Subgroups — #31815653

Order 17792.

806 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×D₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#17984869	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#17984866	C₂	1	1	yes	maximal, characteristic, complemented
4	#121×D₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#22581100	C₂	1	1	yes	maximal, characteristic, complemented
6	#22581098	C₂	1	1	yes	maximal, characteristic, complemented
7	#22581096	C₂	1	1	yes	maximal, characteristic, complemented
8	#22581093	C₂	1	1	yes	maximal, characteristic, complemented
9	#22581090	C₂	1	1	yes	maximal, characteristic, complemented
10	#22581088	C₂	1	1	yes	maximal, characteristic, complemented
11	#22581085	C₂	1	1	yes	maximal, characteristic, complemented
12	#22580953	C₂	1	1	yes	maximal, characteristic, complemented
13	#22580951	C₂	1	1	yes	maximal, characteristic, complemented
14	#22580915	C₂	1	1	yes	maximal, characteristic, complemented
15	#449×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14555786	C₂²	1	1	yes	characteristic
17	C₂×#14555785	—	2	1	no	—
18	C₂×#14555785	C₂²	1	1	yes	characteristic, complemented
19	C₂×#14555784	—	2	1	no	—
20	C₂×#14555784	C₂²	1	1	yes	characteristic
21	#41×D₁₃₉	—	2	4	no	—
22	#41×D₁₃₉	—	2	4	no	—
23	C₂×Q₈×D₁₃₉	C₂²	1	1	yes	characteristic, complemented
24	C₂×D₄×D₁₃₉	—	2	1	no	—
25	C₂×D₄×D₁₃₉	—	2	1	no	—
26	C₂×D₄×D₁₃₉	C₂²	1	1	yes	characteristic, complemented
27	C₂×D₄×D₁₃₉	C₂²	1	1	yes	characteristic, complemented
28	C₂²×C₄×D₁₃₉	—	2	1	no	—
29	C₂²×C₄×D₁₃₉	C₂²	1	1	yes	characteristic
30	#17984869	—	2	4	no	—
31	#17984866	—	2	4	no	—
32	C₂×#14555774	C₂²	1	1	yes	characteristic, complemented
33	C₂×#14555773	C₂²	1	1	yes	characteristic, complemented
34	C₂×#14555772	C₂²	1	1	yes	characteristic, complemented
35	C₂×D₁₁₁₂	C₂²	1	1	yes	characteristic, complemented
36	C₂×#14555770	C₂²	1	1	yes	characteristic, complemented
37	C₂×#14555770	C₂²	1	1	yes	characteristic, complemented
38	C₂×#14555768	C₂²	1	1	yes	characteristic, complemented
39	C₂×#14555768	C₂²	1	1	yes	characteristic, complemented
40	#17984817	C₂²	1	1	yes	characteristic
41	#17984816	C₂²	1	1	yes	characteristic, complemented
