Subgroups — #28376448

Order 13952.

1140 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20295654	C₂	1	1	yes	maximal, characteristic, complemented
2	#20295648	C₂	1	2	yes	maximal, complemented
3	#20295647	C₂	1	2	yes	maximal, complemented
4	#20295631	C₂	1	2	yes	maximal, complemented
5	#20295627	C₂	1	2	yes	maximal, complemented
6	#20295609	C₂	1	4	yes	maximal, complemented
7	#20295604	C₂	1	1	yes	maximal, characteristic, complemented
8	#20295595	C₂	1	1	yes	maximal, characteristic, complemented
9	#20295590	C₂	1	1	yes	maximal, characteristic, complemented
10	#20295576	C₂	1	2	yes	maximal, complemented
11	#20295573	C₂	1	2	yes	maximal, complemented
12	#20295563	C₂	1	2	yes	maximal, complemented
13	#20295560	C₂	1	2	yes	maximal, complemented
14	#20295535	C₂	1	4	yes	maximal, complemented
15	C₄×#13182029	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×D₄₃₆	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×#41×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#13182029	C₂²	1	1	yes	characteristic
19	C₂×#13182029	C₂²	1	4	yes	complemented
20	C₂²×D₄₃₆	C₂²	1	1	yes	characteristic
21	C₂²×C₄×D₁₀₉	C₂²	1	2	yes	—
22	#16812699	C₂²	1	2	yes	complemented
23	#16812698	C₂²	1	2	yes	complemented
24	#16812696	C₂²	1	2	yes	—
25	#16812695	C₂²	1	2	yes	—
26	#16812694	C₂²	1	4	yes	complemented
27	#16812693	C₂²	1	4	yes	complemented
28	#16812691	C₂²	1	2	yes	complemented
29	#16812690	C₂²	1	2	yes	complemented
30	#16812688	C₂²	1	2	yes	—
31	#16812687	C₂²	1	2	yes	—
32	#16812687	C₂²	1	4	yes	complemented
33	#16812685	C₂²	1	4	yes	complemented
34	#16812684	C₂²	1	4	yes	complemented
35	#16812684	C₂²	1	4	yes	complemented
36	#16812682	C₂²	1	4	yes	complemented
37	#16812681	C₂²	1	4	yes	complemented
38	#16812678	C₂²	1	2	yes	complemented
39	#16812677	C₂²	1	4	yes	complemented
40	#16812676	C₂²	1	4	yes	—
41	#16812675	C₂²	1	2	yes	complemented
42	#16812674	C₂²	1	2	yes	—
43	#16812674	C₂²	1	2	yes	—
44	#16812673	C₂²	1	2	yes	—
45	#16812673	C₂²	1	2	yes	—
46	#16812673	C₂²	1	2	yes	complemented
47	#16812673	C₂²	1	4	yes	complemented
48	#16812672	C₂²	1	4	yes	complemented
49	#16812672	C₂²	1	4	yes	complemented
50	#16812671	C₂²	1	4	yes	—
51	#16812670	C₂²	1	2	yes	complemented
52	#16812669	C₂²	1	4	yes	—
53	#16812667	C₂²	1	4	yes	—
54	C₄×Dic₂₁₈	C₂²	1	1	yes	characteristic, complemented
55	C₄×Dic₂₁₈	C₂²	1	1	yes	characteristic, complemented
56	C₄×D₄₃₆	C₂²	1	2	yes	—
57	C₄×D₄₃₆	C₂²	1	2	yes	—
58	C₄×D₄₃₆	C₂²	1	2	yes	—
59	C₄×D₄₃₆	C₂²	1	2	yes	—
60	C₄×D₄₃₆	C₂²	1	1	yes	characteristic, complemented
