Subgroups — #532×D₁₀₉ #28376309

Order 13952.

1728 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×D₁₀₉	C₂	1	2	yes	maximal, complemented
2	#20295577	C₂	1	1	yes	maximal, characteristic, complemented
3	#20295576	C₂	1	1	yes	maximal, characteristic, complemented
4	#20295575	C₂	1	2	yes	maximal, complemented
5	#20295574	C₂	1	1	yes	maximal, characteristic, complemented
6	#20295573	C₂	1	4	yes	maximal, complemented
7	#20295572	C₂	1	2	yes	maximal, complemented
8	#20295571	C₂	1	4	yes	maximal, complemented
9	C₄⋊Q₈×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#127×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#124×D₁₀₉	C₂	1	2	yes	maximal, complemented
12	#121×D₁₀₉	C₂	1	4	yes	maximal, complemented
13	C₄×D₄×D₁₀₉	C₂	1	4	yes	maximal, complemented
14	C₂×C₄²×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#532×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13182030	C₂²	1	2	yes	complemented
17	C₂×#13182029	C₂²	1	2	yes	complemented
18	C₂×#13182029	C₂²	1	4	yes	complemented
19	C₂×#13182028	C₂²	1	4	yes	complemented
20	C₂×#13182028	C₂²	1	2	yes	complemented
21	#41×D₁₀₉	—	2	16	no	—
22	C₂×Q₈×D₁₀₉	C₂²	1	2	yes	—
23	C₂×D₄×D₁₀₉	C₂²	1	4	yes	—
24	C₂×D₄×D₁₀₉	C₂²	1	4	yes	—
25	C₂×D₄×D₁₀₉	C₂²	1	2	yes	—
26	C₂²×C₄×D₁₀₉	C₂²	1	2	yes	—
27	C₂²×C₄×D₁₀₉	C₂²	1	4	yes	—
28	C₂²×C₄×D₁₀₉	C₂²	1	1	yes	characteristic
29	#16812699	C₂²	1	1	yes	characteristic, complemented
30	#16812698	C₂²	1	4	yes	complemented
31	#16812697	C₂²	1	2	yes	complemented
32	#16812696	C₂²	1	1	yes	characteristic, complemented
33	#16812695	C₂²	1	4	yes	complemented
34	#16812695	C₂²	1	2	yes	complemented
35	#16812688	C₂²	1	2	yes	complemented
36	#16812687	C₂²	1	2	yes	complemented
37	#16812686	C₂²	1	2	yes	complemented
38	#16812685	C₂²	1	8	yes	complemented
39	#16812674	C₂²	1	4	yes	complemented
40	#16812673	C₂²	1	4	yes	complemented
41	#16812672	C₂²	1	8	yes	complemented
42	#16812671	C₂²	1	8	yes	complemented
43	#16812670	C₂²	1	4	yes	complemented
44	C₄×D₄₃₆	C₂²	1	4	yes	complemented
45	D₄×Dic₁₀₉	C₂²	1	4	yes	complemented
46	#16812661	C₂²	1	4	yes	complemented
47	C₄×C₂²⋊D₁₀₉	C₂²	1	8	yes	complemented
48	#16812659	C₂²	1	8	yes	complemented
49	C₄⋊C₄×D₁₀₉	C₂²	1	4	yes	—
50	C₂²⋊C₄×D₁₀₉	C₂²	1	8	yes	—
51	C₂×C₄×Dic₁₀₉	C₂²	1	2	yes	complemented
