Subgroups — C₁₀₉×#32462 #42150456

Order 27904.

676 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₉×#2485	C₂	1	2	yes	maximal
2	C₁₀₉×#2088	C₂	1	2	yes	maximal, complemented
3	C₁₀₉×#2076	C₂	1	2	yes	maximal, complemented
4	C₁₀₉×#2075	C₂	1	2	yes	maximal, complemented
5	C₁₀₉×#1954	C₂	1	1	yes	maximal, characteristic
6	C₁₀₉×#1942	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₀₉×#1942	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₀₉×#1854	C₂	1	2	yes	maximal, complemented
9	C₁₀₉×#1854	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×D₄×C₁₀₉	C₂²	1	1	yes	characteristic
11	C₂×#117×C₁₀₉	C₂²	1	2	yes	—
12	C₂×#107×C₁₀₉	C₂²	1	1	yes	characteristic
13	C₂×#107×C₁₀₉	C₂²	1	1	yes	characteristic
14	C₂×#107×C₁₀₉	C₂²	1	1	yes	characteristic
15	C₂×#107×C₁₀₉	C₂²	1	1	yes	characteristic
16	C₂×#106×C₁₀₉	C₂²	1	2	yes	—
17	C₂×C₄⋊C₈×C₁₀₉	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊C₈×C₁₀₉	C₂²	1	2	yes	—
19	C₂×C₂²⋊C₈×C₁₀₉	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₁₀₉	C₂²	1	1	yes	characteristic
21	#397×C₁₀₉	—	2	2	no	—
22	#394×C₁₀₉	—	2	2	no	—
23	#389×C₁₀₉	C₂²	1	2	yes	—
24	#389×C₁₀₉	C₂²	1	2	yes	—
25	#388×C₁₀₉	—	2	2	no	—
26	#387×C₁₀₉	—	2	2	no	—
27	#380×C₁₀₉	C₂²	1	2	yes	—
28	#380×C₁₀₉	C₂²	1	2	yes	—
29	#380×C₁₀₉	C₂²	1	2	yes	—
30	#340×C₁₀₉	C₂²	1	2	yes	—
31	#340×C₁₀₉	C₂²	1	2	yes	—
32	#340×C₁₀₉	C₂²	1	2	yes	—
33	#340×C₁₀₉	C₂²	1	2	yes	—
34	#340×C₁₀₉	C₂²	1	2	yes	—
35	C₂²×D₄×C₁₀₉	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₀₉	C₂³	1	2	yes	—
37	C₂²×C₈×C₁₀₉	C₂³	1	2	yes	—
38	C₂²×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
39	C₂²×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
40	C₄×D₄×C₁₀₉	—	4	1	no	—
41	C₄×D₄×C₁₀₉	—	4	1	no	—
42	#117×C₁₀₉	—	4	2	no	—
43	#117×C₁₀₉	—	4	2	no	—
44	C₂×C₄⋊C₄×C₁₀₉	—	2	2	no	—
45	C₂×C₄⋊C₄×C₁₀₉	—	2	2	no	—
46	C₂×C₄⋊C₄×C₁₀₉	D₄	1	1	yes	characteristic
47	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
48	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
49	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
50	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
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×C₂²⋊C₄×C₁₀₉	—	2	2	no	—
55	C₂×C₂²⋊C₄×C₁₀₉	D₄	1	2	yes	—
56	C₂×C₄²×C₁₀₉	—	2	2	no	—
57	C₂×C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
