Subgroups — #435×D₁₀₉ #28371707

Order 13952.

564 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₁₆×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₈×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₄×D₁₀₉	C₂	1	1	yes	maximal, characteristic
4	#20295100	C₂	1	1	yes	maximal, characteristic, complemented
5	#20295099	C₂	1	1	yes	maximal, characteristic, complemented
6	#20295098	C₂	1	1	yes	maximal, characteristic, complemented
7	#20295097	C₂	1	1	yes	maximal, characteristic, complemented
8	#20295096	C₂	1	1	yes	maximal, characteristic, complemented
9	#20295095	C₂	1	1	yes	maximal, characteristic, complemented
10	#20295094	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄⋊C₈×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²⋊C₈×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²⋊C₈×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#97×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#435×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×D₄×D₁₀₉	C₄	1	1	yes	characteristic
17	C₂²×C₄×D₁₀₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₁₀₉	C₂²	1	1	yes	characteristic
19	C₂×#13182013	C₂²	1	1	yes	characteristic, complemented
20	C₂×#13182012	C₂²	1	1	yes	characteristic, complemented
21	C₂×#13182012	C₂²	1	1	yes	characteristic, complemented
22	M₁₆×D₁₀₉	—	2	4	no	—
23	C₂²×#11724784	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₈×D₁₀₉	—	2	4	no	—
25	C₂×C₈×D₁₀₉	C₂²	1	1	yes	characteristic
26	C₂×C₈×D₁₀₉	C₂²	1	1	yes	characteristic
27	C₂×C₈×D₁₀₉	C₂²	1	1	yes	characteristic
28	C₂×C₈×D₁₀₉	C₂²	1	1	yes	characteristic
29	C₂×C₈×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₈×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
31	C₄×D₄₃₆	C₂²	1	1	yes	characteristic
32	D₄×Dic₁₀₉	C₄	1	1	yes	characteristic
33	#16812661	C₄	1	1	yes	characteristic
34	C₄×C₂²⋊D₁₀₉	C₂²	1	1	yes	characteristic
35	C₄×C₂²⋊D₁₀₉	C₂²	1	1	yes	characteristic
36	#16812659	C₄	1	1	yes	characteristic
37	#16812659	C₄	1	1	yes	characteristic
38	C₄⋊C₄×D₁₀₉	C₄	1	1	yes	characteristic
39	C₂²⋊C₄×D₁₀₉	C₄	1	1	yes	characteristic
40	C₂²⋊C₄×D₁₀₉	C₄	1	1	yes	characteristic
41	C₄²×D₁₀₉	C₂²	1	1	yes	characteristic
42	C₄⋊#11724784	C₂²	1	1	yes	characteristic, complemented
43	#16812628	C₂²	1	1	yes	characteristic, complemented
44	#16812628	C₂²	1	1	yes	characteristic, complemented
45	C₂²⋊#11724784	C₂²	1	1	yes	characteristic, complemented
46	C₂²⋊#11724784	C₂²	1	1	yes	characteristic, complemented
47	#16812611	C₂²	1	1	yes	characteristic, complemented
48	#16812611	C₂²	1	1	yes	characteristic, complemented
49	#16812611	C₂²	1	1	yes	characteristic, complemented
50	#16812611	C₂²	1	1	yes	characteristic, complemented
51	#16812610	C₂²	1	1	yes	characteristic, complemented
