Subgroups — C₆₇×#59318 #30738569

Order 17152.

2484 conjugacy classes of subgroups.

The subgroup lattice has 1120 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#553×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#547×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2706	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2698	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2553	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2550	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2535	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2488	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2487	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#2486	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2442	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#2439	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#2430	C₂	1	2	yes	maximal, complemented
14	C₆₇×#2425	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2420	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#2420	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#2419	C₂	1	2	yes	maximal, complemented
18	C₆₇×#2352	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2349	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#2339	C₂	1	2	yes	maximal, complemented
21	C₄×#121×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#121×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#382×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₆₇	C₂²	1	2	yes	—
25	#553×C₆₇	—	2	8	no	—
26	#547×C₆₇	—	2	8	no	—
27	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×#126×C₆₇	C₂²	1	2	yes	—
29	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×#123×C₆₇	C₂²	1	2	yes	—
31	C₂×#123×C₆₇	C₂²	1	2	yes	—
32	C₂×#123×C₆₇	C₂²	1	2	yes	—
33	C₂×#123×C₆₇	C₂²	1	2	yes	—
34	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
35	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×#121×C₆₇	C₂²	1	2	yes	—
39	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
45	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
48	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
49	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
50	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
51	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
52	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
53	#400×C₆₇	C₂²	1	2	yes	—
54	#400×C₆₇	C₂²	1	2	yes	—
55	#399×C₆₇	C₂²	1	2	yes	—
56	#398×C₆₇	C₂²	1	2	yes	—
57	#398×C₆₇	C₂²	1	2	yes	—
58	#398×C₆₇	C₂²	1	2	yes	—
59	#397×C₆₇	C₂²	1	2	yes	—
60	#397×C₆₇	C₂²	1	2	yes	—
61	#397×C₆₇	C₂²	1	2	yes	—
62	#397×C₆₇	C₂²	1	2	yes	—
63	#396×C₆₇	C₂²	1	2	yes	—
64	#395×C₆₇	C₂²	1	2	yes	—
65	#394×C₆₇	C₂²	1	2	yes	—
66	#394×C₆₇	C₂²	1	2	yes	—
67	#393×C₆₇	C₂²	1	2	yes	—
68	#392×C₆₇	C₂²	1	2	yes	—
69	#391×C₆₇	C₂²	1	2	yes	—
70	#391×C₆₇	C₂²	1	2	yes	—
71	#390×C₆₇	C₂²	1	1	yes	characteristic
72	#390×C₆₇	C₂²	1	1	yes	characteristic
73	#389×C₆₇	C₂²	1	2	yes	—
74	#389×C₆₇	C₂²	1	1	yes	characteristic
75	#389×C₆₇	C₂²	1	1	yes	characteristic
76	#389×C₆₇	C₂²	1	1	yes	characteristic
77	#389×C₆₇	C₂²	1	1	yes	characteristic
78	#389×C₆₇	C₂²	1	1	yes	characteristic
79	#389×C₆₇	C₂²	1	1	yes	characteristic
80	#388×C₆₇	C₂²	1	1	yes	characteristic
81	#388×C₆₇	C₂²	1	2	yes	—
82	#388×C₆₇	C₂²	1	1	yes	characteristic
83	#388×C₆₇	C₂²	1	2	yes	—
84	#387×C₆₇	C₂²	1	2	yes	—
85	#387×C₆₇	C₂²	1	2	yes	—
86	#386×C₆₇	C₂²	1	2	yes	—
87	#386×C₆₇	C₂²	1	2	yes	—
88	#386×C₆₇	C₂²	1	1	yes	characteristic
89	#386×C₆₇	C₂²	1	2	yes	—
90	#386×C₆₇	C₂²	1	1	yes	characteristic
91	#386×C₆₇	C₂²	1	2	yes	—
92	#386×C₆₇	C₂²	1	2	yes	—
93	#386×C₆₇	C₂²	1	2	yes	—
94	#386×C₆₇	C₂²	1	2	yes	—
95	#385×C₆₇	C₂²	1	2	yes	—
96	#385×C₆₇	C₂²	1	2	yes	—
97	#385×C₆₇	C₂²	1	2	yes	—
98	#385×C₆₇	C₂²	1	2	yes	—
99	#382×C₆₇	C₂²	1	1	yes	characteristic
100	#382×C₆₇	C₂²	1	2	yes	—
101	#382×C₆₇	C₂²	1	1	yes	characteristic
102	#382×C₆₇	C₂²	1	1	yes	characteristic
103	#382×C₆₇	C₂²	1	1	yes	characteristic
104	#382×C₆₇	C₂²	1	2	yes	—
105	#381×C₆₇	C₂²	1	2	yes	—
106	#381×C₆₇	C₂²	1	2	yes	—
107	#381×C₆₇	C₂²	1	2	yes	—
108	#380×C₆₇	C₂²	1	1	yes	characteristic
109	#380×C₆₇	C₂²	1	1	yes	characteristic
110	#380×C₆₇	C₂²	1	2	yes	—
111	#380×C₆₇	C₂²	1	1	yes	characteristic
112	#380×C₆₇	C₂²	1	1	yes	characteristic
113	#380×C₆₇	C₂²	1	2	yes	—
114	#380×C₆₇	C₂²	1	1	yes	characteristic
115	#380×C₆₇	C₂²	1	1	yes	characteristic
116	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
117	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
118	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
119	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
120	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
121	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
122	C₂×#95×C₆₇	C₂²	1	2	yes	—
123	C₂×#95×C₆₇	C₂²	1	2	yes	—
124	C₂×#95×C₆₇	C₂²	1	2	yes	—
125	C₂×#41×C₆₇	—	2	8	no	—
126	C₂×#41×C₆₇	—	2	8	no	—
127	C₂×#41×C₆₇	—	4	4	no	—
128	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
129	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
