Subgroups — C₁₀₉×#3102 #28360356

Order 13952.

396 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#529×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#41×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#485×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#482×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#479×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#478×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#464×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#463×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#452×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#449×C₁₀₉	C₂	1	1	yes	maximal, characteristic
11	C₄×Q₁₆×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×SD₁₆×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×SD₁₆×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×D₈×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#431×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#41×C₁₀₉	C₂²	1	1	yes	characteristic
17	C₂×Q₁₆×C₁₀₉	C₂²	1	1	yes	characteristic
18	C₂×SD₁₆×C₁₀₉	C₂²	1	1	yes	characteristic
19	C₂×SD₁₆×C₁₀₉	C₂²	1	1	yes	characteristic
20	C₂×D₈×C₁₀₉	C₂²	1	1	yes	characteristic
21	#126×C₁₀₉	—	2	1	no	—
22	#125×C₁₀₉	C₂²	1	1	yes	characteristic
23	#124×C₁₀₉	C₂²	1	1	yes	characteristic
24	#123×C₁₀₉	—	2	1	no	—
25	C₂²⋊Q₈×C₁₀₉	C₂²	1	1	yes	characteristic
26	#121×C₁₀₉	C₂²	1	1	yes	characteristic
27	C₄×Q₈×C₁₀₉	C₂²	1	1	yes	characteristic
28	C₄×Q₈×C₁₀₉	C₂²	1	1	yes	characteristic
29	C₄×Q₈×C₁₀₉	C₂²	1	1	yes	characteristic
30	C₄×D₄×C₁₀₉	—	2	1	no	—
31	C₄×D₄×C₁₀₉	—	2	1	no	—
32	C₄×D₄×C₁₀₉	—	2	1	no	—
33	C₄×D₄×C₁₀₉	C₂²	1	1	yes	characteristic
34	C₄×D₄×C₁₀₉	C₂²	1	1	yes	characteristic
35	C₄×D₄×C₁₀₉	C₂²	1	1	yes	characteristic
36	#117×C₁₀₉	—	2	1	no	—
37	#117×C₁₀₉	—	2	1	no	—
38	#117×C₁₀₉	C₂²	1	1	yes	characteristic
39	C₂×C₄²×C₁₀₉	—	2	1	no	—
40	C₂×C₄²×C₁₀₉	C₂²	1	1	yes	characteristic
41	#107×C₁₀₉	C₂²	1	1	yes	characteristic
42	#107×C₁₀₉	C₂²	1	1	yes	characteristic
43	#106×C₁₀₉	C₂²	1	1	yes	characteristic
44	#106×C₁₀₉	C₂²	1	1	yes	characteristic
45	C₄⋊C₈×C₁₀₉	C₂²	1	1	yes	characteristic
46	C₄⋊C₈×C₁₀₉	C₂²	1	1	yes	characteristic
47	#103×C₁₀₉	C₂²	1	1	yes	characteristic
48	#103×C₁₀₉	C₂²	1	1	yes	characteristic
49	#103×C₁₀₉	C₂²	1	1	yes	characteristic
50	#103×C₁₀₉	C₂²	1	1	yes	characteristic