52	#16812609	C₂²	1	1	yes	characteristic, complemented
53	#16812609	C₂²	1	1	yes	characteristic, complemented
54	C₂×M₁₆×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
55	C₂²×C₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
56	C₄×D₄×C₁₀₉	C₂²	1	1	yes	characteristic
57	C₄⋊C₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
58	C₂²⋊C₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
59	C₂²⋊C₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
60	#97×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₁₀₉	C₂×C₄	1	1	yes	characteristic
62	C₂³×D₁₀₉	C₂×C₄	1	1	yes	characteristic
63	C₂×D₄₃₆	C₂×C₄	1	1	yes	characteristic
64	C₂×C₂²⋊D₁₀₉	C₂×C₄	1	1	yes	characteristic
65	C₂×C₂²⋊D₁₀₉	C₂×C₄	1	1	yes	characteristic
66	D₄×D₁₀₉	—	2	4	no	—
67	C₂²×Dic₁₀₉	C₂×C₄	1	1	yes	characteristic
68	C₂²×Dic₁₀₉	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄×D₁₀₉	—	2	2	no	—
70	C₂×C₄×D₁₀₉	—	2	2	no	—
71	C₂×C₄×D₁₀₉	—	2	2	no	—
72	C₂×C₄×D₁₀₉	—	2	2	no	—
73	C₂×C₄×D₁₀₉	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄×D₁₀₉	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄×D₁₀₉	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄×D₁₀₉	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄×D₁₀₉	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄×D₁₀₉	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
80	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
81	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
82	#13182013	—	2	2	no	—
83	#13182012	—	2	2	no	—
84	#13182012	—	2	2	no	—
85	C₂×#11724784	—	2	2	no	—
86	C₂×#11724784	C₂³	1	1	yes	characteristic
87	C₂×#11724784	C₂³	1	1	yes	characteristic
88	C₂×#11724784	C₂³	1	1	yes	characteristic
89	C₂×#11724784	C₂³	1	1	yes	characteristic
90	C₈×D₁₀₉	—	2	2	no	—
91	C₈×D₁₀₉	—	2	2	no	—
92	C₈×D₁₀₉	—	2	2	no	—
93	C₈×D₁₀₉	—	2	2	no	—
94	C₈×D₁₀₉	—	2	2	no	—
95	C₈×D₁₀₉	D₄	1	4	yes	complemented
96	C₄⋊Dic₁₀₉	C₂×C₄	1	1	yes	characteristic
97	#13182008	C₂×C₄	1	1	yes	characteristic
98	#13182008	C₂×C₄	1	1	yes	characteristic
99	C₂²⋊Dic₁₀₉	C₂×C₄	1	1	yes	characteristic
100	C₂²⋊Dic₁₀₉	C₂×C₄	1	1	yes	characteristic
101	#13182006	C₂×C₄	1	1	yes	characteristic
102	#13182006	C₂×C₄	1	1	yes	characteristic
103	#13182006	C₂×C₄	1	1	yes	characteristic
104	#13182006	C₂×C₄	1	1	yes	characteristic
105	C₄×Dic₁₀₉	C₂×C₄	1	1	yes	characteristic
106	C₄×Dic₁₀₉	C₂×C₄	1	1	yes	characteristic
107	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
108	C₂×D₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
110	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
111	M₁₆×C₁₀₉	—	2	2	no	—
112	C₂×C₈×C₁₀₉	—	2	2	no	—
113	C₂×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
114	C₂×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