52	C₂×C₄×Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
53	C₄²×D₁₀₉	C₂²	1	2	yes	—
54	C₄²×D₁₀₉	C₂²	1	1	yes	characteristic
55	C₄²×D₁₀₉	C₂²	1	1	yes	characteristic
56	C₄²×D₁₀₉	C₂²	1	2	yes	complemented
57	C₄²×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
58	C₄²×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
59	C₂×#41×C₁₀₉	C₂²	1	2	yes	complemented
60	C₄⋊Q₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
61	#127×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
62	#124×C₁₀₉	C₂²	1	2	yes	complemented
63	#121×C₁₀₉	C₂²	1	4	yes	complemented
64	C₄×D₄×C₁₀₉	C₂²	1	4	yes	complemented
65	C₂×C₄²×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
66	C₂³×D₁₀₉	C₂³	1	4	yes	—
67	C₂³×D₁₀₉	C₂³	1	1	yes	characteristic
68	#13182030	—	2	8	no	—
69	#13182029	—	2	8	no	—
70	#13182029	—	2	16	no	—
71	#13182028	—	2	16	no	—
72	#13182028	—	2	8	no	—
73	C₂×Dic₂₁₈	C₂³	1	4	yes	—
74	C₂×Dic₂₁₈	C₂³	1	2	yes	—
75	Q₈×D₁₀₉	—	2	8	no	—
76	C₂×D₄₃₆	C₂³	1	4	yes	—
77	C₂×D₄₃₆	C₂³	1	4	yes	—
78	C₂×D₄₃₆	C₂³	1	2	yes	—
79	C₂×C₂²⋊D₁₀₉	C₂³	1	8	yes	—
80	C₂×C₂²⋊D₁₀₉	C₂³	1	4	yes	—
81	C₂×C₂²⋊D₁₀₉	C₂³	1	4	yes	—
82	C₂×C₂²⋊D₁₀₉	C₂³	1	4	yes	—
83	D₄×D₁₀₉	—	2	16	no	—
84	D₄×D₁₀₉	—	2	8	no	—
85	D₄×D₁₀₉	—	2	16	no	—
86	C₂²×Dic₁₀₉	C₂³	1	2	yes	—
87	C₂²×Dic₁₀₉	C₂³	1	4	yes	—
88	C₂²×Dic₁₀₉	C₂³	1	1	yes	characteristic
89	C₂×C₄×D₁₀₉	—	2	16	no	—
90	C₂×C₄×D₁₀₉	—	2	8	no	—
91	C₂×C₄×D₁₀₉	D₄	1	8	yes	complemented
92	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
93	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
94	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
95	C₂×C₄×D₁₀₉	C₂³	1	4	yes	—
96	C₂×C₄×D₁₀₉	C₂³	1	4	yes	—
97	C₂×C₄×D₁₀₉	C₂³	1	4	yes	—
98	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
99	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
100	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
101	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
102	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
103	C₄⋊Dic₁₀₉	C₂³	1	4	yes	—
104	#13182008	C₂³	1	8	yes	—
105	C₂²⋊Dic₁₀₉	C₂³	1	8	yes	—
106	#13182006	C₂³	1	8	yes	—
107	#13182006	C₂³	1	8	yes	—
108	C₄×Dic₁₀₉	C₂³	1	2	yes	—
109	C₄×Dic₁₀₉	C₂³	1	2	yes	—
110	C₄×Dic₁₀₉	C₂³	1	2	yes	—
111	C₄×Dic₁₀₉	C₂³	1	2	yes	—
112	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
