Subgroups — C₁₀₉×#18713 #42136707

Order 27904.

956 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₉×#3544	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₀₉×#3247	C₂	1	2	yes	maximal, complemented
3	C₁₀₉×#3152	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₉×#1634	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₉×#1633	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₀₉×#1632	C₂	1	2	yes	maximal, complemented
7	C₁₀₉×#1624	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₀₉×#1623	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₀₉×#1622	C₂	1	2	yes	maximal, complemented
10	C₂×#333×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₀₉×#1483	C₂	1	2	yes	maximal, complemented
12	C₂×#137×C₁₀₉	—	2	2	no	—
13	#563×C₁₀₉	—	2	2	no	—
14	Q₈²×C₁₀₉	C₂²	1	1	yes	characteristic
15	#555×C₁₀₉	C₂²	1	1	yes	characteristic
16	#554×C₁₀₉	C₂²	1	2	yes	—
17	#552×C₁₀₉	—	2	2	no	—
18	#547×C₁₀₉	—	2	2	no	—
19	#544×C₁₀₉	—	2	2	no	—
20	#542×C₁₀₉	—	2	2	no	—
21	#536×C₁₀₉	—	2	2	no	—
22	#532×C₁₀₉	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊Q₈×C₁₀₉	C₂²	1	1	yes	characteristic
24	#529×C₁₀₉	C₂²	1	2	yes	—
25	#497×C₁₀₉	—	2	2	no	—
26	#494×C₁₀₉	C₂²	1	1	yes	characteristic
27	#494×C₁₀₉	C₂²	1	1	yes	characteristic
28	#492×C₁₀₉	C₂²	1	1	yes	characteristic
29	#492×C₁₀₉	C₂²	1	1	yes	characteristic
30	#478×C₁₀₉	—	2	2	no	—
31	#477×C₁₀₉	C₂²	1	2	yes	—
32	#476×C₁₀₉	C₂²	1	2	yes	—
33	#466×C₁₀₉	—	2	2	no	—
34	#465×C₁₀₉	—	2	2	no	—
35	#463×C₁₀₉	—	2	2	no	—
36	#460×C₁₀₉	C₂²	1	2	yes	—
37	#459×C₁₀₉	C₂²	1	2	yes	—
38	C₂×C₄⋊C₈×C₁₀₉	C₂²	1	2	yes	—
39	C₄×M₁₆×C₁₀₉	C₂²	1	1	yes	characteristic
40	#333×C₁₀₉	C₂²	1	2	yes	—
41	#333×C₁₀₉	C₂²	1	1	yes	characteristic
42	#333×C₁₀₉	C₂²	1	1	yes	characteristic
43	Q₈⋊C₈×C₁₀₉	C₂²	1	2	yes	—
44	Q₈⋊C₈×C₁₀₉	C₂²	1	2	yes	—
45	D₄⋊C₈×C₁₀₉	C₂²	1	2	yes	—
46	D₄⋊C₈×C₁₀₉	C₂²	1	2	yes	—
47	C₂×#41×C₁₀₉	—	2	2	no	—
48	C₂×#41×C₁₀₉	—	2	1	no	—
49	C₂²×Q₈×C₁₀₉	D₄	1	2	yes	—
50	#137×C₁₀₉	—	4	8	no	—
51	C₂×Q₁₆×C₁₀₉	—	2	2	no	—
52	C₂×Q₁₆×C₁₀₉	—	2	2	no	—
53	C₂×SD₁₆×C₁₀₉	—	2	2	no	—
54	C₂×SD₁₆×C₁₀₉	—	2	2	no	—
