Subgroups — #535×D₁₀₉ #28376336

Order 13952.

1896 conjugacy classes of subgroups.

The subgroup lattice has 480 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	1	yes	maximal, characteristic, complemented
2	C₂²×D₄×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#20295595	C₂	1	1	yes	maximal, characteristic, complemented
4	#20295594	C₂	1	2	yes	maximal, complemented
5	#20295593	C₂	1	1	yes	maximal, characteristic, complemented
6	#20295592	C₂	1	4	yes	maximal, complemented
7	#20295591	C₂	1	4	yes	maximal, complemented
8	#20295590	C₂	1	1	yes	maximal, characteristic, complemented
9	#20295589	C₂	1	2	yes	maximal, complemented
10	#127×D₁₀₉	C₂	1	2	yes	maximal, complemented
11	#124×D₁₀₉	C₂	1	2	yes	maximal, complemented
12	#121×D₁₀₉	C₂	1	4	yes	maximal, complemented
13	#120×D₁₀₉	C₂	1	4	yes	maximal, complemented
14	#117×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#535×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂⁴×D₁₀₉	C₂²	1	2	yes	—
17	C₂×#13182030	C₂²	1	1	yes	characteristic, complemented
18	C₂×#13182029	C₂²	1	1	yes	characteristic, complemented
19	C₂×#13182029	C₂²	1	2	yes	complemented
20	C₂×#13182028	C₂²	1	2	yes	complemented
21	C₂×#13182028	C₂²	1	1	yes	characteristic, complemented
22	#41×D₁₀₉	—	2	8	no	—
23	C₂×Q₈×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
24	C₂²×D₄₃₆	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₂²⋊D₁₀₉	C₂²	1	2	yes	complemented
26	C₂×D₄×D₁₀₉	—	2	8	no	—
27	C₂×D₄×D₁₀₉	C₂²	1	2	yes	—
28	C₂×D₄×D₁₀₉	C₂²	1	2	yes	—
29	C₂×D₄×D₁₀₉	C₂²	1	2	yes	—
30	C₂×D₄×D₁₀₉	C₂²	1	2	yes	complemented
31	C₂×D₄×D₁₀₉	C₂²	1	2	yes	complemented
32	C₂×D₄×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
33	C₂×D₄×D₁₀₉	C₂²	1	8	yes	complemented
34	C₂²×C₄×D₁₀₉	C₂²	1	1	yes	characteristic
35	C₂²×C₄×D₁₀₉	C₂²	1	2	yes	complemented
36	#16812696	C₂²	1	2	yes	complemented
37	#16812695	C₂²	1	2	yes	complemented
38	#16812695	C₂²	1	8	yes	complemented
39	#16812695	C₂²	1	2	yes	complemented
40	#16812688	C₂²	1	2	yes	complemented
41	#16812687	C₂²	1	2	yes	complemented
42	#16812686	C₂²	1	2	yes	complemented
43	#16812685	C₂²	1	8	yes	complemented
44	#16812674	C₂²	1	4	yes	complemented
45	#16812673	C₂²	1	4	yes	complemented
46	#16812672	C₂²	1	8	yes	complemented
47	#16812671	C₂²	1	8	yes	complemented
48	#16812670	C₂²	1	4	yes	complemented
49	#16812669	C₂²	1	4	yes	complemented