130	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
131	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
132	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
133	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
134	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
135	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
136	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
137	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
138	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
142	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
143	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
144	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
145	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
146	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
147	C₄⋊Q₈×C₆₇	—	2	4	no	—
148	#126×C₆₇	—	2	8	no	—
149	#125×C₆₇	—	2	4	no	—
150	#123×C₆₇	—	2	8	no	—
151	#123×C₆₇	—	2	8	no	—
152	#123×C₆₇	—	2	8	no	—
153	#123×C₆₇	—	4	4	no	—
154	C₂²⋊Q₈×C₆₇	—	2	8	no	—
155	#121×C₆₇	—	2	4	no	—
156	#121×C₆₇	—	2	4	no	—
157	#121×C₆₇	—	2	8	no	—
158	#121×C₆₇	—	2	4	no	—
159	#121×C₆₇	D₄	1	8	yes	complemented
160	C₄×D₄×C₆₇	—	2	4	no	—
161	C₄×D₄×C₆₇	—	2	8	no	—
162	C₄×D₄×C₆₇	—	2	4	no	—
163	C₄×D₄×C₆₇	—	2	4	no	—
164	C₄×D₄×C₆₇	—	2	4	no	—
165	C₄×D₄×C₆₇	—	2	4	no	—
166	C₄×D₄×C₆₇	—	2	4	no	—
167	C₄×D₄×C₆₇	—	4	4	no	—
168	#117×C₆₇	—	2	4	no	—
169	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
170	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
171	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
172	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
173	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
176	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
180	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
181	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
182	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
183	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
185	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
186	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
187	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
188	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
189	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
191	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
192	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
194	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
195	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
197	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
200	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
202	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
206	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
208	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
209	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
211	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
212	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
214	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
215	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
216	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
217	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
218	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
219	C₂×C₄²×C₆₇	—	2	4	no	—
220	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
221	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
222	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
223	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
224	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
225	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
226	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
227	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
228	#95×C₆₇	C₂³	1	2	yes	—
229	#95×C₆₇	C₂³	1	1	yes	characteristic
230	#95×C₆₇	C₂³	1	2	yes	—
231	#95×C₆₇	C₂³	1	2	yes	—
232	#95×C₆₇	C₂³	1	2	yes	—
233	#95×C₆₇	C₂³	1	2	yes	—
234	#95×C₆₇	C₂³	1	2	yes	—
235	#95×C₆₇	C₂³	1	2	yes	—
236	#95×C₆₇	C₂³	1	2	yes	—
237	#95×C₆₇	C₂³	1	2	yes	—
238	#95×C₆₇	C₂³	1	2	yes	—
239	#95×C₆₇	C₂³	1	2	yes	—
240	#95×C₆₇	C₂³	1	1	yes	characteristic
241	#95×C₆₇	C₂³	1	1	yes	characteristic
242	#95×C₆₇	C₂³	1	2	yes	—
243	#95×C₆₇	C₂³	1	1	yes	characteristic
244	#95×C₆₇	C₂³	1	2	yes	—
245	#95×C₆₇	C₂³	1	1	yes	characteristic
246	#95×C₆₇	C₂³	1	1	yes	characteristic
247	#95×C₆₇	C₂³	1	2	yes	—
248	#95×C₆₇	C₂³	1	2	yes	—
249	#95×C₆₇	C₂³	1	2	yes	—
250	#95×C₆₇	C₂³	1	2	yes	—
251	#95×C₆₇	C₂³	1	2	yes	—
252	#95×C₆₇	C₂³	1	2	yes	—
253	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
254	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
255	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
256	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
257	#41×C₆₇	—	4	32	no	—
258	C₂×Q₈×C₆₇	—	2	4	no	—
259	C₂×Q₈×C₆₇	—	2	4	no	—
260	C₂×Q₈×C₆₇	—	4	2	no	—
261	C₂×D₄×C₆₇	—	2	2	no	—
262	C₂×D₄×C₆₇	—	2	4	no	—
263	C₂×D₄×C₆₇	—	2	4	no	—
264	C₂×D₄×C₆₇	—	2	2	no	—
