Subgroups — #28376596

Order 13952.

1132 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20295749	C₂	1	1	yes	maximal, characteristic, complemented
2	#20295741	C₂	1	1	yes	maximal, characteristic, complemented
3	#20295736	C₂	1	1	yes	maximal, characteristic, complemented
4	#20295726	C₂	1	2	yes	maximal, complemented
5	#20295717	C₂	1	2	yes	maximal, complemented
6	#20295716	C₂	1	2	yes	maximal, complemented
7	#20295705	C₂	1	4	yes	maximal, complemented
8	#20295681	C₂	1	1	yes	maximal, characteristic, complemented
9	#20295672	C₂	1	2	yes	maximal, complemented
10	#20295583	C₂	1	1	yes	maximal, characteristic, complemented
11	#20295560	C₂	1	2	yes	maximal, complemented
12	#20295554	C₂	1	4	yes	maximal, complemented
13	#20295533	C₂	1	2	yes	maximal, complemented
14	C₄×#13182029	C₂	1	2	yes	maximal, complemented
15	C₂×C₄×D₄₃₆	C₂	1	1	yes	maximal, characteristic, complemented
16	#117×D₁₀₉	C₂	1	2	yes	maximal, complemented
17	C₄×#41×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#13182029	C₂²	1	2	yes	—
19	C₂²×D₄₃₆	C₂²	1	1	yes	characteristic
20	C₂²×C₄×D₁₀₉	C₂²	1	2	yes	—
21	#16812699	C₂²	1	1	yes	characteristic, complemented
22	#16812699	C₂²	1	1	yes	characteristic, complemented
23	#16812694	C₂²	1	4	yes	complemented
24	#16812693	C₂²	1	4	yes	complemented
25	#16812692	C₂²	1	4	yes	complemented
26	#16812691	C₂²	1	2	yes	complemented
27	#16812691	C₂²	1	2	yes	complemented
28	#16812689	C₂²	1	4	yes	complemented
29	#16812687	C₂²	1	2	yes	—
30	#16812685	C₂²	1	4	yes	complemented
31	#16812684	C₂²	1	4	yes	—
32	#16812682	C₂²	1	4	yes	complemented
33	#16812681	C₂²	1	4	yes	complemented
34	#16812680	C₂²	1	4	yes	—
35	#16812678	C₂²	1	2	yes	—
36	#16812678	C₂²	1	2	yes	—
37	#16812678	C₂²	1	2	yes	complemented
38	#16812677	C₂²	1	4	yes	complemented
39	#16812675	C₂²	1	2	yes	complemented
40	#16812675	C₂²	1	2	yes	complemented
41	#16812673	C₂²	1	2	yes	—
42	#16812672	C₂²	1	4	yes	—
43	#16812670	C₂²	1	2	yes	complemented
44	#16812670	C₂²	1	2	yes	complemented
45	#16812667	C₂²	1	4	yes	—
46	C₄×Dic₂₁₈	C₂²	1	2	yes	complemented
47	C₄×Dic₂₁₈	C₂²	1	2	yes	complemented
48	C₄×Dic₂₁₈	C₂²	1	2	yes	complemented
49	C₄×D₄₃₆	C₂²	1	1	yes	characteristic
50	C₄×D₄₃₆	C₂²	1	2	yes	—
51	C₄×D₄₃₆	C₂²	1	2	yes	—
52	C₄×D₄₃₆	C₂²	1	1	yes	characteristic
53	C₄×D₄₃₆	C₂²	1	1	yes	characteristic
54	C₄×D₄₃₆	C₂²	1	2	yes	—
55	C₄×D₄₃₆	C₂²	1	1	yes	characteristic
56	C₄×C₂²⋊D₁₀₉	C₂²	1	4	yes	complemented
57	C₄×C₂²⋊D₁₀₉	C₂²	1	4	yes	complemented
58	C₄×C₂²⋊D₁₀₉	C₂²	1	4	yes	complemented
59	#16812658	C₂²	1	2	yes	—
60	#16812658	C₂²	1	2	yes	complemented
61	#16812657	C₂²	1	2	yes	complemented
62	#16812657	C₂²	1	2	yes	complemented
63	#16812656	C₂²	1	4	yes	complemented
64	#16812656	C₂²	1	4	yes	complemented
