Subgroups — #22624263

Order 9344.

1260 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989327	C₂	1	2	yes	maximal, complemented
2	#17989325	C₂	1	2	yes	maximal, complemented
3	#17989319	C₂	1	1	yes	maximal, characteristic, complemented
4	#17989258	C₂	1	1	yes	maximal, characteristic, complemented
5	#17989256	C₂	1	1	yes	maximal, characteristic, complemented
6	#17989228	C₂	1	1	yes	maximal, characteristic, complemented
7	#17989227	C₂	1	2	yes	maximal, complemented
8	D₄×D₂₉₂	C₂	1	1	yes	maximal, characteristic, complemented
9	#17989221	C₂	1	1	yes	maximal, characteristic, complemented
10	D₄×C₂²⋊D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
11	#17989219	C₂	1	2	yes	maximal, complemented
12	#17989190	C₂	1	1	yes	maximal, characteristic, complemented
13	#17989189	C₂	1	2	yes	maximal, complemented
14	#17989188	C₂	1	1	yes	maximal, characteristic, complemented
15	#17989155	C₂	1	1	yes	maximal, characteristic, complemented
16	#17989153	C₂	1	2	yes	maximal, complemented
17	#17989151	C₂	1	1	yes	maximal, characteristic, complemented
18	#17989149	C₂	1	2	yes	maximal, complemented
19	#17989147	C₂	1	2	yes	maximal, complemented
20	C₂×#14556587	C₂	1	1	yes	maximal, characteristic, complemented
21	#17989123	C₂	1	1	yes	maximal, characteristic, complemented
22	#17989117	C₂	1	1	yes	maximal, characteristic, complemented
23	#546×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#11924029	C₂²	1	1	yes	characteristic, complemented
25	C₂×#11924028	C₂²	1	2	yes	complemented
26	C₂²×D₂₉₂	C₂²	1	1	yes	characteristic, complemented
27	C₂²×D₂₉₂	C₂²	1	1	yes	characteristic, complemented
28	C₂²×C₂²⋊D₇₃	C₂²	1	2	yes	complemented
29	C₂²×C₂²⋊D₇₃	C₂²	1	2	yes	complemented
30	C₂²×C₂²⋊D₇₃	C₂²	1	2	yes	complemented
31	C₂×D₄×D₇₃	C₂²	1	2	yes	complemented
32	C₂×D₄×D₇₃	C₂²	1	2	yes	complemented
33	C₂×D₄×D₇₃	C₂²	1	1	yes	characteristic, complemented
34	#14556588	C₂²	1	1	yes	characteristic, complemented
35	#14556587	C₂²	1	1	yes	characteristic
36	#14556587	C₂²	1	1	yes	characteristic, complemented
37	#14556587	C₂²	1	2	yes	complemented
38	#14556587	C₂²	1	1	yes	characteristic, complemented
39	#14556587	C₂²	1	1	yes	characteristic, complemented
40	#14556587	C₂²	1	2	yes	complemented
41	#14556587	C₂²	1	1	yes	characteristic, complemented
42	#14556587	C₂²	1	2	yes	complemented
43	#14556586	C₂²	1	2	yes	complemented
44	#14556586	C₂²	1	1	yes	characteristic, complemented
45	#14556584	C₂²	1	1	yes	characteristic, complemented
46	#14556582	C₂²	1	1	yes	characteristic, complemented
47	#14556581	C₂²	1	1	yes	characteristic, complemented
48	#14556580	C₂²	1	1	yes	characteristic, complemented
49	#14556580	C₂²	1	1	yes	characteristic, complemented
50	#14556577	C₂²	1	1	yes	characteristic, complemented
51	#14556577	C₂²	1	2	yes	complemented
52	#14556576	C₂²	1	2	yes	complemented
53	#14556575	C₂²	1	2	yes	complemented
54	#14556575	C₂²	1	1	yes	characteristic, complemented
55	#14556575	C₂²	1	2	yes	complemented
56	#14556575	C₂²	1	2	yes	complemented
57	#14556574	C₂²	1	2	yes	complemented
58	#14556573	C₂²	1	2	yes	complemented
59	#14556573	C₂²	1	2	yes	complemented
60	#14556573	C₂²	1	2	yes	complemented
61	#14556572	C₂²	1	1	yes	characteristic, complemented
62	#14556568	C₂²	1	1	yes	characteristic, complemented
63	#14556566	C₂²	1	2	yes	complemented
64	#14556566	C₂²	1	1	yes	characteristic, complemented
65	#14556566	C₂²	1	2	yes	complemented
66	#14556565	C₂²	1	1	yes	characteristic
