Subgroups — C₆₇×#34518 #30713769

Order 17152.

2464 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#560×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2377	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2376	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2374	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2373	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2366	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2361	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2361	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2358	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#2358	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2334	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2333	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2333	C₂	1	2	yes	maximal, complemented
14	C₆₇×#2328	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2322	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2321	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#2321	C₂	1	2	yes	maximal, complemented
18	C₄×#123×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#121×C₆₇	C₂	1	2	yes	maximal, complemented
20	#560×C₆₇	C₄	1	16	yes	complemented
21	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
22	C₂×#126×C₆₇	C₂²	1	2	yes	—
23	C₂×#123×C₆₇	C₂²	1	1	yes	characteristic
24	C₂×#123×C₆₇	C₂²	1	2	yes	—
25	C₂×#121×C₆₇	C₂²	1	2	yes	—
26	C₂×#121×C₆₇	C₂²	1	2	yes	—
27	C₂×#121×C₆₇	C₂²	1	2	yes	—
28	C₂×#120×C₆₇	C₂²	1	2	yes	—
29	C₂×#120×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
36	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
37	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
38	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
39	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
40	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic, complemented
41	#390×C₆₇	C₂²	1	2	yes	—
42	#390×C₆₇	C₂²	1	2	yes	—
43	#390×C₆₇	C₂²	1	2	yes	—
44	#390×C₆₇	C₂²	1	1	yes	characteristic
45	#390×C₆₇	C₂²	1	2	yes	—
46	#390×C₆₇	C₂²	1	1	yes	characteristic, complemented
47	#390×C₆₇	C₂²	1	2	yes	complemented
48	#389×C₆₇	C₂²	1	2	yes	complemented
49	#389×C₆₇	C₂²	1	2	yes	complemented
50	#389×C₆₇	C₂²	1	2	yes	complemented
51	#388×C₆₇	C₂²	1	2	yes	—
52	#388×C₆₇	C₂²	1	2	yes	—
53	#388×C₆₇	C₂²	1	2	yes	—
54	#388×C₆₇	C₂²	1	2	yes	—
55	#388×C₆₇	C₂²	1	2	yes	—
56	#388×C₆₇	C₂²	1	2	yes	—
57	#388×C₆₇	C₂²	1	2	yes	—
58	#388×C₆₇	C₂²	1	2	yes	—
59	#388×C₆₇	C₂²	1	2	yes	—
60	#388×C₆₇	C₂²	1	2	yes	complemented
61	#388×C₆₇	C₂²	1	2	yes	complemented
62	#388×C₆₇	C₂²	1	2	yes	complemented
63	#387×C₆₇	C₂²	1	2	yes	complemented
64	#387×C₆₇	C₂²	1	2	yes	complemented
65	#387×C₆₇	C₂²	1	2	yes	complemented
66	#387×C₆₇	C₂²	1	2	yes	complemented
67	#387×C₆₇	C₂²	1	2	yes	complemented
68	#387×C₆₇	C₂²	1	2	yes	complemented
69	#386×C₆₇	C₂²	1	2	yes	—
70	#386×C₆₇	C₂²	1	1	yes	characteristic
71	#386×C₆₇	C₂²	1	2	yes	—
72	#386×C₆₇	C₂²	1	2	yes	—
73	#386×C₆₇	C₂²	1	2	yes	—
74	#386×C₆₇	C₂²	1	1	yes	characteristic
75	#386×C₆₇	C₂²	1	2	yes	—
76	#386×C₆₇	C₂²	1	2	yes	—
77	#386×C₆₇	C₂²	1	2	yes	—
78	#386×C₆₇	C₂²	1	2	yes	—
79	#386×C₆₇	C₂²	1	2	yes	complemented
80	#386×C₆₇	C₂²	1	2	yes	complemented
81	#386×C₆₇	C₂²	1	2	yes	complemented
82	#385×C₆₇	C₂²	1	1	yes	characteristic
83	#385×C₆₇	C₂²	1	2	yes	—
84	#385×C₆₇	C₂²	1	2	yes	—
85	#385×C₆₇	C₂²	1	2	yes	—
86	#385×C₆₇	C₂²	1	2	yes	—
87	#385×C₆₇	C₂²	1	1	yes	characteristic, complemented
88	#385×C₆₇	C₂²	1	2	yes	complemented
89	#382×C₆₇	C₂²	1	1	yes	characteristic, complemented
90	#381×C₆₇	C₂²	1	1	yes	characteristic, complemented
91	#381×C₆₇	C₂²	1	2	yes	complemented
92	#380×C₆₇	C₂²	1	2	yes	complemented
93	#379×C₆₇	C₂²	1	1	yes	characteristic
94	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
95	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
96	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
97	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
98	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
99	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
100	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
101	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
102	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
103	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
104	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
105	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
106	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
107	#376×C₆₇	C₂²	1	1	yes	characteristic, complemented
108	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
