Subgroups — #575×D₁₀₉ #28377774

Order 13952.

1484 conjugacy classes of subgroups.

The subgroup lattice has 476 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	#20295826	C₂	1	1	yes	maximal, characteristic, complemented
3	#20295825	C₂	1	4	yes	maximal, complemented
4	#20295824	C₂	1	2	yes	maximal, complemented
5	#20295823	C₂	1	4	yes	maximal, complemented
6	#20295822	C₂	1	4	yes	maximal, complemented
7	#137×D₁₀₉	C₂	1	4	yes	maximal, complemented
8	AGL(1,ℤ/8)×D₁₀₉	C₂	1	4	yes	maximal, complemented
9	#135×D₁₀₉	C₂	1	4	yes	maximal, complemented
10	C₂×M₁₆×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#575×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13182030	C₂²	1	2	yes	complemented
13	C₂×#13182029	—	2	2	no	—
14	C₂×#13182029	C₂²	1	2	yes	complemented
15	C₂×#13182028	—	2	2	no	—
16	C₂×#13182028	C₂²	1	2	yes	complemented
17	#41×D₁₀₉	—	2	2	no	—
18	#41×D₁₀₉	—	2	2	no	—
19	#41×D₁₀₉	—	2	2	no	—
20	#41×D₁₀₉	—	2	2	no	—
21	#41×D₁₀₉	C₂²	1	4	yes	—
22	#41×D₁₀₉	C₂²	1	4	yes	complemented
23	#41×D₁₀₉	C₂²	1	4	yes	complemented
24	#41×D₁₀₉	C₂²	1	4	yes	complemented
25	C₂×Q₈×D₁₀₉	C₂²	1	2	yes	complemented
26	C₂×D₄×D₁₀₉	—	2	2	no	—
27	C₂×D₄×D₁₀₉	C₂²	1	2	yes	complemented
28	C₂²×C₄×D₁₀₉	—	2	2	no	—
29	C₂²×C₄×D₁₀₉	C₂²	1	1	yes	characteristic
30	#16812732	C₂²	1	4	yes	complemented
31	#16812731	C₂²	1	8	yes	complemented
32	#16812730	C₂²	1	4	yes	complemented
33	#16812729	C₂²	1	4	yes	complemented
34	#16812728	C₂²	1	8	yes	complemented
35	#16812727	C₂²	1	4	yes	complemented
36	#16812726	C₂²	1	8	yes	complemented
37	#16812725	C₂²	1	4	yes	complemented
38	#16812724	C₂²	1	4	yes	complemented
39	#16812723	C₂²	1	8	yes	complemented
40	#16812722	C₂²	1	4	yes	complemented
41	#16812721	C₂²	1	4	yes	complemented
42	#16812720	C₂²	1	8	yes	complemented
43	#16812719	C₂²	1	8	yes	complemented
44	#16812718	C₂²	1	4	yes	complemented
45	Q₁₆×D₁₀₉	C₂²	1	4	yes	complemented
46	SD₁₆×D₁₀₉	C₂²	1	8	yes	complemented
47	D₈×D₁₀₉	C₂²	1	4	yes	complemented
48	C₂×#13182013	C₂²	1	1	yes	characteristic, complemented
49	C₂×#13182012	C₂²	1	2	yes	complemented
50	M₁₆×D₁₀₉	C₂²	1	4	yes	complemented
51	M₁₆×D₁₀₉	C₂²	1	4	yes	complemented
52	C₂×C₈×D₁₀₉	C₂²	1	2	yes	complemented