42	#17984815	—	2	1	no	—
43	#17984814	—	2	1	no	—
44	#17984813	C₂²	1	1	yes	characteristic
45	C₄⋊C₄×D₁₃₉	C₂²	1	1	yes	characteristic, complemented
46	C₂²⋊C₄×D₁₃₉	—	2	1	no	—
47	#17984767	C₂²	1	1	yes	characteristic, complemented
48	#17984766	C₂²	1	1	yes	characteristic, complemented
49	#17984765	C₂²	1	1	yes	characteristic, complemented
50	#17984764	C₂²	1	1	yes	characteristic, complemented
51	#17984763	C₂²	1	1	yes	characteristic, complemented
52	#17984762	C₂²	1	1	yes	characteristic, complemented
53	C₂²⋊(C₁₃₉⋊C₈)	C₂²	1	1	yes	characteristic, complemented
54	(C₂×D₁₃₉)⋊C₈	C₂²	1	1	yes	characteristic, complemented
55	(C₂×D₁₃₉)⋊C₈	C₂²	1	1	yes	characteristic, complemented
56	C₂×#41×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
57	C₂×SD₁₆×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
58	C₂×D₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
59	#121×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
60	#103×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
61	#102×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
62	C₂²⋊C₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
63	C₂³×D₁₃₉	—	2	1	no	—
64	C₂³×D₁₃₉	—	2	1	no	—
65	C₂³×D₁₃₉	D₄	1	1	yes	characteristic
66	#14555786	—	2	2	no	—
67	#14555786	D₄	1	4	yes	complemented
68	#14555785	—	2	8	no	—
69	#14555785	—	2	2	no	—
70	#14555785	—	2	2	no	—
71	#14555784	—	2	8	no	—
72	#14555784	—	2	2	no	—
73	#14555784	D₄	1	4	yes	complemented
74	C₂×Dic₂₇₈	—	2	1	no	—
75	C₂×Dic₂₇₈	C₂³	1	1	yes	characteristic
76	Q₈×D₁₃₉	—	2	2	no	—
77	Q₈×D₁₃₉	—	2	2	no	—
78	C₂×D₅₅₆	—	2	1	no	—
79	C₂×D₅₅₆	—	2	1	no	—
80	C₂×D₅₅₆	C₂³	1	1	yes	characteristic
81	C₂×D₅₅₆	C₂³	1	1	yes	characteristic
82	C₂×C₂²⋊D₁₃₉	—	2	1	no	—
83	C₂×C₂²⋊D₁₃₉	—	2	1	no	—
84	C₂×C₂²⋊D₁₃₉	—	2	1	no	—
85	C₂×C₂²⋊D₁₃₉	—	2	1	no	—
86	C₂×C₂²⋊D₁₃₉	—	2	1	no	—
87	C₂×C₂²⋊D₁₃₉	—	2	1	no	—
88	D₄×D₁₃₉	—	2	8	no	—
89	D₄×D₁₃₉	—	2	2	no	—
90	D₄×D₁₃₉	—	2	2	no	—
91	D₄×D₁₃₉	—	2	2	no	—
92	D₄×D₁₃₉	—	2	2	no	—
93	D₄×D₁₃₉	—	4	4	no	—
94	C₂²×Dic₁₃₉	—	2	1	no	—
95	C₂²×Dic₁₃₉	D₄	1	1	yes	characteristic
96	C₂×C₄×D₁₃₉	—	2	8	no	—
97	C₂×C₄×D₁₃₉	—	2	1	no	—
98	C₂×C₄×D₁₃₉	—	2	1	no	—
99	C₂×C₄×D₁₃₉	—	2	2	no	—
100	C₂×C₄×D₁₃₉	—	2	2	no	—
101	C₂×C₄×D₁₃₉	—	2	1	no	—
