Subgroups — C₁₃₉×#36102 #48030698

Order 35584.

3590 conjugacy classes of subgroups.

The subgroup lattice has 864 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	#2854×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2849×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2463×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#2456×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	#2452×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2433×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#2428×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2411×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2408×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#2404×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2366×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2361×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2344×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×#123×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₁₃₉	C₂²	1	2	yes	—
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	C₂×#127×C₁₃₉	C₂²	1	2	yes	—
24	#525×C₁₃₉	—	2	16	no	—
25	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
26	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
27	C₂×#123×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×#123×C₁₃₉	C₂²	1	2	yes	complemented
29	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	complemented
30	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	complemented
31	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
33	C₂×#121×C₁₃₉	C₂²	1	4	yes	complemented
34	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
35	C₂×#120×C₁₃₉	C₂²	1	2	yes	—
36	C₂×#120×C₁₃₉	C₂²	1	2	yes	—
37	C₂×#120×C₁₃₉	C₂²	1	2	yes	—
38	C₂×C₄×D₄×C₁₃₉	—	2	8	no	—
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	2	yes	—
42	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	—
43	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	complemented
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	—
47	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
48	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
49	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
50	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
51	#396×C₁₃₉	C₂²	1	4	yes	complemented
52	#394×C₁₃₉	C₂²	1	2	yes	—
53	#394×C₁₃₉	C₂²	1	4	yes	complemented
54	#393×C₁₃₉	C₂²	1	4	yes	complemented
55	#392×C₁₃₉	C₂²	1	2	yes	—
56	#392×C₁₃₉	C₂²	1	4	yes	—
57	#392×C₁₃₉	C₂²	1	4	yes	complemented
58	#390×C₁₃₉	C₂²	1	2	yes	—
59	#390×C₁₃₉	C₂²	1	2	yes	—
60	#390×C₁₃₉	C₂²	1	2	yes	complemented
61	#390×C₁₃₉	C₂²	1	4	yes	complemented
62	#389×C₁₃₉	C₂²	1	2	yes	complemented
63	#389×C₁₃₉	C₂²	1	2	yes	complemented
64	#388×C₁₃₉	C₂²	1	2	yes	complemented
65	#388×C₁₃₉	C₂²	1	4	yes	complemented
66	#388×C₁₃₉	C₂²	1	4	yes	complemented
67	#387×C₁₃₉	C₂²	1	2	yes	complemented
68	#387×C₁₃₉	C₂²	1	4	yes	complemented
69	#386×C₁₃₉	C₂²	1	1	yes	characteristic
70	#386×C₁₃₉	C₂²	1	2	yes	—
71	#386×C₁₃₉	C₂²	1	4	yes	complemented
72	#386×C₁₃₉	C₂²	1	4	yes	complemented
73	#386×C₁₃₉	C₂²	1	4	yes	complemented
74	#386×C₁₃₉	C₂²	1	4	yes	complemented
75	#385×C₁₃₉	C₂²	1	1	yes	characteristic
76	#385×C₁₃₉	C₂²	1	4	yes	complemented
77	#385×C₁₃₉	C₂²	1	4	yes	complemented
78	#381×C₁₃₉	C₂²	1	1	yes	characteristic
79	#381×C₁₃₉	C₂²	1	2	yes	—
80	#380×C₁₃₉	C₂²	1	1	yes	characteristic
81	#379×C₁₃₉	C₂²	1	2	yes	—
82	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
83	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
84	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
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	8	no	—
92	C₂²×D₄×C₁₃₉	—	2	4	no	—
93	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
94	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
95	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
96	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
97	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
98	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
99	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