58	#107×C₁₀₉	—	2	2	no	—
59	#107×C₁₀₉	—	2	2	no	—
60	#107×C₁₀₉	—	4	1	no	—
61	#107×C₁₀₉	—	4	1	no	—
62	#106×C₁₀₉	—	4	2	no	—
63	C₄⋊C₈×C₁₀₉	—	4	1	no	—
64	C₂²⋊C₈×C₁₀₉	—	2	4	no	—
65	C₂²⋊C₈×C₁₀₉	—	2	4	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	—	2	2	no	—
72	C₂⁴×C₁₀₉	C₂×D₄	1	2	yes	—
73	C₂×D₄×C₁₀₉	—	2	2	no	—
74	C₂×D₄×C₁₀₉	—	4	1	no	—
75	C₂×D₄×C₁₀₉	—	4	1	no	—
76	C₂²×C₄×C₁₀₉	—	2	2	no	—
77	C₂²×C₄×C₁₀₉	—	2	2	no	—
78	C₂²×C₄×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	—	2	2	no	—
83	C₂²×C₄×C₁₀₉	—	2	2	no	—
84	C₂²×C₄×C₁₀₉	—	2	2	no	—
85	C₂²×C₄×C₁₀₉	—	2	2	no	—
86	C₂²×C₄×C₁₀₉	C₂×D₄	1	2	yes	—
87	C₂²×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
90	C₂×C₈×C₁₀₉	—	2	1	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	2	no	—
95	C₂×C₈×C₁₀₉	—	2	2	no	—
96	C₂×C₈×C₁₀₉	—	2	2	no	—
97	C₂×C₈×C₁₀₉	#41	1	2	yes	—
98	C₂×C₈×C₁₀₉	#41	1	2	yes	—
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	—	2	2	no	—
105	C₄⋊C₄×C₁₀₉	—	2	2	no	—
106	C₄⋊C₄×C₁₀₉	—	2	2	no	—
107	C₄⋊C₄×C₁₀₉	—	4	1	no	—
108	C₄⋊C₄×C₁₀₉	—	4	4	no	—
109	C₄⋊C₄×C₁₀₉	—	8	2	no	—
110	C₂²⋊C₄×C₁₀₉	—	4	2	no	—
111	C₂²⋊C₄×C₁₀₉	—	4	4	no	—
112	C₂²⋊C₄×C₁₀₉	—	4	4	no	—
113	C₂²⋊C₄×C₁₀₉	—	8	2	no	—
114	C₂²⋊C₄×C₁₀₉	—	8	2	no	—
115	C₄²×C₁₀₉	—	2	1	no	—
116	C₄²×C₁₀₉	—	2	1	no	—
117	C₄²×C₁₀₉	—	4	4	no	—
118	C₂³×C₁₀₉	—	2	2	no	—
119	C₂³×C₁₀₉	—	2	2	no	—
120	C₂³×C₁₀₉	—	2	2	no	—
121	C₂³×C₁₀₉	—	2	2	no	—
122	C₂³×C₁₀₉	—	2	2	no	—
123	C₂³×C₁₀₉	—	2	2	no	—
124	C₂³×C₁₀₉	—	2	2	no	—
125	C₂³×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
126	D₄×C₁₀₉	—	4	4	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	2	no	—
131	C₂×C₄×C₁₀₉	—	2	2	no	—
132	C₂×C₄×C₁₀₉	—	2	2	no	—
133	C₂×C₄×C₁₀₉	—	2	1	no	—
134	C₂×C₄×C₁₀₉	—	2	1	no	—
135	C₂×C₄×C₁₀₉	—	4	2	no	—
136	C₂×C₄×C₁₀₉	—	4	2	no	—
137	C₂×C₄×C₁₀₉	—	4	2	no	—
138	C₂×C₄×C₁₀₉	—	4	2	no	—
139	C₂×C₄×C₁₀₉	—	4	2	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	—	4	2	no	—
150	C₂×C₄×C₁₀₉	—	4	2	no	—
151	C₂×C₄×C₁₀₉	#135	1	2	yes	—
152	C₂×C₄×C₁₀₉	C₂×#41	1	1	yes	characteristic
153	C₂×C₄×C₁₀₉	C₂×#41	1	1	yes	characteristic
154	C₂×C₄×C₁₀₉	H(5,𝔽₂)	1	1	yes	characteristic
155	C₂×C₄×C₁₀₉	H(5,𝔽₂)	1	1	yes	characteristic
156	C₂×C₄×C₁₀₉	2₋¹⁺⁴	1	1	yes	characteristic
157	C₂×C₄×C₁₀₉	2₋¹⁺⁴	1	1	yes	characteristic
158	C₈×C₁₀₉	—	2	2	no	—
159	C₈×C₁₀₉	—	2	2	no	—
160	C₈×C₁₀₉	—	4	2	no	—