113	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
114	C₄×Dic₁₀₉	C₂³	1	2	yes	—
115	#41×C₁₀₉	—	2	8	no	—
116	C₂×Q₈×C₁₀₉	C₂³	1	2	yes	—
117	C₂×D₄×C₁₀₉	C₂³	1	4	yes	—
118	C₂×D₄×C₁₀₉	C₂³	1	4	yes	—
119	C₂×D₄×C₁₀₉	C₂³	1	2	yes	—
120	C₂²×C₄×C₁₀₉	C₂³	1	2	yes	—
121	C₂²×C₄×C₁₀₉	C₂³	1	4	yes	—
122	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
123	C₄⋊C₄×C₁₀₉	C₂³	1	4	yes	—
124	C₂²⋊C₄×C₁₀₉	C₂³	1	8	yes	—
125	C₄²×C₁₀₉	C₂³	1	2	yes	—
126	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
127	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
128	C₂³×C₁₀₉	C₂⁴	1	4	yes	—
129	C₂³×C₁₀₉	C₂⁴	1	1	yes	characteristic
130	C₂²×D₁₀₉	—	2	4	no	—
131	C₂²×D₁₀₉	—	2	8	no	—
132	C₂²×D₁₀₉	—	2	16	no	—
133	C₂²×D₁₀₉	C₂×D₄	1	4	yes	—
134	C₂²×D₁₀₉	C₂⁴	1	4	yes	—
135	C₂²×D₁₀₉	C₂⁴	1	1	yes	characteristic
136	C₂²×D₁₀₉	C₂⁴	1	1	yes	characteristic
137	Q₈×C₁₀₉	—	2	4	no	—
138	D₄×C₁₀₉	—	2	8	no	—
139	D₄×C₁₀₉	—	2	4	no	—
140	D₄×C₁₀₉	—	2	8	no	—
141	C₂×C₄×C₁₀₉	—	2	8	no	—
142	C₂×C₄×C₁₀₉	—	2	4	no	—
143	C₂×C₄×C₁₀₉	C₂×D₄	1	4	yes	complemented
144	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
145	C₂×C₄×C₁₀₉	C₂⁴	1	4	yes	—
146	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
147	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
148	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
149	C₂²⋊D₁₀₉	—	2	8	no	—
150	C₂²⋊D₁₀₉	—	2	8	no	—
151	C₂²⋊D₁₀₉	—	2	8	no	—
152	C₂²⋊D₁₀₉	—	2	16	no	—
153	C₂×Dic₁₀₉	—	2	8	no	—
154	C₂×Dic₁₀₉	—	2	4	no	—
155	C₂×Dic₁₀₉	C₂×D₄	1	4	yes	complemented
156	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
157	C₂×Dic₁₀₉	C₂⁴	1	4	yes	—
158	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
159	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
160	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
161	D₄₃₆	—	2	8	no	—
162	D₄₃₆	—	2	4	no	—
163	D₄₃₆	—	2	8	no	—
164	C₄×D₁₀₉	—	2	8	no	—
165	C₄×D₁₀₉	—	2	4	no	—
166	C₄×D₁₀₉	—	2	8	no	—
167	C₄×D₁₀₉	—	2	4	no	—
168	C₄×D₁₀₉	—	2	8	no	—
169	C₄×D₁₀₉	—	2	4	no	—
170	C₄×D₁₀₉	C₂×D₄	1	4	yes	—
171	C₄×D₁₀₉	C₂×D₄	1	4	yes	—
172	C₄×D₁₀₉	C₂×D₄	1	4	yes	complemented
173	C₄×D₁₀₉	C₂×D₄	1	4	yes	complemented
174	C₄×D₁₀₉	#41	1	8	yes	complemented
175	Dic₂₁₈	—	2	4	no	—
176	Dic₂₁₈	—	2	8	no	—
177	C₂²×C₁₀₉	—	2	2	no	—
178	C₂²×C₁₀₉	—	2	4	no	—
179	C₂²×C₁₀₉	—	2	8	no	—
180	C₂²×C₁₀₉	C₂²×D₄	1	2	yes	—
