Subgroups — C₂×#104×D₁₃₉ #31814939

Order 17792.

856 conjugacy classes of subgroups.

The subgroup lattice has 404 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
2	C₂×M₁₆×D₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄²×D₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#17984770	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#17984769	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#17984768	C₂	1	1	yes	maximal, characteristic, complemented
7	#104×D₁₃₉	C₂	1	8	yes	maximal, direct product factor
8	C₂×#104×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#14555786	C₄	1	1	yes	characteristic, complemented
10	C₂×#14555785	—	2	1	no	—
11	C₂×#14555785	C₂²	1	1	yes	characteristic
12	C₂×#14555784	—	2	1	no	—
13	C₂×#14555784	C₄	1	1	yes	characteristic, complemented
14	#41×D₁₃₉	—	2	2	no	—
15	#41×D₁₃₉	—	2	2	no	—
16	#41×D₁₃₉	C₄	1	4	yes	complemented
17	#41×D₁₃₉	C₂²	1	4	yes	—
18	C₂×Q₈×D₁₃₉	C₄	1	1	yes	characteristic, complemented
19	C₂×D₄×D₁₃₉	—	2	1	no	—
20	C₂×D₄×D₁₃₉	C₄	1	1	yes	characteristic, complemented
21	C₂²×C₄×D₁₃₉	—	2	1	no	—
22	C₂²×C₄×D₁₃₉	—	2	1	no	—
23	C₂²×C₄×D₁₃₉	C₂²	1	1	yes	characteristic
24	C₂×#14555769	C₂²	1	1	yes	characteristic, complemented
25	C₂×#14555768	—	2	1	no	—
26	M₁₆×D₁₃₉	—	2	2	no	—
27	M₁₆×D₁₃₉	C₂²	1	4	yes	complemented
28	C₂×C₈×D₁₃₉	—	2	1	no	—
29	C₂×C₄×Dic₁₃₉	—	2	1	no	—
30	C₂×C₄×Dic₁₃₉	C₂²	1	1	yes	characteristic, complemented
31	C₄²×D₁₃₉	—	2	2	no	—
32	C₄²×D₁₃₉	C₂²	1	4	yes	complemented
33	#17984770	C₂²	1	4	yes	complemented
34	#17984769	C₂²	1	4	yes	complemented
35	#17984768	C₂²	1	4	yes	complemented
36	C₂×#41×C₁₃₉	C₂²	1	1	yes	characteristic
37	C₂×M₁₆×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
39	#104×C₁₃₉	C₂²	1	4	yes	complemented
40	C₂³×D₁₃₉	—	2	1	no	—
41	C₂³×D₁₃₉	D₄	1	1	yes	characteristic
42	#14555786	—	2	2	no	—
43	#14555786	C₂×C₄	1	4	yes	complemented
44	#14555785	—	2	4	no	—
45	#14555785	—	2	4	no	—
46	#14555785	—	2	1	no	—
47	#14555785	—	2	1	no	—
48	#14555785	C₂×C₄	1	2	yes	complemented
49	#14555785	C₂³	1	2	yes	—
50	#14555784	—	2	4	no	—
51	#14555784	—	2	4	no	—
52	#14555784	—	2	2	no	—
53	#14555784	C₂×C₄	1	4	yes	complemented
54	C₂×Dic₂₇₈	—	2	1	no	—
55	C₂×Dic₂₇₈	C₂×C₄	1	1	yes	characteristic, complemented
56	Q₈×D₁₃₉	—	2	2	no	—
57	Q₈×D₁₃₉	C₂×C₄	1	4	yes	complemented
58	C₂×D₅₅₆	—	2	1	no	—
59	C₂×D₅₅₆	C₂×C₄	1	1	yes	characteristic, complemented
60	C₂×C₂²⋊D₁₃₉	—	2	1	no	—
61	C₂×C₂²⋊D₁₃₉	—	2	1	no	—
62	C₂×C₂²⋊D₁₃₉	—	2	1	no	—
63	D₄×D₁₃₉	—	2	4	no	—
