Subgroups — #28372530

Order 13952.

526 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16812723	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₈×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#20295589	C₂	1	1	yes	maximal, characteristic, complemented
4	#20295498	C₂	1	1	yes	maximal, characteristic, complemented
5	#20295242	C₂	1	1	yes	maximal, characteristic, complemented
6	#20295241	C₂	1	1	yes	maximal, characteristic, complemented
7	#20295240	C₂	1	1	yes	maximal, characteristic, complemented
8	#20295239	C₂	1	1	yes	maximal, characteristic, complemented
9	#20295220	C₂	1	1	yes	maximal, characteristic, complemented
10	#20295219	C₂	1	1	yes	maximal, characteristic, complemented
11	#20295218	C₂	1	1	yes	maximal, characteristic, complemented
12	#20295051	C₂	1	1	yes	maximal, characteristic, complemented
13	#20295029	C₂	1	1	yes	maximal, characteristic, complemented
14	#20295019	C₂	1	1	yes	maximal, characteristic, complemented
15	#459×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13182028	C₂²	1	1	yes	characteristic
17	C₂×D₄×D₁₀₉	C₂²	1	1	yes	characteristic
18	C₂×D₄×D₁₀₉	C₂²	1	1	yes	characteristic
19	#16812723	—	2	4	no	—
20	C₂×#13182018	C₂²	1	1	yes	characteristic, complemented
21	C₂×#13182017	C₂²	1	1	yes	characteristic, complemented
22	C₂×D₈₇₂	C₂²	1	1	yes	characteristic
23	C₂×#13182014	C₂²	1	1	yes	characteristic
24	C₂×#13182014	C₂²	1	1	yes	characteristic
25	C₂×#13182014	C₂²	1	1	yes	characteristic, complemented
26	D₈×D₁₀₉	—	2	4	no	—
27	C₂×#13182012	C₂²	1	1	yes	characteristic
28	C₂×C₈×D₁₀₉	C₂²	1	1	yes	characteristic
29	#16812695	C₂²	1	1	yes	characteristic, complemented
30	#16812687	C₂²	1	1	yes	characteristic, complemented
31	#16812686	C₂²	1	1	yes	characteristic, complemented
32	#16812671	—	2	1	no	—
33	#16812671	—	2	1	no	—
34	#16812667	—	2	1	no	—
35	#16812667	—	2	1	no	—
36	C₄×D₄₃₆	C₂²	1	1	yes	characteristic, complemented
37	D₄×Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
38	#16812661	C₂²	1	1	yes	characteristic, complemented
39	C₄×C₂²⋊D₁₀₉	—	2	1	no	—
40	#16812659	—	2	1	no	—
41	#16812657	C₂²	1	1	yes	characteristic
42	#16812656	C₂²	1	1	yes	characteristic
43	C₂×#13182006	—	2	1	no	—
44	C₂²⋊C₄×D₁₀₉	—	2	1	no	—
45	C₄⋊#11724784	C₂²	1	1	yes	characteristic, complemented
46	#16812628	C₂²	1	1	yes	characteristic, complemented
47	#16812628	C₂²	1	1	yes	characteristic, complemented
48	#16812624	C₂²	1	1	yes	characteristic, complemented
49	#16812622	C₂²	1	1	yes	characteristic, complemented
50	#16812621	C₂²	1	1	yes	characteristic, complemented