61	C₄×D₄₃₆	C₂²	1	1	yes	characteristic, complemented
62	C₄×D₄₃₆	C₂²	1	4	yes	complemented
63	C₄×C₂²⋊D₁₀₉	C₂²	1	2	yes	—
64	C₄×C₂²⋊D₁₀₉	C₂²	1	2	yes	—
65	C₄×C₂²⋊D₁₀₉	C₂²	1	4	yes	complemented
66	#16812658	C₂²	1	1	yes	characteristic
67	#16812656	C₂²	1	2	yes	complemented
68	#16812656	C₂²	1	4	yes	complemented
69	C₂×C₄⋊Dic₁₀₉	C₂²	1	1	yes	characteristic
70	C₂×#13182006	C₂²	1	2	yes	—
71	C₄²×D₁₀₉	C₂²	1	2	yes	complemented
72	C₂×#41×C₁₀₉	C₂²	1	1	yes	characteristic
73	C₄×Q₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
74	C₄×Q₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
75	C₄×D₄×C₁₀₉	C₂²	1	2	yes	—
76	C₄×D₄×C₁₀₉	C₂²	1	2	yes	—
77	C₄×D₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
78	C₄×D₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
79	#117×C₁₀₉	C₂²	1	1	yes	characteristic
80	#117×C₁₀₉	C₂²	1	2	yes	complemented
81	C₂×C₄²×C₁₀₉	C₂²	1	1	yes	characteristic
82	C₂×C₄²×C₁₀₉	C₂²	1	2	yes	complemented
83	C₂³×D₁₀₉	C₂³	1	2	yes	—
84	#13182029	—	2	4	no	—
85	#13182029	—	4	8	no	—
86	C₂×Dic₂₁₈	C₂³	1	1	yes	characteristic
87	C₂×Dic₂₁₈	C₂³	1	4	yes	—
88	C₂×D₄₃₆	—	2	4	no	—
89	C₂×D₄₃₆	C₂³	1	2	yes	—
90	C₂×D₄₃₆	C₂³	1	2	yes	—
91	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
92	C₂×D₄₃₆	C₂³	1	4	yes	—
93	C₂×D₄₃₆	C₂³	1	4	yes	—
94	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	—
95	C₂×C₂²⋊D₁₀₉	C₂³	1	4	yes	—
96	C₂×C₂²⋊D₁₀₉	C₂³	1	4	yes	—
97	C₂×C₂²⋊D₁₀₉	C₂³	1	4	yes	—
98	C₂²×Dic₁₀₉	C₂³	1	2	yes	—
99	C₂×C₄×D₁₀₉	—	4	4	no	—
100	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
101	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
102	C₂×C₄×D₁₀₉	C₂³	1	4	yes	—
103	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
104	C₂×C₄×D₁₀₉	C₂³	1	4	yes	—
105	C₄⋊Dic₁₀₉	C₂³	1	2	yes	—
106	C₄⋊Dic₁₀₉	C₂³	1	2	yes	—
107	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
108	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
109	C₄⋊Dic₁₀₉	C₂³	1	4	yes	—
110	#13182008	C₂³	1	2	yes	—
111	#13182008	C₂³	1	2	yes	—
112	#13182008	C₂³	1	4	yes	—
113	#13182008	C₂³	1	4	yes	—
114	#13182008	C₂³	1	4	yes	—
115	C₂²⋊Dic₁₀₉	C₂³	1	2	yes	—
116	C₂²⋊Dic₁₀₉	C₂³	1	4	yes	—
117	#13182006	C₂³	1	4	yes	—
118	#13182006	C₂³	1	4	yes	—
119	#13182006	C₂³	1	2	yes	—
120	#13182006	C₂³	1	2	yes	—
121	#13182006	C₂³	1	4	yes	—
122	#13182006	C₂³	1	4	yes	—
123	#13182006	C₂³	1	4	yes	—
124	#13182006	C₂³	1	4	yes	—
125	#13182006	C₂³	1	4	yes	—
126	C₄×Dic₁₀₉	C₂³	1	2	yes	—
127	C₄×Dic₁₀₉	C₂³	1	2	yes	—
128	C₄×Dic₁₀₉	C₂³	1	2	yes	—
129	#41×C₁₀₉	—	2	4	no	—
130	C₂×Q₈×C₁₀₉	C₂³	1	1	yes	characteristic