67	#14556565	C₂²	1	2	yes	complemented
68	#14556565	C₂²	1	2	yes	complemented
69	#14556565	C₂²	1	2	yes	complemented
70	#14556565	C₂²	1	2	yes	complemented
71	#14556565	C₂²	1	2	yes	complemented
72	#14556565	C₂²	1	1	yes	characteristic, complemented
73	#14556564	C₂²	1	2	yes	complemented
74	#14556564	C₂²	1	2	yes	complemented
75	#14556564	C₂²	1	2	yes	complemented
76	#14556564	C₂²	1	2	yes	complemented
77	#14556564	C₂²	1	2	yes	complemented
78	#14556564	C₂²	1	2	yes	complemented
79	#14556563	C₂²	1	1	yes	characteristic
80	#14556563	C₂²	1	2	yes	complemented
81	#14556563	C₂²	1	2	yes	complemented
82	#14556562	C₂²	1	2	yes	complemented
83	#14556562	C₂²	1	2	yes	complemented
84	#14556562	C₂²	1	1	yes	characteristic, complemented
85	#14556561	C₂²	1	2	yes	complemented
86	#14556561	C₂²	1	2	yes	complemented
87	#14556561	C₂²	1	2	yes	complemented
88	#14556561	C₂²	1	2	yes	complemented
89	#14556561	C₂²	1	2	yes	complemented
90	#14556561	C₂²	1	2	yes	complemented
91	#14556560	C₂²	1	2	yes	complemented
92	#14556559	C₂²	1	2	yes	complemented
93	#14556559	C₂²	1	2	yes	complemented
94	#14556559	C₂²	1	2	yes	complemented
95	#14556559	C₂²	1	2	yes	complemented
96	Q₈×Dic₇₃	C₂²	1	1	yes	characteristic, complemented
97	C₄×Dic₁₄₆	C₂²	1	1	yes	characteristic, complemented
98	C₄×D₂₉₂	C₂²	1	1	yes	characteristic, complemented
99	D₄×Dic₇₃	C₂²	1	1	yes	characteristic, complemented
100	#14556553	C₂²	1	1	yes	characteristic, complemented
101	#14556553	C₂²	1	1	yes	characteristic, complemented
102	C₄×C₂²⋊D₇₃	C₂²	1	2	yes	complemented
103	C₄×C₂²⋊D₇₃	C₂²	1	1	yes	characteristic, complemented
104	C₄×C₂²⋊D₇₃	C₂²	1	1	yes	characteristic, complemented
105	#14556551	C₂²	1	2	yes	complemented
106	#14556551	C₂²	1	2	yes	complemented
107	#14556550	C₂²	1	1	yes	characteristic, complemented
108	#14556549	C₂²	1	2	yes	complemented
109	#14556548	C₂²	1	1	yes	characteristic, complemented
110	C₂²⋊C₄×D₇₃	C₂²	1	2	yes	complemented
111	C₂×C₄×Dic₇₃	C₂²	1	1	yes	characteristic, complemented
112	C₂×#41×C₇₃	C₂²	1	1	yes	characteristic, complemented
113	C₂²×D₄×C₇₃	C₂²	1	1	yes	characteristic, complemented
114	#124×C₇₃	C₂²	1	1	yes	characteristic, complemented
115	#123×C₇₃	C₂²	1	2	yes	complemented
116	C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
117	#121×C₇₃	C₂²	1	2	yes	complemented
118	#121×C₇₃	C₂²	1	1	yes	characteristic, complemented
119	#120×C₇₃	C₂²	1	2	yes	complemented
120	C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	complemented
123	C₂³×D₇₃	C₂³	1	2	yes	—
124	C₂³×D₇₃	C₂³	1	2	yes	—
125	C₂³×D₇₃	C₂³	1	2	yes	—
126	#11924029	—	4	2	no	—
127	#11924028	—	4	4	no	—
128	C₂×Dic₁₄₆	C₂³	1	1	yes	characteristic
129	C₂×D₂₉₂	—	4	2	no	—
130	C₂×D₂₉₂	—	4	2	no	—
131	C₂×D₂₉₂	C₂³	1	1	yes	characteristic
132	C₂×D₂₉₂	C₂³	1	1	yes	characteristic
133	C₂×D₂₉₂	C₂³	1	1	yes	characteristic
134	C₂×D₂₉₂	C₂³	1	2	yes	—
135	C₂×D₂₉₂	C₂³	1	2	yes	—
136	C₂×D₂₉₂	C₂³	1	2	yes	—
137	C₂×D₂₉₂	C₂³	1	2	yes	—
138	C₂×D₂₉₂	C₂³	1	2	yes	—
139	C₂×D₂₉₂	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₇₃	—	4	4	no	—
141	C₂×C₂²⋊D₇₃	—	4	4	no	—
142	C₂×C₂²⋊D₇₃	—	4	4	no	—
143	C₂×C₂²⋊D₇₃	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₇₃	C₂³	1	2	yes	—
145	C₂×C₂²⋊D₇₃	C₂³	1	1	yes	characteristic
146	C₂×C₂²⋊D₇₃	C₂³	1	1	yes	characteristic
147	C₂×C₂²⋊D₇₃	C₂³	1	2	yes	—
148	C₂×C₂²⋊D₇₃	C₂³	1	2	yes	—
149	C₂×C₂²⋊D₇₃	C₂³	1	2	yes	—
150	C₂×C₂²⋊D₇₃	C₂³	1	2	yes	—
151	C₂×C₂²⋊D₇₃	C₂³	1	2	yes	—
