Subgroups — C₆₇×#20998 #30700249

Order 17152.

1704 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#575×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#3428	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#421×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2896	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#410×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#1905	C₂	1	4	yes	maximal, complemented
7	C₆₇×#1904	C₂	1	4	yes	maximal, complemented
8	C₂×#344×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×H(3,ℤ/4)×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
11	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
12	#575×C₆₇	—	2	2	no	—
13	#575×C₆₇	—	2	2	no	—
14	#575×C₆₇	—	2	2	no	—
15	#575×C₆₇	—	2	2	no	—
16	C₂×#137×C₆₇	C₄	1	2	yes	complemented
17	C₂×#137×C₆₇	C₂²	1	2	yes	—
18	C₂×AGL(1,ℤ/8)×C₆₇	C₄	1	2	yes	complemented
19	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	—
20	C₂×#135×C₆₇	C₄	1	4	yes	complemented
21	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
22	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
23	#520×C₆₇	—	2	2	no	—
24	#520×C₆₇	—	2	2	no	—
25	#519×C₆₇	C₂²	1	2	yes	complemented
26	#518×C₆₇	—	2	2	no	—
27	#518×C₆₇	C₂²	1	2	yes	complemented
28	C₄×#41×C₆₇	—	2	2	no	—
29	C₄×#41×C₆₇	—	2	2	no	—
30	C₂×#117×C₆₇	—	2	2	no	—
31	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
32	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
34	#421×C₆₇	—	2	2	no	—
35	#421×C₆₇	C₂²	1	4	yes	—
36	C₂×#104×C₆₇	—	2	2	no	—
37	#419×C₆₇	C₂²	1	2	yes	complemented
38	#418×C₆₇	C₂²	1	2	yes	complemented
39	#417×C₆₇	—	2	2	no	—
40	#416×C₆₇	—	2	2	no	—
41	#410×C₆₇	—	2	2	no	—
42	#410×C₆₇	C₂²	1	4	yes	—
43	C₂×#99×C₆₇	—	2	2	no	—
44	#344×C₆₇	C₂²	1	4	yes	complemented
45	H(3,ℤ/4)×C₆₇	C₂²	1	4	yes	complemented
46	C₂×#41×C₆₇	—	2	1	no	—
47	C₂×#41×C₆₇	—	2	1	no	—
48	C₂×#41×C₆₇	—	2	1	no	—
49	C₂×#41×C₆₇	—	2	1	no	—
50	C₂×#41×C₆₇	—	2	1	no	—
51	C₂×#41×C₆₇	—	2	1	no	—
52	C₂×#41×C₆₇	—	2	1	no	—
53	C₂×#41×C₆₇	—	2	1	no	—
54	C₂×#41×C₆₇	—	2	1	no	—
55	C₂×#41×C₆₇	—	2	1	no	—
56	C₂×#41×C₆₇	—	2	1	no	—
57	C₂×#41×C₆₇	—	2	1	no	—
58	C₂×#41×C₆₇	—	2	1	no	—
59	C₂×#41×C₆₇	—	2	1	no	—
60	C₂×#41×C₆₇	—	2	1	no	—
61	C₂×#41×C₆₇	—	2	1	no	—
62	C₂×#41×C₆₇	C₂×C₄	1	2	yes	—
63	C₂×#41×C₆₇	C₂×C₄	1	2	yes	—
64	C₂×#41×C₆₇	C₂×C₄	1	2	yes	complemented
65	C₂×#41×C₆₇	D₄	1	2	yes	—
66	C₂×#41×C₆₇	D₄	1	2	yes	—
67	C₂×#41×C₆₇	D₄	1	2	yes	—
68	C₂×#41×C₆₇	D₄	1	2	yes	—
69	C₂×#41×C₆₇	C₂³	1	2	yes	—
70	C₂²×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic, complemented
71	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
72	C₂²×D₄×C₆₇	—	2	1	no	—
73	C₂²×D₄×C₆₇	—	2	1	no	—
74	C₂²×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic, complemented
75	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₆₇	—	2	1	no	—
77	C₂³×C₄×C₆₇	—	2	1	no	—
78	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
79	#137×C₆₇	—	2	4	no	—
80	#137×C₆₇	—	2	4	no	—
81	#137×C₆₇	—	2	4	no	—
82	#137×C₆₇	—	2	4	no	—
83	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
84	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
85	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
86	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
87	#135×C₆₇	—	2	8	no	—
88	#135×C₆₇	—	2	8	no	—
89	C₂×Q₁₆×C₆₇	C₂×C₄	1	4	yes	complemented
90	C₂×SD₁₆×C₆₇	C₂×C₄	1	4	yes	complemented
91	C₂×SD₁₆×C₆₇	C₂×C₄	1	4	yes	complemented
92	C₂×D₈×C₆₇	C₂×C₄	1	4	yes	complemented
93	C₂×M₁₆×C₆₇	—	2	1	no	—
94	C₂×M₁₆×C₆₇	—	2	1	no	—
95	C₂×M₁₆×C₆₇	—	2	1	no	—
96	C₂×M₁₆×C₆₇	—	2	1	no	—
97	C₂×M₁₆×C₆₇	—	2	1	no	—
98	C₂×M₁₆×C₆₇	—	2	1	no	—
99	C₂×M₁₆×C₆₇	—	2	1	no	—