64	D₄×D₁₃₉	—	2	4	no	—
65	D₄×D₁₃₉	—	2	2	no	—
66	D₄×D₁₃₉	C₂×C₄	1	4	yes	complemented
67	C₂²×Dic₁₃₉	—	2	1	no	—
68	C₂²×Dic₁₃₉	—	2	1	no	—
69	C₂²×Dic₁₃₉	D₄	1	1	yes	characteristic
70	C₂×C₄×D₁₃₉	—	2	8	no	—
71	C₂×C₄×D₁₃₉	—	2	1	no	—
72	C₂×C₄×D₁₃₉	—	2	4	no	—
73	C₂×C₄×D₁₃₉	—	2	1	no	—
74	C₂×C₄×D₁₃₉	—	2	4	no	—
75	C₂×C₄×D₁₃₉	—	2	4	no	—
76	C₂×C₄×D₁₃₉	—	2	1	no	—
77	C₂×C₄×D₁₃₉	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄×D₁₃₉	C₂×C₄	1	2	yes	—
79	C₂×C₄×D₁₃₉	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄×D₁₃₉	D₄	1	2	yes	—
81	C₂×C₄×D₁₃₉	D₄	1	1	yes	characteristic
82	C₂×C₄×D₁₃₉	D₄	1	2	yes	—
83	C₂×C₄×D₁₃₉	D₄	1	1	yes	characteristic
84	C₂×C₄×D₁₃₉	C₂³	1	2	yes	—
85	#14555769	—	2	1	no	—
86	#14555769	C₂³	1	2	yes	complemented
87	#14555768	—	2	4	no	—
88	C₂×C₁₃₉⋊C₈	—	2	1	no	—
89	C₈×D₁₃₉	—	2	4	no	—
90	C₄×Dic₁₃₉	—	2	4	no	—
91	C₄×Dic₁₃₉	—	2	1	no	—
92	C₄×Dic₁₃₉	C₂³	1	2	yes	complemented
93	#41×C₁₃₉	—	2	1	no	—
94	#41×C₁₃₉	—	2	1	no	—
95	#41×C₁₃₉	C₂×C₄	1	2	yes	complemented
96	#41×C₁₃₉	C₂³	1	2	yes	—
97	C₂×Q₈×C₁₃₉	C₂×C₄	1	1	yes	characteristic, complemented
98	C₂×D₄×C₁₃₉	—	2	1	no	—
99	C₂×D₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic, complemented
100	C₂²×C₄×C₁₃₉	—	2	1	no	—
101	C₂²×C₄×C₁₃₉	—	2	1	no	—
102	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
103	M₁₆×C₁₃₉	—	2	1	no	—
104	M₁₆×C₁₃₉	C₂³	1	2	yes	complemented
105	C₂×C₈×C₁₃₉	—	2	1	no	—
106	C₄²×C₁₃₉	—	2	1	no	—
107	C₄²×C₁₃₉	C₂³	1	2	yes	complemented
108	C₂²×D₁₃₉	—	2	4	no	—
109	C₂²×D₁₃₉	—	2	1	no	—
110	C₂²×D₁₃₉	—	2	4	no	—
111	C₂²×D₁₃₉	—	4	4	no	—
112	C₂²×D₁₃₉	C₂²⋊C₄	1	2	yes	—
113	C₂²×D₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
114	C₂²×D₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
115	C₂²×D₁₃₉	C₂×D₄	1	2	yes	—
116	Dic₂₇₈	—	2	1	no	—
117	Dic₂₇₈	—	2	4	no	—
118	Dic₂₇₈	C₂²×C₄	1	2	yes	complemented
119	D₅₅₆	—	2	4	no	—
120	D₅₅₆	—	2	1	no	—
121	D₅₅₆	C₂²×C₄	1	2	yes	complemented
122	C₂²⋊D₁₃₉	—	2	2	no	—
123	C₂²⋊D₁₃₉	—	2	2	no	—
124	C₂²⋊D₁₃₉	—	2	4	no	—
125	C₂²⋊D₁₃₉	—	2	4	no	—
126	C₂×Dic₁₃₉	—	2	4	no	—
127	C₂×Dic₁₃₉	—	2	1	no	—
128	C₂×Dic₁₃₉	—	2	2	no	—
129	C₂×Dic₁₃₉	—	2	4	no	—
130	C₂×Dic₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
131	C₂×Dic₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
132	C₂×Dic₁₃₉	C₂²⋊C₄	1	2	yes	—
133	C₂×Dic₁₃₉	C₂×D₄	1	2	yes	—
134	C₄×D₁₃₉	—	2	16	no	—
135	C₄×D₁₃₉	—	2	4	no	—
136	C₄×D₁₃₉	—	2	2	no	—
137	C₄×D₁₃₉	—	2	2	no	—
138	C₄×D₁₃₉	—	2	4	no	—
139	C₄×D₁₃₉	C₂²⋊C₄	1	2	yes	—
