Subgroups — C₁₃₉×#36410 #48031006

Order 35584.

2836 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#550×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×#41×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2856×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2854×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2582×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2548×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2476×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	#2464×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#2445×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2431×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2414×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2407×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2367×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2363×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2354×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₂²⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	#2297×C₁₃₉	C₂	1	2	yes	maximal, complemented
18	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
19	C₂²×#41×C₁₃₉	C₂²	1	2	yes	—
20	#550×C₁₃₉	—	2	8	no	—
21	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
22	C₂×#127×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#123×C₁₃₉	C₂²	1	4	yes	—
25	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
27	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
28	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
29	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
30	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
31	C₄×#41×C₁₃₉	—	2	8	no	—
32	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
34	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
39	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
40	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
41	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
42	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
43	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
44	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
45	#398×C₁₃₉	C₂²	1	4	yes	—
46	#394×C₁₃₉	C₂²	1	4	yes	—
47	#394×C₁₃₉	C₂²	1	4	yes	—
48	#394×C₁₃₉	C₂²	1	4	yes	—
49	#392×C₁₃₉	C₂²	1	4	yes	—
50	#392×C₁₃₉	C₂²	1	4	yes	—
51	#391×C₁₃₉	C₂²	1	1	yes	characteristic
52	#391×C₁₃₉	C₂²	1	2	yes	—
53	#391×C₁₃₉	C₂²	1	2	yes	—
54	#390×C₁₃₉	C₂²	1	2	yes	—
55	#390×C₁₃₉	C₂²	1	2	yes	—
56	#390×C₁₃₉	C₂²	1	2	yes	—
57	#390×C₁₃₉	C₂²	1	2	yes	—
58	#390×C₁₃₉	C₂²	1	2	yes	—
59	#390×C₁₃₉	C₂²	1	2	yes	—
60	#390×C₁₃₉	C₂²	1	2	yes	—
61	#390×C₁₃₉	C₂²	1	4	yes	—
62	#389×C₁₃₉	C₂²	1	1	yes	characteristic
63	#389×C₁₃₉	C₂²	1	2	yes	—
64	#389×C₁₃₉	C₂²	1	2	yes	—
65	#388×C₁₃₉	C₂²	1	4	yes	—
66	#388×C₁₃₉	C₂²	1	4	yes	—
67	#388×C₁₃₉	C₂²	1	4	yes	—
68	#388×C₁₃₉	C₂²	1	4	yes	—
69	#387×C₁₃₉	C₂²	1	2	yes	—
70	#386×C₁₃₉	C₂²	1	4	yes	—
71	#386×C₁₃₉	C₂²	1	4	yes	—
72	#386×C₁₃₉	C₂²	1	4	yes	—
73	#386×C₁₃₉	C₂²	1	4	yes	—
74	#385×C₁₃₉	C₂²	1	2	yes	—
75	#385×C₁₃₉	C₂²	1	4	yes	—
76	#384×C₁₃₉	C₂²	1	1	yes	characteristic
77	#380×C₁₃₉	C₂²	1	1	yes	characteristic
78	#380×C₁₃₉	C₂²	1	2	yes	—
79	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
80	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
81	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
82	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
83	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
84	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
85	C₂×#41×C₁₃₉	—	2	4	no	—
86	C₂×#41×C₁₃₉	—	2	8	no	—
87	C₂×#41×C₁₃₉	—	2	4	no	—
88	C₂×#41×C₁₃₉	—	2	8	no	—
89	C₂×#41×C₁₃₉	—	2	4	no	—
90	C₂×#41×C₁₃₉	—	4	4	no	—
91	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
92	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
93	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