51	#16812620	C₂²	1	1	yes	characteristic, complemented
52	#16812620	C₂²	1	1	yes	characteristic, complemented
53	#16812619	C₂²	1	1	yes	characteristic, complemented
54	C₂×D₈×C₁₀₉	C₂²	1	1	yes	characteristic
55	C₂×D₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
56	#127×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
57	C₄×D₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
58	C₄⋊C₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
59	#102×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
60	#102×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₁₀₉	—	2	1	no	—
62	C₂³×D₁₀₉	—	2	1	no	—
63	#13182028	—	2	2	no	—
64	#13182028	—	2	2	no	—
65	C₂×Dic₂₁₈	C₂³	1	1	yes	characteristic
66	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
67	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
68	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
69	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
70	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
71	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
72	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
73	D₄×D₁₀₉	—	2	2	no	—
74	D₄×D₁₀₉	—	2	2	no	—
75	D₄×D₁₀₉	—	2	2	no	—
76	D₄×D₁₀₉	D₄	1	4	yes	complemented
77	C₂²×Dic₁₀₉	—	2	1	no	—
78	C₂²×Dic₁₀₉	—	2	1	no	—
79	C₂×C₄×D₁₀₉	—	2	1	no	—
80	C₂×C₄×D₁₀₉	—	2	1	no	—
81	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
82	#13182018	—	2	2	no	—
83	#13182017	—	2	2	no	—
84	D₈₇₂	—	2	2	no	—
85	#13182014	—	2	2	no	—
86	#13182014	—	2	2	no	—
87	#13182014	—	2	2	no	—
88	#13182012	—	2	2	no	—
89	C₂×#11724784	C₂³	1	1	yes	characteristic
90	C₂×#11724784	C₂³	1	1	yes	characteristic
91	C₈×D₁₀₉	—	2	2	no	—
92	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
93	#13182008	D₄	1	1	yes	characteristic
94	#13182008	D₄	1	1	yes	characteristic
95	C₂²⋊Dic₁₀₉	—	2	1	no	—
96	C₂²⋊Dic₁₀₉	—	2	1	no	—
97	C₂²⋊Dic₁₀₉	—	2	1	no	—
98	#13182006	—	2	1	no	—
99	#13182006	—	2	1	no	—
100	#13182006	—	2	1	no	—
101	#13182006	—	2	1	no	—
102	#13182006	—	2	1	no	—
103	#13182006	D₄	1	1	yes	characteristic
104	#13182006	D₄	1	1	yes	characteristic
105	C₄×Dic₁₀₉	—	2	1	no	—
106	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
107	C₂×D₄×C₁₀₉	—	2	1	no	—
108	C₂×D₄×C₁₀₉	—	2	1	no	—
109	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
110	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
111	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
112	C₂²×C₄×C₁₀₉	—	2	1	no	—
113	D₈×C₁₀₉	—	2	2	no	—
114	D₈×C₁₀₉	—	2	2	no	—
115	C₂×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