140	C₄×D₁₃₉	C₂²⋊C₄	1	2	yes	—
141	C₄×D₁₃₉	C₂²⋊C₄	1	2	yes	—
142	C₄×D₁₃₉	C₂²⋊C₄	1	2	yes	—
143	C₄×D₁₃₉	C₂²×C₄	1	2	yes	—
144	C₄×D₁₃₉	C₂²×C₄	1	2	yes	—
145	C₄×D₁₃₉	C₂×D₄	1	2	yes	—
146	C₄×D₁₃₉	C₂×D₄	1	2	yes	—
147	C₁₃₉⋊C₈	—	2	2	no	—
148	C₂³×C₁₃₉	—	2	1	no	—
149	C₂³×C₁₃₉	C₂×D₄	1	1	yes	characteristic
150	Q₈×C₁₃₉	—	2	1	no	—
151	Q₈×C₁₃₉	C₂²×C₄	1	2	yes	complemented
152	D₄×C₁₃₉	—	2	2	no	—
153	D₄×C₁₃₉	—	2	2	no	—
154	D₄×C₁₃₉	—	2	1	no	—
155	D₄×C₁₃₉	C₂²×C₄	1	2	yes	complemented
156	C₂×C₄×C₁₃₉	—	2	4	no	—
157	C₂×C₄×C₁₃₉	—	2	1	no	—
158	C₂×C₄×C₁₃₉	—	2	2	no	—
159	C₂×C₄×C₁₃₉	—	2	2	no	—
160	C₂×C₄×C₁₃₉	—	2	2	no	—
161	C₂×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
164	C₂×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
165	C₂×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
166	C₂×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
167	C₈×C₁₃₉	—	2	2	no	—
168	C₂²×C₁₃₉	—	2	2	no	—
169	C₂²×C₁₃₉	—	2	2	no	—
170	C₂²×C₁₃₉	—	4	2	no	—
171	C₂²×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
172	C₂²×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
173	C₂²×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
174	C₂×D₁₃₉	—	2	2	no	—
175	C₂×D₁₃₉	—	2	4	no	—
176	C₂×D₁₃₉	—	2	4	no	—
177	C₂×D₁₃₉	—	2	2	no	—
178	C₂×D₁₃₉	—	4	2	no	—
179	C₂×D₁₃₉	—	4	8	no	—
180	C₂×D₁₃₉	#104	1	4	yes	direct product factor
181	C₂×D₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
182	C₂×D₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
183	C₄×C₁₃₉	—	2	4	no	—
184	C₄×C₁₃₉	—	2	2	no	—
185	C₄×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
186	C₄×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
187	C₄×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
188	C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
189	Dic₁₃₉	—	2	4	no	—
190	Dic₁₃₉	—	2	2	no	—
191	Dic₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
192	Dic₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
193	C₂×C₁₃₉	—	2	1	no	—
194	C₂×C₁₃₉	—	2	1	no	—
195	C₂×C₁₃₉	—	4	2	no	—
196	C₂×C₁₃₉	C₂×#104	1	2	yes	complemented
197	C₂×C₁₃₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
198	D₁₃₉	—	2	2	no	—
199	D₁₃₉	—	4	2	no	—
200	D₁₃₉	C₂×#104	1	4	yes	direct product factor
201	C₁₃₉	C₂²×#104	1	1	yes	characteristic, complemented, Sylow
202	C₂²×#104	—	139	1	no	maximal, Sylow
203	C₂²×#41	—	139	1	no	—
204	C₂²×M₁₆	—	139	1	no	—
205	C₂²×C₄²	—	139	1	no	—
206	C₂×#104	—	139	1	no	—
207	C₂×#104	—	139	1	no	—
208	C₂×#104	—	139	1	no	—
209	C₂×#104	—	139	8	no	—