94	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
95	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
96	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
97	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
98	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
99	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
100	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
101	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
102	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
103	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
105	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
106	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
107	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
108	#127×C₁₃₉	—	2	8	no	—
109	#127×C₁₃₉	—	2	4	no	—
110	#124×C₁₃₉	—	2	8	no	—
111	#123×C₁₃₉	—	4	8	no	—
112	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
113	#121×C₁₃₉	—	2	8	no	—
114	#121×C₁₃₉	—	2	8	no	—
115	#121×C₁₃₉	—	2	16	no	—
116	#121×C₁₃₉	—	4	4	no	—
117	#121×C₁₃₉	—	4	4	no	—
118	C₄×Q₈×C₁₃₉	—	2	4	no	—
119	C₄×Q₈×C₁₃₉	—	2	4	no	—
120	C₄×Q₈×C₁₃₉	—	2	4	no	—
121	C₄×D₄×C₁₃₉	—	2	4	no	—
122	C₄×D₄×C₁₃₉	—	2	8	no	—
123	C₄×D₄×C₁₃₉	—	2	8	no	—
124	C₄×D₄×C₁₃₉	—	2	8	no	—
125	C₄×D₄×C₁₃₉	D₄	1	8	yes	complemented
126	#117×C₁₃₉	—	2	4	no	—
127	#117×C₁₃₉	—	2	8	no	—
128	#117×C₁₃₉	—	4	4	no	—
129	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
132	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
134	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	4	yes	—
142	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
146	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
147	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
148	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
150	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
151	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
152	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
153	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
154	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	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	2	yes	—
158	C₂×C₄²×C₁₃₉	—	2	8	no	—
159	C₂×C₄²×C₁₃₉	—	2	4	no	—
160	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
162	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
164	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
166	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
167	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
168	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
169	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
170	#95×C₁₃₉	C₂³	1	4	yes	—
171	#95×C₁₃₉	C₂³	1	4	yes	—
172	#95×C₁₃₉	C₂³	1	4	yes	—
173	#95×C₁₃₉	C₂³	1	2	yes	—
174	#95×C₁₃₉	C₂³	1	2	yes	—
175	#95×C₁₃₉	C₂³	1	2	yes	—
176	#95×C₁₃₉	C₂³	1	4	yes	—
177	#95×C₁₃₉	C₂³	1	2	yes	—
178	#95×C₁₃₉	C₂³	1	2	yes	—
179	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
180	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
181	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
182	#41×C₁₃₉	—	2	32	no	—
183	#41×C₁₃₉	—	4	32	no	—
184	C₂×Q₈×C₁₃₉	—	2	2	no	—
185	C₂×Q₈×C₁₃₉	—	2	2	no	—
186	C₂×Q₈×C₁₃₉	—	2	2	no	—
187	C₂×Q₈×C₁₃₉	—	2	2	no	—
188	C₂×Q₈×C₁₃₉	#41	1	4	yes	complemented
189	C₂×Q₈×C₁₃₉	#41	1	4	yes	complemented
190	C₂×D₄×C₁₃₉	—	2	4	no	—
191	C₂×D₄×C₁₃₉	—	2	4	no	—
192	C₂×D₄×C₁₃₉	—	2	8	no	—
193	C₂×D₄×C₁₃₉	—	2	8	no	—
194	C₂×D₄×C₁₃₉	—	2	8	no	—
195	C₂×D₄×C₁₃₉	—	2	4	no	—
196	C₂×D₄×C₁₃₉	—	2	4	no	—
197	C₂×D₄×C₁₃₉	—	2	4	no	—
198	C₂×D₄×C₁₃₉	—	2	4	no	—
199	C₂×D₄×C₁₃₉	—	2	2	no	—
200	C₂×D₄×C₁₃₉	—	2	2	no	—
201	C₂×D₄×C₁₃₉	—	2	4	no	—
202	C₂×D₄×C₁₃₉	—	2	4	no	—
203	C₂×D₄×C₁₃₉	—	2	8	no	—
204	C₂×D₄×C₁₃₉	—	2	4	no	—
205	C₂×D₄×C₁₃₉	—	2	4	no	—
206	C₂×D₄×C₁₃₉	—	4	4	no	—
207	C₂×D₄×C₁₃₉	—	4	2	no	—
208	C₂×D₄×C₁₃₉	—	4	4	no	—
209	C₂×D₄×C₁₃₉	—	4	4	no	—
210	C₂×D₄×C₁₃₉	—	4	4	no	—