65	#16812655	C₂²	1	4	yes	—
66	C₂×C₄⋊Dic₁₀₉	C₂²	1	1	yes	characteristic
67	C₄⋊C₄×D₁₀₉	C₂²	1	2	yes	complemented
68	C₄⋊C₄×D₁₀₉	C₂²	1	2	yes	complemented
69	C₂×#13182006	C₂²	1	2	yes	—
70	C₂²⋊C₄×D₁₀₉	C₂²	1	4	yes	—
71	C₄²×D₁₀₉	C₂²	1	4	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	8	no	—
85	C₂×Dic₂₁₈	C₂³	1	2	yes	—
86	C₂×Dic₂₁₈	C₂³	1	2	yes	—
87	C₂×D₄₃₆	—	2	4	no	—
88	C₂×D₄₃₆	C₂³	1	2	yes	—
89	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
90	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
91	C₂×C₂²⋊D₁₀₉	C₂³	1	4	yes	—
92	C₂×C₂²⋊D₁₀₉	C₂³	1	4	yes	—
93	C₂²×Dic₁₀₉	C₂³	1	2	yes	—
94	C₂×C₄×D₁₀₉	—	2	8	no	—
95	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
96	C₂×C₄×D₁₀₉	C₂³	1	4	yes	—
97	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
98	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
99	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
100	C₂×C₄×D₁₀₉	C₂³	1	4	yes	—
101	C₄⋊Dic₁₀₉	C₂³	1	2	yes	—
102	C₄⋊Dic₁₀₉	C₂³	1	2	yes	—
103	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
104	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
105	C₄⋊Dic₁₀₉	C₂³	1	2	yes	—
106	C₄⋊Dic₁₀₉	C₂³	1	2	yes	—
107	C₄⋊Dic₁₀₉	C₂³	1	2	yes	—
108	#13182008	C₂³	1	4	yes	—
109	#13182008	C₂³	1	4	yes	—
110	#13182008	C₂³	1	4	yes	—
111	#13182008	C₂³	1	4	yes	—
112	#13182008	C₂³	1	4	yes	—
113	#13182008	C₂³	1	4	yes	—
114	C₂²⋊Dic₁₀₉	C₂³	1	4	yes	—
115	C₂²⋊Dic₁₀₉	C₂³	1	4	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	2	yes	—
122	#13182006	C₂³	1	2	yes	—
123	#13182006	C₂³	1	4	yes	—
124	#13182006	C₂³	1	4	yes	—
125	C₄×Dic₁₀₉	C₂³	1	4	yes	—
126	C₄×Dic₁₀₉	C₂³	1	4	yes	—
127	C₄×Dic₁₀₉	C₂³	1	4	yes	—
128	#41×C₁₀₉	—	2	4	no	—
129	C₂×Q₈×C₁₀₉	C₂³	1	1	yes	characteristic
130	C₂×D₄×C₁₀₉	C₂³	1	2	yes	—
131	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
132	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
133	C₂²×C₄×C₁₀₉	C₂³	1	2	yes	—
134	C₂²×C₄×C₁₀₉	C₂³	1	2	yes	—
135	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
136	C₂²×C₄×C₁₀₉	C₂³	1	2	yes	—
137	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
138	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
139	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
140	C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
141	C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
142	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
143	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
144	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
145	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
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	2	yes	—
150	C₄²×C₁₀₉	C₂³	1	2	yes	—
151	C₄²×C₁₀₉	C₂³	1	2	yes	—