115	C₂×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
116	C₂×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
117	C₄⋊C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
118	C₂²⋊C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
119	C₂²⋊C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
120	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
121	C₂³×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
122	C₂³×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
123	C₂²×D₁₀₉	—	2	2	no	—
124	C₂²×D₁₀₉	—	2	2	no	—
125	C₂²×D₁₀₉	—	2	2	no	—
126	C₂²×D₁₀₉	—	2	2	no	—
127	C₂²×D₁₀₉	—	2	2	no	—
128	C₂²×D₁₀₉	M₁₆	1	4	yes	complemented
129	C₂²×D₁₀₉	C₂²×C₄	1	1	yes	characteristic
130	C₂²×D₁₀₉	C₂²×C₄	1	1	yes	characteristic
131	C₂²×D₁₀₉	C₂²×C₄	1	1	yes	characteristic
132	D₄×C₁₀₉	—	2	2	no	—
133	C₂×C₄×C₁₀₉	—	2	1	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	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
142	C₂²⋊D₁₀₉	—	2	2	no	—
143	C₂²⋊D₁₀₉	—	2	2	no	—
144	C₂×Dic₁₀₉	—	2	2	no	—
145	C₂×Dic₁₀₉	—	2	2	no	—
146	C₂×Dic₁₀₉	C₂²×C₄	1	1	yes	characteristic
147	C₂×Dic₁₀₉	C₂²×C₄	1	1	yes	characteristic
148	C₂×Dic₁₀₉	C₂²×C₄	1	1	yes	characteristic
149	C₂×Dic₁₀₉	C₂²×C₄	1	1	yes	characteristic
150	C₂×Dic₁₀₉	C₂²×C₄	1	1	yes	characteristic
151	D₄₃₆	—	2	2	no	—
152	C₄×D₁₀₉	—	2	2	no	—
153	C₄×D₁₀₉	—	2	2	no	—
154	C₄×D₁₀₉	—	2	2	no	—
155	C₄×D₁₀₉	—	2	2	no	—
156	C₄×D₁₀₉	—	2	1	no	—
157	C₄×D₁₀₉	—	2	1	no	—
158	C₄×D₁₀₉	—	2	1	no	—
159	C₄×D₁₀₉	—	2	1	no	—
160	C₄×D₁₀₉	—	2	2	no	—
161	C₄×D₁₀₉	—	2	2	no	—
162	C₄×D₁₀₉	C₂×D₄	1	2	yes	—
163	C₄×D₁₀₉	#41	1	2	yes	—
164	C₈×C₁₀₉	—	2	1	no	—
165	C₈×C₁₀₉	—	2	1	no	—
166	C₈×C₁₀₉	—	2	1	no	—
167	C₈×C₁₀₉	C₂×D₄	1	2	yes	complemented
168	#11724784	—	2	1	no	—
169	#11724784	—	2	1	no	—
170	#11724784	—	2	1	no	—
171	#11724784	C₂×D₄	1	2	yes	complemented
172	C₂²×C₁₀₉	—	2	1	no	—
173	C₂²×C₁₀₉	—	2	1	no	—
174	C₂²×C₁₀₉	—	2	1	no	—
175	C₂²×C₁₀₉	—	2	1	no	—
176	C₂²×C₁₀₉	—	2	1	no	—
177	C₂²×C₁₀₉	C₂×M₁₆	1	2	yes	complemented
178	C₂²×C₁₀₉	C₂³×C₄	1	1	yes	characteristic
179	C₂×D₁₀₉	—	2	1	no	—
180	C₂×D₁₀₉	—	2	1	no	—
181	C₂×D₁₀₉	—	2	8	no	—
182	C₂×D₁₀₉	—	2	1	no	—
183	C₂×D₁₀₉	—	2	1	no	—
184	C₂×D₁₀₉	—	2	1	no	—
185	C₂×D₁₀₉	—	4	4	no	—
186	C₂×D₁₀₉	C₄×D₄	1	2	yes	—
187	C₂×D₁₀₉	C₂×M₁₆	1	2	yes	—
188	C₂×D₁₀₉	C₂×M₁₆	1	2	yes	complemented
189	C₂×D₁₀₉	#131	1	2	yes	—
190	C₄×C₁₀₉	—	2	1	no	—
191	C₄×C₁₀₉	—	2	1	no	—
192	C₄×C₁₀₉	—	2	1	no	—
193	C₄×C₁₀₉	—	2	1	no	—
194	C₄×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
195	C₄×C₁₀₉	C₂×#41	1	1	yes	characteristic
196	Dic₁₀₉	—	2	1	no	—
197	Dic₁₀₉	—	2	1	no	—
198	Dic₁₀₉	—	2	1	no	—
199	Dic₁₀₉	—	2	1	no	—
200	Dic₁₀₉	C₄×D₄	1	2	yes	—
201	C₂×C₁₀₉	—	2	2	no	—
202	C₂×C₁₀₉	—	4	1	no	—
203	C₂×C₁₀₉	C₂×C₄×D₄	1	1	yes	characteristic