161	C₂²×C₁₀₉	—	4	2	no	—
162	C₂²×C₁₀₉	—	4	2	no	—
163	C₂²×C₁₀₉	—	4	2	no	—
164	C₂²×C₁₀₉	—	4	2	no	—
165	C₂²×C₁₀₉	—	4	2	no	—
166	C₂²×C₁₀₉	—	4	2	no	—
167	C₂²×C₁₀₉	—	4	2	no	—
168	C₂²×C₁₀₉	#534	1	1	yes	characteristic
169	C₂²×C₁₀₉	#547	1	1	yes	characteristic
170	C₂²×C₁₀₉	#547	1	1	yes	characteristic
171	C₂²×C₁₀₉	C₂×#135	1	1	yes	characteristic
172	C₂²×C₁₀₉	#575	1	1	yes	characteristic
173	C₂²×C₁₀₉	#576	1	1	yes	characteristic
174	C₂²×C₁₀₉	#578	1	1	yes	characteristic
175	C₄×C₁₀₉	—	2	2	no	—
176	C₄×C₁₀₉	—	4	1	no	—
177	C₄×C₁₀₉	—	4	2	no	—
178	C₄×C₁₀₉	—	8	2	no	—
179	C₄×C₁₀₉	—	8	2	no	—
180	C₄×C₁₀₉	—	8	2	no	—
181	C₄×C₁₀₉	—	8	2	no	—
182	C₄×C₁₀₉	#539	1	1	yes	characteristic
183	C₄×C₁₀₉	#539	1	1	yes	characteristic
184	C₄×C₁₀₉	#559	1	1	yes	characteristic
185	C₄×C₁₀₉	#563	1	1	yes	characteristic
186	#32462	C₁₀₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
187	C₂×C₁₀₉	—	8	2	no	—
188	C₂×C₁₀₉	#2724	1	1	yes	characteristic
189	C₂×C₁₀₉	#3191	1	1	yes	characteristic
190	C₂×C₁₀₉	#3203	1	1	yes	characteristic
191	C₂×C₁₀₉	#3341	1	1	yes	characteristic
192	C₂×C₁₀₉	#3342	1	1	yes	characteristic
193	C₂×C₁₀₉	#3352	1	1	yes	characteristic
194	C₂×C₁₀₉	#3355	1	1	yes	characteristic
195	#2485	C₂×C₁₀₉	1	2	yes	—
196	#2088	C₂×C₁₀₉	1	2	yes	complemented
197	#2076	C₂×C₁₀₉	1	2	yes	complemented
198	#2075	C₂×C₁₀₉	1	2	yes	complemented
199	#1954	C₂×C₁₀₉	1	1	yes	characteristic
200	#1942	C₂×C₁₀₉	1	1	yes	characteristic, complemented
201	#1942	C₂×C₁₀₉	1	1	yes	characteristic, complemented
202	#1854	C₂×C₁₀₉	1	2	yes	complemented
203	#1854	C₂×C₁₀₉	1	2	yes	complemented
204	C₁₀₉	#32462	1	1	yes	characteristic, direct product factor, Sylow
205	C₂×C₄×D₄	C₂²×C₁₀₉	1	1	yes	characteristic
206	C₂×#117	C₂²×C₁₀₉	1	2	yes	—
207	C₂×#107	C₂²×C₁₀₉	1	1	yes	characteristic
208	C₂×#107	C₂²×C₁₀₉	1	1	yes	characteristic
209	C₂×#107	C₂²×C₁₀₉	1	1	yes	characteristic
210	C₂×#107	C₂²×C₁₀₉	1	1	yes	characteristic
211	C₂×#106	C₂²×C₁₀₉	1	2	yes	—
212	C₂×C₄⋊C₈	C₂²×C₁₀₉	1	1	yes	characteristic
213	C₂×C₂²⋊C₈	C₂²×C₁₀₉	1	2	yes	—
214	C₂×C₂²⋊C₈	C₂²×C₁₀₉	1	2	yes	—
215	C₂×C₄×C₈	C₂²×C₁₀₉	1	1	yes	characteristic
216	#397	—	2	2	no	—
217	#394	—	2	2	no	—
218	#389	C₂²×C₁₀₉	1	2	yes	—
219	#389	C₂²×C₁₀₉	1	2	yes	—
220	#388	—	2	2	no	—
221	#387	—	2	2	no	—
222	#380	C₂²×C₁₀₉	1	2	yes	—
223	#380	C₂²×C₁₀₉	1	2	yes	—
224	#380	C₂²×C₁₀₉	1	2	yes	—