211	C₂×D₄×C₁₃₉	—	4	2	no	—
212	C₂×D₄×C₁₃₉	—	4	4	no	—
213	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
214	C₂²×C₄×C₁₃₉	—	2	4	no	—
215	C₂²×C₄×C₁₃₉	—	2	2	no	—
216	C₂²×C₄×C₁₃₉	—	2	4	no	—
217	C₂²×C₄×C₁₃₉	—	2	4	no	—
218	C₂²×C₄×C₁₃₉	—	2	2	no	—
219	C₂²×C₄×C₁₃₉	—	2	4	no	—
220	C₂²×C₄×C₁₃₉	—	2	4	no	—
221	C₂²×C₄×C₁₃₉	—	2	4	no	—
222	C₂²×C₄×C₁₃₉	—	2	2	no	—
223	C₂²×C₄×C₁₃₉	—	2	2	no	—
224	C₂²×C₄×C₁₃₉	—	2	8	no	—
225	C₂²×C₄×C₁₃₉	—	2	2	no	—
226	C₂²×C₄×C₁₃₉	—	2	8	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	—	4	1	no	—
231	C₂²×C₄×C₁₃₉	—	4	2	no	—
232	C₂²×C₄×C₁₃₉	—	4	4	no	—
233	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
234	C₂²×C₄×C₁₃₉	#41	1	4	yes	complemented
235	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
238	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
240	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
248	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
249	C₄⋊C₄×C₁₃₉	—	2	4	no	—
250	C₄⋊C₄×C₁₃₉	—	2	4	no	—
251	C₄⋊C₄×C₁₃₉	—	2	2	no	—
252	C₄⋊C₄×C₁₃₉	—	2	4	no	—
253	C₄⋊C₄×C₁₃₉	—	2	2	no	—
254	C₄⋊C₄×C₁₃₉	—	2	4	no	—
255	C₄⋊C₄×C₁₃₉	—	2	2	no	—
256	C₄⋊C₄×C₁₃₉	—	2	4	no	—
257	C₄⋊C₄×C₁₃₉	—	2	2	no	—
258	C₄⋊C₄×C₁₃₉	—	2	4	no	—
259	C₄⋊C₄×C₁₃₉	—	2	4	no	—
260	C₄⋊C₄×C₁₃₉	—	4	2	no	—
261	C₄⋊C₄×C₁₃₉	—	4	4	no	—
262	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
263	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
264	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
265	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
266	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
267	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
268	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
269	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
270	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
271	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
272	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
273	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
274	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
275	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
276	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
277	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
278	C₄²×C₁₃₉	—	2	2	no	—
279	C₄²×C₁₃₉	—	2	4	no	—
280	C₄²×C₁₃₉	—	2	2	no	—
281	C₄²×C₁₃₉	—	2	4	no	—
282	C₄²×C₁₃₉	—	2	2	no	—
283	C₄²×C₁₃₉	—	2	4	no	—
284	C₄²×C₁₃₉	—	2	4	no	—
285	C₄²×C₁₃₉	—	2	4	no	—
286	C₄²×C₁₃₉	—	4	4	no	—
287	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
288	C₂³×C₁₃₉	—	2	1	no	—
289	C₂³×C₁₃₉	—	2	1	no	—
290	C₂³×C₁₃₉	—	2	2	no	—
291	C₂³×C₁₃₉	—	2	2	no	—
292	C₂³×C₁₃₉	—	2	1	no	—
293	C₂³×C₁₃₉	—	2	2	no	—
294	C₂³×C₁₃₉	—	2	2	no	—
295	C₂³×C₁₃₉	—	2	2	no	—
296	C₂³×C₁₃₉	—	2	1	no	—
297	C₂³×C₁₃₉	—	2	1	no	—
298	C₂³×C₁₃₉	—	2	1	no	—
299	C₂³×C₁₃₉	—	2	2	no	—
300	C₂³×C₁₃₉	—	2	4	no	—
301	C₂³×C₁₃₉	—	2	4	no	—
302	C₂³×C₁₃₉	—	2	4	no	—
303	C₂³×C₁₃₉	—	2	4	no	—
304	C₂³×C₁₃₉	—	2	4	no	—
305	C₂³×C₁₃₉	—	2	4	no	—
306	C₂³×C₁₃₉	—	2	4	no	—
307	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
308	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
309	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
310	Q₈×C₁₃₉	—	2	8	no	—
311	Q₈×C₁₃₉	—	2	8	no	—
312	D₄×C₁₃₉	—	2	16	no	—
313	D₄×C₁₃₉	—	2	8	no	—
314	D₄×C₁₃₉	—	4	16	no	—
315	D₄×C₁₃₉	—	4	8	no	—
316	D₄×C₁₃₉	—	4	8	no	—
317	D₄×C₁₃₉	—	8	4	no	—
318	D₄×C₁₃₉	—	8	8	no	—
319	D₄×C₁₃₉	—	8	8	no	—
320	C₂×C₄×C₁₃₉	—	2	16	no	—
321	C₂×C₄×C₁₃₉	—	2	1	no	—
322	C₂×C₄×C₁₃₉	—	2	1	no	—
323	C₂×C₄×C₁₃₉	—	2	2	no	—
324	C₂×C₄×C₁₃₉	—	2	2	no	—
325	C₂×C₄×C₁₃₉	—	2	1	no	—
326	C₂×C₄×C₁₃₉	—	2	2	no	—
327	C₂×C₄×C₁₃₉	—	2	2	no	—
328	C₂×C₄×C₁₃₉	—	2	2	no	—
329	C₂×C₄×C₁₃₉	—	2	1	no	—
330	C₂×C₄×C₁₃₉	—	2	2	no	—
331	C₂×C₄×C₁₃₉	—	2	1	no	—
332	C₂×C₄×C₁₃₉	—	2	1	no	—
333	C₂×C₄×C₁₃₉	—	2	8	no	—
334	C₂×C₄×C₁₃₉	—	2	16	no	—
335	C₂×C₄×C₁₃₉	—	2	1	no	—