55	C₂×SD₁₆×C₁₀₉	—	2	2	no	—
56	C₂×D₈×C₁₀₉	—	2	2	no	—
57	C₂×M₁₆×C₁₀₉	—	2	1	no	—
58	C₂²×C₈×C₁₀₉	—	2	2	no	—
59	C₄⋊Q₈×C₁₀₉	—	2	2	no	—
60	C₄⋊Q₈×C₁₀₉	—	2	2	no	—
61	C₄⋊Q₈×C₁₀₉	—	2	2	no	—
62	C₄⋊Q₈×C₁₀₉	—	2	2	no	—
63	C₄⋊Q₈×C₁₀₉	D₄	1	2	yes	—
64	C₄⋊Q₈×C₁₀₉	C₂³	1	1	yes	characteristic
65	C₄⋊Q₈×C₁₀₉	C₂³	1	1	yes	characteristic
66	C₄⋊Q₈×C₁₀₉	C₂³	1	1	yes	characteristic
67	#127×C₁₀₉	C₂³	1	1	yes	characteristic
68	#126×C₁₀₉	—	2	4	no	—
69	#126×C₁₀₉	—	2	2	no	—
70	#125×C₁₀₉	—	2	4	no	—
71	#125×C₁₀₉	—	2	2	no	—
72	#125×C₁₀₉	D₄	1	2	yes	—
73	#124×C₁₀₉	—	2	2	no	—
74	#124×C₁₀₉	—	2	2	no	—
75	#124×C₁₀₉	—	2	1	no	—
76	#124×C₁₀₉	D₄	1	2	yes	—
77	#123×C₁₀₉	—	2	4	no	—
78	#123×C₁₀₉	—	2	4	no	—
79	#123×C₁₀₉	—	2	2	no	—
80	C₂²⋊Q₈×C₁₀₉	—	2	4	no	—
81	C₂²⋊Q₈×C₁₀₉	—	2	4	no	—
82	C₂²⋊Q₈×C₁₀₉	—	2	4	no	—
83	C₂²⋊Q₈×C₁₀₉	—	2	2	no	—
84	C₂²⋊Q₈×C₁₀₉	D₄	1	2	yes	—
85	#121×C₁₀₉	—	2	2	no	—
86	#121×C₁₀₉	—	2	2	no	—
87	#121×C₁₀₉	D₄	1	2	yes	—
88	C₄×Q₈×C₁₀₉	—	2	2	no	—
89	C₄×Q₈×C₁₀₉	C₂³	1	2	yes	—
90	C₄×D₄×C₁₀₉	—	2	2	no	—
91	C₄×D₄×C₁₀₉	—	2	2	no	—
92	C₄×D₄×C₁₀₉	—	2	2	no	—
93	C₄×D₄×C₁₀₉	C₂³	1	2	yes	—
94	#117×C₁₀₉	—	2	2	no	—
95	#117×C₁₀₉	—	2	2	no	—
96	#117×C₁₀₉	—	2	2	no	—
97	C₂×C₄⋊C₄×C₁₀₉	—	2	2	no	—
98	C₂×C₄⋊C₄×C₁₀₉	—	2	2	no	—
99	C₂×C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
100	#107×C₁₀₉	—	2	2	no	—
101	#106×C₁₀₉	—	2	2	no	—
102	C₄⋊C₈×C₁₀₉	—	2	2	no	—
103	C₄⋊C₈×C₁₀₉	C₂³	1	2	yes	—
104	C₄⋊C₈×C₁₀₉	C₂³	1	2	yes	—
105	#103×C₁₀₉	—	2	2	no	—
106	#102×C₁₀₉	—	2	2	no	—
107	#102×C₁₀₉	—	2	2	no	—
108	#102×C₁₀₉	—	2	2	no	—
109	#97×C₁₀₉	—	2	1	no	—
110	C₄×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
111	C₄×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
112	#41×C₁₀₉	—	4	4	no	—
113	#41×C₁₀₉	—	8	4	no	—
114	C₂×Q₈×C₁₀₉	—	2	2	no	—
115	C₂×Q₈×C₁₀₉	—	2	2	no	—
116	C₂×Q₈×C₁₀₉	—	2	1	no	—
117	C₂×Q₈×C₁₀₉	—	4	4	no	—
118	C₂×Q₈×C₁₀₉	C₂×D₄	1	2	yes	—
119	C₂×Q₈×C₁₀₉	C₂×D₄	1	2	yes	—
120	C₂×Q₈×C₁₀₉	C₂×D₄	1	2	yes	—
121	C₂×D₄×C₁₀₉	—	2	2	no	—
122	C₂×D₄×C₁₀₉	—	2	2	no	—
123	C₂×D₄×C₁₀₉	—	2	2	no	—
124	C₂×D₄×C₁₀₉	—	2	1	no	—
125	C₂×D₄×C₁₀₉	—	4	1	no	—