131	C₂×D₄×C₁₀₉	C₂³	1	2	yes	—
132	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
133	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
134	C₂²×C₄×C₁₀₉	C₂³	1	2	yes	—
135	C₂²×C₄×C₁₀₉	C₂³	1	2	yes	—
136	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
137	C₂²×C₄×C₁₀₉	C₂³	1	2	yes	—
138	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
139	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
140	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
141	C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
142	C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
143	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
144	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
145	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
146	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
147	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
148	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
149	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
150	C₄²×C₁₀₉	C₂³	1	2	yes	—
151	C₄²×C₁₀₉	C₂³	1	2	yes	—
152	C₄²×C₁₀₉	C₂³	1	2	yes	—
153	C₂³×C₁₀₉	C₂⁴	1	2	yes	—
154	C₂³×C₁₀₉	C₂⁴	1	1	yes	characteristic
155	C₂²×D₁₀₉	—	2	4	no	—
156	C₂²×D₁₀₉	—	4	2	no	—
157	C₂²×D₁₀₉	—	4	2	no	—
158	C₂²×D₁₀₉	C₂⁴	1	4	yes	—
159	C₂²×D₁₀₉	C₂⁴	1	2	yes	—
160	Q₈×C₁₀₉	—	2	2	no	—
161	D₄×C₁₀₉	—	2	4	no	—
162	D₄×C₁₀₉	—	2	2	no	—
163	C₂×C₄×C₁₀₉	—	2	4	no	—
164	C₂×C₄×C₁₀₉	—	2	2	no	—
165	C₂×C₄×C₁₀₉	—	2	4	no	—
166	C₂×C₄×C₁₀₉	—	4	1	no	—
167	C₂×C₄×C₁₀₉	—	4	2	no	—
168	C₂×C₄×C₁₀₉	#41	1	4	yes	complemented
169	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
170	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
171	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
172	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
173	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
174	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
175	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
176	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
177	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
178	C₂²⋊D₁₀₉	—	2	4	no	—
179	C₂²⋊D₁₀₉	—	4	4	no	—
180	C₂²⋊D₁₀₉	—	4	4	no	—
181	C₂²⋊D₁₀₉	—	4	4	no	—
182	C₂×Dic₁₀₉	—	4	2	no	—
183	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
184	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
185	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
186	C₂×Dic₁₀₉	C₂⁴	1	4	yes	—
187	D₄₃₆	—	2	4	no	—
188	D₄₃₆	—	2	4	no	—
189	D₄₃₆	—	2	2	no	—
190	D₄₃₆	—	4	4	no	—
191	D₄₃₆	—	4	4	no	—