53	C₂×#41×C₁₀₉	C₂²	1	2	yes	complemented
54	#137×C₁₀₉	C₂²	1	4	yes	complemented
55	AGL(1,ℤ/8)×C₁₀₉	C₂²	1	4	yes	complemented
56	#135×C₁₀₉	C₂²	1	4	yes	complemented
57	C₂×M₁₆×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
58	C₂³×D₁₀₉	—	2	2	no	—
59	C₂³×D₁₀₉	D₄	1	1	yes	characteristic
60	#13182030	—	2	2	no	—
61	#13182030	—	2	2	no	—
62	#13182030	C₂³	1	4	yes	—
63	#13182030	C₂³	1	4	yes	complemented
64	#13182029	—	2	2	no	—
65	#13182029	—	2	2	no	—
66	#13182029	—	2	4	no	—
67	#13182029	—	2	4	no	—
68	#13182029	—	2	4	no	—
69	#13182029	—	2	4	no	—
70	#13182029	C₂³	1	4	yes	—
71	#13182029	C₂³	1	4	yes	complemented
72	#13182028	—	2	4	no	—
73	#13182028	—	2	4	no	—
74	#13182028	—	2	4	no	—
75	#13182028	—	2	4	no	—
76	#13182028	—	2	2	no	—
77	#13182028	—	2	2	no	—
78	#13182028	C₂³	1	4	yes	—
79	#13182028	C₂³	1	4	yes	complemented
80	C₂×Dic₂₁₈	—	2	2	no	—
81	C₂×Dic₂₁₈	C₂³	1	2	yes	complemented
82	Q₈×D₁₀₉	—	2	2	no	—
83	Q₈×D₁₀₉	—	2	2	no	—
84	Q₈×D₁₀₉	C₂³	1	4	yes	—
85	Q₈×D₁₀₉	C₂³	1	4	yes	complemented
86	C₂×D₄₃₆	—	2	2	no	—
87	C₂×D₄₃₆	C₂³	1	2	yes	complemented
88	C₂×C₂²⋊D₁₀₉	—	2	2	no	—
89	C₂×C₂²⋊D₁₀₉	—	2	2	no	—
90	C₂×C₂²⋊D₁₀₉	—	2	2	no	—
91	D₄×D₁₀₉	—	2	4	no	—
92	D₄×D₁₀₉	—	2	4	no	—
93	D₄×D₁₀₉	—	2	4	no	—
94	D₄×D₁₀₉	—	2	4	no	—
95	D₄×D₁₀₉	—	2	2	no	—
96	D₄×D₁₀₉	—	2	2	no	—
97	D₄×D₁₀₉	C₂³	1	4	yes	—
98	D₄×D₁₀₉	C₂³	1	4	yes	complemented
99	C₂²×Dic₁₀₉	—	2	2	no	—
100	C₂²×Dic₁₀₉	D₄	1	1	yes	characteristic
101	C₂×C₄×D₁₀₉	—	2	2	no	—
102	C₂×C₄×D₁₀₉	—	2	2	no	—
103	C₂×C₄×D₁₀₉	—	2	2	no	—
104	C₂×C₄×D₁₀₉	—	2	4	no	—
105	C₂×C₄×D₁₀₉	—	2	4	no	—
106	C₂×C₄×D₁₀₉	—	2	4	no	—
107	C₂×C₄×D₁₀₉	—	2	4	no	—
108	C₂×C₄×D₁₀₉	D₄	1	2	yes	—
109	C₂×C₄×D₁₀₉	D₄	1	1	yes	characteristic
110	C₂×C₄×D₁₀₉	D₄	1	1	yes	characteristic
111	C₂×C₄×D₁₀₉	D₄	1	2	yes	—
112	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
113	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
114	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
115	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
116	Dic₄₃₆	C₂³	1	4	yes	complemented
117	#13182019	C₂³	1	8	yes	complemented
118	#13182018	C₂³	1	8	yes	complemented
119	#13182017	C₂³	1	8	yes	complemented