51	#102×C₁₀₉	C₂²	1	1	yes	characteristic
52	#102×C₁₀₉	C₂²	1	1	yes	characteristic
53	#102×C₁₀₉	C₂²	1	1	yes	characteristic
54	#102×C₁₀₉	C₂²	1	1	yes	characteristic
55	C₂²⋊C₈×C₁₀₉	C₂²	1	1	yes	characteristic
56	C₂²⋊C₈×C₁₀₉	C₂²	1	1	yes	characteristic
57	C₄×C₈×C₁₀₉	C₂²	1	1	yes	characteristic
58	C₄×C₈×C₁₀₉	C₂²	1	1	yes	characteristic
59	#41×C₁₀₉	—	2	2	no	—
60	#41×C₁₀₉	—	2	2	no	—
61	C₂×Q₈×C₁₀₉	C₂³	1	1	yes	characteristic
62	C₂×Q₈×C₁₀₉	C₂³	1	1	yes	characteristic
63	C₂×D₄×C₁₀₉	—	2	1	no	—
64	C₂×D₄×C₁₀₉	—	2	1	no	—
65	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
66	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
67	C₂²×C₄×C₁₀₉	—	2	1	no	—
68	C₂²×C₄×C₁₀₉	—	2	1	no	—
69	C₂²×C₄×C₁₀₉	—	2	1	no	—
70	C₂²×C₄×C₁₀₉	—	2	1	no	—
71	C₂²×C₄×C₁₀₉	D₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₀₉	D₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
74	Q₁₆×C₁₀₉	—	2	2	no	—
75	SD₁₆×C₁₀₉	—	2	2	no	—
76	SD₁₆×C₁₀₉	—	2	2	no	—
77	D₈×C₁₀₉	—	2	2	no	—
78	C₂×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
79	C₂×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
80	C₂×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
81	C₂×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
82	C₄⋊C₄×C₁₀₉	—	2	1	no	—
83	C₄⋊C₄×C₁₀₉	—	2	1	no	—
84	C₄⋊C₄×C₁₀₉	—	2	1	no	—
85	C₄⋊C₄×C₁₀₉	—	2	1	no	—
86	C₄⋊C₄×C₁₀₉	—	2	1	no	—
87	C₄⋊C₄×C₁₀₉	—	2	1	no	—
88	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
89	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
90	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
91	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
92	C₂²⋊C₄×C₁₀₉	—	2	1	no	—
93	C₂²⋊C₄×C₁₀₉	—	2	1	no	—
94	C₂²⋊C₄×C₁₀₉	—	2	1	no	—
95	C₂²⋊C₄×C₁₀₉	—	2	1	no	—
96	C₂²⋊C₄×C₁₀₉	—	2	1	no	—
97	C₂²⋊C₄×C₁₀₉	—	2	1	no	—
98	C₂²⋊C₄×C₁₀₉	—	2	1	no	—
99	C₂²⋊C₄×C₁₀₉	—	2	1	no	—
100	C₄²×C₁₀₉	—	2	1	no	—
101	C₄²×C₁₀₉	—	2	1	no	—
102	C₄²×C₁₀₉	—	2	1	no	—
103	C₄²×C₁₀₉	—	2	1	no	—
104	C₄²×C₁₀₉	D₄	1	1	yes	characteristic
105	C₄²×C₁₀₉	D₄	1	1	yes	characteristic
106	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
107	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
108	C₂³×C₁₀₉	—	2	1	no	—
109	C₂³×C₁₀₉	—	2	1	no	—
110	C₂³×C₁₀₉	C₂×D₄	1	1	yes	characteristic
111	Q₈×C₁₀₉	—	2	1	no	—
112	Q₈×C₁₀₉	—	2	1	no	—
113	Q₈×C₁₀₉	—	2	1	no	—
114	Q₈×C₁₀₉	#41	1	2	yes	—
