Subgroups — C₁₀₉×#32529 #42150523

Order 27904.

664 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₉×#2513	C₂	1	2	yes	maximal, complemented
2	C₁₀₉×#2092	C₂	1	2	yes	maximal, complemented
3	C₁₀₉×#2065	C₂	1	2	yes	maximal, complemented
4	C₁₀₉×#2054	C₂	1	2	yes	maximal
5	C₁₀₉×#1970	C₂	1	1	yes	maximal, characteristic
6	C₁₀₉×#1949	C₂	1	2	yes	maximal, complemented
7	C₁₀₉×#1942	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₀₉×#1939	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₀₉×#1925	C₂	1	2	yes	maximal, complemented
10	C₂²×D₈×C₁₀₉	C₂²	1	1	yes	characteristic
11	C₂×#107×C₁₀₉	C₂²	1	1	yes	characteristic
12	C₂×#107×C₁₀₉	C₂²	1	1	yes	characteristic
13	C₂×#107×C₁₀₉	C₂²	1	1	yes	characteristic
14	C₂×#106×C₁₀₉	C₂²	1	2	yes	—
15	C₂×C₄⋊C₈×C₁₀₉	C₂²	1	2	yes	—
16	C₂×C₄⋊C₈×C₁₀₉	C₂²	1	1	yes	characteristic
17	C₂×#102×C₁₀₉	C₂²	1	2	yes	—
18	C₂×#102×C₁₀₉	C₂²	1	2	yes	—
19	C₂×#102×C₁₀₉	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₁₀₉	C₂²	1	1	yes	characteristic
21	#397×C₁₀₉	—	2	2	no	—
22	#397×C₁₀₉	—	2	2	no	—
23	#390×C₁₀₉	C₂²	1	2	yes	—
24	#390×C₁₀₉	C₂²	1	2	yes	—
25	#390×C₁₀₉	C₂²	1	2	yes	—
26	#389×C₁₀₉	C₂²	1	2	yes	—
27	#388×C₁₀₉	—	2	2	no	—
28	#388×C₁₀₉	—	2	2	no	—
29	#382×C₁₀₉	C₂²	1	2	yes	—
30	C₄×C₄⋊C₄×C₁₀₉	C₂²	1	2	yes	—
31	C₄×C₄⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
32	#340×C₁₀₉	C₂²	1	2	yes	—
33	#340×C₁₀₉	C₂²	1	2	yes	—
34	#336×C₁₀₉	C₂²	1	2	yes	—
35	C₂²×D₄×C₁₀₉	C₂³	1	2	yes	—
36	C₂×D₈×C₁₀₉	—	2	2	no	—
37	C₂×D₈×C₁₀₉	—	4	1	no	—
38	C₂×D₈×C₁₀₉	—	4	1	no	—
39	C₂²×C₈×C₁₀₉	C₂³	1	2	yes	—
40	C₂²×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
41	C₂²×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
42	C₂×C₄⋊C₄×C₁₀₉	—	2	2	no	—
43	C₂×C₄⋊C₄×C₁₀₉	D₄	1	1	yes	characteristic
44	C₂×C₄⋊C₄×C₁₀₉	D₄	1	1	yes	characteristic
45	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
46	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
47	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
48	C₂×C₂²⋊C₄×C₁₀₉	—	2	2	no	—
49	C₂×C₂²⋊C₄×C₁₀₉	—	2	2	no	—
50	C₂×C₂²⋊C₄×C₁₀₉	—	2	2	no	—