100	C₂×M₁₆×C₆₇	—	2	1	no	—
101	C₂×M₁₆×C₆₇	—	2	1	no	—
102	C₂×M₁₆×C₆₇	C₂×C₄	1	2	yes	complemented
103	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
104	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
105	C₂²×C₈×C₆₇	—	2	1	no	—
106	C₂²×C₈×C₆₇	C₂×C₄	1	2	yes	complemented
107	C₄×Q₈×C₆₇	—	2	4	no	—
108	C₄×Q₈×C₆₇	—	2	4	no	—
109	C₄×D₄×C₆₇	—	2	8	no	—
110	C₄×D₄×C₆₇	—	2	8	no	—
111	C₄×D₄×C₆₇	—	2	4	no	—
112	C₄×D₄×C₆₇	—	2	4	no	—
113	#117×C₆₇	—	2	4	no	—
114	#117×C₆₇	—	2	4	no	—
115	#117×C₆₇	—	2	1	no	—
116	#117×C₆₇	—	2	1	no	—
117	#117×C₆₇	—	2	1	no	—
118	#117×C₆₇	—	2	1	no	—
119	#117×C₆₇	—	2	4	no	—
120	#117×C₆₇	—	2	1	no	—
121	#117×C₆₇	—	2	1	no	—
122	#117×C₆₇	—	2	1	no	—
123	#117×C₆₇	D₄	1	2	yes	—
124	#117×C₆₇	D₄	1	2	yes	—
125	#117×C₆₇	C₂³	1	2	yes	—
126	#117×C₆₇	C₂³	1	2	yes	—
127	#117×C₆₇	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
129	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
130	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
131	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
132	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
133	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
134	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
135	C₂×C₂²⋊C₄×C₆₇	D₄	1	2	yes	—
136	C₂×C₄²×C₆₇	—	2	4	no	—
137	C₂×C₄²×C₆₇	—	2	1	no	—
138	C₂×C₄²×C₆₇	—	2	1	no	—
139	C₂×C₄²×C₆₇	D₄	1	2	yes	—
140	#104×C₆₇	—	2	8	no	—
141	#103×C₆₇	—	2	4	no	—
142	#102×C₆₇	—	2	4	no	—
143	#99×C₆₇	—	2	8	no	—
144	C₂⁴×C₆₇	—	2	1	no	—
145	C₂⁴×C₆₇	—	2	1	no	—
146	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
147	#41×C₆₇	—	2	2	no	—
148	#41×C₆₇	—	2	2	no	—
149	#41×C₆₇	—	2	2	no	—
150	#41×C₆₇	—	2	2	no	—
151	#41×C₆₇	—	2	2	no	—
152	#41×C₆₇	—	2	2	no	—
153	#41×C₆₇	—	2	2	no	—
154	#41×C₆₇	—	2	2	no	—
155	#41×C₆₇	—	2	2	no	—
156	#41×C₆₇	—	2	2	no	—
157	#41×C₆₇	—	2	2	no	—
158	#41×C₆₇	—	2	2	no	—
159	#41×C₆₇	—	2	2	no	—
160	#41×C₆₇	—	2	2	no	—
161	#41×C₆₇	—	2	2	no	—
162	#41×C₆₇	—	2	2	no	—
163	#41×C₆₇	—	2	2	no	—
164	#41×C₆₇	—	2	2	no	—
165	#41×C₆₇	—	2	2	no	—
166	#41×C₆₇	—	2	2	no	—
167	#41×C₆₇	—	4	1	no	—
168	#41×C₆₇	—	4	1	no	—
169	#41×C₆₇	—	4	1	no	—
170	#41×C₆₇	—	4	1	no	—
171	#41×C₆₇	—	4	1	no	—
172	#41×C₆₇	—	4	1	no	—
173	#41×C₆₇	—	4	1	no	—
174	#41×C₆₇	—	4	1	no	—
175	#41×C₆₇	C₂²⋊C₄	1	4	yes	—
176	#41×C₆₇	C₂²⋊C₄	1	4	yes	—
177	#41×C₆₇	C₂²⋊C₄	1	4	yes	—
178	#41×C₆₇	C₂²⋊C₄	1	4	yes	—
179	C₂×Q₈×C₆₇	—	2	1	no	—
180	C₂×Q₈×C₆₇	—	2	1	no	—
181	C₂×Q₈×C₆₇	—	2	1	no	—
182	C₂×Q₈×C₆₇	—	2	1	no	—
183	C₂×Q₈×C₆₇	—	2	1	no	—
184	C₂×Q₈×C₆₇	—	2	1	no	—
185	C₂×Q₈×C₆₇	—	2	1	no	—
186	C₂×Q₈×C₆₇	—	2	1	no	—
187	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
188	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
189	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
190	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
191	C₂×D₄×C₆₇	—	2	2	no	—
192	C₂×D₄×C₆₇	—	2	2	no	—
193	C₂×D₄×C₆₇	—	2	2	no	—
194	C₂×D₄×C₆₇	—	2	2	no	—
195	C₂×D₄×C₆₇	—	2	2	no	—
196	C₂×D₄×C₆₇	—	2	2	no	—
197	C₂×D₄×C₆₇	—	2	2	no	—
198	C₂×D₄×C₆₇	—	2	2	no	—
199	C₂×D₄×C₆₇	—	2	1	no	—
200	C₂×D₄×C₆₇	—	2	1	no	—
201	C₂×D₄×C₆₇	—	2	1	no	—
202	C₂×D₄×C₆₇	—	2	1	no	—
203	C₂×D₄×C₆₇	—	2	1	no	—
204	C₂×D₄×C₆₇	—	2	1	no	—
205	C₂×D₄×C₆₇	—	2	1	no	—
206	C₂×D₄×C₆₇	—	2	1	no	—
207	C₂×D₄×C₆₇	—	4	1	no	—
208	C₂×D₄×C₆₇	—	4	1	no	—
209	C₂×D₄×C₆₇	—	4	1	no	—
210	C₂×D₄×C₆₇	—	4	1	no	—
211	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
212	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
213	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
214	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
215	C₂²×C₄×C₆₇	—	2	1	no	—
216	C₂²×C₄×C₆₇	—	2	2	no	—