102	C₂×C₄×D₁₃₉	—	2	1	no	—
103	C₂×C₄×D₁₃₉	D₄	1	1	yes	characteristic
104	C₂×C₄×D₁₃₉	D₄	1	1	yes	characteristic
105	C₂×C₄×D₁₃₉	C₂³	1	1	yes	characteristic
106	C₂×C₄×D₁₃₉	C₂³	1	1	yes	characteristic
107	#14555774	—	2	2	no	—
108	#14555773	—	2	2	no	—
109	#14555772	—	2	2	no	—
110	D₁₁₁₂	—	2	2	no	—
111	#14555770	—	2	2	no	—
112	#14555770	—	2	2	no	—
113	#14555768	—	2	2	no	—
114	#14555768	—	2	2	no	—
115	C₂×C₁₃₉⋊C₈	C₂³	1	1	yes	characteristic
116	C₂×C₁₃₉⋊C₈	C₂³	1	1	yes	characteristic
117	C₄⋊Dic₁₃₉	C₂³	1	1	yes	characteristic
118	Dic₁₃₉⋊C₄	—	2	1	no	—
119	C₂²⋊Dic₁₃₉	—	2	1	no	—
120	(C₂×D₁₃₉)⋊C₄	—	2	1	no	—
121	(C₂×D₁₃₉)⋊C₄	—	2	1	no	—
122	#41×C₁₃₉	—	2	2	no	—
123	#41×C₁₃₉	—	2	2	no	—
124	C₂×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
125	C₂×D₄×C₁₃₉	—	2	1	no	—
126	C₂×D₄×C₁₃₉	—	2	1	no	—
127	C₂×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
128	C₂×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₁₃₉	—	2	1	no	—
130	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
131	SD₁₆×C₁₃₉	—	2	2	no	—
132	D₈×C₁₃₉	—	2	2	no	—
133	C₂×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
134	C₂×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
135	C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
136	C₂²⋊C₄×C₁₃₉	—	2	1	no	—
137	C₂²×D₁₃₉	—	2	4	no	—
138	C₂²×D₁₃₉	—	2	1	no	—
139	C₂²×D₁₃₉	—	2	2	no	—
140	C₂²×D₁₃₉	—	2	2	no	—
141	C₂²×D₁₃₉	—	2	1	no	—
142	C₂²×D₁₃₉	—	4	1	no	—
143	C₂²×D₁₃₉	—	4	2	no	—
144	C₂²×D₁₃₉	—	4	2	no	—
145	C₂²×D₁₃₉	—	4	2	no	—
146	C₂²×D₁₃₉	—	4	2	no	—
147	C₂²×D₁₃₉	—	4	2	no	—
148	C₂²×D₁₃₉	C₂×D₄	1	1	yes	characteristic
149	C₂²×D₁₃₉	C₂×D₄	1	1	yes	characteristic
150	Dic₂₇₈	—	2	4	no	—
151	Dic₂₇₈	—	2	1	no	—
152	Dic₂₇₈	C₂×D₄	1	2	yes	complemented
153	D₅₅₆	—	2	4	no	—
154	D₅₅₆	—	2	1	no	—
155	D₅₅₆	—	2	1	no	—
156	D₅₅₆	—	2	1	no	—
157	D₅₅₆	—	4	2	no	—
158	D₅₅₆	C₂×D₄	1	2	yes	complemented
159	C₂²⋊D₁₃₉	—	2	4	no	—
160	C₂²⋊D₁₃₉	—	2	4	no	—
161	C₂²⋊D₁₃₉	—	2	4	no	—
162	C₂²⋊D₁₃₉	—	4	2	no	—
163	C₂²⋊D₁₃₉	—	4	2	no	—
164	C₂²⋊D₁₃₉	—	4	2	no	—
165	C₂×Dic₁₃₉	—	2	1	no	—
166	C₂×Dic₁₃₉	—	2	4	no	—
167	C₂×Dic₁₃₉	—	2	2	no	—
168	C₂×Dic₁₃₉	—	2	1	no	—
169	C₂×Dic₁₃₉	C₂×D₄	1	1	yes	characteristic
170	C₂×Dic₁₃₉	C₂×D₄	1	1	yes	characteristic