51	C₂×C₂²⋊C₄×C₁₀₉	—	2	2	no	—
52	C₂×C₂²⋊C₄×C₁₀₉	—	2	2	no	—
53	C₂×C₂²⋊C₄×C₁₀₉	—	2	2	no	—
54	C₂×C₄²×C₁₀₉	—	2	2	no	—
55	C₂×C₄²×C₁₀₉	C₂³	1	2	yes	—
56	C₂×C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
57	#107×C₁₀₉	—	2	2	no	—
58	#107×C₁₀₉	—	4	1	no	—
59	#107×C₁₀₉	—	4	1	no	—
60	#106×C₁₀₉	—	4	2	no	—
61	C₄⋊C₈×C₁₀₉	—	2	4	no	—
62	C₄⋊C₈×C₁₀₉	—	4	1	no	—
63	#102×C₁₀₉	—	2	4	no	—
64	#102×C₁₀₉	—	4	2	no	—
65	#102×C₁₀₉	—	4	2	no	—
66	C₄×C₈×C₁₀₉	—	4	1	no	—
67	#95×C₁₀₉	—	2	2	no	—
68	#95×C₁₀₉	—	2	2	no	—
69	#95×C₁₀₉	—	2	2	no	—
70	#95×C₁₀₉	—	2	2	no	—
71	#95×C₁₀₉	D₄	1	2	yes	—
72	C₂⁴×C₁₀₉	—	2	2	no	—
73	C₂×D₄×C₁₀₉	—	2	2	no	—
74	C₂×D₄×C₁₀₉	—	2	2	no	—
75	C₂×D₄×C₁₀₉	—	2	2	no	—
76	C₂×D₄×C₁₀₉	—	2	2	no	—
77	C₂×D₄×C₁₀₉	—	2	2	no	—
78	C₂×D₄×C₁₀₉	—	2	2	no	—
79	C₂²×C₄×C₁₀₉	—	2	2	no	—
80	C₂²×C₄×C₁₀₉	—	2	2	no	—
81	C₂²×C₄×C₁₀₉	—	2	2	no	—
82	C₂²×C₄×C₁₀₉	C₂×D₄	1	2	yes	—
83	C₂²×C₄×C₁₀₉	C₂×D₄	1	2	yes	—
84	C₂²×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
87	D₈×C₁₀₉	—	4	4	no	—
88	C₂×C₈×C₁₀₉	—	2	1	no	—
89	C₂×C₈×C₁₀₉	—	2	1	no	—
90	C₂×C₈×C₁₀₉	—	2	1	no	—
91	C₂×C₈×C₁₀₉	—	2	1	no	—
92	C₂×C₈×C₁₀₉	—	2	2	no	—
93	C₂×C₈×C₁₀₉	—	2	2	no	—
94	C₂×C₈×C₁₀₉	—	2	2	no	—
95	C₂×C₈×C₁₀₉	#41	1	2	yes	—
96	C₂×C₈×C₁₀₉	#41	1	2	yes	—
97	C₄⋊C₄×C₁₀₉	—	2	2	no	—
98	C₄⋊C₄×C₁₀₉	—	2	2	no	—
99	C₄⋊C₄×C₁₀₉	—	2	2	no	—
100	C₄⋊C₄×C₁₀₉	—	2	2	no	—
101	C₄⋊C₄×C₁₀₉	—	2	2	no	—
102	C₄⋊C₄×C₁₀₉	—	2	2	no	—
103	C₄⋊C₄×C₁₀₉	—	2	2	no	—
104	C₄⋊C₄×C₁₀₉	—	4	1	no	—
105	C₄⋊C₄×C₁₀₉	—	8	2	no	—
106	C₂²⋊C₄×C₁₀₉	—	4	4	no	—
107	C₂²⋊C₄×C₁₀₉	—	4	4	no	—
108	C₂²⋊C₄×C₁₀₉	—	8	2	no	—
109	C₂²⋊C₄×C₁₀₉	—	8	2	no	—
110	C₂²⋊C₄×C₁₀₉	—	8	2	no	—
111	C₂²⋊C₄×C₁₀₉	—	8	2	no	—
112	C₄²×C₁₀₉	—	2	2	no	—
113	C₄²×C₁₀₉	—	2	1	no	—
114	C₄²×C₁₀₉	—	2	1	no	—
115	C₄²×C₁₀₉	—	2	2	no	—
116	C₄²×C₁₀₉	—	8	2	no	—
117	C₂³×C₁₀₉	—	4	2	no	—
118	C₂³×C₁₀₉	—	4	2	no	—
119	C₂³×C₁₀₉	—	4	2	no	—
120	C₂³×C₁₀₉	—	4	2	no	—
121	C₂³×C₁₀₉	—	4	2	no	—
122	C₂³×C₁₀₉	—	4	2	no	—
123	C₂³×C₁₀₉	—	4	2	no	—
124	C₂³×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
125	D₄×C₁₀₉	—	4	2	no	—
126	D₄×C₁₀₉	—	4	2	no	—
127	D₄×C₁₀₉	—	4	2	no	—