152	C₂³×C₁₀₉	C₂⁴	1	2	yes	—
153	C₂³×C₁₀₉	C₂⁴	1	1	yes	characteristic
154	C₂²×D₁₀₉	—	2	4	no	—
155	C₂²×D₁₀₉	—	2	4	no	—
156	C₂²×D₁₀₉	—	4	2	no	—
157	C₂²×D₁₀₉	C₂⁴	1	2	yes	—
158	C₂²×D₁₀₉	C₂⁴	1	2	yes	—
159	Q₈×C₁₀₉	—	2	2	no	—
160	D₄×C₁₀₉	—	2	4	no	—
161	D₄×C₁₀₉	—	2	2	no	—
162	C₂×C₄×C₁₀₉	—	2	4	no	—
163	C₂×C₄×C₁₀₉	—	2	2	no	—
164	C₂×C₄×C₁₀₉	—	2	4	no	—
165	C₂×C₄×C₁₀₉	—	4	1	no	—
166	C₂×C₄×C₁₀₉	—	4	2	no	—
167	C₂×C₄×C₁₀₉	#41	1	4	yes	complemented
168	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
169	C₂×C₄×C₁₀₉	C₂⁴	1	2	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	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
174	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
175	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
176	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
177	C₂²⋊D₁₀₉	—	2	8	no	—
178	C₂²⋊D₁₀₉	—	4	4	no	—
179	C₂×Dic₁₀₉	—	2	4	no	—
180	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
181	C₂×Dic₁₀₉	C₂⁴	1	4	yes	—
182	C₂×Dic₁₀₉	C₂⁴	1	4	yes	—
183	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
184	D₄₃₆	—	2	4	no	—
185	D₄₃₆	—	2	2	no	—
186	D₄₃₆	#41	1	4	yes	complemented
187	C₄×D₁₀₉	—	2	8	no	—
188	C₄×D₁₀₉	—	2	4	no	—
189	C₄×D₁₀₉	—	2	4	no	—
190	C₄×D₁₀₉	—	2	4	no	—
191	C₄×D₁₀₉	—	2	4	no	—
192	C₄×D₁₀₉	—	4	4	no	—
193	Dic₂₁₈	—	2	4	no	—
194	Dic₂₁₈	—	4	2	no	—
195	C₂²×C₁₀₉	—	2	1	no	—
196	C₂²×C₁₀₉	—	2	1	no	—
197	C₂²×C₁₀₉	—	2	2	no	—
198	C₂²×C₁₀₉	—	2	2	no	—
199	C₂²×C₁₀₉	—	2	2	no	—
200	C₂²×C₁₀₉	C₂×#41	1	2	yes	—
201	C₂²×C₁₀₉	C₂⁵	1	1	yes	characteristic
202	C₂×D₁₀₉	—	2	2	no	—
203	C₂×D₁₀₉	—	2	2	no	—
204	C₂×D₁₀₉	—	2	2	no	—
205	C₂×D₁₀₉	—	2	2	no	—
206	C₂×D₁₀₉	—	2	2	no	—
207	C₂×D₁₀₉	—	4	8	no	—
208	C₂×D₁₀₉	C₂×#41	1	4	yes	—
209	C₄×C₁₀₉	—	2	2	no	—
210	C₄×C₁₀₉	—	2	1	no	—
211	C₄×C₁₀₉	—	2	2	no	—
212	C₄×C₁₀₉	—	2	1	no	—
213	C₄×C₁₀₉	—	2	2	no	—
214	C₄×C₁₀₉	—	2	1	no	—
215	C₄×C₁₀₉	C₂×#41	1	2	yes	—
216	C₄×C₁₀₉	C₂×#41	1	2	yes	—
217	C₄×C₁₀₉	C₂×#41	1	2	yes	—
218	Dic₁₀₉	—	2	4	no	—
219	Dic₁₀₉	—	2	2	no	—
220	Dic₁₀₉	—	2	2	no	—
221	Dic₁₀₉	—	2	4	no	—
222	C₂×C₁₀₉	—	2	2	no	—
223	C₂×C₁₀₉	—	4	2	no	—
224	C₂×C₁₀₉	C₂²×#41	1	1	yes	characteristic
225	C₂×C₁₀₉	C₂²×#41	1	1	yes	characteristic
226	C₂×C₁₀₉	#585	1	1	yes	characteristic
227	D₁₀₉	—	2	4	no	—
228	D₁₀₉	—	4	2	no	—
229	#3475	—	109	1	no	maximal, Sylow
230	C₁₀₉	#3475	1	1	yes	characteristic, complemented, Sylow
231	#556	—	109	1	no	—
232	#555	—	109	1	no	—
233	#554	—	109	1	no	—
234	#553	—	109	2	no	—
235	#552	—	109	2	no	—
236	#552	—	109	2	no	—
237	#551	—	109	4	no	—
238	#547	—	109	1	no	—
239	#546	—	109	2	no	—
240	#533	—	109	1	no	—
241	#529	—	109	4	no	—
242	#529	—	109	2	no	—
243	#525	—	109	2	no	—
244	C₄×#41	—	109	2	no	—
245	C₄×#41	D₁₀₉	1	1	yes	characteristic, complemented