100	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
101	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
102	C₂³×C₄×C₁₃₉	—	2	8	no	—
103	C₂³×C₄×C₁₃₉	—	2	8	no	—
104	C₂³×C₄×C₁₃₉	—	4	4	no	—
105	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
107	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
108	C₂³×C₄×C₁₃₉	C₂³	1	4	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	1	yes	characteristic
114	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
115	#127×C₁₃₉	—	2	8	no	—
116	#123×C₁₃₉	—	2	8	no	—
117	#123×C₁₃₉	—	2	8	no	—
118	#123×C₁₃₉	—	2	8	no	—
119	#123×C₁₃₉	D₄	1	8	yes	complemented
120	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
121	C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
122	#121×C₁₃₉	—	2	8	no	—
123	#121×C₁₃₉	—	2	4	no	—
124	#121×C₁₃₉	—	2	4	no	—
125	#121×C₁₃₉	—	2	16	no	—
126	#120×C₁₃₉	—	2	8	no	—
127	#120×C₁₃₉	—	2	8	no	—
128	#120×C₁₃₉	—	4	4	no	—
129	C₄×D₄×C₁₃₉	—	2	4	no	—
130	C₄×D₄×C₁₃₉	—	2	8	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	16	no	—
135	C₄×D₄×C₁₃₉	—	2	16	no	—
136	#117×C₁₃₉	—	2	8	no	—
137	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
138	C₂×C₄⋊C₄×C₁₃₉	D₄	1	8	yes	complemented
139	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	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	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
151	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
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	1	yes	characteristic
157	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
158	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
159	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
160	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
162	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	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	4	yes	—
166	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	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	1	yes	characteristic
170	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
171	C₂×C₄²×C₁₃₉	—	2	4	no	—
172	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
173	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
174	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
175	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
177	#95×C₁₃₉	C₂³	1	4	yes	—
178	#95×C₁₃₉	C₂³	1	2	yes	—
179	#95×C₁₃₉	C₂³	1	2	yes	—
180	#95×C₁₃₉	C₂³	1	2	yes	—
181	#95×C₁₃₉	C₂³	1	2	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	C₂⁴×C₁₃₉	—	2	4	no	—
187	C₂⁴×C₁₃₉	—	2	8	no	—
188	C₂⁴×C₁₃₉	—	2	4	no	—
189	C₂⁴×C₁₃₉	—	2	4	no	—
190	C₂⁴×C₁₃₉	—	4	4	no	—
191	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
192	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
193	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
194	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
195	#41×C₁₃₉	—	4	32	no	—
196	C₂×Q₈×C₁₃₉	—	2	4	no	—
197	C₂×Q₈×C₁₃₉	—	2	4	no	—
198	C₂×Q₈×C₁₃₉	—	4	2	no	—
199	C₂×D₄×C₁₃₉	—	2	32	no	—
200	C₂×D₄×C₁₃₉	—	2	2	no	—
201	C₂×D₄×C₁₃₉	—	2	8	no	—
202	C₂×D₄×C₁₃₉	—	2	2	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	—	2	4	no	—
207	C₂×D₄×C₁₃₉	—	2	8	no	—
208	C₂×D₄×C₁₃₉	—	2	8	no	—
209	C₂×D₄×C₁₃₉	—	2	4	no	—
210	C₂×D₄×C₁₃₉	—	2	8	no	—
211	C₂×D₄×C₁₃₉	—	2	4	no	—
212	C₂×D₄×C₁₃₉	—	2	4	no	—
213	C₂×D₄×C₁₃₉	—	2	8	no	—
214	C₂×D₄×C₁₃₉	—	2	2	no	—
215	C₂×D₄×C₁₃₉	—	2	4	no	—
216	C₂×D₄×C₁₃₉	—	2	4	no	—
217	C₂×D₄×C₁₃₉	—	2	4	no	—
218	C₂×D₄×C₁₃₉	—	4	4	no	—
219	C₂×D₄×C₁₃₉	—	4	4	no	—
220	C₂×D₄×C₁₃₉	—	4	2	no	—
221	C₂×D₄×C₁₃₉	—	4	4	no	—
222	C₂×D₄×C₁₃₉	—	4	4	no	—
223	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
224	C₂×D₄×C₁₃₉	#41	1	8	yes	complemented
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	4	no	—
229	C₂²×C₄×C₁₃₉	—	2	4	no	—
230	C₂²×C₄×C₁₃₉	—	2	2	no	—
231	C₂²×C₄×C₁₃₉	—	2	4	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	8	no	—
236	C₂²×C₄×C₁₃₉	—	2	8	no	—
237	C₂²×C₄×C₁₃₉	—	2	4	no	—
238	C₂²×C₄×C₁₃₉	—	2	4	no	—
239	C₂²×C₄×C₁₃₉	—	2	8	no	—
240	C₂²×C₄×C₁₃₉	—	2	4	no	—
241	C₂²×C₄×C₁₃₉	—	4	4	no	—