109	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
110	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
111	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
112	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
113	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
114	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
115	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
119	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
121	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
123	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
124	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
126	#127×C₆₇	C₂×C₄	1	8	yes	complemented
127	#126×C₆₇	C₂×C₄	1	16	yes	complemented
128	#123×C₆₇	C₂×C₄	1	8	yes	complemented
129	#123×C₆₇	C₂×C₄	1	16	yes	complemented
130	#121×C₆₇	C₂×C₄	1	16	yes	complemented
131	#121×C₆₇	C₂×C₄	1	16	yes	complemented
132	#121×C₆₇	C₂×C₄	1	16	yes	complemented
133	#120×C₆₇	C₂×C₄	1	16	yes	complemented
134	#120×C₆₇	C₂×C₄	1	8	yes	complemented
135	C₄×D₄×C₆₇	—	4	4	no	—
136	C₄×D₄×C₆₇	—	4	2	no	—
137	C₄×D₄×C₆₇	—	4	2	no	—
138	C₄×D₄×C₆₇	—	4	4	no	—
139	C₄×D₄×C₆₇	—	4	4	no	—
140	C₄×D₄×C₆₇	—	4	4	no	—
141	C₄×D₄×C₆₇	—	4	4	no	—
142	C₂×C₄⋊C₄×C₆₇	—	4	4	no	—
143	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₆₇	—	4	4	no	—
157	C₂×C₂²⋊C₄×C₆₇	—	4	2	no	—
158	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
167	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
171	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
174	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
175	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
183	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₆₇	—	4	2	no	—
186	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
187	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
189	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
190	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
191	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
192	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
193	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
195	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
196	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
197	#95×C₆₇	C₂³	1	2	yes	—
198	#95×C₆₇	C₂³	1	2	yes	—
199	#95×C₆₇	C₂³	1	2	yes	—
200	#95×C₆₇	C₂³	1	2	yes	—
201	#95×C₆₇	C₂³	1	2	yes	—
202	#95×C₆₇	C₂³	1	2	yes	—
203	#95×C₆₇	C₂³	1	2	yes	—
204	#95×C₆₇	C₂³	1	2	yes	—
205	#95×C₆₇	C₂³	1	2	yes	—
206	#95×C₆₇	C₂³	1	2	yes	—
207	#95×C₆₇	C₂³	1	2	yes	—
208	#95×C₆₇	C₂³	1	2	yes	—
209	#95×C₆₇	C₂³	1	2	yes	—
210	#95×C₆₇	C₂³	1	2	yes	—
211	#95×C₆₇	C₂³	1	2	yes	—
212	#95×C₆₇	C₂³	1	2	yes	—
213	#95×C₆₇	C₂³	1	2	yes	—
214	#95×C₆₇	C₂³	1	2	yes	—
215	C₂⁴×C₆₇	—	4	1	no	—
216	C₂⁴×C₆₇	—	4	2	no	—
217	C₂⁴×C₆₇	—	4	2	no	—
218	C₂⁴×C₆₇	—	4	1	no	—
219	C₂⁴×C₆₇	C₂²×C₄	1	4	yes	—
220	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
221	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
222	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
223	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
224	C₂×D₄×C₆₇	—	4	2	no	—
225	C₂×D₄×C₆₇	—	4	1	no	—
226	C₂×D₄×C₆₇	—	4	1	no	—
227	C₂×D₄×C₆₇	—	4	2	no	—
228	C₂×D₄×C₆₇	—	4	2	no	—
229	C₂×D₄×C₆₇	—	4	2	no	—
230	C₂×D₄×C₆₇	—	4	2	no	—
231	C₂×D₄×C₆₇	—	4	2	no	—
232	C₂×D₄×C₆₇	—	4	2	no	—
233	C₂×D₄×C₆₇	—	4	1	no	—
234	C₂×D₄×C₆₇	—	4	1	no	—
235	C₂×D₄×C₆₇	—	4	2	no	—
236	C₂×D₄×C₆₇	—	4	2	no	—
237	C₂×D₄×C₆₇	—	4	2	no	—
238	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
239	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
240	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
241	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
242	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
243	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
244	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
245	C₂²×C₄×C₆₇	—	2	2	no	—
246	C₂²×C₄×C₆₇	—	2	4	no	—
247	C₂²×C₄×C₆₇	—	2	4	no	—
248	C₂²×C₄×C₆₇	—	2	2	no	—
249	C₂²×C₄×C₆₇	—	2	4	no	—
250	C₂²×C₄×C₆₇	—	4	1	no	—
251	C₂²×C₄×C₆₇	—	4	1	no	—
252	C₂²×C₄×C₆₇	—	4	2	no	—
253	C₂²×C₄×C₆₇	—	4	2	no	—
254	C₂²×C₄×C₆₇	—	4	2	no	—
255	C₂²×C₄×C₆₇	—	4	1	no	—
256	C₂²×C₄×C₆₇	—	4	2	no	—
257	C₂²×C₄×C₆₇	—	4	1	no	—
258	C₂²×C₄×C₆₇	—	4	2	no	—
259	C₂²×C₄×C₆₇	—	4	2	no	—
260	C₂²×C₄×C₆₇	—	4	2	no	—
261	C₂²×C₄×C₆₇	—	4	2	no	—
262	C₂²×C₄×C₆₇	—	4	2	no	—
263	C₂²×C₄×C₆₇	—	4	2	no	—
264	C₂²×C₄×C₆₇	—	4	2	no	—
265	C₂²×C₄×C₆₇	—	4	2	no	—
266	C₂²×C₄×C₆₇	—	4	2	no	—
267	C₂²×C₄×C₆₇	—	4	2	no	—
268	C₂²×C₄×C₆₇	—	4	2	no	—
269	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