204	C₂×C₁₀₉	C₂²×M₁₆	1	1	yes	characteristic
205	C₂×C₁₀₉	C₂×#131	1	1	yes	characteristic
206	D₁₀₉	—	2	2	no	—
207	D₁₀₉	—	4	1	no	—
208	D₁₀₉	#435	1	4	yes	direct product factor
209	C₂×#435	—	109	1	no	maximal, Sylow
210	C₁₀₉	C₂×#435	1	1	yes	characteristic, complemented, Sylow
211	C₂²×M₁₆	—	109	1	no	—
212	C₂³×C₈	—	109	1	no	—
213	C₂×C₄×D₄	—	109	1	no	—
214	#435	—	109	1	no	—
215	#435	—	109	1	no	—
216	#435	—	109	1	no	—
217	#435	—	109	1	no	—
218	#435	—	109	1	no	—
219	#435	—	109	1	no	—
220	#435	—	109	1	no	—
221	#435	D₁₀₉	1	1	yes	characteristic, direct product factor
222	C₂×C₄⋊C₈	—	109	1	no	—
223	C₂×C₂²⋊C₈	—	109	1	no	—
224	C₂×C₂²⋊C₈	—	109	1	no	—
225	C₂×#97	—	109	1	no	—
226	C₂²×D₄	—	109	1	no	—
227	C₂³×C₄	—	109	1	no	—
228	C₂³×C₄	—	109	1	no	—
229	C₂×M₁₆	—	109	1	no	—
230	C₂×M₁₆	—	109	1	no	—
231	C₂×M₁₆	—	109	1	no	—
232	C₂×M₁₆	—	218	4	no	—
233	C₂×M₁₆	C₂×D₁₀₉	1	1	yes	characteristic, complemented
234	C₂²×C₈	—	109	1	no	—
235	C₂²×C₈	—	109	1	no	—
236	C₂²×C₈	—	109	1	no	—
237	C₂²×C₈	—	109	1	no	—
238	C₂²×C₈	—	109	1	no	—
239	C₂²×C₈	—	109	1	no	—
240	C₂²×C₈	—	109	1	no	—
241	C₂²×C₈	—	218	4	no	—
242	C₂²×C₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
243	C₄×D₄	—	109	1	no	—
244	C₄×D₄	—	109	1	no	—
245	C₄×D₄	—	109	1	no	—
246	C₄×D₄	—	109	1	no	—
247	C₄×D₄	—	109	1	no	—
248	C₄×D₄	—	109	1	no	—
249	C₄×D₄	—	109	1	no	—
250	C₄×D₄	C₂×D₁₀₉	1	1	yes	characteristic
251	C₂×C₄⋊C₄	—	109	1	no	—
252	C₂×C₂²⋊C₄	—	109	1	no	—
253	C₂×C₂²⋊C₄	—	109	1	no	—
254	C₂×C₄²	—	109	1	no	—
255	C₄⋊C₈	—	109	1	no	—
256	C₄⋊C₈	—	109	1	no	—
257	C₄⋊C₈	—	109	1	no	—
258	C₄⋊C₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
259	C₂²⋊C₈	—	109	1	no	—
260	C₂²⋊C₈	—	109	1	no	—
261	C₂²⋊C₈	—	109	1	no	—
262	C₂²⋊C₈	—	109	1	no	—
263	C₂²⋊C₈	—	109	1	no	—
264	C₂²⋊C₈	—	109	1	no	—
265	C₂²⋊C₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
266	C₂²⋊C₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
267	#97	—	109	1	no	—
268	#97	—	109	1	no	—
269	#97	—	109	1	no	—
270	#97	C₂×D₁₀₉	1	1	yes	characteristic, complemented
271	C₂⁴	—	109	1	no	—
272	C₂⁴	—	109	1	no	—
273	C₂×D₄	—	109	1	no	—
274	C₂×D₄	—	109	1	no	—
275	C₂×D₄	—	109	1	no	—
276	C₂×D₄	—	218	4	no	—
277	C₂×D₄	C₄×D₁₀₉	1	1	yes	characteristic
278	C₂²×C₄	—	109	1	no	—
279	C₂²×C₄	—	109	1	no	—
280	C₂²×C₄	—	109	1	no	—
281	C₂²×C₄	—	109	1	no	—
282	C₂²×C₄	—	109	1	no	—
283	C₂²×C₄	—	109	1	no	—
284	C₂²×C₄	—	109	1	no	—
285	C₂²×C₄	—	109	1	no	—
286	C₂²×C₄	—	109	1	no	—
287	C₂²×C₄	—	109	1	no	—
288	C₂²×C₄	—	109	1	no	—
289	C₂²×C₄	—	218	2	no	—
290	C₂²×C₄	—	218	2	no	—
291	C₂²×C₄	—	218	2	no	—
292	C₂²×C₄	—	218	2	no	—
293	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
294	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
295	M₁₆	—	2	2	no	—
296	M₁₆	—	218	2	no	—