225	#340	C₂²×C₁₀₉	1	2	yes	—
226	#340	C₂²×C₁₀₉	1	2	yes	—
227	#340	C₂²×C₁₀₉	1	2	yes	—
228	#340	C₂²×C₁₀₉	1	2	yes	—
229	#340	C₂²×C₁₀₉	1	2	yes	—
230	C₂²×D₄	D₄×C₁₀₉	1	1	yes	characteristic
231	C₂³×C₄	C₂³×C₁₀₉	1	2	yes	—
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	C₄×D₄	—	4	1	no	—
236	C₄×D₄	—	4	1	no	—
237	#117	—	4	2	no	—
238	#117	—	4	2	no	—
239	C₂×C₄⋊C₄	—	2	2	no	—
240	C₂×C₄⋊C₄	—	2	2	no	—
241	C₂×C₄⋊C₄	D₄×C₁₀₉	1	1	yes	characteristic
242	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
243	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
244	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
245	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
246	C₂×C₂²⋊C₄	—	2	2	no	—
247	C₂×C₂²⋊C₄	—	2	2	no	—
248	C₂×C₂²⋊C₄	—	2	2	no	—
249	C₂×C₂²⋊C₄	—	2	2	no	—
250	C₂×C₂²⋊C₄	D₄×C₁₀₉	1	2	yes	—
251	C₂×C₄²	—	2	2	no	—
252	C₂×C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
253	#107	—	2	2	no	—
254	#107	—	2	2	no	—
255	#107	—	4	1	no	—
256	#107	—	4	1	no	—
257	#106	—	4	2	no	—
258	C₄⋊C₈	—	4	1	no	—
259	C₂²⋊C₈	—	2	4	no	—
260	C₂²⋊C₈	—	2	4	no	—
261	C₄×C₈	—	4	1	no	—
262	#95	—	2	2	no	—
263	#95	—	2	2	no	—
264	#95	—	2	2	no	—
265	#95	—	2	2	no	—
266	#95	—	2	2	no	—
267	C₂⁴	C₂×D₄×C₁₀₉	1	2	yes	—
268	C₂×D₄	—	2	2	no	—
269	C₂×D₄	—	4	1	no	—
270	C₂×D₄	—	4	1	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	C₂×D₄×C₁₀₉	1	2	yes	—
282	C₂²×C₄	C₂×D₄×C₁₀₉	1	1	yes	characteristic
283	C₂²×C₄	C₂×D₄×C₁₀₉	1	1	yes	characteristic
284	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
285	C₂×C₈	—	2	1	no	—
286	C₂×C₈	—	2	1	no	—
287	C₂×C₈	—	2	1	no	—
288	C₂×C₈	—	2	1	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	#41×C₁₀₉	1	2	yes	—
293	C₂×C₈	#41×C₁₀₉	1	2	yes	—
294	C₄⋊C₄	—	2	2	no	—
295	C₄⋊C₄	—	2	2	no	—
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	4	1	no	—
303	C₄⋊C₄	—	4	4	no	—
304	C₄⋊C₄	—	8	2	no	—
305	C₂²⋊C₄	—	4	2	no	—
306	C₂²⋊C₄	—	4	4	no	—
307	C₂²⋊C₄	—	4	4	no	—
308	C₂²⋊C₄	—	8	2	no	—
309	C₂²⋊C₄	—	8	2	no	—
310	C₄²	—	2	1	no	—
311	C₄²	—	2	1	no	—
312	C₄²	—	4	4	no	—
313	C₂³	—	2	2	no	—
314	C₂³	—	2	2	no	—
315	C₂³	—	2	2	no	—
316	C₂³	—	2	2	no	—
317	C₂³	—	2	2	no	—
318	C₂³	—	2	2	no	—
319	C₂³	—	2	2	no	—
320	C₂³	C₂²×D₄×C₁₀₉	1	1	yes	characteristic