270	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	—
271	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
286	C₄⋊C₄×C₆₇	—	2	4	no	—
287	C₄⋊C₄×C₆₇	—	2	4	no	—
288	C₄⋊C₄×C₆₇	—	2	4	no	—
289	C₄⋊C₄×C₆₇	—	4	2	no	—
290	C₄⋊C₄×C₆₇	—	4	2	no	—
291	C₄⋊C₄×C₆₇	—	4	2	no	—
292	C₄⋊C₄×C₆₇	—	4	2	no	—
293	C₄⋊C₄×C₆₇	—	4	2	no	—
294	C₄⋊C₄×C₆₇	—	4	1	no	—
295	C₄⋊C₄×C₆₇	—	4	1	no	—
296	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
297	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
298	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
299	C₂²⋊C₄×C₆₇	—	2	4	no	—
300	C₂²⋊C₄×C₆₇	—	2	4	no	—
301	C₂²⋊C₄×C₆₇	—	2	4	no	—
302	C₂²⋊C₄×C₆₇	—	2	4	no	—
303	C₂²⋊C₄×C₆₇	—	2	4	no	—
304	C₂²⋊C₄×C₆₇	—	4	2	no	—
305	C₂²⋊C₄×C₆₇	—	4	2	no	—
306	C₂²⋊C₄×C₆₇	—	4	2	no	—
307	C₂²⋊C₄×C₆₇	—	4	2	no	—
308	C₂²⋊C₄×C₆₇	—	4	2	no	—
309	C₂²⋊C₄×C₆₇	—	4	1	no	—
310	C₂²⋊C₄×C₆₇	—	4	2	no	—
311	C₂²⋊C₄×C₆₇	—	4	1	no	—
312	C₂²⋊C₄×C₆₇	—	4	2	no	—
313	C₂²⋊C₄×C₆₇	—	4	1	no	—
314	C₂²⋊C₄×C₆₇	—	4	1	no	—
315	C₂²⋊C₄×C₆₇	—	4	2	no	—
316	C₂²⋊C₄×C₆₇	—	4	2	no	—
317	C₂²⋊C₄×C₆₇	—	4	2	no	—
318	C₂²⋊C₄×C₆₇	—	4	2	no	—
319	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
320	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
321	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
322	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
323	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
324	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
325	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
326	C₄²×C₆₇	—	2	4	no	—
327	C₄²×C₆₇	—	2	2	no	—
328	C₄²×C₆₇	—	4	2	no	—
329	C₄²×C₆₇	—	4	2	no	—
330	C₄²×C₆₇	—	4	2	no	—
331	C₄²×C₆₇	—	4	1	no	—
332	C₄²×C₆₇	—	4	2	no	—
333	C₄²×C₆₇	—	4	2	no	—
334	C₄²×C₆₇	—	4	2	no	—
335	C₄²×C₆₇	—	4	2	no	—
336	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
337	C₂³×C₆₇	—	2	2	no	—
338	C₂³×C₆₇	—	2	2	no	—
339	C₂³×C₆₇	—	2	2	no	—
340	C₂³×C₆₇	—	2	2	no	—
341	C₂³×C₆₇	—	2	2	no	—
342	C₂³×C₆₇	—	2	2	no	—
343	C₂³×C₆₇	—	2	1	no	—
344	C₂³×C₆₇	—	2	2	no	—
345	C₂³×C₆₇	—	2	1	no	—
346	C₂³×C₆₇	—	2	2	no	—
347	C₂³×C₆₇	—	2	2	no	—
348	C₂³×C₆₇	—	2	1	no	—
349	C₂³×C₆₇	—	2	2	no	—
350	C₂³×C₆₇	—	2	2	no	—
351	C₂³×C₆₇	—	2	2	no	—
352	C₂³×C₆₇	—	2	1	no	—
353	C₂³×C₆₇	—	2	2	no	—
354	C₂³×C₆₇	—	2	2	no	—
355	C₂³×C₆₇	—	2	2	no	—
356	C₂³×C₆₇	—	2	2	no	—
357	C₂³×C₆₇	—	4	8	no	—
358	C₂³×C₆₇	—	4	4	no	—
359	C₂³×C₆₇	—	8	2	no	—
360	C₂³×C₆₇	—	8	2	no	—
361	C₂³×C₆₇	—	8	4	no	—
362	C₂³×C₆₇	C₂³×C₄	1	4	yes	—
363	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
364	C₂³×C₆₇	C₂³×C₄	1	4	yes	—
365	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
366	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
367	D₄×C₆₇	—	4	8	no	—
368	D₄×C₆₇	—	4	8	no	—
369	D₄×C₆₇	—	4	8	no	—
370	D₄×C₆₇	—	4	4	no	—
371	D₄×C₆₇	—	4	8	no	—
372	D₄×C₆₇	—	4	4	no	—
373	D₄×C₆₇	—	4	8	no	—
374	C₂×C₄×C₆₇	—	2	2	no	—
375	C₂×C₄×C₆₇	—	2	2	no	—
376	C₂×C₄×C₆₇	—	2	1	no	—
377	C₂×C₄×C₆₇	—	2	2	no	—
378	C₂×C₄×C₆₇	—	2	2	no	—
379	C₂×C₄×C₆₇	—	2	2	no	—
380	C₂×C₄×C₆₇	—	2	2	no	—
381	C₂×C₄×C₆₇	—	2	2	no	—
382	C₂×C₄×C₆₇	—	2	2	no	—
383	C₂×C₄×C₆₇	—	2	2	no	—
384	C₂×C₄×C₆₇	—	2	1	no	—
385	C₂×C₄×C₆₇	—	2	2	no	—
386	C₂×C₄×C₆₇	—	2	2	no	—
387	C₂×C₄×C₆₇	—	2	1	no	—
388	C₂×C₄×C₆₇	—	2	2	no	—
389	C₂×C₄×C₆₇	—	2	1	no	—
390	C₂×C₄×C₆₇	—	2	2	no	—
391	C₂×C₄×C₆₇	—	2	2	no	—
392	C₂×C₄×C₆₇	—	2	2	no	—
393	C₂×C₄×C₆₇	—	2	2	no	—
394	C₂×C₄×C₆₇	—	2	2	no	—
395	C₂×C₄×C₆₇	—	2	2	no	—
396	C₂×C₄×C₆₇	—	2	1	no	—
397	C₂×C₄×C₆₇	—	2	2	no	—
398	C₂×C₄×C₆₇	—	2	2	no	—
399	C₂×C₄×C₆₇	—	2	2	no	—
400	C₂×C₄×C₆₇	—	2	2	no	—
401	C₂×C₄×C₆₇	—	2	2	no	—
402	C₂×C₄×C₆₇	—	2	2	no	—
403	C₂×C₄×C₆₇	—	2	2	no	—
404	C₂×C₄×C₆₇	—	2	2	no	—
405	C₂×C₄×C₆₇	—	2	2	no	—
406	C₂×C₄×C₆₇	—	2	2	no	—
407	C₂×C₄×C₆₇	—	2	2	no	—
408	C₂×C₄×C₆₇	—	4	4	no	—
409	C₂×C₄×C₆₇	—	4	8	no	—
410	C₂×C₄×C₆₇	—	4	4	no	—
411	C₂×C₄×C₆₇	—	4	4	no	—
412	C₂×C₄×C₆₇	—	8	2	no	—
413	C₂×C₄×C₆₇	—	8	4	no	—
414	C₂×C₄×C₆₇	—	8	4	no	—
415	C₂×C₄×C₆₇	—	8	4	no	—
416	C₂×C₄×C₆₇	—	8	2	no	—
417	C₂×C₄×C₆₇	—	8	4	no	—
418	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
419	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
420	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
421	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
422	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
423	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
424	C₂×C₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
425	C₂²×C₆₇	—	2	2	no	—
426	C₂²×C₆₇	—	2	4	no	—
427	C₂²×C₆₇	—	2	4	no	—
428	C₂²×C₆₇	—	2	4	no	—
429	C₂²×C₆₇	—	2	4	no	—
430	C₂²×C₆₇	—	2	4	no	—
431	C₂²×C₆₇	—	2	4	no	—
432	C₂²×C₆₇	—	2	4	no	—
433	C₂²×C₆₇	—	2	2	no	—
434	C₂²×C₆₇	—	2	4	no	—
435	C₂²×C₆₇	—	4	1	no	—