171	C₄×D₁₃₉	—	2	4	no	—
172	C₄×D₁₃₉	—	2	4	no	—
173	C₄×D₁₃₉	—	2	2	no	—
174	C₄×D₁₃₉	—	2	1	no	—
175	C₄×D₁₃₉	—	2	1	no	—
176	C₄×D₁₃₉	—	2	2	no	—
177	C₄×D₁₃₉	—	2	4	no	—
178	C₄×D₁₃₉	—	4	2	no	—
179	C₄×D₁₃₉	C₂×D₄	1	2	yes	—
180	C₄×D₁₃₉	C₂×D₄	1	2	yes	—
181	C₁₃₉⋊C₈	—	2	1	no	—
182	C₁₃₉⋊C₈	—	2	1	no	—
183	C₂³×C₁₃₉	—	2	1	no	—
184	C₂³×C₁₃₉	—	2	1	no	—
185	C₂³×C₁₃₉	C₂×D₄	1	1	yes	characteristic
186	Q₈×C₁₃₉	—	2	1	no	—
187	Q₈×C₁₃₉	C₂×D₄	1	2	yes	complemented
188	D₄×C₁₃₉	—	2	4	no	—
189	D₄×C₁₃₉	—	2	1	no	—
190	D₄×C₁₃₉	—	2	1	no	—
191	D₄×C₁₃₉	—	2	1	no	—
192	D₄×C₁₃₉	—	4	2	no	—
193	D₄×C₁₃₉	C₂×D₄	1	2	yes	complemented
194	C₂×C₄×C₁₃₉	—	2	4	no	—
195	C₂×C₄×C₁₃₉	—	2	1	no	—
196	C₂×C₄×C₁₃₉	—	2	1	no	—
197	C₂×C₄×C₁₃₉	—	2	1	no	—
198	C₂×C₄×C₁₃₉	—	2	1	no	—
199	C₂×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
200	C₂×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
201	C₈×C₁₃₉	—	2	1	no	—
202	C₈×C₁₃₉	—	2	1	no	—
203	C₂²×C₁₃₉	—	2	1	no	—
204	C₂²×C₁₃₉	—	2	2	no	—
205	C₂²×C₁₃₉	—	2	1	no	—
206	C₂²×C₁₃₉	—	2	1	no	—
207	C₂²×C₁₃₉	—	4	1	no	—
208	C₂²×C₁₃₉	—	4	1	no	—
209	C₂²×C₁₃₉	—	4	1	no	—
210	C₂²×C₁₃₉	—	4	1	no	—
211	C₂²×C₁₃₉	—	4	1	no	—
212	C₂²×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
213	C₂×D₁₃₉	—	2	1	no	—
214	C₂×D₁₃₉	—	2	1	no	—
215	C₂×D₁₃₉	—	2	1	no	—
216	C₂×D₁₃₉	—	2	1	no	—
217	C₂×D₁₃₉	—	2	2	no	—
218	C₂×D₁₃₉	—	4	4	no	—
219	C₂×D₁₃₉	—	4	8	no	—
220	C₂×D₁₃₉	—	4	1	no	—
221	C₂×D₁₃₉	—	4	1	no	—
222	C₂×D₁₃₉	—	4	1	no	—
223	C₂×D₁₃₉	—	4	1	no	—
224	C₂×D₁₃₉	—	4	1	no	—
225	C₂×D₁₃₉	—	8	4	no	—
226	C₂×D₁₃₉	#120	1	2	yes	—
227	C₂×D₁₃₉	AGL(1,ℤ/8)	1	2	yes	complemented
228	C₄×C₁₃₉	—	2	1	no	—
229	C₄×C₁₃₉	—	2	2	no	—
230	C₄×C₁₃₉	—	4	1	no	—
231	C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
232	C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
233	Dic₁₃₉	—	2	2	no	—
234	Dic₁₃₉	—	2	1	no	—
235	Dic₁₃₉	—	4	1	no	—
236	Dic₁₃₉	#120	1	2	yes	—
237	C₂×C₁₃₉	—	4	1	no	—
238	C₂×C₁₃₉	—	4	2	no	—
239	C₂×C₁₃₉	—	8	1	no	—
240	C₂×C₁₃₉	C₂×#120	1	1	yes	characteristic
241	C₂×C₁₃₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
242	C₂×C₁₃₉	#575	1	1	yes	characteristic
243	D₁₃₉	—	2	2	no	—
244	D₁₃₉	—	2	2	no	—
245	D₁₃₉	—	4	2	no	—
246	D₁₃₉	—	8	1	no	—