116	C₂×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
117	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
118	C₂²⋊C₄×C₁₀₉	—	2	1	no	—
119	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
120	C₂³×C₁₀₉	—	2	1	no	—
121	C₂³×C₁₀₉	—	2	1	no	—
122	C₂³×C₁₀₉	—	2	1	no	—
123	C₂²×D₁₀₉	—	2	1	no	—
124	C₂²×D₁₀₉	—	2	4	no	—
125	C₂²×D₁₀₉	—	2	1	no	—
126	C₂²×D₁₀₉	—	4	2	no	—
127	C₂²×D₁₀₉	—	8	1	no	—
128	C₂²×D₁₀₉	—	8	1	no	—
129	C₂²×D₁₀₉	—	8	1	no	—
130	C₂²×D₁₀₉	—	8	1	no	—
131	C₂²×D₁₀₉	C₂×D₄	1	1	yes	characteristic
132	D₄×C₁₀₉	—	2	1	no	—
133	D₄×C₁₀₉	—	2	1	no	—
134	D₄×C₁₀₉	—	2	1	no	—
135	D₄×C₁₀₉	—	2	1	no	—
136	D₄×C₁₀₉	—	2	1	no	—
137	D₄×C₁₀₉	—	8	1	no	—
138	D₄×C₁₀₉	—	8	1	no	—
139	D₄×C₁₀₉	C₂×D₄	1	2	yes	—
140	C₂×C₄×C₁₀₉	—	2	1	no	—
141	C₂×C₄×C₁₀₉	—	8	1	no	—
142	C₂×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
143	C₂×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
144	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
145	C₂²⋊D₁₀₉	—	2	4	no	—
146	C₂²⋊D₁₀₉	—	4	2	no	—
147	C₂²⋊D₁₀₉	—	4	2	no	—
148	C₂²⋊D₁₀₉	—	8	1	no	—
149	C₂²⋊D₁₀₉	—	8	1	no	—
150	C₂×Dic₁₀₉	—	2	1	no	—
151	C₂×Dic₁₀₉	—	2	1	no	—
152	C₂×Dic₁₀₉	—	4	2	no	—
153	C₂×Dic₁₀₉	—	8	1	no	—
154	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
155	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
156	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
157	D₄₃₆	—	2	1	no	—
158	D₄₃₆	—	2	1	no	—
159	D₄₃₆	—	2	1	no	—
160	D₄₃₆	C₂×D₄	1	2	yes	—
161	C₄×D₁₀₉	—	8	1	no	—
162	C₄×D₁₀₉	—	8	1	no	—
163	C₄×D₁₀₉	C₂×D₄	1	2	yes	—
164	C₄×D₁₀₉	#41	1	2	yes	—
165	Dic₂₁₈	—	2	1	no	—
166	Dic₂₁₈	—	2	1	no	—
167	C₈×C₁₀₉	—	2	1	no	—
168	C₈×C₁₀₉	—	2	1	no	—
169	#11724784	—	2	1	no	—
170	#11724784	—	2	1	no	—
171	C₂²×C₁₀₉	—	2	2	no	—
172	C₂²×C₁₀₉	—	4	1	no	—
173	C₂²×C₁₀₉	—	4	1	no	—
174	C₂²×C₁₀₉	—	4	1	no	—
175	C₂²×C₁₀₉	—	4	1	no	—
176	C₂²×C₁₀₉	—	4	1	no	—
177	C₂²×C₁₀₉	—	4	1	no	—
178	C₂²×C₁₀₉	—	4	1	no	—
179	C₂²×C₁₀₉	—	4	1	no	—
180	C₂²×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
181	C₂×D₁₀₉	—	2	1	no	—
182	C₂×D₁₀₉	—	2	1	no	—
183	C₂×D₁₀₉	—	2	2	no	—
184	C₂×D₁₀₉	—	4	1	no	—
185	C₂×D₁₀₉	—	4	1	no	—
186	C₂×D₁₀₉	—	4	1	no	—
187	C₂×D₁₀₉	—	4	1	no	—
188	C₂×D₁₀₉	—	4	1	no	—
189	C₂×D₁₀₉	—	8	4	no	—
190	C₂×D₁₀₉	—	8	4	no	—
191	C₂×D₁₀₉	#121	1	2	yes	—
192	C₄×C₁₀₉	—	2	1	no	—
193	C₄×C₁₀₉	—	2	1	no	—
194	C₄×C₁₀₉	—	4	1	no	—
195	C₄×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
196	C₄×C₁₀₉	C₂×#41	1	1	yes	characteristic
197	Dic₁₀₉	—	2	1	no	—
198	Dic₁₀₉	—	2	1	no	—
199	Dic₁₀₉	—	4	1	no	—
200	Dic₁₀₉	—	4	1	no	—
201	Dic₁₀₉	#121	1	2	yes	—
202	C₂×C₁₀₉	—	4	2	no	—
203	C₂×C₁₀₉	—	8	1	no	—
