Subgroups — #31817893

Order 17792.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×SD₁₆×D₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#22581610	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×C₂²⋊D₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#22581341	C₂	1	1	yes	maximal, characteristic, complemented
5	#22581199	C₂	1	1	yes	maximal, characteristic, complemented
6	#22581186	C₂	1	1	yes	maximal, characteristic, complemented
7	#22581166	C₂	1	1	yes	maximal, characteristic, complemented
8	#22581151	C₂	1	1	yes	maximal, characteristic, complemented
9	#22581104	C₂	1	1	yes	maximal, characteristic, complemented
10	#22581098	C₂	1	1	yes	maximal, characteristic, complemented
11	#22581090	C₂	1	1	yes	maximal, characteristic, complemented
12	#22581085	C₂	1	1	yes	maximal, characteristic, complemented
13	#22581054	C₂	1	1	yes	maximal, characteristic, complemented
14	#22581022	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×AGL(1,ℤ/8)×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×Q₈×D₁₃₉	C₂²	1	1	yes	characteristic, complemented
17	C₂²×C₂²⋊D₁₃₉	—	2	1	no	—
18	C₂×D₄×D₁₃₉	C₂²	1	1	yes	characteristic
19	C₂×#14555774	C₂²	1	1	yes	characteristic, complemented
20	C₂×#14555773	C₂²	1	1	yes	characteristic
21	C₂×#14555773	C₂²	1	1	yes	characteristic, complemented
22	C₂×#14555772	C₂²	1	1	yes	characteristic, complemented
23	SD₁₆×D₁₃₉	—	2	4	no	—
24	C₂×#14555770	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₈×D₁₃₉	C₂²	1	1	yes	characteristic, complemented
26	#17984838	C₂²	1	1	yes	characteristic
27	#17984829	—	2	1	no	—
28	#17984829	C₂²	1	1	yes	characteristic, complemented
29	#17984821	—	2	1	no	—
30	#17984821	C₂²	1	1	yes	characteristic, complemented
31	#17984816	C₂²	1	1	yes	characteristic
32	#17984814	—	2	1	no	—
33	#17984813	—	2	1	no	—
34	#17984813	C₂²	1	1	yes	characteristic
35	#17984813	C₂²	1	1	yes	characteristic, complemented
36	#17984811	—	2	1	no	—
37	#17984810	—	2	1	no	—
38	Q₈×Dic₁₃₉	C₂²	1	1	yes	characteristic, complemented
39	D₄×Dic₁₃₉	C₂²	1	1	yes	characteristic
40	C₄×C₂²⋊D₁₃₉	—	2	1	no	—
41	C₄×C₂²⋊D₁₃₉	C₂²	1	1	yes	characteristic
42	#17984776	C₂²	1	1	yes	characteristic, complemented
43	Dic₁₃₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