126	C₂×D₄×C₁₀₉	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₁₀₉	—	2	2	no	—
128	C₂²×C₄×C₁₀₉	—	2	4	no	—
129	C₂²×C₄×C₁₀₉	—	2	2	no	—
130	C₂²×C₄×C₁₀₉	—	4	1	no	—
131	C₂²×C₄×C₁₀₉	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
133	Q₁₆×C₁₀₉	—	4	4	no	—
134	Q₁₆×C₁₀₉	—	4	4	no	—
135	SD₁₆×C₁₀₉	—	4	4	no	—
136	SD₁₆×C₁₀₉	—	4	4	no	—
137	SD₁₆×C₁₀₉	—	8	2	no	—
138	D₈×C₁₀₉	—	8	2	no	—
139	M₁₆×C₁₀₉	—	2	4	no	—
140	C₂×C₈×C₁₀₉	—	2	1	no	—
141	C₂×C₈×C₁₀₉	—	2	1	no	—
142	C₂×C₈×C₁₀₉	—	2	2	no	—
143	C₂×C₈×C₁₀₉	—	2	2	no	—
144	C₂×C₈×C₁₀₉	—	8	2	no	—
145	C₄⋊C₄×C₁₀₉	—	2	4	no	—
146	C₄⋊C₄×C₁₀₉	—	2	4	no	—
147	C₄⋊C₄×C₁₀₉	—	2	4	no	—
148	C₄⋊C₄×C₁₀₉	—	2	4	no	—
149	C₄⋊C₄×C₁₀₉	—	2	2	no	—
150	C₄⋊C₄×C₁₀₉	—	2	2	no	—
151	C₄⋊C₄×C₁₀₉	—	2	2	no	—
152	C₄⋊C₄×C₁₀₉	—	2	2	no	—
153	C₄⋊C₄×C₁₀₉	—	2	2	no	—
154	C₄⋊C₄×C₁₀₉	—	2	2	no	—
155	C₄⋊C₄×C₁₀₉	—	2	2	no	—
156	C₄⋊C₄×C₁₀₉	C₂×D₄	1	2	yes	—
157	C₄⋊C₄×C₁₀₉	C₂×D₄	1	2	yes	—
158	C₂²⋊C₄×C₁₀₉	—	2	4	no	—
159	C₂²⋊C₄×C₁₀₉	—	2	4	no	—
160	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
161	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
162	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
163	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
164	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
165	C₂²⋊C₄×C₁₀₉	—	4	2	no	—
166	C₄²×C₁₀₉	—	2	2	no	—
167	C₄²×C₁₀₉	—	2	2	no	—
168	C₄²×C₁₀₉	—	2	2	no	—
169	C₄²×C₁₀₉	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₁₀₉	C₂×D₄	1	2	yes	—
171	C₄²×C₁₀₉	C₂⁴	1	1	yes	characteristic
172	C₂³×C₁₀₉	—	2	2	no	—
173	C₂³×C₁₀₉	—	4	1	no	—
174	C₂³×C₁₀₉	#120	1	1	yes	characteristic
175	Q₈×C₁₀₉	—	2	2	no	—
176	Q₈×C₁₀₉	—	2	2	no	—
177	Q₈×C₁₀₉	—	4	2	no	—
178	Q₈×C₁₀₉	—	4	2	no	—
179	Q₈×C₁₀₉	—	4	2	no	—
180	Q₈×C₁₀₉	—	8	2	no	—
181	Q₈×C₁₀₉	—	8	2	no	—
182	D₄×C₁₀₉	—	2	2	no	—
183	D₄×C₁₀₉	—	2	2	no	—
184	D₄×C₁₀₉	—	4	2	no	—
185	D₄×C₁₀₉	—	4	4	no	—
186	D₄×C₁₀₉	—	4	2	no	—
187	D₄×C₁₀₉	—	4	2	no	—
188	D₄×C₁₀₉	—	8	2	no	—
189	D₄×C₁₀₉	—	8	2	no	—
190	C₂×C₄×C₁₀₉	—	2	2	no	—
191	C₂×C₄×C₁₀₉	—	2	2	no	—
192	C₂×C₄×C₁₀₉	—	2	2	no	—
193	C₂×C₄×C₁₀₉	—	2	2	no	—
194	C₂×C₄×C₁₀₉	—	2	2	no	—
195	C₂×C₄×C₁₀₉	—	2	2	no	—
196	C₂×C₄×C₁₀₉	—	2	2	no	—