265	C₂×D₄×C₆₇	—	2	2	no	—
266	C₂×D₄×C₆₇	—	2	4	no	—
267	C₂×D₄×C₆₇	—	2	2	no	—
268	C₂×D₄×C₆₇	—	2	2	no	—
269	C₂×D₄×C₆₇	—	2	4	no	—
270	C₂×D₄×C₆₇	—	2	2	no	—
271	C₂×D₄×C₆₇	—	2	4	no	—
272	C₂×D₄×C₆₇	—	2	2	no	—
273	C₂×D₄×C₆₇	—	2	2	no	—
274	C₂×D₄×C₆₇	—	2	2	no	—
275	C₂×D₄×C₆₇	—	4	1	no	—
276	C₂×D₄×C₆₇	—	4	2	no	—
277	C₂×D₄×C₆₇	—	4	2	no	—
278	C₂×D₄×C₆₇	—	4	2	no	—
279	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
280	C₂×D₄×C₆₇	C₂×D₄	1	8	yes	—
281	C₂×D₄×C₆₇	#41	1	4	yes	—
282	C₂²×C₄×C₆₇	—	2	2	no	—
283	C₂²×C₄×C₆₇	—	2	2	no	—
284	C₂²×C₄×C₆₇	—	2	4	no	—
285	C₂²×C₄×C₆₇	—	2	4	no	—
286	C₂²×C₄×C₆₇	—	2	2	no	—
287	C₂²×C₄×C₆₇	—	2	4	no	—
288	C₂²×C₄×C₆₇	—	2	4	no	—
289	C₂²×C₄×C₆₇	—	2	2	no	—
290	C₂²×C₄×C₆₇	—	2	4	no	—
291	C₂²×C₄×C₆₇	—	2	4	no	—
292	C₂²×C₄×C₆₇	—	2	4	no	—
293	C₂²×C₄×C₆₇	—	2	2	no	—
294	C₂²×C₄×C₆₇	—	2	4	no	—
295	C₂²×C₄×C₆₇	—	2	2	no	—
296	C₂²×C₄×C₆₇	—	2	2	no	—
297	C₂²×C₄×C₆₇	—	2	2	no	—
298	C₂²×C₄×C₆₇	—	2	2	no	—
299	C₂²×C₄×C₆₇	—	2	2	no	—
300	C₂²×C₄×C₆₇	—	2	4	no	—
301	C₂²×C₄×C₆₇	—	2	2	no	—
302	C₂²×C₄×C₆₇	—	2	2	no	—
303	C₂²×C₄×C₆₇	—	2	4	no	—
304	C₂²×C₄×C₆₇	—	4	1	no	—
305	C₂²×C₄×C₆₇	—	4	1	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	2	no	—
310	C₂²×C₄×C₆₇	—	4	2	no	—
311	C₂²×C₄×C₆₇	—	4	2	no	—
312	C₂²×C₄×C₆₇	—	4	2	no	—
313	C₂²×C₄×C₆₇	—	4	2	no	—
314	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
315	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
316	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
317	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
318	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
319	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
320	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
322	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
323	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
325	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
326	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
327	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
328	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
329	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
330	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
331	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
332	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
333	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
334	C₄⋊C₄×C₆₇	—	2	2	no	—
335	C₄⋊C₄×C₆₇	—	2	2	no	—
336	C₄⋊C₄×C₆₇	—	2	2	no	—
337	C₄⋊C₄×C₆₇	—	2	2	no	—
338	C₄⋊C₄×C₆₇	—	2	4	no	—
339	C₄⋊C₄×C₆₇	—	2	4	no	—
340	C₄⋊C₄×C₆₇	—	2	4	no	—
341	C₄⋊C₄×C₆₇	—	2	2	no	—
342	C₄⋊C₄×C₆₇	—	2	4	no	—
343	C₄⋊C₄×C₆₇	—	2	2	no	—
344	C₄⋊C₄×C₆₇	—	2	4	no	—
345	C₄⋊C₄×C₆₇	—	2	4	no	—
346	C₄⋊C₄×C₆₇	—	2	2	no	—
347	C₄⋊C₄×C₆₇	—	2	2	no	—
348	C₄⋊C₄×C₆₇	—	2	2	no	—
349	C₄⋊C₄×C₆₇	—	2	2	no	—
350	C₄⋊C₄×C₆₇	—	4	1	no	—
351	C₄⋊C₄×C₆₇	—	4	2	no	—
352	C₄⋊C₄×C₆₇	—	4	2	no	—
353	C₄⋊C₄×C₆₇	—	4	2	no	—
354	C₄⋊C₄×C₆₇	—	4	2	no	—
355	C₄⋊C₄×C₆₇	—	4	2	no	—
356	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
357	C₂²⋊C₄×C₆₇	—	2	2	no	—
358	C₂²⋊C₄×C₆₇	—	2	4	no	—
359	C₂²⋊C₄×C₆₇	—	2	4	no	—
360	C₂²⋊C₄×C₆₇	—	2	2	no	—
361	C₂²⋊C₄×C₆₇	—	2	4	no	—
362	C₂²⋊C₄×C₆₇	—	2	4	no	—
363	C₂²⋊C₄×C₆₇	—	2	2	no	—
364	C₂²⋊C₄×C₆₇	—	2	4	no	—
365	C₂²⋊C₄×C₆₇	—	2	4	no	—
366	C₂²⋊C₄×C₆₇	—	2	2	no	—
367	C₂²⋊C₄×C₆₇	—	2	2	no	—
368	C₂²⋊C₄×C₆₇	—	2	4	no	—
369	C₂²⋊C₄×C₆₇	—	2	2	no	—
370	C₂²⋊C₄×C₆₇	—	2	2	no	—
371	C₂²⋊C₄×C₆₇	—	2	2	no	—
372	C₂²⋊C₄×C₆₇	—	4	2	no	—
373	C₂²⋊C₄×C₆₇	—	4	2	no	—
374	C₂²⋊C₄×C₆₇	—	4	1	no	—
375	C₂²⋊C₄×C₆₇	—	4	1	no	—
376	C₂²⋊C₄×C₆₇	—	4	2	no	—
377	C₂²⋊C₄×C₆₇	—	4	2	no	—
378	C₂²⋊C₄×C₆₇	—	4	2	no	—
379	C₂²⋊C₄×C₆₇	—	4	2	no	—
380	C₂²⋊C₄×C₆₇	C₂×D₄	1	8	yes	—
381	C₄²×C₆₇	—	2	4	no	—
382	C₄²×C₆₇	—	2	2	no	—
383	C₄²×C₆₇	—	2	2	no	—
384	C₄²×C₆₇	—	2	2	no	—
385	C₄²×C₆₇	—	2	2	no	—
386	C₄²×C₆₇	—	2	2	no	—
387	C₄²×C₆₇	—	4	2	no	—
388	C₄²×C₆₇	#41	1	4	yes	complemented
389	C₂³×C₆₇	—	2	1	no	—
390	C₂³×C₆₇	—	2	1	no	—
391	C₂³×C₆₇	—	2	1	no	—
392	C₂³×C₆₇	—	2	1	no	—
393	C₂³×C₆₇	—	2	1	no	—
394	C₂³×C₆₇	—	2	2	no	—
395	C₂³×C₆₇	—	2	1	no	—
396	C₂³×C₆₇	—	2	2	no	—
397	C₂³×C₆₇	—	2	2	no	—
398	C₂³×C₆₇	—	2	1	no	—
399	C₂³×C₆₇	—	2	1	no	—
400	C₂³×C₆₇	—	2	2	no	—
401	C₂³×C₆₇	—	2	1	no	—
402	C₂³×C₆₇	—	2	1	no	—
403	C₂³×C₆₇	—	2	2	no	—
404	C₂³×C₆₇	—	2	2	no	—
405	C₂³×C₆₇	—	2	1	no	—
406	C₂³×C₆₇	—	2	1	no	—
407	C₂³×C₆₇	—	2	1	no	—
408	C₂³×C₆₇	—	2	1	no	—
409	C₂³×C₆₇	—	2	1	no	—
410	C₂³×C₆₇	—	2	1	no	—
411	C₂³×C₆₇	—	2	1	no	—
412	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
413	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
414	C₂³×C₆₇	C₂×#41	1	2	yes	—
415	C₂³×C₆₇	C₂×#41	1	2	yes	—
416	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
417	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
418	Q₈×C₆₇	—	4	8	no	—
419	D₄×C₆₇	—	2	16	no	—
420	D₄×C₆₇	—	2	8	no	—
421	D₄×C₆₇	—	2	8	no	—
422	D₄×C₆₇	—	4	4	no	—
423	D₄×C₆₇	—	4	8	no	—
424	D₄×C₆₇	—	4	4	no	—
425	D₄×C₆₇	—	8	4	no	—
426	C₂×C₄×C₆₇	—	2	1	no	—
427	C₂×C₄×C₆₇	—	2	1	no	—
428	C₂×C₄×C₆₇	—	2	1	no	—
429	C₂×C₄×C₆₇	—	2	2	no	—
430	C₂×C₄×C₆₇	—	2	1	no	—
431	C₂×C₄×C₆₇	—	2	2	no	—
