Subgroups — C₁₃₉×#35776 #48030372

Order 35584.

2662 conjugacy classes of subgroups.

The subgroup lattice has 1110 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#554×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#518×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2629×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2626×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2579×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2566×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2538×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2454×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#2452×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#2450×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2449×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2441×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#2439×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2437×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2437×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2417×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	#2396×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#396×C₁₃₉	C₂	1	2	yes	maximal, complemented
19	#2349×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	D₄×C₄⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
21	D₄×C₄⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
22	D₄×C₂²⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic
23	D₄×C₂²⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic
24	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
25	#554×C₁₃₉	—	2	8	no	—
26	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
27	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
28	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	complemented
30	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	complemented
31	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	complemented
32	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	complemented
33	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	complemented
34	#518×C₁₃₉	—	2	8	no	—
35	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
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	1	yes	characteristic
39	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
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
46	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
47	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
48	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
49	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
50	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
51	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
52	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
53	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
54	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
55	#400×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
56	#399×C₁₃₉	C₂²	1	2	yes	—
57	#399×C₁₃₉	C₂²	1	1	yes	characteristic
58	#399×C₁₃₉	C₂²	1	2	yes	complemented
59	#398×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
60	#398×C₁₃₉	C₂²	1	2	yes	complemented
61	#398×C₁₃₉	C₂²	1	2	yes	complemented
62	#398×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
63	#396×C₁₃₉	C₂²	1	1	yes	characteristic
64	#396×C₁₃₉	C₂²	1	2	yes	—
65	#396×C₁₃₉	C₂²	1	2	yes	—
66	#396×C₁₃₉	C₂²	1	1	yes	characteristic
67	#396×C₁₃₉	C₂²	1	2	yes	—
68	#396×C₁₃₉	C₂²	1	2	yes	—
69	#396×C₁₃₉	C₂²	1	2	yes	complemented
70	#396×C₁₃₉	C₂²	1	2	yes	complemented
71	#396×C₁₃₉	C₂²	1	2	yes	complemented
72	#396×C₁₃₉	C₂²	1	2	yes	complemented
73	#396×C₁₃₉	C₂²	1	2	yes	complemented
74	#396×C₁₃₉	C₂²	1	2	yes	complemented
75	#395×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
76	#393×C₁₃₉	C₂²	1	2	yes	—
77	#393×C₁₃₉	C₂²	1	1	yes	characteristic
78	#393×C₁₃₉	C₂²	1	2	yes	complemented
79	#391×C₁₃₉	C₂²	1	2	yes	complemented
80	#390×C₁₃₉	C₂²	1	1	yes	characteristic
81	#390×C₁₃₉	C₂²	1	1	yes	characteristic
82	#390×C₁₃₉	C₂²	1	1	yes	characteristic
83	#390×C₁₃₉	C₂²	1	1	yes	characteristic
84	#389×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
85	#389×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
86	#389×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
87	#389×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
88	#389×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
89	#389×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
90	#389×C₁₃₉	C₂²	1	2	yes	complemented
91	#387×C₁₃₉	C₂²	1	2	yes	complemented
92	#387×C₁₃₉	C₂²	1	2	yes	complemented
93	#386×C₁₃₉	C₂²	1	2	yes	—
94	#386×C₁₃₉	C₂²	1	2	yes	—
95	#386×C₁₃₉	C₂²	1	2	yes	—
96	#386×C₁₃₉	C₂²	1	2	yes	—
97	#385×C₁₃₉	C₂²	1	2	yes	complemented
98	#385×C₁₃₉	C₂²	1	2	yes	complemented
99	#385×C₁₃₉	C₂²	1	2	yes	complemented
100	#385×C₁₃₉	C₂²	1	2	yes	complemented
101	#385×C₁₃₉	C₂²	1	2	yes	complemented
102	#385×C₁₃₉	C₂²	1	2	yes	complemented
103	#385×C₁₃₉	C₂²	1	2	yes	complemented
104	#385×C₁₃₉	C₂²	1	2	yes	complemented
105	#385×C₁₃₉	C₂²	1	2	yes	complemented
106	#385×C₁₃₉	C₂²	1	2	yes	complemented
107	#384×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
108	#384×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
109	#382×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
110	#380×C₁₃₉	C₂²	1	1	yes	characteristic
111	#380×C₁₃₉	C₂²	1	1	yes	characteristic
112	#380×C₁₃₉	C₂²	1	2	yes	complemented
113	#380×C₁₃₉	C₂²	1	2	yes	complemented
114	#380×C₁₃₉	C₂²	1	2	yes	complemented
115	#380×C₁₃₉	C₂²	1	2	yes	complemented
116	#380×C₁₃₉	C₂²	1	2	yes	complemented
117	#379×C₁₃₉	C₂²	1	2	yes	—
118	#379×C₁₃₉	C₂²	1	2	yes	—
119	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
120	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
121	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
122	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
123	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
124	C₂×#95×C₁₃₉	C₂²	1	2	yes	complemented
125	C₂⁵×C₁₃₉	C₂³	1	2	yes	—