50	#16812669	C₂²	1	8	yes	complemented
51	#16812668	C₂²	1	4	yes	complemented
52	#16812667	C₂²	1	4	yes	complemented
53	#16812667	C₂²	1	8	yes	complemented
54	#16812658	C₂²	1	1	yes	characteristic, complemented
55	#16812657	C₂²	1	2	yes	complemented
56	#16812656	C₂²	1	2	yes	complemented
57	#16812655	C₂²	1	2	yes	complemented
58	C₄⋊C₄×D₁₀₉	C₂²	1	2	yes	complemented
59	C₂²⋊C₄×D₁₀₉	C₂²	1	2	yes	—
60	C₂²⋊C₄×D₁₀₉	C₂²	1	8	yes	complemented
61	C₄²×D₁₀₉	C₂²	1	2	yes	complemented
62	C₂×#41×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
63	C₂²×D₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
64	#127×C₁₀₉	C₂²	1	2	yes	complemented
65	#124×C₁₀₉	C₂²	1	2	yes	complemented
66	#121×C₁₀₉	C₂²	1	4	yes	complemented
67	#120×C₁₀₉	C₂²	1	4	yes	complemented
68	#117×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
69	C₂³×D₁₀₉	—	2	8	no	—
70	C₂³×D₁₀₉	—	4	8	no	—
71	C₂³×D₁₀₉	C₂³	1	4	yes	—
72	C₂³×D₁₀₉	C₂³	1	2	yes	—
73	C₂³×D₁₀₉	C₂³	1	1	yes	characteristic
74	C₂³×D₁₀₉	C₂³	1	4	yes	—
75	C₂³×D₁₀₉	C₂³	1	2	yes	—
76	#13182030	—	2	4	no	—
77	#13182029	—	2	4	no	—
78	#13182029	—	2	8	no	—
79	#13182028	—	2	8	no	—
80	#13182028	—	2	4	no	—
81	C₂×Dic₂₁₈	C₂³	1	2	yes	complemented
82	C₂×Dic₂₁₈	C₂³	1	1	yes	characteristic, complemented
83	Q₈×D₁₀₉	—	2	4	no	—
84	C₂×D₄₃₆	—	2	4	no	—
85	C₂×D₄₃₆	C₂³	1	2	yes	—
86	C₂×D₄₃₆	C₂³	1	2	yes	—
87	C₂×D₄₃₆	C₂³	1	2	yes	—
88	C₂×D₄₃₆	C₂³	1	1	yes	characteristic, complemented
89	C₂×D₄₃₆	C₂³	1	8	yes	complemented
90	C₂×C₂²⋊D₁₀₉	—	2	8	no	—
91	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	—
92	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	—
93	C₂×C₂²⋊D₁₀₉	C₂³	1	4	yes	—
94	C₂×C₂²⋊D₁₀₉	C₂³	1	4	yes	—
95	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	complemented
96	C₂×C₂²⋊D₁₀₉	C₂³	1	8	yes	complemented
97	C₂×C₂²⋊D₁₀₉	C₂³	1	8	yes	complemented
98	D₄×D₁₀₉	—	2	8	no	—
99	D₄×D₁₀₉	—	2	8	no	—
100	D₄×D₁₀₉	—	2	8	no	—
101	D₄×D₁₀₉	—	2	4	no	—
102	D₄×D₁₀₉	—	2	8	no	—
103	D₄×D₁₀₉	—	2	8	no	—
104	D₄×D₁₀₉	—	4	16	no	—
105	C₂²×Dic₁₀₉	C₂³	1	1	yes	characteristic
106	C₂²×Dic₁₀₉	C₂³	1	2	yes	complemented
107	C₂×C₄×D₁₀₉	—	2	8	no	—
108	C₂×C₄×D₁₀₉	D₄	1	8	yes	complemented
109	C₂×C₄×D₁₀₉	C₂³	1	4	yes	—
110	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
111	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
112	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