192	C₄×D₁₀₉	—	2	4	no	—
193	C₄×D₁₀₉	—	2	8	no	—
194	C₄×D₁₀₉	—	2	4	no	—
195	C₄×D₁₀₉	—	4	4	no	—
196	C₄×D₁₀₉	—	4	2	no	—
197	Dic₂₁₈	—	2	2	no	—
198	Dic₂₁₈	—	4	4	no	—
199	C₂²×C₁₀₉	—	2	1	no	—
200	C₂²×C₁₀₉	—	2	1	no	—
201	C₂²×C₁₀₉	—	2	2	no	—
202	C₂²×C₁₀₉	—	2	2	no	—
203	C₂²×C₁₀₉	—	2	2	no	—
204	C₂²×C₁₀₉	C₂×#41	1	2	yes	—
205	C₂²×C₁₀₉	C₂⁵	1	1	yes	characteristic
206	C₂×D₁₀₉	—	2	2	no	—
207	C₂×D₁₀₉	—	2	4	no	—
208	C₂×D₁₀₉	—	2	4	no	—
209	C₂×D₁₀₉	—	2	2	no	—
210	C₂×D₁₀₉	—	2	2	no	—
211	C₂×D₁₀₉	—	2	4	no	—
212	C₂×D₁₀₉	—	4	8	no	—
213	C₄×C₁₀₉	—	2	2	no	—
214	C₄×C₁₀₉	—	2	2	no	—
215	C₄×C₁₀₉	—	2	1	no	—
216	C₄×C₁₀₉	—	2	1	no	—
217	C₄×C₁₀₉	—	2	2	no	—
218	C₄×C₁₀₉	—	2	1	no	—
219	C₄×C₁₀₉	C₂×#41	1	2	yes	—
220	C₄×C₁₀₉	C₂×#41	1	2	yes	—
221	C₄×C₁₀₉	H(5,𝔽₂)	1	2	yes	—
222	Dic₁₀₉	—	2	2	no	—
223	Dic₁₀₉	—	2	2	no	—
224	Dic₁₀₉	—	2	4	no	—
225	Dic₁₀₉	—	2	2	no	—
226	C₂×C₁₀₉	—	2	2	no	—
227	C₂×C₁₀₉	—	4	2	no	—
228	C₂×C₁₀₉	C₂²×#41	1	1	yes	characteristic
229	C₂×C₁₀₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
230	C₂×C₁₀₉	#585	1	1	yes	characteristic
231	D₁₀₉	—	4	2	no	—
232	D₁₀₉	—	4	4	no	—
233	#3460	—	109	1	no	maximal, Sylow
234	C₁₀₉	#3460	1	1	yes	characteristic, complemented, Sylow
235	#544	—	109	1	no	—
236	#542	—	109	2	no	—
237	#542	—	109	2	no	—
238	#540	—	109	2	no	—
239	#540	—	109	2	no	—
240	#538	—	109	4	no	—
241	#537	—	109	1	no	—
242	#535	—	109	1	no	—
243	#535	—	109	1	no	—
244	#532	—	109	2	no	—
245	#532	—	109	2	no	—
246	#529	—	109	2	no	—
247	#529	—	109	2	no	—
248	#525	—	109	4	no	—
249	C₄×#41	—	109	1	no	—
250	C₄×#41	D₁₀₉	1	1	yes	characteristic, complemented
251	C₂×C₄×D₄	—	109	1	no	—
252	C₂×#41	—	109	4	no	—
253	C₂×#41	—	109	1	no	—
254	C₂×#41	C₂×D₁₀₉	1	1	yes	characteristic
255	C₂²×D₄	—	109	1	no	—
256	C₂³×C₄	—	109	2	no	—
257	C₄⋊Q₈	—	109	2	no	—
258	C₄⋊Q₈	—	109	2	no	—
259	#127	—	109	2	no	—
260	#127	—	109	2	no	—
261	#126	—	109	4	no	—
262	#126	—	109	4	no	—
263	#125	—	109	2	no	—
264	#125	—	109	2	no	—
265	#124	—	109	2	no	—
266	#124	—	109	4	no	—
267	#124	—	109	2	no	—
268	#124	—	109	4	no	—
269	#123	—	109	4	no	—
270	#123	—	109	4	no	—
271	#123	—	109	4	no	—
272	#123	—	109	4	no	—
273	C₂²⋊Q₈	—	109	2	no	—
274	C₂²⋊Q₈	—	109	2	no	—
275	C₂²⋊Q₈	—	109	4	no	—
276	C₂²⋊Q₈	—	109	4	no	—
277	#121	—	109	4	no	—
278	#121	—	109	2	no	—
279	#121	—	109	2	no	—
280	#121	—	109	2	no	—
281	#121	—	109	2	no	—
282	#121	—	109	4	no	—
283	#121	—	109	2	no	—
284	#121	—	109	2	no	—
285	#121	—	109	4	no	—
286	#121	—	109	4	no	—
287	#120	—	109	4	no	—
288	#120	—	109	4	no	—
289	C₄×Q₈	—	109	1	no	—
290	C₄×Q₈	—	109	1	no	—