336	C₂×C₄×C₁₃₉	—	2	2	no	—
337	C₂×C₄×C₁₃₉	—	2	2	no	—
338	C₂×C₄×C₁₃₉	—	2	2	no	—
339	C₂×C₄×C₁₃₉	—	2	2	no	—
340	C₂×C₄×C₁₃₉	—	2	2	no	—
341	C₂×C₄×C₁₃₉	—	2	4	no	—
342	C₂×C₄×C₁₃₉	—	2	1	no	—
343	C₂×C₄×C₁₃₉	—	2	2	no	—
344	C₂×C₄×C₁₃₉	—	2	4	no	—
345	C₂×C₄×C₁₃₉	—	2	4	no	—
346	C₂×C₄×C₁₃₉	—	2	2	no	—
347	C₂×C₄×C₁₃₉	—	2	1	no	—
348	C₂×C₄×C₁₃₉	—	2	2	no	—
349	C₂×C₄×C₁₃₉	—	2	2	no	—
350	C₂×C₄×C₁₃₉	—	2	2	no	—
351	C₂×C₄×C₁₃₉	—	2	2	no	—
352	C₂×C₄×C₁₃₉	—	2	2	no	—
353	C₂×C₄×C₁₃₉	—	4	4	no	—
354	C₂×C₄×C₁₃₉	—	4	16	no	—
355	C₂×C₄×C₁₃₉	—	4	8	no	—
356	C₂×C₄×C₁₃₉	—	4	4	no	—
357	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
358	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
359	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
360	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
361	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
362	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
363	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
364	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
365	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
366	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
367	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
368	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
369	C₂²×C₁₃₉	—	2	4	no	—
370	C₂²×C₁₃₉	—	2	2	no	—
371	C₂²×C₁₃₉	—	2	4	no	—
372	C₂²×C₁₃₉	—	2	2	no	—
373	C₂²×C₁₃₉	—	2	4	no	—
374	C₂²×C₁₃₉	—	2	2	no	—
375	C₂²×C₁₃₉	—	4	1	no	—
376	C₂²×C₁₃₉	—	4	2	no	—
377	C₂²×C₁₃₉	—	4	1	no	—
378	C₂²×C₁₃₉	—	4	2	no	—
379	C₂²×C₁₃₉	—	4	1	no	—
380	C₂²×C₁₃₉	—	4	2	no	—
381	C₂²×C₁₃₉	—	4	2	no	—
382	C₂²×C₁₃₉	—	4	1	no	—
383	C₂²×C₁₃₉	—	4	4	no	—
384	C₂²×C₁₃₉	—	4	4	no	—
385	C₂²×C₁₃₉	—	4	4	no	—
386	C₂²×C₁₃₉	—	4	4	no	—
387	C₂²×C₁₃₉	—	4	4	no	—
388	C₂²×C₁₃₉	—	4	4	no	—
389	C₂²×C₁₃₉	—	4	4	no	—
390	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
391	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
392	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
393	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
394	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
395	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
396	C₂²×C₁₃₉	#585	1	1	yes	characteristic
397	C₄×C₁₃₉	—	2	2	no	—
398	C₄×C₁₃₉	—	2	4	no	—
399	C₄×C₁₃₉	—	2	4	no	—
400	C₄×C₁₃₉	—	2	4	no	—
401	C₄×C₁₃₉	—	2	2	no	—
402	C₄×C₁₃₉	—	2	2	no	—
403	C₄×C₁₃₉	—	4	1	no	—
404	C₄×C₁₃₉	—	4	2	no	—
405	C₄×C₁₃₉	—	4	2	no	—
406	C₄×C₁₃₉	—	4	2	no	—
407	C₄×C₁₃₉	—	4	4	no	—
408	C₄×C₁₃₉	—	4	2	no	—
409	C₄×C₁₃₉	#525	1	4	yes	—
410	C₄×C₁₃₉	#546	1	4	yes	—
411	C₂×C₁₃₉	—	4	4	no	—
412	C₂×C₁₃₉	—	4	2	no	—
413	C₂×C₁₃₉	—	8	4	no	—
414	C₂×C₁₃₉	C₂×#525	1	1	yes	characteristic
415	C₂×C₁₃₉	C₂×#546	1	1	yes	characteristic
416	C₂×C₁₃₉	#3480	1	1	yes	characteristic
417	C₂×C₁₃₉	#3483	1	1	yes	characteristic
418	C₂×C₁₃₉	#3488	1	1	yes	characteristic
419	C₂×C₁₃₉	#3508	1	1	yes	characteristic
420	C₂×C₁₃₉	#3517	1	1	yes	characteristic
421	#36410	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
422	C₁₃₉	#36410	1	1	yes	characteristic, direct product factor, Sylow
423	C₂×#550	C₂×C₁₃₉	1	1	yes	characteristic, complemented
424	C₂×C₄×#41	C₂×C₁₃₉	1	1	yes	characteristic, complemented
425	#2856	C₂×C₁₃₉	1	1	yes	characteristic, complemented
426	#2854	C₂×C₁₃₉	1	2	yes	complemented
427	#2582	C₂×C₁₃₉	1	1	yes	characteristic, complemented
428	#2548	C₂×C₁₃₉	1	1	yes	characteristic, complemented
429	#2476	C₂×C₁₃₉	1	4	yes	complemented
430	#2464	C₂×C₁₃₉	1	4	yes	complemented
431	#2445	C₂×C₁₃₉	1	2	yes	complemented
432	#2431	C₂×C₁₃₉	1	2	yes	complemented
433	#2414	C₂×C₁₃₉	1	2	yes	complemented
434	#2407	C₂×C₁₃₉	1	2	yes	complemented
435	#2367	C₂×C₁₃₉	1	2	yes	complemented
436	#2363	C₂×C₁₃₉	1	2	yes	complemented
437	#2354	C₂×C₁₃₉	1	1	yes	characteristic, complemented
438	C₄×C₂²⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
439	#2297	C₂×C₁₃₉	1	2	yes	complemented