113	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
114	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
115	C₂×C₄×D₁₀₉	C₂³	1	2	yes	complemented
116	C₂×C₄×D₁₀₉	C₂³	1	2	yes	complemented
117	C₄⋊Dic₁₀₉	C₂³	1	2	yes	complemented
118	#13182008	C₂³	1	4	yes	complemented
119	C₂²⋊Dic₁₀₉	C₂³	1	2	yes	—
120	C₂²⋊Dic₁₀₉	C₂³	1	8	yes	complemented
121	#13182006	C₂³	1	4	yes	—
122	#13182006	C₂³	1	8	yes	complemented
123	#13182006	C₂³	1	8	yes	complemented
124	C₄×Dic₁₀₉	C₂³	1	4	yes	complemented
125	C₄×Dic₁₀₉	C₂³	1	2	yes	complemented
126	C₂⁴×C₁₀₉	C₂³	1	2	yes	—
127	#41×C₁₀₉	—	2	4	no	—
128	C₂×Q₈×C₁₀₉	C₂³	1	1	yes	characteristic, complemented
129	C₂×D₄×C₁₀₉	—	2	4	no	—
130	C₂×D₄×C₁₀₉	C₂³	1	2	yes	—
131	C₂×D₄×C₁₀₉	C₂³	1	2	yes	—
132	C₂×D₄×C₁₀₉	C₂³	1	2	yes	—
133	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic, complemented
134	C₂×D₄×C₁₀₉	C₂³	1	8	yes	complemented
135	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
136	C₂²×C₄×C₁₀₉	C₂³	1	2	yes	complemented
137	C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	complemented
138	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
139	C₂²⋊C₄×C₁₀₉	C₂³	1	8	yes	complemented
140	C₄²×C₁₀₉	C₂³	1	2	yes	complemented
141	C₂³×C₁₀₉	—	2	4	no	—
142	C₂³×C₁₀₉	—	4	4	no	—
143	C₂³×C₁₀₉	C₂⁴	1	4	yes	—
144	C₂³×C₁₀₉	C₂⁴	1	2	yes	—
145	C₂³×C₁₀₉	C₂⁴	1	1	yes	characteristic
146	C₂²×D₁₀₉	—	2	4	no	—
147	C₂²×D₁₀₉	—	2	4	no	—
148	C₂²×D₁₀₉	—	2	4	no	—
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	C₂²×D₁₀₉	—	4	8	no	—
154	C₂²×D₁₀₉	—	4	4	no	—
155	C₂²×D₁₀₉	—	4	32	no	—
156	C₂²×D₁₀₉	C₂×D₄	1	4	yes	—
157	C₂²×D₁₀₉	C₂⁴	1	4	yes	—
158	C₂²×D₁₀₉	C₂⁴	1	2	yes	—
159	C₂²×D₁₀₉	C₂⁴	1	1	yes	characteristic
160	C₂²×D₁₀₉	C₂⁴	1	1	yes	characteristic
161	Q₈×C₁₀₉	—	2	2	no	—
162	D₄×C₁₀₉	—	2	4	no	—
163	D₄×C₁₀₉	—	2	4	no	—
164	D₄×C₁₀₉	—	2	4	no	—
165	D₄×C₁₀₉	—	2	2	no	—
166	D₄×C₁₀₉	—	4	8	no	—
167	C₂×C₄×C₁₀₉	—	2	4	no	—
168	C₂×C₄×C₁₀₉	C₂×D₄	1	4	yes	complemented
169	C₂×C₄×C₁₀₉	C₂⁴	1	4	yes	—
170	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
171	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
172	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
173	C₂²⋊D₁₀₉	—	2	4	no	—
174	C₂²⋊D₁₀₉	—	2	4	no	—
175	C₂²⋊D₁₀₉	—	2	8	no	—
176	C₂²⋊D₁₀₉	—	2	8	no	—
177	C₂²⋊D₁₀₉	—	2	4	no	—
178	C₂²⋊D₁₀₉	—	4	8	no	—
179	C₂²⋊D₁₀₉	—	4	8	no	—
180	C₂×Dic₁₀₉	—	2	4	no	—