204	C₂×C₁₀₉	—	8	1	no	—
205	C₂×C₁₀₉	C₂×#121	1	1	yes	characteristic
206	C₂×C₁₀₉	#576	1	1	yes	characteristic
207	C₂×C₁₀₉	#576	1	1	yes	characteristic
208	D₁₀₉	—	2	2	no	—
209	D₁₀₉	—	4	2	no	—
210	D₁₀₉	—	8	1	no	—
211	#3041	—	109	1	no	maximal, Sylow
212	C₁₀₉	#3041	1	1	yes	characteristic, complemented, Sylow
213	C₂×AGL(1,ℤ/8)	—	109	1	no	—
214	C₂²×D₈	—	109	1	no	—
215	#535	—	109	1	no	—
216	#518	—	109	1	no	—
217	#463	—	109	1	no	—
218	#463	—	109	1	no	—
219	#463	—	109	1	no	—
220	#463	—	109	1	no	—
221	#459	—	109	1	no	—
222	#459	—	109	1	no	—
223	#459	—	109	1	no	—
224	#459	D₁₀₉	1	1	yes	characteristic, complemented
225	#424	—	109	1	no	—
226	#418	—	109	1	no	—
227	#416	—	109	1	no	—
228	C₂×#41	—	109	1	no	—
229	C₂²×D₄	—	109	1	no	—
230	C₂²×D₄	—	109	1	no	—
231	AGL(1,ℤ/8)	—	218	4	no	—
232	C₂×SD₁₆	—	109	1	no	—
233	C₂×SD₁₆	—	109	1	no	—
234	C₂×D₈	—	109	1	no	—
235	C₂×D₈	—	109	1	no	—
236	C₂×D₈	—	109	1	no	—
237	C₂×D₈	—	109	1	no	—
238	C₂×D₈	—	218	4	no	—
239	C₂×D₈	C₂×D₁₀₉	1	1	yes	characteristic
240	C₂×D₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
241	C₂×M₁₆	—	109	1	no	—
242	C₂²×C₈	—	109	1	no	—
243	#127	—	109	1	no	—
244	#127	C₂×D₁₀₉	1	1	yes	characteristic, complemented
245	#124	—	109	1	no	—
246	#124	—	109	1	no	—
247	#121	—	218	1	no	—
248	#121	—	218	1	no	—
249	#120	—	218	1	no	—
250	#120	—	218	1	no	—
251	C₄×D₄	—	109	1	no	—
252	C₄×D₄	—	109	1	no	—
253	C₄×D₄	—	109	1	no	—
254	C₄×D₄	—	218	1	no	—
255	C₄×D₄	—	218	1	no	—
256	C₄×D₄	C₂×D₁₀₉	1	1	yes	characteristic, complemented
257	#117	—	109	1	no	—
258	#117	—	109	1	no	—
259	C₂×C₂²⋊C₄	—	218	1	no	—
260	C₂×C₂²⋊C₄	—	218	1	no	—
261	C₄⋊C₈	—	109	1	no	—
262	C₄⋊C₈	—	109	1	no	—
263	C₄⋊C₈	—	109	1	no	—
264	C₄⋊C₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
265	#103	—	109	1	no	—
266	#103	—	109	1	no	—
267	#102	—	109	1	no	—
268	#102	—	109	1	no	—
269	#102	—	109	1	no	—
270	#102	—	109	1	no	—
271	#102	C₂×D₁₀₉	1	1	yes	characteristic, complemented
272	#102	C₂×D₁₀₉	1	1	yes	characteristic, complemented
273	C₂⁴	—	218	1	no	—
274	C₂⁴	—	218	1	no	—
275	#41	—	218	2	no	—
276	#41	—	218	2	no	—
277	C₂×Q₈	—	109	1	no	—
278	C₂×D₄	—	2	1	no	—
279	C₂×D₄	—	2	1	no	—
280	C₂×D₄	—	109	4	no	—
281	C₂×D₄	—	109	1	no	—
282	C₂×D₄	—	109	1	no	—
283	C₂×D₄	—	218	2	no	—
284	C₂×D₄	—	218	2	no	—
285	C₂×D₄	—	218	2	no	—
286	C₂×D₄	—	218	1	no	—
287	C₂×D₄	—	218	1	no	—
288	C₂×D₄	—	218	1	no	—
289	C₂×D₄	—	218	1	no	—
290	C₂×D₄	—	218	1	no	—
291	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
292	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
293	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	109	1	no	—