44	#17984767	C₂²	1	1	yes	characteristic, complemented
45	#17984766	C₂²	1	1	yes	characteristic, complemented
46	#17984764	C₂²	1	1	yes	characteristic, complemented
47	#17984763	C₂²	1	1	yes	characteristic
48	#17984763	C₂²	1	1	yes	characteristic, complemented
49	#17984763	C₂²	1	1	yes	characteristic, complemented
50	C₂²⋊(C₁₃₉⋊C₈)	C₂²	1	1	yes	characteristic, complemented
51	(C₂×D₁₃₉)⋊C₈	C₂²	1	1	yes	characteristic, complemented
52	#17984752	C₂²	1	1	yes	characteristic, complemented
53	C₂×#41×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
54	C₂²×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
55	AGL(1,ℤ/8)×C₁₃₉	—	2	4	no	—
56	C₂×SD₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
57	C₂×SD₁₆×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
58	C₂×D₈×C₁₃₉	C₂²	1	1	yes	characteristic
59	C₂×D₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
60	C₂×M₁₆×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₁₃₉	—	2	1	no	—
62	C₂×Dic₂₇₈	—	2	1	no	—
63	C₂×Dic₂₇₈	C₂³	1	1	yes	characteristic
64	Q₈×D₁₃₉	—	2	2	no	—
65	Q₈×D₁₃₉	—	4	1	no	—
66	C₂×D₅₅₆	C₂³	1	1	yes	characteristic
67	C₂×C₂²⋊D₁₃₉	—	2	1	no	—
68	C₂×C₂²⋊D₁₃₉	—	2	1	no	—
69	C₂×C₂²⋊D₁₃₉	—	2	1	no	—
70	C₂×C₂²⋊D₁₃₉	—	2	1	no	—
71	C₂×C₂²⋊D₁₃₉	—	2	1	no	—
72	C₂×C₂²⋊D₁₃₉	—	2	1	no	—
73	C₂×C₂²⋊D₁₃₉	—	4	4	no	—
74	C₂×C₂²⋊D₁₃₉	D₄	1	1	yes	characteristic
75	D₄×D₁₃₉	—	2	2	no	—
76	D₄×D₁₃₉	—	4	1	no	—
77	C₂²×Dic₁₃₉	—	2	1	no	—
78	C₂×C₄×D₁₃₉	—	2	1	no	—
79	C₂×C₄×D₁₃₉	C₂³	1	1	yes	characteristic
80	#14555774	—	2	2	no	—
81	#14555773	—	2	2	no	—
82	#14555773	—	4	1	no	—
83	#14555772	—	2	2	no	—
84	#14555770	—	4	1	no	—
85	C₂×C₁₃₉⋊C₈	C₂³	1	1	yes	characteristic
86	C₂×C₁₃₉⋊C₈	C₂³	1	1	yes	characteristic
87	C₈×D₁₃₉	—	2	2	no	—
88	C₄⋊Dic₁₃₉	—	2	1	no	—
89	C₄⋊Dic₁₃₉	C₂³	1	1	yes	characteristic
90	C₄⋊Dic₁₃₉	C₂³	1	1	yes	characteristic
91	Dic₁₃₉⋊C₄	—	2	1	no	—
92	Dic₁₃₉⋊C₄	D₄	1	1	yes	characteristic
93	C₂²⋊Dic₁₃₉	—	2	1	no	—
94	C₂²⋊Dic₁₃₉	—	2	1	no	—
95	C₂²⋊Dic₁₃₉	—	2	1	no	—
96	C₂²⋊Dic₁₃₉	—	2	1	no	—
97	C₂²⋊Dic₁₃₉	—	2	1	no	—
98	C₂²⋊Dic₁₃₉	—	2	1	no	—
99	C₂²⋊Dic₁₃₉	D₄	1	1	yes	characteristic
100	(C₂×D₁₃₉)⋊C₄	—	2	1	no	—
101	(C₂×D₁₃₉)⋊C₄	D₄	1	1	yes	characteristic
102	C₄×Dic₁₃₉	—	2	1	no	—
103	C₄×Dic₁₃₉	C₂³	1	1	yes	characteristic