242	C₂²×C₄×C₁₃₉	—	4	4	no	—
243	C₂²×C₄×C₁₃₉	—	4	2	no	—
244	C₂²×C₄×C₁₃₉	—	4	2	no	—
245	C₂²×C₄×C₁₃₉	—	4	2	no	—
246	C₂²×C₄×C₁₃₉	—	4	32	no	—
247	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
248	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
249	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
250	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
253	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
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	4	no	—
265	C₄⋊C₄×C₁₃₉	—	2	8	no	—
266	C₄⋊C₄×C₁₃₉	—	2	2	no	—
267	C₄⋊C₄×C₁₃₉	—	2	8	no	—
268	C₄⋊C₄×C₁₃₉	—	2	4	no	—
269	C₄⋊C₄×C₁₃₉	—	2	4	no	—
270	C₄⋊C₄×C₁₃₉	—	4	2	no	—
271	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
272	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
273	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
274	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	complemented
275	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
276	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
277	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
278	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
279	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
280	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
281	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
282	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
283	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
284	C₂²⋊C₄×C₁₃₉	—	2	2	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	—	4	4	no	—
289	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
290	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
291	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
292	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
293	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	complemented
294	C₄²×C₁₃₉	—	2	4	no	—
295	C₄²×C₁₃₉	—	2	4	no	—
296	C₄²×C₁₃₉	—	2	8	no	—
297	C₄²×C₁₃₉	—	2	2	no	—
298	C₄²×C₁₃₉	—	2	4	no	—
299	C₂³×C₁₃₉	—	2	2	no	—
300	C₂³×C₁₃₉	—	2	2	no	—
301	C₂³×C₁₃₉	—	2	16	no	—
302	C₂³×C₁₃₉	—	2	4	no	—
303	C₂³×C₁₃₉	—	2	4	no	—
304	C₂³×C₁₃₉	—	2	1	no	—
305	C₂³×C₁₃₉	—	2	2	no	—
306	C₂³×C₁₃₉	—	2	4	no	—
307	C₂³×C₁₃₉	—	2	4	no	—
308	C₂³×C₁₃₉	—	2	1	no	—
309	C₂³×C₁₃₉	—	2	2	no	—
310	C₂³×C₁₃₉	—	2	4	no	—
311	C₂³×C₁₃₉	—	2	4	no	—
312	C₂³×C₁₃₉	—	2	2	no	—
313	C₂³×C₁₃₉	—	2	2	no	—
314	C₂³×C₁₃₉	—	2	4	no	—
315	C₂³×C₁₃₉	—	2	2	no	—
316	C₂³×C₁₃₉	—	2	4	no	—
317	C₂³×C₁₃₉	—	4	16	no	—
318	C₂³×C₁₃₉	—	4	16	no	—
319	C₂³×C₁₃₉	—	4	8	no	—
320	C₂³×C₁₃₉	—	4	8	no	—
321	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
322	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
323	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
324	C₂³×C₁₃₉	C₂×#41	1	8	yes	—
325	C₂³×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
326	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
327	Q₈×C₁₃₉	—	4	8	no	—
328	D₄×C₁₃₉	—	2	16	no	—
329	D₄×C₁₃₉	—	2	8	no	—
330	D₄×C₁₃₉	—	2	16	no	—
331	D₄×C₁₃₉	—	4	16	no	—
332	D₄×C₁₃₉	—	4	8	no	—
333	D₄×C₁₃₉	—	4	16	no	—
334	D₄×C₁₃₉	—	4	8	no	—
335	D₄×C₁₃₉	—	4	4	no	—
336	D₄×C₁₃₉	—	8	8	no	—
337	C₂×C₄×C₁₃₉	—	2	8	no	—
338	C₂×C₄×C₁₃₉	—	2	16	no	—
339	C₂×C₄×C₁₃₉	—	2	2	no	—
340	C₂×C₄×C₁₃₉	—	2	2	no	—
341	C₂×C₄×C₁₃₉	—	2	1	no	—
342	C₂×C₄×C₁₃₉	—	2	2	no	—
343	C₂×C₄×C₁₃₉	—	2	2	no	—
344	C₂×C₄×C₁₃₉	—	2	2	no	—
345	C₂×C₄×C₁₃₉	—	2	2	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	2	no	—
350	C₂×C₄×C₁₃₉	—	2	8	no	—
351	C₂×C₄×C₁₃₉	—	2	2	no	—
352	C₂×C₄×C₁₃₉	—	2	1	no	—
353	C₂×C₄×C₁₃₉	—	2	4	no	—
354	C₂×C₄×C₁₃₉	—	2	1	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	4	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	2	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	—	4	16	no	—
368	C₂×C₄×C₁₃₉	—	4	16	no	—
369	C₂×C₄×C₁₃₉	—	4	8	no	—
370	C₂×C₄×C₁₃₉	—	4	8	no	—
371	C₂×C₄×C₁₃₉	—	4	4	no	—
372	C₂×C₄×C₁₃₉	—	4	4	no	—
373	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
374	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
375	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