197	C₂×C₄×C₁₀₉	—	2	2	no	—
198	C₂×C₄×C₁₀₉	—	4	4	no	—
199	C₂×C₄×C₁₀₉	—	4	2	no	—
200	C₂×C₄×C₁₀₉	—	4	2	no	—
201	C₂×C₄×C₁₀₉	—	4	1	no	—
202	C₂×C₄×C₁₀₉	—	8	2	no	—
203	C₂×C₄×C₁₀₉	—	8	4	no	—
204	C₂×C₄×C₁₀₉	#120	1	2	yes	—
205	C₂×C₄×C₁₀₉	#120	1	1	yes	characteristic
206	C₂×C₄×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₁₀₉	C₂²×D₄	1	2	yes	—
208	C₈×C₁₀₉	—	2	2	no	—
209	C₈×C₁₀₉	—	2	2	no	—
210	C₈×C₁₀₉	—	4	2	no	—
211	C₈×C₁₀₉	—	4	2	no	—
212	C₂²×C₁₀₉	—	2	2	no	—
213	C₂²×C₁₀₉	—	4	2	no	—
214	C₂²×C₁₀₉	—	4	2	no	—
215	C₂²×C₁₀₉	—	4	2	no	—
216	C₂²×C₁₀₉	—	8	2	no	—
217	C₂²×C₁₀₉	—	8	1	no	—
218	C₂²×C₁₀₉	#453	1	2	yes	—
219	C₂²×C₁₀₉	C₂×#120	1	1	yes	characteristic
220	C₄×C₁₀₉	—	2	2	no	—
221	C₄×C₁₀₉	—	2	1	no	—
222	C₄×C₁₀₉	—	2	1	no	—
223	C₄×C₁₀₉	—	4	2	no	—
224	C₄×C₁₀₉	—	4	2	no	—
225	C₄×C₁₀₉	—	4	2	no	—
226	C₄×C₁₀₉	—	4	2	no	—
227	C₄×C₁₀₉	—	4	2	no	—
228	C₄×C₁₀₉	—	8	1	no	—
229	C₄×C₁₀₉	#577	1	2	yes	—
230	C₄×C₁₀₉	#578	1	2	yes	—
231	#18713	C₁₀₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
232	C₂×C₁₀₉	—	2	2	no	—
233	C₂×C₁₀₉	—	8	2	no	—
234	C₂×C₁₀₉	—	16	1	no	—
235	C₂×C₁₀₉	#3013	1	2	yes	—
236	C₂×C₁₀₉	C₂×#453	1	1	yes	characteristic
237	#3544	C₂×C₁₀₉	1	1	yes	characteristic, complemented
238	#3247	C₂×C₁₀₉	1	2	yes	complemented
239	#3152	C₂×C₁₀₉	1	1	yes	characteristic, complemented
240	#1634	C₂×C₁₀₉	1	1	yes	characteristic, complemented
241	#1633	C₂×C₁₀₉	1	1	yes	characteristic, complemented
242	#1632	C₂×C₁₀₉	1	2	yes	complemented
243	#1624	C₂×C₁₀₉	1	1	yes	characteristic, complemented
244	#1623	C₂×C₁₀₉	1	1	yes	characteristic, complemented
245	#1622	C₂×C₁₀₉	1	2	yes	complemented
246	C₂×#333	C₂×C₁₀₉	1	1	yes	characteristic, complemented
247	#1483	C₂×C₁₀₉	1	2	yes	complemented
248	C₁₀₉	#18713	1	1	yes	characteristic, direct product factor, Sylow
249	C₂×#137	—	2	2	no	—
250	#563	—	2	2	no	—
251	Q₈²	C₂²×C₁₀₉	1	1	yes	characteristic
252	#555	C₂²×C₁₀₉	1	1	yes	characteristic
253	#554	C₂²×C₁₀₉	1	2	yes	—
254	#552	—	2	2	no	—
255	#547	—	2	2	no	—
256	#544	—	2	2	no	—
257	#542	—	2	2	no	—
258	#536	—	2	2	no	—
259	#532	C₂²×C₁₀₉	1	1	yes	characteristic