217	C₂²×C₄×C₆₇	—	2	2	no	—
218	C₂²×C₄×C₆₇	—	2	2	no	—
219	C₂²×C₄×C₆₇	—	2	2	no	—
220	C₂²×C₄×C₆₇	—	2	2	no	—
221	C₂²×C₄×C₆₇	—	2	2	no	—
222	C₂²×C₄×C₆₇	—	2	1	no	—
223	C₂²×C₄×C₆₇	—	2	8	no	—
224	C₂²×C₄×C₆₇	—	2	2	no	—
225	C₂²×C₄×C₆₇	—	2	2	no	—
226	C₂²×C₄×C₆₇	—	2	2	no	—
227	C₂²×C₄×C₆₇	—	2	2	no	—
228	C₂²×C₄×C₆₇	—	4	1	no	—
229	C₂²×C₄×C₆₇	—	4	1	no	—
230	C₂²×C₄×C₆₇	—	4	1	no	—
231	C₂²×C₄×C₆₇	—	4	1	no	—
232	C₂²×C₄×C₆₇	—	4	1	no	—
233	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
234	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
235	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
236	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
237	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
238	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
243	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
244	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
245	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
246	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
247	Q₁₆×C₆₇	—	2	8	no	—
248	SD₁₆×C₆₇	—	2	8	no	—
249	SD₁₆×C₆₇	—	2	8	no	—
250	D₈×C₆₇	—	2	8	no	—
251	M₁₆×C₆₇	—	2	2	no	—
252	M₁₆×C₆₇	—	2	2	no	—
253	M₁₆×C₆₇	—	2	2	no	—
254	M₁₆×C₆₇	—	2	2	no	—
255	M₁₆×C₆₇	—	2	2	no	—
256	M₁₆×C₆₇	—	2	2	no	—
257	M₁₆×C₆₇	—	4	1	no	—
258	M₁₆×C₆₇	—	4	1	no	—
259	C₂×C₈×C₆₇	—	2	2	no	—
260	C₂×C₈×C₆₇	—	2	2	no	—
261	C₂×C₈×C₆₇	—	2	2	no	—
262	C₂×C₈×C₆₇	—	4	1	no	—
263	C₂×C₈×C₆₇	—	4	1	no	—
264	C₂×C₈×C₆₇	C₂²×C₄	1	4	yes	—
265	C₄⋊C₄×C₆₇	—	2	8	no	—
266	C₄⋊C₄×C₆₇	—	2	2	no	—
267	C₄⋊C₄×C₆₇	—	2	2	no	—
268	C₄⋊C₄×C₆₇	—	2	2	no	—
269	C₄⋊C₄×C₆₇	—	2	2	no	—
270	C₄⋊C₄×C₆₇	—	2	2	no	—
271	C₄⋊C₄×C₆₇	—	4	1	no	—
272	C₂²⋊C₄×C₆₇	—	2	8	no	—
273	C₂²⋊C₄×C₆₇	—	2	2	no	—
274	C₂²⋊C₄×C₆₇	—	2	2	no	—
275	C₂²⋊C₄×C₆₇	—	2	2	no	—
276	C₂²⋊C₄×C₆₇	—	2	2	no	—
277	C₂²⋊C₄×C₆₇	—	4	1	no	—
278	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
279	C₄²×C₆₇	—	2	8	no	—
280	C₄²×C₆₇	—	2	2	no	—
281	C₄²×C₆₇	—	2	2	no	—
282	C₄²×C₆₇	—	2	2	no	—
283	C₄²×C₆₇	—	2	2	no	—
284	C₄²×C₆₇	—	4	1	no	—
285	C₄²×C₆₇	C₂×D₄	1	4	yes	—
286	C₂³×C₆₇	—	2	2	no	—
287	C₂³×C₆₇	—	2	2	no	—
288	C₂³×C₆₇	—	2	2	no	—
289	C₂³×C₆₇	—	2	2	no	—
290	C₂³×C₆₇	—	4	1	no	—
291	C₂³×C₆₇	—	4	1	no	—
292	C₂³×C₆₇	—	8	1	no	—
293	C₂³×C₆₇	—	8	2	no	—
294	C₂³×C₆₇	—	8	2	no	—
295	C₂³×C₆₇	C₄×D₄	1	1	yes	characteristic
296	C₂³×C₆₇	C₄×D₄	1	1	yes	characteristic
297	C₂³×C₆₇	#120	1	1	yes	characteristic
298	C₂³×C₆₇	#120	1	1	yes	characteristic
299	C₂³×C₆₇	#121	1	1	yes	characteristic
300	C₂³×C₆₇	#121	1	1	yes	characteristic
301	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
302	Q₈×C₆₇	—	2	2	no	—
303	Q₈×C₆₇	—	2	2	no	—
304	Q₈×C₆₇	—	2	2	no	—
305	Q₈×C₆₇	—	2	2	no	—
306	Q₈×C₆₇	—	2	2	no	—
307	Q₈×C₆₇	—	4	1	no	—
308	Q₈×C₆₇	—	4	1	no	—
309	Q₈×C₆₇	C₂×C₂²⋊C₄	1	4	yes	—
310	D₄×C₆₇	—	2	4	no	—
311	D₄×C₆₇	—	2	4	no	—
312	D₄×C₆₇	—	2	4	no	—
313	D₄×C₆₇	—	2	4	no	—
314	D₄×C₆₇	—	2	2	no	—
315	D₄×C₆₇	—	2	2	no	—
316	D₄×C₆₇	—	2	2	no	—
317	D₄×C₆₇	—	2	2	no	—
318	D₄×C₆₇	—	2	2	no	—
319	D₄×C₆₇	—	4	2	no	—
320	D₄×C₆₇	—	4	2	no	—
321	D₄×C₆₇	—	4	2	no	—
322	D₄×C₆₇	—	4	2	no	—
323	D₄×C₆₇	—	4	1	no	—
324	D₄×C₆₇	—	4	1	no	—
325	D₄×C₆₇	C₂×C₂²⋊C₄	1	4	yes	—
326	C₂×C₄×C₆₇	—	2	2	no	—
327	C₂×C₄×C₆₇	—	2	2	no	—
328	C₂×C₄×C₆₇	—	2	2	no	—
329	C₂×C₄×C₆₇	—	2	4	no	—
330	C₂×C₄×C₆₇	—	2	4	no	—
331	C₂×C₄×C₆₇	—	2	4	no	—
332	C₂×C₄×C₆₇	—	2	4	no	—
333	C₂×C₄×C₆₇	—	2	2	no	—
334	C₂×C₄×C₆₇	—	2	4	no	—
335	C₂×C₄×C₆₇	—	2	4	no	—
336	C₂×C₄×C₆₇	—	4	1	no	—
337	C₂×C₄×C₆₇	—	4	1	no	—
338	C₂×C₄×C₆₇	—	4	2	no	—
339	C₂×C₄×C₆₇	—	4	2	no	—
340	C₂×C₄×C₆₇	—	4	2	no	—
341	C₂×C₄×C₆₇	—	4	2	no	—
342	C₂×C₄×C₆₇	—	4	2	no	—
343	C₂×C₄×C₆₇	—	8	2	no	—
344	C₂×C₄×C₆₇	—	8	2	no	—