126	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
127	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
128	C₂²×D₄×C₁₃₉	—	2	4	no	—
129	C₂²×D₄×C₁₃₉	—	2	4	no	—
130	C₂²×D₄×C₁₃₉	Q₈	1	8	yes	complemented
131	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
132	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
133	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
135	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
136	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
137	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
138	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
139	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
140	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
141	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
142	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
143	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
144	#125×C₁₃₉	—	2	4	no	—
145	#125×C₁₃₉	—	2	4	no	—
146	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
147	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
148	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
149	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
150	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
151	C₄×Q₈×C₁₃₉	—	2	4	no	—
152	C₄×D₄×C₁₃₉	—	2	4	no	—
153	C₄×D₄×C₁₃₉	—	2	4	no	—
154	C₄×D₄×C₁₃₉	—	2	4	no	—
155	C₄×D₄×C₁₃₉	—	2	4	no	—
156	C₄×D₄×C₁₃₉	—	2	4	no	—
157	C₄×D₄×C₁₃₉	—	2	8	no	—
158	C₄×D₄×C₁₃₉	—	2	4	no	—
159	C₄×D₄×C₁₃₉	—	2	8	no	—
160	C₄×D₄×C₁₃₉	—	2	4	no	—
161	C₄×D₄×C₁₃₉	D₄	1	8	yes	—
162	#117×C₁₃₉	—	2	4	no	—
163	#117×C₁₃₉	—	2	4	no	—
164	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
165	C₂×C₄⋊C₄×C₁₃₉	—	4	4	no	—
166	C₂×C₄⋊C₄×C₁₃₉	—	4	4	no	—
167	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
168	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
169	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
170	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
171	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
173	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
175	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
176	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
180	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
181	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
182	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
183	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
185	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
186	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
187	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
188	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
189	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
190	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
191	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
192	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
194	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
195	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
196	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
197	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
198	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
199	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
200	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
201	C₂×C₂²⋊C₄×C₁₃₉	—	4	4	no	—
202	C₂×C₂²⋊C₄×C₁₃₉	—	4	4	no	—
203	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
208	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
209	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
210	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
211	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
212	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
214	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
215	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
216	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
217	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
218	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
219	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
220	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
221	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
222	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
223	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
224	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
225	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
226	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
227	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
228	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
229	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
230	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
231	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
233	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
235	#95×C₁₃₉	C₂³	1	1	yes	characteristic
236	#95×C₁₃₉	C₂³	1	1	yes	characteristic
237	#95×C₁₃₉	C₂³	1	1	yes	characteristic
238	#95×C₁₃₉	C₂³	1	1	yes	characteristic
239	#95×C₁₃₉	C₂³	1	2	yes	—
240	#95×C₁₃₉	C₂³	1	2	yes	—
241	#95×C₁₃₉	C₂³	1	2	yes	—
242	#95×C₁₃₉	C₂³	1	2	yes	—
243	#95×C₁₃₉	C₂³	1	1	yes	characteristic
244	#95×C₁₃₉	C₂³	1	2	yes	—
245	#95×C₁₃₉	C₂³	1	2	yes	—
246	#95×C₁₃₉	C₂³	1	2	yes	—
247	#95×C₁₃₉	C₂³	1	2	yes	—
248	#95×C₁₃₉	C₂³	1	1	yes	characteristic
249	#95×C₁₃₉	C₂³	1	1	yes	characteristic
250	#95×C₁₃₉	C₂³	1	1	yes	characteristic
251	#95×C₁₃₉	C₂³	1	1	yes	characteristic
252	#95×C₁₃₉	C₂³	1	2	yes	—
253	#95×C₁₃₉	C₂³	1	2	yes	—
254	#95×C₁₃₉	C₂³	1	1	yes	characteristic
255	C₂⁴×C₁₃₉	—	2	4	no	—
256	C₂⁴×C₁₃₉	—	2	4	no	—
257	C₂⁴×C₁₃₉	—	4	2	no	—
258	C₂⁴×C₁₃₉	—	4	2	no	—
259	C₂⁴×C₁₃₉	—	4	2	no	—
260	C₂⁴×C₁₃₉	—	4	2	no	—
261	C₂⁴×C₁₃₉	C₂×Q₈	1	8	yes	—
262	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
263	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
264	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
265	C₂×Q₈×C₁₃₉	—	2	2	no	—
266	C₂×Q₈×C₁₃₉	—	2	4	no	—