181	C₂×Dic₁₀₉	C₂×D₄	1	4	yes	complemented
182	C₂×Dic₁₀₉	C₂⁴	1	4	yes	—
183	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
184	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
185	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
186	D₄₃₆	—	2	4	no	—
187	D₄₃₆	—	2	4	no	—
188	D₄₃₆	—	2	4	no	—
189	D₄₃₆	—	2	2	no	—
190	D₄₃₆	—	4	8	no	—
191	C₄×D₁₀₉	—	2	4	no	—
192	C₄×D₁₀₉	—	2	8	no	—
193	C₄×D₁₀₉	—	2	4	no	—
194	C₄×D₁₀₉	—	2	4	no	—
195	C₄×D₁₀₉	C₂×D₄	1	4	yes	—
196	C₄×D₁₀₉	C₂×D₄	1	4	yes	—
197	C₄×D₁₀₉	C₂×D₄	1	4	yes	complemented
198	C₄×D₁₀₉	C₂×D₄	1	4	yes	complemented
199	Dic₂₁₈	—	2	2	no	—
200	Dic₂₁₈	—	2	4	no	—
201	C₂²×C₁₀₉	—	2	2	no	—
202	C₂²×C₁₀₉	—	2	2	no	—
203	C₂²×C₁₀₉	—	2	4	no	—
204	C₂²×C₁₀₉	—	2	4	no	—
205	C₂²×C₁₀₉	—	2	8	no	—
206	C₂²×C₁₀₉	—	4	8	no	—
207	C₂²×C₁₀₉	C₂²×D₄	1	2	yes	—
208	C₂²×C₁₀₉	C₂⁵	1	1	yes	characteristic
209	C₂×D₁₀₉	—	2	2	no	—
210	C₂×D₁₀₉	—	2	8	no	—
211	C₂×D₁₀₉	—	2	2	no	—
212	C₂×D₁₀₉	—	2	4	no	—
213	C₂×D₁₀₉	—	2	4	no	—
214	C₂×D₁₀₉	—	2	8	no	—
215	C₂×D₁₀₉	—	4	16	no	—
216	C₂×D₁₀₉	—	4	8	no	—
217	C₂×D₁₀₉	—	4	8	no	—
218	C₂×D₁₀₉	—	4	16	no	—
219	C₂×D₁₀₉	C₂²×D₄	1	2	yes	—
220	C₂×D₁₀₉	C₂²×D₄	1	2	yes	—
221	C₂×D₁₀₉	H(5,𝔽₂)	1	4	yes	—
222	C₄×C₁₀₉	—	2	2	no	—
223	C₄×C₁₀₉	—	2	4	no	—
224	C₄×C₁₀₉	C₂²×D₄	1	2	yes	—
225	C₄×C₁₀₉	C₂²×D₄	1	2	yes	—
226	Dic₁₀₉	—	2	2	no	—
227	Dic₁₀₉	—	2	4	no	—
228	Dic₁₀₉	C₂²×D₄	1	2	yes	—
229	Dic₁₀₉	C₂²×D₄	1	2	yes	—
230	C₂×C₁₀₉	—	2	2	no	—
231	C₂×C₁₀₉	—	4	4	no	—
232	C₂×C₁₀₉	—	4	2	no	—
233	C₂×C₁₀₉	C₂³×D₄	1	1	yes	characteristic
234	C₂×C₁₀₉	C₂×H(5,𝔽₂)	1	2	yes	—
235	D₁₀₉	—	2	2	no	—
236	D₁₀₉	—	4	2	no	—
237	D₁₀₉	—	4	4	no	—
238	D₁₀₉	#535	1	4	yes	direct product factor
239	C₂×#535	—	109	1	no	maximal, Sylow
240	C₁₀₉	C₂×#535	1	1	yes	characteristic, complemented, Sylow
241	C₂²×#41	—	109	1	no	—
242	C₂³×D₄	—	109	1	no	—
243	#535	—	109	1	no	—
244	#535	—	109	1	no	—
245	#535	—	109	2	no	—
246	#535	—	109	2	no	—
247	#535	—	109	4	no	—
248	#535	—	109	4	no	—
249	#535	—	109	1	no	—
250	#535	D₁₀₉	1	1	yes	characteristic, direct product factor
251	C₂×#127	—	109	2	no	—
252	C₂×#124	—	109	2	no	—
253	C₂×#121	—	109	4	no	—
254	C₂×#120	—	109	4	no	—
255	C₂×#117	—	109	1	no	—
256	C₂⁵	—	109	2	no	—
257	C₂×#41	—	109	1	no	—
258	C₂×#41	—	109	2	no	—
259	C₂×#41	—	109	1	no	—
260	C₂×#41	—	109	1	no	—
261	C₂×#41	—	109	2	no	—
262	C₂×#41	—	218	8	no	—
263	C₂×#41	C₂×D₁₀₉	1	1	yes	characteristic, complemented