260	C₂×C₄⋊Q₈	C₂²×C₁₀₉	1	1	yes	characteristic
261	#529	C₂²×C₁₀₉	1	2	yes	—
262	#497	—	2	2	no	—
263	#494	C₂²×C₁₀₉	1	1	yes	characteristic
264	#494	C₂²×C₁₀₉	1	1	yes	characteristic
265	#492	C₂²×C₁₀₉	1	1	yes	characteristic
266	#492	C₂²×C₁₀₉	1	1	yes	characteristic
267	#478	—	2	2	no	—
268	#477	C₂²×C₁₀₉	1	2	yes	—
269	#476	C₂²×C₁₀₉	1	2	yes	—
270	#466	—	2	2	no	—
271	#465	—	2	2	no	—
272	#463	—	2	2	no	—
273	#460	C₂²×C₁₀₉	1	2	yes	—
274	#459	C₂²×C₁₀₉	1	2	yes	—
275	C₂×C₄⋊C₈	C₂²×C₁₀₉	1	2	yes	—
276	C₄×M₁₆	C₂²×C₁₀₉	1	1	yes	characteristic
277	#333	C₂²×C₁₀₉	1	2	yes	—
278	#333	C₂²×C₁₀₉	1	1	yes	characteristic
279	#333	C₂²×C₁₀₉	1	1	yes	characteristic
280	Q₈⋊C₈	C₂²×C₁₀₉	1	2	yes	—
281	Q₈⋊C₈	C₂²×C₁₀₉	1	2	yes	—
282	D₄⋊C₈	C₂²×C₁₀₉	1	2	yes	—
283	D₄⋊C₈	C₂²×C₁₀₉	1	2	yes	—
284	C₂×#41	—	2	2	no	—
285	C₂×#41	—	2	1	no	—
286	C₂²×Q₈	D₄×C₁₀₉	1	2	yes	—
287	#137	—	4	8	no	—
288	C₂×Q₁₆	—	2	2	no	—
289	C₂×Q₁₆	—	2	2	no	—
290	C₂×SD₁₆	—	2	2	no	—
291	C₂×SD₁₆	—	2	2	no	—
292	C₂×SD₁₆	—	2	2	no	—
293	C₂×D₈	—	2	2	no	—
294	C₂×M₁₆	—	2	1	no	—
295	C₂²×C₈	—	2	2	no	—
296	C₄⋊Q₈	—	2	2	no	—
297	C₄⋊Q₈	—	2	2	no	—
298	C₄⋊Q₈	—	2	2	no	—
299	C₄⋊Q₈	—	2	2	no	—
300	C₄⋊Q₈	D₄×C₁₀₉	1	2	yes	—
301	C₄⋊Q₈	C₂³×C₁₀₉	1	1	yes	characteristic
302	C₄⋊Q₈	C₂³×C₁₀₉	1	1	yes	characteristic
303	C₄⋊Q₈	C₂³×C₁₀₉	1	1	yes	characteristic
304	#127	C₂³×C₁₀₉	1	1	yes	characteristic
305	#126	—	2	4	no	—
306	#126	—	2	2	no	—
307	#125	—	2	4	no	—
308	#125	—	2	2	no	—
309	#125	D₄×C₁₀₉	1	2	yes	—
310	#124	—	2	2	no	—
311	#124	—	2	2	no	—
312	#124	—	2	1	no	—
313	#124	D₄×C₁₀₉	1	2	yes	—
314	#123	—	2	4	no	—
315	#123	—	2	4	no	—
316	#123	—	2	2	no	—
317	C₂²⋊Q₈	—	2	4	no	—
318	C₂²⋊Q₈	—	2	4	no	—
319	C₂²⋊Q₈	—	2	4	no	—
320	C₂²⋊Q₈	—	2	2	no	—
321	C₂²⋊Q₈	D₄×C₁₀₉	1	2	yes	—
322	#121	—	2	2	no	—
323	#121	—	2	2	no	—
324	#121	D₄×C₁₀₉	1	2	yes	—
325	C₄×Q₈	—	2	2	no	—
326	C₄×Q₈	C₂³×C₁₀₉	1	2	yes	—
327	C₄×D₄	—	2	2	no	—
328	C₄×D₄	—	2	2	no	—
329	C₄×D₄	—	2	2	no	—
330	C₄×D₄	C₂³×C₁₀₉	1	2	yes	—
331	#117	—	2	2	no	—
332	#117	—	2	2	no	—
333	#117	—	2	2	no	—
334	C₂×C₄⋊C₄	—	2	2	no	—
335	C₂×C₄⋊C₄	—	2	2	no	—