246	C₂×C₄×D₄	—	109	1	no	—
247	C₂×#117	—	109	2	no	—
248	C₂×#41	—	109	2	no	—
249	C₂×#41	C₂×D₁₀₉	1	1	yes	characteristic
250	C₂²×D₄	—	109	1	no	—
251	C₂³×C₄	—	109	2	no	—
252	C₄⋊Q₈	—	109	1	no	—
253	C₄⋊Q₈	—	109	1	no	—
254	#126	—	109	4	no	—
255	#126	—	109	4	no	—
256	#126	—	109	4	no	—
257	#125	—	109	4	no	—
258	#125	—	109	2	no	—
259	#125	—	109	2	no	—
260	#124	—	109	4	no	—
261	#124	—	109	2	no	—
262	#123	—	109	4	no	—
263	#123	—	109	4	no	—
264	#123	—	109	4	no	—
265	#123	—	109	4	no	—
266	C₂²⋊Q₈	—	109	2	no	—
267	C₂²⋊Q₈	—	109	2	no	—
268	C₂²⋊Q₈	—	109	2	no	—
269	C₂²⋊Q₈	—	109	2	no	—
270	C₂²⋊Q₈	—	109	2	no	—
271	C₂²⋊Q₈	—	109	4	no	—
272	#121	—	109	2	no	—
273	#121	—	109	2	no	—
274	#121	—	109	2	no	—
275	#121	—	109	4	no	—
276	#120	—	109	4	no	—
277	C₄×Q₈	—	109	2	no	—
278	C₄×Q₈	—	109	2	no	—
279	C₄×Q₈	—	109	2	no	—
280	C₄×Q₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
281	C₄×Q₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
282	C₄×D₄	—	109	4	no	—
283	C₄×D₄	—	109	4	no	—
284	C₄×D₄	—	109	4	no	—
285	C₄×D₄	—	109	1	no	—
286	C₄×D₄	—	109	1	no	—
287	C₄×D₄	—	109	2	no	—
288	C₄×D₄	—	109	1	no	—
289	C₄×D₄	—	109	2	no	—
290	C₄×D₄	—	109	1	no	—
291	C₄×D₄	—	109	2	no	—
292	C₄×D₄	C₂×D₁₀₉	1	2	yes	—
293	C₄×D₄	C₂×D₁₀₉	1	2	yes	—
294	C₄×D₄	C₂×D₁₀₉	1	1	yes	characteristic, complemented
295	C₄×D₄	C₂×D₁₀₉	1	1	yes	characteristic, complemented
296	#117	—	109	2	no	—
297	#117	—	109	2	no	—
298	#117	—	109	2	no	—
299	#117	—	109	2	no	—
300	#117	—	109	4	no	—
301	#117	—	109	4	no	—
302	#117	—	109	4	no	—
303	#117	C₂×D₁₀₉	1	1	yes	characteristic
304	#117	C₂×D₁₀₉	1	2	yes	complemented
305	C₂×C₄⋊C₄	—	109	1	no	—
306	C₂×C₄⋊C₄	—	109	2	no	—
307	C₂×C₄⋊C₄	—	109	2	no	—
308	C₂×C₂²⋊C₄	—	109	2	no	—
309	C₂×C₂²⋊C₄	—	109	4	no	—
310	C₂×C₄²	—	109	4	no	—
311	C₂×C₄²	C₂×D₁₀₉	1	1	yes	characteristic
312	C₂×C₄²	C₂×D₁₀₉	1	2	yes	complemented
313	C₂⁴	—	109	2	no	—
314	#41	—	2	4	no	—
315	#41	—	218	8	no	—
316	C₂×Q₈	—	109	2	no	—
317	C₂×Q₈	—	109	2	no	—
318	C₂×Q₈	C₂²×D₁₀₉	1	1	yes	characteristic
319	C₂×D₄	—	109	4	no	—
320	C₂×D₄	—	109	4	no	—
321	C₂×D₄	—	109	1	no	—
322	C₂×D₄	—	109	2	no	—
323	C₂×D₄	—	109	1	no	—
324	C₂×D₄	—	218	4	no	—
325	C₂×D₄	C₂²×D₁₀₉	1	2	yes	—
326	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
327	C₂²×C₄	—	109	2	no	—
328	C₂²×C₄	—	109	4	no	—
329	C₂²×C₄	—	109	4	no	—
330	C₂²×C₄	—	109	2	no	—
331	C₂²×C₄	—	109	2	no	—
332	C₂²×C₄	—	109	2	no	—
333	C₂²×C₄	—	109	2	no	—
334	C₂²×C₄	—	218	8	no	—
335	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
336	C₂²×C₄	C₂²×D₁₀₉	1	2	yes	—
337	C₂²×C₄	C₂²×D₁₀₉	1	2	yes	—
338	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
339	C₂²×C₄	C₂²×D₁₀₉	1	2	yes	—
340	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
341	C₄⋊C₄	—	109	4	no	—