264	C₂²×Q₈	—	109	1	no	—
265	C₂²×D₄	—	109	2	no	—
266	C₂²×D₄	—	109	8	no	—
267	C₂²×D₄	—	109	2	no	—
268	C₂²×D₄	—	109	2	no	—
269	C₂²×D₄	—	109	2	no	—
270	C₂²×D₄	—	109	2	no	—
271	C₂²×D₄	—	109	2	no	—
272	C₂²×D₄	—	109	1	no	—
273	C₂²×D₄	—	109	1	no	—
274	C₂²×D₄	—	218	8	no	—
275	C₂²×D₄	C₂×D₁₀₉	1	1	yes	characteristic, complemented
276	C₂³×C₄	—	109	1	no	—
277	C₂³×C₄	—	109	2	no	—
278	#127	—	109	2	no	—
279	#127	—	109	2	no	—
280	#127	—	109	8	no	—
281	#127	—	109	2	no	—
282	#127	C₂×D₁₀₉	1	2	yes	complemented
283	#124	—	109	2	no	—
284	#124	—	109	2	no	—
285	#124	—	109	8	no	—
286	#124	—	109	2	no	—
287	#124	C₂×D₁₀₉	1	2	yes	complemented
288	#121	—	109	4	no	—
289	#121	—	109	8	no	—
290	#121	—	109	4	no	—
291	#121	—	109	4	no	—
292	#121	—	109	8	no	—
293	#121	C₂×D₁₀₉	1	4	yes	complemented
294	#120	—	109	4	no	—
295	#120	—	109	4	no	—
296	#120	—	109	8	no	—
297	#120	—	109	4	no	—
298	#120	—	109	8	no	—
299	#120	C₂×D₁₀₉	1	4	yes	complemented
300	#117	—	109	1	no	—
301	#117	—	109	2	no	—
302	#117	—	109	2	no	—
303	#117	—	109	2	no	—
304	#117	C₂×D₁₀₉	1	1	yes	characteristic, complemented
305	C₂×C₄⋊C₄	—	109	2	no	—
306	C₂×C₂²⋊C₄	—	109	2	no	—
307	C₂×C₂²⋊C₄	—	109	8	no	—
308	C₂×C₄²	—	109	2	no	—
309	C₂⁴	—	109	1	no	—
310	C₂⁴	—	109	4	no	—
311	C₂⁴	—	109	2	no	—
312	C₂⁴	—	109	4	no	—
313	C₂⁴	—	109	2	no	—
314	C₂⁴	—	436	8	no	—
315	C₂⁴	—	218	8	no	—
316	C₂⁴	C₂²×D₁₀₉	1	2	yes	—
317	#41	—	2	4	no	—
318	#41	—	218	8	no	—
319	#41	—	218	8	no	—
320	#41	—	218	4	no	—
321	#41	—	218	4	no	—
322	#41	—	218	4	no	—
323	C₂×Q₈	—	109	2	no	—
324	C₂×Q₈	—	109	1	no	—
325	C₂×Q₈	—	218	4	no	—
326	C₂×Q₈	C₂²×D₁₀₉	1	1	yes	characteristic, complemented
327	C₂×D₄	—	2	4	no	—
328	C₂×D₄	—	109	8	no	—
329	C₂×D₄	—	109	8	no	—
330	C₂×D₄	—	109	2	no	—
331	C₂×D₄	—	109	2	no	—
332	C₂×D₄	—	109	4	no	—
333	C₂×D₄	—	109	4	no	—
334	C₂×D₄	—	109	2	no	—
335	C₂×D₄	—	109	8	no	—
336	C₂×D₄	—	109	2	no	—
337	C₂×D₄	—	109	2	no	—
338	C₂×D₄	—	109	2	no	—
339	C₂×D₄	—	109	1	no	—
340	C₂×D₄	—	436	16	no	—
341	C₂×D₄	—	218	8	no	—
342	C₂×D₄	—	218	8	no	—
343	C₂×D₄	—	218	8	no	—
344	C₂×D₄	—	218	8	no	—
345	C₂×D₄	—	218	4	no	—
346	C₂×D₄	—	218	8	no	—
347	C₂×D₄	—	218	8	no	—
348	C₂×D₄	—	218	4	no	—
349	C₂×D₄	C₂²×D₁₀₉	1	2	yes	—
350	C₂×D₄	C₂²×D₁₀₉	1	2	yes	—
351	C₂×D₄	C₂²×D₁₀₉	1	2	yes	—
352	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic, complemented