436	C₂²×C₆₇	—	4	1	no	—
437	C₂²×C₆₇	—	4	2	no	—
438	C₂²×C₆₇	—	4	2	no	—
439	C₂²×C₆₇	—	4	1	no	—
440	C₂²×C₆₇	—	4	2	no	—
441	C₂²×C₆₇	—	4	2	no	—
442	C₂²×C₆₇	—	4	1	no	—
443	C₂²×C₆₇	—	4	2	no	—
444	C₂²×C₆₇	—	4	2	no	—
445	C₂²×C₆₇	—	4	2	no	—
446	C₂²×C₆₇	—	4	2	no	—
447	C₂²×C₆₇	—	4	2	no	—
448	C₂²×C₆₇	—	4	2	no	—
449	C₂²×C₆₇	—	8	8	no	—
450	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
451	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
452	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
453	C₂²×C₆₇	#585	1	2	yes	—
454	C₂²×C₆₇	#585	1	1	yes	characteristic
455	C₄×C₆₇	—	2	4	no	—
456	C₄×C₆₇	—	2	4	no	—
457	C₄×C₆₇	—	2	4	no	—
458	C₄×C₆₇	—	2	2	no	—
459	C₄×C₆₇	—	2	4	no	—
460	C₄×C₆₇	—	2	2	no	—
461	C₄×C₆₇	—	2	4	no	—
462	C₄×C₆₇	—	4	1	no	—
463	C₄×C₆₇	—	4	1	no	—
464	C₄×C₆₇	—	4	1	no	—
465	C₄×C₆₇	—	4	2	no	—
466	C₄×C₆₇	—	4	2	no	—
467	C₄×C₆₇	—	4	2	no	—
468	C₄×C₆₇	—	4	2	no	—
469	C₄×C₆₇	—	4	2	no	—
470	#34518	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
471	C₂×C₆₇	—	4	2	no	—
472	C₂×C₆₇	—	4	4	no	—
473	C₂×C₆₇	—	4	2	no	—
474	C₂×C₆₇	—	4	4	no	—
475	C₂×C₆₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
476	C₂×C₆₇	C₄×H(5,𝔽₂)	1	2	yes	—
477	C₂×C₆₇	#3533	1	1	yes	characteristic
478	C₂×C₆₇	#3537	1	1	yes	characteristic
479	C₂×C₆₇	#3562	1	2	yes	—
480	C₂×#560	C₂×C₆₇	1	1	yes	characteristic
481	#2377	C₂×C₆₇	1	2	yes	complemented
482	#2376	C₂×C₆₇	1	1	yes	characteristic, complemented
483	#2374	C₂×C₆₇	1	2	yes	complemented
484	#2373	C₂×C₆₇	1	2	yes	complemented
485	#2366	C₂×C₆₇	1	1	yes	characteristic, complemented
486	#2361	C₂×C₆₇	1	2	yes	complemented
487	#2361	C₂×C₆₇	1	2	yes	complemented
488	#2358	C₂×C₆₇	1	2	yes	complemented
489	#2358	C₂×C₆₇	1	1	yes	characteristic, complemented
490	#2334	C₂×C₆₇	1	2	yes	complemented
491	#2333	C₂×C₆₇	1	2	yes	complemented
492	#2333	C₂×C₆₇	1	2	yes	complemented
493	#2328	C₂×C₆₇	1	1	yes	characteristic, complemented
494	#2322	C₂×C₆₇	1	2	yes	complemented
495	#2321	C₂×C₆₇	1	1	yes	characteristic, complemented
496	#2321	C₂×C₆₇	1	2	yes	complemented
497	C₄×#123	C₂×C₆₇	1	1	yes	characteristic, complemented
498	C₄×#121	C₂×C₆₇	1	2	yes	complemented
499	C₆₇	#34518	1	1	yes	characteristic, direct product factor, Sylow
500	#560	C₄×C₆₇	1	16	yes	complemented
501	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
502	C₂×#126	C₂²×C₆₇	1	2	yes	—
503	C₂×#123	C₂²×C₆₇	1	2	yes	—
504	C₂×#123	C₂²×C₆₇	1	1	yes	characteristic
505	C₂×#121	C₂²×C₆₇	1	2	yes	—
506	C₂×#121	C₂²×C₆₇	1	2	yes	—
507	C₂×#121	C₂²×C₆₇	1	2	yes	—
508	C₂×#120	C₂²×C₆₇	1	1	yes	characteristic
509	C₂×#120	C₂²×C₆₇	1	2	yes	—
510	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
511	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
512	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
513	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
514	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
515	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
516	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
517	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
518	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
519	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
520	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic, complemented
521	#390	C₂²×C₆₇	1	2	yes	—
522	#390	C₂²×C₆₇	1	2	yes	—
523	#390	C₂²×C₆₇	1	2	yes	—
524	#390	C₂²×C₆₇	1	1	yes	characteristic
525	#390	C₂²×C₆₇	1	2	yes	—
526	#390	C₂²×C₆₇	1	1	yes	characteristic, complemented
527	#390	C₂²×C₆₇	1	2	yes	complemented
528	#389	C₂²×C₆₇	1	2	yes	complemented
529	#389	C₂²×C₆₇	1	2	yes	complemented
530	#389	C₂²×C₆₇	1	2	yes	complemented
531	#388	C₂²×C₆₇	1	2	yes	—
532	#388	C₂²×C₆₇	1	2	yes	—
533	#388	C₂²×C₆₇	1	2	yes	—
534	#388	C₂²×C₆₇	1	2	yes	—
535	#388	C₂²×C₆₇	1	2	yes	—
536	#388	C₂²×C₆₇	1	2	yes	—
537	#388	C₂²×C₆₇	1	2	yes	—
538	#388	C₂²×C₆₇	1	2	yes	—
539	#388	C₂²×C₆₇	1	2	yes	—
540	#388	C₂²×C₆₇	1	2	yes	complemented
541	#388	C₂²×C₆₇	1	2	yes	complemented
542	#388	C₂²×C₆₇	1	2	yes	complemented
543	#387	C₂²×C₆₇	1	2	yes	complemented
544	#387	C₂²×C₆₇	1	2	yes	complemented
545	#387	C₂²×C₆₇	1	2	yes	complemented
546	#387	C₂²×C₆₇	1	2	yes	complemented
547	#387	C₂²×C₆₇	1	2	yes	complemented
548	#387	C₂²×C₆₇	1	2	yes	complemented
549	#386	C₂²×C₆₇	1	2	yes	—
550	#386	C₂²×C₆₇	1	2	yes	—
551	#386	C₂²×C₆₇	1	2	yes	—
552	#386	C₂²×C₆₇	1	2	yes	—
553	#386	C₂²×C₆₇	1	1	yes	characteristic
554	#386	C₂²×C₆₇	1	2	yes	—
555	#386	C₂²×C₆₇	1	2	yes	—
556	#386	C₂²×C₆₇	1	2	yes	—
557	#386	C₂²×C₆₇	1	2	yes	—
558	#386	C₂²×C₆₇	1	1	yes	characteristic
559	#386	C₂²×C₆₇	1	2	yes	complemented
560	#386	C₂²×C₆₇	1	2	yes	complemented