297	M₁₆	—	218	2	no	—
298	M₁₆	—	218	2	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	109	1	no	—
301	C₂×C₈	—	109	4	no	—
302	C₂×C₈	—	109	1	no	—
303	C₂×C₈	—	109	1	no	—
304	C₂×C₈	—	109	1	no	—
305	C₂×C₈	—	218	2	no	—
306	C₂×C₈	—	218	2	no	—
307	C₂×C₈	—	218	2	no	—
308	C₂×C₈	—	218	2	no	—
309	C₂×C₈	—	218	2	no	—
310	C₂×C₈	—	218	2	no	—
311	C₂×C₈	C₂²×D₁₀₉	1	1	yes	characteristic
312	C₂×C₈	C₂²×D₁₀₉	1	1	yes	characteristic
313	C₂×C₈	C₂²×D₁₀₉	1	1	yes	characteristic
314	C₂×C₈	C₂²×D₁₀₉	1	1	yes	characteristic
315	C₄⋊C₄	—	109	1	no	—
316	C₄⋊C₄	—	109	1	no	—
317	C₄⋊C₄	—	109	1	no	—
318	C₄⋊C₄	C₄×D₁₀₉	1	1	yes	characteristic
319	C₂²⋊C₄	—	109	1	no	—
320	C₂²⋊C₄	—	109	1	no	—
321	C₂²⋊C₄	—	109	1	no	—
322	C₂²⋊C₄	—	109	1	no	—
323	C₂²⋊C₄	—	109	1	no	—
324	C₂²⋊C₄	—	109	1	no	—
325	C₂²⋊C₄	C₄×D₁₀₉	1	1	yes	characteristic
326	C₂²⋊C₄	C₄×D₁₀₉	1	1	yes	characteristic
327	C₄²	—	109	1	no	—
328	C₄²	—	109	1	no	—
329	C₄²	—	109	1	no	—
330	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic
331	C₂³	—	109	1	no	—
332	C₂³	—	109	4	no	—
333	C₂³	—	109	1	no	—
334	C₂³	—	109	1	no	—
335	C₂³	—	218	2	no	—
336	C₂³	—	218	2	no	—
337	C₂³	—	218	2	no	—
338	C₂³	—	218	2	no	—
339	C₂³	—	218	2	no	—
340	C₂³	C₂×C₄×D₁₀₉	1	1	yes	characteristic
341	C₂³	C₂×C₄×D₁₀₉	1	1	yes	characteristic
342	D₄	—	2	2	no	—
343	D₄	—	218	2	no	—
344	D₄	—	218	2	no	—
345	D₄	—	218	2	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	109	1	no	—
351	C₂×C₄	—	109	2	no	—
352	C₂×C₄	—	109	2	no	—
353	C₂×C₄	—	109	1	no	—
354	C₂×C₄	—	109	1	no	—
355	C₂×C₄	—	109	1	no	—
356	C₂×C₄	—	109	1	no	—
357	C₂×C₄	—	218	2	no	—
358	C₂×C₄	—	218	2	no	—
359	C₂×C₄	—	218	2	no	—
360	C₂×C₄	—	218	2	no	—
361	C₂×C₄	—	218	2	no	—
362	C₂×C₄	—	218	2	no	—
363	C₂×C₄	—	218	2	no	—
364	C₂×C₄	—	218	2	no	—
365	C₂×C₄	—	218	1	no	—
366	C₂×C₄	—	218	1	no	—
367	C₂×C₄	—	218	1	no	—
368	C₂×C₄	—	218	1	no	—
369	C₂×C₄	C₂×C₄×D₁₀₉	1	1	yes	characteristic
370	C₂×C₄	C₂×C₄×D₁₀₉	1	1	yes	characteristic
371	C₂×C₄	C₂×C₄×D₁₀₉	1	1	yes	characteristic
372	C₂×C₄	C₂×C₄×D₁₀₉	1	1	yes	characteristic
373	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
374	C₈	—	2	1	no	—
375	C₈	—	2	1	no	—
376	C₈	—	2	1	no	—
377	C₈	—	109	2	no	—
378	C₈	—	218	1	no	—
379	C₈	—	218	1	no	—
380	C₈	—	218	1	no	—
381	C₈	D₄×D₁₀₉	1	2	yes	complemented
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	2	1	no	—
387	C₂²	—	109	2	no	—
388	C₂²	—	109	2	no	—
389	C₂²	—	109	2	no	—
390	C₂²	—	109	2	no	—
391	C₂²	—	436	4	no	—
392	C₂²	—	218	8	no	—
393	C₂²	—	218	1	no	—
394	C₂²	—	218	1	no	—
395	C₂²	—	218	1	no	—
396	C₂²	—	218	1	no	—
397	C₂²	—	218	1	no	—
398	C₂²	M₁₆×D₁₀₉	1	2	yes	complemented
399	C₂²	C₂²×C₄×D₁₀₉	1	1	yes	characteristic
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	109	2	no	—
405	C₄	—	218	1	no	—