115	D₄×C₁₀₉	—	2	4	no	—
116	D₄×C₁₀₉	—	2	1	no	—
117	D₄×C₁₀₉	—	2	1	no	—
118	D₄×C₁₀₉	—	2	1	no	—
119	D₄×C₁₀₉	—	4	2	no	—
120	D₄×C₁₀₉	#41	1	2	yes	—
121	C₂×C₄×C₁₀₉	—	2	4	no	—
122	C₂×C₄×C₁₀₉	—	2	1	no	—
123	C₂×C₄×C₁₀₉	—	2	2	no	—
124	C₂×C₄×C₁₀₉	—	2	1	no	—
125	C₂×C₄×C₁₀₉	—	2	1	no	—
126	C₂×C₄×C₁₀₉	—	2	1	no	—
127	C₂×C₄×C₁₀₉	—	2	1	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	—	4	1	no	—
132	C₂×C₄×C₁₀₉	—	4	2	no	—
133	C₂×C₄×C₁₀₉	—	4	2	no	—
134	C₂×C₄×C₁₀₉	—	4	2	no	—
135	C₂×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
136	C₂×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
137	C₂×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
138	C₂×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
139	C₂×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
140	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
141	C₈×C₁₀₉	—	2	1	no	—
142	C₈×C₁₀₉	—	2	1	no	—
143	C₈×C₁₀₉	—	2	1	no	—
144	C₈×C₁₀₉	—	2	1	no	—
145	C₂²×C₁₀₉	—	2	1	no	—
146	C₂²×C₁₀₉	—	2	2	no	—
147	C₂²×C₁₀₉	—	2	1	no	—
148	C₂²×C₁₀₉	—	2	1	no	—
149	C₂²×C₁₀₉	—	4	1	no	—
150	C₂²×C₁₀₉	—	4	1	no	—
151	C₂²×C₁₀₉	—	4	1	no	—
152	C₂²×C₁₀₉	—	4	1	no	—
153	C₂²×C₁₀₉	—	4	1	no	—
154	C₂²×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
155	C₄×C₁₀₉	—	2	1	no	—
156	C₄×C₁₀₉	—	2	2	no	—
157	C₄×C₁₀₉	—	2	1	no	—
158	C₄×C₁₀₉	—	2	1	no	—
159	C₄×C₁₀₉	—	2	1	no	—
160	C₄×C₁₀₉	—	4	1	no	—
161	C₄×C₁₀₉	—	4	1	no	—
162	C₄×C₁₀₉	—	4	1	no	—
163	C₄×C₁₀₉	—	4	1	no	—
164	C₄×C₁₀₉	—	4	1	no	—
165	C₄×C₁₀₉	#135	1	2	yes	—
166	C₄×C₁₀₉	C₂×#41	1	1	yes	characteristic
167	C₄×C₁₀₉	C₂×#41	1	1	yes	characteristic
168	C₂×C₁₀₉	—	4	1	no	—
169	C₂×C₁₀₉	—	4	2	no	—
170	C₂×C₁₀₉	—	8	1	no	—
171	C₂×C₁₀₉	#525	1	1	yes	characteristic
172	C₂×C₁₀₉	C₂×#135	1	1	yes	characteristic
173	C₂×C₁₀₉	#575	1	1	yes	characteristic
174	#3102	C₁₀₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
175	C₁₀₉	#3102	1	1	yes	characteristic, direct product factor, Sylow
176	#529	C₂×C₁₀₉	1	1	yes	characteristic, complemented
177	C₄×#41	C₂×C₁₀₉	1	1	yes	characteristic, complemented
178	#485	C₂×C₁₀₉	1	1	yes	characteristic, complemented
179	#482	C₂×C₁₀₉	1	1	yes	characteristic, complemented
180	#479	C₂×C₁₀₉	1	1	yes	characteristic, complemented
181	#478	C₂×C₁₀₉	1	1	yes	characteristic, complemented
182	#464	C₂×C₁₀₉	1	1	yes	characteristic, complemented