440	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
441	C₂²×#41	C₂²×C₁₃₉	1	2	yes	—
442	#550	—	2	8	no	—
443	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
444	C₂×#127	C₂²×C₁₃₉	1	2	yes	—
445	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
446	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
447	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
448	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
449	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
450	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
451	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
452	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
453	C₄×#41	—	2	8	no	—
454	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
455	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
456	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
457	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
458	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
459	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
460	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
461	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
462	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
463	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
464	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
465	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
466	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
467	#398	C₂²×C₁₃₉	1	4	yes	—
468	#394	C₂²×C₁₃₉	1	4	yes	—
469	#394	C₂²×C₁₃₉	1	4	yes	—
470	#394	C₂²×C₁₃₉	1	4	yes	—
471	#392	C₂²×C₁₃₉	1	4	yes	—
472	#392	C₂²×C₁₃₉	1	4	yes	—
473	#391	C₂²×C₁₃₉	1	2	yes	—
474	#391	C₂²×C₁₃₉	1	2	yes	—
475	#391	C₂²×C₁₃₉	1	1	yes	characteristic
476	#390	C₂²×C₁₃₉	1	2	yes	—
477	#390	C₂²×C₁₃₉	1	2	yes	—
478	#390	C₂²×C₁₃₉	1	2	yes	—
479	#390	C₂²×C₁₃₉	1	2	yes	—
480	#390	C₂²×C₁₃₉	1	2	yes	—
481	#390	C₂²×C₁₃₉	1	4	yes	—
482	#390	C₂²×C₁₃₉	1	2	yes	—
483	#390	C₂²×C₁₃₉	1	2	yes	—
484	#389	C₂²×C₁₃₉	1	2	yes	—
485	#389	C₂²×C₁₃₉	1	2	yes	—
486	#389	C₂²×C₁₃₉	1	1	yes	characteristic
487	#388	C₂²×C₁₃₉	1	4	yes	—
488	#388	C₂²×C₁₃₉	1	4	yes	—
489	#388	C₂²×C₁₃₉	1	4	yes	—
490	#388	C₂²×C₁₃₉	1	4	yes	—
491	#387	C₂²×C₁₃₉	1	2	yes	—
492	#386	C₂²×C₁₃₉	1	4	yes	—
493	#386	C₂²×C₁₃₉	1	4	yes	—
494	#386	C₂²×C₁₃₉	1	4	yes	—
495	#386	C₂²×C₁₃₉	1	4	yes	—
496	#385	C₂²×C₁₃₉	1	4	yes	—
497	#385	C₂²×C₁₃₉	1	2	yes	—
498	#384	C₂²×C₁₃₉	1	1	yes	characteristic
499	#380	C₂²×C₁₃₉	1	2	yes	—
500	#380	C₂²×C₁₃₉	1	1	yes	characteristic
501	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
502	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
503	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
504	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
505	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
506	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
507	C₂×#41	—	2	4	no	—
508	C₂×#41	—	2	8	no	—
509	C₂×#41	—	2	4	no	—
510	C₂×#41	—	2	8	no	—
511	C₂×#41	—	2	4	no	—
512	C₂×#41	—	4	4	no	—
513	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
514	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
515	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
516	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
517	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
518	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
519	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
520	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
521	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
522	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
523	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
524	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
525	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
526	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