267	C₂×Q₈×C₁₃₉	—	2	2	no	—
268	C₂×Q₈×C₁₃₉	—	4	1	no	—
269	C₂×Q₈×C₁₃₉	—	4	2	no	—
270	C₂×Q₈×C₁₃₉	—	4	2	no	—
271	C₂×D₄×C₁₃₉	—	2	4	no	—
272	C₂×D₄×C₁₃₉	—	2	4	no	—
273	C₂×D₄×C₁₃₉	—	2	32	no	—
274	C₂×D₄×C₁₃₉	—	2	2	no	—
275	C₂×D₄×C₁₃₉	—	2	2	no	—
276	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
277	C₂×D₄×C₁₃₉	C₂×Q₈	1	8	yes	—
278	C₂×D₄×C₁₃₉	C₂×Q₈	1	4	yes	—
279	C₂×D₄×C₁₃₉	C₂×Q₈	1	4	yes	—
280	C₂×D₄×C₁₃₉	#41	1	4	yes	—
281	C₂²×C₄×C₁₃₉	—	2	2	no	—
282	C₂²×C₄×C₁₃₉	—	2	2	no	—
283	C₂²×C₄×C₁₃₉	—	2	4	no	—
284	C₂²×C₄×C₁₃₉	—	2	4	no	—
285	C₂²×C₄×C₁₃₉	—	2	4	no	—
286	C₂²×C₄×C₁₃₉	—	2	4	no	—
287	C₂²×C₄×C₁₃₉	—	2	4	no	—
288	C₂²×C₄×C₁₃₉	—	2	4	no	—
289	C₂²×C₄×C₁₃₉	—	2	4	no	—
290	C₂²×C₄×C₁₃₉	—	2	4	no	—
291	C₂²×C₄×C₁₃₉	—	2	4	no	—
292	C₂²×C₄×C₁₃₉	—	4	2	no	—
293	C₂²×C₄×C₁₃₉	—	4	2	no	—
294	C₂²×C₄×C₁₃₉	—	4	2	no	—
295	C₂²×C₄×C₁₃₉	—	4	2	no	—
296	C₂²×C₄×C₁₃₉	—	4	2	no	—
297	C₂²×C₄×C₁₃₉	—	4	2	no	—
298	C₂²×C₄×C₁₃₉	—	4	2	no	—
299	C₂²×C₄×C₁₃₉	—	4	2	no	—
300	C₂²×C₄×C₁₃₉	—	4	2	no	—
301	C₂²×C₄×C₁₃₉	—	4	2	no	—
302	C₂²×C₄×C₁₃₉	—	4	2	no	—
303	C₂²×C₄×C₁₃₉	—	4	2	no	—
304	C₂²×C₄×C₁₃₉	—	4	2	no	—
305	C₂²×C₄×C₁₃₉	—	4	2	no	—
306	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
307	C₂²×C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
308	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
313	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
314	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
316	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
317	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
318	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
319	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
321	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
322	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
323	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
327	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
328	C₄⋊C₄×C₁₃₉	—	2	2	no	—
329	C₄⋊C₄×C₁₃₉	—	2	4	no	—
330	C₄⋊C₄×C₁₃₉	—	2	4	no	—
331	C₄⋊C₄×C₁₃₉	—	2	4	no	—
332	C₄⋊C₄×C₁₃₉	—	2	2	no	—
333	C₄⋊C₄×C₁₃₉	—	2	2	no	—
334	C₄⋊C₄×C₁₃₉	—	2	2	no	—
335	C₄⋊C₄×C₁₃₉	—	2	2	no	—
336	C₄⋊C₄×C₁₃₉	—	2	2	no	—
337	C₄⋊C₄×C₁₃₉	—	2	2	no	—
338	C₄⋊C₄×C₁₃₉	—	2	2	no	—
339	C₄⋊C₄×C₁₃₉	—	2	4	no	—
340	C₄⋊C₄×C₁₃₉	—	2	4	no	—
341	C₄⋊C₄×C₁₃₉	—	2	2	no	—
342	C₄⋊C₄×C₁₃₉	—	2	2	no	—
343	C₄⋊C₄×C₁₃₉	—	2	2	no	—
344	C₄⋊C₄×C₁₃₉	—	2	2	no	—
345	C₄⋊C₄×C₁₃₉	—	2	4	no	—
346	C₄⋊C₄×C₁₃₉	—	2	4	no	—
347	C₄⋊C₄×C₁₃₉	—	2	2	no	—
348	C₄⋊C₄×C₁₃₉	—	4	2	no	—
349	C₄⋊C₄×C₁₃₉	—	4	2	no	—
350	C₄⋊C₄×C₁₃₉	—	4	2	no	—
351	C₄⋊C₄×C₁₃₉	—	4	2	no	—
352	C₄⋊C₄×C₁₃₉	—	4	1	no	—
353	C₄⋊C₄×C₁₃₉	—	4	1	no	—
354	C₄⋊C₄×C₁₃₉	—	4	2	no	—
355	C₄⋊C₄×C₁₃₉	—	4	1	no	—
356	C₄⋊C₄×C₁₃₉	—	4	2	no	—
357	C₄⋊C₄×C₁₃₉	—	4	2	no	—
358	C₄⋊C₄×C₁₃₉	—	4	2	no	—
359	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
360	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
361	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
362	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
363	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
364	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
365	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
366	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
367	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
368	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
369	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
370	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
371	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
372	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
373	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
374	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
375	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
376	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
377	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
378	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
379	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
380	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
381	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
382	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
383	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
384	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
385	C₄²×C₁₃₉	—	2	4	no	—
386	C₄²×C₁₃₉	—	2	2	no	—
387	C₄²×C₁₃₉	—	2	2	no	—
388	C₄²×C₁₃₉	—	2	2	no	—
389	C₄²×C₁₃₉	—	2	2	no	—
390	C₄²×C₁₃₉	—	2	2	no	—
391	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
392	C₂³×C₁₃₉	—	2	2	no	—
393	C₂³×C₁₃₉	—	2	2	no	—
394	C₂³×C₁₃₉	—	2	2	no	—
395	C₂³×C₁₃₉	—	2	2	no	—
396	C₂³×C₁₃₉	—	2	1	no	—
397	C₂³×C₁₃₉	—	2	2	no	—
398	C₂³×C₁₃₉	—	2	1	no	—
399	C₂³×C₁₃₉	—	2	2	no	—
400	C₂³×C₁₃₉	—	2	2	no	—
401	C₂³×C₁₃₉	—	2	2	no	—
402	C₂³×C₁₃₉	—	2	1	no	—
403	C₂³×C₁₃₉	—	2	1	no	—
404	C₂³×C₁₃₉	—	2	2	no	—
405	C₂³×C₁₃₉	—	2	2	no	—
406	C₂³×C₁₃₉	—	2	1	no	—
407	C₂³×C₁₃₉	—	2	1	no	—
408	C₂³×C₁₃₉	—	2	16	no	—
409	C₂³×C₁₃₉	—	4	8	no	—
410	C₂³×C₁₃₉	—	4	8	no	—
411	C₂³×C₁₃₉	—	8	4	no	—
412	C₂³×C₁₃₉	—	8	4	no	—
413	C₂³×C₁₃₉	—	8	4	no	—
414	C₂³×C₁₃₉	—	8	4	no	—
415	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
416	C₂³×C₁₃₉	C₂²×Q₈	1	2	yes	—
417	C₂³×C₁₃₉	C₂²×Q₈	1	4	yes	—
418	C₂³×C₁₃₉	C₂²×Q₈	1	4	yes	—
419	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
420	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
421	Q₈×C₁₃₉	—	4	4	no	—
422	Q₈×C₁₃₉	—	8	4	no	—
423	D₄×C₁₃₉	—	2	16	no	—
424	D₄×C₁₃₉	—	2	8	no	—
425	D₄×C₁₃₉	C₂²⋊Q₈	1	16	yes	complemented
426	C₂×C₄×C₁₃₉	—	2	1	no	—
427	C₂×C₄×C₁₃₉	—	2	1	no	—
428	C₂×C₄×C₁₃₉	—	2	1	no	—
429	C₂×C₄×C₁₃₉	—	2	1	no	—
430	C₂×C₄×C₁₃₉	—	2	1	no	—
431	C₂×C₄×C₁₃₉	—	2	1	no	—
432	C₂×C₄×C₁₃₉	—	2	2	no	—
433	C₂×C₄×C₁₃₉	—	2	1	no	—
434	C₂×C₄×C₁₃₉	—	2	1	no	—
435	C₂×C₄×C₁₃₉	—	2	1	no	—
436	C₂×C₄×C₁₃₉	—	2	1	no	—
437	C₂×C₄×C₁₃₉	—	2	2	no	—
438	C₂×C₄×C₁₃₉	—	2	8	no	—
439	C₂×C₄×C₁₃₉	—	2	2	no	—
440	C₂×C₄×C₁₃₉	—	2	1	no	—
441	C₂×C₄×C₁₃₉	—	2	1	no	—
442	C₂×C₄×C₁₃₉	—	2	1	no	—
443	C₂×C₄×C₁₃₉	—	2	1	no	—
444	C₂×C₄×C₁₃₉	—	2	1	no	—
445	C₂×C₄×C₁₃₉	—	2	2	no	—
446	C₂×C₄×C₁₃₉	—	2	2	no	—