432	C₂×C₄×C₆₇	—	2	1	no	—
433	C₂×C₄×C₆₇	—	2	1	no	—
434	C₂×C₄×C₆₇	—	2	1	no	—
435	C₂×C₄×C₆₇	—	2	1	no	—
436	C₂×C₄×C₆₇	—	2	8	no	—
437	C₂×C₄×C₆₇	—	2	1	no	—
438	C₂×C₄×C₆₇	—	2	1	no	—
439	C₂×C₄×C₆₇	—	2	1	no	—
440	C₂×C₄×C₆₇	—	2	2	no	—
441	C₂×C₄×C₆₇	—	2	1	no	—
442	C₂×C₄×C₆₇	—	2	1	no	—
443	C₂×C₄×C₆₇	—	2	2	no	—
444	C₂×C₄×C₆₇	—	2	2	no	—
445	C₂×C₄×C₆₇	—	2	2	no	—
446	C₂×C₄×C₆₇	—	2	1	no	—
447	C₂×C₄×C₆₇	—	2	1	no	—
448	C₂×C₄×C₆₇	—	2	1	no	—
449	C₂×C₄×C₆₇	—	2	1	no	—
450	C₂×C₄×C₆₇	—	2	1	no	—
451	C₂×C₄×C₆₇	—	2	2	no	—
452	C₂×C₄×C₆₇	—	2	1	no	—
453	C₂×C₄×C₆₇	—	2	2	no	—
454	C₂×C₄×C₆₇	—	2	2	no	—
455	C₂×C₄×C₆₇	—	2	2	no	—
456	C₂×C₄×C₆₇	—	2	2	no	—
457	C₂×C₄×C₆₇	—	2	1	no	—
458	C₂×C₄×C₆₇	—	2	2	no	—
459	C₂×C₄×C₆₇	—	2	2	no	—
460	C₂×C₄×C₆₇	—	2	1	no	—
461	C₂×C₄×C₆₇	—	2	2	no	—
462	C₂×C₄×C₆₇	—	2	1	no	—
463	C₂×C₄×C₆₇	—	2	1	no	—
464	C₂×C₄×C₆₇	—	2	2	no	—
465	C₂×C₄×C₆₇	—	2	1	no	—
466	C₂×C₄×C₆₇	—	2	1	no	—
467	C₂×C₄×C₆₇	—	2	1	no	—
468	C₂×C₄×C₆₇	—	2	2	no	—
469	C₂×C₄×C₆₇	—	2	2	no	—
470	C₂×C₄×C₆₇	—	2	1	no	—
471	C₂×C₄×C₆₇	—	2	2	no	—
472	C₂×C₄×C₆₇	—	2	1	no	—
473	C₂×C₄×C₆₇	—	2	1	no	—
474	C₂×C₄×C₆₇	—	2	2	no	—
475	C₂×C₄×C₆₇	—	2	2	no	—
476	C₂×C₄×C₆₇	—	4	4	no	—
477	C₂×C₄×C₆₇	—	4	4	no	—
478	C₂×C₄×C₆₇	—	4	8	no	—
479	C₂×C₄×C₆₇	—	4	8	no	—
480	C₂×C₄×C₆₇	—	4	8	no	—
481	C₂×C₄×C₆₇	—	4	4	no	—
482	C₂×C₄×C₆₇	—	4	4	no	—
483	C₂×C₄×C₆₇	—	8	4	no	—
484	C₂×C₄×C₆₇	—	8	4	no	—
485	C₂×C₄×C₆₇	—	8	4	no	—
486	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
487	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
488	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
489	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
490	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
491	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
492	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
493	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
494	C₂²×C₆₇	—	2	2	no	—
495	C₂²×C₆₇	—	2	2	no	—
496	C₂²×C₆₇	—	2	2	no	—
497	C₂²×C₆₇	—	2	2	no	—
498	C₂²×C₆₇	—	2	2	no	—
499	C₂²×C₆₇	—	2	2	no	—
500	C₂²×C₆₇	—	2	2	no	—
501	C₂²×C₆₇	—	2	4	no	—
502	C₂²×C₆₇	—	2	4	no	—
503	C₂²×C₆₇	—	2	2	no	—
504	C₂²×C₆₇	—	2	4	no	—
505	C₂²×C₆₇	—	2	2	no	—
506	C₂²×C₆₇	—	4	1	no	—
507	C₂²×C₆₇	—	4	2	no	—
508	C₂²×C₆₇	—	4	2	no	—
509	C₂²×C₆₇	—	4	1	no	—
510	C₂²×C₆₇	—	4	1	no	—
511	C₂²×C₆₇	—	4	2	no	—
512	C₂²×C₆₇	—	4	2	no	—
513	C₂²×C₆₇	—	4	1	no	—
514	C₂²×C₆₇	—	4	1	no	—
515	C₂²×C₆₇	—	4	1	no	—
516	C₂²×C₆₇	—	4	1	no	—
517	C₂²×C₆₇	—	4	1	no	—
518	C₂²×C₆₇	—	4	1	no	—
519	C₂²×C₆₇	—	4	1	no	—
520	C₂²×C₆₇	—	4	1	no	—
521	C₂²×C₆₇	#546	1	4	yes	—
522	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
523	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
524	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
525	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
526	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
527	C₂²×C₆₇	#585	1	1	yes	characteristic
528	C₂²×C₆₇	#585	1	1	yes	characteristic
529	C₄×C₆₇	—	2	2	no	—
530	C₄×C₆₇	—	2	4	no	—
531	C₄×C₆₇	—	2	2	no	—
532	C₄×C₆₇	—	2	2	no	—
533	C₄×C₆₇	—	2	2	no	—
534	C₄×C₆₇	—	4	2	no	—
535	C₄×C₆₇	—	4	2	no	—
536	C₄×C₆₇	—	4	1	no	—
537	C₄×C₆₇	—	4	1	no	—
538	C₄×C₆₇	—	4	1	no	—
539	C₄×C₆₇	—	4	1	no	—
540	C₄×C₆₇	—	4	1	no	—
541	C₄×C₆₇	—	4	2	no	—
542	C₄×C₆₇	—	4	1	no	—
543	C₄×C₆₇	—	4	2	no	—
544	C₄×C₆₇	—	4	1	no	—
545	C₄×C₆₇	—	4	2	no	—
546	C₄×C₆₇	—	4	2	no	—
547	C₄×C₆₇	#547	1	4	yes	—
548	#59318	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
549	C₂×C₆₇	—	2	4	no	—
550	C₂×C₆₇	—	4	2	no	—
551	C₂×C₆₇	—	4	4	no	—
552	C₂×C₆₇	—	8	1	no	—
553	C₂×C₆₇	C₂×#546	1	1	yes	characteristic
554	C₂×C₆₇	C₂×#547	1	1	yes	characteristic
555	C₂×C₆₇	#3475	1	1	yes	characteristic
556	C₂×C₆₇	#3494	1	1	yes	characteristic
557	C₂×C₆₇	#3500	1	1	yes	characteristic
558	C₂×C₆₇	#3515	1	1	yes	characteristic
559	C₂×C₆₇	#3559	1	1	yes	characteristic
560	C₂×#553	C₂×C₆₇	1	1	yes	characteristic, complemented
561	C₂×#547	C₂×C₆₇	1	1	yes	characteristic, complemented
562	#2706	C₂×C₆₇	1	2	yes	complemented
563	#2698	C₂×C₆₇	1	2	yes	complemented
564	#2553	C₂×C₆₇	1	2	yes	complemented
565	#2550	C₂×C₆₇	1	1	yes	characteristic, complemented
566	#2535	C₂×C₆₇	1	1	yes	characteristic, complemented
567	#2488	C₂×C₆₇	1	2	yes	complemented
568	#2487	C₂×C₆₇	1	1	yes	characteristic, complemented
569	#2486	C₂×C₆₇	1	1	yes	characteristic, complemented
570	#2442	C₂×C₆₇	1	1	yes	characteristic, complemented
571	#2439	C₂×C₆₇	1	1	yes	characteristic, complemented
572	#2430	C₂×C₆₇	1	2	yes	complemented
573	#2425	C₂×C₆₇	1	2	yes	complemented
574	#2420	C₂×C₆₇	1	1	yes	characteristic, complemented
575	#2420	C₂×C₆₇	1	1	yes	characteristic, complemented
576	#2419	C₂×C₆₇	1	2	yes	complemented
577	#2352	C₂×C₆₇	1	1	yes	characteristic, complemented
578	#2349	C₂×C₆₇	1	1	yes	characteristic, complemented
579	#2339	C₂×C₆₇	1	2	yes	complemented
580	C₄×#121	C₂×C₆₇	1	1	yes	characteristic, complemented
581	C₄×#121	C₂×C₆₇	1	1	yes	characteristic, complemented
582	C₂×#382	C₂×C₆₇	1	1	yes	characteristic, complemented
583	C₆₇	#59318	1	1	yes	characteristic, direct product factor, Sylow