336	C₂×C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
337	#107	—	2	2	no	—
338	#106	—	2	2	no	—
339	C₄⋊C₈	—	2	2	no	—
340	C₄⋊C₈	C₂³×C₁₀₉	1	2	yes	—
341	C₄⋊C₈	C₂³×C₁₀₉	1	2	yes	—
342	#103	—	2	2	no	—
343	#102	—	2	2	no	—
344	#102	—	2	2	no	—
345	#102	—	2	2	no	—
346	#97	—	2	1	no	—
347	C₄×C₈	C₂³×C₁₀₉	1	1	yes	characteristic
348	C₄×C₈	C₂³×C₁₀₉	1	1	yes	characteristic
349	#41	—	4	4	no	—
350	#41	—	8	4	no	—
351	C₂×Q₈	—	2	2	no	—
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	—	2	1	no	—
354	C₂×Q₈	—	4	4	no	—
355	C₂×Q₈	C₂×D₄×C₁₀₉	1	2	yes	—
356	C₂×Q₈	C₂×D₄×C₁₀₉	1	2	yes	—
357	C₂×Q₈	C₂×D₄×C₁₀₉	1	2	yes	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	4	1	no	—
363	C₂×D₄	C₂×D₄×C₁₀₉	1	2	yes	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	4	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	4	1	no	—
368	C₂²×C₄	C₂×D₄×C₁₀₉	1	2	yes	—
369	C₂²×C₄	C₂×D₄×C₁₀₉	1	1	yes	characteristic
370	Q₁₆	—	4	4	no	—
371	Q₁₆	—	4	4	no	—
372	SD₁₆	—	4	4	no	—
373	SD₁₆	—	4	4	no	—
374	SD₁₆	—	8	2	no	—
375	D₈	—	8	2	no	—
376	M₁₆	—	2	4	no	—
377	C₂×C₈	—	2	1	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	8	2	no	—
382	C₄⋊C₄	—	2	4	no	—
383	C₄⋊C₄	—	2	4	no	—
384	C₄⋊C₄	—	2	4	no	—
385	C₄⋊C₄	—	2	4	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	C₂×D₄×C₁₀₉	1	2	yes	—
394	C₄⋊C₄	C₂×D₄×C₁₀₉	1	2	yes	—
395	C₂²⋊C₄	—	2	4	no	—
396	C₂²⋊C₄	—	2	4	no	—
397	C₂²⋊C₄	—	2	2	no	—
398	C₂²⋊C₄	—	2	2	no	—
399	C₂²⋊C₄	—	2	2	no	—
400	C₂²⋊C₄	—	2	2	no	—
401	C₂²⋊C₄	—	2	2	no	—
402	C₂²⋊C₄	—	4	2	no	—
403	C₄²	—	2	2	no	—
404	C₄²	—	2	2	no	—
405	C₄²	—	2	2	no	—
406	C₄²	C₂×D₄×C₁₀₉	1	1	yes	characteristic
407	C₄²	C₂×D₄×C₁₀₉	1	2	yes	—
408	C₄²	C₂⁴×C₁₀₉	1	1	yes	characteristic
409	C₂³	—	2	2	no	—
410	C₂³	—	4	1	no	—
411	C₂³	#120×C₁₀₉	1	1	yes	characteristic
412	Q₈	—	2	2	no	—
413	Q₈	—	2	2	no	—
414	Q₈	—	4	2	no	—
415	Q₈	—	4	2	no	—
416	Q₈	—	4	2	no	—
417	Q₈	—	8	2	no	—
418	Q₈	—	8	2	no	—
419	D₄	—	2	2	no	—
420	D₄	—	2	2	no	—
421	D₄	—	4	2	no	—
422	D₄	—	4	4	no	—
423	D₄	—	4	2	no	—
424	D₄	—	4	2	no	—
425	D₄	—	8	2	no	—
426	D₄	—	8	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	4	4	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	8	2	no	—