447	C₂×C₄×C₁₃₉	—	2	1	no	—
448	C₂×C₄×C₁₃₉	—	2	1	no	—
449	C₂×C₄×C₁₃₉	—	2	1	no	—
450	C₂×C₄×C₁₃₉	—	2	2	no	—
451	C₂×C₄×C₁₃₉	—	2	2	no	—
452	C₂×C₄×C₁₃₉	—	2	1	no	—
453	C₂×C₄×C₁₃₉	—	2	1	no	—
454	C₂×C₄×C₁₃₉	—	2	2	no	—
455	C₂×C₄×C₁₃₉	—	2	2	no	—
456	C₂×C₄×C₁₃₉	—	2	1	no	—
457	C₂×C₄×C₁₃₉	—	2	2	no	—
458	C₂×C₄×C₁₃₉	—	2	2	no	—
459	C₂×C₄×C₁₃₉	—	2	1	no	—
460	C₂×C₄×C₁₃₉	—	2	2	no	—
461	C₂×C₄×C₁₃₉	—	2	2	no	—
462	C₂×C₄×C₁₃₉	—	2	1	no	—
463	C₂×C₄×C₁₃₉	—	2	2	no	—
464	C₂×C₄×C₁₃₉	—	2	1	no	—
465	C₂×C₄×C₁₃₉	—	2	1	no	—
466	C₂×C₄×C₁₃₉	—	2	1	no	—
467	C₂×C₄×C₁₃₉	—	2	1	no	—
468	C₂×C₄×C₁₃₉	—	2	1	no	—
469	C₂×C₄×C₁₃₉	—	2	1	no	—
470	C₂×C₄×C₁₃₉	—	2	2	no	—
471	C₂×C₄×C₁₃₉	—	2	1	no	—
472	C₂×C₄×C₁₃₉	—	2	2	no	—
473	C₂×C₄×C₁₃₉	—	2	1	no	—
474	C₂×C₄×C₁₃₉	—	2	2	no	—
475	C₂×C₄×C₁₃₉	—	2	1	no	—
476	C₂×C₄×C₁₃₉	—	2	1	no	—
477	C₂×C₄×C₁₃₉	—	2	1	no	—
478	C₂×C₄×C₁₃₉	—	4	8	no	—
479	C₂×C₄×C₁₃₉	—	4	8	no	—
480	C₂×C₄×C₁₃₉	—	4	8	no	—
481	C₂×C₄×C₁₃₉	—	8	4	no	—
482	C₂×C₄×C₁₃₉	—	8	4	no	—
483	C₂×C₄×C₁₃₉	—	8	4	no	—
484	C₂×C₄×C₁₃₉	—	8	4	no	—
485	C₂×C₄×C₁₃₉	—	8	4	no	—
486	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
487	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
488	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
489	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
490	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
491	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
492	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
493	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
494	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
495	C₂²×C₁₃₉	—	2	4	no	—
496	C₂²×C₁₃₉	—	2	4	no	—
497	C₂²×C₁₃₉	—	2	4	no	—
498	C₂²×C₁₃₉	—	2	4	no	—
499	C₂²×C₁₃₉	—	2	4	no	—
500	C₂²×C₁₃₉	—	2	4	no	—
501	C₂²×C₁₃₉	—	2	2	no	—
502	C₂²×C₁₃₉	—	2	4	no	—
503	C₂²×C₁₃₉	—	2	2	no	—
504	C₂²×C₁₃₉	—	2	2	no	—
505	C₂²×C₁₃₉	—	2	4	no	—
506	C₂²×C₁₃₉	—	2	4	no	—
507	C₂²×C₁₃₉	—	4	2	no	—
508	C₂²×C₁₃₉	—	4	1	no	—
509	C₂²×C₁₃₉	—	4	2	no	—
510	C₂²×C₁₃₉	—	4	1	no	—
511	C₂²×C₁₃₉	—	4	2	no	—
512	C₂²×C₁₃₉	—	4	1	no	—
513	C₂²×C₁₃₉	—	4	2	no	—
514	C₂²×C₁₃₉	—	4	1	no	—
515	C₂²×C₁₃₉	—	8	16	no	—
516	C₂²×C₁₃₉	C₂×C₂²⋊Q₈	1	8	yes	—
517	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
518	C₂²×C₁₃₉	C₂³×Q₈	1	1	yes	characteristic
519	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
520	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
521	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
522	C₂²×C₁₃₉	#585	1	1	yes	characteristic
523	C₂²×C₁₃₉	#585	1	1	yes	characteristic
524	C₄×C₁₃₉	—	2	2	no	—
525	C₄×C₁₃₉	—	2	2	no	—
526	C₄×C₁₃₉	—	2	2	no	—
527	C₄×C₁₃₉	—	2	2	no	—
528	C₄×C₁₃₉	—	2	4	no	—
529	C₄×C₁₃₉	—	2	2	no	—
530	C₄×C₁₃₉	—	4	2	no	—
531	C₄×C₁₃₉	—	4	2	no	—
532	C₄×C₁₃₉	—	4	1	no	—
533	C₄×C₁₃₉	—	4	1	no	—
534	C₄×C₁₃₉	—	4	1	no	—
535	C₄×C₁₃₉	—	4	1	no	—
536	C₄×C₁₃₉	—	4	2	no	—
537	C₄×C₁₃₉	—	4	1	no	—
538	C₄×C₁₃₉	—	4	2	no	—
539	C₄×C₁₃₉	—	4	2	no	—
540	C₄×C₁₃₉	—	4	1	no	—
541	C₄×C₁₃₉	—	4	1	no	—
542	C₄×C₁₃₉	—	4	1	no	—
543	C₄×C₁₃₉	C₂×C₂²⋊Q₈	1	4	yes	—
544	C₂×C₁₃₉	—	2	8	no	—
545	C₂×C₁₃₉	—	4	4	no	—
546	C₂×C₁₃₉	—	4	2	no	—
547	C₂×C₁₃₉	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
548	C₂×C₁₃₉	#3488	1	1	yes	characteristic
549	C₂×C₁₃₉	#3496	1	1	yes	characteristic
550	C₂×C₁₃₉	#3501	1	1	yes	characteristic
551	C₂×C₁₃₉	#3501	1	1	yes	characteristic
552	C₂×C₁₃₉	#3519	1	1	yes	characteristic
553	C₂×C₁₃₉	#3521	1	1	yes	characteristic
554	#35776	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
555	C₁₃₉	#35776	1	1	yes	characteristic, direct product factor, Sylow
556	C₂×#554	C₂×C₁₃₉	1	1	yes	characteristic, complemented
557	C₂×#518	C₂×C₁₃₉	1	1	yes	characteristic
558	#2629	C₂×C₁₃₉	1	1	yes	characteristic, complemented
559	#2626	C₂×C₁₃₉	1	2	yes	complemented
560	#2579	C₂×C₁₃₉	1	2	yes	complemented
561	#2566	C₂×C₁₃₉	1	1	yes	characteristic, complemented
562	#2538	C₂×C₁₃₉	1	1	yes	characteristic, complemented
563	#2454	C₂×C₁₃₉	1	1	yes	characteristic, complemented
564	#2452	C₂×C₁₃₉	1	1	yes	characteristic, complemented
565	#2450	C₂×C₁₃₉	1	2	yes	complemented
566	#2449	C₂×C₁₃₉	1	2	yes	complemented
567	#2441	C₂×C₁₃₉	1	1	yes	characteristic, complemented
568	#2439	C₂×C₁₃₉	1	1	yes	characteristic, complemented
569	#2437	C₂×C₁₃₉	1	2	yes	complemented
570	#2437	C₂×C₁₃₉	1	2	yes	complemented
571	#2417	C₂×C₁₃₉	1	2	yes	complemented
572	#2396	C₂×C₁₃₉	1	1	yes	characteristic, complemented
573	C₂×#396	C₂×C₁₃₉	1	2	yes	complemented
574	#2349	C₂×C₁₃₉	1	1	yes	characteristic, complemented
575	D₄×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
576	D₄×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
577	D₄×C₂²⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic
578	D₄×C₂²⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic
579	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
580	#554	—	2	8	no	—
581	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
582	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
583	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
584	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	complemented
585	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	complemented
586	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	complemented
587	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	complemented
588	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	complemented
589	#518	—	2	8	no	—
590	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
591	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
592	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
593	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
594	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
595	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
596	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
597	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
598	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
599	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
600	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