128	D₄×C₁₀₉	—	4	2	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	2	no	—
135	C₂×C₄×C₁₀₉	—	2	2	no	—
136	C₂×C₄×C₁₀₉	—	2	2	no	—
137	C₂×C₄×C₁₀₉	—	2	2	no	—
138	C₂×C₄×C₁₀₉	—	2	1	no	—
139	C₂×C₄×C₁₀₉	—	2	1	no	—
140	C₂×C₄×C₁₀₉	—	4	2	no	—
141	C₂×C₄×C₁₀₉	—	4	2	no	—
142	C₂×C₄×C₁₀₉	—	4	2	no	—
143	C₂×C₄×C₁₀₉	—	4	2	no	—
144	C₂×C₄×C₁₀₉	—	4	2	no	—
145	C₂×C₄×C₁₀₉	—	4	2	no	—
146	C₂×C₄×C₁₀₉	—	4	2	no	—
147	C₂×C₄×C₁₀₉	—	4	2	no	—
148	C₂×C₄×C₁₀₉	—	4	2	no	—
149	C₂×C₄×C₁₀₉	#135	1	2	yes	—
150	C₂×C₄×C₁₀₉	C₂×#41	1	1	yes	characteristic
151	C₂×C₄×C₁₀₉	C₂×#41	1	1	yes	characteristic
152	C₂×C₄×C₁₀₉	H(5,𝔽₂)	1	1	yes	characteristic
153	C₂×C₄×C₁₀₉	H(5,𝔽₂)	1	1	yes	characteristic
154	C₂×C₄×C₁₀₉	2₋¹⁺⁴	1	1	yes	characteristic
155	C₂×C₄×C₁₀₉	2₋¹⁺⁴	1	1	yes	characteristic
156	C₈×C₁₀₉	—	2	2	no	—
157	C₈×C₁₀₉	—	2	2	no	—
158	C₈×C₁₀₉	—	4	2	no	—
159	C₂²×C₁₀₉	—	8	2	no	—
160	C₂²×C₁₀₉	—	8	2	no	—
161	C₂²×C₁₀₉	—	8	2	no	—
162	C₂²×C₁₀₉	—	8	2	no	—
163	C₂²×C₁₀₉	—	8	2	no	—
164	C₂²×C₁₀₉	—	8	2	no	—
165	C₂²×C₁₀₉	—	8	2	no	—
166	C₂²×C₁₀₉	#537	1	1	yes	characteristic
167	C₂²×C₁₀₉	#547	1	1	yes	characteristic
168	C₂²×C₁₀₉	#550	1	1	yes	characteristic
169	C₂²×C₁₀₉	C₂×#135	1	1	yes	characteristic
170	C₂²×C₁₀₉	#575	1	1	yes	characteristic
171	C₂²×C₁₀₉	#576	1	1	yes	characteristic
172	C₂²×C₁₀₉	#576	1	1	yes	characteristic
173	C₄×C₁₀₉	—	2	2	no	—
174	C₄×C₁₀₉	—	4	2	no	—
175	C₄×C₁₀₉	—	4	2	no	—
176	C₄×C₁₀₉	—	4	1	no	—
177	C₄×C₁₀₉	—	8	2	no	—
178	C₄×C₁₀₉	—	8	2	no	—
179	C₄×C₁₀₉	—	8	2	no	—
180	C₄×C₁₀₉	#538	1	1	yes	characteristic
181	C₄×C₁₀₉	#539	1	1	yes	characteristic
182	C₄×C₁₀₉	#556	1	1	yes	characteristic
183	C₄×C₁₀₉	#563	1	1	yes	characteristic
184	#32529	C₁₀₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
185	C₂×C₁₀₉	—	16	2	no	—
186	C₂×C₁₀₉	#2727	1	1	yes	characteristic
187	C₂×C₁₀₉	#3250	1	1	yes	characteristic
188	C₂×C₁₀₉	#3259	1	1	yes	characteristic
189	C₂×C₁₀₉	#3341	1	1	yes	characteristic
190	C₂×C₁₀₉	#3355	1	1	yes	characteristic
191	C₂×C₁₀₉	#3396	1	1	yes	characteristic
192	C₂×C₁₀₉	#3403	1	1	yes	characteristic