120	#13182016	C₂³	1	8	yes	complemented
121	D₈₇₂	C₂³	1	4	yes	complemented
122	#13182014	C₂³	1	8	yes	complemented
123	#13182013	C₂³	1	4	yes	complemented
124	#13182012	C₂³	1	8	yes	complemented
125	C₂×#11724784	C₂³	1	2	yes	complemented
126	C₈×D₁₀₉	C₂³	1	4	yes	—
127	C₈×D₁₀₉	C₂³	1	4	yes	complemented
128	#41×C₁₀₉	—	2	2	no	—
129	#41×C₁₀₉	—	2	2	no	—
130	#41×C₁₀₉	C₂³	1	4	yes	—
131	#41×C₁₀₉	C₂³	1	4	yes	complemented
132	C₂×Q₈×C₁₀₉	C₂³	1	2	yes	complemented
133	C₂×D₄×C₁₀₉	—	2	2	no	—
134	C₂×D₄×C₁₀₉	C₂³	1	2	yes	complemented
135	C₂²×C₄×C₁₀₉	—	2	2	no	—
136	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
137	Q₁₆×C₁₀₉	C₂³	1	4	yes	complemented
138	SD₁₆×C₁₀₉	C₂³	1	8	yes	complemented
139	D₈×C₁₀₉	C₂³	1	4	yes	complemented
140	M₁₆×C₁₀₉	C₂³	1	4	yes	complemented
141	C₂×C₈×C₁₀₉	C₂³	1	2	yes	complemented
142	C₂³×C₁₀₉	—	2	2	no	—
143	C₂³×C₁₀₉	C₂×D₄	1	1	yes	characteristic
144	C₂²×D₁₀₉	—	2	2	no	—
145	C₂²×D₁₀₉	—	2	4	no	—
146	C₂²×D₁₀₉	—	2	4	no	—
147	C₂²×D₁₀₉	—	4	2	no	—
148	C₂²×D₁₀₉	—	4	8	no	—
149	C₂²×D₁₀₉	C₂×D₄	1	2	yes	—
150	C₂²×D₁₀₉	C₂×D₄	1	1	yes	characteristic
151	C₂²×D₁₀₉	C₂×D₄	1	1	yes	characteristic
152	C₂²×D₁₀₉	C₂×D₄	1	2	yes	—
153	Q₈×C₁₀₉	—	2	2	no	—
154	Q₈×C₁₀₉	C₂⁴	1	4	yes	—
155	D₄×C₁₀₉	—	2	4	no	—
156	D₄×C₁₀₉	—	2	4	no	—
157	D₄×C₁₀₉	—	2	2	no	—
158	D₄×C₁₀₉	C₂⁴	1	4	yes	—
159	C₂×C₄×C₁₀₉	—	2	2	no	—
160	C₂×C₄×C₁₀₉	—	2	4	no	—
161	C₂×C₄×C₁₀₉	—	2	4	no	—
162	C₂×C₄×C₁₀₉	C₂×D₄	1	2	yes	—
163	C₂×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
164	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
165	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
166	C₂²⋊D₁₀₉	—	2	4	no	—
167	C₂²⋊D₁₀₉	—	2	4	no	—
168	C₂²⋊D₁₀₉	—	2	4	no	—
169	C₂²⋊D₁₀₉	—	2	4	no	—
170	C₂²⋊D₁₀₉	—	2	4	no	—
171	C₂²⋊D₁₀₉	—	2	4	no	—
172	C₂×Dic₁₀₉	—	2	2	no	—
173	C₂×Dic₁₀₉	—	2	4	no	—
174	C₂×Dic₁₀₉	—	2	4	no	—
175	C₂×Dic₁₀₉	C₂×D₄	1	2	yes	—
176	C₂×Dic₁₀₉	C₂×D₄	1	2	yes	—
177	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
178	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
179	D₄₃₆	—	2	4	no	—
180	D₄₃₆	—	2	4	no	—
181	D₄₃₆	—	2	2	no	—
182	D₄₃₆	C₂⁴	1	4	yes	—
183	C₄×D₁₀₉	—	2	4	no	—
184	C₄×D₁₀₉	—	2	4	no	—
185	C₄×D₁₀₉	—	2	4	no	—
186	C₄×D₁₀₉	—	2	4	no	—
187	C₄×D₁₀₉	—	2	4	no	—