152	C₂×C₂²⋊D₇₃	C₂³	1	2	yes	—
153	C₂×C₂²⋊D₇₃	C₂³	1	2	yes	—
154	C₂×C₂²⋊D₇₃	C₂³	1	2	yes	—
155	C₂×C₂²⋊D₇₃	C₂³	1	2	yes	—
156	C₂×C₂²⋊D₇₃	C₂³	1	2	yes	—
157	C₂×C₂²⋊D₇₃	C₂³	1	2	yes	—
158	C₂×C₂²⋊D₇₃	C₂³	1	2	yes	—
159	D₄×D₇₃	—	4	2	no	—
160	D₄×D₇₃	—	4	4	no	—
161	D₄×D₇₃	—	4	4	no	—
162	C₂²×Dic₇₃	C₂³	1	1	yes	characteristic
163	C₂²×Dic₇₃	C₂³	1	1	yes	characteristic
164	C₂²×Dic₇₃	C₂³	1	2	yes	—
165	C₂×C₄×D₇₃	C₂³	1	1	yes	characteristic
166	C₂×C₄×D₇₃	C₂³	1	2	yes	—
167	C₂×C₄×D₇₃	C₂³	1	2	yes	—
168	C₂×C₄×D₇₃	C₂³	1	2	yes	—
169	C₂×C₄×D₇₃	C₂³	1	2	yes	—
170	C₄⋊Dic₇₃	C₂³	1	2	yes	—
171	C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
172	C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
173	C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
174	C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
175	C₄⋊Dic₇₃	C₂³	1	2	yes	—
176	#11924007	C₂³	1	1	yes	characteristic
177	#11924007	C₂³	1	1	yes	characteristic
178	#11924007	C₂³	1	1	yes	characteristic
179	#11924007	C₂³	1	2	yes	—
180	#11924007	C₂³	1	1	yes	characteristic
181	#11924007	C₂³	1	1	yes	characteristic
182	#11924007	C₂³	1	1	yes	characteristic
183	C₂²⋊Dic₇₃	C₂³	1	1	yes	characteristic
184	C₂²⋊Dic₇₃	C₂³	1	1	yes	characteristic
185	C₂²⋊Dic₇₃	C₂³	1	1	yes	characteristic
186	C₂²⋊Dic₇₃	C₂³	1	1	yes	characteristic
187	C₂²⋊Dic₇₃	C₂³	1	2	yes	—
188	C₂²⋊Dic₇₃	C₂³	1	2	yes	—
189	#11924005	C₂³	1	2	yes	—
190	#11924005	C₂³	1	2	yes	—
191	#11924005	C₂³	1	1	yes	characteristic
192	#11924005	C₂³	1	1	yes	characteristic
193	#11924005	C₂³	1	2	yes	—
194	#11924005	C₂³	1	2	yes	—
195	#11924005	C₂³	1	2	yes	—
196	#11924005	C₂³	1	2	yes	—
197	#11924005	C₂³	1	1	yes	characteristic
198	#11924005	C₂³	1	1	yes	characteristic
199	#11924005	C₂³	1	2	yes	—
200	#11924005	C₂³	1	2	yes	—
201	#11924005	C₂³	1	2	yes	—
202	#11924005	C₂³	1	2	yes	—
203	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
204	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
205	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
206	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
207	C₄×Dic₇₃	C₂³	1	2	yes	—
208	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
209	C₂⁴×C₇₃	C₂³	1	2	yes	—
210	#41×C₇₃	—	4	2	no	—
211	C₂×Q₈×C₇₃	C₂³	1	1	yes	characteristic
212	C₂×D₄×C₇₃	—	4	2	no	—
213	C₂×D₄×C₇₃	C₂³	1	1	yes	characteristic
214	C₂×D₄×C₇₃	C₂³	1	1	yes	characteristic
215	C₂×D₄×C₇₃	C₂³	1	1	yes	characteristic
216	C₂×D₄×C₇₃	C₂³	1	2	yes	—
217	C₂×D₄×C₇₃	C₂³	1	2	yes	—
218	C₂×D₄×C₇₃	C₂³	1	2	yes	—
219	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
220	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
221	C₂²×C₄×C₇₃	C₂³	1	2	yes	—
222	C₂²×C₄×C₇₃	C₂³	1	2	yes	—
223	C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
224	C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
225	C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
226	C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
227	C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
228	C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
229	C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
230	C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
231	C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
232	C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
233	C₄²×C₇₃	C₂³	1	1	yes	characteristic
234	C₂³×C₇₃	—	2	4	no	—
235	C₂³×C₇₃	—	4	2	no	—
236	C₂³×C₇₃	—	4	2	no	—
237	C₂³×C₇₃	C₂⁴	1	2	yes	—
238	C₂³×C₇₃	C₂⁴	1	2	yes	—