561	#386	C₂²×C₆₇	1	2	yes	complemented
562	#385	C₂²×C₆₇	1	1	yes	characteristic
563	#385	C₂²×C₆₇	1	2	yes	—
564	#385	C₂²×C₆₇	1	2	yes	—
565	#385	C₂²×C₆₇	1	2	yes	—
566	#385	C₂²×C₆₇	1	2	yes	—
567	#385	C₂²×C₆₇	1	2	yes	complemented
568	#385	C₂²×C₆₇	1	1	yes	characteristic, complemented
569	#382	C₂²×C₆₇	1	1	yes	characteristic, complemented
570	#381	C₂²×C₆₇	1	2	yes	complemented
571	#381	C₂²×C₆₇	1	1	yes	characteristic, complemented
572	#380	C₂²×C₆₇	1	2	yes	complemented
573	#379	C₂²×C₆₇	1	1	yes	characteristic
574	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
575	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
576	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
577	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
578	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
579	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
580	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
581	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
582	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
583	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
584	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
585	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
586	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
587	#376	C₂²×C₆₇	1	1	yes	characteristic, complemented
588	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
589	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
590	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
591	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
592	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
593	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
594	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
595	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
596	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
597	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
598	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
599	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
600	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
601	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
602	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
603	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
604	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
605	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
606	#127	C₂×C₄×C₆₇	1	8	yes	complemented
607	#126	C₂×C₄×C₆₇	1	16	yes	complemented
608	#123	C₂×C₄×C₆₇	1	16	yes	complemented
609	#123	C₂×C₄×C₆₇	1	8	yes	complemented
610	#121	C₂×C₄×C₆₇	1	16	yes	complemented
611	#121	C₂×C₄×C₆₇	1	16	yes	complemented
612	#121	C₂×C₄×C₆₇	1	16	yes	complemented
613	#120	C₂×C₄×C₆₇	1	8	yes	complemented
614	#120	C₂×C₄×C₆₇	1	16	yes	complemented
615	C₄×D₄	—	4	4	no	—
616	C₄×D₄	—	4	2	no	—
617	C₄×D₄	—	4	2	no	—
618	C₄×D₄	—	4	4	no	—
619	C₄×D₄	—	4	4	no	—
620	C₄×D₄	—	4	4	no	—
621	C₄×D₄	—	4	4	no	—
622	C₂×C₄⋊C₄	—	4	4	no	—
623	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
624	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
625	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
626	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
627	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
628	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
629	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
630	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
631	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
632	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
633	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
634	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
635	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
636	C₂×C₂²⋊C₄	—	4	4	no	—
637	C₂×C₂²⋊C₄	—	4	2	no	—
638	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
639	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
640	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
641	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
642	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
643	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
644	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
645	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
646	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
647	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
648	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
649	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
650	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