601	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
602	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
603	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
604	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
605	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
606	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
607	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
608	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
609	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
610	#400	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
611	#399	C₂²×C₁₃₉	1	2	yes	—
612	#399	C₂²×C₁₃₉	1	1	yes	characteristic
613	#399	C₂²×C₁₃₉	1	2	yes	complemented
614	#398	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
615	#398	C₂²×C₁₃₉	1	2	yes	complemented
616	#398	C₂²×C₁₃₉	1	2	yes	complemented
617	#398	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
618	#396	C₂²×C₁₃₉	1	1	yes	characteristic
619	#396	C₂²×C₁₃₉	1	2	yes	—
620	#396	C₂²×C₁₃₉	1	2	yes	—
621	#396	C₂²×C₁₃₉	1	1	yes	characteristic
622	#396	C₂²×C₁₃₉	1	2	yes	—
623	#396	C₂²×C₁₃₉	1	2	yes	—
624	#396	C₂²×C₁₃₉	1	2	yes	complemented
625	#396	C₂²×C₁₃₉	1	2	yes	complemented
626	#396	C₂²×C₁₃₉	1	2	yes	complemented
627	#396	C₂²×C₁₃₉	1	2	yes	complemented
628	#396	C₂²×C₁₃₉	1	2	yes	complemented
629	#396	C₂²×C₁₃₉	1	2	yes	complemented
630	#395	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
631	#393	C₂²×C₁₃₉	1	2	yes	—
632	#393	C₂²×C₁₃₉	1	1	yes	characteristic
633	#393	C₂²×C₁₃₉	1	2	yes	complemented
634	#391	C₂²×C₁₃₉	1	2	yes	complemented
635	#390	C₂²×C₁₃₉	1	1	yes	characteristic
636	#390	C₂²×C₁₃₉	1	1	yes	characteristic
637	#390	C₂²×C₁₃₉	1	1	yes	characteristic
638	#390	C₂²×C₁₃₉	1	1	yes	characteristic
639	#389	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
640	#389	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
641	#389	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
642	#389	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
643	#389	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
644	#389	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
645	#389	C₂²×C₁₃₉	1	2	yes	complemented
646	#387	C₂²×C₁₃₉	1	2	yes	complemented
647	#387	C₂²×C₁₃₉	1	2	yes	complemented
648	#386	C₂²×C₁₃₉	1	2	yes	—
649	#386	C₂²×C₁₃₉	1	2	yes	—
650	#386	C₂²×C₁₃₉	1	2	yes	—
651	#386	C₂²×C₁₃₉	1	2	yes	—
652	#385	C₂²×C₁₃₉	1	2	yes	complemented
653	#385	C₂²×C₁₃₉	1	2	yes	complemented
654	#385	C₂²×C₁₃₉	1	2	yes	complemented
655	#385	C₂²×C₁₃₉	1	2	yes	complemented
656	#385	C₂²×C₁₃₉	1	2	yes	complemented
657	#385	C₂²×C₁₃₉	1	2	yes	complemented
658	#385	C₂²×C₁₃₉	1	2	yes	complemented
659	#385	C₂²×C₁₃₉	1	2	yes	complemented
660	#385	C₂²×C₁₃₉	1	2	yes	complemented
661	#385	C₂²×C₁₃₉	1	2	yes	complemented
662	#384	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
663	#384	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
664	#382	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
665	#380	C₂²×C₁₃₉	1	1	yes	characteristic
666	#380	C₂²×C₁₃₉	1	1	yes	characteristic
667	#380	C₂²×C₁₃₉	1	2	yes	complemented
668	#380	C₂²×C₁₃₉	1	2	yes	complemented
669	#380	C₂²×C₁₃₉	1	2	yes	complemented
670	#380	C₂²×C₁₃₉	1	2	yes	complemented
671	#380	C₂²×C₁₃₉	1	2	yes	complemented
672	#379	C₂²×C₁₃₉	1	2	yes	—
673	#379	C₂²×C₁₃₉	1	2	yes	—
674	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
675	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
676	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
677	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
678	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
679	C₂×#95	C₂²×C₁₃₉	1	2	yes	complemented
680	C₂⁵	C₂³×C₁₃₉	1	2	yes	—
681	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
682	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
683	C₂²×D₄	—	2	4	no	—
684	C₂²×D₄	—	2	4	no	—
685	C₂²×D₄	Q₈×C₁₃₉	1	8	yes	complemented
686	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
687	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
688	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
689	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
690	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
691	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
692	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
693	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
694	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
695	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
696	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
697	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
698	C₄⋊Q₈	—	2	4	no	—
699	#125	—	2	4	no	—
700	#125	—	2	4	no	—
701	C₂²⋊Q₈	—	2	8	no	—
702	C₂²⋊Q₈	—	2	8	no	—
703	C₂²⋊Q₈	—	2	8	no	—
704	C₂²⋊Q₈	—	4	4	no	—
705	C₂²⋊Q₈	—	4	4	no	—
706	C₄×Q₈	—	2	4	no	—
707	C₄×D₄	—	2	4	no	—
708	C₄×D₄	—	2	4	no	—
709	C₄×D₄	—	2	4	no	—
710	C₄×D₄	—	2	4	no	—
711	C₄×D₄	—	2	4	no	—
712	C₄×D₄	—	2	8	no	—
713	C₄×D₄	—	2	4	no	—
714	C₄×D₄	—	2	8	no	—
715	C₄×D₄	—	2	4	no	—
716	C₄×D₄	D₄×C₁₃₉	1	8	yes	—
717	#117	—	2	4	no	—
718	#117	—	2	4	no	—
719	C₂×C₄⋊C₄	—	2	8	no	—
720	C₂×C₄⋊C₄	—	4	4	no	—
721	C₂×C₄⋊C₄	—	4	4	no	—
722	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
723	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
724	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
725	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
726	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
727	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
728	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
729	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
730	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
731	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
732	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
733	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
734	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
735	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
736	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