342	C₄⋊C₄	—	109	4	no	—
343	C₄⋊C₄	—	109	4	no	—
344	C₄⋊C₄	—	109	4	no	—
345	C₄⋊C₄	—	109	4	no	—
346	C₄⋊C₄	—	109	4	no	—
347	C₄⋊C₄	—	109	1	no	—
348	C₄⋊C₄	—	109	2	no	—
349	C₄⋊C₄	—	109	2	no	—
350	C₄⋊C₄	—	109	1	no	—
351	C₄⋊C₄	—	109	2	no	—
352	C₄⋊C₄	—	109	2	no	—
353	C₄⋊C₄	—	109	2	no	—
354	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
355	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
356	C₄⋊C₄	C₂²×D₁₀₉	1	2	yes	—
357	C₄⋊C₄	C₂²×D₁₀₉	1	2	yes	—
358	C₂²⋊C₄	—	109	4	no	—
359	C₂²⋊C₄	—	109	4	no	—
360	C₂²⋊C₄	—	109	4	no	—
361	C₂²⋊C₄	—	109	2	no	—
362	C₂²⋊C₄	—	109	4	no	—
363	C₂²⋊C₄	—	109	4	no	—
364	C₂²⋊C₄	—	109	2	no	—
365	C₂²⋊C₄	—	109	2	no	—
366	C₂²⋊C₄	—	109	2	no	—
367	C₂²⋊C₄	—	109	4	no	—
368	C₂²⋊C₄	—	109	4	no	—
369	C₂²⋊C₄	C₂²×D₁₀₉	1	2	yes	—
370	C₂²⋊C₄	C₂²×D₁₀₉	1	2	yes	—
371	C₂²⋊C₄	C₂²×D₁₀₉	1	2	yes	—
372	C₄²	—	109	4	no	—
373	C₄²	—	109	4	no	—
374	C₄²	—	109	4	no	—
375	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic
376	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic
377	C₄²	C₂²×D₁₀₉	1	2	yes	—
378	C₄²	C₂²×D₁₀₉	1	2	yes	—
379	C₄²	C₂²×D₁₀₉	1	2	yes	—
380	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic
381	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic
382	C₂³	—	109	2	no	—
383	C₂³	—	109	2	no	—
384	C₂³	—	436	2	no	—
385	C₂³	—	218	4	no	—
386	C₂³	—	218	4	no	—
387	C₂³	C₂³×D₁₀₉	1	2	yes	—
388	C₂³	C₂³×D₁₀₉	1	1	yes	characteristic
389	Q₈	—	2	2	no	—
390	Q₈	—	436	2	no	—
391	Q₈	—	218	4	no	—
392	D₄	—	2	4	no	—
393	D₄	—	2	2	no	—
394	D₄	—	109	4	no	—
395	D₄	—	436	4	no	—
396	D₄	—	218	4	no	—
397	D₄	—	218	8	no	—
398	D₄	—	218	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	109	2	no	—
405	C₂×C₄	—	109	4	no	—
406	C₂×C₄	—	109	4	no	—
407	C₂×C₄	—	109	2	no	—
408	C₂×C₄	—	436	4	no	—
409	C₂×C₄	—	218	8	no	—
410	C₂×C₄	—	218	4	no	—
411	C₂×C₄	—	218	4	no	—
412	C₂×C₄	—	218	4	no	—
413	C₂×C₄	—	218	4	no	—
414	C₂×C₄	—	218	4	no	—
415	C₂×C₄	#13182029	1	4	yes	complemented
416	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
417	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
418	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
419	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
420	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
421	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
422	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
423	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
424	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
425	C₂²	—	2	1	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	2	2	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	109	4	no	—
431	C₂²	—	436	8	no	—
432	C₂²	—	218	2	no	—
433	C₂²	—	218	2	no	—
434	C₂²	—	218	2	no	—