291	C₄×Q₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
292	C₄×Q₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
293	C₄×D₄	—	109	2	no	—
294	C₄×D₄	—	109	2	no	—
295	C₄×D₄	—	109	4	no	—
296	C₄×D₄	—	109	2	no	—
297	C₄×D₄	—	109	2	no	—
298	C₄×D₄	—	109	2	no	—
299	C₄×D₄	—	109	2	no	—
300	C₄×D₄	—	109	1	no	—
301	C₄×D₄	—	109	1	no	—
302	C₄×D₄	—	109	4	no	—
303	C₄×D₄	C₂×D₁₀₉	1	2	yes	—
304	C₄×D₄	C₂×D₁₀₉	1	2	yes	—
305	C₄×D₄	C₂×D₁₀₉	1	1	yes	characteristic, complemented
306	C₄×D₄	C₂×D₁₀₉	1	1	yes	characteristic, complemented
307	#117	—	109	1	no	—
308	#117	—	109	2	no	—
309	#117	—	109	4	no	—
310	#117	C₂×D₁₀₉	1	1	yes	characteristic
311	#117	C₂×D₁₀₉	1	2	yes	complemented
312	C₂×C₄⋊C₄	—	109	1	no	—
313	C₂×C₂²⋊C₄	—	109	2	no	—
314	C₂×C₄²	—	109	2	no	—
315	C₂×C₄²	C₂×D₁₀₉	1	1	yes	characteristic
316	C₂×C₄²	C₂×D₁₀₉	1	2	yes	complemented
317	C₂⁴	—	109	2	no	—
318	#41	—	2	4	no	—
319	#41	—	436	8	no	—
320	#41	—	218	4	no	—
321	C₂×Q₈	—	109	4	no	—
322	C₂×Q₈	—	109	1	no	—
323	C₂×Q₈	C₂²×D₁₀₉	1	1	yes	characteristic
324	C₂×D₄	—	109	4	no	—
325	C₂×D₄	—	109	4	no	—
326	C₂×D₄	—	109	4	no	—
327	C₂×D₄	—	109	2	no	—
328	C₂×D₄	—	109	4	no	—
329	C₂×D₄	—	109	4	no	—
330	C₂×D₄	—	109	2	no	—
331	C₂×D₄	—	109	2	no	—
332	C₂×D₄	—	109	1	no	—
333	C₂×D₄	—	218	4	no	—
334	C₂×D₄	C₂²×D₁₀₉	1	2	yes	—
335	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
336	C₂²×C₄	—	109	2	no	—
337	C₂²×C₄	—	109	2	no	—
338	C₂²×C₄	—	109	4	no	—
339	C₂²×C₄	—	109	2	no	—
340	C₂²×C₄	—	109	2	no	—
341	C₂²×C₄	—	109	4	no	—
342	C₂²×C₄	—	436	4	no	—
343	C₂²×C₄	C₂²×D₁₀₉	1	2	yes	—
344	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
345	C₂²×C₄	C₂²×D₁₀₉	1	2	yes	—
346	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
347	C₂²×C₄	C₂²×D₁₀₉	1	2	yes	—
348	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
349	C₄⋊C₄	—	109	2	no	—
350	C₄⋊C₄	—	109	2	no	—
351	C₄⋊C₄	—	109	4	no	—
352	C₄⋊C₄	—	109	4	no	—
353	C₄⋊C₄	—	109	4	no	—
354	C₄⋊C₄	—	109	2	no	—
355	C₄⋊C₄	—	109	2	no	—
356	C₄⋊C₄	—	109	1	no	—
357	C₄⋊C₄	—	109	1	no	—
358	C₄⋊C₄	—	109	4	no	—
359	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
360	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
361	C₄⋊C₄	C₂²×D₁₀₉	1	2	yes	—
362	C₄⋊C₄	C₂²×D₁₀₉	1	2	yes	—
363	C₂²⋊C₄	—	109	2	no	—
364	C₂²⋊C₄	—	109	4	no	—
365	C₂²⋊C₄	—	109	4	no	—
366	C₂²⋊C₄	—	109	4	no	—
367	C₂²⋊C₄	—	109	2	no	—
368	C₂²⋊C₄	—	109	2	no	—
369	C₂²⋊C₄	—	109	4	no	—
370	C₂²⋊C₄	—	109	4	no	—
371	C₂²⋊C₄	—	109	4	no	—
372	C₂²⋊C₄	—	109	4	no	—
373	C₂²⋊C₄	—	109	4	no	—
374	C₂²⋊C₄	C₂²×D₁₀₉	1	2	yes	—
375	C₂²⋊C₄	C₂²×D₁₀₉	1	2	yes	—