247	C₁₃₉	#3006	1	1	yes	characteristic, complemented, Sylow
248	#3006	—	139	1	no	maximal, Sylow
249	C₂²×#41	—	139	1	no	—
250	C₂×AGL(1,ℤ/8)	—	139	1	no	—
251	C₂×AGL(1,ℤ/8)	—	139	1	no	—
252	C₂×#121	—	139	1	no	—
253	#449	—	139	1	no	—
254	#449	—	139	1	no	—
255	#449	—	139	1	no	—
256	#449	D₁₃₉	1	1	yes	characteristic, complemented
257	#448	—	139	1	no	—
258	#448	—	139	1	no	—
259	#447	—	139	1	no	—
260	#447	—	139	1	no	—
261	#417	—	139	1	no	—
262	#417	—	139	1	no	—
263	#407	—	139	1	no	—
264	C₂×#41	—	278	1	no	—
265	C₂×#41	—	278	4	no	—
266	C₂×#41	—	278	4	no	—
267	C₂×#41	—	278	1	no	—
268	C₂×#41	—	139	1	no	—
269	C₂×#41	—	139	1	no	—
270	C₂×#41	—	139	1	no	—
271	C₂×#41	C₂×D₁₃₉	1	1	yes	characteristic, complemented
272	C₂²×Q₈	—	139	1	no	—
273	C₂²×D₄	—	278	1	no	—
274	C₂²×D₄	—	278	1	no	—
275	C₂²×D₄	—	139	1	no	—
276	C₂²×D₄	—	139	1	no	—
277	C₂³×C₄	—	278	1	no	—
278	C₂³×C₄	—	139	1	no	—
279	AGL(1,ℤ/8)	—	278	4	no	—
280	AGL(1,ℤ/8)	—	278	4	no	—
281	C₂×SD₁₆	—	139	1	no	—
282	C₂×SD₁₆	—	139	1	no	—
283	C₂×SD₁₆	—	139	1	no	—
284	C₂×SD₁₆	C₂×D₁₃₉	1	1	yes	characteristic, complemented
285	C₂×D₈	—	139	1	no	—
286	C₂×D₈	—	139	1	no	—
287	C₂×D₈	—	139	1	no	—
288	C₂×D₈	C₂×D₁₃₉	1	1	yes	characteristic, complemented
289	C₂×M₁₆	—	139	1	no	—
290	C₂×M₁₆	—	139	1	no	—
291	#121	—	278	1	no	—
292	#121	—	278	1	no	—
293	#121	—	139	1	no	—
294	#121	—	139	1	no	—
295	#121	—	139	1	no	—
296	#121	C₂×D₁₃₉	1	1	yes	characteristic, complemented
297	C₂×C₄⋊C₄	—	139	1	no	—
298	C₂×C₂²⋊C₄	—	278	1	no	—
299	#103	—	139	1	no	—
300	#103	—	139	1	no	—
301	#103	—	139	1	no	—
302	#103	C₂×D₁₃₉	1	1	yes	characteristic, complemented
303	#102	—	139	1	no	—
304	#102	—	139	1	no	—
305	#102	—	139	1	no	—
306	#102	C₂×D₁₃₉	1	1	yes	characteristic, complemented
307	C₂²⋊C₈	—	139	1	no	—
308	C₂²⋊C₈	—	139	1	no	—
309	C₂²⋊C₈	—	139	1	no	—
310	C₂²⋊C₈	C₂×D₁₃₉	1	1	yes	characteristic, complemented
311	C₂⁴	—	278	1	no	—
312	C₂⁴	—	278	1	no	—
313	C₂⁴	—	139	1	no	—
314	#41	—	2	2	no	—
315	#41	—	2	2	no	—
316	#41	—	278	8	no	—
317	#41	—	278	2	no	—
318	#41	—	278	2	no	—
319	#41	—	278	8	no	—
320	#41	—	278	2	no	—
321	#41	—	278	2	no	—
322	#41	—	139	4	no	—
323	#41	—	139	4	no	—
324	C₂×Q₈	—	278	1	no	—
325	C₂×Q₈	—	278	2	no	—