193	#2513	C₂×C₁₀₉	1	2	yes	complemented
194	#2092	C₂×C₁₀₉	1	2	yes	complemented
195	#2065	C₂×C₁₀₉	1	2	yes	complemented
196	#2054	C₂×C₁₀₉	1	2	yes	—
197	#1970	C₂×C₁₀₉	1	1	yes	characteristic
198	#1949	C₂×C₁₀₉	1	2	yes	complemented
199	#1942	C₂×C₁₀₉	1	1	yes	characteristic, complemented
200	#1939	C₂×C₁₀₉	1	1	yes	characteristic, complemented
201	#1925	C₂×C₁₀₉	1	2	yes	complemented
202	C₁₀₉	#32529	1	1	yes	characteristic, direct product factor, Sylow
203	C₂²×D₈	C₂²×C₁₀₉	1	1	yes	characteristic
204	C₂×#107	C₂²×C₁₀₉	1	1	yes	characteristic
205	C₂×#107	C₂²×C₁₀₉	1	1	yes	characteristic
206	C₂×#107	C₂²×C₁₀₉	1	1	yes	characteristic
207	C₂×#106	C₂²×C₁₀₉	1	2	yes	—
208	C₂×C₄⋊C₈	C₂²×C₁₀₉	1	2	yes	—
209	C₂×C₄⋊C₈	C₂²×C₁₀₉	1	1	yes	characteristic
210	C₂×#102	C₂²×C₁₀₉	1	2	yes	—
211	C₂×#102	C₂²×C₁₀₉	1	2	yes	—
212	C₂×#102	C₂²×C₁₀₉	1	2	yes	—
213	C₂×C₄×C₈	C₂²×C₁₀₉	1	1	yes	characteristic
214	#397	—	2	2	no	—
215	#397	—	2	2	no	—
216	#390	C₂²×C₁₀₉	1	2	yes	—
217	#390	C₂²×C₁₀₉	1	2	yes	—
218	#390	C₂²×C₁₀₉	1	2	yes	—
219	#389	C₂²×C₁₀₉	1	2	yes	—
220	#388	—	2	2	no	—
221	#388	—	2	2	no	—
222	#382	C₂²×C₁₀₉	1	2	yes	—
223	C₄×C₄⋊C₄	C₂²×C₁₀₉	1	2	yes	—
224	C₄×C₄⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
225	#340	C₂²×C₁₀₉	1	2	yes	—
226	#340	C₂²×C₁₀₉	1	2	yes	—
227	#336	C₂²×C₁₀₉	1	2	yes	—
228	C₂²×D₄	C₂³×C₁₀₉	1	2	yes	—
229	C₂×D₈	—	2	2	no	—
230	C₂×D₈	—	4	1	no	—
231	C₂×D₈	—	4	1	no	—
232	C₂²×C₈	C₂³×C₁₀₉	1	2	yes	—
233	C₂²×C₈	C₂³×C₁₀₉	1	1	yes	characteristic
234	C₂²×C₈	C₂³×C₁₀₉	1	1	yes	characteristic
235	C₂×C₄⋊C₄	—	2	2	no	—
236	C₂×C₄⋊C₄	D₄×C₁₀₉	1	1	yes	characteristic
237	C₂×C₄⋊C₄	D₄×C₁₀₉	1	1	yes	characteristic
238	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
239	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
240	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
241	C₂×C₂²⋊C₄	—	2	2	no	—
242	C₂×C₂²⋊C₄	—	2	2	no	—
243	C₂×C₂²⋊C₄	—	2	2	no	—
244	C₂×C₂²⋊C₄	—	2	2	no	—
245	C₂×C₂²⋊C₄	—	2	2	no	—
246	C₂×C₂²⋊C₄	—	2	2	no	—
247	C₂×C₄²	—	2	2	no	—
248	C₂×C₄²	C₂³×C₁₀₉	1	2	yes	—
249	C₂×C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