737	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
738	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
739	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
740	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
741	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
742	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
743	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
744	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
745	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
746	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
747	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
748	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
749	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
750	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
751	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
752	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
753	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
754	C₂×C₂²⋊C₄	—	2	8	no	—
755	C₂×C₂²⋊C₄	—	2	8	no	—
756	C₂×C₂²⋊C₄	—	4	4	no	—
757	C₂×C₂²⋊C₄	—	4	4	no	—
758	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
759	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
760	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
761	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
762	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
763	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
764	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
765	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
766	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
767	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
768	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
769	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
770	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
771	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
772	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
773	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
774	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
775	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
776	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
777	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
778	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
779	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
780	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
781	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
782	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
783	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
784	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
785	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
786	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
787	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
788	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
789	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
790	#95	C₂³×C₁₃₉	1	1	yes	characteristic
791	#95	C₂³×C₁₃₉	1	2	yes	—
792	#95	C₂³×C₁₃₉	1	2	yes	—
793	#95	C₂³×C₁₃₉	1	2	yes	—
794	#95	C₂³×C₁₃₉	1	1	yes	characteristic
795	#95	C₂³×C₁₃₉	1	1	yes	characteristic
796	#95	C₂³×C₁₃₉	1	1	yes	characteristic
797	#95	C₂³×C₁₃₉	1	1	yes	characteristic
798	#95	C₂³×C₁₃₉	1	1	yes	characteristic
799	#95	C₂³×C₁₃₉	1	1	yes	characteristic
800	#95	C₂³×C₁₃₉	1	1	yes	characteristic
801	#95	C₂³×C₁₃₉	1	1	yes	characteristic
802	#95	C₂³×C₁₃₉	1	1	yes	characteristic
803	#95	C₂³×C₁₃₉	1	2	yes	—
804	#95	C₂³×C₁₃₉	1	2	yes	—
805	#95	C₂³×C₁₃₉	1	2	yes	—
806	#95	C₂³×C₁₃₉	1	2	yes	—
807	#95	C₂³×C₁₃₉	1	2	yes	—
808	#95	C₂³×C₁₃₉	1	2	yes	—
809	#95	C₂³×C₁₃₉	1	2	yes	—
810	C₂⁴	—	2	4	no	—
811	C₂⁴	—	2	4	no	—
812	C₂⁴	—	4	2	no	—
813	C₂⁴	—	4	2	no	—
814	C₂⁴	—	4	2	no	—
815	C₂⁴	—	4	2	no	—
816	C₂⁴	C₂×Q₈×C₁₃₉	1	8	yes	—
817	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
818	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
819	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
820	C₂×Q₈	—	2	2	no	—
821	C₂×Q₈	—	2	4	no	—
822	C₂×Q₈	—	2	2	no	—
823	C₂×Q₈	—	4	1	no	—
824	C₂×Q₈	—	4	2	no	—
825	C₂×Q₈	—	4	2	no	—
826	C₂×D₄	—	2	4	no	—
827	C₂×D₄	—	2	4	no	—
828	C₂×D₄	—	2	32	no	—
829	C₂×D₄	—	2	2	no	—
830	C₂×D₄	—	2	2	no	—
831	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
832	C₂×D₄	C₂×Q₈×C₁₃₉	1	8	yes	—
833	C₂×D₄	C₂×Q₈×C₁₃₉	1	4	yes	—
834	C₂×D₄	C₂×Q₈×C₁₃₉	1	4	yes	—
835	C₂×D₄	#41×C₁₃₉	1	4	yes	—
836	C₂²×C₄	—	2	2	no	—
837	C₂²×C₄	—	2	2	no	—
838	C₂²×C₄	—	2	4	no	—
839	C₂²×C₄	—	2	4	no	—
840	C₂²×C₄	—	2	4	no	—
841	C₂²×C₄	—	2	4	no	—
842	C₂²×C₄	—	2	4	no	—
843	C₂²×C₄	—	2	4	no	—
844	C₂²×C₄	—	2	4	no	—
845	C₂²×C₄	—	2	4	no	—
846	C₂²×C₄	—	2	4	no	—
847	C₂²×C₄	—	4	2	no	—
848	C₂²×C₄	—	4	2	no	—
849	C₂²×C₄	—	4	2	no	—
850	C₂²×C₄	—	4	2	no	—
851	C₂²×C₄	—	4	2	no	—
852	C₂²×C₄	—	4	2	no	—
853	C₂²×C₄	—	4	2	no	—
854	C₂²×C₄	—	4	2	no	—
855	C₂²×C₄	—	4	2	no	—
856	C₂²×C₄	—	4	2	no	—
857	C₂²×C₄	—	4	2	no	—
858	C₂²×C₄	—	4	2	no	—
859	C₂²×C₄	—	4	2	no	—
860	C₂²×C₄	—	4	2	no	—
861	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
862	C₂²×C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
863	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
864	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
865	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
866	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
867	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
868	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
869	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
870	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
871	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
872	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
873	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
874	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
875	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
876	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