326	C₂×Q₈	—	278	2	no	—
327	C₂×Q₈	—	139	1	no	—
328	C₂×Q₈	C₂²×D₁₃₉	1	1	yes	characteristic
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	—	278	1	no	—
332	C₂×D₄	—	278	1	no	—
333	C₂×D₄	—	278	8	no	—
334	C₂×D₄	—	278	2	no	—
335	C₂×D₄	—	278	1	no	—
336	C₂×D₄	—	278	1	no	—
337	C₂×D₄	—	278	2	no	—
338	C₂×D₄	—	278	1	no	—
339	C₂×D₄	—	278	1	no	—
340	C₂×D₄	—	278	2	no	—
341	C₂×D₄	—	278	2	no	—
342	C₂×D₄	—	278	1	no	—
343	C₂×D₄	—	278	1	no	—
344	C₂×D₄	—	556	4	no	—
345	C₂×D₄	—	139	1	no	—
346	C₂×D₄	—	139	1	no	—
347	C₂×D₄	C₂²×D₁₃₉	1	1	yes	characteristic
348	C₂×D₄	C₂²×D₁₃₉	1	1	yes	characteristic
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	278	8	no	—
351	C₂²×C₄	—	278	1	no	—
352	C₂²×C₄	—	278	1	no	—
353	C₂²×C₄	—	278	2	no	—
354	C₂²×C₄	—	278	2	no	—
355	C₂²×C₄	—	278	1	no	—
356	C₂²×C₄	—	278	1	no	—
357	C₂²×C₄	—	278	1	no	—
358	C₂²×C₄	—	139	1	no	—
359	C₂²×C₄	—	139	1	no	—
360	C₂²×C₄	—	139	1	no	—
361	C₂²×C₄	—	139	1	no	—
362	C₂²×C₄	—	139	1	no	—
363	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
364	SD₁₆	—	2	2	no	—
365	SD₁₆	—	278	2	no	—
366	SD₁₆	—	278	2	no	—
367	SD₁₆	—	278	2	no	—
368	D₈	—	2	2	no	—
369	D₈	—	278	2	no	—
370	D₈	—	278	2	no	—
371	D₈	—	278	2	no	—
372	M₁₆	—	278	2	no	—
373	M₁₆	—	278	2	no	—
374	C₂×C₈	—	139	1	no	—
375	C₂×C₈	—	139	1	no	—
376	C₂×C₈	C₂²×D₁₃₉	1	1	yes	characteristic
377	C₂×C₈	C₂²×D₁₃₉	1	1	yes	characteristic
378	C₄⋊C₄	—	278	1	no	—
379	C₄⋊C₄	—	139	1	no	—
380	C₄⋊C₄	C₂²×D₁₃₉	1	1	yes	characteristic
381	C₂²⋊C₄	—	2	1	no	—
382	C₂²⋊C₄	—	278	1	no	—
383	C₂²⋊C₄	—	278	1	no	—
384	C₂²⋊C₄	—	278	1	no	—
385	C₂³	—	2	1	no	—
386	C₂³	—	2	1	no	—
387	C₂³	—	278	4	no	—
388	C₂³	—	278	2	no	—
389	C₂³	—	278	2	no	—
390	C₂³	—	278	1	no	—
391	C₂³	—	278	1	no	—
392	C₂³	—	556	1	no	—
393	C₂³	—	556	2	no	—
394	C₂³	—	556	2	no	—
395	C₂³	—	556	2	no	—
396	C₂³	—	556	2	no	—
397	C₂³	—	556	2	no	—
398	C₂³	—	139	1	no	—
399	C₂³	—	139	1	no	—
400	C₂³	D₄×D₁₃₉	1	1	yes	characteristic
401	Q₈	—	2	1	no	—
402	Q₈	—	278	4	no	—
403	Q₈	—	278	1	no	—
404	Q₈	—	139	2	no	—
405	Q₈	D₄×D₁₃₉	1	2	yes	complemented
406	D₄	—	2	4	no	—
407	D₄	—	2	1	no	—
408	D₄	—	2	1	no	—
409	D₄	—	2	1	no	—
410	D₄	—	4	2	no	—
411	D₄	—	278	4	no	—
412	D₄	—	278	4	no	—
413	D₄	—	278	4	no	—
