	C₂²	semidirect
70. #390×C₁₃₉	C₂²	semidirect
71. #390×C₁₃₉	C₂²	semidirect
72. #388×C₁₃₉	C₂²	semidirect
73. #388×C₁₃₉	C₂²	semidirect
74. #388×C₁₃₉	C₂²	semidirect
75. #388×C₁₃₉	C₂²	semidirect
77. #386×C₁₃₉	C₂²	semidirect
78. #386×C₁₃₉	C₂²	semidirect
79. #386×C₁₃₉	C₂²	semidirect
81. #385×C₁₃₉	C₂²	semidirect
82. #384×C₁₃₉	C₂²	semidirect
83. #384×C₁₃₉	C₂²	semidirect
84. #382×C₁₃₉	C₂²	semidirect
85. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
86. C₄×C₄⋊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
142. C₄×D₄×C₁₃₉	D₄	semidirect
310. C₂²⋊C₄×C₁₃₉	#41	semidirect
463. #36362	C₁₃₉	direct (N × H)
464. C₁₃₉	#36362	direct (N × H)
465. C₂×#553	C₂×C₁₃₉	semidirect
466. C₂×#546	C₂×C₁₃₉	semidirect
467. #2861	C₂×C₁₃₉	semidirect
468. #2856	C₂×C₁₃₉	semidirect
469. #2850	C₂×C₁₃₉	semidirect
470. #2566	C₂×C₁₃₉	semidirect
471. #2554	C₂×C₁₃₉	semidirect
472. #2544	C₂×C₁₃₉	semidirect
473. #2502	C₂×C₁₃₉	semidirect
474. #2500	C₂×C₁₃₉	semidirect
475. #2464	C₂×C₁₃₉	semidirect
476. #2433	C₂×C₁₃₉	semidirect
477. #2431	C₂×C₁₃₉	semidirect
478. #2424	C₂×C₁₃₉	semidirect
479. #2358	C₂×C₁₃₉	semidirect
480. C₄×#127	C₂×C₁₃₉	semidirect
481. #2297	C₂×C₁₃₉	semidirect
482. C₂×#390	C₂×C₁₃₉	semidirect
483. C₄²×D₄	C₂×C₁₃₉	semidirect
490. C₂×#126	C₂²×C₁₃₉	semidirect
491. C₂×#125	C₂²×C₁₃₉	semidirect
493. C₂×#124	C₂²×C₁₃₉	semidirect
495. C₂×#123	C₂²×C₁₃₉	semidirect
501. C₂×#121	C₂²×C₁₃₉	semidirect
502. C₂×#121	C₂²×C₁₃₉	semidirect
509. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
510. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
511. C₂×#117	C₂²×C₁₃₉	semidirect
516. C₂²×C₄²	C₂²×C₁₃₉	semidirect
517. #398	C₂²×C₁₃₉	semidirect
518. #396	C₂²×C₁₃₉	semidirect
519. #394	C₂²×C₁₃₉	semidirect
520. #394	C₂²×C₁₃₉	semidirect
522. #392	C₂²×C₁₃₉	semidirect
523. #391	C₂²×C₁₃₉	semidirect
524. #391	C₂²×C₁₃₉	semidirect
525. #391	C₂²×C₁₃₉	semidirect
533. #390	C₂²×C₁₃₉	semidirect
534. #390	C₂²×C₁₃₉	semidirect
535. #390	C₂²×C₁₃₉	semidirect
536. #388	C₂²×C₁₃₉	semidirect
537. #388	C₂²×C₁₃₉	semidirect
538. #388	C₂²×C₁₃₉	semidirect
539. #388	C₂²×C₁₃₉	semidirect
541. #386	C₂²×C₁₃₉	semidirect
542. #386	C₂²×C₁₃₉	semidirect
543. #386	C₂²×C₁₃₉	semidirect
545. #385	C₂²×C₁₃₉	semidirect
546. #384	C₂²×C₁₃₉	semidirect
547. #384	C₂²×C₁₃₉	semidirect
548. #382	C₂²×C₁₃₉	semidirect
549. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
550. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
553. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
554. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
555. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
556. C₄³	C₂²×C₁₃₉	semidirect
606. C₄×D₄	D₄×C₁₃₉	semidirect
774. 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×#553×C₁₃₉	2
C₂×#546×C₁₃₉	2
#2861×C₁₃₉	2
#2856×C₁₃₉	2
#2850×C₁₃₉	2
#2566×C₁₃₉	2
#2554×C₁₃₉	2
#2544×C₁₃₉	2
#2502×C₁₃₉	2
#2500×C₁₃₉	2
#2464×C₁₃₉	2
#2433×C₁₃₉	2
#2431×C₁₃₉	2
#2424×C₁₃₉	2
#2358×C₁₃₉	2
C₄×#127×C₁₃₉	2
#2297×C₁₃₉	2
C₂×#390×C₁₃₉	2
C₄²×D₄×C₁₃₉	2
#36362	139

Subgroups — C139×#36362 #48030958

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36362 #48030958