376	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
377	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
378	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
379	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
380	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
381	C₂²×C₁₃₉	—	2	2	no	—
382	C₂²×C₁₃₉	—	2	4	no	—
383	C₂²×C₁₃₉	—	2	2	no	—
384	C₂²×C₁₃₉	—	2	4	no	—
385	C₂²×C₁₃₉	—	2	8	no	—
386	C₂²×C₁₃₉	—	2	2	no	—
387	C₂²×C₁₃₉	—	2	8	no	—
388	C₂²×C₁₃₉	—	2	4	no	—
389	C₂²×C₁₃₉	—	2	8	no	—
390	C₂²×C₁₃₉	—	4	32	no	—
391	C₂²×C₁₃₉	—	4	1	no	—
392	C₂²×C₁₃₉	—	4	4	no	—
393	C₂²×C₁₃₉	—	4	4	no	—
394	C₂²×C₁₃₉	—	4	1	no	—
395	C₂²×C₁₃₉	—	4	4	no	—
396	C₂²×C₁₃₉	—	4	2	no	—
397	C₂²×C₁₃₉	—	4	4	no	—
398	C₂²×C₁₃₉	—	4	2	no	—
399	C₂²×C₁₃₉	—	4	2	no	—
400	C₂²×C₁₃₉	—	4	4	no	—
401	C₂²×C₁₃₉	—	4	2	no	—
402	C₂²×C₁₃₉	—	4	4	no	—
403	C₂²×C₁₃₉	D₄²	1	4	yes	—
404	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
405	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
406	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
407	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
408	C₂²×C₁₃₉	#585	1	2	yes	—
409	C₄×C₁₃₉	—	2	2	no	—
410	C₄×C₁₃₉	—	2	4	no	—
411	C₄×C₁₃₉	—	2	4	no	—
412	C₄×C₁₃₉	—	2	4	no	—
413	C₄×C₁₃₉	—	2	2	no	—
414	C₄×C₁₃₉	—	2	4	no	—
415	C₄×C₁₃₉	—	4	1	no	—
416	C₄×C₁₃₉	—	4	2	no	—
417	C₄×C₁₃₉	—	4	4	no	—
418	C₄×C₁₃₉	—	4	1	no	—
419	C₄×C₁₃₉	—	4	2	no	—
420	C₄×C₁₃₉	—	4	2	no	—
421	C₄×C₁₃₉	#525	1	4	yes	complemented
422	C₂×C₁₃₉	—	2	4	no	—
423	C₂×C₁₃₉	—	4	2	no	—
424	C₂×C₁₃₉	—	4	8	no	—
425	C₂×C₁₃₉	—	8	2	no	—
426	C₂×C₁₃₉	C₂×#525	1	1	yes	characteristic
427	C₂×C₁₃₉	C₂×D₄²	1	1	yes	characteristic
428	C₂×C₁₃₉	D₄×#41	1	2	yes	—
429	C₂×C₁₃₉	#3487	1	1	yes	characteristic
430	C₂×C₁₃₉	#3513	1	2	yes	—
431	#36102	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
432	C₁₃₉	#36102	1	1	yes	characteristic, direct product factor, Sylow
433	C₂×#547	C₂×C₁₃₉	1	1	yes	characteristic, complemented
434	C₂×#525	C₂×C₁₃₉	1	2	yes	complemented
435	C₂²×C₄×D₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
436	#2854	C₂×C₁₃₉	1	1	yes	characteristic, complemented
437	#2849	C₂×C₁₃₉	1	2	yes	complemented
438	#2463	C₂×C₁₃₉	1	4	yes	complemented
439	#2456	C₂×C₁₃₉	1	4	yes	complemented
440	#2452	C₂×C₁₃₉	1	2	yes	complemented
441	#2433	C₂×C₁₃₉	1	1	yes	characteristic, complemented
442	#2428	C₂×C₁₃₉	1	2	yes	complemented
443	#2411	C₂×C₁₃₉	1	2	yes	complemented
444	#2408	C₂×C₁₃₉	1	1	yes	characteristic, complemented
445	#2404	C₂×C₁₃₉	1	2	yes	complemented
446	#2366	C₂×C₁₃₉	1	2	yes	complemented
447	#2361	C₂×C₁₃₉	1	2	yes	complemented
448	#2344	C₂×C₁₃₉	1	1	yes	characteristic, complemented
449	C₄×#123	C₂×C₁₃₉	1	1	yes	characteristic, complemented
450	C₂²×#41	C₂²×C₁₃₉	1	2	yes	—
451	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
452	C₂⁴×C₄	C₂²×C₁₃₉	1	2	yes	—
453	#547	—	2	8	no	—
454	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
455	C₂×#127	C₂²×C₁₃₉	1	2	yes	—
456	#525	—	2	16	no	—
457	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
458	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
459	C₂×#123	C₂²×C₁₃₉	1	1	yes	characteristic
460	C₂×#123	C₂²×C₁₃₉	1	2	yes	complemented
461	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	complemented
462	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	complemented
463	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
464	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
465	C₂×#121	C₂²×C₁₃₉	1	4	yes	complemented
466	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
467	C₂×#120	C₂²×C₁₃₉	1	2	yes	—
468	C₂×#120	C₂²×C₁₃₉	1	2	yes	—
469	C₂×#120	C₂²×C₁₃₉	1	2	yes	—
470	C₂×C₄×D₄	—	2	8	no	—
471	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
472	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
473	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	—
474	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
475	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	complemented
476	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
477	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	complemented