188	C₄×D₁₀₉	—	2	4	no	—
189	C₄×D₁₀₉	C₂×D₄	1	1	yes	characteristic
190	C₄×D₁₀₉	C₂×D₄	1	2	yes	—
191	C₄×D₁₀₉	C₂×D₄	1	2	yes	—
192	C₄×D₁₀₉	C₂×D₄	1	2	yes	—
193	C₄×D₁₀₉	C₂×D₄	1	2	yes	—
194	C₄×D₁₀₉	C₂×D₄	1	2	yes	—
195	C₄×D₁₀₉	C₂×D₄	1	1	yes	characteristic
196	C₄×D₁₀₉	C₂⁴	1	1	yes	characteristic
197	C₄×D₁₀₉	C₂⁴	1	1	yes	characteristic
198	C₄×D₁₀₉	C₂⁴	1	2	yes	—
199	Dic₂₁₈	—	2	2	no	—
200	Dic₂₁₈	—	2	4	no	—
201	Dic₂₁₈	—	2	4	no	—
202	Dic₂₁₈	C₂⁴	1	4	yes	—
203	C₈×C₁₀₉	C₂⁴	1	4	yes	—
204	#11724784	C₂⁴	1	4	yes	—
205	C₂²×C₁₀₉	—	2	4	no	—
206	C₂²×C₁₀₉	—	4	1	no	—
207	C₂²×C₁₀₉	—	4	4	no	—
208	C₂²×C₁₀₉	C₂²×D₄	1	2	yes	—
209	C₂²×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
210	C₂×D₁₀₉	—	2	4	no	—
211	C₂×D₁₀₉	—	2	2	no	—
212	C₂×D₁₀₉	—	2	4	no	—
213	C₂×D₁₀₉	—	4	1	no	—
214	C₂×D₁₀₉	—	4	2	no	—
215	C₂×D₁₀₉	—	4	8	no	—
216	C₂×D₁₀₉	—	4	4	no	—
217	C₂×D₁₀₉	—	4	8	no	—
218	C₂×D₁₀₉	C₂²×D₄	1	2	yes	—
219	C₂×D₁₀₉	C₂²×D₄	1	1	yes	characteristic
220	C₂×D₁₀₉	C₂²×D₄	1	1	yes	characteristic
221	C₄×C₁₀₉	—	2	4	no	—
222	C₄×C₁₀₉	C₂²×D₄	1	2	yes	—
223	C₄×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
224	C₄×C₁₀₉	C₂⁵	1	1	yes	characteristic
225	Dic₁₀₉	—	2	4	no	—
226	Dic₁₀₉	C₂²×D₄	1	1	yes	characteristic
227	Dic₁₀₉	C₂²×D₄	1	2	yes	—
228	Dic₁₀₉	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₁₀₉	—	2	2	no	—
230	C₂×C₁₀₉	—	2	1	no	—
231	C₂×C₁₀₉	—	4	4	no	—
232	C₂×C₁₀₉	C₂³×D₄	1	1	yes	characteristic
233	D₁₀₉	—	2	2	no	—
234	D₁₀₉	—	2	1	no	—
235	D₁₀₉	—	4	4	no	—
236	D₁₀₉	#575	1	2	yes	direct product factor
237	C₂×#575	—	109	1	no	maximal, Sylow
238	C₁₀₉	C₂×#575	1	1	yes	characteristic, complemented, Sylow
239	C₂²×#41	—	109	2	no	—
240	#575	—	109	2	no	—
241	#575	—	109	4	no	—
242	#575	—	109	4	no	—
243	#575	—	109	4	no	—
244	#575	—	109	1	no	—
245	#575	D₁₀₉	1	1	yes	characteristic, direct product factor
246	C₂×#137	—	109	4	no	—
247	C₂×AGL(1,ℤ/8)	—	109	4	no	—
248	C₂×#135	—	109	4	no	—
249	C₂²×M₁₆	—	109	1	no	—
250	C₂×#41	—	109	4	no	—
251	C₂×#41	—	109	4	no	—
252	C₂×#41	—	109	4	no	—
253	C₂×#41	—	109	4	no	—
254	C₂×#41	—	109	2	no	—
255	C₂×#41	—	109	2	no	—
256	C₂×#41	—	109	2	no	—
257	C₂×#41	—	218	2	no	—
258	C₂×#41	—	218	2	no	—
259	C₂×#41	—	218	2	no	—