584	C₂²×#41	C₂²×C₆₇	1	2	yes	—
585	#553	—	2	8	no	—
586	#547	—	2	8	no	—
587	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
588	C₂×#126	C₂²×C₆₇	1	2	yes	—
589	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
590	C₂×#123	C₂²×C₆₇	1	2	yes	—
591	C₂×#123	C₂²×C₆₇	1	2	yes	—
592	C₂×#123	C₂²×C₆₇	1	2	yes	—
593	C₂×#123	C₂²×C₆₇	1	2	yes	—
594	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
595	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
596	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
597	C₂×#121	C₂²×C₆₇	1	2	yes	—
598	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
599	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
600	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
601	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
602	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
603	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
604	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
605	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
606	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
607	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
608	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
609	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
610	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
611	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
612	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
613	#400	C₂²×C₆₇	1	2	yes	—
614	#400	C₂²×C₆₇	1	2	yes	—
615	#399	C₂²×C₆₇	1	2	yes	—
616	#398	C₂²×C₆₇	1	2	yes	—
617	#398	C₂²×C₆₇	1	2	yes	—
618	#398	C₂²×C₆₇	1	2	yes	—
619	#397	C₂²×C₆₇	1	2	yes	—
620	#397	C₂²×C₆₇	1	2	yes	—
621	#397	C₂²×C₆₇	1	2	yes	—
622	#397	C₂²×C₆₇	1	2	yes	—
623	#396	C₂²×C₆₇	1	2	yes	—
624	#395	C₂²×C₆₇	1	2	yes	—
625	#394	C₂²×C₆₇	1	2	yes	—
626	#394	C₂²×C₆₇	1	2	yes	—
627	#393	C₂²×C₆₇	1	2	yes	—
628	#392	C₂²×C₆₇	1	2	yes	—
629	#391	C₂²×C₆₇	1	2	yes	—
630	#391	C₂²×C₆₇	1	2	yes	—
631	#390	C₂²×C₆₇	1	1	yes	characteristic
632	#390	C₂²×C₆₇	1	1	yes	characteristic
633	#389	C₂²×C₆₇	1	1	yes	characteristic
634	#389	C₂²×C₆₇	1	1	yes	characteristic
635	#389	C₂²×C₆₇	1	1	yes	characteristic
636	#389	C₂²×C₆₇	1	1	yes	characteristic
637	#389	C₂²×C₆₇	1	2	yes	—
638	#389	C₂²×C₆₇	1	1	yes	characteristic
639	#389	C₂²×C₆₇	1	1	yes	characteristic
640	#388	C₂²×C₆₇	1	2	yes	—
641	#388	C₂²×C₆₇	1	2	yes	—
642	#388	C₂²×C₆₇	1	1	yes	characteristic
643	#388	C₂²×C₆₇	1	1	yes	characteristic
644	#387	C₂²×C₆₇	1	2	yes	—
645	#387	C₂²×C₆₇	1	2	yes	—
646	#386	C₂²×C₆₇	1	1	yes	characteristic
647	#386	C₂²×C₆₇	1	2	yes	—
648	#386	C₂²×C₆₇	1	2	yes	—
649	#386	C₂²×C₆₇	1	2	yes	—
650	#386	C₂²×C₆₇	1	2	yes	—
651	#386	C₂²×C₆₇	1	2	yes	—
652	#386	C₂²×C₆₇	1	2	yes	—
653	#386	C₂²×C₆₇	1	1	yes	characteristic
654	#386	C₂²×C₆₇	1	2	yes	—
655	#385	C₂²×C₆₇	1	2	yes	—
656	#385	C₂²×C₆₇	1	2	yes	—
657	#385	C₂²×C₆₇	1	2	yes	—
658	#385	C₂²×C₆₇	1	2	yes	—
659	#382	C₂²×C₆₇	1	1	yes	characteristic
660	#382	C₂²×C₆₇	1	1	yes	characteristic
661	#382	C₂²×C₆₇	1	1	yes	characteristic
662	#382	C₂²×C₆₇	1	2	yes	—
663	#382	C₂²×C₆₇	1	2	yes	—
664	#382	C₂²×C₆₇	1	1	yes	characteristic
665	#381	C₂²×C₆₇	1	2	yes	—
666	#381	C₂²×C₆₇	1	2	yes	—
667	#381	C₂²×C₆₇	1	2	yes	—
668	#380	C₂²×C₆₇	1	2	yes	—
669	#380	C₂²×C₆₇	1	2	yes	—
670	#380	C₂²×C₆₇	1	1	yes	characteristic
671	#380	C₂²×C₆₇	1	1	yes	characteristic
672	#380	C₂²×C₆₇	1	1	yes	characteristic
673	#380	C₂²×C₆₇	1	1	yes	characteristic
674	#380	C₂²×C₆₇	1	1	yes	characteristic
675	#380	C₂²×C₆₇	1	1	yes	characteristic
676	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
677	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
678	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
679	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
680	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
681	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
682	C₂×#95	C₂²×C₆₇	1	2	yes	—
683	C₂×#95	C₂²×C₆₇	1	2	yes	—
684	C₂×#95	C₂²×C₆₇	1	2	yes	—
685	C₂×#41	—	2	8	no	—
686	C₂×#41	—	2	8	no	—
687	C₂×#41	—	4	4	no	—
688	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
689	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
690	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
691	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
692	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
693	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
694	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
695	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
696	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
697	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
698	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
699	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
700	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
701	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
702	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
703	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
704	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