104	C₂⁴×C₁₃₉	—	2	1	no	—
105	#41×C₁₃₉	—	2	2	no	—
106	#41×C₁₃₉	—	4	1	no	—
107	C₂×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
108	C₂×D₄×C₁₃₉	—	2	2	no	—
109	C₂×D₄×C₁₃₉	—	2	1	no	—
110	C₂×D₄×C₁₃₉	—	2	1	no	—
111	C₂×D₄×C₁₃₉	—	4	1	no	—
112	C₂×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
113	C₂×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
114	C₂×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
115	C₂²×C₄×C₁₃₉	—	2	1	no	—
116	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
117	SD₁₆×C₁₃₉	—	2	2	no	—
118	SD₁₆×C₁₃₉	D₄	1	4	yes	complemented
119	D₈×C₁₃₉	—	2	2	no	—
120	D₈×C₁₃₉	—	2	2	no	—
121	M₁₆×C₁₃₉	—	2	2	no	—
122	C₂×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
123	C₂×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
124	C₂²×D₁₃₉	—	2	1	no	—
125	C₂²×D₁₃₉	—	4	2	no	—
126	C₂²×D₁₃₉	—	4	2	no	—
127	C₂²×D₁₃₉	—	8	1	no	—
128	C₂²×D₁₃₉	C₂×D₄	1	1	yes	characteristic
129	Dic₂₇₈	—	2	1	no	—
130	Dic₂₇₈	—	2	1	no	—
131	Dic₂₇₈	—	4	2	no	—
132	D₅₅₆	—	2	1	no	—
133	D₅₅₆	—	2	1	no	—
134	C₂²⋊D₁₃₉	—	2	2	no	—
135	C₂²⋊D₁₃₉	—	4	2	no	—
136	C₂²⋊D₁₃₉	—	4	2	no	—
137	C₂²⋊D₁₃₉	—	4	2	no	—
138	C₂²⋊D₁₃₉	—	4	2	no	—
139	C₂²⋊D₁₃₉	—	4	2	no	—
140	C₂²⋊D₁₃₉	—	8	1	no	—
141	C₂×Dic₁₃₉	—	2	1	no	—
142	C₂×Dic₁₃₉	—	2	1	no	—
143	C₂×Dic₁₃₉	—	2	1	no	—
144	C₂×Dic₁₃₉	—	4	2	no	—
145	C₂×Dic₁₃₉	C₂×D₄	1	1	yes	characteristic
146	C₂×Dic₁₃₉	C₂×D₄	1	1	yes	characteristic
147	C₂×Dic₁₃₉	C₂×D₄	1	1	yes	characteristic
148	C₄×D₁₃₉	—	2	1	no	—
149	C₄×D₁₃₉	—	2	1	no	—
150	C₄×D₁₃₉	—	4	2	no	—
151	C₁₃₉⋊C₈	—	2	1	no	—
152	C₁₃₉⋊C₈	—	2	1	no	—
153	C₂³×C₁₃₉	—	2	1	no	—
154	C₂³×C₁₃₉	—	2	1	no	—
155	C₂³×C₁₃₉	—	2	1	no	—
156	C₂³×C₁₃₉	—	4	2	no	—
157	C₂³×C₁₃₉	—	4	2	no	—
158	C₂³×C₁₃₉	—	8	1	no	—
159	C₂³×C₁₃₉	C₂×D₄	1	1	yes	characteristic
160	Q₈×C₁₃₉	—	2	1	no	—
161	Q₈×C₁₃₉	C₂×D₄	1	2	yes	complemented
162	D₄×C₁₃₉	—	2	1	no	—
163	D₄×C₁₃₉	—	2	1	no	—
164	D₄×C₁₃₉	—	2	1	no	—
165	D₄×C₁₃₉	—	2	1	no	—
166	D₄×C₁₃₉	—	2	1	no	—
167	D₄×C₁₃₉	—	4	2	no	—
168	D₄×C₁₃₉	—	4	2	no	—
169	D₄×C₁₃₉	C₂×D₄	1	2	yes	—
170	C₂×C₄×C₁₃₉	—	2	1	no	—
171	C₂×C₄×C₁₃₉	—	2	1	no	—
172	C₂×C₄×C₁₃₉	—	2	1	no	—
173	C₂×C₄×C₁₃₉	—	4	2	no	—
174	C₂×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
175	C₂×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