406	C₄	—	218	1	no	—
407	C₄	—	218	1	no	—
408	C₄	—	218	1	no	—
409	C₄	C₂×D₄×D₁₀₉	1	1	yes	characteristic
410	C₄	#41×D₁₀₉	1	1	yes	characteristic
411	C₂	—	2	2	no	—
412	C₂	—	4	1	no	—
413	C₂	—	109	4	no	—
414	C₂	—	436	1	no	—
415	C₂	—	218	2	no	—
416	C₂	C₄×D₄×D₁₀₉	1	1	yes	characteristic
417	C₂	C₂×M₁₆×D₁₀₉	1	1	yes	characteristic
418	C₂	#131×D₁₀₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₁₀₉
commutator, socle	C₂²×C₁₀₉	C₂³×C₄
Fitting	#435×C₁₀₉	C₂
prime radical	C₂×D₄×D₁₀₉	C₄
cosocle	C₂×C₄×C₁₀₉	C₂⁴
hypercenter	#435	D₁₀₉
hypocenter	C₁₀₉	C₂×#435
LCS	G ▷ C₂²×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂×C₄ ◁ #435

Complements

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

N	H ≅ G/N	type
1. C₂×M₁₆×D₁₀₉	C₂	semidirect
2. C₂²×C₈×D₁₀₉	C₂	semidirect
4. #20295100	C₂	semidirect
5. #20295099	C₂	semidirect
6. #20295098	C₂	semidirect
7. #20295097	C₂	semidirect
8. #20295096	C₂	semidirect
9. #20295095	C₂	semidirect
10. #20295094	C₂	semidirect
11. C₄⋊C₈×D₁₀₉	C₂	semidirect
12. C₂²⋊C₈×D₁₀₉	C₂	semidirect
13. C₂²⋊C₈×D₁₀₉	C₂	semidirect
14. #97×D₁₀₉	C₂	semidirect
15. #435×C₁₀₉	C₂	semidirect
19. C₂×#13182013	C₂²	semidirect
20. C₂×#13182012	C₂²	semidirect
21. C₂×#13182012	C₂²	semidirect
23. C₂²×#11724784	C₂²	semidirect
29. C₂×C₈×D₁₀₉	C₂²	semidirect
30. C₂×C₈×D₁₀₉	C₂²	semidirect
42. C₄⋊#11724784	C₂²	semidirect
43. #16812628	C₂²	semidirect
44. #16812628	C₂²	semidirect
45. C₂²⋊#11724784	C₂²	semidirect
46. C₂²⋊#11724784	C₂²	semidirect
47. #16812611	C₂²	semidirect
48. #16812611	C₂²	semidirect
49. #16812611	C₂²	semidirect
50. #16812611	C₂²	semidirect
51. #16812610	C₂²	semidirect
52. #16812609	C₂²	semidirect
53. #16812609	C₂²	semidirect
54. C₂×M₁₆×C₁₀₉	C₂²	semidirect
55. C₂²×C₈×C₁₀₉	C₂²	semidirect
57. C₄⋊C₈×C₁₀₉	C₂²	semidirect
58. C₂²⋊C₈×C₁₀₉	C₂²	semidirect
59. C₂²⋊C₈×C₁₀₉	C₂²	semidirect
60. #97×C₁₀₉	C₂²	semidirect
95. C₈×D₁₀₉	D₄	semidirect
128. C₂²×D₁₀₉	M₁₆	semidirect
167. C₈×C₁₀₉	C₂×D₄	semidirect
171. #11724784	C₂×D₄	semidirect
177. C₂²×C₁₀₉	C₂×M₁₆	semidirect
188. C₂×D₁₀₉	C₂×M₁₆	semidirect
208. D₁₀₉	#435	direct (N × H)
210. C₁₀₉	C₂×#435	semidirect
221. #435	D₁₀₉	direct (N × H)
233. C₂×M₁₆	C₂×D₁₀₉	semidirect
242. C₂²×C₈	C₂×D₁₀₉	semidirect
258. C₄⋊C₈	C₂×D₁₀₉	semidirect
265. C₂²⋊C₈	C₂×D₁₀₉	semidirect
266. C₂²⋊C₈	C₂×D₁₀₉	semidirect
270. #97	C₂×D₁₀₉	semidirect
381. C₈	D₄×D₁₀₉	semidirect
398. C₂²	M₁₆×D₁₀₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×M₁₆×D₁₀₉	2
C₂²×C₈×D₁₀₉	2
C₄×D₄×D₁₀₉	2
#20295100	2
#20295099	2
#20295098	2
#20295097	2
#20295096	2
#20295095	2
#20295094	2
C₄⋊C₈×D₁₀₉	2
C₂²⋊C₈×D₁₀₉	2
#97×D₁₀₉	2
#435×C₁₀₉	2
C₂×#435	109

Subgroups — #435×D109 #28371707

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #435×D₁₀₉ #28371707