651	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
652	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
653	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
654	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
655	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
656	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
657	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
658	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
659	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
660	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
661	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
662	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
664	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
665	C₂×C₄²	—	4	2	no	—
666	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
667	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
668	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
669	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
670	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
671	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
672	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
673	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
674	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
675	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
676	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
677	#95	C₂³×C₆₇	1	2	yes	—
678	#95	C₂³×C₆₇	1	2	yes	—
679	#95	C₂³×C₆₇	1	2	yes	—
680	#95	C₂³×C₆₇	1	2	yes	—
681	#95	C₂³×C₆₇	1	2	yes	—
682	#95	C₂³×C₆₇	1	2	yes	—
683	#95	C₂³×C₆₇	1	2	yes	—
684	#95	C₂³×C₆₇	1	2	yes	—
685	#95	C₂³×C₆₇	1	2	yes	—
686	#95	C₂³×C₆₇	1	2	yes	—
687	#95	C₂³×C₆₇	1	2	yes	—
688	#95	C₂³×C₆₇	1	2	yes	—
689	#95	C₂³×C₆₇	1	2	yes	—
690	#95	C₂³×C₆₇	1	2	yes	—
691	#95	C₂³×C₆₇	1	2	yes	—
692	#95	C₂³×C₆₇	1	2	yes	—
693	#95	C₂³×C₆₇	1	2	yes	—
694	#95	C₂³×C₆₇	1	2	yes	—
695	C₂⁴	—	4	1	no	—
696	C₂⁴	—	4	2	no	—
697	C₂⁴	—	4	2	no	—
698	C₂⁴	—	4	1	no	—
699	C₂⁴	C₂²×C₄×C₆₇	1	4	yes	—
700	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
701	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
702	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
703	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
704	C₂×D₄	—	4	2	no	—
705	C₂×D₄	—	4	1	no	—
706	C₂×D₄	—	4	1	no	—
707	C₂×D₄	—	4	2	no	—
708	C₂×D₄	—	4	2	no	—
709	C₂×D₄	—	4	2	no	—
710	C₂×D₄	—	4	2	no	—
711	C₂×D₄	—	4	2	no	—
712	C₂×D₄	—	4	2	no	—
713	C₂×D₄	—	4	1	no	—
714	C₂×D₄	—	4	1	no	—
715	C₂×D₄	—	4	2	no	—
716	C₂×D₄	—	4	2	no	—
717	C₂×D₄	—	4	2	no	—
718	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
719	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
720	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
721	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
722	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
723	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
724	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
725	C₂²×C₄	—	2	2	no	—
726	C₂²×C₄	—	2	4	no	—
727	C₂²×C₄	—	2	4	no	—
728	C₂²×C₄	—	2	2	no	—
729	C₂²×C₄	—	2	4	no	—
730	C₂²×C₄	—	4	1	no	—
731	C₂²×C₄	—	4	1	no	—
732	C₂²×C₄	—	4	2	no	—
733	C₂²×C₄	—	4	2	no	—
734	C₂²×C₄	—	4	2	no	—
735	C₂²×C₄	—	4	1	no	—
736	C₂²×C₄	—	4	2	no	—
737	C₂²×C₄	—	4	1	no	—
738	C₂²×C₄	—	4	2	no	—
739	C₂²×C₄	—	4	2	no	—
740	C₂²×C₄	—	4	2	no	—
741	C₂²×C₄	—	4	2	no	—
742	C₂²×C₄	—	4	2	no	—
743	C₂²×C₄	—	4	2	no	—
744	C₂²×C₄	—	4	2	no	—
745	C₂²×C₄	—	4	2	no	—
746	C₂²×C₄	—	4	2	no	—
747	C₂²×C₄	—	4	2	no	—
748	C₂²×C₄	—	4	2	no	—
749	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	—
750	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
751	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
752	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
753	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
754	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
755	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
756	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
757	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
758	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
759	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
760	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
761	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
762	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
763	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
764	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
765	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
766	C₄⋊C₄	—	2	4	no	—
767	C₄⋊C₄	—	2	4	no	—