176	C₈×C₁₃₉	—	2	1	no	—
177	C₈×C₁₃₉	C₂×D₄	1	2	yes	complemented
178	C₂²×C₁₃₉	—	2	1	no	—
179	C₂²×C₁₃₉	—	2	2	no	—
180	C₂²×C₁₃₉	—	2	1	no	—
181	C₂²×C₁₃₉	—	2	1	no	—
182	C₂²×C₁₃₉	—	4	1	no	—
183	C₂²×C₁₃₉	—	4	1	no	—
184	C₂²×C₁₃₉	—	4	1	no	—
185	C₂²×C₁₃₉	—	4	1	no	—
186	C₂²×C₁₃₉	—	4	1	no	—
187	C₂²×C₁₃₉	—	4	1	no	—
188	C₂²×C₁₃₉	—	4	1	no	—
189	C₂²×C₁₃₉	—	4	1	no	—
190	C₂²×C₁₃₉	—	8	4	no	—
191	C₂²×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
192	C₂×D₁₃₉	—	2	1	no	—
193	C₂×D₁₃₉	—	2	1	no	—
194	C₂×D₁₃₉	—	4	1	no	—
195	C₂×D₁₃₉	—	4	1	no	—
196	C₂×D₁₃₉	—	4	1	no	—
197	C₂×D₁₃₉	—	8	4	no	—
198	C₂×D₁₃₉	AGL(1,ℤ/8)	1	2	yes	complemented
199	C₄×C₁₃₉	—	2	1	no	—
200	C₄×C₁₃₉	—	2	2	no	—
201	C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
202	C₄×C₁₃₉	H(5,𝔽₂)	1	1	yes	characteristic
203	Dic₁₃₉	—	2	1	no	—
204	Dic₁₃₉	—	2	1	no	—
205	Dic₁₃₉	—	2	1	no	—
206	Dic₁₃₉	—	4	1	no	—
207	Dic₁₃₉	—	4	1	no	—
208	Dic₁₃₉	—	4	1	no	—
209	C₂×C₁₃₉	—	4	2	no	—
210	C₂×C₁₃₉	—	4	1	no	—
211	C₂×C₁₃₉	—	8	1	no	—
212	C₂×C₁₃₉	—	8	1	no	—
213	C₂×C₁₃₉	D₄²	1	1	yes	characteristic
214	C₂×C₁₃₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
215	C₂×C₁₃₉	#577	1	1	yes	characteristic
216	D₁₃₉	—	2	2	no	—
217	D₁₃₉	—	8	1	no	—
218	C₁₃₉	#3265	1	1	yes	characteristic, complemented, Sylow
219	#3265	—	139	1	no	maximal, Sylow
220	C₂×AGL(1,ℤ/8)	D₁₃₉	1	1	yes	characteristic, complemented
221	C₂²×SD₁₆	—	139	1	no	—
222	#548	—	139	1	no	—
223	D₄²	—	139	1	no	—
224	#496	—	139	1	no	—
225	#468	—	139	1	no	—
226	#466	—	139	1	no	—
227	#463	—	139	1	no	—
228	#460	—	139	1	no	—
229	#450	—	139	1	no	—
230	#449	—	139	1	no	—
231	#448	—	139	1	no	—
232	#447	—	139	1	no	—
233	#440	—	139	1	no	—
234	#435	—	139	1	no	—
235	C₂×#41	C₂×D₁₃₉	1	1	yes	characteristic, complemented
236	C₂²×Q₈	—	139	1	no	—
237	C₂²×D₄	—	278	1	no	—
238	C₂²×D₄	—	139	1	no	—
239	C₂²×D₄	C₂×D₁₃₉	1	1	yes	characteristic
240	AGL(1,ℤ/8)	—	2	4	no	—
241	C₂×SD₁₆	—	278	4	no	—
242	C₂×SD₁₆	—	139	1	no	—
243	C₂×SD₁₆	—	139	1	no	—
244	C₂×SD₁₆	—	139	1	no	—
245	C₂×SD₁₆	—	139	1	no	—
246	C₂×SD₁₆	C₂×D₁₃₉	1	1	yes	characteristic
247	C₂×SD₁₆	C₂×D₁₃₉	1	1	yes	characteristic, complemented
248	C₂×D₈	—	139	1	no	—
249	C₂×D₈	C₂×D₁₃₉	1	1	yes	characteristic
250	C₂×D₈	C₂×D₁₃₉	1	1	yes	characteristic, complemented