353	C₂×D₄	C₂²×D₁₀₉	1	8	yes	complemented
354	C₂²×C₄	—	109	1	no	—
355	C₂²×C₄	—	109	8	no	—
356	C₂²×C₄	—	109	1	no	—
357	C₂²×C₄	—	109	1	no	—
358	C₂²×C₄	—	109	1	no	—
359	C₂²×C₄	—	109	1	no	—
360	C₂²×C₄	—	109	2	no	—
361	C₂²×C₄	—	109	4	no	—
362	C₂²×C₄	—	109	2	no	—
363	C₂²×C₄	—	109	2	no	—
364	C₂²×C₄	—	109	2	no	—
365	C₂²×C₄	—	218	8	no	—
366	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
367	C₂²×C₄	C₂²×D₁₀₉	1	2	yes	complemented
368	C₄⋊C₄	—	109	4	no	—
369	C₄⋊C₄	—	109	2	no	—
370	C₄⋊C₄	C₂²×D₁₀₉	1	2	yes	complemented
371	C₂²⋊C₄	—	109	2	no	—
372	C₂²⋊C₄	—	109	8	no	—
373	C₂²⋊C₄	—	109	4	no	—
374	C₂²⋊C₄	—	109	8	no	—
375	C₂²⋊C₄	—	109	8	no	—
376	C₂²⋊C₄	C₂²×D₁₀₉	1	2	yes	—
377	C₂²⋊C₄	C₂²×D₁₀₉	1	8	yes	complemented
378	C₄²	—	109	4	no	—
379	C₄²	—	109	2	no	—
380	C₄²	C₂²×D₁₀₉	1	2	yes	complemented
381	C₂³	—	2	4	no	—
382	C₂³	—	4	4	no	—
383	C₂³	—	109	1	no	—
384	C₂³	—	109	4	no	—
385	C₂³	—	109	1	no	—
386	C₂³	—	109	4	no	—
387	C₂³	—	109	2	no	—
388	C₂³	—	436	4	no	—
389	C₂³	—	436	8	no	—
390	C₂³	—	436	32	no	—
391	C₂³	—	218	4	no	—
392	C₂³	—	218	8	no	—
393	C₂³	—	218	16	no	—
394	C₂³	—	218	8	no	—
395	C₂³	—	218	8	no	—
396	C₂³	—	218	4	no	—
397	C₂³	—	218	4	no	—
398	C₂³	C₂³×D₁₀₉	1	4	yes	—
399	C₂³	C₂³×D₁₀₉	1	2	yes	—
400	C₂³	C₂³×D₁₀₉	1	1	yes	characteristic
401	Q₈	—	2	2	no	—
402	Q₈	—	218	4	no	—
403	Q₈	—	218	2	no	—
404	D₄	—	2	4	no	—
405	D₄	—	2	4	no	—
406	D₄	—	2	4	no	—
407	D₄	—	2	2	no	—
408	D₄	—	4	8	no	—
409	D₄	—	436	8	no	—
410	D₄	—	436	8	no	—
411	D₄	—	436	8	no	—
412	D₄	—	218	4	no	—
413	D₄	—	218	8	no	—
414	D₄	—	218	8	no	—
415	D₄	—	218	4	no	—
416	D₄	—	218	4	no	—
417	D₄	—	218	4	no	—
418	D₄	—	218	4	no	—
419	D₄	—	218	4	no	—
420	D₄	—	218	2	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	109	4	no	—
423	C₂×C₄	—	109	1	no	—
424	C₂×C₄	—	109	1	no	—
425	C₂×C₄	—	109	4	no	—
426	C₂×C₄	—	109	4	no	—
427	C₂×C₄	—	109	4	no	—
428	C₂×C₄	—	109	4	no	—
429	C₂×C₄	—	109	4	no	—
430	C₂×C₄	—	109	2	no	—
431	C₂×C₄	—	218	4	no	—
432	C₂×C₄	—	218	4	no	—
433	C₂×C₄	—	218	8	no	—
434	C₂×C₄	—	218	4	no	—
435	C₂×C₄	—	218	4	no	—
436	C₂×C₄	D₄×D₁₀₉	1	4	yes	complemented
437	C₂×C₄	C₂³×D₁₀₉	1	4	yes	—
438	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
439	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
440	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
441	C₂²	—	2	2	no	—
442	C₂²	—	2	2	no	—
443	C₂²	—	2	4	no	—
444	C₂²	—	2	4	no	—