768	C₄⋊C₄	—	2	4	no	—
769	C₄⋊C₄	—	4	2	no	—
770	C₄⋊C₄	—	4	2	no	—
771	C₄⋊C₄	—	4	2	no	—
772	C₄⋊C₄	—	4	1	no	—
773	C₄⋊C₄	—	4	1	no	—
774	C₄⋊C₄	—	4	2	no	—
775	C₄⋊C₄	—	4	2	no	—
776	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
777	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
778	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
779	C₂²⋊C₄	—	2	4	no	—
780	C₂²⋊C₄	—	2	4	no	—
781	C₂²⋊C₄	—	2	4	no	—
782	C₂²⋊C₄	—	2	4	no	—
783	C₂²⋊C₄	—	2	4	no	—
784	C₂²⋊C₄	—	4	2	no	—
785	C₂²⋊C₄	—	4	2	no	—
786	C₂²⋊C₄	—	4	2	no	—
787	C₂²⋊C₄	—	4	1	no	—
788	C₂²⋊C₄	—	4	1	no	—
789	C₂²⋊C₄	—	4	2	no	—
790	C₂²⋊C₄	—	4	2	no	—
791	C₂²⋊C₄	—	4	2	no	—
792	C₂²⋊C₄	—	4	2	no	—
793	C₂²⋊C₄	—	4	2	no	—
794	C₂²⋊C₄	—	4	2	no	—
795	C₂²⋊C₄	—	4	1	no	—
796	C₂²⋊C₄	—	4	2	no	—
797	C₂²⋊C₄	—	4	1	no	—
798	C₂²⋊C₄	—	4	2	no	—
799	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
800	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
801	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
802	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
803	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
804	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
805	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
806	C₄²	—	2	4	no	—
807	C₄²	—	2	2	no	—
808	C₄²	—	4	2	no	—
809	C₄²	—	4	2	no	—
810	C₄²	—	4	2	no	—
811	C₄²	—	4	2	no	—
812	C₄²	—	4	2	no	—
813	C₄²	—	4	2	no	—
814	C₄²	—	4	2	no	—
815	C₄²	—	4	1	no	—
816	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
817	C₂³	—	2	2	no	—
818	C₂³	—	2	2	no	—
819	C₂³	—	2	2	no	—
820	C₂³	—	2	2	no	—
821	C₂³	—	2	2	no	—
822	C₂³	—	2	2	no	—
823	C₂³	—	2	1	no	—
824	C₂³	—	2	2	no	—
825	C₂³	—	2	1	no	—
826	C₂³	—	2	2	no	—
827	C₂³	—	2	2	no	—
828	C₂³	—	2	1	no	—
829	C₂³	—	2	2	no	—
830	C₂³	—	2	2	no	—
831	C₂³	—	2	2	no	—
832	C₂³	—	2	1	no	—
833	C₂³	—	2	2	no	—
834	C₂³	—	2	2	no	—
835	C₂³	—	2	2	no	—
836	C₂³	—	2	2	no	—
837	C₂³	—	4	8	no	—
838	C₂³	—	4	4	no	—
839	C₂³	—	8	2	no	—
840	C₂³	—	8	2	no	—
841	C₂³	—	8	4	no	—
842	C₂³	C₂³×C₄×C₆₇	1	4	yes	—
843	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
844	C₂³	C₂³×C₄×C₆₇	1	4	yes	—
845	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
846	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
847	D₄	—	4	8	no	—
848	D₄	—	4	8	no	—
849	D₄	—	4	8	no	—
850	D₄	—	4	4	no	—
851	D₄	—	4	8	no	—
852	D₄	—	4	4	no	—
853	D₄	—	4	8	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	4	4	no	—
889	C₂×C₄	—	4	8	no	—
890	C₂×C₄	—	4	4	no	—
891	C₂×C₄	—	4	4	no	—
892	C₂×C₄	—	8	2	no	—
893	C₂×C₄	—	8	4	no	—
894	C₂×C₄	—	8	4	no	—
895	C₂×C₄	—	8	4	no	—
896	C₂×C₄	—	8	2	no	—
897	C₂×C₄	—	8	4	no	—
898	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
899	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
900	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
901	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
902	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
903	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
904	C₂×C₄	H(5,𝔽₂)×C₆₇	1	4	yes	—
905	C₂²	—	2	2	no	—
906	C₂²	—	2	4	no	—
907	C₂²	—	2	4	no	—
908	C₂²	—	2	4	no	—
909	C₂²	—	2	4	no	—
910	C₂²	—	2	4	no	—
911	C₂²	—	2	4	no	—
912	C₂²	—	2	4	no	—
913	C₂²	—	2	2	no	—
914	C₂²	—	2	4	no	—
915	C₂²	—	4	1	no	—
916	C₂²	—	4	1	no	—
917	C₂²	—	4	2	no	—
918	C₂²	—	4	2	no	—
919	C₂²	—	4	1	no	—
920	C₂²	—	4	2	no	—
921	C₂²	—	4	2	no	—
922	C₂²	—	4	1	no	—
923	C₂²	—	4	2	no	—
924	C₂²	—	4	2	no	—
925	C₂²	—	4	2	no	—
926	C₂²	—	4	2	no	—
927	C₂²	—	4	2	no	—
928	C₂²	—	4	2	no	—
929	C₂²	—	8	8	no	—
930	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
931	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
932	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
933	C₂²	#585×C₆₇	1	2	yes	—
934	C₂²	#585×C₆₇	1	1	yes	characteristic
935	C₄	—	2	2	no	—
936	C₄	—	2	4	no	—
937	C₄	—	2	4	no	—
938	C₄	—	2	4	no	—
939	C₄	—	2	4	no	—
940	C₄	—	2	2	no	—
941	C₄	—	2	4	no	—
942	C₄	—	4	1	no	—
943	C₄	—	4	1	no	—
944	C₄	—	4	1	no	—
945	C₄	—	4	2	no	—
946	C₄	—	4	2	no	—
947	C₄	—	4	2	no	—
948	C₄	—	4	2	no	—
949	C₄	—	4	2	no	—
950	C₂	—	4	2	no	—
951	C₂	—	4	4	no	—
952	C₂	—	4	2	no	—
953	C₂	—	4	4	no	—
954	C₂	C₄×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
955	C₂	C₄×H(5,𝔽₂)×C₆₇	1	2	yes	—
956	C₂	C₆₇×#3533	1	1	yes	characteristic
957	C₂	C₆₇×#3537	1	1	yes	characteristic
958	C₂	C₆₇×#3562	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₆₇
Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₂×#560×C₆₇	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₇×#2377	C₂	semidirect
3. C₆₇×#2376	C₂	semidirect
4. C₆₇×#2374	C₂	semidirect
5. C₆₇×#2373	C₂	semidirect
6. C₆₇×#2366	C₂	semidirect