877	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
878	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
879	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
880	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
881	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
882	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
883	C₄⋊C₄	—	2	2	no	—
884	C₄⋊C₄	—	2	4	no	—
885	C₄⋊C₄	—	2	4	no	—
886	C₄⋊C₄	—	2	4	no	—
887	C₄⋊C₄	—	2	2	no	—
888	C₄⋊C₄	—	2	2	no	—
889	C₄⋊C₄	—	2	2	no	—
890	C₄⋊C₄	—	2	2	no	—
891	C₄⋊C₄	—	2	2	no	—
892	C₄⋊C₄	—	2	2	no	—
893	C₄⋊C₄	—	2	2	no	—
894	C₄⋊C₄	—	2	4	no	—
895	C₄⋊C₄	—	2	4	no	—
896	C₄⋊C₄	—	2	2	no	—
897	C₄⋊C₄	—	2	2	no	—
898	C₄⋊C₄	—	2	2	no	—
899	C₄⋊C₄	—	2	2	no	—
900	C₄⋊C₄	—	2	4	no	—
901	C₄⋊C₄	—	2	4	no	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	4	2	no	—
904	C₄⋊C₄	—	4	2	no	—
905	C₄⋊C₄	—	4	2	no	—
906	C₄⋊C₄	—	4	2	no	—
907	C₄⋊C₄	—	4	1	no	—
908	C₄⋊C₄	—	4	1	no	—
909	C₄⋊C₄	—	4	2	no	—
910	C₄⋊C₄	—	4	1	no	—
911	C₄⋊C₄	—	4	2	no	—
912	C₄⋊C₄	—	4	2	no	—
913	C₄⋊C₄	—	4	2	no	—
914	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
915	C₂²⋊C₄	—	2	4	no	—
916	C₂²⋊C₄	—	2	4	no	—
917	C₂²⋊C₄	—	2	4	no	—
918	C₂²⋊C₄	—	2	4	no	—
919	C₂²⋊C₄	—	2	4	no	—
920	C₂²⋊C₄	—	2	4	no	—
921	C₂²⋊C₄	—	2	2	no	—
922	C₂²⋊C₄	—	2	2	no	—
923	C₂²⋊C₄	—	2	4	no	—
924	C₂²⋊C₄	—	2	4	no	—
925	C₂²⋊C₄	—	2	2	no	—
926	C₂²⋊C₄	—	2	2	no	—
927	C₂²⋊C₄	—	2	4	no	—
928	C₂²⋊C₄	—	2	4	no	—
929	C₂²⋊C₄	—	4	2	no	—
930	C₂²⋊C₄	—	4	2	no	—
931	C₂²⋊C₄	—	4	2	no	—
932	C₂²⋊C₄	—	4	2	no	—
933	C₂²⋊C₄	—	4	2	no	—
934	C₂²⋊C₄	—	4	2	no	—
935	C₂²⋊C₄	—	4	1	no	—
936	C₂²⋊C₄	—	4	1	no	—
937	C₂²⋊C₄	—	4	2	no	—
938	C₂²⋊C₄	—	4	2	no	—
939	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
940	C₄²	—	2	4	no	—
941	C₄²	—	2	2	no	—
942	C₄²	—	2	2	no	—
943	C₄²	—	2	2	no	—
944	C₄²	—	2	2	no	—
945	C₄²	—	2	2	no	—
946	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
947	C₂³	—	2	2	no	—
948	C₂³	—	2	2	no	—
949	C₂³	—	2	2	no	—
950	C₂³	—	2	2	no	—
951	C₂³	—	2	1	no	—
952	C₂³	—	2	2	no	—
953	C₂³	—	2	1	no	—
954	C₂³	—	2	2	no	—
955	C₂³	—	2	2	no	—
956	C₂³	—	2	2	no	—
957	C₂³	—	2	1	no	—
958	C₂³	—	2	1	no	—
959	C₂³	—	2	2	no	—
960	C₂³	—	2	2	no	—
961	C₂³	—	2	1	no	—
962	C₂³	—	2	1	no	—
963	C₂³	—	2	16	no	—
964	C₂³	—	4	8	no	—
965	C₂³	—	4	8	no	—
966	C₂³	—	8	4	no	—
967	C₂³	—	8	4	no	—
968	C₂³	—	8	4	no	—
969	C₂³	—	8	4	no	—
970	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
971	C₂³	C₂²×Q₈×C₁₃₉	1	2	yes	—
972	C₂³	C₂²×Q₈×C₁₃₉	1	4	yes	—
973	C₂³	C₂²×Q₈×C₁₃₉	1	4	yes	—
974	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
975	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
976	Q₈	—	4	4	no	—
977	Q₈	—	8	4	no	—
978	D₄	—	2	16	no	—
979	D₄	—	2	8	no	—
980	D₄	C₂²⋊Q₈×C₁₃₉	1	16	yes	complemented
981	C₂×C₄	—	2	1	no	—
982	C₂×C₄	—	2	1	no	—
983	C₂×C₄	—	2	1	no	—
984	C₂×C₄	—	2	1	no	—
985	C₂×C₄	—	2	1	no	—
986	C₂×C₄	—	2	1	no	—
987	C₂×C₄	—	2	2	no	—
988	C₂×C₄	—	2	1	no	—
989	C₂×C₄	—	2	1	no	—
990	C₂×C₄	—	2	1	no	—
991	C₂×C₄	—	2	1	no	—
992	C₂×C₄	—	2	2	no	—
993	C₂×C₄	—	2	8	no	—
994	C₂×C₄	—	2	2	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	1	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	1	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	2	no	—
1006	C₂×C₄	—	2	2	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	2	no	—
1010	C₂×C₄	—	2	2	no	—
1011	C₂×C₄	—	2	1	no	—
1012	C₂×C₄	—	2	2	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	1	no	—
1015	C₂×C₄	—	2	2	no	—
1016	C₂×C₄	—	2	2	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	2	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	2	no	—
1026	C₂×C₄	—	2	1	no	—
1027	C₂×C₄	—	2	2	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	2	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	4	8	no	—
1034	C₂×C₄	—	4	8	no	—
1035	C₂×C₄	—	4	8	no	—
1036	C₂×C₄	—	8	4	no	—
1037	C₂×C₄	—	8	4	no	—
1038	C₂×C₄	—	8	4	no	—
1039	C₂×C₄	—	8	4	no	—
1040	C₂×C₄	—	8	4	no	—
1041	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
1042	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1043	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1044	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
1045	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
1046	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
1047	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
1048	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
1049	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
1050	C₂²	—	2	4	no	—
1051	C₂²	—	2	4	no	—
1052	C₂²	—	2	4	no	—
1053	C₂²	—	2	4	no	—
1054	C₂²	—	2	4	no	—
1055	C₂²	—	2	4	no	—
1056	C₂²	—	2	2	no	—
1057	C₂²	—	2	4	no	—
1058	C₂²	—	2	2	no	—
1059	C₂²	—	2	2	no	—
1060	C₂²	—	2	4	no	—
1061	C₂²	—	2	4	no	—
1062	C₂²	—	4	2	no	—
1063	C₂²	—	4	1	no	—
1064	C₂²	—	4	2	no	—
1065	C₂²	—	4	1	no	—
1066	C₂²	—	4	1	no	—
1067	C₂²	—	4	2	no	—
1068	C₂²	—	4	1	no	—
1069	C₂²	—	4	2	no	—
1070	C₂²	—	8	16	no	—
1071	C₂²	C₂×C₂²⋊Q₈×C₁₃₉	1	8	yes	—
1072	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
1073	C₂²	C₂³×Q₈×C₁₃₉	1	1	yes	characteristic
1074	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
1075	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
1076	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
1077	C₂²	#585×C₁₃₉	1	1	yes	characteristic
1078	C₂²	#585×C₁₃₉	1	1	yes	characteristic
1079	C₄	—	2	2	no	—
1080	C₄	—	2	2	no	—
1081	C₄	—	2	2	no	—
1082	C₄	—	2	2	no	—
1083	C₄	—	2	4	no	—
1084	C₄	—	2	2	no	—
1085	C₄	—	4	2	no	—
1086	C₄	—	4	2	no	—
1087	C₄	—	4	1	no	—
1088	C₄	—	4	1	no	—
1089	C₄	—	4	1	no	—
1090	C₄	—	4	1	no	—
1091	C₄	—	4	2	no	—
1092	C₄	—	4	1	no	—
1093	C₄	—	4	2	no	—
1094	C₄	—	4	1	no	—
1095	C₄	—	4	2	no	—
1096	C₄	—	4	1	no	—
1097	C₄	—	4	1	no	—
1098	C₄	C₂×C₂²⋊Q₈×C₁₃₉	1	4	yes	—
1099	C₂	—	2	8	no	—
1100	C₂	—	4	2	no	—
1101	C₂	—	4	4	no	—
1102	C₂	C₂²×C₂²⋊Q₈×C₁₃₉	1	1	yes	characteristic
1103	C₂	#3488×C₁₃₉	1	1	yes	characteristic
1104	C₂	#3496×C₁₃₉	1	1	yes	characteristic
1105	C₂	#3501×C₁₃₉	1	1	yes	characteristic
1106	C₂	#3501×C₁₃₉	1	1	yes	characteristic
1107	C₂	#3519×C₁₃₉	1	1	yes	characteristic