181	C₂²×C₁₀₉	C₂⁵	1	1	yes	characteristic
182	C₂×D₁₀₉	—	2	2	no	—
183	C₂×D₁₀₉	—	2	8	no	—
184	C₂×D₁₀₉	—	2	4	no	—
185	C₂×D₁₀₉	—	2	8	no	—
186	C₂×D₁₀₉	—	4	16	no	—
187	C₂×D₁₀₉	C₂²×D₄	1	2	yes	—
188	C₂×D₁₀₉	C₂²×D₄	1	2	yes	—
189	C₂×D₁₀₉	C₂×#41	1	4	yes	—
190	C₄×C₁₀₉	—	2	4	no	—
191	C₄×C₁₀₉	—	2	2	no	—
192	C₄×C₁₀₉	C₂²×D₄	1	2	yes	—
193	C₄×C₁₀₉	C₂²×D₄	1	2	yes	—
194	C₄×C₁₀₉	C₂×#41	1	4	yes	complemented
195	Dic₁₀₉	—	2	4	no	—
196	Dic₁₀₉	—	2	2	no	—
197	Dic₁₀₉	C₂²×D₄	1	2	yes	—
198	Dic₁₀₉	C₂²×D₄	1	2	yes	—
199	Dic₁₀₉	C₂×#41	1	4	yes	complemented
200	C₂×C₁₀₉	—	2	2	no	—
201	C₂×C₁₀₉	—	4	4	no	—
202	C₂×C₁₀₉	C₂³×D₄	1	1	yes	characteristic
203	C₂×C₁₀₉	C₂²×#41	1	2	yes	—
204	D₁₀₉	—	2	2	no	—
205	D₁₀₉	—	4	4	no	—
206	D₁₀₉	#532	1	4	yes	direct product factor
207	C₂×#532	—	109	1	no	maximal, Sylow
208	C₁₀₉	C₂×#532	1	1	yes	characteristic, complemented, Sylow
209	C₂²×#41	—	109	2	no	—
210	#532	—	109	2	no	—
211	#532	—	109	1	no	—
212	#532	—	109	1	no	—
213	#532	—	109	2	no	—
214	#532	—	109	4	no	—
215	#532	—	109	4	no	—
216	#532	—	109	1	no	—
217	#532	D₁₀₉	1	1	yes	characteristic, direct product factor
218	C₂×C₄⋊Q₈	—	109	1	no	—
219	C₂×#127	—	109	1	no	—
220	C₂×#124	—	109	2	no	—
221	C₂×#121	—	109	4	no	—
222	C₂×C₄×D₄	—	109	4	no	—
223	C₂²×C₄²	—	109	1	no	—
224	C₂×#41	—	109	2	no	—
225	C₂×#41	—	109	4	no	—
226	C₂×#41	—	109	2	no	—
227	C₂×#41	—	109	4	no	—
228	C₂×#41	—	109	2	no	—
229	C₂×#41	—	218	16	no	—
230	C₂×#41	C₂×D₁₀₉	1	2	yes	complemented
231	C₂²×Q₈	—	109	2	no	—
232	C₂²×D₄	—	109	4	no	—
233	C₂²×D₄	—	109	4	no	—
234	C₂²×D₄	—	109	2	no	—
235	C₂³×C₄	—	109	1	no	—
236	C₂³×C₄	—	109	4	no	—
237	C₂³×C₄	—	109	2	no	—
238	C₄⋊Q₈	—	109	2	no	—
239	C₄⋊Q₈	—	109	4	no	—
240	C₄⋊Q₈	—	109	1	no	—
241	C₄⋊Q₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
242	#127	—	109	2	no	—
243	#127	—	109	4	no	—
244	#127	—	109	1	no	—
245	#127	C₂×D₁₀₉	1	1	yes	characteristic, complemented
246	#124	—	109	2	no	—
247	#124	—	109	2	no	—
248	#124	—	109	8	no	—
249	#124	—	109	2	no	—
250	#124	C₂×D₁₀₉	1	2	yes	complemented
251	#121	—	109	4	no	—
252	#121	—	109	8	no	—
253	#121	—	109	4	no	—
254	#121	—	109	4	no	—
255	#121	—	109	8	no	—
256	#121	C₂×D₁₀₉	1	4	yes	complemented
257	C₄×D₄	—	109	4	no	—
258	C₄×D₄	—	109	8	no	—
259	C₄×D₄	—	109	4	no	—
260	C₄×D₄	—	109	8	no	—
261	C₄×D₄	—	109	4	no	—