7. C₆₇×#2361	C₂	semidirect
8. C₆₇×#2361	C₂	semidirect
9. C₆₇×#2358	C₂	semidirect
10. C₆₇×#2358	C₂	semidirect
11. C₆₇×#2334	C₂	semidirect
12. C₆₇×#2333	C₂	semidirect
13. C₆₇×#2333	C₂	semidirect
14. C₆₇×#2328	C₂	semidirect
15. C₆₇×#2322	C₂	semidirect
16. C₆₇×#2321	C₂	semidirect
17. C₆₇×#2321	C₂	semidirect
18. C₄×#123×C₆₇	C₂	semidirect
19. C₄×#121×C₆₇	C₂	semidirect
20. #560×C₆₇	C₄	semidirect
35. C₂×C₄×D₄×C₆₇	C₂²	semidirect
36. C₂×C₄×D₄×C₆₇	C₂²	semidirect
37. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
40. C₂²×C₄²×C₆₇	C₂²	semidirect
46. #390×C₆₇	C₂²	semidirect
47. #390×C₆₇	C₂²	semidirect
48. #389×C₆₇	C₂²	semidirect
49. #389×C₆₇	C₂²	semidirect
50. #389×C₆₇	C₂²	semidirect
60. #388×C₆₇	C₂²	semidirect
61. #388×C₆₇	C₂²	semidirect
62. #388×C₆₇	C₂²	semidirect
63. #387×C₆₇	C₂²	semidirect
64. #387×C₆₇	C₂²	semidirect
65. #387×C₆₇	C₂²	semidirect
66. #387×C₆₇	C₂²	semidirect
67. #387×C₆₇	C₂²	semidirect
68. #387×C₆₇	C₂²	semidirect
79. #386×C₆₇	C₂²	semidirect
80. #386×C₆₇	C₂²	semidirect
81. #386×C₆₇	C₂²	semidirect
87. #385×C₆₇	C₂²	semidirect
88. #385×C₆₇	C₂²	semidirect
89. #382×C₆₇	C₂²	semidirect
90. #381×C₆₇	C₂²	semidirect
91. #381×C₆₇	C₂²	semidirect
92. #380×C₆₇	C₂²	semidirect
94. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
95. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
96. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
97. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
103. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
104. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
105. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
106. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
107. #376×C₆₇	C₂²	semidirect
126. #127×C₆₇	C₂×C₄	semidirect
127. #126×C₆₇	C₂×C₄	semidirect
128. #123×C₆₇	C₂×C₄	semidirect
129. #123×C₆₇	C₂×C₄	semidirect
130. #121×C₆₇	C₂×C₄	semidirect
131. #121×C₆₇	C₂×C₄	semidirect
132. #121×C₆₇	C₂×C₄	semidirect
133. #120×C₆₇	C₂×C₄	semidirect
134. #120×C₆₇	C₂×C₄	semidirect
470. #34518	C₆₇	direct (N × H)
481. #2377	C₂×C₆₇	semidirect
482. #2376	C₂×C₆₇	semidirect
483. #2374	C₂×C₆₇	semidirect
484. #2373	C₂×C₆₇	semidirect
485. #2366	C₂×C₆₇	semidirect
486. #2361	C₂×C₆₇	semidirect
487. #2361	C₂×C₆₇	semidirect
488. #2358	C₂×C₆₇	semidirect
489. #2358	C₂×C₆₇	semidirect
490. #2334	C₂×C₆₇	semidirect
491. #2333	C₂×C₆₇	semidirect
492. #2333	C₂×C₆₇	semidirect
493. #2328	C₂×C₆₇	semidirect
494. #2322	C₂×C₆₇	semidirect
495. #2321	C₂×C₆₇	semidirect
496. #2321	C₂×C₆₇	semidirect
497. C₄×#123	C₂×C₆₇	semidirect
498. C₄×#121	C₂×C₆₇	semidirect
499. C₆₇	#34518	direct (N × H)
500. #560	C₄×C₆₇	semidirect
515. C₂×C₄×D₄	C₂²×C₆₇	semidirect
516. C₂×C₄×D₄	C₂²×C₆₇	semidirect
517. C₂²×C₄⋊C₄	C₂²×C₆₇	semidirect
520. C₂²×C₄²	C₂²×C₆₇	semidirect
526. #390	C₂²×C₆₇	semidirect
527. #390	C₂²×C₆₇	semidirect
528. #389	C₂²×C₆₇	semidirect
529. #389	C₂²×C₆₇	semidirect
530. #389	C₂²×C₆₇	semidirect
540. #388	C₂²×C₆₇	semidirect
541. #388	C₂²×C₆₇	semidirect
542. #388	C₂²×C₆₇	semidirect
543. #387	C₂²×C₆₇	semidirect
544. #387	C₂²×C₆₇	semidirect
545. #387	C₂²×C₆₇	semidirect
546. #387	C₂²×C₆₇	semidirect
547. #387	C₂²×C₆₇	semidirect
548. #387	C₂²×C₆₇	semidirect
559. #386	C₂²×C₆₇	semidirect
560. #386	C₂²×C₆₇	semidirect
561. #386	C₂²×C₆₇	semidirect
567. #385	C₂²×C₆₇	semidirect
568. #385	C₂²×C₆₇	semidirect
569. #382	C₂²×C₆₇	semidirect
570. #381	C₂²×C₆₇	semidirect
571. #381	C₂²×C₆₇	semidirect
572. #380	C₂²×C₆₇	semidirect
574. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
575. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
576. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
577. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
583. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
584. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
585. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
586. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
587. #376	C₂²×C₆₇	semidirect
606. #127	C₂×C₄×C₆₇	semidirect
607. #126	C₂×C₄×C₆₇	semidirect
608. #123	C₂×C₄×C₆₇	semidirect
609. #123	C₂×C₄×C₆₇	semidirect
610. #121	C₂×C₄×C₆₇	semidirect
611. #121	C₂×C₄×C₆₇	semidirect
612. #121	C₂×C₄×C₆₇	semidirect
613. #120	C₂×C₄×C₆₇	semidirect
614. #120	C₂×C₄×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#560×C₆₇	2
C₆₇×#2377	2
C₆₇×#2376	2
C₆₇×#2374	2
C₆₇×#2373	2
C₆₇×#2366	2
C₆₇×#2361	2
C₆₇×#2358	2
C₆₇×#2334	2
C₆₇×#2333	2
C₆₇×#2328	2
C₆₇×#2322	2
C₆₇×#2321	2
C₄×#123×C₆₇	2
C₄×#121×C₆₇	2
#34518	67

Subgroups — C67×#34518 #30713769

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#34518 #30713769