Subgroups — C₁₀₉×#12978 #42130972

Order 27904.

494 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×M₃₂×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₀₉×#2929	C₂	1	1	yes	maximal, characteristic
3	C₂×#350×C₁₀₉	C₂	1	2	yes	maximal, complemented
4	C₂×C₂²⋊C₁₆×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₉×#1379	C₂	1	2	yes	maximal, complemented
6	C₂×#131×C₁₀₉	C₂²	1	1	yes	characteristic
7	C₂³×C₈×C₁₀₉	C₂²	1	1	yes	characteristic
8	#525×C₁₀₉	C₄	1	1	yes	characteristic
9	C₂×M₃₂×C₁₀₉	—	2	1	no	—
10	C₂×M₃₂×C₁₀₉	—	2	4	no	—
11	C₂×M₃₂×C₁₀₉	C₂²	1	2	yes	—
12	C₂²×C₁₆×C₁₀₉	—	2	1	no	—
13	C₂²×C₁₆×C₁₀₉	C₂²	1	2	yes	—
14	#435×C₁₀₉	—	2	1	no	—
15	#435×C₁₀₉	—	2	1	no	—
16	C₈×D₄×C₁₀₉	—	2	1	no	—
17	C₈×D₄×C₁₀₉	—	2	1	no	—
18	#424×C₁₀₉	C₄	1	1	yes	characteristic
19	#408×C₁₀₉	C₄	1	1	yes	characteristic
20	#407×C₁₀₉	C₄	1	1	yes	characteristic
21	#405×C₁₀₉	C₂²	1	1	yes	characteristic
22	#350×C₁₀₉	—	2	4	no	—
23	C₂²⋊C₁₆×C₁₀₉	—	2	1	no	—
24	C₂²⋊C₁₆×C₁₀₉	—	2	1	no	—
25	C₂×#41×C₁₀₉	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
27	#131×C₁₀₉	—	2	2	no	—
28	#131×C₁₀₉	—	2	2	no	—
29	C₂×M₁₆×C₁₀₉	—	2	1	no	—
30	C₂×M₁₆×C₁₀₉	C₂×C₄	1	1	yes	characteristic
31	C₂×M₁₆×C₁₀₉	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₈×C₁₀₉	—	2	2	no	—
33	C₂²×C₈×C₁₀₉	—	2	2	no	—
34	C₂²×C₈×C₁₀₉	—	2	1	no	—
35	C₂²×C₈×C₁₀₉	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₈×C₁₀₉	D₄	1	1	yes	characteristic
37	C₂²×C₈×C₁₀₉	D₄	1	1	yes	characteristic
38	C₂²×C₈×C₁₀₉	D₄	1	1	yes	characteristic
39	C₂²×C₈×C₁₀₉	D₄	1	1	yes	characteristic
40	C₂²×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
41	#123×C₁₀₉	—	2	1	no	—
42	C₂²⋊Q₈×C₁₀₉	C₈	1	1	yes	characteristic
43	C₂²⋊Q₈×C₁₀₉	C₈	1	1	yes	characteristic
44	#121×C₁₀₉	C₈	1	1	yes	characteristic
45	#121×C₁₀₉	C₈	1	1	yes	characteristic
46	#120×C₁₀₉	—	2	1	no	—
47	C₄×D₄×C₁₀₉	—	2	1	no	—
48	C₄×D₄×C₁₀₉	—	2	1	no	—
49	#117×C₁₀₉	C₂×C₄	1	1	yes	characteristic
50	M₃₂×C₁₀₉	—	2	4	no	—
51	M₃₂×C₁₀₉	—	2	2	no	—
52	M₃₂×C₁₀₉	D₄	1	4	yes	complemented
53	C₂×C₁₆×C₁₀₉	—	2	4	no	—