262	C₄×D₄	C₂×D₁₀₉	1	4	yes	complemented
263	C₂×C₄⋊C₄	—	109	4	no	—
264	C₂×C₂²⋊C₄	—	109	8	no	—
265	C₂×C₄²	—	109	2	no	—
266	C₂×C₄²	—	109	1	no	—
267	C₂×C₄²	—	109	2	no	—
268	C₂×C₄²	—	109	1	no	—
269	C₂×C₄²	—	109	1	no	—
270	C₂×C₄²	—	109	1	no	—
271	C₂×C₄²	—	109	1	no	—
272	C₂×C₄²	—	109	2	no	—
273	C₂×C₄²	C₂×D₁₀₉	1	1	yes	characteristic, complemented
274	C₂⁴	—	109	1	no	—
275	C₂⁴	—	109	4	no	—
276	#41	—	2	8	no	—
277	#41	—	218	16	no	—
278	#41	—	218	16	no	—
279	#41	—	218	8	no	—
280	#41	—	218	8	no	—
281	#41	—	218	8	no	—
282	C₂×Q₈	—	109	4	no	—
283	C₂×Q₈	—	109	2	no	—
284	C₂×Q₈	—	218	8	no	—
285	C₂×Q₈	C₂²×D₁₀₉	1	2	yes	—
286	C₂×D₄	—	109	8	no	—
287	C₂×D₄	—	109	4	no	—
288	C₂×D₄	—	109	4	no	—
289	C₂×D₄	—	109	4	no	—
290	C₂×D₄	—	109	4	no	—
291	C₂×D₄	—	109	4	no	—
292	C₂×D₄	—	109	2	no	—
293	C₂×D₄	—	218	16	no	—
294	C₂×D₄	—	218	8	no	—
295	C₂×D₄	—	218	16	no	—
296	C₂×D₄	C₂²×D₁₀₉	1	4	yes	—
297	C₂×D₄	C₂²×D₁₀₉	1	4	yes	—
298	C₂×D₄	C₂²×D₁₀₉	1	2	yes	—
299	C₂²×C₄	—	109	1	no	—
300	C₂²×C₄	—	109	8	no	—
301	C₂²×C₄	—	109	2	no	—
302	C₂²×C₄	—	109	1	no	—
303	C₂²×C₄	—	109	1	no	—
304	C₂²×C₄	—	109	1	no	—
305	C₂²×C₄	—	109	1	no	—
306	C₂²×C₄	—	109	2	no	—
307	C₂²×C₄	—	109	4	no	—
308	C₂²×C₄	—	109	2	no	—
309	C₂²×C₄	—	109	2	no	—
310	C₂²×C₄	—	109	2	no	—
311	C₂²×C₄	—	109	4	no	—
312	C₂²×C₄	—	109	4	no	—
313	C₂²×C₄	—	109	4	no	—
314	C₂²×C₄	—	218	8	no	—
315	C₂²×C₄	—	218	16	no	—
316	C₂²×C₄	C₂²×D₁₀₉	1	2	yes	—
317	C₂²×C₄	C₂²×D₁₀₉	1	4	yes	—
318	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
319	C₄⋊C₄	—	109	8	no	—
320	C₄⋊C₄	—	109	4	no	—
321	C₄⋊C₄	C₂²×D₁₀₉	1	4	yes	—
322	C₂²⋊C₄	—	109	8	no	—
323	C₂²⋊C₄	—	109	8	no	—
324	C₂²⋊C₄	—	109	8	no	—
325	C₂²⋊C₄	C₂²×D₁₀₉	1	8	yes	—
326	C₄²	—	109	2	no	—
327	C₄²	—	109	2	no	—
328	C₄²	—	109	2	no	—
329	C₄²	—	109	1	no	—
330	C₄²	—	109	1	no	—
331	C₄²	—	109	2	no	—
332	C₄²	—	109	2	no	—
333	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic
334	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic
335	C₄²	C₂²×D₁₀₉	1	2	yes	—
336	C₂³	—	109	1	no	—
337	C₂³	—	109	4	no	—
338	C₂³	—	109	1	no	—
339	C₂³	—	109	4	no	—
340	C₂³	—	218	8	no	—
341	C₂³	—	218	16	no	—
342	C₂³	—	218	4	no	—
343	C₂³	C₂³×D₁₀₉	1	4	yes	—
344	C₂³	C₂³×D₁₀₉	1	1	yes	characteristic
345	Q₈	—	2	4	no	—
346	Q₈	—	218	8	no	—
347	Q₈	—	218	4	no	—
348	D₄	—	2	8	no	—
349	D₄	—	2	4	no	—