705	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
706	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
707	C₄⋊Q₈	—	2	4	no	—
708	#126	—	2	8	no	—
709	#125	—	2	4	no	—
710	#123	—	2	8	no	—
711	#123	—	2	8	no	—
712	#123	—	2	8	no	—
713	#123	—	4	4	no	—
714	C₂²⋊Q₈	—	2	8	no	—
715	#121	—	2	4	no	—
716	#121	—	2	4	no	—
717	#121	—	2	8	no	—
718	#121	—	2	4	no	—
719	#121	D₄×C₆₇	1	8	yes	complemented
720	C₄×D₄	—	2	4	no	—
721	C₄×D₄	—	2	8	no	—
722	C₄×D₄	—	2	4	no	—
723	C₄×D₄	—	2	4	no	—
724	C₄×D₄	—	2	4	no	—
725	C₄×D₄	—	2	4	no	—
726	C₄×D₄	—	2	4	no	—
727	C₄×D₄	—	4	4	no	—
728	#117	—	2	4	no	—
729	C₂×C₄⋊C₄	—	2	4	no	—
730	C₂×C₄⋊C₄	—	2	4	no	—
731	C₂×C₄⋊C₄	—	2	4	no	—
732	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
733	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
734	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
735	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
736	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
737	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
738	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
739	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
740	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
741	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
742	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
743	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
744	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
745	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
746	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
747	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
748	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
749	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
750	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
751	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
752	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
753	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
754	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
755	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
756	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
757	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
758	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
759	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
760	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
761	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
762	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
763	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
764	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
765	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
766	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
767	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
768	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
769	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
770	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
771	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
772	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
773	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
774	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
775	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
776	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
777	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
778	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
779	C₂×C₄²	—	2	4	no	—
780	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
781	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
782	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
783	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
784	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
785	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
786	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
787	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
788	#95	C₂³×C₆₇	1	2	yes	—
789	#95	C₂³×C₆₇	1	1	yes	characteristic
790	#95	C₂³×C₆₇	1	2	yes	—
791	#95	C₂³×C₆₇	1	2	yes	—
792	#95	C₂³×C₆₇	1	2	yes	—
793	#95	C₂³×C₆₇	1	2	yes	—
794	#95	C₂³×C₆₇	1	2	yes	—
795	#95	C₂³×C₆₇	1	2	yes	—
796	#95	C₂³×C₆₇	1	2	yes	—
797	#95	C₂³×C₆₇	1	2	yes	—
798	#95	C₂³×C₆₇	1	2	yes	—
799	#95	C₂³×C₆₇	1	2	yes	—
800	#95	C₂³×C₆₇	1	1	yes	characteristic
801	#95	C₂³×C₆₇	1	1	yes	characteristic
802	#95	C₂³×C₆₇	1	2	yes	—
803	#95	C₂³×C₆₇	1	1	yes	characteristic
804	#95	C₂³×C₆₇	1	2	yes	—
805	#95	C₂³×C₆₇	1	1	yes	characteristic
806	#95	C₂³×C₆₇	1	1	yes	characteristic
807	#95	C₂³×C₆₇	1	2	yes	—
808	#95	C₂³×C₆₇	1	2	yes	—
809	#95	C₂³×C₆₇	1	2	yes	—
810	#95	C₂³×C₆₇	1	2	yes	—
811	#95	C₂³×C₆₇	1	2	yes	—
812	#95	C₂³×C₆₇	1	2	yes	—
813	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
814	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
815	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
816	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
817	#41	—	4	32	no	—
818	C₂×Q₈	—	2	4	no	—