54	C₂×C₁₆×C₁₀₉	—	2	2	no	—
55	C₂×C₁₆×C₁₀₉	—	2	2	no	—
56	C₂×C₁₆×C₁₀₉	—	2	2	no	—
57	C₂×C₁₆×C₁₀₉	—	2	2	no	—
58	C₄⋊C₈×C₁₀₉	—	2	1	no	—
59	C₄⋊C₈×C₁₀₉	—	2	1	no	—
60	C₂²⋊C₈×C₁₀₉	—	2	1	no	—
61	C₂²⋊C₈×C₁₀₉	—	2	1	no	—
62	C₂²⋊C₈×C₁₀₉	—	2	1	no	—
63	C₂²⋊C₈×C₁₀₉	—	2	1	no	—
64	#97×C₁₀₉	—	2	1	no	—
65	C₄×C₈×C₁₀₉	—	2	1	no	—
66	C₂⁴×C₁₀₉	M₁₆	1	1	yes	characteristic
67	#41×C₁₀₉	—	2	2	no	—
68	#41×C₁₀₉	—	2	2	no	—
69	C₂×Q₈×C₁₀₉	C₂×C₈	1	1	yes	characteristic
70	C₂×D₄×C₁₀₉	—	2	1	no	—
71	C₂×D₄×C₁₀₉	—	2	1	no	—
72	C₂×D₄×C₁₀₉	—	2	1	no	—
73	C₂×D₄×C₁₀₉	C₂×C₈	1	1	yes	characteristic
74	C₂²×C₄×C₁₀₉	—	2	2	no	—
75	C₂²×C₄×C₁₀₉	—	2	2	no	—
76	C₂²×C₄×C₁₀₉	—	2	1	no	—
77	C₂²×C₄×C₁₀₉	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₀₉	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₀₉	C₂×C₈	1	1	yes	characteristic
80	C₂²×C₄×C₁₀₉	C₂×C₈	1	1	yes	characteristic
81	C₂²×C₄×C₁₀₉	M₁₆	1	1	yes	characteristic
82	C₂²×C₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
83	M₁₆×C₁₀₉	—	2	2	no	—
84	M₁₆×C₁₀₉	—	2	2	no	—
85	M₁₆×C₁₀₉	—	4	2	no	—
86	C₂×C₈×C₁₀₉	—	2	2	no	—
87	C₂×C₈×C₁₀₉	—	2	1	no	—
88	C₂×C₈×C₁₀₉	—	2	1	no	—
89	C₂×C₈×C₁₀₉	—	2	2	no	—
90	C₂×C₈×C₁₀₉	—	2	2	no	—
91	C₂×C₈×C₁₀₉	—	2	1	no	—
92	C₂×C₈×C₁₀₉	—	2	1	no	—
93	C₂×C₈×C₁₀₉	—	2	1	no	—
94	C₂×C₈×C₁₀₉	—	2	1	no	—
95	C₂×C₈×C₁₀₉	—	4	1	no	—
96	C₂×C₈×C₁₀₉	—	4	1	no	—
97	C₂×C₈×C₁₀₉	C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₈×C₁₀₉	C₂²⋊C₄	1	1	yes	characteristic
99	C₂×C₈×C₁₀₉	C₂×D₄	1	2	yes	—
100	C₂×C₈×C₁₀₉	C₂×D₄	1	1	yes	characteristic
101	C₂×C₈×C₁₀₉	C₂×D₄	1	1	yes	characteristic
102	C₂×C₈×C₁₀₉	#41	1	2	yes	—
103	C₄⋊C₄×C₁₀₉	—	2	1	no	—
104	C₄⋊C₄×C₁₀₉	—	2	1	no	—
105	C₄⋊C₄×C₁₀₉	C₂×C₈	1	1	yes	characteristic
106	C₄⋊C₄×C₁₀₉	C₂×C₈	1	1	yes	characteristic
107	C₂²⋊C₄×C₁₀₉	—	2	1	no	—
108	C₂²⋊C₄×C₁₀₉	—	2	1	no	—
109	C₂²⋊C₄×C₁₀₉	—	2	1	no	—
110	C₂²⋊C₄×C₁₀₉	—	2	1	no	—
111	C₂²⋊C₄×C₁₀₉	—	2	1	no	—
112	C₄²×C₁₀₉	—	2	1	no	—
113	C₁₆×C₁₀₉	—	2	4	no	—
114	C₁₆×C₁₀₉	—	4	2	no	—
115	C₂³×C₁₀₉	—	2	2	no	—
116	C₂³×C₁₀₉	—	2	2	no	—
117	C₂³×C₁₀₉	—	2	1	no	—
118	C₂³×C₁₀₉	—	4	1	no	—