440	C₂×C₄	—	8	4	no	—
441	C₂×C₄	#120×C₁₀₉	1	2	yes	—
442	C₂×C₄	#120×C₁₀₉	1	1	yes	characteristic
443	C₂×C₄	C₂²×D₄×C₁₀₉	1	1	yes	characteristic
444	C₂×C₄	C₂²×D₄×C₁₀₉	1	2	yes	—
445	C₈	—	2	2	no	—
446	C₈	—	2	2	no	—
447	C₈	—	4	2	no	—
448	C₈	—	4	2	no	—
449	C₂²	—	2	2	no	—
450	C₂²	—	4	2	no	—
451	C₂²	—	4	2	no	—
452	C₂²	—	4	2	no	—
453	C₂²	—	8	2	no	—
454	C₂²	—	8	1	no	—
455	C₂²	#453×C₁₀₉	1	2	yes	—
456	C₂²	C₂×#120×C₁₀₉	1	1	yes	characteristic
457	C₄	—	2	2	no	—
458	C₄	—	2	1	no	—
459	C₄	—	2	1	no	—
460	C₄	—	4	2	no	—
461	C₄	—	4	2	no	—
462	C₄	—	4	2	no	—
463	C₄	—	4	2	no	—
464	C₄	—	4	2	no	—
465	C₄	—	8	1	no	—
466	C₄	#577×C₁₀₉	1	2	yes	—
467	C₄	#578×C₁₀₉	1	2	yes	—
468	C₂	—	2	2	no	—
469	C₂	—	8	2	no	—
470	C₂	—	16	1	no	—
471	C₂	C₁₀₉×#3013	1	2	yes	—
472	C₂	C₂×#453×C₁₀₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₀₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₀₉
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₉ ◁ C₂×C₄²×C₁₀₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₀₉×#3544	C₂	semidirect
2. C₁₀₉×#3247	C₂	semidirect
3. C₁₀₉×#3152	C₂	semidirect
4. C₁₀₉×#1634	C₂	semidirect
5. C₁₀₉×#1633	C₂	semidirect
6. C₁₀₉×#1632	C₂	semidirect
7. C₁₀₉×#1624	C₂	semidirect
8. C₁₀₉×#1623	C₂	semidirect
9. C₁₀₉×#1622	C₂	semidirect
10. C₂×#333×C₁₀₉	C₂	semidirect
11. C₁₀₉×#1483	C₂	semidirect
231. #18713	C₁₀₉	direct (N × H)
237. #3544	C₂×C₁₀₉	semidirect
238. #3247	C₂×C₁₀₉	semidirect
239. #3152	C₂×C₁₀₉	semidirect
240. #1634	C₂×C₁₀₉	semidirect
241. #1633	C₂×C₁₀₉	semidirect
242. #1632	C₂×C₁₀₉	semidirect
243. #1624	C₂×C₁₀₉	semidirect
244. #1623	C₂×C₁₀₉	semidirect
245. #1622	C₂×C₁₀₉	semidirect
246. C₂×#333	C₂×C₁₀₉	semidirect
247. #1483	C₂×C₁₀₉	semidirect
248. C₁₀₉	#18713	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×#3544	2
C₁₀₉×#3247	2
C₁₀₉×#3152	2
C₁₀₉×#1634	2
C₁₀₉×#1633	2
C₁₀₉×#1632	2
C₁₀₉×#1624	2
C₁₀₉×#1623	2
C₁₀₉×#1622	2
C₂×#333×C₁₀₉	2
C₁₀₉×#1483	2
#18713	109

Subgroups — C109×#18713 #42136707

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₉×#18713 #42136707