239	C₂³×C₇₃	C₂⁴	1	1	yes	characteristic
240	C₂³×C₇₃	C₂⁴	1	1	yes	characteristic
241	C₂²×D₇₃	—	2	4	no	—
242	C₂²×D₇₃	—	4	2	no	—
243	C₂²×D₇₃	—	4	2	no	—
244	C₂²×D₇₃	—	4	2	no	—
245	C₂²×D₇₃	—	4	2	no	—
246	C₂²×D₇₃	—	4	2	no	—
247	C₂²×D₇₃	—	4	2	no	—
248	C₂²×D₇₃	—	4	2	no	—
249	C₂²×D₇₃	—	4	2	no	—
250	C₂²×D₇₃	C₂⁴	1	1	yes	characteristic
251	C₂²×D₇₃	C₂⁴	1	2	yes	—
252	C₂²×D₇₃	C₂⁴	1	2	yes	—
253	C₂²×D₇₃	C₂⁴	1	2	yes	—
254	Q₈×C₇₃	—	2	2	no	—
255	D₄×C₇₃	—	2	2	no	—
256	D₄×C₇₃	—	2	2	no	—
257	D₄×C₇₃	—	2	2	no	—
258	D₄×C₇₃	—	4	2	no	—
259	D₄×C₇₃	—	4	2	no	—
260	D₄×C₇₃	—	4	2	no	—
261	C₂×C₄×C₇₃	—	2	2	no	—
262	C₂×C₄×C₇₃	—	2	2	no	—
263	C₂×C₄×C₇₃	—	4	2	no	—
264	C₂×C₄×C₇₃	—	4	2	no	—
265	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
266	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
267	C₂×C₄×C₇₃	C₂⁴	1	2	yes	—
268	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
269	C₂×C₄×C₇₃	C₂⁴	1	2	yes	—
270	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
271	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
272	C₂²⋊D₇₃	—	2	4	no	—
273	C₂²⋊D₇₃	—	2	2	no	—
274	C₂²⋊D₇₃	—	2	2	no	—
275	C₂²⋊D₇₃	—	2	4	no	—
276	C₂²⋊D₇₃	—	2	4	no	—
277	C₂²⋊D₇₃	—	4	2	no	—
278	C₂²⋊D₇₃	—	4	2	no	—
279	C₂²⋊D₇₃	—	4	2	no	—
280	C₂²⋊D₇₃	—	4	2	no	—
281	C₂²⋊D₇₃	—	4	2	no	—
282	C₂²⋊D₇₃	—	4	2	no	—
283	C₂²⋊D₇₃	—	4	2	no	—
284	C₂²⋊D₇₃	—	4	2	no	—
285	C₂²⋊D₇₃	—	4	2	no	—
286	C₂²⋊D₇₃	—	4	2	no	—
287	C₂²⋊D₇₃	—	4	2	no	—
288	C₂×Dic₇₃	—	2	2	no	—
289	C₂×Dic₇₃	—	2	2	no	—
290	C₂×Dic₇₃	—	4	2	no	—
291	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
292	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
293	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
294	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
295	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
296	C₂×Dic₇₃	C₂⁴	1	2	yes	—
297	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
298	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
299	D₂₉₂	—	2	2	no	—
300	D₂₉₂	—	2	2	no	—
301	D₂₉₂	—	2	2	no	—
302	D₂₉₂	—	4	2	no	—
303	D₂₉₂	—	4	2	no	—
304	D₂₉₂	—	4	2	no	—
305	D₂₉₂	—	4	2	no	—
306	D₂₉₂	—	4	2	no	—
307	D₂₉₂	—	4	2	no	—
308	C₄×D₇₃	—	2	2	no	—
309	C₄×D₇₃	—	2	4	no	—
310	C₄×D₇₃	—	4	2	no	—
311	C₄×D₇₃	—	4	2	no	—
312	C₄×D₇₃	—	4	2	no	—
313	Dic₁₄₆	—	2	2	no	—
314	C₂²×C₇₃	—	2	1	no	—
315	C₂²×C₇₃	—	2	1	no	—
316	C₂²×C₇₃	—	2	2	no	—
317	C₂²×C₇₃	—	2	2	no	—
318	C₂²×C₇₃	—	2	2	no	—
319	C₂²×C₇₃	—	2	1	no	—
320	C₂²×C₇₃	—	2	2	no	—
321	C₂²×C₇₃	—	2	1	no	—
322	C₂²×C₇₃	—	2	2	no	—
323	C₂²×C₇₃	—	2	1	no	—
324	C₂²×C₇₃	—	2	2	no	—
325	C₂²×C₇₃	—	8	4	no	—
326	C₂²×C₇₃	H(5,𝔽₂)	1	2	yes	—
327	C₂²×C₇₃	C₂⁵	1	1	yes	characteristic
328	C₂×D₇₃	—	2	1	no	—
329	C₂×D₇₃	—	2	2	no	—
330	C₂×D₇₃	—	2	2	no	—
331	C₂×D₇₃	—	2	2	no	—
332	C₂×D₇₃	—	2	2	no	—
333	C₂×D₇₃	—	2	2	no	—
334	C₂×D₇₃	—	2	2	no	—
335	C₂×D₇₃	—	2	1	no	—
336	C₂×D₇₃	—	2	2	no	—
337	C₂×D₇₃	—	2	2	no	—
338	C₂×D₇₃	—	2	2	no	—
339	C₂×D₇₃	—	2	1	no	—
340	C₂×D₇₃	—	8	4	no	—
341	C₂×D₇₃	—	8	4	no	—
342	C₂×D₇₃	—	8	4	no	—
343	C₄×C₇₃	—	2	1	no	—
344	C₄×C₇₃	—	2	2	no	—
345	C₄×C₇₃	—	2	1	no	—
346	C₄×C₇₃	—	2	2	no	—
347	C₄×C₇₃	—	2	1	no	—
348	C₄×C₇₃	—	2	1	no	—
349	C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
350	Dic₇₃	—	2	1	no	—
351	Dic₇₃	—	2	1	no	—
352	Dic₇₃	—	2	2	no	—
353	Dic₇₃	—	2	1	no	—
354	Dic₇₃	—	2	1	no	—
355	Dic₇₃	—	2	1	no	—
356	Dic₇₃	—	2	1	no	—
357	Dic₇₃	H(5,𝔽₂)	1	2	yes	—
358	C₂×C₇₃	—	2	2	no	—
359	C₂×C₇₃	—	4	1	no	—
360	C₂×C₇₃	—	4	2	no	—
361	C₂×C₇₃	—	4	2	no	—