376	C₂²⋊C₄	C₂²×D₁₀₉	1	2	yes	—
377	C₄²	—	109	2	no	—
378	C₄²	—	109	2	no	—
379	C₄²	—	109	2	no	—
380	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic
381	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic
382	C₄²	C₂²×D₁₀₉	1	2	yes	—
383	C₄²	C₂²×D₁₀₉	1	2	yes	—
384	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic
385	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic
386	C₄²	C₂²×D₁₀₉	1	2	yes	—
387	C₂³	—	109	4	no	—
388	C₂³	—	109	2	no	—
389	C₂³	—	436	2	no	—
390	C₂³	—	436	2	no	—
391	C₂³	—	218	4	no	—
392	C₂³	C₂³×D₁₀₉	1	2	yes	—
393	C₂³	C₂³×D₁₀₉	1	1	yes	characteristic
394	Q₈	—	2	2	no	—
395	Q₈	—	436	4	no	—
396	Q₈	—	218	2	no	—
397	D₄	—	2	4	no	—
398	D₄	—	2	2	no	—
399	D₄	—	436	4	no	—
400	D₄	—	436	4	no	—
401	D₄	—	436	4	no	—
402	D₄	—	436	4	no	—
403	D₄	—	436	4	no	—
404	D₄	—	218	4	no	—
405	D₄	—	218	4	no	—
406	D₄	—	218	4	no	—
407	D₄	—	218	2	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	109	2	no	—
414	C₂×C₄	—	109	2	no	—
415	C₂×C₄	—	109	2	no	—
416	C₂×C₄	—	109	4	no	—
417	C₂×C₄	—	436	4	no	—
418	C₂×C₄	—	436	2	no	—
419	C₂×C₄	—	436	2	no	—
420	C₂×C₄	—	218	4	no	—
421	C₂×C₄	—	218	8	no	—
422	C₂×C₄	—	218	4	no	—
423	C₂×C₄	#13182029	1	4	yes	complemented
424	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
425	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
426	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
427	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
428	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
429	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
430	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
431	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
432	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
433	C₂²	—	2	1	no	—
434	C₂²	—	2	1	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	2	2	no	—
438	C₂²	—	436	8	no	—
439	C₂²	—	218	2	no	—
440	C₂²	—	218	4	no	—
441	C₂²	—	218	4	no	—
442	C₂²	—	218	2	no	—
443	C₂²	—	218	2	no	—
444	C₂²	—	218	4	no	—
445	C₂²	C₂×#13182029	1	2	yes	—
446	C₂²	C₂⁴×D₁₀₉	1	1	yes	characteristic
447	C₄	—	2	2	no	—
448	C₄	—	2	1	no	—
449	C₄	—	2	2	no	—
450	C₄	—	2	1	no	—
451	C₄	—	2	1	no	—
452	C₄	—	2	2	no	—
453	C₄	—	218	2	no	—
454	C₄	—	218	4	no	—
455	C₄	—	218	2	no	—
456	C₄	—	218	2	no	—
457	C₄	C₂×#13182029	1	2	yes	—
458	C₄	C₂×#13182029	1	2	yes	—
459	C₄	#16812745	1	2	yes	—
460	C₂	—	2	2	no	—
461	C₂	—	4	2	no	—
462	C₂	—	436	4	no	—
463	C₂	—	436	2	no	—
464	C₂	C₂²×#13182029	1	1	yes	characteristic
465	C₂	C₂×#16812745	1	1	yes	characteristic