414	D₄	—	278	4	no	—
415	D₄	—	278	1	no	—
416	D₄	—	278	1	no	—
417	D₄	—	278	1	no	—
418	D₄	—	556	2	no	—
419	D₄	—	556	2	no	—
420	D₄	—	556	2	no	—
421	D₄	—	556	2	no	—
422	D₄	—	139	2	no	—
423	D₄	D₄×D₁₃₉	1	2	yes	complemented
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	278	4	no	—
430	C₂×C₄	—	278	4	no	—
431	C₂×C₄	—	278	2	no	—
432	C₂×C₄	—	278	2	no	—
433	C₂×C₄	—	278	4	no	—
434	C₂×C₄	—	278	1	no	—
435	C₂×C₄	—	278	4	no	—
436	C₂×C₄	—	278	2	no	—
437	C₂×C₄	—	278	1	no	—
438	C₂×C₄	—	278	1	no	—
439	C₂×C₄	—	278	1	no	—
440	C₂×C₄	—	556	2	no	—
441	C₂×C₄	—	139	1	no	—
442	C₂×C₄	—	139	1	no	—
443	C₂×C₄	—	139	2	no	—
444	C₂×C₄	—	139	2	no	—
445	C₂×C₄	D₄×D₁₃₉	1	1	yes	characteristic
446	C₂×C₄	C₂³×D₁₃₉	1	1	yes	characteristic
447	C₈	—	2	1	no	—
448	C₈	—	2	1	no	—
449	C₈	—	278	1	no	—
450	C₈	—	278	1	no	—
451	C₂²	—	2	1	no	—
452	C₂²	—	2	2	no	—
453	C₂²	—	2	1	no	—
454	C₂²	—	2	1	no	—
455	C₂²	—	4	1	no	—
456	C₂²	—	4	1	no	—
457	C₂²	—	4	1	no	—
458	C₂²	—	4	1	no	—
459	C₂²	—	4	1	no	—
460	C₂²	—	278	1	no	—
461	C₂²	—	278	1	no	—
462	C₂²	—	278	1	no	—
463	C₂²	—	278	1	no	—
464	C₂²	—	278	2	no	—
465	C₂²	—	556	4	no	—
466	C₂²	—	556	8	no	—
467	C₂²	—	556	1	no	—
468	C₂²	—	556	1	no	—
469	C₂²	—	556	1	no	—
470	C₂²	—	556	1	no	—
471	C₂²	—	556	1	no	—
472	C₂²	—	1112	4	no	—
473	C₂²	—	139	2	no	—
474	C₂²	—	139	2	no	—
475	C₂²	C₂×D₄×D₁₃₉	1	1	yes	characteristic
476	C₄	—	2	1	no	—
477	C₄	—	2	2	no	—
478	C₄	—	4	1	no	—
479	C₄	—	278	2	no	—
480	C₄	—	278	1	no	—
481	C₄	—	556	1	no	—
482	C₄	—	139	2	no	—
483	C₄	C₂×D₄×D₁₃₉	1	1	yes	characteristic
484	C₄	C₂×D₄×D₁₃₉	1	1	yes	characteristic
485	C₂	—	4	1	no	—
486	C₂	—	4	2	no	—
487	C₂	—	8	1	no	—
488	C₂	—	278	2	no	—
489	C₂	—	278	2	no	—
490	C₂	—	556	2	no	—
491	C₂	—	1112	1	no	—
492	C₂	#120×D₁₃₉	1	1	yes	characteristic
493	C₂	AGL(1,ℤ/8)×D₁₃₉	1	1	yes	characteristic
494	C₂	#22581750	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₃₉
commutator, cosocle	C₂×C₄×C₁₃₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₃₉
Fitting	#449×C₁₃₉	C₂
socle	C₂²×C₁₃₉	C₂²×D₄
hypercenter	#449	D₁₃₉
hypocenter	C₁₃₉	#3006
LCS	G ▷ C₂×C₄×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #449

Complements

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