345	C₂×C₄×C₆₇	—	8	8	no	—
346	C₂×C₄×C₆₇	—	8	2	no	—
347	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
348	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
349	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
350	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
351	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
352	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
353	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
354	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
355	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
356	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
357	C₂×C₄×C₆₇	#120	1	1	yes	characteristic
358	C₂×C₄×C₆₇	#120	1	1	yes	characteristic
359	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
360	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
361	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
362	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
363	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
364	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
365	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
366	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
367	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
368	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
369	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
370	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
371	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
372	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
373	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
374	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
375	C₈×C₆₇	—	2	4	no	—
376	C₈×C₆₇	—	4	2	no	—
377	C₂²×C₆₇	—	2	4	no	—
378	C₂²×C₆₇	—	4	1	no	—
379	C₂²×C₆₇	—	4	1	no	—
380	C₂²×C₆₇	—	4	1	no	—
381	C₂²×C₆₇	—	4	1	no	—
382	C₂²×C₆₇	—	4	1	no	—
383	C₂²×C₆₇	—	4	1	no	—
384	C₂²×C₆₇	—	4	1	no	—
385	C₂²×C₆₇	—	4	4	no	—
386	C₂²×C₆₇	—	4	2	no	—
387	C₂²×C₆₇	—	8	2	no	—
388	C₂²×C₆₇	—	8	2	no	—
389	C₂²×C₆₇	—	8	2	no	—
390	C₂²×C₆₇	—	8	2	no	—
391	C₂²×C₆₇	—	8	2	no	—
392	C₂²×C₆₇	#386	1	1	yes	characteristic
393	C₂²×C₆₇	#386	1	1	yes	characteristic
394	C₂²×C₆₇	#386	1	1	yes	characteristic
395	C₂²×C₆₇	#386	1	1	yes	characteristic
396	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
397	C₂²×C₆₇	C₂×#120	1	1	yes	characteristic
398	C₂²×C₆₇	C₂×#121	1	1	yes	characteristic
399	C₄×C₆₇	—	2	4	no	—
400	C₄×C₆₇	—	4	4	no	—
401	C₄×C₆₇	—	4	4	no	—
402	C₄×C₆₇	—	4	2	no	—
403	C₄×C₆₇	—	8	2	no	—
404	C₄×C₆₇	#386	1	1	yes	characteristic
405	C₄×C₆₇	#386	1	1	yes	characteristic
406	C₄×C₆₇	#386	1	1	yes	characteristic
407	C₄×C₆₇	#386	1	1	yes	characteristic
408	C₄×C₆₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
409	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
410	C₄×C₆₇	C₂×#121	1	1	yes	characteristic
411	C₄×C₆₇	C₂×#123	1	1	yes	characteristic
412	#20998	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
413	C₂×C₆₇	—	2	1	no	—
414	C₂×C₆₇	—	2	1	no	—
415	C₂×C₆₇	—	2	1	no	—
416	C₂×C₆₇	—	2	1	no	—
417	C₂×C₆₇	—	2	1	no	—
418	C₂×C₆₇	—	2	1	no	—
419	C₂×C₆₇	—	2	1	no	—
420	C₂×C₆₇	—	4	4	no	—
421	C₂×C₆₇	—	8	2	no	—
422	C₂×C₆₇	C₂×#386	1	1	yes	characteristic
423	C₂×#575	C₂×C₆₇	1	1	yes	characteristic
424	#3428	C₂×C₆₇	1	1	yes	characteristic, complemented
425	C₂×#421	C₂×C₆₇	1	1	yes	characteristic, complemented
426	#2896	C₂×C₆₇	1	1	yes	characteristic, complemented
427	C₂×#410	C₂×C₆₇	1	1	yes	characteristic, complemented
428	#1905	C₂×C₆₇	1	4	yes	complemented
429	#1904	C₂×C₆₇	1	4	yes	complemented
430	C₂×#344	C₂×C₆₇	1	1	yes	characteristic, complemented