819	C₂×Q₈	—	2	4	no	—
820	C₂×Q₈	—	4	2	no	—
821	C₂×D₄	—	2	2	no	—
822	C₂×D₄	—	2	4	no	—
823	C₂×D₄	—	2	4	no	—
824	C₂×D₄	—	2	2	no	—
825	C₂×D₄	—	2	2	no	—
826	C₂×D₄	—	2	4	no	—
827	C₂×D₄	—	2	2	no	—
828	C₂×D₄	—	2	2	no	—
829	C₂×D₄	—	2	4	no	—
830	C₂×D₄	—	2	2	no	—
831	C₂×D₄	—	2	4	no	—
832	C₂×D₄	—	2	2	no	—
833	C₂×D₄	—	2	2	no	—
834	C₂×D₄	—	2	2	no	—
835	C₂×D₄	—	4	2	no	—
836	C₂×D₄	—	4	1	no	—
837	C₂×D₄	—	4	2	no	—
838	C₂×D₄	—	4	2	no	—
839	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
840	C₂×D₄	C₂×D₄×C₆₇	1	8	yes	—
841	C₂×D₄	#41×C₆₇	1	4	yes	—
842	C₂²×C₄	—	2	2	no	—
843	C₂²×C₄	—	2	2	no	—
844	C₂²×C₄	—	2	4	no	—
845	C₂²×C₄	—	2	4	no	—
846	C₂²×C₄	—	2	2	no	—
847	C₂²×C₄	—	2	4	no	—
848	C₂²×C₄	—	2	4	no	—
849	C₂²×C₄	—	2	2	no	—
850	C₂²×C₄	—	2	4	no	—
851	C₂²×C₄	—	2	4	no	—
852	C₂²×C₄	—	2	4	no	—
853	C₂²×C₄	—	2	2	no	—
854	C₂²×C₄	—	2	4	no	—
855	C₂²×C₄	—	2	2	no	—
856	C₂²×C₄	—	2	2	no	—
857	C₂²×C₄	—	2	2	no	—
858	C₂²×C₄	—	2	2	no	—
859	C₂²×C₄	—	2	2	no	—
860	C₂²×C₄	—	2	4	no	—
861	C₂²×C₄	—	2	2	no	—
862	C₂²×C₄	—	2	2	no	—
863	C₂²×C₄	—	2	4	no	—
864	C₂²×C₄	—	4	2	no	—
865	C₂²×C₄	—	4	2	no	—
866	C₂²×C₄	—	4	1	no	—
867	C₂²×C₄	—	4	1	no	—
868	C₂²×C₄	—	4	2	no	—
869	C₂²×C₄	—	4	2	no	—
870	C₂²×C₄	—	4	2	no	—
871	C₂²×C₄	—	4	2	no	—
872	C₂²×C₄	—	4	2	no	—
873	C₂²×C₄	—	4	2	no	—
874	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
875	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
876	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
877	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
878	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
879	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
880	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
881	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
882	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
883	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
884	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
885	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
886	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
887	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
888	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
889	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
890	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
891	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
892	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
893	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
894	C₄⋊C₄	—	2	2	no	—
895	C₄⋊C₄	—	2	2	no	—
896	C₄⋊C₄	—	2	2	no	—
897	C₄⋊C₄	—	2	2	no	—
898	C₄⋊C₄	—	2	4	no	—
899	C₄⋊C₄	—	2	4	no	—
900	C₄⋊C₄	—	2	4	no	—
901	C₄⋊C₄	—	2	2	no	—
902	C₄⋊C₄	—	2	4	no	—
903	C₄⋊C₄	—	2	2	no	—
904	C₄⋊C₄	—	2	4	no	—
905	C₄⋊C₄	—	2	4	no	—
906	C₄⋊C₄	—	2	2	no	—
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	—	2	2	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	4	2	no	—
911	C₄⋊C₄	—	4	2	no	—
912	C₄⋊C₄	—	4	2	no	—
913	C₄⋊C₄	—	4	1	no	—
914	C₄⋊C₄	—	4	2	no	—
915	C₄⋊C₄	—	4	2	no	—
916	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
917	C₂²⋊C₄	—	2	2	no	—
918	C₂²⋊C₄	—	2	4	no	—
919	C₂²⋊C₄	—	2	4	no	—
920	C₂²⋊C₄	—	2	2	no	—
921	C₂²⋊C₄	—	2	4	no	—
922	C₂²⋊C₄	—	2	4	no	—
923	C₂²⋊C₄	—	2	2	no	—
924	C₂²⋊C₄	—	2	4	no	—
925	C₂²⋊C₄	—	2	4	no	—
926	C₂²⋊C₄	—	2	2	no	—
927	C₂²⋊C₄	—	2	2	no	—
928	C₂²⋊C₄	—	2	4	no	—
929	C₂²⋊C₄	—	2	2	no	—
930	C₂²⋊C₄	—	2	2	no	—
931	C₂²⋊C₄	—	2	2	no	—
932	C₂²⋊C₄	—	4	2	no	—
933	C₂²⋊C₄	—	4	2	no	—
934	C₂²⋊C₄	—	4	2	no	—
935	C₂²⋊C₄	—	4	2	no	—
936	C₂²⋊C₄	—	4	2	no	—
937	C₂²⋊C₄	—	4	1	no	—
938	C₂²⋊C₄	—	4	1	no	—
939	C₂²⋊C₄	—	4	2	no	—
940	C₂²⋊C₄	C₂×D₄×C₆₇	1	8	yes	—
941	C₄²	—	2	4	no	—
942	C₄²	—	2	2	no	—
943	C₄²	—	2	2	no	—
944	C₄²	—	2	2	no	—
945	C₄²	—	2	2	no	—
946	C₄²	—	2	2	no	—
947	C₄²	—	4	2	no	—
948	C₄²	#41×C₆₇	1	4	yes	complemented
949	C₂³	—	2	1	no	—
950	C₂³	—	2	1	no	—
951	C₂³	—	2	1	no	—
952	C₂³	—	2	1	no	—
953	C₂³	—	2	1	no	—
954	C₂³	—	2	2	no	—
955	C₂³	—	2	1	no	—
956	C₂³	—	2	2	no	—
957	C₂³	—	2	2	no	—
958	C₂³	—	2	1	no	—
959	C₂³	—	2	1	no	—
960	C₂³	—	2	2	no	—
961	C₂³	—	2	1	no	—
962	C₂³	—	2	1	no	—
963	C₂³	—	2	2	no	—
964	C₂³	—	2	2	no	—
965	C₂³	—	2	1	no	—
966	C₂³	—	2	1	no	—
967	C₂³	—	2	1	no	—
968	C₂³	—	2	1	no	—
969	C₂³	—	2	1	no	—
970	C₂³	—	2	1	no	—
971	C₂³	—	2	1	no	—
972	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
973	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
974	C₂³	C₂×#41×C₆₇	1	2	yes	—
975	C₂³	C₂×#41×C₆₇	1	2	yes	—
976	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
977	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
978	Q₈	—	4	8	no	—
979	D₄	—	2	16	no	—
980	D₄	—	2	8	no	—
981	D₄	—	2	8	no	—
982	D₄	—	4	4	no	—
983	D₄	—	4	8	no	—
984	D₄	—	4	4	no	—
985	D₄	—	8	4	no	—
986	C₂×C₄	—	2	1	no	—
987	C₂×C₄	—	2	1	no	—
988	C₂×C₄	—	2	1	no	—
989	C₂×C₄	—	2	2	no	—
990	C₂×C₄	—	2	1	no	—
991	C₂×C₄	—	2	2	no	—
992	C₂×C₄	—	2	1	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	8	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	2	1	no	—
1002	C₂×C₄	—	2	1	no	—
1003	C₂×C₄	—	2	2	no	—
1004	C₂×C₄	—	2	2	no	—