478	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
479	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
480	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
481	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
482	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
483	#396	C₂²×C₁₃₉	1	4	yes	complemented
484	#394	C₂²×C₁₃₉	1	2	yes	—
485	#394	C₂²×C₁₃₉	1	4	yes	complemented
486	#393	C₂²×C₁₃₉	1	4	yes	complemented
487	#392	C₂²×C₁₃₉	1	2	yes	—
488	#392	C₂²×C₁₃₉	1	4	yes	—
489	#392	C₂²×C₁₃₉	1	4	yes	complemented
490	#390	C₂²×C₁₃₉	1	2	yes	—
491	#390	C₂²×C₁₃₉	1	2	yes	—
492	#390	C₂²×C₁₃₉	1	2	yes	complemented
493	#390	C₂²×C₁₃₉	1	4	yes	complemented
494	#389	C₂²×C₁₃₉	1	2	yes	complemented
495	#389	C₂²×C₁₃₉	1	2	yes	complemented
496	#388	C₂²×C₁₃₉	1	4	yes	complemented
497	#388	C₂²×C₁₃₉	1	4	yes	complemented
498	#388	C₂²×C₁₃₉	1	2	yes	complemented
499	#387	C₂²×C₁₃₉	1	4	yes	complemented
500	#387	C₂²×C₁₃₉	1	2	yes	complemented
501	#386	C₂²×C₁₃₉	1	2	yes	—
502	#386	C₂²×C₁₃₉	1	1	yes	characteristic
503	#386	C₂²×C₁₃₉	1	4	yes	complemented
504	#386	C₂²×C₁₃₉	1	4	yes	complemented
505	#386	C₂²×C₁₃₉	1	4	yes	complemented
506	#386	C₂²×C₁₃₉	1	4	yes	complemented
507	#385	C₂²×C₁₃₉	1	1	yes	characteristic
508	#385	C₂²×C₁₃₉	1	4	yes	complemented
509	#385	C₂²×C₁₃₉	1	4	yes	complemented
510	#381	C₂²×C₁₃₉	1	1	yes	characteristic
511	#381	C₂²×C₁₃₉	1	2	yes	—
512	#380	C₂²×C₁₃₉	1	1	yes	characteristic
513	#379	C₂²×C₁₃₉	1	2	yes	—
514	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
515	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
516	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
517	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
518	C₂⁵	C₂³×C₁₃₉	1	2	yes	—
519	C₂×#41	—	2	8	no	—
520	C₂×#41	—	2	8	no	—
521	C₂×#41	—	4	4	no	—
522	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
523	C₂²×D₄	—	2	8	no	—
524	C₂²×D₄	—	2	4	no	—
525	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
526	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
527	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
528	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
529	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
530	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
531	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
532	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
533	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
534	C₂³×C₄	—	2	8	no	—
535	C₂³×C₄	—	2	8	no	—
536	C₂³×C₄	—	4	4	no	—
537	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
538	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
539	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
540	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
541	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
542	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
543	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
544	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
545	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
546	C₄⋊Q₈	—	2	4	no	—
547	#127	—	2	8	no	—
548	#123	—	2	8	no	—
549	#123	—	2	8	no	—
550	#123	—	2	8	no	—
551	#123	D₄×C₁₃₉	1	8	yes	complemented
552	C₂²⋊Q₈	—	2	8	no	—
553	C₂²⋊Q₈	—	2	16	no	—
554	#121	—	2	8	no	—
555	#121	—	2	4	no	—
556	#121	—	2	4	no	—
557	#121	—	2	16	no	—
558	#120	—	2	8	no	—
559	#120	—	2	8	no	—
560	#120	—	4	4	no	—
561	C₄×D₄	—	2	4	no	—
562	C₄×D₄	—	2	8	no	—
563	C₄×D₄	—	2	8	no	—
564	C₄×D₄	—	2	16	no	—
565	C₄×D₄	—	2	4	no	—
566	C₄×D₄	—	2	16	no	—
567	C₄×D₄	—	2	16	no	—
568	#117	—	2	8	no	—
569	C₂×C₄⋊C₄	—	2	4	no	—
570	C₂×C₄⋊C₄	D₄×C₁₃₉	1	8	yes	complemented
571	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
572	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
573	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
574	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
575	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
576	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
577	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