250	#107	—	2	2	no	—
251	#107	—	4	1	no	—
252	#107	—	4	1	no	—
253	#106	—	4	2	no	—
254	C₄⋊C₈	—	2	4	no	—
255	C₄⋊C₈	—	4	1	no	—
256	#102	—	2	4	no	—
257	#102	—	4	2	no	—
258	#102	—	4	2	no	—
259	C₄×C₈	—	4	1	no	—
260	#95	—	2	2	no	—
261	#95	—	2	2	no	—
262	#95	—	2	2	no	—
263	#95	—	2	2	no	—
264	#95	D₄×C₁₀₉	1	2	yes	—
265	C₂⁴	—	2	2	no	—
266	C₂×D₄	—	2	2	no	—
267	C₂×D₄	—	2	2	no	—
268	C₂×D₄	—	2	2	no	—
269	C₂×D₄	—	2	2	no	—
270	C₂×D₄	—	2	2	no	—
271	C₂×D₄	—	2	2	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	C₂×D₄×C₁₀₉	1	2	yes	—
276	C₂²×C₄	C₂×D₄×C₁₀₉	1	2	yes	—
277	C₂²×C₄	C₂×D₄×C₁₀₉	1	1	yes	characteristic
278	C₂²×C₄	C₂×D₄×C₁₀₉	1	1	yes	characteristic
279	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
280	D₈	—	4	4	no	—
281	C₂×C₈	—	2	1	no	—
282	C₂×C₈	—	2	1	no	—
283	C₂×C₈	—	2	1	no	—
284	C₂×C₈	—	2	1	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	#41×C₁₀₉	1	2	yes	—
289	C₂×C₈	#41×C₁₀₉	1	2	yes	—
290	C₄⋊C₄	—	2	2	no	—
291	C₄⋊C₄	—	2	2	no	—
292	C₄⋊C₄	—	2	2	no	—
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	—	2	2	no	—
295	C₄⋊C₄	—	2	2	no	—
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	—	4	1	no	—
298	C₄⋊C₄	—	8	2	no	—
299	C₂²⋊C₄	—	4	4	no	—
300	C₂²⋊C₄	—	4	4	no	—
301	C₂²⋊C₄	—	8	2	no	—
302	C₂²⋊C₄	—	8	2	no	—
303	C₂²⋊C₄	—	8	2	no	—
304	C₂²⋊C₄	—	8	2	no	—
305	C₄²	—	2	2	no	—
306	C₄²	—	2	1	no	—
307	C₄²	—	2	1	no	—
308	C₄²	—	2	2	no	—
309	C₄²	—	8	2	no	—
310	C₂³	—	4	2	no	—
311	C₂³	—	4	2	no	—
312	C₂³	—	4	2	no	—
313	C₂³	—	4	2	no	—
314	C₂³	—	4	2	no	—
315	C₂³	—	4	2	no	—
316	C₂³	—	4	2	no	—
317	C₂³	C₂²×D₄×C₁₀₉	1	1	yes	characteristic
318	D₄	—	4	2	no	—
319	D₄	—	4	2	no	—
320	D₄	—	4	2	no	—
321	D₄	—	4	2	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	#135×C₁₀₉	1	2	yes	—
343	C₂×C₄	C₂×#41×C₁₀₉	1	1	yes	characteristic
344	C₂×C₄	C₂×#41×C₁₀₉	1	1	yes	characteristic
345	C₂×C₄	H(5,𝔽₂)×C₁₀₉	1	1	yes	characteristic
346	C₂×C₄	H(5,𝔽₂)×C₁₀₉	1	1	yes	characteristic
347	C₂×C₄	2₋¹⁺⁴×C₁₀₉	1	1	yes	characteristic
348	C₂×C₄	2₋¹⁺⁴×C₁₀₉	1	1	yes	characteristic
349	C₈	—	2	2	no	—
350	C₈	—	2	2	no	—