466	C₂	#20295862	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₁₀₉
commutator, socle, cosocle	C₂²×C₁₀₉	C₂⁵
Frattini	C₂²	C₂⁴×D₁₀₉
Fitting	C₄×#41×C₁₀₉	C₂
hypercenter	C₄×#41	D₁₀₉
hypocenter	C₁₀₉	#3460
LCS	G ▷ C₂²×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41

Complements

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

N	H ≅ G/N	type
1. #20295654	C₂	semidirect
2. #20295648	C₂	semidirect
3. #20295647	C₂	semidirect
4. #20295631	C₂	semidirect
5. #20295627	C₂	semidirect
6. #20295609	C₂	semidirect
7. #20295604	C₂	semidirect
8. #20295595	C₂	semidirect
9. #20295590	C₂	semidirect
10. #20295576	C₂	semidirect
11. #20295573	C₂	semidirect
12. #20295563	C₂	semidirect
13. #20295560	C₂	semidirect
14. #20295535	C₂	semidirect
15. C₄×#13182029	C₂	semidirect
16. C₂×C₄×D₄₃₆	C₂	semidirect
17. C₄×#41×C₁₀₉	C₂	semidirect
19. C₂×#13182029	C₂²	semidirect
22. #16812699	C₂²	semidirect
23. #16812698	C₂²	semidirect
26. #16812694	C₂²	semidirect
27. #16812693	C₂²	semidirect
28. #16812691	C₂²	semidirect
29. #16812690	C₂²	semidirect
32. #16812687	C₂²	semidirect
33. #16812685	C₂²	semidirect
34. #16812684	C₂²	semidirect
35. #16812684	C₂²	semidirect
36. #16812682	C₂²	semidirect
37. #16812681	C₂²	semidirect
38. #16812678	C₂²	semidirect
39. #16812677	C₂²	semidirect
41. #16812675	C₂²	semidirect
46. #16812673	C₂²	semidirect
47. #16812673	C₂²	semidirect
48. #16812672	C₂²	semidirect
49. #16812672	C₂²	semidirect
51. #16812670	C₂²	semidirect
54. C₄×Dic₂₁₈	C₂²	semidirect
55. C₄×Dic₂₁₈	C₂²	semidirect
60. C₄×D₄₃₆	C₂²	semidirect
61. C₄×D₄₃₆	C₂²	semidirect
62. C₄×D₄₃₆	C₂²	semidirect
65. C₄×C₂²⋊D₁₀₉	C₂²	semidirect
67. #16812656	C₂²	semidirect
68. #16812656	C₂²	semidirect
71. C₄²×D₁₀₉	C₂²	semidirect
73. C₄×Q₈×C₁₀₉	C₂²	semidirect
74. C₄×Q₈×C₁₀₉	C₂²	semidirect
77. C₄×D₄×C₁₀₉	C₂²	semidirect
78. C₄×D₄×C₁₀₉	C₂²	semidirect
80. #117×C₁₀₉	C₂²	semidirect
82. C₂×C₄²×C₁₀₉	C₂²	semidirect
168. C₂×C₄×C₁₀₉	#41	semidirect
234. C₁₀₉	#3460	semidirect
250. C₄×#41	D₁₀₉	semidirect
291. C₄×Q₈	C₂×D₁₀₉	semidirect
292. C₄×Q₈	C₂×D₁₀₉	semidirect
305. C₄×D₄	C₂×D₁₀₉	semidirect
306. C₄×D₄	C₂×D₁₀₉	semidirect
311. #117	C₂×D₁₀₉	semidirect
316. C₂×C₄²	C₂×D₁₀₉	semidirect
423. C₂×C₄	#13182029	semidirect

Maximal subgroups

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

subgroup	index
#20295654	2
#20295648	2
#20295647	2
#20295631	2
#20295627	2
#20295609	2
#20295604	2
#20295595	2
#20295590	2
#20295576	2
#20295573	2
#20295563	2
#20295560	2
#20295535	2
C₄×#13182029	2
C₂×C₄×D₄₃₆	2
C₄×#41×C₁₀₉	2
#3460	109