579	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
580	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
581	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
582	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
583	C₂×C₂²⋊C₄	—	2	8	no	—
584	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
586	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
588	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
589	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
590	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
594	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	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	2	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	1	yes	characteristic
602	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
603	C₂×C₄²	—	2	4	no	—
604	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
605	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
606	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
607	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
608	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
609	#95	C₂³×C₁₃₉	1	2	yes	—
610	#95	C₂³×C₁₃₉	1	2	yes	—
611	#95	C₂³×C₁₃₉	1	2	yes	—
612	#95	C₂³×C₁₃₉	1	2	yes	—
613	#95	C₂³×C₁₃₉	1	4	yes	—
614	#95	C₂³×C₁₃₉	1	2	yes	—
615	#95	C₂³×C₁₃₉	1	2	yes	—
616	#95	C₂³×C₁₃₉	1	4	yes	—
617	#95	C₂³×C₁₃₉	1	4	yes	—
618	C₂⁴	—	2	4	no	—
619	C₂⁴	—	2	8	no	—
620	C₂⁴	—	2	4	no	—
621	C₂⁴	—	2	4	no	—
622	C₂⁴	—	4	4	no	—
623	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
624	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
625	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
626	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
627	#41	—	4	32	no	—
628	C₂×Q₈	—	2	4	no	—
629	C₂×Q₈	—	2	4	no	—
630	C₂×Q₈	—	4	2	no	—
631	C₂×D₄	—	2	32	no	—
632	C₂×D₄	—	2	2	no	—
633	C₂×D₄	—	2	8	no	—
634	C₂×D₄	—	2	2	no	—
635	C₂×D₄	—	2	8	no	—
636	C₂×D₄	—	2	4	no	—
637	C₂×D₄	—	2	4	no	—
638	C₂×D₄	—	2	4	no	—
639	C₂×D₄	—	2	8	no	—
640	C₂×D₄	—	2	8	no	—
641	C₂×D₄	—	2	4	no	—
642	C₂×D₄	—	2	8	no	—
643	C₂×D₄	—	2	4	no	—
644	C₂×D₄	—	2	4	no	—
645	C₂×D₄	—	2	8	no	—
646	C₂×D₄	—	2	2	no	—
647	C₂×D₄	—	2	4	no	—
648	C₂×D₄	—	2	4	no	—
649	C₂×D₄	—	2	4	no	—
650	C₂×D₄	—	4	4	no	—
651	C₂×D₄	—	4	4	no	—
652	C₂×D₄	—	4	2	no	—
653	C₂×D₄	—	4	4	no	—
654	C₂×D₄	—	4	4	no	—
655	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
656	C₂×D₄	#41×C₁₃₉	1	8	yes	complemented
657	C₂²×C₄	—	2	2	no	—
658	C₂²×C₄	—	2	4	no	—
659	C₂²×C₄	—	2	2	no	—
660	C₂²×C₄	—	2	4	no	—
661	C₂²×C₄	—	2	4	no	—
662	C₂²×C₄	—	2	2	no	—
663	C₂²×C₄	—	2	4	no	—
664	C₂²×C₄	—	2	2	no	—
665	C₂²×C₄	—	2	4	no	—
666	C₂²×C₄	—	2	8	no	—
667	C₂²×C₄	—	2	8	no	—
668	C₂²×C₄	—	2	8	no	—
669	C₂²×C₄	—	2	4	no	—
670	C₂²×C₄	—	2	4	no	—
671	C₂²×C₄	—	2	8	no	—
672	C₂²×C₄	—	2	4	no	—
673	C₂²×C₄	—	4	4	no	—
674	C₂²×C₄	—	4	4	no	—
675	C₂²×C₄	—	4	2	no	—
676	C₂²×C₄	—	4	2	no	—
677	C₂²×C₄	—	4	2	no	—
678	C₂²×C₄	—	4	32	no	—
679	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
680	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
681	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
682	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
683	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
685	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
686	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
687	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
688	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
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	1	yes	characteristic
693	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
694	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
695	C₄⋊C₄	—	2	2	no	—
696	C₄⋊C₄	—	2	4	no	—
697	C₄⋊C₄	—	2	8	no	—
698	C₄⋊C₄	—	2	2	no	—
699	C₄⋊C₄	—	2	8	no	—
700	C₄⋊C₄	—	2	4	no	—
701	C₄⋊C₄	—	2	4	no	—
702	C₄⋊C₄	—	4	2	no	—
703	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
704	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
705	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
706	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	complemented