296	C₂²×C₄	—	218	1	no	—
297	C₂²×C₄	—	218	1	no	—
298	C₂²×C₄	—	218	1	no	—
299	C₂²×C₄	—	218	1	no	—
300	SD₁₆	—	218	2	no	—
301	SD₁₆	—	218	2	no	—
302	D₈	—	2	2	no	—
303	D₈	—	2	2	no	—
304	D₈	—	218	2	no	—
305	D₈	—	218	2	no	—
306	D₈	—	218	2	no	—
307	D₈	—	218	2	no	—
308	M₁₆	—	218	2	no	—
309	C₂×C₈	—	109	1	no	—
310	C₂×C₈	—	109	1	no	—
311	C₂×C₈	—	218	2	no	—
312	C₂×C₈	C₂²×D₁₀₉	1	1	yes	characteristic
313	C₂×C₈	C₂²×D₁₀₉	1	1	yes	characteristic
314	C₄⋊C₄	—	109	1	no	—
315	C₄⋊C₄	—	109	1	no	—
316	C₄⋊C₄	—	109	1	no	—
317	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
318	C₂²⋊C₄	—	2	1	no	—
319	C₂²⋊C₄	—	109	1	no	—
320	C₂²⋊C₄	—	109	1	no	—
321	C₂²⋊C₄	—	218	1	no	—
322	C₂²⋊C₄	—	218	1	no	—
323	C₂²⋊C₄	—	218	1	no	—
324	C₂²⋊C₄	—	218	1	no	—
325	C₂²⋊C₄	—	218	1	no	—
326	C₂²⋊C₄	—	218	1	no	—
327	C₂²⋊C₄	—	218	1	no	—
328	C₂²⋊C₄	—	218	1	no	—
329	C₄²	—	109	1	no	—
330	C₄²	—	218	1	no	—
331	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic
332	C₂³	—	2	1	no	—
333	C₂³	—	2	1	no	—
334	C₂³	—	2	1	no	—
335	C₂³	—	872	1	no	—
336	C₂³	—	872	1	no	—
337	C₂³	—	872	1	no	—
338	C₂³	—	872	1	no	—
339	C₂³	—	109	1	no	—
340	C₂³	—	436	2	no	—
341	C₂³	—	218	4	no	—
342	C₂³	—	218	1	no	—
343	C₂³	—	218	1	no	—
344	Q₈	—	218	1	no	—
345	Q₈	—	218	1	no	—
346	D₄	—	2	1	no	—
347	D₄	—	2	1	no	—
348	D₄	—	2	1	no	—
349	D₄	—	2	1	no	—
350	D₄	—	2	1	no	—
351	D₄	—	8	1	no	—
352	D₄	—	8	1	no	—
353	D₄	—	872	1	no	—
354	D₄	—	872	1	no	—
355	D₄	—	109	2	no	—
356	D₄	—	436	2	no	—
357	D₄	—	436	2	no	—
358	D₄	—	218	4	no	—
359	D₄	—	218	1	no	—
360	D₄	—	218	1	no	—
361	D₄	—	218	1	no	—
362	D₄	D₄×D₁₀₉	1	2	yes	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	8	1	no	—
365	C₂×C₄	—	872	1	no	—
366	C₂×C₄	—	872	1	no	—
367	C₂×C₄	—	872	1	no	—
368	C₂×C₄	—	109	1	no	—
369	C₂×C₄	—	109	2	no	—
370	C₂×C₄	—	109	2	no	—
371	C₂×C₄	—	109	1	no	—
372	C₂×C₄	—	109	1	no	—
373	C₂×C₄	—	436	2	no	—
374	C₂×C₄	—	218	1	no	—
375	C₂×C₄	—	218	1	no	—
376	C₂×C₄	D₄×D₁₀₉	1	1	yes	characteristic
377	C₂×C₄	D₄×D₁₀₉	1	1	yes	characteristic
378	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
379	C₈	—	2	1	no	—
380	C₈	—	2	1	no	—
381	C₈	—	218	1	no	—
382	C₈	—	218	1	no	—
383	C₂²	—	2	2	no	—
384	C₂²	—	4	1	no	—
385	C₂²	—	4	1	no	—
386	C₂²	—	4	1	no	—
387	C₂²	—	4	1	no	—
388	C₂²	—	4	1	no	—
389	C₂²	—	4	1	no	—
390	C₂²	—	4	1	no	—
391	C₂²	—	4	1	no	—
392	C₂²	—	872	4	no	—
393	C₂²	—	872	4	no	—
394	C₂²	—	109	2	no	—
395	C₂²	—	436	1	no	—
396	C₂²	—	436	1	no	—
397	C₂²	—	436	1	no	—
398	C₂²	—	436	1	no	—
399	C₂²	—	436	1	no	—
400	C₂²	—	218	2	no	—
401	C₂²	—	218	1	no	—
402	C₂²	—	218	1	no	—