119	C₂³×C₁₀₉	C₂²⋊C₈	1	1	yes	characteristic
120	C₂³×C₁₀₉	C₂²⋊C₈	1	1	yes	characteristic
121	C₂³×C₁₀₉	C₂×M₁₆	1	1	yes	characteristic
122	Q₈×C₁₀₉	—	2	2	no	—
123	D₄×C₁₀₉	—	2	2	no	—
124	D₄×C₁₀₉	—	4	2	no	—
125	D₄×C₁₀₉	—	4	2	no	—
126	D₄×C₁₀₉	—	4	2	no	—
127	C₂×C₄×C₁₀₉	—	2	2	no	—
128	C₂×C₄×C₁₀₉	—	2	1	no	—
129	C₂×C₄×C₁₀₉	—	2	1	no	—
130	C₂×C₄×C₁₀₉	—	2	1	no	—
131	C₂×C₄×C₁₀₉	—	2	1	no	—
132	C₂×C₄×C₁₀₉	—	2	2	no	—
133	C₂×C₄×C₁₀₉	—	2	2	no	—
134	C₂×C₄×C₁₀₉	—	2	1	no	—
135	C₂×C₄×C₁₀₉	—	2	1	no	—
136	C₂×C₄×C₁₀₉	—	2	1	no	—
137	C₂×C₄×C₁₀₉	—	4	1	no	—
138	C₂×C₄×C₁₀₉	—	4	1	no	—
139	C₂×C₄×C₁₀₉	C₂²⋊C₈	1	1	yes	characteristic
140	C₂×C₄×C₁₀₉	C₂²⋊C₈	1	1	yes	characteristic
141	C₂×C₄×C₁₀₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₁₀₉	C₄×D₄	1	2	yes	—
143	C₂×C₄×C₁₀₉	C₂²×C₈	1	1	yes	characteristic
144	C₂×C₄×C₁₀₉	#131	1	2	yes	—
145	C₈×C₁₀₉	—	2	1	no	—
146	C₈×C₁₀₉	—	2	1	no	—
147	C₈×C₁₀₉	—	4	1	no	—
148	C₈×C₁₀₉	—	4	1	no	—
149	C₈×C₁₀₉	#120	1	1	yes	characteristic
150	C₈×C₁₀₉	#121	1	2	yes	—
151	C₈×C₁₀₉	#123	1	1	yes	characteristic
152	C₂²×C₁₀₉	—	2	1	no	—
153	C₂²×C₁₀₉	—	2	1	no	—
154	C₂²×C₁₀₉	—	2	1	no	—
155	C₂²×C₁₀₉	—	2	1	no	—
156	C₂²×C₁₀₉	—	2	1	no	—
157	C₂²×C₁₀₉	—	2	1	no	—
158	C₂²×C₁₀₉	—	2	1	no	—
159	C₂²×C₁₀₉	—	4	4	no	—
160	C₂²×C₁₀₉	—	4	1	no	—
161	C₂²×C₁₀₉	—	4	1	no	—
162	C₂²×C₁₀₉	—	4	1	no	—
163	C₂²×C₁₀₉	#350	1	2	yes	complemented
164	C₂²×C₁₀₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
165	C₂²×C₁₀₉	#435	1	2	yes	—
166	C₄×C₁₀₉	—	2	1	no	—
167	C₄×C₁₀₉	—	2	1	no	—
168	C₄×C₁₀₉	—	4	1	no	—
169	C₄×C₁₀₉	—	4	1	no	—
170	C₄×C₁₀₉	—	4	1	no	—
171	C₄×C₁₀₉	#386	1	1	yes	characteristic
172	C₄×C₁₀₉	#408	1	1	yes	characteristic
173	C₄×C₁₀₉	C₈×D₄	1	2	yes	—
174	#12978	C₁₀₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
175	C₂×C₁₀₉	—	2	2	no	—
176	C₂×C₁₀₉	—	2	2	no	—
177	C₂×C₁₀₉	—	4	1	no	—
178	C₂×C₁₀₉	—	8	1	no	—
179	C₂×C₁₀₉	#1869	1	1	yes	characteristic
180	C₂×C₁₀₉	C₂×#350	1	1	yes	characteristic
181	C₂×C₁₀₉	#2117	1	1	yes	characteristic
182	C₂²×M₃₂	C₂×C₁₀₉	1	1	yes	characteristic, complemented
183	#2929	C₂×C₁₀₉	1	1	yes	characteristic