210	C₂×#104	D₁₃₉	1	1	yes	characteristic, direct product factor
211	C₂×#41	—	278	1	no	—
212	C₂×#41	—	278	1	no	—
213	C₂×#41	—	278	2	no	—
214	C₂×#41	—	278	2	no	—
215	C₂×#41	—	139	4	no	—
216	C₂×#41	—	139	4	no	—
217	C₂×#41	—	139	1	no	—
218	C₂×#41	—	139	1	no	—
219	C₂×#41	—	139	1	no	—
220	C₂×#41	C₂×D₁₃₉	1	1	yes	characteristic
221	C₂²×Q₈	—	139	1	no	—
222	C₂²×D₄	—	278	1	no	—
223	C₂²×D₄	—	139	1	no	—
224	C₂³×C₄	—	278	1	no	—
225	C₂³×C₄	—	278	1	no	—
226	C₂³×C₄	—	139	1	no	—
227	C₂×M₁₆	—	278	1	no	—
228	C₂×M₁₆	—	278	2	no	—
229	C₂×M₁₆	—	139	1	no	—
230	C₂×M₁₆	—	139	4	no	—
231	C₂×M₁₆	C₂×D₁₃₉	1	1	yes	characteristic, complemented
232	C₂²×C₈	—	278	1	no	—
233	C₂×C₄²	—	278	2	no	—
234	C₂×C₄²	—	278	1	no	—
235	C₂×C₄²	—	139	1	no	—
236	C₂×C₄²	—	139	4	no	—
237	C₂×C₄²	C₂×D₁₃₉	1	1	yes	characteristic, complemented
238	#104	—	139	4	no	—
239	#104	—	139	4	no	—
240	#104	—	139	4	no	—
241	#104	C₂×D₁₃₉	1	4	yes	direct product factor
242	C₂⁴	—	278	1	no	—
243	C₂⁴	—	139	1	no	—
244	#41	—	2	1	no	—
245	#41	—	2	1	no	—
246	#41	—	278	4	no	—
247	#41	—	278	4	no	—
248	#41	—	278	4	no	—
249	#41	—	278	4	no	—
250	#41	—	278	2	no	—
251	#41	—	278	2	no	—
252	#41	—	278	1	no	—
253	#41	—	278	1	no	—
254	#41	—	139	4	no	—
255	#41	—	139	4	no	—
256	#41	—	139	2	no	—
257	#41	—	139	2	no	—
258	#41	C₄×D₁₃₉	1	2	yes	complemented
259	#41	C₂²×D₁₃₉	1	2	yes	—
260	C₂×Q₈	—	278	1	no	—
261	C₂×Q₈	—	278	2	no	—
262	C₂×Q₈	—	139	4	no	—
263	C₂×Q₈	—	139	1	no	—
264	C₂×Q₈	C₄×D₁₃₉	1	1	yes	characteristic, complemented
265	C₂×D₄	—	2	1	no	—
266	C₂×D₄	—	278	1	no	—
267	C₂×D₄	—	278	4	no	—
268	C₂×D₄	—	278	4	no	—
269	C₂×D₄	—	278	1	no	—
270	C₂×D₄	—	278	1	no	—
271	C₂×D₄	—	278	2	no	—
272	C₂×D₄	—	278	1	no	—
273	C₂×D₄	—	139	4	no	—
274	C₂×D₄	—	139	1	no	—
275	C₂×D₄	C₄×D₁₃₉	1	1	yes	characteristic, complemented
276	C₂²×C₄	—	2	1	no	—
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	278	8	no	—
279	C₂²×C₄	—	278	4	no	—
280	C₂²×C₄	—	278	1	no	—
281	C₂²×C₄	—	278	1	no	—
282	C₂²×C₄	—	278	4	no	—
283	C₂²×C₄	—	278	4	no	—
284	C₂²×C₄	—	278	1	no	—
285	C₂²×C₄	—	278	1	no	—
286	C₂²×C₄	—	278	1	no	—
287	C₂²×C₄	—	139	1	no	—
288	C₂²×C₄	—	139	1	no	—
289	C₂²×C₄	—	139	1	no	—
290	C₂²×C₄	—	139	2	no	—
291	C₂²×C₄	—	139	2	no	—
292	C₂²×C₄	—	139	2	no	—
293	C₂²×C₄	—	139	1	no	—
294	C₂²×C₄	—	139	1	no	—
295	C₂²×C₄	—	139	2	no	—
296	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
297	M₁₆	—	2	1	no	—
298	M₁₆	—	278	4	no	—
299	M₁₆	—	278	1	no	—
300	M₁₆	—	139	2	no	—
301	M₁₆	C₂²×D₁₃₉	1	2	yes	complemented