445	C₂²	—	2	8	no	—
446	C₂²	—	4	8	no	—
447	C₂²	—	109	2	no	—
448	C₂²	—	109	4	no	—
449	C₂²	—	109	2	no	—
450	C₂²	—	436	8	no	—
451	C₂²	—	436	16	no	—
452	C₂²	—	436	8	no	—
453	C₂²	—	436	16	no	—
454	C₂²	—	218	8	no	—
455	C₂²	—	218	2	no	—
456	C₂²	—	218	4	no	—
457	C₂²	—	218	4	no	—
458	C₂²	—	218	8	no	—
459	C₂²	—	218	2	no	—
460	C₂²	C₂×D₄×D₁₀₉	1	2	yes	—
461	C₂²	C₂⁴×D₁₀₉	1	1	yes	characteristic
462	C₄	—	2	2	no	—
463	C₄	—	2	4	no	—
464	C₄	—	109	2	no	—
465	C₄	—	109	2	no	—
466	C₄	—	218	2	no	—
467	C₄	—	218	4	no	—
468	C₄	C₂×D₄×D₁₀₉	1	2	yes	—
469	C₄	C₂×D₄×D₁₀₉	1	2	yes	—
470	C₂	—	2	2	no	—
471	C₂	—	4	4	no	—
472	C₂	—	4	2	no	—
473	C₂	—	109	4	no	—
474	C₂	—	436	4	no	—
475	C₂	—	436	2	no	—
476	C₂	—	218	2	no	—
477	C₂	C₂²×D₄×D₁₀₉	1	1	yes	characteristic
478	C₂	H(5,𝔽₂)×D₁₀₉	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₀₉
commutator, socle, cosocle	C₂²×C₁₀₉	C₂⁵
Fitting	#535×C₁₀₉	C₂
hypercenter	#535	D₁₀₉
hypocenter	C₁₀₉	C₂×#535
LCS	G ▷ C₂²×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ #535

Complements

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

N	H ≅ G/N	type
1. C₂×#41×D₁₀₉	C₂	semidirect
2. C₂²×D₄×D₁₀₉	C₂	semidirect
3. #20295595	C₂	semidirect
4. #20295594	C₂	semidirect
5. #20295593	C₂	semidirect
6. #20295592	C₂	semidirect
7. #20295591	C₂	semidirect
8. #20295590	C₂	semidirect
9. #20295589	C₂	semidirect
10. #127×D₁₀₉	C₂	semidirect
11. #124×D₁₀₉	C₂	semidirect
12. #121×D₁₀₉	C₂	semidirect
13. #120×D₁₀₉	C₂	semidirect
14. #117×D₁₀₉	C₂	semidirect
15. #535×C₁₀₉	C₂	semidirect
17. C₂×#13182030	C₂²	semidirect
18. C₂×#13182029	C₂²	semidirect
19. C₂×#13182029	C₂²	semidirect
20. C₂×#13182028	C₂²	semidirect
21. C₂×#13182028	C₂²	semidirect
23. C₂×Q₈×D₁₀₉	C₂²	semidirect
24. C₂²×D₄₃₆	C₂²	semidirect
25. C₂²×C₂²⋊D₁₀₉	C₂²	semidirect
30. C₂×D₄×D₁₀₉	C₂²	semidirect
31. C₂×D₄×D₁₀₉	C₂²	semidirect
32. C₂×D₄×D₁₀₉	C₂²	semidirect
33. C₂×D₄×D₁₀₉	C₂²	semidirect
35. C₂²×C₄×D₁₀₉	C₂²	semidirect
36. #16812696	C₂²	semidirect
37. #16812695	C₂²	semidirect
38. #16812695	C₂²	semidirect
39. #16812695	C₂²	semidirect
40. #16812688	C₂²	semidirect
41. #16812687	C₂²	semidirect
42. #16812686	C₂²	semidirect
43. #16812685	C₂²	semidirect
44. #16812674	C₂²	semidirect
45. #16812673	C₂²	semidirect
46. #16812672	C₂²	semidirect
47. #16812671	C₂²	semidirect
48. #16812670	C₂²	semidirect
49. #16812669	C₂²	semidirect