184	C₂×#350	C₂×C₁₀₉	1	2	yes	complemented
185	C₂×C₂²⋊C₁₆	C₂×C₁₀₉	1	1	yes	characteristic, complemented
186	#1379	C₂×C₁₀₉	1	2	yes	complemented
187	C₁₀₉	#12978	1	1	yes	characteristic, direct product factor, Sylow
188	C₂×#131	C₂²×C₁₀₉	1	1	yes	characteristic
189	C₂³×C₈	C₂²×C₁₀₉	1	1	yes	characteristic
190	#525	C₄×C₁₀₉	1	1	yes	characteristic
191	C₂×M₃₂	—	2	1	no	—
192	C₂×M₃₂	—	2	4	no	—
193	C₂×M₃₂	C₂²×C₁₀₉	1	2	yes	—
194	C₂²×C₁₆	—	2	1	no	—
195	C₂²×C₁₆	C₂²×C₁₀₉	1	2	yes	—
196	#435	—	2	1	no	—
197	#435	—	2	1	no	—
198	C₈×D₄	—	2	1	no	—
199	C₈×D₄	—	2	1	no	—
200	#424	C₄×C₁₀₉	1	1	yes	characteristic
201	#408	C₄×C₁₀₉	1	1	yes	characteristic
202	#407	C₄×C₁₀₉	1	1	yes	characteristic
203	#405	C₂²×C₁₀₉	1	1	yes	characteristic
204	#350	—	2	4	no	—
205	C₂²⋊C₁₆	—	2	1	no	—
206	C₂²⋊C₁₆	—	2	1	no	—
207	C₂×#41	C₂×C₄×C₁₀₉	1	1	yes	characteristic
208	C₂³×C₄	C₂×C₄×C₁₀₉	1	1	yes	characteristic
209	#131	—	2	2	no	—
210	#131	—	2	2	no	—
211	C₂×M₁₆	—	2	1	no	—
212	C₂×M₁₆	C₂×C₄×C₁₀₉	1	1	yes	characteristic
213	C₂×M₁₆	C₂×C₄×C₁₀₉	1	1	yes	characteristic
214	C₂²×C₈	—	2	2	no	—
215	C₂²×C₈	—	2	2	no	—
216	C₂²×C₈	—	2	1	no	—
217	C₂²×C₈	C₂×C₄×C₁₀₉	1	1	yes	characteristic
218	C₂²×C₈	D₄×C₁₀₉	1	1	yes	characteristic
219	C₂²×C₈	D₄×C₁₀₉	1	1	yes	characteristic
220	C₂²×C₈	D₄×C₁₀₉	1	1	yes	characteristic
221	C₂²×C₈	D₄×C₁₀₉	1	1	yes	characteristic
222	C₂²×C₈	C₂³×C₁₀₉	1	1	yes	characteristic
223	#123	—	2	1	no	—
224	C₂²⋊Q₈	C₈×C₁₀₉	1	1	yes	characteristic
225	C₂²⋊Q₈	C₈×C₁₀₉	1	1	yes	characteristic
226	#121	C₈×C₁₀₉	1	1	yes	characteristic
227	#121	C₈×C₁₀₉	1	1	yes	characteristic
228	#120	—	2	1	no	—
229	C₄×D₄	—	2	1	no	—
230	C₄×D₄	—	2	1	no	—
231	#117	C₂×C₄×C₁₀₉	1	1	yes	characteristic
232	M₃₂	—	2	4	no	—
233	M₃₂	—	2	2	no	—
234	M₃₂	D₄×C₁₀₉	1	4	yes	complemented
235	C₂×C₁₆	—	2	4	no	—
236	C₂×C₁₆	—	2	2	no	—
237	C₂×C₁₆	—	2	2	no	—
238	C₂×C₁₆	—	2	2	no	—
239	C₂×C₁₆	—	2	2	no	—
240	C₄⋊C₈	—	2	1	no	—
241	C₄⋊C₈	—	2	1	no	—
242	C₂²⋊C₈	—	2	1	no	—
243	C₂²⋊C₈	—	2	1	no	—
244	C₂²⋊C₈	—	2	1	no	—
245	C₂²⋊C₈	—	2	1	no	—
246	#97	—	2	1	no	—