302	C₂×C₈	—	2	1	no	—
303	C₂×C₈	—	278	4	no	—
304	C₂×C₈	—	278	1	no	—
305	C₄²	—	2	1	no	—
306	C₄²	—	278	4	no	—
307	C₄²	—	278	1	no	—
308	C₄²	—	139	2	no	—
309	C₄²	C₂²×D₁₃₉	1	2	yes	complemented
310	C₂³	—	2	1	no	—
311	C₂³	—	278	4	no	—
312	C₂³	—	278	4	no	—
313	C₂³	—	278	1	no	—
314	C₂³	—	556	4	no	—
315	C₂³	—	139	2	no	—
316	C₂³	—	139	1	no	—
317	C₂³	—	139	2	no	—
318	C₂³	—	139	1	no	—
319	C₂³	D₄×D₁₃₉	1	1	yes	characteristic
320	Q₈	—	2	1	no	—
321	Q₈	—	278	4	no	—
322	Q₈	—	278	1	no	—
323	Q₈	—	139	2	no	—
324	Q₈	C₂×C₄×D₁₃₉	1	2	yes	complemented
325	D₄	—	2	2	no	—
326	D₄	—	2	2	no	—
327	D₄	—	2	1	no	—
328	D₄	—	278	4	no	—
329	D₄	—	278	4	no	—
330	D₄	—	278	2	no	—
331	D₄	—	278	2	no	—
332	D₄	—	278	4	no	—
333	D₄	—	278	1	no	—
334	D₄	—	139	2	no	—
335	D₄	C₂×C₄×D₁₃₉	1	2	yes	complemented
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	278	16	no	—
342	C₂×C₄	—	278	4	no	—
343	C₂×C₄	—	278	4	no	—
344	C₂×C₄	—	278	4	no	—
345	C₂×C₄	—	278	1	no	—
346	C₂×C₄	—	278	2	no	—
347	C₂×C₄	—	278	4	no	—
348	C₂×C₄	—	278	2	no	—
349	C₂×C₄	—	278	2	no	—
350	C₂×C₄	—	139	1	no	—
351	C₂×C₄	—	139	1	no	—
352	C₂×C₄	—	139	2	no	—
353	C₂×C₄	—	139	2	no	—
354	C₂×C₄	—	139	2	no	—
355	C₂×C₄	—	139	2	no	—
356	C₂×C₄	—	139	2	no	—
357	C₂×C₄	—	139	2	no	—
358	C₂×C₄	—	139	2	no	—
359	C₂×C₄	—	139	2	no	—
360	C₂×C₄	—	139	2	no	—
361	C₂×C₄	—	139	2	no	—
362	C₂×C₄	C₂×C₄×D₁₃₉	1	1	yes	characteristic
363	C₂×C₄	C₂×C₄×D₁₃₉	1	1	yes	characteristic
364	C₂×C₄	D₄×D₁₃₉	1	1	yes	characteristic
365	C₂×C₄	D₄×D₁₃₉	1	1	yes	characteristic
366	C₂×C₄	D₄×D₁₃₉	1	1	yes	characteristic
367	C₂×C₄	C₂³×D₁₃₉	1	1	yes	characteristic
368	C₈	—	2	2	no	—
369	C₈	—	278	2	no	—
370	C₂²	—	2	2	no	—
371	C₂²	—	2	2	no	—
372	C₂²	—	4	2	no	—
373	C₂²	—	278	4	no	—
374	C₂²	—	278	4	no	—
375	C₂²	—	278	2	no	—
376	C₂²	—	278	2	no	—
377	C₂²	—	556	8	no	—
378	C₂²	—	556	2	no	—
379	C₂²	—	139	2	no	—
380	C₂²	—	139	2	no	—
381	C₂²	—	139	4	no	—
382	C₂²	C₂²⋊C₄×D₁₃₉	1	1	yes	characteristic
383	C₂²	C₂²⋊C₄×D₁₃₉	1	1	yes	characteristic
384	C₂²	C₂×D₄×D₁₃₉	1	1	yes	characteristic
385	C₄	—	2	4	no	—
386	C₄	—	2	2	no	—
387	C₄	—	278	4	no	—
388	C₄	—	278	2	no	—
389	C₄	—	139	2	no	—
390	C₄	—	139	2	no	—
391	C₄	C₂²⋊C₄×D₁₃₉	1	1	yes	characteristic
392	C₄	C₂²⋊C₄×D₁₃₉	1	1	yes	characteristic
393	C₄	C₂²×C₄×D₁₃₉	1	1	yes	characteristic
394	C₄	C₂×D₄×D₁₃₉	1	1	yes	characteristic
395	C₂	—	2	1	no	—
396	C₂	—	2	1	no	—
397	C₂	—	4	2	no	—
398	C₂	—	278	2	no	—
399	C₂	—	556	2	no	—
400	C₂	—	139	4	no	—
401	C₂	#104×D₁₃₉	1	2	yes	direct product factor