260	C₂×#41	—	218	2	no	—
261	C₂×#41	—	218	2	no	—
262	C₂×#41	—	218	2	no	—
263	C₂×#41	C₂×D₁₀₉	1	2	yes	complemented
264	C₂²×Q₈	—	109	2	no	—
265	C₂²×D₄	—	109	2	no	—
266	C₂²×D₄	—	218	2	no	—
267	C₂³×C₄	—	109	1	no	—
268	C₂³×C₄	—	218	2	no	—
269	#137	—	109	4	no	—
270	#137	—	109	4	no	—
271	#137	—	109	8	no	—
272	#137	—	109	8	no	—
273	#137	—	109	4	no	—
274	#137	C₂×D₁₀₉	1	4	yes	complemented
275	AGL(1,ℤ/8)	—	109	4	no	—
276	AGL(1,ℤ/8)	—	109	4	no	—
277	AGL(1,ℤ/8)	—	109	8	no	—
278	AGL(1,ℤ/8)	—	109	8	no	—
279	AGL(1,ℤ/8)	—	109	4	no	—
280	AGL(1,ℤ/8)	C₂×D₁₀₉	1	4	yes	complemented
281	#135	—	109	8	no	—
282	#135	—	109	4	no	—
283	#135	—	109	8	no	—
284	#135	—	109	4	no	—
285	#135	—	109	4	no	—
286	#135	C₂×D₁₀₉	1	4	yes	complemented
287	C₂×Q₁₆	—	109	4	no	—
288	C₂×SD₁₆	—	109	8	no	—
289	C₂×D₈	—	109	4	no	—
290	C₂×M₁₆	—	109	1	no	—
291	C₂×M₁₆	—	109	4	no	—
292	C₂×M₁₆	—	109	4	no	—
293	C₂×M₁₆	—	109	2	no	—
294	C₂×M₁₆	C₂×D₁₀₉	1	1	yes	characteristic, complemented
295	C₂²×C₈	—	109	2	no	—
296	C₂⁴	—	109	1	no	—
297	C₂⁴	—	218	2	no	—
298	#41	—	2	2	no	—
299	#41	—	2	2	no	—
300	#41	—	109	4	no	—
301	#41	—	109	4	no	—
302	#41	—	109	4	no	—
303	#41	—	109	4	no	—
304	#41	—	109	4	no	—
305	#41	—	109	4	no	—
306	#41	—	218	4	no	—
307	#41	—	218	4	no	—
308	#41	—	218	4	no	—
309	#41	—	218	4	no	—
310	#41	—	218	4	no	—
311	#41	—	218	4	no	—
312	#41	—	218	4	no	—
313	#41	—	218	4	no	—
314	#41	—	218	2	no	—
315	#41	—	218	2	no	—
316	#41	—	218	2	no	—
317	#41	—	218	2	no	—
318	#41	—	218	2	no	—
319	#41	—	218	2	no	—
320	#41	C₂²×D₁₀₉	1	4	yes	—
321	#41	C₂²×D₁₀₉	1	4	yes	complemented
322	C₂×Q₈	—	109	4	no	—
323	C₂×Q₈	—	109	4	no	—
324	C₂×Q₈	—	109	2	no	—
325	C₂×Q₈	—	218	2	no	—
326	C₂×Q₈	—	218	2	no	—
327	C₂×Q₈	—	218	2	no	—
328	C₂×Q₈	C₂²×D₁₀₉	1	2	yes	complemented
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	109	4	no	—
331	C₂×D₄	—	109	4	no	—
332	C₂×D₄	—	109	2	no	—
333	C₂×D₄	—	218	2	no	—
334	C₂×D₄	—	218	2	no	—
335	C₂×D₄	—	218	2	no	—
336	C₂×D₄	—	218	2	no	—
337	C₂×D₄	—	218	4	no	—
338	C₂×D₄	—	218	4	no	—
339	C₂×D₄	—	218	4	no	—
340	C₂×D₄	—	218	4	no	—
341	C₂×D₄	—	218	2	no	—
342	C₂×D₄	—	218	2	no	—
343	C₂×D₄	C₂²×D₁₀₉	1	2	yes	complemented