431	C₂×H(3,ℤ/4)	C₂×C₆₇	1	1	yes	characteristic, complemented
432	C₆₇	#20998	1	1	yes	characteristic, direct product factor, Sylow
433	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
434	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
435	#575	—	2	2	no	—
436	#575	—	2	2	no	—
437	#575	—	2	2	no	—
438	#575	—	2	2	no	—
439	C₂×#137	C₄×C₆₇	1	2	yes	complemented
440	C₂×#137	C₂²×C₆₇	1	2	yes	—
441	C₂×AGL(1,ℤ/8)	C₄×C₆₇	1	2	yes	complemented
442	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	—
443	C₂×#135	C₄×C₆₇	1	4	yes	complemented
444	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
445	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
446	#520	—	2	2	no	—
447	#520	—	2	2	no	—
448	#519	C₂²×C₆₇	1	2	yes	complemented
449	#518	—	2	2	no	—
450	#518	C₂²×C₆₇	1	2	yes	complemented
451	C₄×#41	—	2	2	no	—
452	C₄×#41	—	2	2	no	—
453	C₂×#117	—	2	2	no	—
454	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
455	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
456	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
457	#421	—	2	2	no	—
458	#421	C₂²×C₆₇	1	4	yes	—
459	C₂×#104	—	2	2	no	—
460	#419	C₂²×C₆₇	1	2	yes	complemented
461	#418	C₂²×C₆₇	1	2	yes	complemented
462	#417	—	2	2	no	—
463	#416	—	2	2	no	—
464	#410	—	2	2	no	—
465	#410	C₂²×C₆₇	1	4	yes	—
466	C₂×#99	—	2	2	no	—
467	#344	C₂²×C₆₇	1	4	yes	complemented
468	H(3,ℤ/4)	C₂²×C₆₇	1	4	yes	complemented
469	C₂×#41	—	2	1	no	—
470	C₂×#41	—	2	1	no	—
471	C₂×#41	—	2	1	no	—
472	C₂×#41	—	2	1	no	—
473	C₂×#41	—	2	1	no	—
474	C₂×#41	—	2	1	no	—
475	C₂×#41	—	2	1	no	—
476	C₂×#41	—	2	1	no	—
477	C₂×#41	—	2	1	no	—
478	C₂×#41	—	2	1	no	—
479	C₂×#41	—	2	1	no	—
480	C₂×#41	—	2	1	no	—
481	C₂×#41	—	2	1	no	—
482	C₂×#41	—	2	1	no	—
483	C₂×#41	—	2	1	no	—
484	C₂×#41	—	2	1	no	—
485	C₂×#41	C₂×C₄×C₆₇	1	2	yes	—
486	C₂×#41	C₂×C₄×C₆₇	1	2	yes	—
487	C₂×#41	C₂×C₄×C₆₇	1	2	yes	complemented
488	C₂×#41	D₄×C₆₇	1	2	yes	—
489	C₂×#41	D₄×C₆₇	1	2	yes	—
490	C₂×#41	D₄×C₆₇	1	2	yes	—
491	C₂×#41	D₄×C₆₇	1	2	yes	—
492	C₂×#41	C₂³×C₆₇	1	2	yes	—
493	C₂²×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic, complemented
494	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
495	C₂²×D₄	—	2	1	no	—
496	C₂²×D₄	—	2	1	no	—
497	C₂²×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic, complemented
498	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
499	C₂³×C₄	—	2	1	no	—
500	C₂³×C₄	—	2	1	no	—
501	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
502	#137	—	2	4	no	—
503	#137	—	2	4	no	—
504	#137	—	2	4	no	—
505	#137	—	2	4	no	—
506	AGL(1,ℤ/8)	—	2	4	no	—
507	AGL(1,ℤ/8)	—	2	4	no	—
508	AGL(1,ℤ/8)	—	2	4	no	—
509	AGL(1,ℤ/8)	—	2	4	no	—
510	#135	—	2	8	no	—
511	#135	—	2	8	no	—
512	C₂×Q₁₆	C₂×C₄×C₆₇	1	4	yes	complemented
513	C₂×SD₁₆	C₂×C₄×C₆₇	1	4	yes	complemented
514	C₂×SD₁₆	C₂×C₄×C₆₇	1	4	yes	complemented
515	C₂×D₈	C₂×C₄×C₆₇	1	4	yes	complemented
516	C₂×M₁₆	—	2	1	no	—
517	C₂×M₁₆	—	2	1	no	—
518	C₂×M₁₆	—	2	1	no	—
519	C₂×M₁₆	—	2	1	no	—
520	C₂×M₁₆	—	2	1	no	—
521	C₂×M₁₆	—	2	1	no	—
522	C₂×M₁₆	—	2	1	no	—
523	C₂×M₁₆	—	2	1	no	—
524	C₂×M₁₆	—	2	1	no	—
525	C₂×M₁₆	C₂×C₄×C₆₇	1	2	yes	complemented
526	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
527	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
528	C₂²×C₈	—	2	1	no	—
529	C₂²×C₈	C₂×C₄×C₆₇	1	2	yes	complemented
530	C₄×Q₈	—	2	4	no	—
531	C₄×Q₈	—	2	4	no	—
532	C₄×D₄	—	2	8	no	—
533	C₄×D₄	—	2	8	no	—
534	C₄×D₄	—	2	4	no	—
535	C₄×D₄	—	2	4	no	—
536	#117	—	2	4	no	—
537	#117	—	2	4	no	—
538	#117	—	2	1	no	—
539	#117	—	2	1	no	—
540	#117	—	2	1	no	—
541	#117	—	2	1	no	—
542	#117	—	2	4	no	—
543	#117	—	2	1	no	—
544	#117	—	2	1	no	—
545	#117	—	2	1	no	—