251	C₂×M₁₆	C₂×D₁₃₉	1	1	yes	characteristic, complemented
252	C₂²×C₈	—	139	1	no	—
253	#127	—	139	1	no	—
254	#124	—	278	1	no	—
255	#124	—	139	1	no	—
256	C₂²⋊Q₈	—	278	1	no	—
257	C₂²⋊Q₈	—	139	1	no	—
258	#121	—	278	1	no	—
259	#121	—	278	1	no	—
260	#121	—	139	1	no	—
261	#121	—	139	1	no	—
262	#121	—	139	1	no	—
263	#120	—	278	1	no	—
264	#120	—	278	1	no	—
265	C₄×Q₈	—	139	1	no	—
266	C₄×D₄	—	278	1	no	—
267	C₄×D₄	—	139	1	no	—
268	C₄×D₄	—	139	1	no	—
269	#107	—	139	1	no	—
270	C₄⋊C₈	—	139	1	no	—
271	#103	—	139	1	no	—
272	#103	—	139	1	no	—
273	#102	—	139	1	no	—
274	#102	—	139	1	no	—
275	#102	—	139	1	no	—
276	#102	—	139	1	no	—
277	C₂²⋊C₈	—	139	1	no	—
278	C₂²⋊C₈	—	139	1	no	—
279	#97	—	139	1	no	—
280	C₂⁴	—	2	1	no	—
281	C₂⁴	—	278	1	no	—
282	#41	—	2	2	no	—
283	#41	—	4	1	no	—
284	C₂×Q₈	—	278	1	no	—
285	C₂×Q₈	—	278	2	no	—
286	C₂×Q₈	—	556	1	no	—
287	C₂×Q₈	—	139	1	no	—
288	C₂×Q₈	C₂²×D₁₃₉	1	1	yes	characteristic
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	1	no	—
291	C₂×D₄	—	2	1	no	—
292	C₂×D₄	—	4	1	no	—
293	C₂×D₄	—	278	2	no	—
294	C₂×D₄	—	278	1	no	—
295	C₂×D₄	—	278	1	no	—
296	C₂×D₄	—	278	1	no	—
297	C₂×D₄	—	278	1	no	—
298	C₂×D₄	—	278	1	no	—
299	C₂×D₄	—	278	1	no	—
300	C₂×D₄	—	556	1	no	—
301	C₂×D₄	—	556	4	no	—
302	C₂×D₄	—	139	1	no	—
303	C₂×D₄	—	139	1	no	—
304	C₂×D₄	C₂²×D₁₃₉	1	1	yes	characteristic
305	C₂×D₄	C₂²×D₁₃₉	1	1	yes	characteristic
306	C₂×D₄	C₂²×D₁₃₉	1	1	yes	characteristic
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	278	1	no	—
309	C₂²×C₄	—	278	1	no	—
310	C₂²×C₄	—	139	1	no	—
311	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
312	SD₁₆	—	2	2	no	—
313	SD₁₆	—	278	2	no	—
314	SD₁₆	—	278	2	no	—
315	SD₁₆	—	278	2	no	—
316	SD₁₆	—	556	1	no	—
317	SD₁₆	C₂²⋊D₁₃₉	1	4	yes	complemented
318	D₈	—	2	2	no	—
319	D₈	—	2	2	no	—
320	D₈	—	556	1	no	—
321	M₁₆	—	2	2	no	—
322	C₂×C₈	—	278	2	no	—
323	C₂×C₈	—	139	1	no	—
324	C₂×C₈	—	139	1	no	—
325	C₂×C₈	C₂²×D₁₃₉	1	1	yes	characteristic
326	C₂×C₈	C₂²×D₁₃₉	1	1	yes	characteristic
327	C₄⋊C₄	—	278	1	no	—
328	C₄⋊C₄	—	278	1	no	—
329	C₄⋊C₄	—	139	1	no	—
330	C₄⋊C₄	—	139	1	no	—
331	C₄⋊C₄	—	139	1	no	—
332	C₂²⋊C₄	—	278	1	no	—
333	C₂²⋊C₄	—	278	1	no	—
334	C₂²⋊C₄	—	278	1	no	—
335	C₂²⋊C₄	—	278	1	no	—
336	C₂²⋊C₄	—	278	1	no	—
337	C₂²⋊C₄	—	278	1	no	—