1005	C₂×C₄	—	2	2	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	2	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	2	2	no	—
1016	C₂×C₄	—	2	2	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	2	no	—
1019	C₂×C₄	—	2	2	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	2	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	2	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	1	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	2	2	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	2	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	2	no	—
1035	C₂×C₄	—	2	2	no	—
1036	C₂×C₄	—	4	8	no	—
1037	C₂×C₄	—	4	8	no	—
1038	C₂×C₄	—	4	4	no	—
1039	C₂×C₄	—	4	4	no	—
1040	C₂×C₄	—	4	8	no	—
1041	C₂×C₄	—	4	4	no	—
1042	C₂×C₄	—	4	4	no	—
1043	C₂×C₄	—	8	4	no	—
1044	C₂×C₄	—	8	4	no	—
1045	C₂×C₄	—	8	4	no	—
1046	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
1047	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1048	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1049	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1050	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1051	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1052	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1053	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
1054	C₂²	—	2	2	no	—
1055	C₂²	—	2	2	no	—
1056	C₂²	—	2	2	no	—
1057	C₂²	—	2	2	no	—
1058	C₂²	—	2	2	no	—
1059	C₂²	—	2	2	no	—
1060	C₂²	—	2	2	no	—
1061	C₂²	—	2	4	no	—
1062	C₂²	—	2	4	no	—
1063	C₂²	—	2	2	no	—
1064	C₂²	—	2	4	no	—
1065	C₂²	—	2	2	no	—
1066	C₂²	—	4	2	no	—
1067	C₂²	—	4	1	no	—
1068	C₂²	—	4	1	no	—
1069	C₂²	—	4	2	no	—
1070	C₂²	—	4	2	no	—
1071	C₂²	—	4	1	no	—
1072	C₂²	—	4	1	no	—
1073	C₂²	—	4	2	no	—
1074	C₂²	—	4	1	no	—
1075	C₂²	—	4	1	no	—
1076	C₂²	—	4	1	no	—
1077	C₂²	—	4	1	no	—
1078	C₂²	—	4	1	no	—
1079	C₂²	—	4	1	no	—
1080	C₂²	—	4	1	no	—
1081	C₂²	#546×C₆₇	1	4	yes	—
1082	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1083	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1084	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1085	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1086	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
1087	C₂²	#585×C₆₇	1	1	yes	characteristic
1088	C₂²	#585×C₆₇	1	1	yes	characteristic
1089	C₄	—	2	2	no	—
1090	C₄	—	2	4	no	—
1091	C₄	—	2	2	no	—
1092	C₄	—	2	2	no	—
1093	C₄	—	2	2	no	—
1094	C₄	—	4	2	no	—
1095	C₄	—	4	2	no	—
1096	C₄	—	4	2	no	—
1097	C₄	—	4	1	no	—
1098	C₄	—	4	1	no	—
1099	C₄	—	4	1	no	—
1100	C₄	—	4	1	no	—
1101	C₄	—	4	1	no	—
1102	C₄	—	4	2	no	—
1103	C₄	—	4	2	no	—
1104	C₄	—	4	1	no	—
1105	C₄	—	4	2	no	—
1106	C₄	—	4	1	no	—
1107	C₄	#547×C₆₇	1	4	yes	—
1108	C₂	—	2	4	no	—
1109	C₂	—	4	2	no	—
1110	C₂	—	4	4	no	—
1111	C₂	—	8	1	no	—
1112	C₂	C₂×#546×C₆₇	1	1	yes	characteristic
1113	C₂	C₂×#547×C₆₇	1	1	yes	characteristic
1114	C₂	C₆₇×#3475	1	1	yes	characteristic
1115	C₂	C₆₇×#3494	1	1	yes	characteristic
1116	C₂	C₆₇×#3500	1	1	yes	characteristic
1117	C₂	C₆₇×#3515	1	1	yes	characteristic
1118	C₂	C₆₇×#3559	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#553×C₆₇	C₂	semidirect
2. C₂×#547×C₆₇	C₂	semidirect
3. C₆₇×#2706	C₂	semidirect
4. C₆₇×#2698	C₂	semidirect
5. C₆₇×#2553	C₂	semidirect
6. C₆₇×#2550	C₂	semidirect
7. C₆₇×#2535	C₂	semidirect
8. C₆₇×#2488	C₂	semidirect
9. C₆₇×#2487	C₂	semidirect
10. C₆₇×#2486	C₂	semidirect
11. C₆₇×#2442	C₂	semidirect
12. C₆₇×#2439	C₂	semidirect
13. C₆₇×#2430	C₂	semidirect
14. C₆₇×#2425	C₂	semidirect
15. C₆₇×#2420	C₂	semidirect
16. C₆₇×#2420	C₂	semidirect
17. C₆₇×#2419	C₂	semidirect
18. C₆₇×#2352	C₂	semidirect
19. C₆₇×#2349	C₂	semidirect
20. C₆₇×#2339	C₂	semidirect
21. C₄×#121×C₆₇	C₂	semidirect
22. C₄×#121×C₆₇	C₂	semidirect
23. C₂×#382×C₆₇	C₂	semidirect
159. #121×C₆₇	D₄	semidirect
388. C₄²×C₆₇	#41	semidirect
548. #59318	C₆₇	direct (N × H)
560. C₂×#553	C₂×C₆₇	semidirect
561. C₂×#547	C₂×C₆₇	semidirect
562. #2706	C₂×C₆₇	semidirect
563. #2698	C₂×C₆₇	semidirect
564. #2553	C₂×C₆₇	semidirect
565. #2550	C₂×C₆₇	semidirect
566. #2535	C₂×C₆₇	semidirect
567. #2488	C₂×C₆₇	semidirect
568. #2487	C₂×C₆₇	semidirect
569. #2486	C₂×C₆₇	semidirect
570. #2442	C₂×C₆₇	semidirect
571. #2439	C₂×C₆₇	semidirect
572. #2430	C₂×C₆₇	semidirect
573. #2425	C₂×C₆₇	semidirect
574. #2420	C₂×C₆₇	semidirect
575. #2420	C₂×C₆₇	semidirect
576. #2419	C₂×C₆₇	semidirect
577. #2352	C₂×C₆₇	semidirect
578. #2349	C₂×C₆₇	semidirect
579. #2339	C₂×C₆₇	semidirect
580. C₄×#121	C₂×C₆₇	semidirect
581. C₄×#121	C₂×C₆₇	semidirect
582. C₂×#382	C₂×C₆₇	semidirect
583. C₆₇	#59318	direct (N × H)
719. #121	D₄×C₆₇	semidirect
948. C₄²	#41×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#553×C₆₇	2
C₂×#547×C₆₇	2
C₆₇×#2706	2
C₆₇×#2698	2
C₆₇×#2553	2
C₆₇×#2550	2
C₆₇×#2535	2
C₆₇×#2488	2
C₆₇×#2487	2
C₆₇×#2486	2
C₆₇×#2442	2
C₆₇×#2439	2
C₆₇×#2430	2
C₆₇×#2425	2
C₆₇×#2420	2
C₆₇×#2419	2
C₆₇×#2352	2
C₆₇×#2349	2
C₆₇×#2339	2
C₄×#121×C₆₇	2
C₂×#382×C₆₇	2
#59318	67

Subgroups — C67×#59318 #30738569

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59318 #30738569