546	#117	D₄×C₆₇	1	2	yes	—
547	#117	D₄×C₆₇	1	2	yes	—
548	#117	C₂³×C₆₇	1	2	yes	—
549	#117	C₂³×C₆₇	1	2	yes	—
550	#117	C₂³×C₆₇	1	2	yes	—
551	C₂×C₄⋊C₄	—	2	4	no	—
552	C₂×C₄⋊C₄	—	2	1	no	—
553	C₂×C₄⋊C₄	—	2	1	no	—
554	C₂×C₄⋊C₄	—	2	1	no	—
555	C₂×C₂²⋊C₄	—	2	1	no	—
556	C₂×C₂²⋊C₄	—	2	4	no	—
557	C₂×C₂²⋊C₄	—	2	1	no	—
558	C₂×C₂²⋊C₄	D₄×C₆₇	1	2	yes	—
559	C₂×C₄²	—	2	4	no	—
560	C₂×C₄²	—	2	1	no	—
561	C₂×C₄²	—	2	1	no	—
562	C₂×C₄²	D₄×C₆₇	1	2	yes	—
563	#104	—	2	8	no	—
564	#103	—	2	4	no	—
565	#102	—	2	4	no	—
566	#99	—	2	8	no	—
567	C₂⁴	—	2	1	no	—
568	C₂⁴	—	2	1	no	—
569	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
570	#41	—	2	2	no	—
571	#41	—	2	2	no	—
572	#41	—	2	2	no	—
573	#41	—	2	2	no	—
574	#41	—	2	2	no	—
575	#41	—	2	2	no	—
576	#41	—	2	2	no	—
577	#41	—	2	2	no	—
578	#41	—	2	2	no	—
579	#41	—	2	2	no	—
580	#41	—	2	2	no	—
581	#41	—	2	2	no	—
582	#41	—	2	2	no	—
583	#41	—	2	2	no	—
584	#41	—	2	2	no	—
585	#41	—	2	2	no	—
586	#41	—	2	2	no	—
587	#41	—	2	2	no	—
588	#41	—	2	2	no	—
589	#41	—	2	2	no	—
590	#41	—	4	1	no	—
591	#41	—	4	1	no	—
592	#41	—	4	1	no	—
593	#41	—	4	1	no	—
594	#41	—	4	1	no	—
595	#41	—	4	1	no	—
596	#41	—	4	1	no	—
597	#41	—	4	1	no	—
598	#41	C₂²⋊C₄×C₆₇	1	4	yes	—
599	#41	C₂²⋊C₄×C₆₇	1	4	yes	—
600	#41	C₂²⋊C₄×C₆₇	1	4	yes	—
601	#41	C₂²⋊C₄×C₆₇	1	4	yes	—
602	C₂×Q₈	—	2	1	no	—
603	C₂×Q₈	—	2	1	no	—
604	C₂×Q₈	—	2	1	no	—
605	C₂×Q₈	—	2	1	no	—
606	C₂×Q₈	—	2	1	no	—
607	C₂×Q₈	—	2	1	no	—
608	C₂×Q₈	—	2	1	no	—
609	C₂×Q₈	—	2	1	no	—
610	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
611	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
612	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
613	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
614	C₂×D₄	—	2	2	no	—
615	C₂×D₄	—	2	2	no	—
616	C₂×D₄	—	2	2	no	—
617	C₂×D₄	—	2	2	no	—
618	C₂×D₄	—	2	2	no	—
619	C₂×D₄	—	2	2	no	—
620	C₂×D₄	—	2	2	no	—
621	C₂×D₄	—	2	2	no	—
622	C₂×D₄	—	2	1	no	—
623	C₂×D₄	—	2	1	no	—
624	C₂×D₄	—	2	1	no	—
625	C₂×D₄	—	2	1	no	—
626	C₂×D₄	—	2	1	no	—
627	C₂×D₄	—	2	1	no	—
628	C₂×D₄	—	2	1	no	—
629	C₂×D₄	—	2	1	no	—
630	C₂×D₄	—	4	1	no	—
631	C₂×D₄	—	4	1	no	—
632	C₂×D₄	—	4	1	no	—
633	C₂×D₄	—	4	1	no	—
634	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
635	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
636	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
637	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
638	C₂²×C₄	—	2	1	no	—
639	C₂²×C₄	—	2	2	no	—
640	C₂²×C₄	—	2	2	no	—
641	C₂²×C₄	—	2	2	no	—
642	C₂²×C₄	—	2	2	no	—
643	C₂²×C₄	—	2	2	no	—
644	C₂²×C₄	—	2	2	no	—
645	C₂²×C₄	—	2	1	no	—
646	C₂²×C₄	—	2	8	no	—
647	C₂²×C₄	—	2	2	no	—
648	C₂²×C₄	—	2	2	no	—
649	C₂²×C₄	—	2	2	no	—
650	C₂²×C₄	—	2	2	no	—
651	C₂²×C₄	—	4	1	no	—
652	C₂²×C₄	—	4	1	no	—
653	C₂²×C₄	—	4	1	no	—
654	C₂²×C₄	—	4	1	no	—
655	C₂²×C₄	—	4	1	no	—
656	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
657	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
658	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
659	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
660	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
661	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
662	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
663	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
664	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
665	C₂²×C₄	#41×C₆₇	1	1	yes	characteristic
666	C₂²×C₄	#41×C₆₇	1	1	yes	characteristic
667	C₂²×C₄	#41×C₆₇	1	1	yes	characteristic
668	C₂²×C₄	#41×C₆₇	1	1	yes	characteristic
669	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
670	Q₁₆	—	2	8	no	—
671	SD₁₆	—	2	8	no	—
672	SD₁₆	—	2	8	no	—
673	D₈	—	2	8	no	—