338	C₂²⋊C₄	—	278	1	no	—
339	C₂²⋊C₄	—	139	1	no	—
340	C₂²⋊C₄	—	139	1	no	—
341	C₄²	—	278	1	no	—
342	C₄²	—	139	1	no	—
343	C₂³	—	2	1	no	—
344	C₂³	—	2	1	no	—
345	C₂³	—	2	1	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	4	2	no	—
348	C₂³	—	8	1	no	—
349	C₂³	—	278	1	no	—
350	C₂³	—	556	2	no	—
351	C₂³	—	556	2	no	—
352	C₂³	—	1112	1	no	—
353	C₂³	—	139	1	no	—
354	C₂³	D₄×D₁₃₉	1	1	yes	characteristic
355	Q₈	—	2	1	no	—
356	Q₈	—	278	1	no	—
357	Q₈	—	278	1	no	—
358	Q₈	—	556	2	no	—
359	Q₈	C₂×C₂²⋊D₁₃₉	1	2	yes	complemented
360	D₄	—	2	1	no	—
361	D₄	—	2	1	no	—
362	D₄	—	2	1	no	—
363	D₄	—	2	1	no	—
364	D₄	—	2	1	no	—
365	D₄	—	4	2	no	—
366	D₄	—	4	2	no	—
367	D₄	—	278	2	no	—
368	D₄	—	278	1	no	—
369	D₄	—	278	1	no	—
370	D₄	—	556	2	no	—
371	D₄	—	556	2	no	—
372	D₄	—	556	2	no	—
373	D₄	—	556	2	no	—
374	D₄	—	556	2	no	—
375	D₄	—	1112	1	no	—
376	D₄	C₂×C₂²⋊D₁₃₉	1	2	yes	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	278	1	no	—
382	C₂×C₄	—	278	1	no	—
383	C₂×C₄	—	278	1	no	—
384	C₂×C₄	—	278	1	no	—
385	C₂×C₄	—	278	1	no	—
386	C₂×C₄	—	556	2	no	—
387	C₂×C₄	—	556	2	no	—
388	C₂×C₄	—	139	1	no	—
389	C₂×C₄	—	139	1	no	—
390	C₂×C₄	—	139	1	no	—
391	C₂×C₄	D₄×D₁₃₉	1	1	yes	characteristic
392	C₂×C₄	C₂³×D₁₃₉	1	1	yes	characteristic
393	C₈	—	2	1	no	—
394	C₈	—	278	1	no	—
395	C₈	—	278	1	no	—
396	C₈	C₂×C₂²⋊D₁₃₉	1	2	yes	complemented
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	2	no	—
400	C₂²	—	2	1	no	—
401	C₂²	—	4	1	no	—
402	C₂²	—	4	1	no	—
403	C₂²	—	4	1	no	—
404	C₂²	—	4	1	no	—
405	C₂²	—	4	1	no	—
406	C₂²	—	4	1	no	—
407	C₂²	—	4	1	no	—
408	C₂²	—	4	1	no	—
409	C₂²	—	8	4	no	—
410	C₂²	—	278	1	no	—
411	C₂²	—	278	1	no	—
412	C₂²	—	556	1	no	—
413	C₂²	—	556	1	no	—
414	C₂²	—	556	1	no	—
415	C₂²	—	1112	4	no	—
416	C₂²	—	139	2	no	—
417	C₂²	C₂×D₄×D₁₃₉	1	1	yes	characteristic
418	C₄	—	2	1	no	—
419	C₄	—	2	2	no	—
420	C₄	—	278	1	no	—
421	C₄	—	278	1	no	—
422	C₄	—	278	1	no	—
423	C₄	—	556	1	no	—
424	C₄	—	556	1	no	—
425	C₄	—	556	1	no	—
426	C₄	C₂²×C₂²⋊D₁₃₉	1	1	yes	characteristic
427	C₄	#17984887	1	1	yes	characteristic
428	C₂	—	4	1	no	—
429	C₂	—	4	2	no	—
430	C₂	—	8	1	no	—
431	C₂	—	8	1	no	—
432	C₂	—	278	2	no	—
433	C₂	—	1112	1	no	—
434	C₂	D₄×C₂²⋊D₁₃₉	1	1	yes	characteristic
435	C₂	AGL(1,ℤ/8)×D₁₃₉	1	1	yes	characteristic