527	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
528	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
529	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
530	#127	—	2	8	no	—
531	#127	—	2	4	no	—
532	#124	—	2	8	no	—
533	#123	—	4	8	no	—
534	C₂²⋊Q₈	—	2	4	no	—
535	#121	—	2	8	no	—
536	#121	—	2	8	no	—
537	#121	—	2	16	no	—
538	#121	—	4	4	no	—
539	#121	—	4	4	no	—
540	C₄×Q₈	—	2	4	no	—
541	C₄×Q₈	—	2	4	no	—
542	C₄×Q₈	—	2	4	no	—
543	C₄×D₄	—	2	4	no	—
544	C₄×D₄	—	2	8	no	—
545	C₄×D₄	—	2	8	no	—
546	C₄×D₄	—	2	8	no	—
547	C₄×D₄	D₄×C₁₃₉	1	8	yes	complemented
548	#117	—	2	4	no	—
549	#117	—	2	8	no	—
550	#117	—	4	4	no	—
551	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
552	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
553	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
554	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
555	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
556	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
557	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
558	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
559	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
560	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
561	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
562	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
563	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
564	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
565	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
566	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
567	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
568	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
569	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
570	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
571	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
574	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
576	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
577	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
578	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
579	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
580	C₂×C₄²	—	2	8	no	—
581	C₂×C₄²	—	2	4	no	—
582	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
583	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
584	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
585	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
586	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
587	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
588	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
589	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
590	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
591	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
592	#95	C₂³×C₁₃₉	1	2	yes	—
593	#95	C₂³×C₁₃₉	1	2	yes	—
594	#95	C₂³×C₁₃₉	1	4	yes	—
595	#95	C₂³×C₁₃₉	1	2	yes	—
596	#95	C₂³×C₁₃₉	1	4	yes	—
597	#95	C₂³×C₁₃₉	1	4	yes	—
598	#95	C₂³×C₁₃₉	1	2	yes	—
599	#95	C₂³×C₁₃₉	1	2	yes	—
600	#95	C₂³×C₁₃₉	1	4	yes	—
601	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
602	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
603	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
604	#41	—	2	32	no	—
605	#41	—	4	32	no	—
606	C₂×Q₈	—	2	2	no	—
607	C₂×Q₈	—	2	2	no	—
608	C₂×Q₈	—	2	2	no	—
609	C₂×Q₈	—	2	2	no	—
610	C₂×Q₈	#41×C₁₃₉	1	4	yes	complemented
611	C₂×Q₈	#41×C₁₃₉	1	4	yes	complemented
612	C₂×D₄	—	2	4	no	—
613	C₂×D₄	—	2	4	no	—
614	C₂×D₄	—	2	8	no	—
615	C₂×D₄	—	2	8	no	—
616	C₂×D₄	—	2	8	no	—
617	C₂×D₄	—	2	4	no	—
618	C₂×D₄	—	2	4	no	—
619	C₂×D₄	—	2	4	no	—
620	C₂×D₄	—	2	4	no	—
621	C₂×D₄	—	2	2	no	—
622	C₂×D₄	—	2	2	no	—
623	C₂×D₄	—	2	4	no	—
624	C₂×D₄	—	2	4	no	—
625	C₂×D₄	—	2	8	no	—
626	C₂×D₄	—	2	4	no	—
627	C₂×D₄	—	2	4	no	—
628	C₂×D₄	—	4	4	no	—
629	C₂×D₄	—	4	2	no	—