674	M₁₆	—	2	2	no	—
675	M₁₆	—	2	2	no	—
676	M₁₆	—	2	2	no	—
677	M₁₆	—	2	2	no	—
678	M₁₆	—	2	2	no	—
679	M₁₆	—	2	2	no	—
680	M₁₆	—	4	1	no	—
681	M₁₆	—	4	1	no	—
682	C₂×C₈	—	2	2	no	—
683	C₂×C₈	—	2	2	no	—
684	C₂×C₈	—	2	2	no	—
685	C₂×C₈	—	4	1	no	—
686	C₂×C₈	—	4	1	no	—
687	C₂×C₈	C₂²×C₄×C₆₇	1	4	yes	—
688	C₄⋊C₄	—	2	8	no	—
689	C₄⋊C₄	—	2	2	no	—
690	C₄⋊C₄	—	2	2	no	—
691	C₄⋊C₄	—	2	2	no	—
692	C₄⋊C₄	—	2	2	no	—
693	C₄⋊C₄	—	2	2	no	—
694	C₄⋊C₄	—	4	1	no	—
695	C₂²⋊C₄	—	2	8	no	—
696	C₂²⋊C₄	—	2	2	no	—
697	C₂²⋊C₄	—	2	2	no	—
698	C₂²⋊C₄	—	2	2	no	—
699	C₂²⋊C₄	—	2	2	no	—
700	C₂²⋊C₄	—	4	1	no	—
701	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
702	C₄²	—	2	8	no	—
703	C₄²	—	2	2	no	—
704	C₄²	—	2	2	no	—
705	C₄²	—	2	2	no	—
706	C₄²	—	2	2	no	—
707	C₄²	—	4	1	no	—
708	C₄²	C₂×D₄×C₆₇	1	4	yes	—
709	C₂³	—	2	2	no	—
710	C₂³	—	2	2	no	—
711	C₂³	—	2	2	no	—
712	C₂³	—	2	2	no	—
713	C₂³	—	4	1	no	—
714	C₂³	—	4	1	no	—
715	C₂³	—	8	1	no	—
716	C₂³	—	8	2	no	—
717	C₂³	—	8	2	no	—
718	C₂³	C₄×D₄×C₆₇	1	1	yes	characteristic
719	C₂³	C₄×D₄×C₆₇	1	1	yes	characteristic
720	C₂³	#120×C₆₇	1	1	yes	characteristic
721	C₂³	#120×C₆₇	1	1	yes	characteristic
722	C₂³	#121×C₆₇	1	1	yes	characteristic
723	C₂³	#121×C₆₇	1	1	yes	characteristic
724	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
725	Q₈	—	2	2	no	—
726	Q₈	—	2	2	no	—
727	Q₈	—	2	2	no	—
728	Q₈	—	2	2	no	—
729	Q₈	—	2	2	no	—
730	Q₈	—	4	1	no	—
731	Q₈	—	4	1	no	—
732	Q₈	C₂×C₂²⋊C₄×C₆₇	1	4	yes	—
733	D₄	—	2	4	no	—
734	D₄	—	2	4	no	—
735	D₄	—	2	4	no	—
736	D₄	—	2	4	no	—
737	D₄	—	2	2	no	—
738	D₄	—	2	2	no	—
739	D₄	—	2	2	no	—
740	D₄	—	2	2	no	—
741	D₄	—	2	2	no	—
742	D₄	—	4	2	no	—
743	D₄	—	4	2	no	—
744	D₄	—	4	2	no	—
745	D₄	—	4	2	no	—
746	D₄	—	4	1	no	—
747	D₄	—	4	1	no	—
748	D₄	C₂×C₂²⋊C₄×C₆₇	1	4	yes	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	4	no	—
753	C₂×C₄	—	2	4	no	—
754	C₂×C₄	—	2	4	no	—
755	C₂×C₄	—	2	4	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	4	no	—
758	C₂×C₄	—	2	4	no	—
759	C₂×C₄	—	4	1	no	—
760	C₂×C₄	—	4	1	no	—
761	C₂×C₄	—	4	2	no	—
762	C₂×C₄	—	4	2	no	—
763	C₂×C₄	—	4	2	no	—
764	C₂×C₄	—	4	2	no	—
765	C₂×C₄	—	4	2	no	—
766	C₂×C₄	—	8	2	no	—
767	C₂×C₄	—	8	2	no	—
768	C₂×C₄	—	8	8	no	—
769	C₂×C₄	—	8	2	no	—
770	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
771	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
772	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
773	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
774	C₂×C₄	C₄×D₄×C₆₇	1	1	yes	characteristic
775	C₂×C₄	C₄×D₄×C₆₇	1	1	yes	characteristic
776	C₂×C₄	C₄×D₄×C₆₇	1	1	yes	characteristic
777	C₂×C₄	C₄×D₄×C₆₇	1	1	yes	characteristic
778	C₂×C₄	C₄×D₄×C₆₇	1	1	yes	characteristic
779	C₂×C₄	C₄×D₄×C₆₇	1	1	yes	characteristic
780	C₂×C₄	#120×C₆₇	1	1	yes	characteristic
781	C₂×C₄	#120×C₆₇	1	1	yes	characteristic
782	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
783	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
784	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
785	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
786	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
787	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
788	C₂×C₄	#123×C₆₇	1	1	yes	characteristic
789	C₂×C₄	#123×C₆₇	1	1	yes	characteristic
790	C₂×C₄	#123×C₆₇	1	1	yes	characteristic
791	C₂×C₄	#123×C₆₇	1	1	yes	characteristic
792	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
793	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
794	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
795	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
796	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