247	C₄×C₈	—	2	1	no	—
248	C₂⁴	M₁₆×C₁₀₉	1	1	yes	characteristic
249	#41	—	2	2	no	—
250	#41	—	2	2	no	—
251	C₂×Q₈	C₂×C₈×C₁₀₉	1	1	yes	characteristic
252	C₂×D₄	—	2	1	no	—
253	C₂×D₄	—	2	1	no	—
254	C₂×D₄	—	2	1	no	—
255	C₂×D₄	C₂×C₈×C₁₀₉	1	1	yes	characteristic
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	2	2	no	—
258	C₂²×C₄	—	2	1	no	—
259	C₂²×C₄	C₂²⋊C₄×C₁₀₉	1	1	yes	characteristic
260	C₂²×C₄	C₂²⋊C₄×C₁₀₉	1	1	yes	characteristic
261	C₂²×C₄	C₂×C₈×C₁₀₉	1	1	yes	characteristic
262	C₂²×C₄	C₂×C₈×C₁₀₉	1	1	yes	characteristic
263	C₂²×C₄	M₁₆×C₁₀₉	1	1	yes	characteristic
264	C₂²×C₄	C₂²×C₄×C₁₀₉	1	1	yes	characteristic
265	M₁₆	—	2	2	no	—
266	M₁₆	—	2	2	no	—
267	M₁₆	—	4	2	no	—
268	C₂×C₈	—	2	2	no	—
269	C₂×C₈	—	2	1	no	—
270	C₂×C₈	—	2	1	no	—
271	C₂×C₈	—	2	2	no	—
272	C₂×C₈	—	2	2	no	—
273	C₂×C₈	—	2	1	no	—
274	C₂×C₈	—	2	1	no	—
275	C₂×C₈	—	2	1	no	—
276	C₂×C₈	—	2	1	no	—
277	C₂×C₈	—	4	1	no	—
278	C₂×C₈	—	4	1	no	—
279	C₂×C₈	C₂²⋊C₄×C₁₀₉	1	1	yes	characteristic
280	C₂×C₈	C₂²⋊C₄×C₁₀₉	1	1	yes	characteristic
281	C₂×C₈	C₂×D₄×C₁₀₉	1	2	yes	—
282	C₂×C₈	C₂×D₄×C₁₀₉	1	1	yes	characteristic
283	C₂×C₈	C₂×D₄×C₁₀₉	1	1	yes	characteristic
284	C₂×C₈	#41×C₁₀₉	1	2	yes	—
285	C₄⋊C₄	—	2	1	no	—
286	C₄⋊C₄	—	2	1	no	—
287	C₄⋊C₄	C₂×C₈×C₁₀₉	1	1	yes	characteristic
288	C₄⋊C₄	C₂×C₈×C₁₀₉	1	1	yes	characteristic
289	C₂²⋊C₄	—	2	1	no	—
290	C₂²⋊C₄	—	2	1	no	—
291	C₂²⋊C₄	—	2	1	no	—
292	C₂²⋊C₄	—	2	1	no	—
293	C₂²⋊C₄	—	2	1	no	—
294	C₄²	—	2	1	no	—
295	C₁₆	—	2	4	no	—
296	C₁₆	—	4	2	no	—
297	C₂³	—	2	2	no	—
298	C₂³	—	2	2	no	—
299	C₂³	—	2	1	no	—
300	C₂³	—	4	1	no	—
301	C₂³	C₂²⋊C₈×C₁₀₉	1	1	yes	characteristic
302	C₂³	C₂²⋊C₈×C₁₀₉	1	1	yes	characteristic
303	C₂³	C₂×M₁₆×C₁₀₉	1	1	yes	characteristic
304	Q₈	—	2	2	no	—
305	D₄	—	2	2	no	—
306	D₄	—	4	2	no	—
307	D₄	—	4	2	no	—
308	D₄	—	4	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	1	no	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	4	1	no	—
320	C₂×C₄	—	4	1	no	—
321	C₂×C₄	C₂²⋊C₈×C₁₀₉	1	1	yes	characteristic
322	C₂×C₄	C₂²⋊C₈×C₁₀₉	1	1	yes	characteristic