321	D₄	—	4	4	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	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	2	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	—	4	2	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	#135×C₁₀₉	1	2	yes	—
347	C₂×C₄	C₂×#41×C₁₀₉	1	1	yes	characteristic
348	C₂×C₄	C₂×#41×C₁₀₉	1	1	yes	characteristic
349	C₂×C₄	H(5,𝔽₂)×C₁₀₉	1	1	yes	characteristic
350	C₂×C₄	H(5,𝔽₂)×C₁₀₉	1	1	yes	characteristic
351	C₂×C₄	2₋¹⁺⁴×C₁₀₉	1	1	yes	characteristic
352	C₂×C₄	2₋¹⁺⁴×C₁₀₉	1	1	yes	characteristic
353	C₈	—	2	2	no	—
354	C₈	—	2	2	no	—
355	C₈	—	4	2	no	—
356	C₂²	—	4	2	no	—
357	C₂²	—	4	2	no	—
358	C₂²	—	4	2	no	—
359	C₂²	—	4	2	no	—
360	C₂²	—	4	2	no	—
361	C₂²	—	4	2	no	—
362	C₂²	—	4	2	no	—
363	C₂²	#534×C₁₀₉	1	1	yes	characteristic
364	C₂²	#547×C₁₀₉	1	1	yes	characteristic
365	C₂²	#547×C₁₀₉	1	1	yes	characteristic
366	C₂²	C₂×#135×C₁₀₉	1	1	yes	characteristic
367	C₂²	#575×C₁₀₉	1	1	yes	characteristic
368	C₂²	#576×C₁₀₉	1	1	yes	characteristic
369	C₂²	#578×C₁₀₉	1	1	yes	characteristic
370	C₄	—	2	2	no	—
371	C₄	—	4	1	no	—
372	C₄	—	4	2	no	—
373	C₄	—	8	2	no	—
374	C₄	—	8	2	no	—
375	C₄	—	8	2	no	—
376	C₄	—	8	2	no	—
377	C₄	#539×C₁₀₉	1	1	yes	characteristic
378	C₄	#539×C₁₀₉	1	1	yes	characteristic
379	C₄	#559×C₁₀₉	1	1	yes	characteristic
380	C₄	#563×C₁₀₉	1	1	yes	characteristic
381	C₂	—	8	2	no	—
382	C₂	C₁₀₉×#2724	1	1	yes	characteristic
383	C₂	C₁₀₉×#3191	1	1	yes	characteristic
384	C₂	C₁₀₉×#3203	1	1	yes	characteristic
385	C₂	C₁₀₉×#3341	1	1	yes	characteristic
386	C₂	C₁₀₉×#3342	1	1	yes	characteristic
387	C₂	C₁₀₉×#3352	1	1	yes	characteristic
388	C₂	C₁₀₉×#3355	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₁₀₉×#2088	C₂	semidirect
3. C₁₀₉×#2076	C₂	semidirect
4. C₁₀₉×#2075	C₂	semidirect
6. C₁₀₉×#1942	C₂	semidirect
7. C₁₀₉×#1942	C₂	semidirect
8. C₁₀₉×#1854	C₂	semidirect
9. C₁₀₉×#1854	C₂	semidirect
186. #32462	C₁₀₉	direct (N × H)
196. #2088	C₂×C₁₀₉	semidirect
197. #2076	C₂×C₁₀₉	semidirect
198. #2075	C₂×C₁₀₉	semidirect
200. #1942	C₂×C₁₀₉	semidirect
201. #1942	C₂×C₁₀₉	semidirect
202. #1854	C₂×C₁₀₉	semidirect
203. #1854	C₂×C₁₀₉	semidirect
204. C₁₀₉	#32462	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×#2485	2
C₁₀₉×#2088	2
C₁₀₉×#2076	2
C₁₀₉×#2075	2
C₁₀₉×#1954	2
C₁₀₉×#1942	2
C₁₀₉×#1854	2
#32462	109

Subgroups — C109×#32462 #42150456

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₉×#32462 #42150456