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	109	1	no	—
346	C₂²×C₄	—	109	2	no	—
347	C₂²×C₄	—	109	2	no	—
348	C₂²×C₄	—	109	1	no	—
349	C₂²×C₄	—	109	1	no	—
350	C₂²×C₄	—	109	1	no	—
351	C₂²×C₄	—	109	2	no	—
352	C₂²×C₄	—	109	2	no	—
353	C₂²×C₄	—	109	1	no	—
354	C₂²×C₄	—	218	2	no	—
355	C₂²×C₄	—	218	4	no	—
356	C₂²×C₄	—	218	4	no	—
357	C₂²×C₄	—	218	4	no	—
358	C₂²×C₄	—	218	4	no	—
359	C₂²×C₄	—	218	2	no	—
360	C₂²×C₄	—	218	2	no	—
361	C₂²×C₄	—	218	2	no	—
362	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
363	Q₁₆	—	109	8	no	—
364	Q₁₆	—	109	4	no	—
365	Q₁₆	C₂²×D₁₀₉	1	4	yes	complemented
366	SD₁₆	—	109	8	no	—
367	SD₁₆	—	109	8	no	—
368	SD₁₆	—	109	8	no	—
369	SD₁₆	C₂²×D₁₀₉	1	8	yes	complemented
370	D₈	—	109	8	no	—
371	D₈	—	109	4	no	—
372	D₈	C₂²×D₁₀₉	1	4	yes	complemented
373	M₁₆	—	109	4	no	—
374	M₁₆	—	109	8	no	—
375	M₁₆	C₂²×D₁₀₉	1	4	yes	complemented
376	C₂×C₈	—	109	2	no	—
377	C₂×C₈	—	109	4	no	—
378	C₂×C₈	—	109	4	no	—
379	C₂×C₈	C₂²×D₁₀₉	1	2	yes	complemented
380	C₂³	—	2	2	no	—
381	C₂³	—	109	1	no	—
382	C₂³	—	109	2	no	—
383	C₂³	—	109	2	no	—
384	C₂³	—	109	1	no	—
385	C₂³	—	436	8	no	—
386	C₂³	—	436	2	no	—
387	C₂³	—	218	4	no	—
388	C₂³	—	218	4	no	—
389	C₂³	—	218	2	no	—
390	C₂³	D₄×D₁₀₉	1	1	yes	characteristic
391	Q₈	—	2	2	no	—
392	Q₈	—	109	4	no	—
393	Q₈	—	218	4	no	—
394	Q₈	—	218	4	no	—
395	Q₈	—	218	2	no	—
396	Q₈	C₂³×D₁₀₉	1	4	yes	—
397	D₄	—	2	4	no	—
398	D₄	—	2	4	no	—
399	D₄	—	2	2	no	—
400	D₄	—	109	4	no	—
401	D₄	—	218	4	no	—
402	D₄	—	218	4	no	—
403	D₄	—	218	4	no	—
404	D₄	—	218	4	no	—
405	D₄	—	218	4	no	—
406	D₄	—	218	4	no	—
407	D₄	—	218	4	no	—
408	D₄	—	218	4	no	—
409	D₄	—	218	2	no	—
410	D₄	C₂³×D₁₀₉	1	4	yes	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	109	2	no	—
415	C₂×C₄	—	109	2	no	—
416	C₂×C₄	—	109	1	no	—
417	C₂×C₄	—	109	1	no	—
418	C₂×C₄	—	109	2	no	—
419	C₂×C₄	—	109	2	no	—
420	C₂×C₄	—	109	2	no	—
421	C₂×C₄	—	109	2	no	—
422	C₂×C₄	—	109	1	no	—
423	C₂×C₄	—	109	2	no	—
424	C₂×C₄	—	109	1	no	—
425	C₂×C₄	—	109	1	no	—
426	C₂×C₄	—	109	1	no	—
427	C₂×C₄	—	109	2	no	—
428	C₂×C₄	—	218	4	no	—
429	C₂×C₄	—	218	4	no	—
430	C₂×C₄	—	218	4	no	—
431	C₂×C₄	—	218	4	no	—
432	C₂×C₄	—	218	4	no	—
433	C₂×C₄	—	218	4	no	—
434	C₂×C₄	—	218	2	no	—
435	C₂×C₄	—	218	4	no	—