362	C₂×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
363	C₂×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
364	C₂×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
365	D₇₃	—	4	2	no	—
366	D₇₃	—	4	1	no	—
367	D₇₃	—	4	2	no	—
368	D₇₃	—	4	2	no	—
369	#3543	—	73	1	no	maximal, Sylow
370	C₇₃	#3543	1	1	yes	characteristic, complemented, Sylow
371	#560	—	73	2	no	—
372	#560	—	73	2	no	—
373	#559	—	73	1	no	—
374	#550	—	73	1	no	—
375	#550	—	73	1	no	—
376	#546	—	73	1	no	—
377	#546	—	73	2	no	—
378	#546	D₇₃	1	1	yes	characteristic, complemented
379	D₄²	—	73	1	no	—
380	D₄²	—	73	1	no	—
381	D₄²	—	73	2	no	—
382	D₄²	—	73	1	no	—
383	#540	—	73	2	no	—
384	#540	—	73	1	no	—
385	#540	—	73	1	no	—
386	#535	—	73	1	no	—
387	#535	—	73	1	no	—
388	#535	—	73	2	no	—
389	#534	—	73	2	no	—
390	#534	—	73	2	no	—
391	C₂×#127	—	73	1	no	—
392	#529	—	73	1	no	—
393	#529	—	73	1	no	—
394	C₂×#41	—	73	1	no	—
395	C₂×#41	—	73	2	no	—
396	C₂×#41	C₂×D₇₃	1	1	yes	characteristic, complemented
397	C₂²×D₄	—	73	2	no	—
398	C₂²×D₄	—	73	2	no	—
399	C₂²×D₄	—	73	2	no	—
400	C₂²×D₄	—	73	2	no	—
401	C₂²×D₄	—	73	1	no	—
402	C₂²×D₄	—	73	2	no	—
403	C₂²×D₄	—	73	1	no	—
404	C₂²×D₄	—	73	1	no	—
405	C₂²×D₄	C₂×D₇₃	1	1	yes	characteristic, complemented
406	#127	—	73	1	no	—
407	#127	—	73	1	no	—
408	#127	—	73	2	no	—
409	#127	—	73	1	no	—
410	#127	—	73	1	no	—
411	#127	—	73	2	no	—
412	#127	—	73	1	no	—
413	#127	—	73	2	no	—
414	#127	—	73	1	no	—
415	#126	—	73	2	no	—
416	#126	—	73	1	no	—
417	#126	—	73	1	no	—
418	#125	—	73	1	no	—
419	#125	—	73	1	no	—
420	#124	—	73	1	no	—
421	#124	—	73	1	no	—
422	#124	—	73	1	no	—
423	#124	—	73	2	no	—
424	#124	C₂×D₇₃	1	1	yes	characteristic, complemented
425	#123	—	73	1	no	—
426	#123	—	73	2	no	—
427	#123	—	73	2	no	—
428	#123	—	73	2	no	—
429	#123	—	73	1	no	—
430	#123	—	73	2	no	—
431	#123	—	73	2	no	—
432	#123	—	73	2	no	—
433	#123	—	73	2	no	—
434	#123	—	73	2	no	—
435	#123	C₂×D₇₃	1	2	yes	complemented
436	C₂²⋊Q₈	—	73	1	no	—
437	C₂²⋊Q₈	C₂×D₇₃	1	1	yes	characteristic, complemented
438	#121	—	73	1	no	—
439	#121	—	73	2	no	—
440	#121	—	73	2	no	—
441	#121	—	73	1	no	—
442	#121	—	73	2	no	—
443	#121	—	73	2	no	—
444	#121	—	73	1	no	—
445	#121	—	73	2	no	—
446	#121	—	73	2	no	—
447	#121	—	73	2	no	—
448	#121	—	73	2	no	—
449	#121	—	73	2	no	—
450	#121	—	73	1	no	—
451	#121	—	73	2	no	—
452	#121	—	73	1	no	—
453	#121	—	73	2	no	—
454	#121	—	73	2	no	—
455	#121	—	73	2	no	—
456	#121	—	73	2	no	—
457	#121	—	73	2	no	—
458	#121	—	73	2	no	—
459	#121	—	73	2	no	—
460	#121	C₂×D₇₃	1	2	yes	complemented
461	#121	C₂×D₇₃	1	1	yes	characteristic, complemented
462	#120	—	73	2	no	—
463	#120	—	73	2	no	—
464	#120	—	73	2	no	—
465	#120	—	73	2	no	—
466	#120	—	73	2	no	—
467	#120	—	73	2	no	—
468	#120	—	73	2	no	—
469	#120	—	73	2	no	—
470	#120	—	73	2	no	—
471	#120	—	73	2	no	—
472	#120	—	73	2	no	—
473	#120	C₂×D₇₃	1	2	yes	complemented
474	C₄×Q₈	—	73	1	no	—
475	C₄×Q₈	—	73	1	no	—
476	C₄×D₄	—	73	1	no	—
477	C₄×D₄	—	73	1	no	—
478	C₄×D₄	—	73	1	no	—
479	C₄×D₄	—	73	2	no	—
480	C₄×D₄	—	73	1	no	—
481	C₄×D₄	—	73	1	no	—
482	C₄×D₄	—	73	2	no	—
483	C₄×D₄	—	73	2	no	—
484	C₄×D₄	—	73	1	no	—
485	C₄×D₄	C₂×D₇₃	1	1	yes	characteristic, complemented
486	C₄×D₄	C₂×D₇₃	1	1	yes	characteristic, complemented
487	#117	—	73	1	no	—
488	#117	—	73	2	no	—
489	#117	—	73	1	no	—
490	C₂×C₂²⋊C₄	—	73	2	no	—
491	C₂×C₂²⋊C₄	C₂×D₇₃	1	2	yes	complemented
492	C₂×C₄²	—	73	1	no	—
493	C₂⁴	—	73	2	no	—
494	C₂⁴	—	73	2	no	—
495	C₂⁴	—	73	2	no	—