351	C₈	—	4	2	no	—
352	C₂²	—	8	2	no	—
353	C₂²	—	8	2	no	—
354	C₂²	—	8	2	no	—
355	C₂²	—	8	2	no	—
356	C₂²	—	8	2	no	—
357	C₂²	—	8	2	no	—
358	C₂²	—	8	2	no	—
359	C₂²	#537×C₁₀₉	1	1	yes	characteristic
360	C₂²	#547×C₁₀₉	1	1	yes	characteristic
361	C₂²	#550×C₁₀₉	1	1	yes	characteristic
362	C₂²	C₂×#135×C₁₀₉	1	1	yes	characteristic
363	C₂²	#575×C₁₀₉	1	1	yes	characteristic
364	C₂²	#576×C₁₀₉	1	1	yes	characteristic
365	C₂²	#576×C₁₀₉	1	1	yes	characteristic
366	C₄	—	2	2	no	—
367	C₄	—	4	1	no	—
368	C₄	—	4	2	no	—
369	C₄	—	4	2	no	—
370	C₄	—	8	2	no	—
371	C₄	—	8	2	no	—
372	C₄	—	8	2	no	—
373	C₄	#538×C₁₀₉	1	1	yes	characteristic
374	C₄	#539×C₁₀₉	1	1	yes	characteristic
375	C₄	#556×C₁₀₉	1	1	yes	characteristic
376	C₄	#563×C₁₀₉	1	1	yes	characteristic
377	C₂	—	16	2	no	—
378	C₂	C₁₀₉×#2727	1	1	yes	characteristic
379	C₂	C₁₀₉×#3250	1	1	yes	characteristic
380	C₂	C₁₀₉×#3259	1	1	yes	characteristic
381	C₂	C₁₀₉×#3341	1	1	yes	characteristic
382	C₂	C₁₀₉×#3355	1	1	yes	characteristic
383	C₂	C₁₀₉×#3396	1	1	yes	characteristic
384	C₂	C₁₀₉×#3403	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₀₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₉
prime radical	C₂²×D₈×C₁₀₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₀₉ ◁ C₄×C₄⋊C₄×C₁₀₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₀₉×#2513	C₂	semidirect
2. C₁₀₉×#2092	C₂	semidirect
3. C₁₀₉×#2065	C₂	semidirect
6. C₁₀₉×#1949	C₂	semidirect
7. C₁₀₉×#1942	C₂	semidirect
8. C₁₀₉×#1939	C₂	semidirect
9. C₁₀₉×#1925	C₂	semidirect
184. #32529	C₁₀₉	direct (N × H)
193. #2513	C₂×C₁₀₉	semidirect
194. #2092	C₂×C₁₀₉	semidirect
195. #2065	C₂×C₁₀₉	semidirect
198. #1949	C₂×C₁₀₉	semidirect
199. #1942	C₂×C₁₀₉	semidirect
200. #1939	C₂×C₁₀₉	semidirect
201. #1925	C₂×C₁₀₉	semidirect
202. C₁₀₉	#32529	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₀₉×#2513	2
C₁₀₉×#2092	2
C₁₀₉×#2065	2
C₁₀₉×#2054	2
C₁₀₉×#1970	2
C₁₀₉×#1949	2
C₁₀₉×#1942	2
C₁₀₉×#1939	2
C₁₀₉×#1925	2
#32529	109

Subgroups — C109×#32529 #42150523

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₉×#32529 #42150523