436	C₂×C₄	—	218	4	no	—
437	C₂×C₄	D₄×D₁₀₉	1	1	yes	characteristic
438	C₂×C₄	D₄×D₁₀₉	1	2	yes	—
439	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
440	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
441	C₈	—	109	4	no	—
442	C₈	C₂³×D₁₀₉	1	4	yes	—
443	C₂²	—	2	4	no	—
444	C₂²	—	4	1	no	—
445	C₂²	—	4	4	no	—
446	C₂²	—	109	1	no	—
447	C₂²	—	109	2	no	—
448	C₂²	—	109	1	no	—
449	C₂²	—	436	4	no	—
450	C₂²	—	436	2	no	—
451	C₂²	—	436	1	no	—
452	C₂²	—	436	8	no	—
453	C₂²	—	436	8	no	—
454	C₂²	—	218	4	no	—
455	C₂²	—	218	2	no	—
456	C₂²	—	218	4	no	—
457	C₂²	C₂×D₄×D₁₀₉	1	2	yes	—
458	C₂²	C₂×D₄×D₁₀₉	1	1	yes	characteristic
459	C₄	—	2	4	no	—
460	C₄	—	109	1	no	—
461	C₄	—	109	2	no	—
462	C₄	—	109	1	no	—
463	C₄	—	218	4	no	—
464	C₄	C₂×D₄×D₁₀₉	1	2	yes	—
465	C₄	C₂×D₄×D₁₀₉	1	1	yes	characteristic
466	C₄	C₂⁴×D₁₀₉	1	1	yes	characteristic
467	C₂	—	2	2	no	—
468	C₂	—	2	1	no	—
469	C₂	—	4	4	no	—
470	C₂	—	109	2	no	—
471	C₂	—	436	4	no	—
472	C₂	—	218	2	no	—
473	C₂	—	218	1	no	—
474	C₂	C₂²×D₄×D₁₀₉	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₄×D₁₀₉
commutator, cosocle	C₄×C₁₀₉	C₂⁵
Frattini	C₄	C₂⁴×D₁₀₉
Fitting	#575×C₁₀₉	C₂
socle	C₂×C₁₀₉	C₂³×D₄
hypercenter	#575	D₁₀₉
hypocenter	C₁₀₉	C₂×#575
LCS	G ▷ C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #575

Complements

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

N	H ≅ G/N	type
1. C₂×#41×D₁₀₉	C₂	semidirect
2. #20295826	C₂	semidirect
3. #20295825	C₂	semidirect
4. #20295824	C₂	semidirect
5. #20295823	C₂	semidirect
6. #20295822	C₂	semidirect
7. #137×D₁₀₉	C₂	semidirect
8. AGL(1,ℤ/8)×D₁₀₉	C₂	semidirect
9. #135×D₁₀₉	C₂	semidirect
10. C₂×M₁₆×D₁₀₉	C₂	semidirect
11. #575×C₁₀₉	C₂	semidirect
12. C₂×#13182030	C₂²	semidirect
14. C₂×#13182029	C₂²	semidirect
16. C₂×#13182028	C₂²	semidirect
22. #41×D₁₀₉	C₂²	semidirect
23. #41×D₁₀₉	C₂²	semidirect
24. #41×D₁₀₉	C₂²	semidirect
25. C₂×Q₈×D₁₀₉	C₂²	semidirect
27. C₂×D₄×D₁₀₉	C₂²	semidirect
30. #16812732	C₂²	semidirect
31. #16812731	C₂²	semidirect
32. #16812730	C₂²	semidirect
33. #16812729	C₂²	semidirect
34. #16812728	C₂²	semidirect
35. #16812727	C₂²	semidirect
36. #16812726	C₂²	semidirect
37. #16812725	C₂²	semidirect