496	C₂⁴	C₂²×D₇₃	1	2	yes	—
497	#41	—	4	2	no	—
498	#41	—	292	4	no	—
499	#41	—	292	2	no	—
500	C₂×Q₈	—	73	1	no	—
501	C₂×Q₈	C₂²×D₇₃	1	1	yes	characteristic
502	C₂×D₄	—	4	2	no	—
503	C₂×D₄	—	292	2	no	—
504	C₂×D₄	—	292	2	no	—
505	C₂×D₄	—	292	4	no	—
506	C₂×D₄	—	292	4	no	—
507	C₂×D₄	—	292	2	no	—
508	C₂×D₄	—	292	4	no	—
509	C₂×D₄	—	292	4	no	—
510	C₂×D₄	—	292	4	no	—
511	C₂×D₄	—	73	2	no	—
512	C₂×D₄	—	73	2	no	—
513	C₂×D₄	—	73	2	no	—
514	C₂×D₄	—	73	2	no	—
515	C₂×D₄	—	73	2	no	—
516	C₂×D₄	—	73	2	no	—
517	C₂×D₄	—	73	2	no	—
518	C₂×D₄	—	73	2	no	—
519	C₂×D₄	—	73	2	no	—
520	C₂×D₄	—	73	2	no	—
521	C₂×D₄	—	73	2	no	—
522	C₂×D₄	—	73	2	no	—
523	C₂×D₄	—	73	1	no	—
524	C₂×D₄	—	73	1	no	—
525	C₂×D₄	—	73	2	no	—
526	C₂×D₄	—	73	2	no	—
527	C₂×D₄	—	73	2	no	—
528	C₂×D₄	—	73	2	no	—
529	C₂×D₄	—	73	2	no	—
530	C₂×D₄	—	73	2	no	—
531	C₂×D₄	—	73	2	no	—
532	C₂×D₄	—	73	2	no	—
533	C₂×D₄	—	73	1	no	—
534	C₂×D₄	—	73	1	no	—
535	C₂×D₄	—	73	1	no	—
536	C₂×D₄	C₂²×D₇₃	1	1	yes	characteristic
537	C₂×D₄	C₂²×D₇₃	1	1	yes	characteristic
538	C₂×D₄	C₂²×D₇₃	1	1	yes	characteristic
539	C₂×D₄	C₂²×D₇₃	1	2	yes	—
540	C₂×D₄	C₂²×D₇₃	1	2	yes	—
541	C₂×D₄	C₂²×D₇₃	1	2	yes	—
542	C₂²×C₄	—	73	2	no	—
543	C₂²×C₄	—	73	2	no	—
544	C₂²×C₄	—	73	2	no	—
545	C₂²×C₄	—	73	2	no	—
546	C₂²×C₄	—	73	1	no	—
547	C₂²×C₄	—	73	1	no	—
548	C₂²×C₄	—	73	2	no	—
549	C₂²×C₄	—	73	1	no	—
550	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
551	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
552	C₂²×C₄	C₂²×D₇₃	1	2	yes	—
553	C₂²×C₄	C₂²×D₇₃	1	2	yes	—
554	C₄⋊C₄	—	73	1	no	—
555	C₄⋊C₄	—	73	1	no	—
556	C₄⋊C₄	—	73	1	no	—
557	C₄⋊C₄	—	73	1	no	—
558	C₄⋊C₄	—	73	2	no	—
559	C₄⋊C₄	—	73	1	no	—
560	C₄⋊C₄	—	73	1	no	—
561	C₄⋊C₄	—	73	1	no	—
562	C₄⋊C₄	—	73	1	no	—
563	C₄⋊C₄	—	73	2	no	—
564	C₄⋊C₄	—	73	1	no	—
565	C₄⋊C₄	—	73	2	no	—
566	C₄⋊C₄	—	73	1	no	—
567	C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
568	C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
569	C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
570	C₂²⋊C₄	—	73	1	no	—
571	C₂²⋊C₄	—	73	1	no	—
572	C₂²⋊C₄	—	73	1	no	—
573	C₂²⋊C₄	—	73	1	no	—
574	C₂²⋊C₄	—	73	2	no	—
575	C₂²⋊C₄	—	73	2	no	—
576	C₂²⋊C₄	—	73	2	no	—
577	C₂²⋊C₄	—	73	2	no	—
578	C₂²⋊C₄	—	73	1	no	—
579	C₂²⋊C₄	—	73	2	no	—
580	C₂²⋊C₄	—	73	2	no	—
581	C₂²⋊C₄	—	73	1	no	—
582	C₂²⋊C₄	—	73	1	no	—
583	C₂²⋊C₄	—	73	2	no	—
584	C₂²⋊C₄	—	73	2	no	—
585	C₂²⋊C₄	—	73	1	no	—
586	C₂²⋊C₄	—	73	2	no	—
587	C₂²⋊C₄	—	73	2	no	—
588	C₂²⋊C₄	—	73	2	no	—
589	C₂²⋊C₄	—	73	2	no	—
590	C₂²⋊C₄	C₂²×D₇₃	1	2	yes	—
591	C₂²⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
592	C₂²⋊C₄	C₂²×D₇₃	1	2	yes	—
593	C₂²⋊C₄	C₂²×D₇₃	1	2	yes	—
594	C₂²⋊C₄	C₂²×D₇₃	1	2	yes	—
595	C₂²⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
596	C₂²⋊C₄	C₂²×D₇₃	1	2	yes	—
597	C₄²	—	73	1	no	—
598	C₄²	—	73	1	no	—
599	C₄²	—	73	1	no	—
600	C₄²	—	73	1	no	—
601	C₄²	—	73	2	no	—
602	C₄²	—	73	1	no	—
603	C₄²	C₂²×D₇₃	1	1	yes	characteristic
604	C₂³	—	2	4	no	—
605	C₂³	—	4	2	no	—
606	C₂³	—	4	2	no	—
607	C₂³	—	292	2	no	—
608	C₂³	—	292	2	no	—
609	C₂³	—	292	2	no	—
610	C₂³	—	292	2	no	—
611	C₂³	—	292	2	no	—
612	C₂³	—	292	2	no	—
613	C₂³	—	292	2	no	—
614	C₂³	—	292	2	no	—
615	C₂³	—	73	2	no	—
616	C₂³	—	73	1	no	—
617	C₂³	—	73	2	no	—
618	C₂³	—	73	2	no	—
619	C₂³	—	146	4	no	—
620	C₂³	C₂³×D₇₃	1	1	yes	characteristic
621	C₂³	C₂³×D₇₃	1	2	yes	—
622	C₂³	C₂³×D₇₃	1	2	yes	—
623	C₂³	C₂³×D₇₃	1	1	yes	characteristic
624	Q₈	—	2	2	no	—
625	Q₈	—	146	2	no	—
626	D₄	—	2	2	no	—