797	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
798	C₈	—	2	4	no	—
799	C₈	—	4	2	no	—
800	C₂²	—	2	4	no	—
801	C₂²	—	4	1	no	—
802	C₂²	—	4	1	no	—
803	C₂²	—	4	1	no	—
804	C₂²	—	4	1	no	—
805	C₂²	—	4	1	no	—
806	C₂²	—	4	1	no	—
807	C₂²	—	4	1	no	—
808	C₂²	—	4	4	no	—
809	C₂²	—	4	2	no	—
810	C₂²	—	8	2	no	—
811	C₂²	—	8	2	no	—
812	C₂²	—	8	2	no	—
813	C₂²	—	8	2	no	—
814	C₂²	—	8	2	no	—
815	C₂²	#386×C₆₇	1	1	yes	characteristic
816	C₂²	#386×C₆₇	1	1	yes	characteristic
817	C₂²	#386×C₆₇	1	1	yes	characteristic
818	C₂²	#386×C₆₇	1	1	yes	characteristic
819	C₂²	C₂×C₄×D₄×C₆₇	1	1	yes	characteristic
820	C₂²	C₂×#120×C₆₇	1	1	yes	characteristic
821	C₂²	C₂×#121×C₆₇	1	1	yes	characteristic
822	C₄	—	2	4	no	—
823	C₄	—	4	4	no	—
824	C₄	—	4	4	no	—
825	C₄	—	4	2	no	—
826	C₄	—	8	2	no	—
827	C₄	#386×C₆₇	1	1	yes	characteristic
828	C₄	#386×C₆₇	1	1	yes	characteristic
829	C₄	#386×C₆₇	1	1	yes	characteristic
830	C₄	#386×C₆₇	1	1	yes	characteristic
831	C₄	C₂²×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
832	C₄	C₂×C₄×D₄×C₆₇	1	1	yes	characteristic
833	C₄	C₂×#121×C₆₇	1	1	yes	characteristic
834	C₄	C₂×#123×C₆₇	1	1	yes	characteristic
835	C₂	—	2	1	no	—
836	C₂	—	2	1	no	—
837	C₂	—	2	1	no	—
838	C₂	—	2	1	no	—
839	C₂	—	2	1	no	—
840	C₂	—	2	1	no	—
841	C₂	—	2	1	no	—
842	C₂	—	4	4	no	—
843	C₂	—	8	2	no	—
844	C₂	C₂×#386×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₆₇	#386
commutator	C₂×C₄	C₂³×C₄×C₆₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
socle	C₂×C₆₇	C₂×#386
prime radical	C₂×#575×C₆₇	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₆₇ ◁ C₂³×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₇×#3428	C₂	semidirect
3. C₂×#421×C₆₇	C₂	semidirect
4. C₆₇×#2896	C₂	semidirect
5. C₂×#410×C₆₇	C₂	semidirect
6. C₆₇×#1905	C₂	semidirect
7. C₆₇×#1904	C₂	semidirect
8. C₂×#344×C₆₇	C₂	semidirect
9. C₂×H(3,ℤ/4)×C₆₇	C₂	semidirect
16. C₂×#137×C₆₇	C₄	semidirect
18. C₂×AGL(1,ℤ/8)×C₆₇	C₄	semidirect
20. C₂×#135×C₆₇	C₄	semidirect
25. #519×C₆₇	C₂²	semidirect
27. #518×C₆₇	C₂²	semidirect
37. #419×C₆₇	C₂²	semidirect
38. #418×C₆₇	C₂²	semidirect
44. #344×C₆₇	C₂²	semidirect
45. H(3,ℤ/4)×C₆₇	C₂²	semidirect
64. C₂×#41×C₆₇	C₂×C₄	semidirect
70. C₂²×Q₈×C₆₇	C₂×C₄	semidirect
74. C₂²×D₄×C₆₇	C₂×C₄	semidirect
89. C₂×Q₁₆×C₆₇	C₂×C₄	semidirect
90. C₂×SD₁₆×C₆₇	C₂×C₄	semidirect
91. C₂×SD₁₆×C₆₇	C₂×C₄	semidirect
92. C₂×D₈×C₆₇	C₂×C₄	semidirect
102. C₂×M₁₆×C₆₇	C₂×C₄	semidirect
106. C₂²×C₈×C₆₇	C₂×C₄	semidirect
412. #20998	C₆₇	direct (N × H)
424. #3428	C₂×C₆₇	semidirect
425. C₂×#421	C₂×C₆₇	semidirect
426. #2896	C₂×C₆₇	semidirect
427. C₂×#410	C₂×C₆₇	semidirect
428. #1905	C₂×C₆₇	semidirect
429. #1904	C₂×C₆₇	semidirect
430. C₂×#344	C₂×C₆₇	semidirect
431. C₂×H(3,ℤ/4)	C₂×C₆₇	semidirect
432. C₆₇	#20998	direct (N × H)
439. C₂×#137	C₄×C₆₇	semidirect
441. C₂×AGL(1,ℤ/8)	C₄×C₆₇	semidirect
443. C₂×#135	C₄×C₆₇	semidirect
448. #519	C₂²×C₆₇	semidirect
450. #518	C₂²×C₆₇	semidirect
460. #419	C₂²×C₆₇	semidirect
461. #418	C₂²×C₆₇	semidirect
467. #344	C₂²×C₆₇	semidirect
468. H(3,ℤ/4)	C₂²×C₆₇	semidirect
487. C₂×#41	C₂×C₄×C₆₇	semidirect
493. C₂²×Q₈	C₂×C₄×C₆₇	semidirect
497. C₂²×D₄	C₂×C₄×C₆₇	semidirect
512. C₂×Q₁₆	C₂×C₄×C₆₇	semidirect
513. C₂×SD₁₆	C₂×C₄×C₆₇	semidirect
514. C₂×SD₁₆	C₂×C₄×C₆₇	semidirect
515. C₂×D₈	C₂×C₄×C₆₇	semidirect
525. C₂×M₁₆	C₂×C₄×C₆₇	semidirect
529. C₂²×C₈	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×#575×C₆₇	2
C₆₇×#3428	2
C₂×#421×C₆₇	2
C₆₇×#2896	2
C₂×#410×C₆₇	2
C₆₇×#1905	2
C₆₇×#1904	2
C₂×#344×C₆₇	2
C₂×H(3,ℤ/4)×C₆₇	2
#20998	67

Subgroups — C67×#20998 #30700249

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#20998 #30700249