183	#463	C₂×C₁₀₉	1	1	yes	characteristic, complemented
184	#452	C₂×C₁₀₉	1	1	yes	characteristic, complemented
185	#449	C₂×C₁₀₉	1	1	yes	characteristic
186	C₄×Q₁₆	C₂×C₁₀₉	1	1	yes	characteristic, complemented
187	C₄×SD₁₆	C₂×C₁₀₉	1	1	yes	characteristic, complemented
188	C₄×SD₁₆	C₂×C₁₀₉	1	1	yes	characteristic, complemented
189	C₄×D₈	C₂×C₁₀₉	1	1	yes	characteristic, complemented
190	#431	C₂×C₁₀₉	1	1	yes	characteristic, complemented
191	C₂×#41	C₂²×C₁₀₉	1	1	yes	characteristic
192	C₂×Q₁₆	C₂²×C₁₀₉	1	1	yes	characteristic
193	C₂×SD₁₆	C₂²×C₁₀₉	1	1	yes	characteristic
194	C₂×SD₁₆	C₂²×C₁₀₉	1	1	yes	characteristic
195	C₂×D₈	C₂²×C₁₀₉	1	1	yes	characteristic
196	#126	—	2	1	no	—
197	#125	C₂²×C₁₀₉	1	1	yes	characteristic
198	#124	C₂²×C₁₀₉	1	1	yes	characteristic
199	#123	—	2	1	no	—
200	C₂²⋊Q₈	C₂²×C₁₀₉	1	1	yes	characteristic
201	#121	C₂²×C₁₀₉	1	1	yes	characteristic
202	C₄×Q₈	C₂²×C₁₀₉	1	1	yes	characteristic
203	C₄×Q₈	C₂²×C₁₀₉	1	1	yes	characteristic
204	C₄×Q₈	C₂²×C₁₀₉	1	1	yes	characteristic
205	C₄×D₄	—	2	1	no	—
206	C₄×D₄	—	2	1	no	—
207	C₄×D₄	—	2	1	no	—
208	C₄×D₄	C₂²×C₁₀₉	1	1	yes	characteristic
209	C₄×D₄	C₂²×C₁₀₉	1	1	yes	characteristic
210	C₄×D₄	C₂²×C₁₀₉	1	1	yes	characteristic
211	#117	—	2	1	no	—
212	#117	—	2	1	no	—
213	#117	C₂²×C₁₀₉	1	1	yes	characteristic
214	C₂×C₄²	—	2	1	no	—
215	C₂×C₄²	C₂²×C₁₀₉	1	1	yes	characteristic
216	#107	C₂²×C₁₀₉	1	1	yes	characteristic
217	#107	C₂²×C₁₀₉	1	1	yes	characteristic
218	#106	C₂²×C₁₀₉	1	1	yes	characteristic
219	#106	C₂²×C₁₀₉	1	1	yes	characteristic
220	C₄⋊C₈	C₂²×C₁₀₉	1	1	yes	characteristic
221	C₄⋊C₈	C₂²×C₁₀₉	1	1	yes	characteristic
222	#103	C₂²×C₁₀₉	1	1	yes	characteristic
223	#103	C₂²×C₁₀₉	1	1	yes	characteristic
224	#103	C₂²×C₁₀₉	1	1	yes	characteristic
225	#103	C₂²×C₁₀₉	1	1	yes	characteristic
226	#102	C₂²×C₁₀₉	1	1	yes	characteristic
227	#102	C₂²×C₁₀₉	1	1	yes	characteristic
228	#102	C₂²×C₁₀₉	1	1	yes	characteristic
229	#102	C₂²×C₁₀₉	1	1	yes	characteristic
230	C₂²⋊C₈	C₂²×C₁₀₉	1	1	yes	characteristic
231	C₂²⋊C₈	C₂²×C₁₀₉	1	1	yes	characteristic
232	C₄×C₈	C₂²×C₁₀₉	1	1	yes	characteristic
233	C₄×C₈	C₂²×C₁₀₉	1	1	yes	characteristic
234	#41	—	2	2	no	—
235	#41	—	2	2	no	—
236	C₂×Q₈	C₂³×C₁₀₉	1	1	yes	characteristic
237	C₂×Q₈	C₂³×C₁₀₉	1	1	yes	characteristic
238	C₂×D₄	—	2	1	no	—
239	C₂×D₄	—	2	1	no	—