1108	C₂	#3521×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂³×D₄×C₁₃₉	C₂²
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×#554×C₁₃₉	C₂	semidirect
3. #2629×C₁₃₉	C₂	semidirect
4. #2626×C₁₃₉	C₂	semidirect
5. #2579×C₁₃₉	C₂	semidirect
6. #2566×C₁₃₉	C₂	semidirect
7. #2538×C₁₃₉	C₂	semidirect
8. #2454×C₁₃₉	C₂	semidirect
9. #2452×C₁₃₉	C₂	semidirect
10. #2450×C₁₃₉	C₂	semidirect
11. #2449×C₁₃₉	C₂	semidirect
12. #2441×C₁₃₉	C₂	semidirect
13. #2439×C₁₃₉	C₂	semidirect
14. #2437×C₁₃₉	C₂	semidirect
15. #2437×C₁₃₉	C₂	semidirect
16. #2417×C₁₃₉	C₂	semidirect
17. #2396×C₁₃₉	C₂	semidirect
18. C₂×#396×C₁₃₉	C₂	semidirect
19. #2349×C₁₃₉	C₂	semidirect
20. D₄×C₄⋊C₄×C₁₃₉	C₂	semidirect
21. D₄×C₄⋊C₄×C₁₃₉	C₂	semidirect
26. C₂×C₄⋊Q₈×C₁₃₉	C₂²	semidirect
27. C₂×#125×C₁₃₉	C₂²	semidirect
28. C₂×#125×C₁₃₉	C₂²	semidirect
29. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
30. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
31. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
32. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
33. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
35. C₂×C₄×Q₈×C₁₃₉	C₂²	semidirect
48. C₂²×C₄⋊C₄×C₁₃₉	C₂²	semidirect
49. C₂²×C₄⋊C₄×C₁₃₉	C₂²	semidirect
50. C₂²×C₄⋊C₄×C₁₃₉	C₂²	semidirect
55. #400×C₁₃₉	C₂²	semidirect
58. #399×C₁₃₉	C₂²	semidirect
59. #398×C₁₃₉	C₂²	semidirect
60. #398×C₁₃₉	C₂²	semidirect
61. #398×C₁₃₉	C₂²	semidirect
62. #398×C₁₃₉	C₂²	semidirect
69. #396×C₁₃₉	C₂²	semidirect
70. #396×C₁₃₉	C₂²	semidirect
71. #396×C₁₃₉	C₂²	semidirect
72. #396×C₁₃₉	C₂²	semidirect
73. #396×C₁₃₉	C₂²	semidirect
74. #396×C₁₃₉	C₂²	semidirect
75. #395×C₁₃₉	C₂²	semidirect
78. #393×C₁₃₉	C₂²	semidirect
79. #391×C₁₃₉	C₂²	semidirect
84. #389×C₁₃₉	C₂²	semidirect
85. #389×C₁₃₉	C₂²	semidirect
86. #389×C₁₃₉	C₂²	semidirect
87. #389×C₁₃₉	C₂²	semidirect
88. #389×C₁₃₉	C₂²	semidirect
89. #389×C₁₃₉	C₂²	semidirect
90. #389×C₁₃₉	C₂²	semidirect
91. #387×C₁₃₉	C₂²	semidirect
92. #387×C₁₃₉	C₂²	semidirect
97. #385×C₁₃₉	C₂²	semidirect
98. #385×C₁₃₉	C₂²	semidirect
99. #385×C₁₃₉	C₂²	semidirect
100. #385×C₁₃₉	C₂²	semidirect
101. #385×C₁₃₉	C₂²	semidirect
102. #385×C₁₃₉	C₂²	semidirect
103. #385×C₁₃₉	C₂²	semidirect
104. #385×C₁₃₉	C₂²	semidirect
105. #385×C₁₃₉	C₂²	semidirect
106. #385×C₁₃₉	C₂²	semidirect
107. #384×C₁₃₉	C₂²	semidirect
108. #384×C₁₃₉	C₂²	semidirect
109. #382×C₁₃₉	C₂²	semidirect
112. #380×C₁₃₉	C₂²	semidirect
113. #380×C₁₃₉	C₂²	semidirect
114. #380×C₁₃₉	C₂²	semidirect
115. #380×C₁₃₉	C₂²	semidirect
116. #380×C₁₃₉	C₂²	semidirect
119. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
120. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
121. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
124. C₂×#95×C₁₃₉	C₂²	semidirect
130. C₂²×D₄×C₁₃₉	Q₈	semidirect
425. D₄×C₁₃₉	C₂²⋊Q₈	semidirect
554. #35776	C₁₃₉	direct (N × H)
555. C₁₃₉	#35776	direct (N × H)
556. C₂×#554	C₂×C₁₃₉	semidirect
558. #2629	C₂×C₁₃₉	semidirect
559. #2626	C₂×C₁₃₉	semidirect
560. #2579	C₂×C₁₃₉	semidirect
561. #2566	C₂×C₁₃₉	semidirect
562. #2538	C₂×C₁₃₉	semidirect
563. #2454	C₂×C₁₃₉	semidirect
564. #2452	C₂×C₁₃₉	semidirect
565. #2450	C₂×C₁₃₉	semidirect
566. #2449	C₂×C₁₃₉	semidirect
567. #2441	C₂×C₁₃₉	semidirect
568. #2439	C₂×C₁₃₉	semidirect
569. #2437	C₂×C₁₃₉	semidirect
570. #2437	C₂×C₁₃₉	semidirect
571. #2417	C₂×C₁₃₉	semidirect
572. #2396	C₂×C₁₃₉	semidirect
573. C₂×#396	C₂×C₁₃₉	semidirect
574. #2349	C₂×C₁₃₉	semidirect
575. D₄×C₄⋊C₄	C₂×C₁₃₉	semidirect
576. D₄×C₄⋊C₄	C₂×C₁₃₉	semidirect
581. C₂×C₄⋊Q₈	C₂²×C₁₃₉	semidirect
582. C₂×#125	C₂²×C₁₃₉	semidirect
583. C₂×#125	C₂²×C₁₃₉	semidirect
584. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
585. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
586. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
587. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
588. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
590. C₂×C₄×Q₈	C₂²×C₁₃₉	semidirect
603. C₂²×C₄⋊C₄	C₂²×C₁₃₉	semidirect
604. C₂²×C₄⋊C₄	C₂²×C₁₃₉	semidirect
605. C₂²×C₄⋊C₄	C₂²×C₁₃₉	semidirect
610. #400	C₂²×C₁₃₉	semidirect
613. #399	C₂²×C₁₃₉	semidirect
614. #398	C₂²×C₁₃₉	semidirect
615. #398	C₂²×C₁₃₉	semidirect
616. #398	C₂²×C₁₃₉	semidirect
617. #398	C₂²×C₁₃₉	semidirect
624. #396	C₂²×C₁₃₉	semidirect
625. #396	C₂²×C₁₃₉	semidirect
626. #396	C₂²×C₁₃₉	semidirect
627. #396	C₂²×C₁₃₉	semidirect
628. #396	C₂²×C₁₃₉	semidirect
629. #396	C₂²×C₁₃₉	semidirect
630. #395	C₂²×C₁₃₉	semidirect
633. #393	C₂²×C₁₃₉	semidirect
634. #391	C₂²×C₁₃₉	semidirect
639. #389	C₂²×C₁₃₉	semidirect
640. #389	C₂²×C₁₃₉	semidirect
641. #389	C₂²×C₁₃₉	semidirect
642. #389	C₂²×C₁₃₉	semidirect
643. #389	C₂²×C₁₃₉	semidirect
644. #389	C₂²×C₁₃₉	semidirect
645. #389	C₂²×C₁₃₉	semidirect
646. #387	C₂²×C₁₃₉	semidirect
647. #387	C₂²×C₁₃₉	semidirect
652. #385	C₂²×C₁₃₉	semidirect
653. #385	C₂²×C₁₃₉	semidirect
654. #385	C₂²×C₁₃₉	semidirect
655. #385	C₂²×C₁₃₉	semidirect
656. #385	C₂²×C₁₃₉	semidirect
657. #385	C₂²×C₁₃₉	semidirect
658. #385	C₂²×C₁₃₉	semidirect
659. #385	C₂²×C₁₃₉	semidirect
660. #385	C₂²×C₁₃₉	semidirect
661. #385	C₂²×C₁₃₉	semidirect
662. #384	C₂²×C₁₃₉	semidirect
663. #384	C₂²×C₁₃₉	semidirect
664. #382	C₂²×C₁₃₉	semidirect
667. #380	C₂²×C₁₃₉	semidirect
668. #380	C₂²×C₁₃₉	semidirect
669. #380	C₂²×C₁₃₉	semidirect
670. #380	C₂²×C₁₃₉	semidirect
671. #380	C₂²×C₁₃₉	semidirect
674. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
675. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
676. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
679. C₂×#95	C₂²×C₁₃₉	semidirect
685. C₂²×D₄	Q₈×C₁₃₉	semidirect
980. D₄	C₂²⋊Q₈×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#554×C₁₃₉	2
C₂×#518×C₁₃₉	2
#2629×C₁₃₉	2
#2626×C₁₃₉	2
#2579×C₁₃₉	2
#2566×C₁₃₉	2
#2538×C₁₃₉	2
#2454×C₁₃₉	2
#2452×C₁₃₉	2
#2450×C₁₃₉	2
#2449×C₁₃₉	2
#2441×C₁₃₉	2
#2439×C₁₃₉	2
#2437×C₁₃₉	2
#2417×C₁₃₉	2
#2396×C₁₃₉	2
C₂×#396×C₁₃₉	2
#2349×C₁₃₉	2
D₄×C₄⋊C₄×C₁₃₉	2
D₄×C₂²⋊C₄×C₁₃₉	2
#35776	139

Subgroups — C139×#35776 #48030372

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#35776 #48030372