435	C₂²	—	218	2	no	—
436	C₂²	—	218	2	no	—
437	C₂²	C₂×#13182029	1	2	yes	—
438	C₂²	C₂⁴×D₁₀₉	1	1	yes	characteristic
439	C₄	—	2	2	no	—
440	C₄	—	2	1	no	—
441	C₄	—	2	2	no	—
442	C₄	—	2	1	no	—
443	C₄	—	2	2	no	—
444	C₄	—	2	1	no	—
445	C₄	—	218	4	no	—
446	C₄	—	218	2	no	—
447	C₄	—	218	2	no	—
448	C₄	—	218	4	no	—
449	C₄	#41×D₁₀₉	1	2	yes	—
450	C₄	C₂×#13182029	1	2	yes	—
451	C₄	C₂×#13182029	1	2	yes	—
452	C₂	—	2	2	no	—
453	C₂	—	4	2	no	—
454	C₂	—	436	2	no	—
455	C₂	—	218	4	no	—
456	C₂	C₂×#41×D₁₀₉	1	1	yes	characteristic
457	C₂	C₂²×#13182029	1	1	yes	characteristic
458	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	#3475
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. #20295749	C₂	semidirect
2. #20295741	C₂	semidirect
3. #20295736	C₂	semidirect
4. #20295726	C₂	semidirect
5. #20295717	C₂	semidirect
6. #20295716	C₂	semidirect
7. #20295705	C₂	semidirect
8. #20295681	C₂	semidirect
9. #20295672	C₂	semidirect
10. #20295583	C₂	semidirect
11. #20295560	C₂	semidirect
12. #20295554	C₂	semidirect
13. #20295533	C₂	semidirect
14. C₄×#13182029	C₂	semidirect
15. C₂×C₄×D₄₃₆	C₂	semidirect
16. #117×D₁₀₉	C₂	semidirect
17. C₄×#41×C₁₀₉	C₂	semidirect
21. #16812699	C₂²	semidirect
22. #16812699	C₂²	semidirect
23. #16812694	C₂²	semidirect
24. #16812693	C₂²	semidirect
25. #16812692	C₂²	semidirect
26. #16812691	C₂²	semidirect
27. #16812691	C₂²	semidirect
28. #16812689	C₂²	semidirect
30. #16812685	C₂²	semidirect
32. #16812682	C₂²	semidirect
33. #16812681	C₂²	semidirect
37. #16812678	C₂²	semidirect
38. #16812677	C₂²	semidirect
39. #16812675	C₂²	semidirect
40. #16812675	C₂²	semidirect
43. #16812670	C₂²	semidirect
44. #16812670	C₂²	semidirect
46. C₄×Dic₂₁₈	C₂²	semidirect
47. C₄×Dic₂₁₈	C₂²	semidirect
48. C₄×Dic₂₁₈	C₂²	semidirect
56. C₄×C₂²⋊D₁₀₉	C₂²	semidirect
57. C₄×C₂²⋊D₁₀₉	C₂²	semidirect
58. C₄×C₂²⋊D₁₀₉	C₂²	semidirect
60. #16812658	C₂²	semidirect
61. #16812657	C₂²	semidirect
62. #16812657	C₂²	semidirect
63. #16812656	C₂²	semidirect
64. #16812656	C₂²	semidirect
67. C₄⋊C₄×D₁₀₉	C₂²	semidirect
68. C₄⋊C₄×D₁₀₉	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
167. C₂×C₄×C₁₀₉	#41	semidirect
186. D₄₃₆	#41	semidirect
230. C₁₀₉	#3475	semidirect
245. C₄×#41	D₁₀₉	semidirect
280. C₄×Q₈	C₂×D₁₀₉	semidirect
281. C₄×Q₈	C₂×D₁₀₉	semidirect
294. C₄×D₄	C₂×D₁₀₉	semidirect
295. C₄×D₄	C₂×D₁₀₉	semidirect
304. #117	C₂×D₁₀₉	semidirect
312. C₂×C₄²	C₂×D₁₀₉	semidirect
415. 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
#20295749	2
#20295741	2
#20295736	2
#20295726	2
#20295717	2
#20295716	2
#20295705	2
#20295681	2
#20295672	2
#20295583	2
#20295560	2
#20295554	2
#20295533	2
C₄×#13182029	2
C₂×C₄×D₄₃₆	2
#117×D₁₀₉	2
C₄×#41×C₁₀₉	2
#3475	109