350	D₄	—	2	8	no	—
351	D₄	—	218	8	no	—
352	D₄	—	218	8	no	—
353	D₄	—	218	16	no	—
354	D₄	—	218	8	no	—
355	D₄	—	218	8	no	—
356	D₄	—	218	4	no	—
357	D₄	—	218	8	no	—
358	C₂×C₄	—	2	8	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	109	4	no	—
361	C₂×C₄	—	109	2	no	—
362	C₂×C₄	—	109	1	no	—
363	C₂×C₄	—	109	1	no	—
364	C₂×C₄	—	109	4	no	—
365	C₂×C₄	—	109	4	no	—
366	C₂×C₄	—	109	4	no	—
367	C₂×C₄	—	109	4	no	—
368	C₂×C₄	—	109	8	no	—
369	C₂×C₄	—	109	2	no	—
370	C₂×C₄	—	109	4	no	—
371	C₂×C₄	—	218	8	no	—
372	C₂×C₄	—	218	4	no	—
373	C₂×C₄	—	218	8	no	—
374	C₂×C₄	—	218	4	no	—
375	C₂×C₄	—	218	8	no	—
376	C₂×C₄	—	218	4	no	—
377	C₂×C₄	—	218	8	no	—
378	C₂×C₄	—	218	4	no	—
379	C₂×C₄	D₄×D₁₀₉	1	4	yes	complemented
380	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
381	C₂×C₄	C₂³×D₁₀₉	1	4	yes	—
382	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
383	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
384	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
385	C₂²	—	2	2	no	—
386	C₂²	—	2	4	no	—
387	C₂²	—	2	8	no	—
388	C₂²	—	109	2	no	—
389	C₂²	—	109	4	no	—
390	C₂²	—	109	2	no	—
391	C₂²	—	436	16	no	—
392	C₂²	—	218	8	no	—
393	C₂²	—	218	4	no	—
394	C₂²	—	218	8	no	—
395	C₂²	—	218	2	no	—
396	C₂²	C₂×D₄×D₁₀₉	1	2	yes	—
397	C₂²	C₂⁴×D₁₀₉	1	1	yes	characteristic
398	C₄	—	2	4	no	—
399	C₄	—	2	2	no	—
400	C₄	—	109	2	no	—
401	C₄	—	109	2	no	—
402	C₄	—	109	4	no	—
403	C₄	—	218	4	no	—
404	C₄	—	218	2	no	—
405	C₄	C₂×D₄×D₁₀₉	1	2	yes	—
406	C₄	C₂×D₄×D₁₀₉	1	2	yes	—
407	C₄	#41×D₁₀₉	1	4	yes	complemented
408	C₂	—	2	2	no	—
409	C₂	—	4	4	no	—
410	C₂	—	109	4	no	—
411	C₂	—	436	4	no	—
412	C₂	—	218	2	no	—
413	C₂	C₂²×D₄×D₁₀₉	1	1	yes	characteristic
414	C₂	C₂×#41×D₁₀₉	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂³×D₁₀₉
commutator, socle, cosocle	C₂²×C₁₀₉	C₂⁵
Frattini	C₂²	C₂⁴×D₁₀₉
Fitting	#532×C₁₀₉	C₂
hypercenter	#532	D₁₀₉
hypocenter	C₁₀₉	C₂×#532
LCS	G ▷ C₂²×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂×C₄ ◁ #532

Complements

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

N	H ≅ G/N	type
1. C₂×#41×D₁₀₉	C₂	semidirect
2. #20295577	C₂	semidirect
3. #20295576	C₂	semidirect
4. #20295575	C₂	semidirect
5. #20295574	C₂	semidirect
6. #20295573	C₂	semidirect
7. #20295572	C₂	semidirect
8. #20295571	C₂	semidirect
9. C₄⋊Q₈×D₁₀₉	C₂	semidirect