707	C₂²⋊C₄	—	2	4	no	—
708	C₂²⋊C₄	—	2	2	no	—
709	C₂²⋊C₄	—	2	8	no	—
710	C₂²⋊C₄	—	2	2	no	—
711	C₂²⋊C₄	—	2	8	no	—
712	C₂²⋊C₄	—	2	8	no	—
713	C₂²⋊C₄	—	2	8	no	—
714	C₂²⋊C₄	—	2	8	no	—
715	C₂²⋊C₄	—	2	8	no	—
716	C₂²⋊C₄	—	2	2	no	—
717	C₂²⋊C₄	—	2	4	no	—
718	C₂²⋊C₄	—	2	4	no	—
719	C₂²⋊C₄	—	2	4	no	—
720	C₂²⋊C₄	—	4	4	no	—
721	C₂²⋊C₄	—	4	4	no	—
722	C₂²⋊C₄	—	4	2	no	—
723	C₂²⋊C₄	—	4	4	no	—
724	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
725	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	complemented
726	C₄²	—	2	4	no	—
727	C₄²	—	2	4	no	—
728	C₄²	—	2	8	no	—
729	C₄²	—	2	2	no	—
730	C₄²	—	2	4	no	—
731	C₂³	—	2	2	no	—
732	C₂³	—	2	2	no	—
733	C₂³	—	2	16	no	—
734	C₂³	—	2	4	no	—
735	C₂³	—	2	4	no	—
736	C₂³	—	2	1	no	—
737	C₂³	—	2	2	no	—
738	C₂³	—	2	4	no	—
739	C₂³	—	2	4	no	—
740	C₂³	—	2	1	no	—
741	C₂³	—	2	2	no	—
742	C₂³	—	2	4	no	—
743	C₂³	—	2	4	no	—
744	C₂³	—	2	2	no	—
745	C₂³	—	2	2	no	—
746	C₂³	—	2	4	no	—
747	C₂³	—	2	2	no	—
748	C₂³	—	2	4	no	—
749	C₂³	—	4	16	no	—
750	C₂³	—	4	16	no	—
751	C₂³	—	4	8	no	—
752	C₂³	—	4	8	no	—
753	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
754	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
755	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
756	C₂³	C₂×#41×C₁₃₉	1	8	yes	—
757	C₂³	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
758	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
759	Q₈	—	4	8	no	—
760	D₄	—	2	16	no	—
761	D₄	—	2	8	no	—
762	D₄	—	2	16	no	—
763	D₄	—	4	8	no	—
764	D₄	—	4	16	no	—
765	D₄	—	4	16	no	—
766	D₄	—	4	8	no	—
767	D₄	—	4	4	no	—
768	D₄	—	8	8	no	—
769	C₂×C₄	—	2	8	no	—
770	C₂×C₄	—	2	16	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	1	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	8	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	4	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	4	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	4	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	4	16	no	—
800	C₂×C₄	—	4	16	no	—
801	C₂×C₄	—	4	8	no	—
802	C₂×C₄	—	4	8	no	—
803	C₂×C₄	—	4	4	no	—
804	C₂×C₄	—	4	4	no	—
805	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
806	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
807	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
808	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
809	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
810	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
811	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
812	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
813	C₂²	—	2	2	no	—
814	C₂²	—	2	4	no	—
815	C₂²	—	2	2	no	—
816	C₂²	—	2	4	no	—
817	C₂²	—	2	8	no	—
818	C₂²	—	2	2	no	—
819	C₂²	—	2	8	no	—
820	C₂²	—	2	4	no	—
821	C₂²	—	2	8	no	—
822	C₂²	—	4	32	no	—
823	C₂²	—	4	1	no	—
824	C₂²	—	4	4	no	—
825	C₂²	—	4	4	no	—
826	C₂²	—	4	4	no	—
827	C₂²	—	4	1	no	—
828	C₂²	—	4	4	no	—
829	C₂²	—	4	2	no	—
830	C₂²	—	4	2	no	—
831	C₂²	—	4	2	no	—
832	C₂²	—	4	4	no	—
833	C₂²	—	4	2	no	—
834	C₂²	—	4	4	no	—
835	C₂²	D₄²×C₁₃₉	1	4	yes	—
836	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
837	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
838	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
839	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
840	C₂²	#585×C₁₃₉	1	2	yes	—
841	C₄	—	2	2	no	—
842	C₄	—	2	4	no	—
843	C₄	—	2	4	no	—
844	C₄	—	2	4	no	—
845	C₄	—	2	2	no	—
846	C₄	—	2	4	no	—
847	C₄	—	4	1	no	—
848	C₄	—	4	2	no	—
849	C₄	—	4	4	no	—
850	C₄	—	4	2	no	—
851	C₄	—	4	1	no	—
852	C₄	—	4	2	no	—
853	C₄	#525×C₁₃₉	1	4	yes	complemented
854	C₂	—	2	4	no	—
855	C₂	—	4	8	no	—
856	C₂	—	4	2	no	—
857	C₂	—	8	2	no	—
858	C₂	C₂×#525×C₁₃₉	1	1	yes	characteristic
859	C₂	C₂×D₄²×C₁₃₉	1	1	yes	characteristic
860	C₂	D₄×#41×C₁₃₉	1	2	yes	—
861	C₂	#3487×C₁₃₉	1	1	yes	characteristic
862	C₂	#3513×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×#547×C₁₃₉	C₂	semidirect
2. C₂×#525×C₁₃₉	C₂	semidirect
3. C₂²×C₄×D₄×C₁₃₉	C₂	semidirect
4. #2854×C₁₃₉	C₂	semidirect
5. #2849×C₁₃₉	C₂	semidirect
6. #2463×C₁₃₉	C₂	semidirect
7. #2456×C₁₃₉	C₂	semidirect