436	C₂	#22581763	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₃₉
commutator, cosocle	C₂×C₄×C₁₃₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₃₉
Fitting	C₂×AGL(1,ℤ/8)×C₁₃₉	C₂
socle	C₂²×C₁₃₉	C₂²×D₄
hypercenter	C₂×AGL(1,ℤ/8)	D₁₃₉
hypocenter	C₁₃₉	#3265
LCS	G ▷ C₂×C₄×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×AGL(1,ℤ/8)

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×SD₁₆×D₁₃₉	C₂	semidirect
2. #22581610	C₂	semidirect
3. D₄×C₂²⋊D₁₃₉	C₂	semidirect
4. #22581341	C₂	semidirect
5. #22581199	C₂	semidirect
6. #22581186	C₂	semidirect
7. #22581166	C₂	semidirect
8. #22581151	C₂	semidirect
9. #22581104	C₂	semidirect
10. #22581098	C₂	semidirect
11. #22581090	C₂	semidirect
12. #22581085	C₂	semidirect
13. #22581054	C₂	semidirect
14. #22581022	C₂	semidirect
15. C₂×AGL(1,ℤ/8)×C₁₃₉	C₂	semidirect
16. C₂×Q₈×D₁₃₉	C₂²	semidirect
19. C₂×#14555774	C₂²	semidirect
21. C₂×#14555773	C₂²	semidirect
22. C₂×#14555772	C₂²	semidirect
24. C₂×#14555770	C₂²	semidirect
25. C₂×C₈×D₁₃₉	C₂²	semidirect
28. #17984829	C₂²	semidirect
30. #17984821	C₂²	semidirect
35. #17984813	C₂²	semidirect
38. Q₈×Dic₁₃₉	C₂²	semidirect
42. #17984776	C₂²	semidirect
43. Dic₁₃₉⋊C₈	C₂²	semidirect
44. #17984767	C₂²	semidirect
45. #17984766	C₂²	semidirect
46. #17984764	C₂²	semidirect
48. #17984763	C₂²	semidirect
49. #17984763	C₂²	semidirect
50. C₂²⋊(C₁₃₉⋊C₈)	C₂²	semidirect
51. (C₂×D₁₃₉)⋊C₈	C₂²	semidirect
52. #17984752	C₂²	semidirect
53. C₂×#41×C₁₃₉	C₂²	semidirect
57. C₂×SD₁₆×C₁₃₉	C₂²	semidirect
59. C₂×D₈×C₁₃₉	C₂²	semidirect
60. C₂×M₁₆×C₁₃₉	C₂²	semidirect
118. SD₁₆×C₁₃₉	D₄	semidirect
161. Q₈×C₁₃₉	C₂×D₄	semidirect
177. C₈×C₁₃₉	C₂×D₄	semidirect
198. C₂×D₁₃₉	AGL(1,ℤ/8)	semidirect
218. C₁₃₉	#3265	semidirect
220. C₂×AGL(1,ℤ/8)	D₁₃₉	semidirect
235. C₂×#41	C₂×D₁₃₉	semidirect
247. C₂×SD₁₆	C₂×D₁₃₉	semidirect
250. C₂×D₈	C₂×D₁₃₉	semidirect
251. C₂×M₁₆	C₂×D₁₃₉	semidirect
317. SD₁₆	C₂²⋊D₁₃₉	semidirect
359. Q₈	C₂×C₂²⋊D₁₃₉	semidirect
396. C₈	C₂×C₂²⋊D₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×SD₁₆×D₁₃₉	2
#22581610	2
D₄×C₂²⋊D₁₃₉	2
#22581341	2
#22581199	2
#22581186	2
#22581166	2
#22581151	2
#22581104	2
#22581098	2
#22581090	2
#22581085	2
#22581054	2
#22581022	2
C₂×AGL(1,ℤ/8)×C₁₃₉	2
#3265	139