403	C₂²	C₂×D₄×D₁₀₉	1	1	yes	characteristic
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	4	1	no	—
407	C₄	—	109	2	no	—
408	C₄	—	436	1	no	—
409	C₄	—	436	1	no	—
410	C₄	—	218	1	no	—
411	C₄	—	218	1	no	—
412	C₄	C₂×D₄×D₁₀₉	1	1	yes	characteristic
413	C₄	#41×D₁₀₉	1	1	yes	characteristic
414	C₂	—	4	2	no	—
415	C₂	—	8	1	no	—
416	C₂	—	8	1	no	—
417	C₂	—	872	1	no	—
418	C₂	—	436	2	no	—
419	C₂	—	218	2	no	—
420	C₂	#121×D₁₀₉	1	1	yes	characteristic
421	C₂	#20295827	1	1	yes	characteristic
422	C₂	#20295830	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₀₉
commutator, cosocle	C₂×C₄×C₁₀₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₀₉
Fitting	#459×C₁₀₉	C₂
socle	C₂²×C₁₀₉	C₂²×D₄
hypercenter	#459	D₁₀₉
hypocenter	C₁₀₉	#3041
LCS	G ▷ C₂×C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #459

Complements

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

N	H ≅ G/N	type
1. C₂×#16812723	C₂	semidirect
2. C₂×D₈×D₁₀₉	C₂	semidirect
3. #20295589	C₂	semidirect
4. #20295498	C₂	semidirect
5. #20295242	C₂	semidirect
6. #20295241	C₂	semidirect
7. #20295240	C₂	semidirect
8. #20295239	C₂	semidirect
9. #20295220	C₂	semidirect
10. #20295219	C₂	semidirect
11. #20295218	C₂	semidirect
12. #20295051	C₂	semidirect
13. #20295029	C₂	semidirect
14. #20295019	C₂	semidirect
15. #459×C₁₀₉	C₂	semidirect
20. C₂×#13182018	C₂²	semidirect
21. C₂×#13182017	C₂²	semidirect
25. C₂×#13182014	C₂²	semidirect
29. #16812695	C₂²	semidirect
30. #16812687	C₂²	semidirect
31. #16812686	C₂²	semidirect
36. C₄×D₄₃₆	C₂²	semidirect
37. D₄×Dic₁₀₉	C₂²	semidirect
38. #16812661	C₂²	semidirect
45. C₄⋊#11724784	C₂²	semidirect
46. #16812628	C₂²	semidirect
47. #16812628	C₂²	semidirect
48. #16812624	C₂²	semidirect
49. #16812622	C₂²	semidirect
50. #16812621	C₂²	semidirect
51. #16812620	C₂²	semidirect
52. #16812620	C₂²	semidirect
53. #16812619	C₂²	semidirect
55. C₂×D₈×C₁₀₉	C₂²	semidirect
56. #127×C₁₀₉	C₂²	semidirect
57. C₄×D₄×C₁₀₉	C₂²	semidirect
58. C₄⋊C₈×C₁₀₉	C₂²	semidirect
59. #102×C₁₀₉	C₂²	semidirect
60. #102×C₁₀₉	C₂²	semidirect
76. D₄×D₁₀₉	D₄	semidirect
212. C₁₀₉	#3041	semidirect
224. #459	D₁₀₉	semidirect
240. C₂×D₈	C₂×D₁₀₉	semidirect
244. #127	C₂×D₁₀₉	semidirect
256. C₄×D₄	C₂×D₁₀₉	semidirect
264. C₄⋊C₈	C₂×D₁₀₉	semidirect
271. #102	C₂×D₁₀₉	semidirect
272. #102	C₂×D₁₀₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16812723	2
C₂×D₈×D₁₀₉	2
#20295589	2
#20295498	2
#20295242	2
#20295241	2
#20295240	2
#20295239	2
#20295220	2
#20295219	2
#20295218	2
#20295051	2
#20295029	2
#20295019	2
#459×C₁₀₉	2
#3041	109