627	D₄	—	2	2	no	—
628	D₄	—	2	2	no	—
629	D₄	—	4	2	no	—
630	D₄	—	4	2	no	—
631	D₄	—	4	2	no	—
632	D₄	—	292	2	no	—
633	D₄	—	292	2	no	—
634	D₄	—	292	2	no	—
635	D₄	—	292	2	no	—
636	D₄	—	292	2	no	—
637	D₄	—	292	2	no	—
638	D₄	—	292	2	no	—
639	D₄	—	292	2	no	—
640	D₄	—	292	2	no	—
641	D₄	—	292	2	no	—
642	D₄	—	292	2	no	—
643	D₄	—	292	2	no	—
644	D₄	—	292	2	no	—
645	D₄	—	292	2	no	—
646	D₄	—	292	2	no	—
647	D₄	—	292	2	no	—
648	D₄	—	292	2	no	—
649	D₄	—	146	2	no	—
650	D₄	—	146	4	no	—
651	D₄	—	146	4	no	—
652	D₄	—	146	4	no	—
653	D₄	—	146	2	no	—
654	D₄	—	146	2	no	—
655	D₄	—	146	2	no	—
656	D₄	—	146	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	4	2	no	—
660	C₂×C₄	—	4	2	no	—
661	C₂×C₄	—	292	2	no	—
662	C₂×C₄	—	292	2	no	—
663	C₂×C₄	—	292	2	no	—
664	C₂×C₄	—	292	2	no	—
665	C₂×C₄	—	73	1	no	—
666	C₂×C₄	—	73	1	no	—
667	C₂×C₄	—	73	1	no	—
668	C₂×C₄	—	73	1	no	—
669	C₂×C₄	—	73	1	no	—
670	C₂×C₄	—	73	1	no	—
671	C₂×C₄	—	73	2	no	—
672	C₂×C₄	—	73	1	no	—
673	C₂×C₄	—	146	4	no	—
674	C₂×C₄	—	146	2	no	—
675	C₂×C₄	—	146	2	no	—
676	C₂×C₄	—	146	2	no	—
677	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
678	C₂×C₄	C₂³×D₇₃	1	2	yes	—
679	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
680	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
681	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
682	C₂×C₄	C₂³×D₇₃	1	2	yes	—
683	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
684	C₂²	—	2	1	no	—
685	C₂²	—	2	1	no	—
686	C₂²	—	2	2	no	—
687	C₂²	—	2	1	no	—
688	C₂²	—	2	2	no	—
689	C₂²	—	2	1	no	—
690	C₂²	—	2	2	no	—
691	C₂²	—	2	2	no	—
692	C₂²	—	2	2	no	—
693	C₂²	—	2	1	no	—
694	C₂²	—	2	2	no	—
695	C₂²	—	8	4	no	—
696	C₂²	—	584	4	no	—
697	C₂²	—	584	4	no	—
698	C₂²	—	584	4	no	—
699	C₂²	—	146	2	no	—
700	C₂²	—	146	2	no	—
701	C₂²	—	146	1	no	—
702	C₂²	—	146	2	no	—
703	C₂²	—	146	2	no	—
704	C₂²	—	146	1	no	—
705	C₂²	—	146	2	no	—
706	C₂²	—	146	2	no	—
707	C₂²	—	146	2	no	—
708	C₂²	—	146	2	no	—
709	C₂²	—	146	2	no	—
710	C₂²	—	146	1	no	—
711	C₂²	#14556637	1	2	yes	—
712	C₂²	C₂⁴×D₇₃	1	1	yes	characteristic
713	C₄	—	2	1	no	—
714	C₄	—	2	2	no	—
715	C₄	—	2	1	no	—
716	C₄	—	2	1	no	—
717	C₄	—	2	2	no	—
718	C₄	—	2	1	no	—
719	C₄	—	73	2	no	—
720	C₄	—	146	1	no	—
721	C₄	—	146	1	no	—
722	C₄	—	146	1	no	—
723	C₄	—	146	2	no	—
724	C₄	—	146	1	no	—
725	C₄	—	146	1	no	—
726	C₄	—	146	1	no	—
727	C₄	#14556636	1	2	yes	—
728	C₂	—	2	2	no	—
729	C₂	—	4	2	no	—
730	C₂	—	4	2	no	—
731	C₂	—	4	1	no	—
732	C₂	—	292	2	no	—
733	C₂	—	292	2	no	—
734	C₂	—	292	1	no	—
735	C₂	—	292	2	no	—
736	C₂	H(5,𝔽₂)×D₇₃	1	1	yes	characteristic
737	C₂	C₂×#14556636	1	1	yes	characteristic
738	C₂	C₂×#14556637	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇₃
commutator, socle	C₂²×C₇₃	C₂⁵
Fitting	#546×C₇₃	C₂
hypercenter	#546	D₇₃
hypocenter	C₇₃	#3543
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ #546

Complements

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

N	H ≅ G/N	type
1. #17989327	C₂	semidirect
2. #17989325	C₂	semidirect
3. #17989319	C₂	semidirect
4. #17989258	C₂	semidirect
5. #17989256	C₂	semidirect
6. #17989228	C₂	semidirect
7. #17989227	C₂	semidirect
8. D₄×D₂₉₂	C₂	semidirect
9. #17989221	C₂	semidirect
10. D₄×C₂²⋊D₇₃	C₂	semidirect
11. #17989219	C₂	semidirect
12. #17989190	C₂	semidirect
13. #17989189	C₂	semidirect
14. #17989188	C₂	semidirect
15. #17989155	C₂	semidirect
16. #17989153	C₂	semidirect
17. #17989151	C₂	semidirect
18. #17989149	C₂	semidirect