240	C₂×D₄	C₂³×C₁₀₉	1	1	yes	characteristic
241	C₂×D₄	C₂³×C₁₀₉	1	1	yes	characteristic
242	C₂²×C₄	—	2	1	no	—
243	C₂²×C₄	—	2	1	no	—
244	C₂²×C₄	—	2	1	no	—
245	C₂²×C₄	—	2	1	no	—
246	C₂²×C₄	D₄×C₁₀₉	1	1	yes	characteristic
247	C₂²×C₄	D₄×C₁₀₉	1	1	yes	characteristic
248	C₂²×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
249	Q₁₆	—	2	2	no	—
250	SD₁₆	—	2	2	no	—
251	SD₁₆	—	2	2	no	—
252	D₈	—	2	2	no	—
253	C₂×C₈	C₂³×C₁₀₉	1	1	yes	characteristic
254	C₂×C₈	C₂³×C₁₀₉	1	1	yes	characteristic
255	C₂×C₈	C₂³×C₁₀₉	1	1	yes	characteristic
256	C₂×C₈	C₂³×C₁₀₉	1	1	yes	characteristic
257	C₄⋊C₄	—	2	1	no	—
258	C₄⋊C₄	—	2	1	no	—
259	C₄⋊C₄	—	2	1	no	—
260	C₄⋊C₄	—	2	1	no	—
261	C₄⋊C₄	—	2	1	no	—
262	C₄⋊C₄	—	2	1	no	—
263	C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
264	C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
265	C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
266	C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
267	C₂²⋊C₄	—	2	1	no	—
268	C₂²⋊C₄	—	2	1	no	—
269	C₂²⋊C₄	—	2	1	no	—
270	C₂²⋊C₄	—	2	1	no	—
271	C₂²⋊C₄	—	2	1	no	—
272	C₂²⋊C₄	—	2	1	no	—
273	C₂²⋊C₄	—	2	1	no	—
274	C₂²⋊C₄	—	2	1	no	—
275	C₄²	—	2	1	no	—
276	C₄²	—	2	1	no	—
277	C₄²	—	2	1	no	—
278	C₄²	—	2	1	no	—
279	C₄²	D₄×C₁₀₉	1	1	yes	characteristic
280	C₄²	D₄×C₁₀₉	1	1	yes	characteristic
281	C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
282	C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
283	C₂³	—	2	1	no	—
284	C₂³	—	2	1	no	—
285	C₂³	C₂×D₄×C₁₀₉	1	1	yes	characteristic
286	Q₈	—	2	1	no	—
287	Q₈	—	2	1	no	—
288	Q₈	—	2	1	no	—
289	Q₈	#41×C₁₀₉	1	2	yes	—
290	D₄	—	2	4	no	—
291	D₄	—	2	1	no	—
292	D₄	—	2	1	no	—
293	D₄	—	2	1	no	—
294	D₄	—	4	2	no	—
295	D₄	#41×C₁₀₉	1	2	yes	—
296	C₂×C₄	—	2	4	no	—
297	C₂×C₄	—	2	1	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	1	no	—
300	C₂×C₄	—	2	1	no	—
301	C₂×C₄	—	2	1	no	—
302	C₂×C₄	—	2	1	no	—
303	C₂×C₄	—	2	1	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	1	no	—
306	C₂×C₄	—	4	1	no	—
307	C₂×C₄	—	4	2	no	—
308	C₂×C₄	—	4	2	no	—
309	C₂×C₄	—	4	2	no	—
310	C₂×C₄	C₂×D₄×C₁₀₉	1	1	yes	characteristic
311	C₂×C₄	C₂×D₄×C₁₀₉	1	1	yes	characteristic
312	C₂×C₄	C₂×D₄×C₁₀₉	1	1	yes	characteristic
313	C₂×C₄	C₂×D₄×C₁₀₉	1	1	yes	characteristic
314	C₂×C₄	C₂×D₄×C₁₀₉	1	1	yes	characteristic
315	C₂×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
316	C₈	—	2	1	no	—