402	C₂	C₂×C₂²⋊C₄×D₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₄×D₁₃₉
commutator	C₄×C₁₃₉	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₁₃₉
Fitting	C₂×#104×C₁₃₉	C₂
socle	C₂²×C₁₃₉	C₂×C₂²⋊C₄
prime radical	C₂×#41×D₁₃₉	C₂
cosocle	C₂×C₄×C₁₃₉	C₂⁴
hypercenter	C₂×#104	D₁₃₉
hypocenter	C₁₃₉	C₂²×#104
LCS	G ▷ C₄×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#104

Complements

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

N	H ≅ G/N	type
2. C₂×M₁₆×D₁₃₉	C₂	semidirect
3. C₂×C₄²×D₁₃₉	C₂	semidirect
4. C₂×#17984770	C₂	semidirect
5. C₂×#17984769	C₂	semidirect
6. C₂×#17984768	C₂	semidirect
7. #104×D₁₃₉	C₂	direct (N × H)
8. C₂×#104×C₁₃₉	C₂	semidirect
9. C₂×#14555786	C₄	semidirect
13. C₂×#14555784	C₄	semidirect
16. #41×D₁₃₉	C₄	semidirect
18. C₂×Q₈×D₁₃₉	C₄	semidirect
20. C₂×D₄×D₁₃₉	C₄	semidirect
24. C₂×#14555769	C₂²	semidirect
27. M₁₆×D₁₃₉	C₂²	semidirect
30. C₂×C₄×Dic₁₃₉	C₂²	semidirect
32. C₄²×D₁₃₉	C₂²	semidirect
33. #17984770	C₂²	semidirect
34. #17984769	C₂²	semidirect
35. #17984768	C₂²	semidirect
37. C₂×M₁₆×C₁₃₉	C₂²	semidirect
38. C₂×C₄²×C₁₃₉	C₂²	semidirect
39. #104×C₁₃₉	C₂²	semidirect
43. #14555786	C₂×C₄	semidirect
48. #14555785	C₂×C₄	semidirect
53. #14555784	C₂×C₄	semidirect
55. C₂×Dic₂₇₈	C₂×C₄	semidirect
57. Q₈×D₁₃₉	C₂×C₄	semidirect
59. C₂×D₅₅₆	C₂×C₄	semidirect
66. D₄×D₁₃₉	C₂×C₄	semidirect
86. #14555769	C₂³	semidirect
92. C₄×Dic₁₃₉	C₂³	semidirect
95. #41×C₁₃₉	C₂×C₄	semidirect
97. C₂×Q₈×C₁₃₉	C₂×C₄	semidirect
99. C₂×D₄×C₁₃₉	C₂×C₄	semidirect
104. M₁₆×C₁₃₉	C₂³	semidirect
107. C₄²×C₁₃₉	C₂³	semidirect
118. Dic₂₇₈	C₂²×C₄	semidirect
121. D₅₅₆	C₂²×C₄	semidirect
151. Q₈×C₁₃₉	C₂²×C₄	semidirect
155. D₄×C₁₃₉	C₂²×C₄	semidirect
180. C₂×D₁₃₉	#104	direct (N × H)
196. C₂×C₁₃₉	C₂×#104	semidirect
200. D₁₃₉	C₂×#104	direct (N × H)
201. C₁₃₉	C₂²×#104	semidirect
210. C₂×#104	D₁₃₉	direct (N × H)
231. C₂×M₁₆	C₂×D₁₃₉	semidirect
237. C₂×C₄²	C₂×D₁₃₉	semidirect
241. #104	C₂×D₁₃₉	direct (N × H)
258. #41	C₄×D₁₃₉	semidirect
264. C₂×Q₈	C₄×D₁₃₉	semidirect
275. C₂×D₄	C₄×D₁₃₉	semidirect
301. M₁₆	C₂²×D₁₃₉	semidirect
309. C₄²	C₂²×D₁₃₉	semidirect
324. Q₈	C₂×C₄×D₁₃₉	semidirect
335. D₄	C₂×C₄×D₁₃₉	semidirect
401. C₂	#104×D₁₃₉	direct (N × H)

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×M₁₆×D₁₃₉	2
C₂×C₄²×D₁₃₉	2
C₂×#17984770	2
C₂×#17984769	2
C₂×#17984768	2
#104×D₁₃₉	2
C₂×#104×C₁₃₉	2
C₂²×#104	139

Subgroups — C2×#104×D139 #31814939

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#104×D₁₃₉ #31814939