323	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₉	1	1	yes	characteristic
324	C₂×C₄	C₄×D₄×C₁₀₉	1	2	yes	—
325	C₂×C₄	C₂²×C₈×C₁₀₉	1	1	yes	characteristic
326	C₂×C₄	#131×C₁₀₉	1	2	yes	—
327	C₈	—	2	1	no	—
328	C₈	—	2	1	no	—
329	C₈	—	4	1	no	—
330	C₈	—	4	1	no	—
331	C₈	#120×C₁₀₉	1	1	yes	characteristic
332	C₈	#121×C₁₀₉	1	2	yes	—
333	C₈	#123×C₁₀₉	1	1	yes	characteristic
334	C₂²	—	2	1	no	—
335	C₂²	—	2	1	no	—
336	C₂²	—	2	1	no	—
337	C₂²	—	2	1	no	—
338	C₂²	—	2	1	no	—
339	C₂²	—	2	1	no	—
340	C₂²	—	2	1	no	—
341	C₂²	—	4	4	no	—
342	C₂²	—	4	1	no	—
343	C₂²	—	4	1	no	—
344	C₂²	—	4	1	no	—
345	C₂²	#350×C₁₀₉	1	2	yes	complemented
346	C₂²	C₂×C₂²⋊C₈×C₁₀₉	1	1	yes	characteristic
347	C₂²	#435×C₁₀₉	1	2	yes	—
348	C₄	—	2	1	no	—
349	C₄	—	2	1	no	—
350	C₄	—	4	1	no	—
351	C₄	—	4	1	no	—
352	C₄	—	4	1	no	—
353	C₄	#386×C₁₀₉	1	1	yes	characteristic
354	C₄	#408×C₁₀₉	1	1	yes	characteristic
355	C₄	C₈×D₄×C₁₀₉	1	2	yes	—
356	C₂	—	2	2	no	—
357	C₂	—	2	2	no	—
358	C₂	—	4	1	no	—
359	C₂	—	8	1	no	—
360	C₂	C₁₀₉×#1869	1	1	yes	characteristic
361	C₂	C₂×#350×C₁₀₉	1	1	yes	characteristic
362	C₂	C₁₀₉×#2117	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₁₀₉	C₂×D₄
commutator	C₂×C₄	C₂²×C₈×C₁₀₉
Frattini, cosocle	C₂²×C₈	C₂³×C₁₀₉
socle	C₂²×C₁₀₉	C₂×C₂²⋊C₈
prime radical	#525×C₁₀₉	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₀₉ ◁ C₂³×C₈×C₁₀₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×M₃₂×C₁₀₉	C₂	semidirect
3. C₂×#350×C₁₀₉	C₂	semidirect
4. C₂×C₂²⋊C₁₆×C₁₀₉	C₂	semidirect
5. C₁₀₉×#1379	C₂	semidirect
52. M₃₂×C₁₀₉	D₄	semidirect
163. C₂²×C₁₀₉	#350	semidirect
174. #12978	C₁₀₉	direct (N × H)
182. C₂²×M₃₂	C₂×C₁₀₉	semidirect
184. C₂×#350	C₂×C₁₀₉	semidirect
185. C₂×C₂²⋊C₁₆	C₂×C₁₀₉	semidirect
186. #1379	C₂×C₁₀₉	semidirect
187. C₁₀₉	#12978	direct (N × H)
234. M₃₂	D₄×C₁₀₉	semidirect
345. C₂²	#350×C₁₀₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×M₃₂×C₁₀₉	2
C₁₀₉×#2929	2
C₂×#350×C₁₀₉	2
C₂×C₂²⋊C₁₆×C₁₀₉	2
C₁₀₉×#1379	2
#12978	109

Subgroups — C109×#12978 #42130972

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₉×#12978 #42130972