10. #127×D₁₀₉	C₂	semidirect
11. #124×D₁₀₉	C₂	semidirect
12. #121×D₁₀₉	C₂	semidirect
13. C₄×D₄×D₁₀₉	C₂	semidirect
14. C₂×C₄²×D₁₀₉	C₂	semidirect
15. #532×C₁₀₉	C₂	semidirect
16. C₂×#13182030	C₂²	semidirect
17. C₂×#13182029	C₂²	semidirect
18. C₂×#13182029	C₂²	semidirect
19. C₂×#13182028	C₂²	semidirect
20. C₂×#13182028	C₂²	semidirect
29. #16812699	C₂²	semidirect
30. #16812698	C₂²	semidirect
31. #16812697	C₂²	semidirect
32. #16812696	C₂²	semidirect
33. #16812695	C₂²	semidirect
34. #16812695	C₂²	semidirect
35. #16812688	C₂²	semidirect
36. #16812687	C₂²	semidirect
37. #16812686	C₂²	semidirect
38. #16812685	C₂²	semidirect
39. #16812674	C₂²	semidirect
40. #16812673	C₂²	semidirect
41. #16812672	C₂²	semidirect
42. #16812671	C₂²	semidirect
43. #16812670	C₂²	semidirect
44. C₄×D₄₃₆	C₂²	semidirect
45. D₄×Dic₁₀₉	C₂²	semidirect
46. #16812661	C₂²	semidirect
47. C₄×C₂²⋊D₁₀₉	C₂²	semidirect
48. #16812659	C₂²	semidirect
51. C₂×C₄×Dic₁₀₉	C₂²	semidirect
52. C₂×C₄×Dic₁₀₉	C₂²	semidirect
56. C₄²×D₁₀₉	C₂²	semidirect
57. C₄²×D₁₀₉	C₂²	semidirect
58. C₄²×D₁₀₉	C₂²	semidirect
59. C₂×#41×C₁₀₉	C₂²	semidirect
60. C₄⋊Q₈×C₁₀₉	C₂²	semidirect
61. #127×C₁₀₉	C₂²	semidirect
62. #124×C₁₀₉	C₂²	semidirect
63. #121×C₁₀₉	C₂²	semidirect
64. C₄×D₄×C₁₀₉	C₂²	semidirect
65. C₂×C₄²×C₁₀₉	C₂²	semidirect
91. C₂×C₄×D₁₀₉	D₄	semidirect
143. C₂×C₄×C₁₀₉	C₂×D₄	semidirect
155. C₂×Dic₁₀₉	C₂×D₄	semidirect
172. C₄×D₁₀₉	C₂×D₄	semidirect
173. C₄×D₁₀₉	C₂×D₄	semidirect
174. C₄×D₁₀₉	#41	semidirect
194. C₄×C₁₀₉	C₂×#41	semidirect
199. Dic₁₀₉	C₂×#41	semidirect
206. D₁₀₉	#532	direct (N × H)
208. C₁₀₉	C₂×#532	semidirect
217. #532	D₁₀₉	direct (N × H)
230. C₂×#41	C₂×D₁₀₉	semidirect
241. C₄⋊Q₈	C₂×D₁₀₉	semidirect
245. #127	C₂×D₁₀₉	semidirect
250. #124	C₂×D₁₀₉	semidirect
256. #121	C₂×D₁₀₉	semidirect
262. C₄×D₄	C₂×D₁₀₉	semidirect
273. C₂×C₄²	C₂×D₁₀₉	semidirect
379. C₂×C₄	D₄×D₁₀₉	semidirect
407. C₄	#41×D₁₀₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#41×D₁₀₉	2
#20295577	2
#20295576	2
#20295575	2
#20295574	2
#20295573	2
#20295572	2
#20295571	2
C₄⋊Q₈×D₁₀₉	2
#127×D₁₀₉	2
#124×D₁₀₉	2
#121×D₁₀₉	2
C₄×D₄×D₁₀₉	2
C₂×C₄²×D₁₀₉	2
#532×C₁₀₉	2
C₂×#532	109

Subgroups — #532×D109 #28376309

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #532×D₁₀₉ #28376309