317	C₈	—	2	1	no	—
318	C₈	—	2	1	no	—
319	C₈	—	2	1	no	—
320	C₂²	—	2	1	no	—
321	C₂²	—	2	2	no	—
322	C₂²	—	2	1	no	—
323	C₂²	—	2	1	no	—
324	C₂²	—	4	1	no	—
325	C₂²	—	4	1	no	—
326	C₂²	—	4	1	no	—
327	C₂²	—	4	1	no	—
328	C₂²	—	4	1	no	—
329	C₂²	C₂²×D₄×C₁₀₉	1	1	yes	characteristic
330	C₄	—	2	1	no	—
331	C₄	—	2	2	no	—
332	C₄	—	2	1	no	—
333	C₄	—	2	1	no	—
334	C₄	—	2	1	no	—
335	C₄	—	4	1	no	—
336	C₄	—	4	1	no	—
337	C₄	—	4	1	no	—
338	C₄	—	4	1	no	—
339	C₄	—	4	1	no	—
340	C₄	#135×C₁₀₉	1	2	yes	—
341	C₄	C₂×#41×C₁₀₉	1	1	yes	characteristic
342	C₄	C₂×#41×C₁₀₉	1	1	yes	characteristic
343	C₂	—	4	1	no	—
344	C₂	—	4	2	no	—
345	C₂	—	8	1	no	—
346	C₂	#525×C₁₀₉	1	1	yes	characteristic
347	C₂	C₂×#135×C₁₀₉	1	1	yes	characteristic
348	C₂	#575×C₁₀₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₀₉	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₀₉
socle	C₂²×C₁₀₉	C₂²×D₄
prime radical	#449×C₁₀₉	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₀₉ ◁ C₂×C₄²×C₁₀₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. #529×C₁₀₉	C₂	semidirect
2. C₄×#41×C₁₀₉	C₂	semidirect
3. #485×C₁₀₉	C₂	semidirect
4. #482×C₁₀₉	C₂	semidirect
5. #479×C₁₀₉	C₂	semidirect
6. #478×C₁₀₉	C₂	semidirect
7. #464×C₁₀₉	C₂	semidirect
8. #463×C₁₀₉	C₂	semidirect
9. #452×C₁₀₉	C₂	semidirect
11. C₄×Q₁₆×C₁₀₉	C₂	semidirect
12. C₄×SD₁₆×C₁₀₉	C₂	semidirect
13. C₄×SD₁₆×C₁₀₉	C₂	semidirect
14. C₄×D₈×C₁₀₉	C₂	semidirect
15. #431×C₁₀₉	C₂	semidirect
174. #3102	C₁₀₉	direct (N × H)
175. C₁₀₉	#3102	direct (N × H)
176. #529	C₂×C₁₀₉	semidirect
177. C₄×#41	C₂×C₁₀₉	semidirect
178. #485	C₂×C₁₀₉	semidirect
179. #482	C₂×C₁₀₉	semidirect
180. #479	C₂×C₁₀₉	semidirect
181. #478	C₂×C₁₀₉	semidirect
182. #464	C₂×C₁₀₉	semidirect
183. #463	C₂×C₁₀₉	semidirect
184. #452	C₂×C₁₀₉	semidirect
186. C₄×Q₁₆	C₂×C₁₀₉	semidirect
187. C₄×SD₁₆	C₂×C₁₀₉	semidirect
188. C₄×SD₁₆	C₂×C₁₀₉	semidirect
189. C₄×D₈	C₂×C₁₀₉	semidirect
190. #431	C₂×C₁₀₉	semidirect

Maximal subgroups

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

subgroup	index
#529×C₁₀₉	2
C₄×#41×C₁₀₉	2
#485×C₁₀₉	2
#482×C₁₀₉	2
#479×C₁₀₉	2
#478×C₁₀₉	2
#464×C₁₀₉	2
#463×C₁₀₉	2
#452×C₁₀₉	2
#449×C₁₀₉	2
C₄×Q₁₆×C₁₀₉	2
C₄×SD₁₆×C₁₀₉	2
C₄×D₈×C₁₀₉	2
#431×C₁₀₉	2
#3102	109

Subgroups — C109×#3102 #28360356

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₉×#3102 #28360356