N	H ≅ G/N	type
1. C₂×#41×D₁₃₉	C₂	semidirect
2. C₂×#17984869	C₂	semidirect
3. C₂×#17984866	C₂	semidirect
4. #121×D₁₃₉	C₂	semidirect
5. #22581100	C₂	semidirect
6. #22581098	C₂	semidirect
7. #22581096	C₂	semidirect
8. #22581093	C₂	semidirect
9. #22581090	C₂	semidirect
10. #22581088	C₂	semidirect
11. #22581085	C₂	semidirect
12. #22580953	C₂	semidirect
13. #22580951	C₂	semidirect
14. #22580915	C₂	semidirect
15. #449×C₁₃₉	C₂	semidirect
18. C₂×#14555785	C₂²	semidirect
23. C₂×Q₈×D₁₃₉	C₂²	semidirect
26. C₂×D₄×D₁₃₉	C₂²	semidirect
27. C₂×D₄×D₁₃₉	C₂²	semidirect
32. C₂×#14555774	C₂²	semidirect
33. C₂×#14555773	C₂²	semidirect
34. C₂×#14555772	C₂²	semidirect
35. C₂×D₁₁₁₂	C₂²	semidirect
36. C₂×#14555770	C₂²	semidirect
37. C₂×#14555770	C₂²	semidirect
38. C₂×#14555768	C₂²	semidirect
39. C₂×#14555768	C₂²	semidirect
41. #17984816	C₂²	semidirect
45. C₄⋊C₄×D₁₃₉	C₂²	semidirect
47. #17984767	C₂²	semidirect
48. #17984766	C₂²	semidirect
49. #17984765	C₂²	semidirect
50. #17984764	C₂²	semidirect
51. #17984763	C₂²	semidirect
52. #17984762	C₂²	semidirect
53. C₂²⋊(C₁₃₉⋊C₈)	C₂²	semidirect
54. (C₂×D₁₃₉)⋊C₈	C₂²	semidirect
55. (C₂×D₁₃₉)⋊C₈	C₂²	semidirect
56. C₂×#41×C₁₃₉	C₂²	semidirect
57. C₂×SD₁₆×C₁₃₉	C₂²	semidirect
58. C₂×D₈×C₁₃₉	C₂²	semidirect
59. #121×C₁₃₉	C₂²	semidirect
60. #103×C₁₃₉	C₂²	semidirect
61. #102×C₁₃₉	C₂²	semidirect
62. C₂²⋊C₈×C₁₃₉	C₂²	semidirect
67. #14555786	D₄	semidirect
73. #14555784	D₄	semidirect
152. Dic₂₇₈	C₂×D₄	semidirect
158. D₅₅₆	C₂×D₄	semidirect
187. Q₈×C₁₃₉	C₂×D₄	semidirect
193. D₄×C₁₃₉	C₂×D₄	semidirect
227. C₂×D₁₃₉	AGL(1,ℤ/8)	semidirect
247. C₁₃₉	#3006	semidirect
256. #449	D₁₃₉	semidirect
271. C₂×#41	C₂×D₁₃₉	semidirect
284. C₂×SD₁₆	C₂×D₁₃₉	semidirect
288. C₂×D₈	C₂×D₁₃₉	semidirect
296. #121	C₂×D₁₃₉	semidirect
302. #103	C₂×D₁₃₉	semidirect
306. #102	C₂×D₁₃₉	semidirect
310. C₂²⋊C₈	C₂×D₁₃₉	semidirect
405. Q₈	D₄×D₁₃₉	semidirect
423. D₄	D₄×D₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#41×D₁₃₉	2
C₂×#17984869	2
C₂×#17984866	2
#121×D₁₃₉	2
#22581100	2
#22581098	2
#22581096	2
#22581093	2
#22581090	2
#22581088	2
#22581085	2
#22580953	2
#22580951	2
#22580915	2
#449×C₁₃₉	2
#3006	139