38. #16812724	C₂²	semidirect
39. #16812723	C₂²	semidirect
40. #16812722	C₂²	semidirect
41. #16812721	C₂²	semidirect
42. #16812720	C₂²	semidirect
43. #16812719	C₂²	semidirect
44. #16812718	C₂²	semidirect
45. Q₁₆×D₁₀₉	C₂²	semidirect
46. SD₁₆×D₁₀₉	C₂²	semidirect
47. D₈×D₁₀₉	C₂²	semidirect
48. C₂×#13182013	C₂²	semidirect
49. C₂×#13182012	C₂²	semidirect
50. M₁₆×D₁₀₉	C₂²	semidirect
51. M₁₆×D₁₀₉	C₂²	semidirect
52. C₂×C₈×D₁₀₉	C₂²	semidirect
53. C₂×#41×C₁₀₉	C₂²	semidirect
54. #137×C₁₀₉	C₂²	semidirect
55. AGL(1,ℤ/8)×C₁₀₉	C₂²	semidirect
56. #135×C₁₀₉	C₂²	semidirect
57. C₂×M₁₆×C₁₀₉	C₂²	semidirect
63. #13182030	C₂³	semidirect
71. #13182029	C₂³	semidirect
79. #13182028	C₂³	semidirect
81. C₂×Dic₂₁₈	C₂³	semidirect
85. Q₈×D₁₀₉	C₂³	semidirect
87. C₂×D₄₃₆	C₂³	semidirect
98. D₄×D₁₀₉	C₂³	semidirect
116. Dic₄₃₆	C₂³	semidirect
117. #13182019	C₂³	semidirect
118. #13182018	C₂³	semidirect
119. #13182017	C₂³	semidirect
120. #13182016	C₂³	semidirect
121. D₈₇₂	C₂³	semidirect
122. #13182014	C₂³	semidirect
123. #13182013	C₂³	semidirect
124. #13182012	C₂³	semidirect
125. C₂×#11724784	C₂³	semidirect
127. C₈×D₁₀₉	C₂³	semidirect
131. #41×C₁₀₉	C₂³	semidirect
132. C₂×Q₈×C₁₀₉	C₂³	semidirect
134. C₂×D₄×C₁₀₉	C₂³	semidirect
137. Q₁₆×C₁₀₉	C₂³	semidirect
138. SD₁₆×C₁₀₉	C₂³	semidirect
139. D₈×C₁₀₉	C₂³	semidirect
140. M₁₆×C₁₀₉	C₂³	semidirect
141. C₂×C₈×C₁₀₉	C₂³	semidirect
236. D₁₀₉	#575	direct (N × H)
238. C₁₀₉	C₂×#575	semidirect
245. #575	D₁₀₉	direct (N × H)
263. C₂×#41	C₂×D₁₀₉	semidirect
274. #137	C₂×D₁₀₉	semidirect
280. AGL(1,ℤ/8)	C₂×D₁₀₉	semidirect
286. #135	C₂×D₁₀₉	semidirect
294. C₂×M₁₆	C₂×D₁₀₉	semidirect
321. #41	C₂²×D₁₀₉	semidirect
328. C₂×Q₈	C₂²×D₁₀₉	semidirect
343. C₂×D₄	C₂²×D₁₀₉	semidirect
365. Q₁₆	C₂²×D₁₀₉	semidirect
369. SD₁₆	C₂²×D₁₀₉	semidirect
372. D₈	C₂²×D₁₀₉	semidirect
375. M₁₆	C₂²×D₁₀₉	semidirect
379. C₂×C₈	C₂²×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
#20295826	2
#20295825	2
#20295824	2
#20295823	2
#20295822	2
#137×D₁₀₉	2
AGL(1,ℤ/8)×D₁₀₉	2
#135×D₁₀₉	2
C₂×M₁₆×D₁₀₉	2
#575×C₁₀₉	2
C₂×#575	109

Subgroups — #575×D109 #28377774

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #575×D₁₀₉ #28377774