8. #2452×C₁₃₉	C₂	semidirect
9. #2433×C₁₃₉	C₂	semidirect
10. #2428×C₁₃₉	C₂	semidirect
11. #2411×C₁₃₉	C₂	semidirect
12. #2408×C₁₃₉	C₂	semidirect
13. #2404×C₁₃₉	C₂	semidirect
14. #2366×C₁₃₉	C₂	semidirect
15. #2361×C₁₃₉	C₂	semidirect
16. #2344×C₁₃₉	C₂	semidirect
17. C₄×#123×C₁₃₉	C₂	semidirect
22. C₂×C₄⋊Q₈×C₁₃₉	C₂²	semidirect
28. C₂×#123×C₁₃₉	C₂²	semidirect
29. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
30. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
33. C₂×#121×C₁₃₉	C₂²	semidirect
34. C₂×#121×C₁₃₉	C₂²	semidirect
43. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
44. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
45. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
48. C₂²×C₄⋊C₄×C₁₃₉	C₂²	semidirect
51. #396×C₁₃₉	C₂²	semidirect
53. #394×C₁₃₉	C₂²	semidirect
54. #393×C₁₃₉	C₂²	semidirect
57. #392×C₁₃₉	C₂²	semidirect
60. #390×C₁₃₉	C₂²	semidirect
61. #390×C₁₃₉	C₂²	semidirect
62. #389×C₁₃₉	C₂²	semidirect
63. #389×C₁₃₉	C₂²	semidirect
64. #388×C₁₃₉	C₂²	semidirect
65. #388×C₁₃₉	C₂²	semidirect
66. #388×C₁₃₉	C₂²	semidirect
67. #387×C₁₃₉	C₂²	semidirect
68. #387×C₁₃₉	C₂²	semidirect
71. #386×C₁₃₉	C₂²	semidirect
72. #386×C₁₃₉	C₂²	semidirect
73. #386×C₁₃₉	C₂²	semidirect
74. #386×C₁₃₉	C₂²	semidirect
76. #385×C₁₃₉	C₂²	semidirect
77. #385×C₁₃₉	C₂²	semidirect
82. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
83. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
85. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
119. #123×C₁₃₉	D₄	semidirect
138. C₂×C₄⋊C₄×C₁₃₉	D₄	semidirect
224. C₂×D₄×C₁₃₉	#41	semidirect
274. C₄⋊C₄×C₁₃₉	C₂×D₄	semidirect
293. C₂²⋊C₄×C₁₃₉	C₂×D₄	semidirect
421. C₄×C₁₃₉	#525	semidirect
431. #36102	C₁₃₉	direct (N × H)
432. C₁₃₉	#36102	direct (N × H)
433. C₂×#547	C₂×C₁₃₉	semidirect
434. C₂×#525	C₂×C₁₃₉	semidirect
435. C₂²×C₄×D₄	C₂×C₁₃₉	semidirect
436. #2854	C₂×C₁₃₉	semidirect
437. #2849	C₂×C₁₃₉	semidirect
438. #2463	C₂×C₁₃₉	semidirect
439. #2456	C₂×C₁₃₉	semidirect
440. #2452	C₂×C₁₃₉	semidirect
441. #2433	C₂×C₁₃₉	semidirect
442. #2428	C₂×C₁₃₉	semidirect
443. #2411	C₂×C₁₃₉	semidirect
444. #2408	C₂×C₁₃₉	semidirect
445. #2404	C₂×C₁₃₉	semidirect
446. #2366	C₂×C₁₃₉	semidirect
447. #2361	C₂×C₁₃₉	semidirect
448. #2344	C₂×C₁₃₉	semidirect
449. C₄×#123	C₂×C₁₃₉	semidirect
454. C₂×C₄⋊Q₈	C₂²×C₁₃₉	semidirect
460. C₂×#123	C₂²×C₁₃₉	semidirect
461. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
462. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
465. C₂×#121	C₂²×C₁₃₉	semidirect
466. C₂×#121	C₂²×C₁₃₉	semidirect
475. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
476. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
477. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
480. C₂²×C₄⋊C₄	C₂²×C₁₃₉	semidirect
483. #396	C₂²×C₁₃₉	semidirect
485. #394	C₂²×C₁₃₉	semidirect
486. #393	C₂²×C₁₃₉	semidirect
489. #392	C₂²×C₁₃₉	semidirect
492. #390	C₂²×C₁₃₉	semidirect
493. #390	C₂²×C₁₃₉	semidirect
494. #389	C₂²×C₁₃₉	semidirect
495. #389	C₂²×C₁₃₉	semidirect
496. #388	C₂²×C₁₃₉	semidirect
497. #388	C₂²×C₁₃₉	semidirect
498. #388	C₂²×C₁₃₉	semidirect
499. #387	C₂²×C₁₃₉	semidirect
500. #387	C₂²×C₁₃₉	semidirect
503. #386	C₂²×C₁₃₉	semidirect
504. #386	C₂²×C₁₃₉	semidirect
505. #386	C₂²×C₁₃₉	semidirect
506. #386	C₂²×C₁₃₉	semidirect
508. #385	C₂²×C₁₃₉	semidirect
509. #385	C₂²×C₁₃₉	semidirect
514. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
515. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
517. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
551. #123	D₄×C₁₃₉	semidirect
570. C₂×C₄⋊C₄	D₄×C₁₃₉	semidirect
656. C₂×D₄	#41×C₁₃₉	semidirect
706. C₄⋊C₄	C₂×D₄×C₁₃₉	semidirect
725. C₂²⋊C₄	C₂×D₄×C₁₃₉	semidirect
853. 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
#2854×C₁₃₉	2
#2849×C₁₃₉	2
#2463×C₁₃₉	2
#2456×C₁₃₉	2
#2452×C₁₃₉	2
#2433×C₁₃₉	2
#2428×C₁₃₉	2
#2411×C₁₃₉	2
#2408×C₁₃₉	2
#2404×C₁₃₉	2
#2366×C₁₃₉	2
#2361×C₁₃₉	2
#2344×C₁₃₉	2
C₄×#123×C₁₃₉	2
#36102	139

Subgroups — C139×#36102 #48030698

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36102 #48030698