630	C₂×D₄	—	4	4	no	—
631	C₂×D₄	—	4	4	no	—
632	C₂×D₄	—	4	4	no	—
633	C₂×D₄	—	4	2	no	—
634	C₂×D₄	—	4	4	no	—
635	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
636	C₂²×C₄	—	2	4	no	—
637	C₂²×C₄	—	2	2	no	—
638	C₂²×C₄	—	2	4	no	—
639	C₂²×C₄	—	2	4	no	—
640	C₂²×C₄	—	2	2	no	—
641	C₂²×C₄	—	2	4	no	—
642	C₂²×C₄	—	2	4	no	—
643	C₂²×C₄	—	2	4	no	—
644	C₂²×C₄	—	2	2	no	—
645	C₂²×C₄	—	2	2	no	—
646	C₂²×C₄	—	2	8	no	—
647	C₂²×C₄	—	2	2	no	—
648	C₂²×C₄	—	2	8	no	—
649	C₂²×C₄	—	2	2	no	—
650	C₂²×C₄	—	2	2	no	—
651	C₂²×C₄	—	2	4	no	—
652	C₂²×C₄	—	4	1	no	—
653	C₂²×C₄	—	4	2	no	—
654	C₂²×C₄	—	4	4	no	—
655	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
656	C₂²×C₄	#41×C₁₃₉	1	4	yes	complemented
657	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
658	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
659	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
660	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
661	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
662	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
663	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
664	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
665	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
666	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
667	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
668	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
669	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
670	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
671	C₄⋊C₄	—	2	4	no	—
672	C₄⋊C₄	—	2	4	no	—
673	C₄⋊C₄	—	2	2	no	—
674	C₄⋊C₄	—	2	4	no	—
675	C₄⋊C₄	—	2	2	no	—
676	C₄⋊C₄	—	2	4	no	—
677	C₄⋊C₄	—	2	2	no	—
678	C₄⋊C₄	—	2	4	no	—
679	C₄⋊C₄	—	2	2	no	—
680	C₄⋊C₄	—	2	4	no	—
681	C₄⋊C₄	—	2	4	no	—
682	C₄⋊C₄	—	4	2	no	—
683	C₄⋊C₄	—	4	4	no	—
684	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
685	C₂²⋊C₄	—	2	4	no	—
686	C₂²⋊C₄	—	2	4	no	—
687	C₂²⋊C₄	—	2	8	no	—
688	C₂²⋊C₄	—	2	8	no	—
689	C₂²⋊C₄	—	2	4	no	—
690	C₂²⋊C₄	—	2	8	no	—
691	C₂²⋊C₄	—	2	8	no	—
692	C₂²⋊C₄	—	2	8	no	—
693	C₂²⋊C₄	—	4	4	no	—
694	C₂²⋊C₄	—	4	2	no	—
695	C₂²⋊C₄	—	4	4	no	—
696	C₂²⋊C₄	—	4	4	no	—
697	C₂²⋊C₄	—	4	4	no	—
698	C₂²⋊C₄	—	4	4	no	—
699	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
700	C₄²	—	2	2	no	—
701	C₄²	—	2	4	no	—
702	C₄²	—	2	2	no	—
703	C₄²	—	2	4	no	—
704	C₄²	—	2	2	no	—
705	C₄²	—	2	4	no	—
706	C₄²	—	2	4	no	—
707	C₄²	—	2	4	no	—
708	C₄²	—	4	4	no	—
709	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
710	C₂³	—	2	1	no	—
711	C₂³	—	2	1	no	—
712	C₂³	—	2	2	no	—
713	C₂³	—	2	2	no	—
714	C₂³	—	2	1	no	—
715	C₂³	—	2	2	no	—
716	C₂³	—	2	2	no	—
717	C₂³	—	2	2	no	—
718	C₂³	—	2	1	no	—
719	C₂³	—	2	1	no	—
720	C₂³	—	2	1	no	—
721	C₂³	—	2	2	no	—
722	C₂³	—	2	4	no	—
723	C₂³	—	2	4	no	—
724	C₂³	—	2	4	no	—
725	C₂³	—	2	4	no	—
726	C₂³	—	2	4	no	—
727	C₂³	—	2	4	no	—
728	C₂³	—	2	4	no	—
729	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
730	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
731	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
732	Q₈	—	2	8	no	—
733	Q₈	—	2	8	no	—
734	D₄	—	2	16	no	—
735	D₄	—	2	8	no	—
736	D₄	—	4	16	no	—
737	D₄	—	4	8	no	—
738	D₄	—	4	8	no	—
739	D₄	—	8	4	no	—
740	D₄	—	8	8	no	—
741	D₄	—	8	8	no	—
742	C₂×C₄	—	2	16	no	—
743	C₂×C₄	—	2	1	no	—
744	C₂×C₄	—	2	1	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	1	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	1	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	8	no	—
756	C₂×C₄	—	2	16	no	—
757	C₂×C₄	—	2	1	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	4	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	4	no	—
767	C₂×C₄	—	2	4	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	4	16	no	—
776	C₂×C₄	—	4	4	no	—
777	C₂×C₄	—	4	8	no	—
778	C₂×C₄	—	4	4	no	—
779	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