50. #16812669	C₂²	semidirect
51. #16812668	C₂²	semidirect
52. #16812667	C₂²	semidirect
53. #16812667	C₂²	semidirect
54. #16812658	C₂²	semidirect
55. #16812657	C₂²	semidirect
56. #16812656	C₂²	semidirect
57. #16812655	C₂²	semidirect
58. C₄⋊C₄×D₁₀₉	C₂²	semidirect
60. C₂²⋊C₄×D₁₀₉	C₂²	semidirect
61. C₄²×D₁₀₉	C₂²	semidirect
62. C₂×#41×C₁₀₉	C₂²	semidirect
63. C₂²×D₄×C₁₀₉	C₂²	semidirect
64. #127×C₁₀₉	C₂²	semidirect
65. #124×C₁₀₉	C₂²	semidirect
66. #121×C₁₀₉	C₂²	semidirect
67. #120×C₁₀₉	C₂²	semidirect
68. #117×C₁₀₉	C₂²	semidirect
81. C₂×Dic₂₁₈	C₂³	semidirect
82. C₂×Dic₂₁₈	C₂³	semidirect
88. C₂×D₄₃₆	C₂³	semidirect
89. C₂×D₄₃₆	C₂³	semidirect
95. C₂×C₂²⋊D₁₀₉	C₂³	semidirect
96. C₂×C₂²⋊D₁₀₉	C₂³	semidirect
97. C₂×C₂²⋊D₁₀₉	C₂³	semidirect
106. C₂²×Dic₁₀₉	C₂³	semidirect
108. C₂×C₄×D₁₀₉	D₄	semidirect
115. C₂×C₄×D₁₀₉	C₂³	semidirect
116. C₂×C₄×D₁₀₉	C₂³	semidirect
117. C₄⋊Dic₁₀₉	C₂³	semidirect
118. #13182008	C₂³	semidirect
120. C₂²⋊Dic₁₀₉	C₂³	semidirect
122. #13182006	C₂³	semidirect
123. #13182006	C₂³	semidirect
124. C₄×Dic₁₀₉	C₂³	semidirect
125. C₄×Dic₁₀₉	C₂³	semidirect
128. C₂×Q₈×C₁₀₉	C₂³	semidirect
133. C₂×D₄×C₁₀₉	C₂³	semidirect
134. C₂×D₄×C₁₀₉	C₂³	semidirect
136. C₂²×C₄×C₁₀₉	C₂³	semidirect
137. C₄⋊C₄×C₁₀₉	C₂³	semidirect
139. C₂²⋊C₄×C₁₀₉	C₂³	semidirect
140. C₄²×C₁₀₉	C₂³	semidirect
168. C₂×C₄×C₁₀₉	C₂×D₄	semidirect
181. C₂×Dic₁₀₉	C₂×D₄	semidirect
197. C₄×D₁₀₉	C₂×D₄	semidirect
198. C₄×D₁₀₉	C₂×D₄	semidirect
238. D₁₀₉	#535	direct (N × H)
240. C₁₀₉	C₂×#535	semidirect
250. #535	D₁₀₉	direct (N × H)
263. C₂×#41	C₂×D₁₀₉	semidirect
275. C₂²×D₄	C₂×D₁₀₉	semidirect
282. #127	C₂×D₁₀₉	semidirect
287. #124	C₂×D₁₀₉	semidirect
293. #121	C₂×D₁₀₉	semidirect
299. #120	C₂×D₁₀₉	semidirect
304. #117	C₂×D₁₀₉	semidirect
326. C₂×Q₈	C₂²×D₁₀₉	semidirect
352. C₂×D₄	C₂²×D₁₀₉	semidirect
353. C₂×D₄	C₂²×D₁₀₉	semidirect
367. C₂²×C₄	C₂²×D₁₀₉	semidirect
370. C₄⋊C₄	C₂²×D₁₀₉	semidirect
377. C₂²⋊C₄	C₂²×D₁₀₉	semidirect
380. C₄²	C₂²×D₁₀₉	semidirect
436. C₂×C₄	D₄×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
C₂²×D₄×D₁₀₉	2
#20295595	2
#20295594	2
#20295593	2
#20295592	2
#20295591	2
#20295590	2
#20295589	2
#127×D₁₀₉	2
#124×D₁₀₉	2
#121×D₁₀₉	2
#120×D₁₀₉	2
#117×D₁₀₉	2
#535×C₁₀₉	2
C₂×#535	109

Subgroups — #535×D109 #28376336

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #535×D₁₀₉ #28376336