19. #17989147	C₂	semidirect
20. C₂×#14556587	C₂	semidirect
21. #17989123	C₂	semidirect
22. #17989117	C₂	semidirect
23. #546×C₇₃	C₂	semidirect
24. C₂×#11924029	C₂²	semidirect
25. C₂×#11924028	C₂²	semidirect
26. C₂²×D₂₉₂	C₂²	semidirect
27. C₂²×D₂₉₂	C₂²	semidirect
28. C₂²×C₂²⋊D₇₃	C₂²	semidirect
29. C₂²×C₂²⋊D₇₃	C₂²	semidirect
30. C₂²×C₂²⋊D₇₃	C₂²	semidirect
31. C₂×D₄×D₇₃	C₂²	semidirect
32. C₂×D₄×D₇₃	C₂²	semidirect
33. C₂×D₄×D₇₃	C₂²	semidirect
34. #14556588	C₂²	semidirect
36. #14556587	C₂²	semidirect
37. #14556587	C₂²	semidirect
38. #14556587	C₂²	semidirect
39. #14556587	C₂²	semidirect
40. #14556587	C₂²	semidirect
41. #14556587	C₂²	semidirect
42. #14556587	C₂²	semidirect
43. #14556586	C₂²	semidirect
44. #14556586	C₂²	semidirect
45. #14556584	C₂²	semidirect
46. #14556582	C₂²	semidirect
47. #14556581	C₂²	semidirect
48. #14556580	C₂²	semidirect
49. #14556580	C₂²	semidirect
50. #14556577	C₂²	semidirect
51. #14556577	C₂²	semidirect
52. #14556576	C₂²	semidirect
53. #14556575	C₂²	semidirect
54. #14556575	C₂²	semidirect
55. #14556575	C₂²	semidirect
56. #14556575	C₂²	semidirect
57. #14556574	C₂²	semidirect
58. #14556573	C₂²	semidirect
59. #14556573	C₂²	semidirect
60. #14556573	C₂²	semidirect
61. #14556572	C₂²	semidirect
62. #14556568	C₂²	semidirect
63. #14556566	C₂²	semidirect
64. #14556566	C₂²	semidirect
65. #14556566	C₂²	semidirect
67. #14556565	C₂²	semidirect
68. #14556565	C₂²	semidirect
69. #14556565	C₂²	semidirect
70. #14556565	C₂²	semidirect
71. #14556565	C₂²	semidirect
72. #14556565	C₂²	semidirect
73. #14556564	C₂²	semidirect
74. #14556564	C₂²	semidirect
75. #14556564	C₂²	semidirect
76. #14556564	C₂²	semidirect
77. #14556564	C₂²	semidirect
78. #14556564	C₂²	semidirect
80. #14556563	C₂²	semidirect
81. #14556563	C₂²	semidirect
82. #14556562	C₂²	semidirect
83. #14556562	C₂²	semidirect
84. #14556562	C₂²	semidirect
85. #14556561	C₂²	semidirect
86. #14556561	C₂²	semidirect
87. #14556561	C₂²	semidirect
88. #14556561	C₂²	semidirect
89. #14556561	C₂²	semidirect
90. #14556561	C₂²	semidirect
91. #14556560	C₂²	semidirect
92. #14556559	C₂²	semidirect
93. #14556559	C₂²	semidirect
94. #14556559	C₂²	semidirect
95. #14556559	C₂²	semidirect
96. Q₈×Dic₇₃	C₂²	semidirect
97. C₄×Dic₁₄₆	C₂²	semidirect
98. C₄×D₂₉₂	C₂²	semidirect
99. D₄×Dic₇₃	C₂²	semidirect
100. #14556553	C₂²	semidirect
101. #14556553	C₂²	semidirect
102. C₄×C₂²⋊D₇₃	C₂²	semidirect
103. C₄×C₂²⋊D₇₃	C₂²	semidirect
104. C₄×C₂²⋊D₇₃	C₂²	semidirect
105. #14556551	C₂²	semidirect
106. #14556551	C₂²	semidirect
107. #14556550	C₂²	semidirect
108. #14556549	C₂²	semidirect
109. #14556548	C₂²	semidirect
110. C₂²⋊C₄×D₇₃	C₂²	semidirect
111. C₂×C₄×Dic₇₃	C₂²	semidirect
112. C₂×#41×C₇₃	C₂²	semidirect
113. C₂²×D₄×C₇₃	C₂²	semidirect
114. #124×C₇₃	C₂²	semidirect
115. #123×C₇₃	C₂²	semidirect
116. C₂²⋊Q₈×C₇₃	C₂²	semidirect
117. #121×C₇₃	C₂²	semidirect
118. #121×C₇₃	C₂²	semidirect
119. #120×C₇₃	C₂²	semidirect
120. C₄×D₄×C₇₃	C₂²	semidirect
121. C₄×D₄×C₇₃	C₂²	semidirect
122. C₂×C₂²⋊C₄×C₇₃	C₂²	semidirect
370. C₇₃	#3543	semidirect
378. #546	D₇₃	semidirect
396. C₂×#41	C₂×D₇₃	semidirect
405. C₂²×D₄	C₂×D₇₃	semidirect
424. #124	C₂×D₇₃	semidirect
435. #123	C₂×D₇₃	semidirect
437. C₂²⋊Q₈	C₂×D₇₃	semidirect
460. #121	C₂×D₇₃	semidirect
461. #121	C₂×D₇₃	semidirect
473. #120	C₂×D₇₃	semidirect
485. C₄×D₄	C₂×D₇₃	semidirect
486. C₄×D₄	C₂×D₇₃	semidirect
491. C₂×C₂²⋊C₄	C₂×D₇₃	semidirect