780	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
781	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
782	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
783	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
784	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
785	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
786	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
787	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
788	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
789	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
790	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
791	C₂²	—	2	4	no	—
792	C₂²	—	2	2	no	—
793	C₂²	—	2	4	no	—
794	C₂²	—	2	2	no	—
795	C₂²	—	2	4	no	—
796	C₂²	—	2	2	no	—
797	C₂²	—	4	1	no	—
798	C₂²	—	4	2	no	—
799	C₂²	—	4	1	no	—
800	C₂²	—	4	2	no	—
801	C₂²	—	4	1	no	—
802	C₂²	—	4	2	no	—
803	C₂²	—	4	2	no	—
804	C₂²	—	4	1	no	—
805	C₂²	—	4	4	no	—
806	C₂²	—	4	4	no	—
807	C₂²	—	4	4	no	—
808	C₂²	—	4	4	no	—
809	C₂²	—	4	4	no	—
810	C₂²	—	4	4	no	—
811	C₂²	—	4	4	no	—
812	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
813	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
814	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
815	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
816	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
817	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
818	C₂²	#585×C₁₃₉	1	1	yes	characteristic
819	C₄	—	2	2	no	—
820	C₄	—	2	4	no	—
821	C₄	—	2	4	no	—
822	C₄	—	2	4	no	—
823	C₄	—	2	2	no	—
824	C₄	—	2	2	no	—
825	C₄	—	4	1	no	—
826	C₄	—	4	2	no	—
827	C₄	—	4	2	no	—
828	C₄	—	4	2	no	—
829	C₄	—	4	4	no	—
830	C₄	—	4	2	no	—
831	C₄	#525×C₁₃₉	1	4	yes	—
832	C₄	#546×C₁₃₉	1	4	yes	—
833	C₂	—	4	4	no	—
834	C₂	—	4	2	no	—
835	C₂	—	8	4	no	—
836	C₂	C₂×#525×C₁₃₉	1	1	yes	characteristic
837	C₂	C₂×#546×C₁₃₉	1	1	yes	characteristic
838	C₂	#3480×C₁₃₉	1	1	yes	characteristic
839	C₂	#3483×C₁₃₉	1	1	yes	characteristic
840	C₂	#3488×C₁₃₉	1	1	yes	characteristic
841	C₂	#3508×C₁₃₉	1	1	yes	characteristic
842	C₂	#3517×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×#550×C₁₃₉	C₂	semidirect
2. C₂×C₄×#41×C₁₃₉	C₂	semidirect
3. #2856×C₁₃₉	C₂	semidirect
4. #2854×C₁₃₉	C₂	semidirect
5. #2582×C₁₃₉	C₂	semidirect
6. #2548×C₁₃₉	C₂	semidirect
7. #2476×C₁₃₉	C₂	semidirect
8. #2464×C₁₃₉	C₂	semidirect
9. #2445×C₁₃₉	C₂	semidirect
10. #2431×C₁₃₉	C₂	semidirect
11. #2414×C₁₃₉	C₂	semidirect
12. #2407×C₁₃₉	C₂	semidirect
13. #2367×C₁₃₉	C₂	semidirect
14. #2363×C₁₃₉	C₂	semidirect
15. #2354×C₁₃₉	C₂	semidirect
16. C₄×C₂²⋊Q₈×C₁₃₉	C₂	semidirect
17. #2297×C₁₃₉	C₂	semidirect
125. C₄×D₄×C₁₃₉	D₄	semidirect
188. C₂×Q₈×C₁₃₉	#41	semidirect
189. C₂×Q₈×C₁₃₉	#41	semidirect
234. C₂²×C₄×C₁₃₉	#41	semidirect
421. #36410	C₁₃₉	direct (N × H)
422. C₁₃₉	#36410	direct (N × H)
423. C₂×#550	C₂×C₁₃₉	semidirect
424. C₂×C₄×#41	C₂×C₁₃₉	semidirect
425. #2856	C₂×C₁₃₉	semidirect
426. #2854	C₂×C₁₃₉	semidirect
427. #2582	C₂×C₁₃₉	semidirect
428. #2548	C₂×C₁₃₉	semidirect
429. #2476	C₂×C₁₃₉	semidirect
430. #2464	C₂×C₁₃₉	semidirect
431. #2445	C₂×C₁₃₉	semidirect
432. #2431	C₂×C₁₃₉	semidirect
433. #2414	C₂×C₁₃₉	semidirect
434. #2407	C₂×C₁₃₉	semidirect
435. #2367	C₂×C₁₃₉	semidirect
436. #2363	C₂×C₁₃₉	semidirect
437. #2354	C₂×C₁₃₉	semidirect
438. C₄×C₂²⋊Q₈	C₂×C₁₃₉	semidirect
439. #2297	C₂×C₁₃₉	semidirect
547. C₄×D₄	D₄×C₁₃₉	semidirect
610. C₂×Q₈	#41×C₁₃₉	semidirect
611. C₂×Q₈	#41×C₁₃₉	semidirect
656. 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×#550×C₁₃₉	2
C₂×C₄×#41×C₁₃₉	2
#2856×C₁₃₉	2
#2854×C₁₃₉	2
#2582×C₁₃₉	2
#2548×C₁₃₉	2
#2476×C₁₃₉	2
#2464×C₁₃₉	2
#2445×C₁₃₉	2
#2431×C₁₃₉	2
#2414×C₁₃₉	2
#2407×C₁₃₉	2
#2367×C₁₃₉	2
#2363×C₁₃₉	2
#2354×C₁₃₉	2
C₄×C₂²⋊Q₈×C₁₃₉	2
#2297×C₁₃₉	2
#36410	139

Subgroups — C139×#36410 #48031006

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36410 #48031006